CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Synthetic-aperture radar - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"1ee85354-440b-4a4b-926e-b3652ad13a85","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Synthetic-aperture_radar","wgTitle":"Synthetic-aperture radar","wgCurRevisionId":1259201286,"wgRevisionId":1259201286,"wgArticleId":645554,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["CS1 maint: numeric names: authors list","CS1 errors: periodical ignored","Articles with short description","Short description is different from Wikidata","Use dmy dates from October 2019","Articles needing additional references from March 2012","All articles needing additional references","Wikipedia articles that are excessively detailed from March 2012","All articles that are excessively detailed","Wikipedia articles with style issues from March 2012", "All articles with style issues","Wikipedia articles that are too technical from November 2024","All articles that are too technical","Articles with multiple maintenance issues","Wikipedia articles needing clarification from October 2012","Articles with excerpts","Webarchive template wayback links","Synthetic aperture radar"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Synthetic-aperture_radar","wgRelevantArticleId":645554,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby": true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":80000,"wgRelatedArticlesCompat":[],"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q740686","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready", "ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","site","mediawiki.page.ready","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.8"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a8/TEIDE.JPG/1200px-TEIDE.JPG"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="727"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a8/TEIDE.JPG/800px-TEIDE.JPG"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="484"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a8/TEIDE.JPG/640px-TEIDE.JPG"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="388"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Synthetic-aperture radar - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Synthetic-aperture_radar"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Synthetic-aperture_radar&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Synthetic-aperture_radar"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Synthetic-aperture_radar rootpage-Synthetic-aperture_radar skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en" class=""><span>Donate</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=Synthetic-aperture+radar" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:UserLogin&returnto=Synthetic-aperture+radar" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Synthetic-aperture+radar" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Synthetic-aperture+radar" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Motivation_and_applications" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Motivation_and_applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Motivation and applications</span> </div> </a> <ul id="toc-Motivation_and_applications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Basic_principle" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Basic_principle"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Basic principle</span> </div> </a> <ul id="toc-Basic_principle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Algorithm" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Algorithm"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Algorithm</span> </div> </a> <ul id="toc-Algorithm-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Existing_spectral_estimation_approaches" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Existing_spectral_estimation_approaches"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Existing spectral estimation approaches</span> </div> </a> <button aria-controls="toc-Existing_spectral_estimation_approaches-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Existing spectral estimation approaches subsection</span> </button> <ul id="toc-Existing_spectral_estimation_approaches-sublist" class="vector-toc-list"> <li id="toc-Non-parametric_methods" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Non-parametric_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Non-parametric methods</span> </div> </a> <ul id="toc-Non-parametric_methods-sublist" class="vector-toc-list"> <li id="toc-FFT" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#FFT"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.1</span> <span>FFT</span> </div> </a> <ul id="toc-FFT-sublist" class="vector-toc-list"> <li id="toc-Advantages" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Advantages"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.1.1</span> <span>Advantages</span> </div> </a> <ul id="toc-Advantages-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Disadvantages" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Disadvantages"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.1.2</span> <span>Disadvantages</span> </div> </a> <ul id="toc-Disadvantages-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Capon_method" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Capon_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.2</span> <span>Capon method</span> </div> </a> <ul id="toc-Capon_method-sublist" class="vector-toc-list"> <li id="toc-Advantages_2" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Advantages_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.2.1</span> <span>Advantages</span> </div> </a> <ul id="toc-Advantages_2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Disadvantages_2" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Disadvantages_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.2.2</span> <span>Disadvantages</span> </div> </a> <ul id="toc-Disadvantages_2-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-APES_method" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#APES_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.3</span> <span>APES method</span> </div> </a> <ul id="toc-APES_method-sublist" class="vector-toc-list"> <li id="toc-Advantages_3" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Advantages_3"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.3.1</span> <span>Advantages</span> </div> </a> <ul id="toc-Advantages_3-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Disadvantages_3" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Disadvantages_3"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.3.2</span> <span>Disadvantages</span> </div> </a> <ul id="toc-Disadvantages_3-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-SAMV_method" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#SAMV_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>SAMV method</span> </div> </a> <ul id="toc-SAMV_method-sublist" class="vector-toc-list"> <li id="toc-Advantages_4" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Advantages_4"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1</span> <span>Advantages</span> </div> </a> <ul id="toc-Advantages_4-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Disadvantages_4" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Disadvantages_4"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.2</span> <span>Disadvantages</span> </div> </a> <ul id="toc-Disadvantages_4-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Parametric_subspace_decomposition_methods" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Parametric_subspace_decomposition_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Parametric subspace decomposition methods</span> </div> </a> <ul id="toc-Parametric_subspace_decomposition_methods-sublist" class="vector-toc-list"> <li id="toc-Eigenvector_method" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Eigenvector_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3.1</span> <span>Eigenvector method</span> </div> </a> <ul id="toc-Eigenvector_method-sublist" class="vector-toc-list"> <li id="toc-Advantages_5" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Advantages_5"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3.1.1</span> <span>Advantages</span> </div> </a> <ul id="toc-Advantages_5-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Disadvantages_5" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Disadvantages_5"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3.1.2</span> <span>Disadvantages</span> </div> </a> <ul id="toc-Disadvantages_5-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-MUSIC_method" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#MUSIC_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3.2</span> <span>MUSIC method</span> </div> </a> <ul id="toc-MUSIC_method-sublist" class="vector-toc-list"> <li id="toc-Advantages_6" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Advantages_6"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3.2.1</span> <span>Advantages</span> </div> </a> <ul id="toc-Advantages_6-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Disadvantages_6" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Disadvantages_6"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3.2.2</span> <span>Disadvantages</span> </div> </a> <ul id="toc-Disadvantages_6-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Backprojection_algorithm" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Backprojection_algorithm"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Backprojection algorithm</span> </div> </a> <ul id="toc-Backprojection_algorithm-sublist" class="vector-toc-list"> <li id="toc-Advantages_7" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Advantages_7"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4.1</span> <span>Advantages</span> </div> </a> <ul id="toc-Advantages_7-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Disadvantages_7" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Disadvantages_7"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4.2</span> <span>Disadvantages</span> </div> </a> <ul id="toc-Disadvantages_7-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Application:_geosynchronous_orbit_synthetic-aperture_radar_(GEO-SAR)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Application:_geosynchronous_orbit_synthetic-aperture_radar_(GEO-SAR)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4.3</span> <span>Application: geosynchronous orbit synthetic-aperture radar (GEO-SAR)</span> </div> </a> <ul id="toc-Application:_geosynchronous_orbit_synthetic-aperture_radar_(GEO-SAR)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Comparison_between_the_algorithms" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Comparison_between_the_algorithms"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Comparison between the algorithms</span> </div> </a> <ul id="toc-Comparison_between_the_algorithms-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Multistatic_operation" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Multistatic_operation"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Multistatic operation</span> </div> </a> <ul id="toc-Multistatic_operation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Scanning_modes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Scanning_modes"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Scanning modes</span> </div> </a> <button aria-controls="toc-Scanning_modes-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Scanning modes subsection</span> </button> <ul id="toc-Scanning_modes-sublist" class="vector-toc-list"> <li id="toc-Stripmap_mode_airborne_SAR" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Stripmap_mode_airborne_SAR"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Stripmap mode airborne SAR</span> </div> </a> <ul id="toc-Stripmap_mode_airborne_SAR-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spotlight_mode_SAR" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Spotlight_mode_SAR"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Spotlight mode SAR</span> </div> </a> <ul id="toc-Spotlight_mode_SAR-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Scan_mode_SAR" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Scan_mode_SAR"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Scan mode SAR</span> </div> </a> <ul id="toc-Scan_mode_SAR-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Special_techniques" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Special_techniques"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Special techniques</span> </div> </a> <button aria-controls="toc-Special_techniques-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Special techniques subsection</span> </button> <ul id="toc-Special_techniques-sublist" class="vector-toc-list"> <li id="toc-Polarimetry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Polarimetry"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Polarimetry</span> </div> </a> <ul id="toc-Polarimetry-sublist" class="vector-toc-list"> <li id="toc-SAR_polarimetry" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#SAR_polarimetry"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1.1</span> <span>SAR polarimetry</span> </div> </a> <ul id="toc-SAR_polarimetry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Three-component_scattering_power_model" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Three-component_scattering_power_model"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1.2</span> <span>Three-component scattering power model</span> </div> </a> <ul id="toc-Three-component_scattering_power_model-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Four-component_scattering_power_model" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Four-component_scattering_power_model"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1.3</span> <span>Four-component scattering power model</span> </div> </a> <ul id="toc-Four-component_scattering_power_model-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Interferometry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Interferometry"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Interferometry</span> </div> </a> <ul id="toc-Interferometry-sublist" class="vector-toc-list"> <li id="toc-Differential_interferometry" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Differential_interferometry"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2.1</span> <span>Differential interferometry</span> </div> </a> <ul id="toc-Differential_interferometry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tomo-SAR" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Tomo-SAR"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2.2</span> <span>Tomo-SAR</span> </div> </a> <ul id="toc-Tomo-SAR-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Ultra-wideband_SAR" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ultra-wideband_SAR"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3</span> <span>Ultra-wideband SAR</span> </div> </a> <ul id="toc-Ultra-wideband_SAR-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Doppler-beam_sharpening" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Doppler-beam_sharpening"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.4</span> <span>Doppler-beam sharpening</span> </div> </a> <ul id="toc-Doppler-beam_sharpening-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Chirped_(pulse-compressed)_radars" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Chirped_(pulse-compressed)_radars"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.5</span> <span>Chirped (pulse-compressed) radars</span> </div> </a> <ul id="toc-Chirped_(pulse-compressed)_radars-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Typical_operation" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Typical_operation"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Typical operation</span> </div> </a> <button aria-controls="toc-Typical_operation-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Typical operation subsection</span> </button> <ul id="toc-Typical_operation-sublist" class="vector-toc-list"> <li id="toc-Data_collection" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Data_collection"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Data collection</span> </div> </a> <ul id="toc-Data_collection-sublist" class="vector-toc-list"> <li id="toc-Image_resolution_and_bandwidth" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Image_resolution_and_bandwidth"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1.1</span> <span>Image resolution and bandwidth</span> </div> </a> <ul id="toc-Image_resolution_and_bandwidth-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Image_resolution_and_beamwidth" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Image_resolution_and_beamwidth"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1.2</span> <span>Image resolution and beamwidth</span> </div> </a> <ul id="toc-Image_resolution_and_beamwidth-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pulse_transmission_and_reception" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Pulse_transmission_and_reception"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1.3</span> <span>Pulse transmission and reception</span> </div> </a> <ul id="toc-Pulse_transmission_and_reception-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Data_processing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Data_processing"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Data processing</span> </div> </a> <ul id="toc-Data_processing-sublist" class="vector-toc-list"> <li id="toc-Amplitude_data" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Amplitude_data"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2.1</span> <span>Amplitude data</span> </div> </a> <ul id="toc-Amplitude_data-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Phase_data" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Phase_data"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2.2</span> <span>Phase data</span> </div> </a> <ul id="toc-Phase_data-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Coherence_speckle" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Coherence_speckle"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2.3</span> <span>Coherence speckle</span> </div> </a> <ul id="toc-Coherence_speckle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Optical_holography" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Optical_holography"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2.4</span> <span>Optical holography</span> </div> </a> <ul id="toc-Optical_holography-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Image_appearance" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Image_appearance"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Image appearance</span> </div> </a> <button aria-controls="toc-Image_appearance-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Image appearance subsection</span> </button> <ul id="toc-Image_appearance-sublist" class="vector-toc-list"> <li id="toc-Range,_cross-range,_and_angles" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Range,_cross-range,_and_angles"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.1</span> <span>Range, cross-range, and angles</span> </div> </a> <ul id="toc-Range,_cross-range,_and_angles-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Visibility" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Visibility"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.2</span> <span>Visibility</span> </div> </a> <ul id="toc-Visibility-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mirroring_artefacts_and_shadows" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mirroring_artefacts_and_shadows"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.3</span> <span>Mirroring artefacts and shadows</span> </div> </a> <ul id="toc-Mirroring_artefacts_and_shadows-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Objects_in_motion" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Objects_in_motion"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.4</span> <span>Objects in motion</span> </div> </a> <ul id="toc-Objects_in_motion-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relationship_to_phased_arrays" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Relationship_to_phased_arrays"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Relationship to phased arrays</span> </div> </a> <ul id="toc-Relationship_to_phased_arrays-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</span> <span>Bibliography</span> </div> </a> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">15</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Synthetic-aperture radar</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 32 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-32" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">32 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Synthetic_Aperture_Radar" title="Synthetic Aperture Radar – Alemannic" lang="gsw" hreflang="gsw" data-title="Synthetic Aperture Radar" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B1%D8%A7%D8%AF%D8%A7%D8%B1_%D8%A7%D9%84%D9%81%D8%AA%D8%AD%D8%A9_%D8%A7%D9%84%D8%AA%D8%B1%D9%83%D9%8A%D8%A8%D9%8A%D8%A9" title="رادار الفتحة التركيبية – Arabic" lang="ar" hreflang="ar" data-title="رادار الفتحة التركيبية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Radar_d%27obertura_sint%C3%A8tica" title="Radar d'obertura sintètica – Catalan" lang="ca" hreflang="ca" data-title="Radar d'obertura sintètica" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Radar_se_syntetickou_aperturou" title="Radar se syntetickou aperturou – Czech" lang="cs" hreflang="cs" data-title="Radar se syntetickou aperturou" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Synthetic_aperture_radar" title="Synthetic aperture radar – Danish" lang="da" hreflang="da" data-title="Synthetic aperture radar" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://de.wikipedia.org/wiki/Synthetic_Aperture_Radar" title="Synthetic Aperture Radar – German" lang="de" hreflang="de" data-title="Synthetic Aperture Radar" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Tehisavaradar" title="Tehisavaradar – Estonian" lang="et" hreflang="et" data-title="Tehisavaradar" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Radar_de_apertura_sint%C3%A9tica" title="Radar de apertura sintética – Spanish" lang="es" hreflang="es" data-title="Radar de apertura sintética" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D8%A7%D8%AF%D8%A7%D8%B1_%D8%AF%D9%87%D8%A7%D9%86%D9%87_%D8%AA%D8%B1%DA%A9%DB%8C%D8%A8%DB%8C" title="رادار دهانه ترکیبی – Persian" lang="fa" hreflang="fa" data-title="رادار دهانه ترکیبی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Radar_%C3%A0_synth%C3%A8se_d%27ouverture" title="Radar à synthèse d'ouverture – French" lang="fr" hreflang="fr" data-title="Radar à synthèse d'ouverture" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Radar_de_apertura_sint%C3%A9tica" title="Radar de apertura sintética – Galician" lang="gl" hreflang="gl" data-title="Radar de apertura sintética" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%95%A9%EC%84%B1%EA%B0%9C%EA%B5%AC%EB%A0%88%EC%9D%B4%EB%8D%94" title="합성개구레이더 – Korean" lang="ko" hreflang="ko" data-title="합성개구레이더" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%BF%E0%A4%82%E0%A4%A5%E0%A5%87%E0%A4%9F%E0%A4%BF%E0%A4%95_%E0%A4%8F%E0%A4%AA%E0%A4%B0%E0%A5%8D%E0%A4%9A%E0%A4%B0_%E0%A4%B0%E0%A4%A1%E0%A4%BE%E0%A4%B0_(%E0%A4%8F%E0%A4%B8%E0%A4%8F%E0%A4%86%E0%A4%B0)" title="सिंथेटिक एपर्चर रडार (एसएआर) – Hindi" lang="hi" hreflang="hi" data-title="सिंथेटिक एपर्चर रडार (एसएआर)" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Radar_apertur_sintetis" title="Radar apertur sintetis – Indonesian" lang="id" hreflang="id" data-title="Radar apertur sintetis" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Radar_ad_apertura_sintetica" title="Radar ad apertura sintetica – Italian" lang="it" hreflang="it" data-title="Radar ad apertura sintetica" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%9B%22%D7%9D_%D7%9E%D7%A4%D7%AA%D7%97_%D7%A1%D7%99%D7%A0%D7%AA%D7%98%D7%99" title="מכ"ם מפתח סינתטי – Hebrew" lang="he" hreflang="he" data-title="מכ"ם מפתח סינתטי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Sintez%C4%93t%C4%81s_apert%C5%ABras_radars" title="Sintezētās apertūras radars – Latvian" lang="lv" hreflang="lv" data-title="Sintezētās apertūras radars" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Szintetikus_apert%C3%BAr%C3%A1j%C3%BA_r%C3%A1di%C3%B3lok%C3%A1tor" title="Szintetikus apertúrájú rádiólokátor – Hungarian" lang="hu" hreflang="hu" data-title="Szintetikus apertúrájú rádiólokátor" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Synthetische_apertuurradar" title="Synthetische apertuurradar – Dutch" lang="nl" hreflang="nl" data-title="Synthetische apertuurradar" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%90%88%E6%88%90%E9%96%8B%E5%8F%A3%E3%83%AC%E3%83%BC%E3%83%80%E3%83%BC" title="合成開口レーダー – Japanese" lang="ja" hreflang="ja" data-title="合成開口レーダー" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Syntetisk_apertur-radar" title="Syntetisk apertur-radar – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Syntetisk apertur-radar" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Syntetisk_apertur-radar" title="Syntetisk apertur-radar – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Syntetisk apertur-radar" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Radar_z_syntetyczn%C4%85_apertur%C4%85" title="Radar z syntetyczną aperturą – Polish" lang="pl" hreflang="pl" data-title="Radar z syntetyczną aperturą" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Radar_de_abertura_sint%C3%A9tica" title="Radar de abertura sintética – Portuguese" lang="pt" hreflang="pt" data-title="Radar de abertura sintética" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D0%BE%D0%BB%D0%BE%D0%BA%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%BD%D0%BE%D0%B5_%D1%81%D0%B8%D0%BD%D1%82%D0%B5%D0%B7%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5_%D0%B0%D0%BF%D0%B5%D1%80%D1%82%D1%83%D1%80%D1%8B" title="Радиолокационное синтезирование апертуры – Russian" lang="ru" hreflang="ru" data-title="Радиолокационное синтезирование апертуры" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/SAR_(radar)" title="SAR (radar) – Slovenian" lang="sl" hreflang="sl" data-title="SAR (radar)" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/SAR_(tutka)" title="SAR (tutka) – Finnish" lang="fi" hreflang="fi" data-title="SAR (tutka)" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Syntetisk_aperturradar" title="Syntetisk aperturradar – Swedish" lang="sv" hreflang="sv" data-title="Syntetisk aperturradar" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AF%8A%E0%AE%95%E0%AF%81%E0%AE%B5%E0%AE%BF%E0%AE%B2%E0%AF%8D%E0%AE%B2%E0%AF%88_%E0%AE%B5%E0%AF%80%E0%AE%B5%E0%AE%BE%E0%AE%A3%E0%AE%BF" title="தொகுவில்லை வீவாணி – Tamil" lang="ta" hreflang="ta" data-title="தொகுவில்லை வீவாணி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Sentetik_aral%C4%B1kl%C4%B1_radar" title="Sentetik aralıklı radar – Turkish" lang="tr" hreflang="tr" data-title="Sentetik aralıklı radar" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B0%D1%80_%D1%96%D0%B7_%D1%81%D0%B8%D0%BD%D1%82%D0%B5%D0%B7%D0%BE%D0%B2%D0%B0%D0%BD%D0%BE%D1%8E_%D0%B0%D0%BF%D0%B5%D1%80%D1%82%D1%83%D1%80%D0%BE%D1%8E" title="Радар із синтезованою апертурою – Ukrainian" lang="uk" hreflang="uk" data-title="Радар із синтезованою апертурою" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%90%88%E6%88%90%E5%AD%94%E5%BE%84%E9%9B%B7%E8%BE%BE" title="合成孔径雷达 – Chinese" lang="zh" hreflang="zh" data-title="合成孔径雷达" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q740686#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Synthetic-aperture_radar" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Synthetic-aperture_radar" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Synthetic-aperture_radar"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Synthetic-aperture_radar&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tools" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tools</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Synthetic-aperture_radar"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Synthetic-aperture_radar&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Synthetic-aperture_radar" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Synthetic-aperture_radar" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Synthetic-aperture_radar&oldid=1259201286" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Synthetic-aperture_radar&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Synthetic-aperture_radar&id=1259201286&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FSynthetic-aperture_radar"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FSynthetic-aperture_radar"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Synthetic-aperture_radar&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Synthetic-aperture_radar&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Synthetic_aperture_radar" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q740686" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Form of radar used to create images of landscapes</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For broader coverage of this topic, see <a href="/wiki/Radar_imaging" class="mw-redirect" title="Radar imaging">Radar imaging</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><style data-mw-deduplicate="TemplateStyles:r1248332772">.mw-parser-output .multiple-issues-text{width:95%;margin:0.2em 0}.mw-parser-output .multiple-issues-text>.mw-collapsible-content{margin-top:0.3em}.mw-parser-output .compact-ambox .ambox{border:none;border-collapse:collapse;background-color:transparent;margin:0 0 0 1.6em!important;padding:0!important;width:auto;display:block}body.mediawiki .mw-parser-output .compact-ambox .ambox.mbox-small-left{font-size:100%;width:auto;margin:0}.mw-parser-output .compact-ambox .ambox .mbox-text{padding:0!important;margin:0!important}.mw-parser-output .compact-ambox .ambox .mbox-text-span{display:list-item;line-height:1.5em;list-style-type:disc}body.skin-minerva .mw-parser-output .multiple-issues-text>.mw-collapsible-toggle,.mw-parser-output .compact-ambox .ambox .mbox-image,.mw-parser-output .compact-ambox .ambox .mbox-imageright,.mw-parser-output .compact-ambox .ambox .mbox-empty-cell,.mw-parser-output .compact-ambox .hide-when-compact{display:none}</style><table class="box-Multiple_issues plainlinks metadata ambox ambox-content ambox-multiple_issues compact-ambox" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span"><div class="multiple-issues-text mw-collapsible"><b>This article has multiple issues.</b> Please help <b><a href="/wiki/Special:EditPage/Synthetic-aperture_radar" title="Special:EditPage/Synthetic-aperture radar">improve it</a></b> or discuss these issues on the <b><a href="/wiki/Talk:Synthetic-aperture_radar" title="Talk:Synthetic-aperture radar">talk page</a></b>. <small><i>(<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove these messages</a>)</i></small> <div class="mw-collapsible-content"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Synthetic-aperture_radar" title="Special:EditPage/Synthetic-aperture radar">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Synthetic-aperture+radar%22">"Synthetic-aperture radar"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Synthetic-aperture+radar%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Synthetic-aperture+radar%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Synthetic-aperture+radar%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Synthetic-aperture+radar%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Synthetic-aperture+radar%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">March 2012</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Overly_detailed plainlinks metadata ambox ambox-style ambox-overly_detailed" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>may contain an excessive amount of intricate detail that may interest only a particular audience</b>.<span class="hide-when-compact"> Please help by <a href="/wiki/Wikipedia:Content_forking#Article_spinoffs:_.22Summary_style.22_meta-articles_and_summary_sections" class="mw-redirect" title="Wikipedia:Content forking">spinning off</a> or <a href="/wiki/Wikipedia:Handling_trivia#Recommendations_for_handling_trivia" title="Wikipedia:Handling trivia">relocating</a> any relevant information, and removing excessive detail that may be against <a href="/wiki/Wikipedia:What_Wikipedia_is_not" title="Wikipedia:What Wikipedia is not">Wikipedia's inclusion policy</a>.</span> <span class="date-container"><i>(<span class="date">March 2012</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Technical plainlinks metadata ambox ambox-style ambox-technical" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>may be too technical for most readers to understand</b>.<span class="hide-when-compact"> Please <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Synthetic-aperture_radar&action=edit">help improve it</a> to <a href="/wiki/Wikipedia:Make_technical_articles_understandable" title="Wikipedia:Make technical articles understandable">make it understandable to non-experts</a>, without removing the technical details.</span> <span class="date-container"><i>(<span class="date">November 2024</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> </div> </div><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:TEIDE.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/TEIDE.JPG/220px-TEIDE.JPG" decoding="async" width="220" height="133" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/TEIDE.JPG/330px-TEIDE.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a8/TEIDE.JPG/440px-TEIDE.JPG 2x" data-file-width="3600" data-file-height="2180" /></a><figcaption>This radar image acquired by the SIR-C/X-SAR radar on board the <a href="/wiki/Space_Shuttle_Endeavour" title="Space Shuttle Endeavour">Space Shuttle Endeavour</a> shows the <a href="/wiki/Teide" title="Teide">Teide</a> volcano. The city of <a href="/wiki/Santa_Cruz_de_Tenerife" title="Santa Cruz de Tenerife">Santa Cruz de Tenerife</a> is visible as the purple and white area on the lower right edge of the island. Lava flows at the summit crater appear in shades of green and brown, while vegetation zones appear as areas of purple, green and yellow on the volcano's flanks.</figcaption></figure> <p><b>Synthetic-aperture radar</b> (<b>SAR</b>) is a form of <a href="/wiki/Radar" title="Radar">radar</a> that is used to create two-dimensional images or <a href="/wiki/3D_reconstruction" title="3D reconstruction">three-dimensional reconstructions</a> of objects, such as landscapes.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> SAR uses the motion of the radar antenna over a target region to provide finer <a href="/wiki/Spatial_resolution" title="Spatial resolution">spatial resolution</a> than conventional stationary beam-scanning radars. SAR is typically mounted on a moving platform, such as an aircraft or spacecraft, and has its origins in an advanced form of <a href="/wiki/Side_looking_airborne_radar" title="Side looking airborne radar">side looking airborne radar</a> (SLAR). The distance the SAR device travels over a target during the period when the target scene is illuminated creates the large <i>synthetic</i> <a href="/wiki/Antenna_aperture" class="mw-redirect" title="Antenna aperture">antenna aperture</a> (the <i>size</i> of the antenna). Typically, the larger the aperture, the higher the image resolution will be, regardless of whether the aperture is physical (a large antenna) or synthetic (a moving antenna) – this allows SAR to create high-resolution images with comparatively small physical antennas. For a fixed antenna size and orientation, objects which are further away remain illuminated longer – therefore SAR has the property of creating larger synthetic apertures for more distant objects, which results in a consistent spatial resolution over a range of viewing distances. </p><p>To create a SAR image, successive pulses of <a href="/wiki/Radio_wave" title="Radio wave">radio waves</a> are transmitted to "illuminate" a target scene, and the <a href="/wiki/Echo" title="Echo">echo</a> of each pulse is received and recorded. The pulses are transmitted and the echoes received using a single <a href="/wiki/Beamforming" title="Beamforming">beam-forming</a> antenna, with <a href="/wiki/Wavelength" title="Wavelength">wavelengths</a> of a meter down to several millimeters. As the SAR device on board the aircraft or spacecraft moves, the antenna location relative to the target changes with time. <a href="/wiki/Signal_processing" title="Signal processing">Signal processing</a> of the successive recorded radar echoes allows the combining of the recordings from these multiple antenna positions. This process forms the <i>synthetic antenna aperture</i> and allows the creation of higher-resolution images than would otherwise be possible with a given physical antenna.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Motivation_and_applications">Motivation and applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=1" title="Edit section: Motivation and applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Venus_globe.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venus_globe.jpg/220px-Venus_globe.jpg" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venus_globe.jpg/330px-Venus_globe.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venus_globe.jpg/440px-Venus_globe.jpg 2x" data-file-width="4096" data-file-height="4096" /></a><figcaption>The surface of <a href="/wiki/Venus" title="Venus">Venus</a>, as imaged by the <a href="/wiki/Magellan_probe" class="mw-redirect" title="Magellan probe">Magellan probe</a> using SAR, colorized with <a href="/wiki/False_color" title="False color">false color</a>.</figcaption></figure> <p>SAR is capable of high-resolution <a href="/wiki/Radar_remote_sensing" title="Radar remote sensing">remote sensing</a>, independent of flight altitude, and independent of weather, as SAR can select frequencies to avoid weather-caused signal attenuation. SAR has day and night imaging capability as illumination is provided by the SAR.<sup id="cite_ref-:2_3-0" class="reference"><a href="#cite_note-:2-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:3_5-0" class="reference"><a href="#cite_note-:3-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>SAR images have wide applications in remote sensing and mapping of surfaces of the Earth and other planets. Applications of SAR are numerous. Examples include topography, oceanography, glaciology, geology (for example, terrain discrimination and subsurface imaging). SAR can also be used in forestry to determine forest height, biomass, and deforestation. Volcano and earthquake monitoring use differential <a href="/wiki/Interferometric_synthetic-aperture_radar" title="Interferometric synthetic-aperture radar">interferometry</a>. SAR can also be applied for monitoring civil infrastructure stability such as bridges.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> SAR is useful in environment monitoring such as oil spills, flooding,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> urban growth,<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> military surveillance: including strategic policy and tactical assessment.<sup id="cite_ref-:3_5-1" class="reference"><a href="#cite_note-:3-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> SAR can be implemented as <a href="/wiki/Inverse_synthetic-aperture_radar" title="Inverse synthetic-aperture radar">inverse SAR</a> by observing a moving target over a substantial time with a stationary antenna. </p> <div class="mw-heading mw-heading2"><h2 id="Basic_principle">Basic principle</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=2" title="Edit section: Basic principle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Synthetic_Aperture_Radar.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Synthetic_Aperture_Radar.svg/220px-Synthetic_Aperture_Radar.svg.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Synthetic_Aperture_Radar.svg/330px-Synthetic_Aperture_Radar.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Synthetic_Aperture_Radar.svg/440px-Synthetic_Aperture_Radar.svg.png 2x" data-file-width="800" data-file-height="600" /></a><figcaption>Basic principle</figcaption></figure><p> A <i>synthetic-aperture radar</i> is an <a href="/wiki/Imaging_radar" title="Imaging radar">imaging radar</a> mounted on a moving platform.<sup id="cite_ref-:4_10-0" class="reference"><a href="#cite_note-:4-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> SAR is a <a href="/wiki/Doppler" class="mw-redirect" title="Doppler">Doppler</a> technique. It is based on the fact that "radar reflections from discrete objects in a passing radar beam field each [have] a minute Doppler, or speed, shift relative to the antenna".<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></p><blockquote><p>Carl Wiley, working at Goodyear, Arizona, (which later became Goodyear Aerospace, and eventually Lockheed Martin Corporation) in 1951, suggested the principle that — because each object in the radar beam has a slightly different speed relative to the antenna — each object will have its own doppler shift. A precise frequency analysis of the radar reflections will thus allow the construction of a detailed image.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>In order to realise this concept, electromagnetic waves are transmitted sequentially, the echoes are collected and the system electronics digitizes and stores the data for subsequent processing. As transmission and reception occur at different times, they map to different small positions. The well ordered combination of the received signals builds a virtual aperture that is much longer than the physical antenna width. That is the source of the term "synthetic aperture," giving it the property of an imaging radar.<sup id="cite_ref-:3_5-2" class="reference"><a href="#cite_note-:3-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The range direction is perpendicular to the flight track and perpendicular to the azimuth direction, which is also known as the <i>along-track</i> direction because it is in line with the position of the object within the antenna's field of view. </p><p>The 3D processing is done in two stages. The <a href="/wiki/Azimuth" title="Azimuth">azimuth</a> and range direction are focused for the generation of 2D (azimuth-range) high-resolution images, after which a digital elevation model (DEM)<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:15_14-0" class="reference"><a href="#cite_note-:15-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> is used to measure the phase differences between complex images, which is determined from different look angles to recover the height information. This height information, along with the azimuth-range coordinates provided by 2-D SAR focusing, gives the third dimension, which is the elevation.<sup id="cite_ref-:2_3-1" class="reference"><a href="#cite_note-:2-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The first step requires only standard processing algorithms,<sup id="cite_ref-:15_14-1" class="reference"><a href="#cite_note-:15-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> for the second step, additional pre-processing such as image co-registration and phase calibration is used.<sup id="cite_ref-:2_3-2" class="reference"><a href="#cite_note-:2-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:9_15-0" class="reference"><a href="#cite_note-:9-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>In addition, multiple baselines can be used to extend 3D imaging to the <i>time dimension</i>. 4D and multi-D SAR imaging allows imaging of complex scenarios, such as urban areas, and has improved performance with respect to classical interferometric techniques such as persistent scatterer interferometry (PSI).<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Algorithm">Algorithm</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=3" title="Edit section: Algorithm"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>SAR algorithms model the scene as a set of point targets that do not interact with each other (the <a href="/wiki/Born_approximation" title="Born approximation">Born approximation</a>). </p><p>While the details of various SAR algorithms differ, SAR processing in each case is the application of a <a href="/wiki/Matched_filter" title="Matched filter">matched filter</a> to the raw data, for each pixel in the output image, where the matched filter coefficients are the response from a single isolated point target.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> In the early days of SAR processing, the raw data was recorded on film and the postprocessing by matched filter was <a rel="nofollow" class="external text" href="https://space.stackexchange.com/a/60561/49488">implemented optically</a> using lenses of conical, cylindrical and spherical shape. The Range-Doppler algorithm is an example of a more recent approach. </p> <div class="mw-heading mw-heading2"><h2 id="Existing_spectral_estimation_approaches">Existing spectral estimation approaches</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=4" title="Edit section: Existing spectral estimation approaches"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Synthetic-aperture radar determines the 3D reflectivity from measured SAR data. It is basically a spectrum estimation, because for a specific cell of an image, the complex-value SAR measurements of the SAR image stack are a sampled version of the Fourier transform of reflectivity in elevation direction, but the Fourier transform is irregular.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Thus the spectral estimation techniques are used to improve the resolution and reduce <a href="/wiki/Speckle_pattern" class="mw-redirect" title="Speckle pattern">speckle</a> compared to the results of conventional Fourier transform SAR imaging techniques.<sup id="cite_ref-:12_19-0" class="reference"><a href="#cite_note-:12-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Non-parametric_methods">Non-parametric methods</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=5" title="Edit section: Non-parametric methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="FFT">FFT</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=6" title="Edit section: FFT"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>FFT (Fast Fourier Transform i.e., <a href="/wiki/Periodogram" title="Periodogram">periodogram</a> or <a href="/wiki/Matched_filter" title="Matched filter">matched filter</a>) is one such method, which is used in majority of the spectral estimation algorithms, and there are many fast algorithms for computing the multidimensional discrete Fourier transform. Computational <i>Kronecker-core array algebra</i><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> is a popular algorithm used as new variant of FFT algorithms for the processing in multidimensional synthetic-aperture radar (SAR) systems. This algorithm uses a study of theoretical properties of input/output data indexing sets and groups of permutations. </p><p>A branch of finite multi-dimensional linear algebra is used to identify similarities and differences among various FFT algorithm variants and to create new variants. Each multidimensional DFT computation is expressed in matrix form. The multidimensional DFT matrix, in turn, is disintegrated into a set of factors, called functional primitives, which are individually identified with an underlying software/hardware computational design.<sup id="cite_ref-:3_5-3" class="reference"><a href="#cite_note-:3-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>The FFT implementation is essentially a realization of the mapping of the mathematical framework through generation of the variants and executing matrix operations. The performance of this implementation may vary from machine to machine, and the objective is to identify on which machine it performs best.<sup id="cite_ref-:13_21-0" class="reference"><a href="#cite_note-:13-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading5"><h5 id="Advantages">Advantages</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=7" title="Edit section: Advantages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Additive group-theoretic properties of multidimensional input/output indexing sets are used for the mathematical formulations, therefore, it is easier to identify mapping between computing structures and mathematical expressions, thus, better than conventional methods.<sup id="cite_ref-:10_22-0" class="reference"><a href="#cite_note-:10-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></li> <li>The language of CKA algebra helps the application developer in understanding which are the more computational efficient FFT variants thus reducing the computational effort and improve their implementation time.<sup id="cite_ref-:10_22-1" class="reference"><a href="#cite_note-:10-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading5"><h5 id="Disadvantages">Disadvantages</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=8" title="Edit section: Disadvantages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>FFT cannot separate sinusoids close in frequency. If the periodicity of the data does not match FFT, edge effects are seen.<sup id="cite_ref-:13_21-1" class="reference"><a href="#cite_note-:13-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading4"><h4 id="Capon_method">Capon method</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=9" title="Edit section: Capon method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Capon spectral method, also called the minimum-variance method, is a multidimensional array-processing technique.<sup id="cite_ref-:5_24-0" class="reference"><a href="#cite_note-:5-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> It is a nonparametric covariance-based method, which uses an adaptive matched-filterbank approach and follows two main steps: </p> <ol><li>Passing the data through a 2D bandpass filter with varying center frequencies (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{1},\omega _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{1},\omega _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc9e7a34c1cd21e1fda694fca931aab81277773b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.034ex; height:2.009ex;" alt="{\displaystyle \omega _{1},\omega _{2}}"></span>).</li> <li>Estimating the power at (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{1},\omega _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{1},\omega _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc9e7a34c1cd21e1fda694fca931aab81277773b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.034ex; height:2.009ex;" alt="{\displaystyle \omega _{1},\omega _{2}}"></span>) for all <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{1}\in [0,2\pi ),\omega _{2}\in [0,2\pi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mi>π</mi> <mo stretchy="false">)</mo> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mi>π</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{1}\in [0,2\pi ),\omega _{2}\in [0,2\pi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/906027ea918a3599fe54d6c602adebf7e1bc494e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.2ex; height:2.843ex;" alt="{\displaystyle \omega _{1}\in [0,2\pi ),\omega _{2}\in [0,2\pi )}"></span> of interest from the filtered data.</li></ol> <p>The adaptive Capon bandpass filter is designed to minimize the power of the filter output, as well as pass the frequencies (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{1},\omega _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{1},\omega _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc9e7a34c1cd21e1fda694fca931aab81277773b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.034ex; height:2.009ex;" alt="{\displaystyle \omega _{1},\omega _{2}}"></span>) without any attenuation, i.e., to satisfy, for each (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{1},\omega _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{1},\omega _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc9e7a34c1cd21e1fda694fca931aab81277773b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.034ex; height:2.009ex;" alt="{\displaystyle \omega _{1},\omega _{2}}"></span>), </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \min _{h}h_{\omega _{1},\omega _{2}}^{*}Rh_{\omega _{1},\omega _{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">min</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </munder> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mi>R</mi> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \min _{h}h_{\omega _{1},\omega _{2}}^{*}Rh_{\omega _{1},\omega _{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5abe8ca3e246e3a2ed60a8d607fc35a4023af611" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:17.499ex; height:3.843ex;" alt="{\displaystyle \min _{h}h_{\omega _{1},\omega _{2}}^{*}Rh_{\omega _{1},\omega _{2}}}"></span> subject to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{\omega _{1},\omega _{2}}^{*}a_{\omega _{1},\omega _{2}}=1,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{\omega _{1},\omega _{2}}^{*}a_{\omega _{1},\omega _{2}}=1,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a74c365a2e41f3afe6d878b50a37232693354876" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:16.271ex; height:2.843ex;" alt="{\displaystyle h_{\omega _{1},\omega _{2}}^{*}a_{\omega _{1},\omega _{2}}=1,}"></span></dd></dl> <p>where <i>R</i> is the <a href="/wiki/Covariance_matrix" title="Covariance matrix">covariance matrix</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{\omega _{1},\omega _{2}}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{\omega _{1},\omega _{2}}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7521caf71c1e2651579d1f090a6f6d43bf783087" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.736ex; height:2.843ex;" alt="{\displaystyle h_{\omega _{1},\omega _{2}}^{*}}"></span> is the complex conjugate transpose of the impulse response of the FIR filter, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{\omega _{1},\omega _{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{\omega _{1},\omega _{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd3dca82955d81b33ae22eb411a3babc82632fee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.627ex; height:2.343ex;" alt="{\displaystyle a_{\omega _{1},\omega _{2}}}"></span> is the 2D Fourier vector, defined as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{\omega _{1},\omega _{2}}\triangleq a_{\omega _{1}}\otimes a_{\omega _{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> <mo>≜</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msub> <mo>⊗</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{\omega _{1},\omega _{2}}\triangleq a_{\omega _{1}}\otimes a_{\omega _{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80f4c23c65699451357f1740524485c242bc7d9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:18.198ex; height:3.176ex;" alt="{\displaystyle a_{\omega _{1},\omega _{2}}\triangleq a_{\omega _{1}}\otimes a_{\omega _{2}}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \otimes }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \otimes }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de29098f5a34ee296a505681a0d5e875070f2aea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \otimes }"></span> denotes Kronecker product.<sup id="cite_ref-:5_24-1" class="reference"><a href="#cite_note-:5-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p><p>Therefore, it passes a 2D sinusoid at a given frequency without distortion while minimizing the variance of the noise of the resulting image. The purpose is to compute the spectral estimate efficiently.<sup id="cite_ref-:5_24-2" class="reference"><a href="#cite_note-:5-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p><p><i>Spectral estimate</i> is given as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{\omega _{1},\omega _{2}}={\frac {1}{a_{\omega _{1},\omega _{2}}^{*}R^{-1}a_{\omega _{1},\omega _{2}}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{\omega _{1},\omega _{2}}={\frac {1}{a_{\omega _{1},\omega _{2}}^{*}R^{-1}a_{\omega _{1},\omega _{2}}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffaf8b9fce164293bc01c83b3c4148514550c350" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:25.755ex; height:6.009ex;" alt="{\displaystyle S_{\omega _{1},\omega _{2}}={\frac {1}{a_{\omega _{1},\omega _{2}}^{*}R^{-1}a_{\omega _{1},\omega _{2}}}},}"></span></dd></dl> <p>where <i>R</i> is the covariance matrix, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{\omega _{1},\omega _{2}}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{\omega _{1},\omega _{2}}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f43d6f6d72b47396e9efb1be677d3d0a2acb579" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.627ex; height:2.843ex;" alt="{\displaystyle a_{\omega _{1},\omega _{2}}^{*}}"></span> is the 2D complex-conjugate transpose of the Fourier vector. The computation of this equation over all frequencies is time-consuming. It is seen that the forward–backward Capon estimator yields better estimation than the forward-only classical capon approach. The main reason behind this is that while the forward–backward Capon uses both the forward and backward data vectors to obtain the estimate of the covariance matrix, the forward-only Capon uses only the forward data vectors to estimate the covariance matrix.<sup id="cite_ref-:5_24-3" class="reference"><a href="#cite_note-:5-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading5"><h5 id="Advantages_2">Advantages</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=10" title="Edit section: Advantages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Capon can yield more accurate spectral estimates with much lower sidelobes and narrower spectral peaks than the fast Fourier transform (FFT) method.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup></li> <li>Capon method can provide much better resolution.</li></ul> <div class="mw-heading mw-heading5"><h5 id="Disadvantages_2">Disadvantages</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=11" title="Edit section: Disadvantages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Implementation requires computation of two intensive tasks: inversion of the covariance matrix <i>R</i> and multiplication by the <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{\omega _{1},\omega _{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{\omega _{1},\omega _{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd3dca82955d81b33ae22eb411a3babc82632fee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.627ex; height:2.343ex;" alt="{\displaystyle a_{\omega _{1},\omega _{2}}}"></span> matrix, which has to be done for each point <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(\omega _{1},\omega _{2}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(\omega _{1},\omega _{2}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa7a20078b5055e86750b52b04e7bcc8674d100a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.843ex; height:2.843ex;" alt="{\displaystyle \left(\omega _{1},\omega _{2}\right)}"></span>.<sup id="cite_ref-:2_3-3" class="reference"><a href="#cite_note-:2-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading4"><h4 id="APES_method">APES method</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=12" title="Edit section: APES method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The APES (amplitude and phase estimation) method is also a matched-filter-bank method, which assumes that the phase history data is a sum of 2D sinusoids in noise. </p><p>APES spectral estimator has 2-step filtering interpretation: </p> <ol><li>Passing data through a bank of FIR bandpass filters with varying center frequency <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"></span>.</li> <li>Obtaining the spectrum estimate for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega \in [0,2\pi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mi>π</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega \in [0,2\pi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/471be2af84b2c6a9955f7b3a239a9302b48b0b28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.529ex; height:2.843ex;" alt="{\displaystyle \omega \in [0,2\pi )}"></span> from the filtered data.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></li></ol> <p>Empirically, the APES method results in wider spectral peaks than the Capon method, but more accurate spectral estimates for amplitude in SAR.<sup id="cite_ref-:6_27-0" class="reference"><a href="#cite_note-:6-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> In the Capon method, although the spectral peaks are narrower than the APES, the sidelobes are higher than that for the APES. As a result, the estimate for the amplitude is expected to be less accurate for the Capon method than for the APES method. The APES method requires about 1.5 times more computation than the Capon method.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading5"><h5 id="Advantages_3">Advantages</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=13" title="Edit section: Advantages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Filtering reduces the number of available samples, but when it is designed tactically, the increase in signal-to-noise ratio (SNR) in the filtered data will compensate this reduction, and the amplitude of a sinusoidal component with frequency <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"></span> can be estimated more accurately from the filtered data than from the original signal.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading5"><h5 id="Disadvantages_3">Disadvantages</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=14" title="Edit section: Disadvantages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>The autocovariance matrix is much larger in 2D than in 1D, therefore it is limited by memory available.<sup id="cite_ref-:3_5-4" class="reference"><a href="#cite_note-:3-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading3"><h3 id="SAMV_method">SAMV method</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=15" title="Edit section: SAMV method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/SAMV_(algorithm)" title="SAMV (algorithm)">SAMV</a> method is a parameter-free sparse signal reconstruction based algorithm. It achieves <a href="/wiki/Super-resolution_imaging" title="Super-resolution imaging">super-resolution</a> and is robust to highly correlated signals. The name emphasizes its basis on the asymptotically minimum variance (AMV) criterion. It is a powerful tool for the recovery of both the amplitude and frequency characteristics of multiple highly correlated sources in challenging environment (e.g., limited number of snapshots, low <a href="/wiki/Signal-to-noise_ratio" title="Signal-to-noise ratio">signal-to-noise ratio</a>. Applications include synthetic-aperture radar imaging and various source localization. </p> <div class="mw-heading mw-heading4"><h4 id="Advantages_4">Advantages</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=16" title="Edit section: Advantages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/SAMV_(algorithm)" title="SAMV (algorithm)">SAMV</a> method is capable of achieving resolution higher than some established parametric methods, e.g., <a href="/wiki/MUSIC_(algorithm)" title="MUSIC (algorithm)">MUSIC</a>, especially with highly correlated signals. </p> <div class="mw-heading mw-heading4"><h4 id="Disadvantages_4">Disadvantages</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=17" title="Edit section: Disadvantages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Computational_complexity" title="Computational complexity">Computational complexity</a> of the <a href="/wiki/SAMV_(algorithm)" title="SAMV (algorithm)">SAMV</a> method is higher due to its iterative procedure. </p> <div class="mw-heading mw-heading3"><h3 id="Parametric_subspace_decomposition_methods">Parametric subspace decomposition methods</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=18" title="Edit section: Parametric subspace decomposition methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Eigenvector_method">Eigenvector method</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=19" title="Edit section: Eigenvector method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This subspace decomposition method separates the eigenvectors of the autocovariance matrix into those corresponding to signals and to clutter.<sup id="cite_ref-:3_5-5" class="reference"><a href="#cite_note-:3-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The amplitude of the image at a point (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{x},\omega _{y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{x},\omega _{y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f7f88627e372838889bb3964bb291c7b5412482" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.147ex; height:2.343ex;" alt="{\displaystyle \omega _{x},\omega _{y}}"></span> ) is given by: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {\phi }}_{EV}\left(\omega _{x},\omega _{y}\right)={\frac {1}{W^{\mathsf {H}}\left(\omega _{x},\omega _{y}\right)\left(\sum _{\text{clutter}}{\frac {1}{\lambda _{i}}}{\underline {v_{i}}}\,{\underline {v_{i}}}^{\mathsf {H}}\right)W\left(\omega _{x},\omega _{y}\right)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ϕ</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> <mi>V</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <msup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">H</mi> </mrow> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>clutter</mtext> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <munder> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>_</mo> </munder> </mrow> <mspace width="thinmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <munder> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>_</mo> </munder> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">H</mi> </mrow> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mi>W</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {\phi }}_{EV}\left(\omega _{x},\omega _{y}\right)={\frac {1}{W^{\mathsf {H}}\left(\omega _{x},\omega _{y}\right)\left(\sum _{\text{clutter}}{\frac {1}{\lambda _{i}}}{\underline {v_{i}}}\,{\underline {v_{i}}}^{\mathsf {H}}\right)W\left(\omega _{x},\omega _{y}\right)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51fd3b72f8d433bf09d2c0277c22e061a9a6df96" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.505ex; width:58.963ex; height:7.843ex;" alt="{\displaystyle {\hat {\phi }}_{EV}\left(\omega _{x},\omega _{y}\right)={\frac {1}{W^{\mathsf {H}}\left(\omega _{x},\omega _{y}\right)\left(\sum _{\text{clutter}}{\frac {1}{\lambda _{i}}}{\underline {v_{i}}}\,{\underline {v_{i}}}^{\mathsf {H}}\right)W\left(\omega _{x},\omega _{y}\right)}}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {\phi }}_{EV}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ϕ</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> <mi>V</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {\phi }}_{EV}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4485152d90df9fcb853c27cc3c3f386c958bd153" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.219ex; height:3.343ex;" alt="{\displaystyle {\hat {\phi }}_{EV}}"></span> is the amplitude of the image at a point <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(\omega _{x},\omega _{y}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(\omega _{x},\omega _{y}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e71775e2aca87c2aa3249d0b4943fd3da702aa3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.957ex; height:3.009ex;" alt="{\displaystyle \left(\omega _{x},\omega _{y}\right)}"></span> , <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\underline {v_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <munder> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>_</mo> </munder> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\underline {v_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7413f11d2b3ffad46ac4a9d6c4d1ca5711645389" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.877ex; margin-bottom: -0.795ex; width:1.93ex; height:3.009ex;" alt="{\displaystyle {\underline {v_{i}}}}"></span> is the <a href="/wiki/Polarization_(waves)#Coherency_matrix" title="Polarization (waves)">coherency matrix</a> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\underline {v_{i}}}^{\mathsf {H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <munder> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>_</mo> </munder> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">H</mi> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\underline {v_{i}}}^{\mathsf {H}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bc745a20c2df8a1cbaef7cfcc1b39ad380c0161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.877ex; margin-bottom: -0.795ex; width:3.325ex; height:4.009ex;" alt="{\displaystyle {\underline {v_{i}}}^{\mathsf {H}}}"></span> is the <a href="/wiki/Hermitian_matrix" title="Hermitian matrix">Hermitian</a> of the coherency matrix, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{\lambda _{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\lambda _{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56142c6eddff65142742250fba1e08c5d23eaea5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:2.991ex; height:5.676ex;" alt="{\displaystyle {\frac {1}{\lambda _{i}}}}"></span> is the inverse of the eigenvalues of the clutter subspace, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W\left(\omega _{x},\omega _{y}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W\left(\omega _{x},\omega _{y}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3562b5483ba35bfba416cadfd0f16f864af56e19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.779ex; height:3.009ex;" alt="{\displaystyle W\left(\omega _{x},\omega _{y}\right)}"></span> are vectors defined as<sup id="cite_ref-:3_5-6" class="reference"><a href="#cite_note-:3-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W\left(\omega _{x},\omega _{y}\right)=\left[1\exp \left(-j\omega _{x}\right)\ldots \exp \left(-j(M-1)\omega _{x}\right)\right]\otimes \left[1\exp \left(-j\omega _{y}\right)\ldots \exp \left(-j(M-1)\omega _{y}\right)\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>[</mo> <mrow> <mn>1</mn> <mi>exp</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mi>j</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>…</mo> <mi>exp</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mi>j</mi> <mo stretchy="false">(</mo> <mi>M</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> <mo>⊗</mo> <mrow> <mo>[</mo> <mrow> <mn>1</mn> <mi>exp</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mi>j</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>…</mo> <mi>exp</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mi>j</mi> <mo stretchy="false">(</mo> <mi>M</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W\left(\omega _{x},\omega _{y}\right)=\left[1\exp \left(-j\omega _{x}\right)\ldots \exp \left(-j(M-1)\omega _{x}\right)\right]\otimes \left[1\exp \left(-j\omega _{y}\right)\ldots \exp \left(-j(M-1)\omega _{y}\right)\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/214b61a1b10335a3d1d80d3089cd7cc7a88dcce0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:88.646ex; height:3.009ex;" alt="{\displaystyle W\left(\omega _{x},\omega _{y}\right)=\left[1\exp \left(-j\omega _{x}\right)\ldots \exp \left(-j(M-1)\omega _{x}\right)\right]\otimes \left[1\exp \left(-j\omega _{y}\right)\ldots \exp \left(-j(M-1)\omega _{y}\right)\right]}"></span></dd></dl> <p>where ⊗ denotes the <a href="/wiki/Kronecker_product" title="Kronecker product">Kronecker product</a> of the two vectors. </p> <div class="mw-heading mw-heading5"><h5 id="Advantages_5">Advantages</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=20" title="Edit section: Advantages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Shows features of image more accurately.<sup id="cite_ref-:3_5-7" class="reference"><a href="#cite_note-:3-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading5"><h5 id="Disadvantages_5">Disadvantages</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=21" title="Edit section: Disadvantages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>High computational complexity.<sup id="cite_ref-:9_15-1" class="reference"><a href="#cite_note-:9-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading4"><h4 id="MUSIC_method">MUSIC method</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=22" title="Edit section: MUSIC method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/MUSIC_(algorithm)" title="MUSIC (algorithm)">MUSIC</a> detects frequencies in a signal by performing an eigen decomposition on the covariance matrix of a data vector of the samples obtained from the samples of the received signal. When all of the eigenvectors are included in the clutter subspace (model order = 0) the EV method becomes identical to the Capon method. Thus the determination of model order is critical to operation of the EV method. The eigenvalue of the R matrix decides whether its corresponding eigenvector corresponds to the clutter or to the signal subspace.<sup id="cite_ref-:3_5-8" class="reference"><a href="#cite_note-:3-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>The MUSIC method is considered to be a poor performer in SAR applications. This method uses a constant instead of the clutter subspace.<sup id="cite_ref-:3_5-9" class="reference"><a href="#cite_note-:3-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>In this method, the denominator is equated to zero when a sinusoidal signal corresponding to a point in the SAR image is in alignment to one of the signal subspace eigenvectors which is the peak in image estimate. Thus this method does not accurately represent the scattering intensity at each point, but show the particular points of the image.<sup id="cite_ref-:3_5-10" class="reference"><a href="#cite_note-:3-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:0_30-0" class="reference"><a href="#cite_note-:0-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading5"><h5 id="Advantages_6">Advantages</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=23" title="Edit section: Advantages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/MUSIC_(algorithm)" title="MUSIC (algorithm)">MUSIC</a> whitens or equalizes, the clutter eigenvalues.<sup id="cite_ref-:12_19-1" class="reference"><a href="#cite_note-:12-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading5"><h5 id="Disadvantages_6">Disadvantages</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=24" title="Edit section: Disadvantages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Resolution loss due to the averaging operation.<sup id="cite_ref-:4_10-1" class="reference"><a href="#cite_note-:4-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading3"><h3 id="Backprojection_algorithm">Backprojection algorithm</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=25" title="Edit section: Backprojection algorithm"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Backprojection Algorithm has two methods: <i>Time-domain Backprojection</i> and <i>Frequency-domain Backprojection</i>. The time-domain Backprojection has more advantages over frequency-domain and thus, is more preferred. The time-domain Backprojection forms images or spectrums by matching the data acquired from the radar and as per what it expects to receive. It can be considered as an ideal matched-filter for synthetic-aperture radar. There is no need of having a different motion compensation step due to its quality of handling non-ideal motion/sampling. It can also be used for various imaging geometries.<sup id="cite_ref-:1_31-0" class="reference"><a href="#cite_note-:1-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Advantages_7">Advantages</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=26" title="Edit section: Advantages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i>It is invariant to the imaging mode</i>: which means, that it uses the same algorithm irrespective of the imaging mode present, whereas, frequency domain methods require changes depending on the mode and geometry.<sup id="cite_ref-:1_31-1" class="reference"><a href="#cite_note-:1-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li> <li>Ambiguous azimuth aliasing usually occurs when the Nyquist spatial sampling requirements are exceeded by frequencies. Unambiguous aliasing occurs in <a href="/wiki/Squint_(antenna)" title="Squint (antenna)">squinted</a> geometries where the signal bandwidth does not exceed the sampling limits, but has undergone "spectral wrapping." Backprojection Algorithm does not get affected by any such kind of aliasing effects.<sup id="cite_ref-:1_31-2" class="reference"><a href="#cite_note-:1-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li> <li><i>It matches the space/time filter:</i> uses the information about the imaging geometry, to produce a pixel-by-pixel varying matched filter to approximate the expected return signal. This usually yields antenna gain compensation.<sup id="cite_ref-:1_31-3" class="reference"><a href="#cite_note-:1-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li> <li>With reference to the previous advantage, the back projection algorithm compensates for the motion. This becomes an advantage at areas having low altitudes.<sup id="cite_ref-:1_31-4" class="reference"><a href="#cite_note-:1-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading4"><h4 id="Disadvantages_7">Disadvantages</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=27" title="Edit section: Disadvantages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>The computational expense is more for Backprojection algorithm as compared to other frequency domain methods.</li> <li>It requires very precise knowledge of imaging geometry.<sup id="cite_ref-:1_31-5" class="reference"><a href="#cite_note-:1-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading4"><h4 id="Application:_geosynchronous_orbit_synthetic-aperture_radar_(GEO-SAR)"><span id="Application:_geosynchronous_orbit_synthetic-aperture_radar_.28GEO-SAR.29"></span>Application: geosynchronous orbit synthetic-aperture radar (GEO-SAR)</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=28" title="Edit section: Application: geosynchronous orbit synthetic-aperture radar (GEO-SAR)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In GEO-SAR, to focus specially on the relative moving track, the backprojection algorithm works very well. It uses the concept of Azimuth Processing in the time domain. For the satellite-ground geometry, GEO-SAR plays a significant role.<sup id="cite_ref-:8_32-0" class="reference"><a href="#cite_note-:8-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p><p>The procedure of this concept is elaborated as follows.<sup id="cite_ref-:8_32-1" class="reference"><a href="#cite_note-:8-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p> <ol><li>The raw data acquired is segmented or drawn into sub-apertures for simplification of speedy conduction of procedure.</li> <li>The range of the data is then compressed, using the concept of "Matched Filtering" for every segment/sub-aperture created. It is given by-<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle s(t,\tau )=\exp \left(-j\cdot {\frac {4\pi }{\lambda }}\cdot R(t)\right)\cdot \operatorname {sinc} \left(\tau -{\frac {2}{c}}\cdot R(t)\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>s</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <mi>τ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>exp</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mi>j</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> </mrow> <mi>λ</mi> </mfrac> </mrow> <mo>⋅</mo> <mi>R</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mo>⋅</mo> <mi>sinc</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mi>τ</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mi>c</mi> </mfrac> </mrow> <mo>⋅</mo> <mi>R</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle s(t,\tau )=\exp \left(-j\cdot {\frac {4\pi }{\lambda }}\cdot R(t)\right)\cdot \operatorname {sinc} \left(\tau -{\frac {2}{c}}\cdot R(t)\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5357407d99acd4ce5c9061eaec6f13108153aaa7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:48.028ex; height:4.843ex;" alt="{\textstyle s(t,\tau )=\exp \left(-j\cdot {\frac {4\pi }{\lambda }}\cdot R(t)\right)\cdot \operatorname {sinc} \left(\tau -{\frac {2}{c}}\cdot R(t)\right)}"></span> where <i>τ</i> is the range time, <i>t</i> is the azimuthal time, <i>λ</i> is the wavelength, <i>c</i> is the speed of light.</li> <li>Accuracy in the "Range Migration Curve" is achieved by range interpolation.</li> <li>The pixel locations of the ground in the image is dependent on the satellite–ground geometry model. Grid-division is now done as per the azimuth time.</li> <li>Calculations for the "slant range" (range between the antenna's phase center and the point on the ground) are done for every azimuth time using coordinate transformations.</li> <li>Azimuth Compression is done after the previous step.</li> <li>Step 5 and 6 are repeated for every pixel, to cover every pixel, and conduct the procedure on every sub-aperture.</li> <li>Lastly, all the sub-apertures of the image created throughout, are superimposed onto each other and the ultimate HD image is generated.</li></ol> <div class="mw-heading mw-heading3"><h3 id="Comparison_between_the_algorithms">Comparison between the algorithms</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=29" title="Edit section: Comparison between the algorithms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Capon and APES can yield more accurate spectral estimates with much lower sidelobes and more narrow spectral peaks than the fast Fourier transform (FFT) method, which is also a special case of the FIR filtering approaches. It is seen that although the APES algorithm gives slightly wider spectral peaks than the Capon method, the former yields more accurate overall spectral estimates than the latter and the FFT method.<sup id="cite_ref-:6_27-1" class="reference"><a href="#cite_note-:6-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p><p>FFT method is fast and simple but have larger sidelobes. Capon has high resolution but high computational complexity. EV also has high resolution and high computational complexity. APES has higher resolution, faster than capon and EV but high computational complexity.<sup id="cite_ref-:4_10-2" class="reference"><a href="#cite_note-:4-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>MUSIC method is not generally suitable for SAR imaging, as whitening the clutter eigenvalues destroys the spatial inhomogeneities associated with terrain clutter or other diffuse scattering in SAR imagery. But it offers higher frequency resolution in the resulting power spectral density (PSD) than the fast Fourier transform (FFT)-based methods.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p><p>The backprojection algorithm is computationally expensive. It is specifically attractive for sensors that are wideband, wide-angle, and/or have long coherent apertures with substantial off-track motion.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Multistatic_operation">Multistatic operation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=30" title="Edit section: Multistatic operation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Multistatic_radar" title="Multistatic radar">Multistatic radar</a></div> <p>SAR requires that echo captures be taken at multiple antenna positions. The more captures taken (at different antenna locations) the more reliable the target characterization. </p><p>Multiple captures can be obtained by moving a single antenna to different locations, by placing multiple stationary antennas at different locations, or combinations thereof. </p><p>The advantage of a single moving antenna is that it can be easily placed in any number of positions to provide any number of monostatic waveforms. For example, an antenna mounted on an airplane takes many captures per second as the plane travels. </p><p>The principal advantages of multiple static antennas are that a moving target can be characterized (assuming the capture electronics are fast enough), that no vehicle or motion machinery is necessary, and that antenna positions need not be derived from other, sometimes unreliable, information. (One problem with SAR aboard an airplane is knowing precise antenna positions as the plane travels). </p><p>For multiple static antennas, all combinations of monostatic and <a href="/wiki/Multistatic_radar" title="Multistatic radar">multistatic radar</a> waveform captures are possible. Note, however, that it is not advantageous to capture a waveform for each of both transmission directions for a given pair of antennas, because those waveforms will be identical. When multiple static antennas are used, the total number of unique echo waveforms that can be captured is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {N^{2}+N}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>N</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {N^{2}+N}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/343d28d988a4f0259c20ff2748bfc5a0c67e3751" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.917ex; height:5.676ex;" alt="{\displaystyle {\frac {N^{2}+N}{2}}}"></span></dd></dl> <p>where <i>N</i> is the number of unique antenna positions. </p> <div class="mw-heading mw-heading2"><h2 id="Scanning_modes">Scanning modes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=31" title="Edit section: Scanning modes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Stripmap_mode_airborne_SAR">Stripmap mode airborne SAR</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=32" title="Edit section: Stripmap mode airborne SAR"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Stripmap_Mode.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Stripmap_Mode.jpg/220px-Stripmap_Mode.jpg" decoding="async" width="220" height="164" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Stripmap_Mode.jpg/330px-Stripmap_Mode.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/Stripmap_Mode.jpg/440px-Stripmap_Mode.jpg 2x" data-file-width="2592" data-file-height="1936" /></a><figcaption>Illustration of the SAR stripmap operation mode.</figcaption></figure> <p>The antenna stays in a fixed position. It may be orthogonal to the flight path, or it may be squinted slightly forward or backward.<sup id="cite_ref-:3_5-11" class="reference"><a href="#cite_note-:3-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>When the antenna aperture travels along the flight path, a signal is transmitted at a rate equal to the <a href="/wiki/Pulse_repetition_frequency" class="mw-redirect" title="Pulse repetition frequency">pulse repetition frequency</a> (PRF). The lower boundary of the PRF is determined by the Doppler bandwidth of the radar. The backscatter of each of these signals is commutatively added on a pixel-by-pixel basis to attain the fine azimuth resolution desired in radar imagery.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Spotlight_mode_SAR">Spotlight mode SAR</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=33" title="Edit section: Spotlight mode SAR"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Spotlight_Imaging_Mode.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Spotlight_Imaging_Mode.jpg/220px-Spotlight_Imaging_Mode.jpg" decoding="async" width="220" height="197" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Spotlight_Imaging_Mode.jpg/330px-Spotlight_Imaging_Mode.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/Spotlight_Imaging_Mode.jpg/440px-Spotlight_Imaging_Mode.jpg 2x" data-file-width="1937" data-file-height="1731" /></a><figcaption>Depiction of the Spotlight Image Mode</figcaption></figure> <p>The spotlight synthetic aperture is given by </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Lsa=r_{0}\Delta \theta _{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mi>s</mi> <mi>a</mi> <mo>=</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi mathvariant="normal">Δ</mi> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Lsa=r_{0}\Delta \theta _{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56251f43720532a8e5bd83be5e0b184b8033984f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.233ex; height:2.509ex;" alt="{\displaystyle Lsa=r_{0}\Delta \theta _{a}}"></span><sup id="cite_ref-:0_30-1" class="reference"><a href="#cite_note-:0-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \theta _{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \theta _{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8dbf35860a1edd22294721123b95daf96debab7d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.128ex; height:2.509ex;" alt="{\displaystyle \Delta \theta _{a}}"></span> is the angle formed between the beginning and end of the imaging, as shown in the diagram of spotlight imaging and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb12fcfddb65e3d1e6a044215f6e833f0cd4337b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.103ex; height:2.009ex;" alt="{\displaystyle r_{0}}"></span> is the range distance. </p><p>The spotlight mode gives better resolution albeit for a smaller ground patch. In this mode, the illuminating radar beam is steered continually as the aircraft moves, so that it illuminates the same patch over a longer period of time. This mode is not a traditional continuous-strip imaging mode; however, it has high azimuth resolution.<sup id="cite_ref-:0_30-2" class="reference"><a href="#cite_note-:0-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> A technical explanation of spotlight SAR from first principles is offered in.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Scan_mode_SAR">Scan mode SAR</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=34" title="Edit section: Scan mode SAR"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:ScanSAR.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/ScanSAR.jpg/220px-ScanSAR.jpg" decoding="async" width="220" height="148" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/ScanSAR.jpg/330px-ScanSAR.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/ScanSAR.jpg/440px-ScanSAR.jpg 2x" data-file-width="1952" data-file-height="1312" /></a><figcaption>Depiction of ScanSAR Imaging Mode</figcaption></figure> <p>While operating as a scan mode SAR, the antenna beam sweeps periodically and thus cover much larger area than the spotlight and stripmap modes. However, the azimuth resolution become much lower than the stripmap mode due to the decreased azimuth bandwidth. Clearly there is a balance achieved between the azimuth resolution and the scan area of SAR.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> Here, the synthetic aperture is shared between the sub swaths, and it is not in direct contact within one subswath. Mosaic operation is required in azimuth and range directions to join the azimuth bursts and the range sub-swaths.<sup id="cite_ref-:0_30-3" class="reference"><a href="#cite_note-:0-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <ul><li>ScanSAR makes the <a href="/wiki/Swathe#Swathe_width" title="Swathe">swath</a> beam huge.</li> <li>The azimuth signal has many bursts.</li> <li>The azimuth resolution is limited due to the burst duration.</li> <li>Each target contains varied frequencies which completely depends on where the azimuth is present.<sup id="cite_ref-:0_30-4" class="reference"><a href="#cite_note-:0-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Special_techniques">Special techniques</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=35" title="Edit section: Special techniques"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Polarimetry">Polarimetry</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=36" title="Edit section: Polarimetry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Polarimetry" title="Polarimetry">Polarimetry</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Space_Radar_Image_of_Lisbon,_Portugal.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Space_Radar_Image_of_Lisbon%2C_Portugal.jpg/220px-Space_Radar_Image_of_Lisbon%2C_Portugal.jpg" decoding="async" width="220" height="132" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Space_Radar_Image_of_Lisbon%2C_Portugal.jpg/330px-Space_Radar_Image_of_Lisbon%2C_Portugal.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/49/Space_Radar_Image_of_Lisbon%2C_Portugal.jpg/440px-Space_Radar_Image_of_Lisbon%2C_Portugal.jpg 2x" data-file-width="4000" data-file-height="2392" /></a><figcaption>Color representation of different polarizations.</figcaption></figure> <p>Radar waves have a <a href="/wiki/Polarization_(waves)" title="Polarization (waves)">polarization</a>. Different materials reflect radar waves with different intensities, but <a href="/wiki/Anisotropic" class="mw-redirect" title="Anisotropic">anisotropic</a> materials such as grass often reflect different polarizations with different intensities. Some materials will also convert one polarization into another. By emitting a mixture of polarizations and using receiving antennas with a specific polarization, several images can be collected from the same series of pulses. Frequently three such RX-TX polarizations (HH-pol, VV-pol, VH-pol) are used as the three color channels in a synthesized image. This is what has been done in the picture at right. Interpretation of the resulting colors requires significant testing of known materials. </p><p>New developments in polarimetry include using the changes in the random polarization returns of some surfaces (such as grass or sand) and between two images of the same location at different times to determine where changes not visible to optical systems occurred. Examples include subterranean tunneling or paths of vehicles driving through the area being imaged. Enhanced SAR sea oil slick observation has been developed by appropriate physical modelling and use of fully polarimetric and dual-polarimetric measurements. </p> <div class="mw-heading mw-heading4"><h4 id="SAR_polarimetry">SAR polarimetry</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=37" title="Edit section: SAR polarimetry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Death-valley-sar.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Death-valley-sar.jpg/220px-Death-valley-sar.jpg" decoding="async" width="220" height="459" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Death-valley-sar.jpg/330px-Death-valley-sar.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/20/Death-valley-sar.jpg/440px-Death-valley-sar.jpg 2x" data-file-width="1200" data-file-height="2501" /></a><figcaption>SAR image of <a href="/wiki/Death_Valley" title="Death Valley">Death Valley</a> colored using polarimetry</figcaption></figure> <p>SAR polarimetry is a technique used for deriving qualitative and quantitative physical information for land, snow and ice, ocean and urban applications based on the measurement and exploration of the polarimetric properties of man-made and natural scatterers. <i>Terrain</i> and <i>land use</i> classification is one of the most important applications of polarimetric synthetic-aperture radar (PolSAR).<sup id="cite_ref-:7_38-0" class="reference"><a href="#cite_note-:7-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p><p>SAR polarimetry uses a scattering matrix (S) to identify the scattering behavior of objects after an interaction with electromagnetic wave. The matrix is represented by a combination of horizontal and vertical polarization states of transmitted and received signals. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S={\begin{bmatrix}S_{HH}&S_{HV}\\S_{VH}&S_{VV}\end{bmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> <mi>H</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> <mi>V</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mi>H</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mi>V</mi> </mrow> </msub> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S={\begin{bmatrix}S_{HH}&S_{HV}\\S_{VH}&S_{VV}\end{bmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65a01d735cadf9e50ea47fab4ddbe68e54d3c3af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:19.082ex; height:6.176ex;" alt="{\displaystyle S={\begin{bmatrix}S_{HH}&S_{HV}\\S_{VH}&S_{VV}\end{bmatrix}}}"></span> </p><p>where, HH is for horizontal transmit and horizontal receive, VV is for vertical transmit and vertical receive, HV is for horizontal transmit and vertical receive, and VH – for vertical transmit and horizontal receive. </p><p>The first two of these polarization combinations are referred to as like-polarized (or co-polarized), because the transmit and receive polarizations are the same. The last two combinations are referred to as cross-polarized because the transmit and receive polarizations are orthogonal to one another.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Three-component_scattering_power_model">Three-component scattering power model</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=38" title="Edit section: Three-component scattering power model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The three-component scattering power model by Freeman and Durden<sup id="cite_ref-:14_40-0" class="reference"><a href="#cite_note-:14-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> is successfully used for the decomposition of a PolSAR image, applying the reflection symmetry condition using covariance matrix. The method is based on simple physical scattering mechanisms (surface scattering, double-bounce scattering, and volume scattering). The advantage of this scattering model is that it is simple and easy to implement for image processing. There are 2 major approaches for a 3<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \times }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>×</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \times }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ffafff1ad26cbe49045f19a67ce532116a32703" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.019ex; margin-bottom: -0.19ex; width:1.808ex; height:1.509ex;" alt="{\displaystyle \times }"></span>3 polarimetric matrix decomposition. One is the lexicographic covariance matrix approach based on physically measurable parameters,<sup id="cite_ref-:14_40-1" class="reference"><a href="#cite_note-:14-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> and the other is the Pauli decomposition which is a coherent decomposition matrix. It represents all the polarimetric information in a single SAR image. The polarimetric information of [S] could be represented by the combination of the intensities <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |S_{HH}|^{2},|S_{VV}|^{2},2|S_{HV}|^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> <mi>H</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mi>V</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> <mi>V</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |S_{HH}|^{2},|S_{VV}|^{2},2|S_{HV}|^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6ef85180305ffb6b16437bfcbcf43f1b0c2578f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.414ex; height:3.343ex;" alt="{\displaystyle |S_{HH}|^{2},|S_{VV}|^{2},2|S_{HV}|^{2}}"></span> in a single RGB image where all the previous intensities will be coded as a color channel.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Four-component_scattering_power_model">Four-component scattering power model</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=39" title="Edit section: Four-component scattering power model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For PolSAR image analysis, there can be cases where reflection symmetry condition does not hold. In those cases a <i>four-component scattering model</i><sup id="cite_ref-:7_38-1" class="reference"><a href="#cite_note-:7-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> can be used to decompose polarimetric synthetic-aperture radar (SAR) images. This approach deals with the non-reflection symmetric scattering case. It includes and extends the three-component decomposition method introduced by Freeman and Durden<sup id="cite_ref-:14_40-2" class="reference"><a href="#cite_note-:14-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> to a fourth component by adding the helix scattering power. This helix power term generally appears in complex urban area but disappears for a natural distributed scatterer.<sup id="cite_ref-:7_38-2" class="reference"><a href="#cite_note-:7-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p><p>There is also an improved method using the four-component decomposition algorithm, which was introduced for the general polSAR data image analyses. The SAR data is first filtered which is known as speckle reduction, then each pixel is decomposed by four-component model to determine the surface scattering power (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe65a99191556a55c0eea7cd971a5cb642ce7be2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.496ex; height:2.509ex;" alt="{\displaystyle P_{s}}"></span>), double-bounce scattering power (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{d}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{d}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31cee957b3cb231d64331beb1d8d398eab758c0b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.584ex; height:2.509ex;" alt="{\displaystyle P_{d}}"></span>), volume scattering power (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{v}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{v}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a5ca3e8cb08e2700ccc8b6988533df691de0761" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.522ex; height:2.509ex;" alt="{\displaystyle P_{v}}"></span>), and helix scattering power (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f5cb998e64c6e024e849f1aa1e5606209507710" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.436ex; height:2.509ex;" alt="{\displaystyle P_{c}}"></span>).<sup id="cite_ref-:7_38-3" class="reference"><a href="#cite_note-:7-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> The pixels are then divided into 5 classes (surface, double-bounce, volume, helix, and mixed pixels) classified with respect to maximum powers. A mixed category is added for the pixels having two or three equal dominant scattering powers after computation. The process continues as the pixels in all these categories are divided in 20 small clutter approximately of same number of pixels and merged as desirable, this is called cluster merging. They are iteratively classified and then automatically color is delivered to each class. The summarization of this algorithm leads to an understanding that, brown colors denotes the surface scattering classes, red colors for double-bounce scattering classes, green colors for volume scattering classes, and blue colors for helix scattering classes.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> </p><p>Although this method is aimed for non-reflection case, it automatically includes the reflection symmetry condition, therefore in can be used as a general case. It also preserves the scattering characteristics by taking the mixed scattering category into account therefore proving to be a better algorithm. </p> <div class="mw-heading mw-heading3"><h3 id="Interferometry">Interferometry</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=40" title="Edit section: Interferometry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Interferometric_synthetic-aperture_radar" title="Interferometric synthetic-aperture radar">Interferometric synthetic-aperture radar</a></div> <p>Rather than discarding the phase data, information can be extracted from it. If two observations of the same terrain from very similar positions are available, <a href="/wiki/Aperture_synthesis" title="Aperture synthesis">aperture synthesis</a> can be performed to provide the resolution performance which would be given by a radar system with dimensions equal to the separation of the two measurements. This technique is called <a href="/wiki/Interferometric_SAR" class="mw-redirect" title="Interferometric SAR">interferometric SAR</a> or InSAR. </p><p>If the two samples are obtained simultaneously (perhaps by placing two antennas on the same aircraft, some distance apart), then any phase difference will contain information about the angle from which the radar echo returned. Combining this with the distance information, one can determine the position in three dimensions of the image pixel. In other words, one can extract terrain altitude as well as radar reflectivity, producing a <a href="/wiki/Digital_elevation_model" title="Digital elevation model">digital elevation model</a> (DEM) with a single airplane pass. One aircraft application at the <a href="/wiki/Canada_Centre_for_Remote_Sensing" class="mw-redirect" title="Canada Centre for Remote Sensing">Canada Centre for Remote Sensing</a> produced digital elevation maps with a resolution of 5 m and altitude errors also about 5 m. Interferometry was used to map many regions of the Earth's surface with unprecedented accuracy using data from the <a href="/wiki/Shuttle_Radar_Topography_Mission" title="Shuttle Radar Topography Mission">Shuttle Radar Topography Mission</a>. </p><p>If the two samples are separated in time, perhaps from two flights over the same terrain, then there are two possible sources of phase shift. The first is terrain altitude, as discussed above. The second is terrain motion: if the terrain has shifted between observations, it will return a different phase. The amount of shift required to cause a significant phase difference is on the order of the wavelength used. This means that if the terrain shifts by centimeters, it can be seen in the resulting image (a <a href="/wiki/Digital_elevation_map" class="mw-redirect" title="Digital elevation map">digital elevation map</a> must be available to separate the two kinds of phase difference; a third pass may be necessary to produce one). </p><p>This second method offers a powerful tool in <a href="/wiki/Geology" title="Geology">geology</a> and <a href="/wiki/Geography" title="Geography">geography</a>. <a href="/wiki/Glacier" title="Glacier">Glacier</a> flow can be mapped with two passes. Maps showing the land deformation after a minor <a href="/wiki/Earthquake" title="Earthquake">earthquake</a> or after a <a href="/wiki/Volcanic_eruption" class="mw-redirect" title="Volcanic eruption">volcanic eruption</a> (showing the shrinkage of the whole volcano by several centimeters) have been published.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Differential_interferometry">Differential interferometry</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=41" title="Edit section: Differential interferometry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Differential interferometry (D-InSAR) requires taking at least two images with addition of a DEM. The DEM can be either produced by GPS measurements or could be generated by interferometry as long as the time between acquisition of the image pairs is short, which guarantees minimal distortion of the image of the target surface. In principle, 3 images of the ground area with similar image acquisition geometry is often adequate for D-InSar. The principle for detecting ground movement is quite simple. One interferogram is created from the first two images; this is also called the reference interferogram or topographical interferogram. A second interferogram is created that captures topography + distortion. Subtracting the latter from the reference interferogram can reveal differential fringes, indicating movement. The described 3 image D-InSAR generation technique is called 3-pass or double-difference method. </p><p>Differential fringes which remain as fringes in the differential interferogram are a result of SAR range changes of any displaced point on the ground from one interferogram to the next. In the differential interferogram, each fringe is directly proportional to the SAR wavelength, which is about 5.6 cm for ERS and RADARSAT single phase cycle. Surface displacement away from the satellite look direction causes an increase in path (translating to phase) difference. Since the signal travels from the SAR antenna to the target and back again, the measured displacement is twice the unit of wavelength. This means in differential interferometry one fringe cycle −<span class="texhtml mvar" style="font-style:italic;">π</span> to +<span class="texhtml mvar" style="font-style:italic;">π</span> or one wavelength corresponds to a displacement relative to SAR antenna of only half wavelength (2.8 cm). There are various publications on measuring subsidence movement, slope stability analysis, landslide, glacier movement, etc. tooling D-InSAR. Further advancement to this technique whereby differential interferometry from satellite SAR ascending pass and descending pass can be used to estimate 3-D ground movement. Research in this area has shown accurate measurements of 3-D ground movement with accuracies comparable to GPS based measurements can be achieved. </p> <div class="mw-heading mw-heading4"><h4 id="Tomo-SAR">Tomo-SAR</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=42" title="Edit section: Tomo-SAR"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>SAR Tomography is a subfield of a concept named as multi-baseline interferometry. It has been developed to give a 3D exposure to the imaging, which uses the beam formation concept. It can be used when the use demands a focused phase concern between the magnitude and the phase components of the SAR data, during information retrieval. One of the major advantages of Tomo-SAR is that it can separate out the parameters which get scattered, irrespective of how different their motions are.<sup id="cite_ref-:11_47-0" class="reference"><a href="#cite_note-:11-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> On using Tomo-SAR with differential interferometry, a new combination named "differential tomography" (Diff-Tomo) is developed.<sup id="cite_ref-:11_47-1" class="reference"><a href="#cite_note-:11-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p><p>Tomo-SAR has an application based on radar imaging, which is the depiction of Ice Volume and Forest Temporal Coherence (<b>Temporal coherence</b> describes the correlation between waves observed at different moments in time).<sup id="cite_ref-:11_47-2" class="reference"><a href="#cite_note-:11-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ultra-wideband_SAR">Ultra-wideband SAR</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=43" title="Edit section: Ultra-wideband SAR"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Ultra-wideband" title="Ultra-wideband">Ultra-wideband</a></div> <p>Conventional radar systems emit bursts of radio energy with a fairly narrow range of frequencies. A narrow-band channel, by definition, does not allow rapid changes in modulation. Since it is the change in a received signal that reveals the time of arrival of the signal (obviously an unchanging signal would reveal nothing about "when" it reflected from the target), a signal with only a slow change in modulation cannot reveal the distance to the target as well as a signal with a quick change in modulation. </p><p><a href="/wiki/Ultra-wideband" title="Ultra-wideband">Ultra-wideband</a> (UWB) refers to any radio transmission that uses a very large bandwidth – which is the same as saying it uses very rapid changes in modulation. Although there is no set bandwidth value that qualifies a signal as "UWB", systems using bandwidths greater than a sizable portion of the center frequency (typically about ten percent, or so) are most often called "UWB" systems. A typical UWB system might use a bandwidth of one-third to one-half of its center frequency. For example, some systems use a bandwidth of about 1 GHz centered around 3 GHz. </p><p>The two most common methods to increase signal bandwidth used in UWB radar, including SAR, are very short pulses and high-bandwidth chirping. A general description of chirping appears elsewhere in this article. The bandwidth of a chirped system can be as narrow or as wide as the designers desire. Pulse-based UWB systems, being the more common method associated with the term "UWB radar", are described here. </p><p>A pulse-based radar system transmits very short pulses of electromagnetic energy, typically only a few waves or less. A very short pulse is, of course, a very rapidly changing signal, and thus occupies a very wide bandwidth. This allows far more accurate measurement of distance, and thus resolution. </p><p>The main disadvantage of pulse-based UWB SAR is that the transmitting and receiving front-end electronics are difficult to design for high-power applications. Specifically, the transmit duty cycle is so exceptionally low and pulse time so exceptionally short, that the electronics must be capable of extremely high instantaneous power to rival the average power of conventional radars. (Although it is true that UWB provides a notable gain in <a href="/wiki/Channel_capacity" title="Channel capacity">channel capacity</a> over a narrow band signal because of the relationship of bandwidth in the <a href="/wiki/Shannon%E2%80%93Hartley_theorem" title="Shannon–Hartley theorem">Shannon–Hartley theorem</a> and because the low receive duty cycle receives less noise, increasing the <a href="/wiki/Signal-to-noise_ratio" title="Signal-to-noise ratio">signal-to-noise ratio</a>, there is still a notable disparity in link budget because conventional radar might be several orders of magnitude more powerful than a typical pulse-based radar.) So pulse-based UWB SAR is typically used in applications requiring average power levels in the microwatt or milliwatt range, and thus is used for scanning smaller, nearer target areas (several tens of meters), or in cases where lengthy integration (over a span of minutes) of the received signal is possible. However, that this limitation is solved in chirped UWB radar systems. </p><p>The principal advantages of UWB radar are better resolution (a few millimeters using <a href="/wiki/Commercial_off-the-shelf" title="Commercial off-the-shelf">commercial off-the-shelf</a> electronics) and more spectral information of target reflectivity. </p> <div class="mw-heading mw-heading3"><h3 id="Doppler-beam_sharpening">Doppler-beam sharpening</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=44" title="Edit section: Doppler-beam sharpening"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Doppler Beam Sharpening commonly refers to the method of processing unfocused real-beam phase history to achieve better resolution than could be achieved by processing the real beam without it. Because the real aperture of the radar antenna is so small (compared to the wavelength in use), the radar energy spreads over a wide area (usually many degrees wide in a direction orthogonal (at right angles) to the direction of the platform (aircraft)). Doppler-beam sharpening takes advantage of the motion of the platform in that targets ahead of the platform return a Doppler upshifted signal (slightly higher in frequency) and targets behind the platform return a Doppler downshifted signal (slightly lower in frequency). </p><p>The amount of shift varies with the angle forward or backward from the ortho-normal direction. By knowing the speed of the platform, target signal return is placed in a specific angle "bin" that changes over time. Signals are integrated over time and thus the radar "beam" is synthetically reduced to a much smaller aperture – or more accurately (and based on the ability to distinguish smaller Doppler shifts) the system can have hundreds of very "tight" beams concurrently. This technique dramatically improves angular resolution; however, it is far more difficult to take advantage of this technique for range resolution. (See <a href="/wiki/Pulse-doppler_radar" class="mw-redirect" title="Pulse-doppler radar">pulse-doppler radar</a>). </p> <div class="mw-heading mw-heading3"><h3 id="Chirped_(pulse-compressed)_radars"><span id="Chirped_.28pulse-compressed.29_radars"></span>Chirped (pulse-compressed) radars</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=45" title="Edit section: Chirped (pulse-compressed) radars"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Chirp" title="Chirp">Chirp</a></div> <p>A common technique for many radar systems (usually also found in SAR systems) is to "<a href="/wiki/Chirp" title="Chirp">chirp</a>" the signal. In a "chirped" radar, the pulse is allowed to be much longer. A longer pulse allows more energy to be emitted, and hence received, but usually hinders range resolution. But in a chirped radar, this longer pulse also has a frequency shift during the pulse (hence the chirp or frequency shift). When the "chirped" signal is returned, it must be correlated with the sent pulse. Classically, in analog systems, it is passed to a dispersive delay line (often a <a href="/wiki/Surface_acoustic_wave" title="Surface acoustic wave">surface acoustic wave</a> device) that has the property of varying velocity of propagation based on frequency. This technique "compresses" the pulse in time – thus having the effect of a much shorter pulse (improved range resolution) while having the benefit of longer pulse length (much more signal returned). Newer systems use digital pulse correlation to find the pulse return in the signal. </p> <div class="mw-heading mw-heading2"><h2 id="Typical_operation">Typical operation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=46" title="Edit section: Typical operation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:AirSAR-instrument-on-aircraft.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/AirSAR-instrument-on-aircraft.jpg/220px-AirSAR-instrument-on-aircraft.jpg" decoding="async" width="220" height="333" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/AirSAR-instrument-on-aircraft.jpg/330px-AirSAR-instrument-on-aircraft.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/AirSAR-instrument-on-aircraft.jpg/440px-AirSAR-instrument-on-aircraft.jpg 2x" data-file-width="1670" data-file-height="2528" /></a><figcaption><a href="/wiki/NASA" title="NASA">NASA</a>'s AirSAR instrument is attached to the side of a <a href="/wiki/DC-8" class="mw-redirect" title="DC-8">DC-8</a></figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Data_collection">Data collection</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=47" title="Edit section: Data collection"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In a typical SAR application, a single radar antenna is attached to an aircraft or spacecraft such that a substantial component of the antenna's radiated beam has a <a href="/wiki/Wave_propagation" class="mw-redirect" title="Wave propagation">wave-propagation</a> direction perpendicular to the flight-path direction. The beam is allowed to be broad in the vertical direction so it will illuminate the terrain from nearly beneath the aircraft out toward the horizon. </p> <div class="mw-heading mw-heading4"><h4 id="Image_resolution_and_bandwidth">Image resolution and bandwidth</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=48" title="Edit section: Image resolution and bandwidth"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Resolution in the range dimension of the image is accomplished by creating pulses which define very short time intervals, either by emitting short pulses consisting of a carrier frequency and the necessary sidebands, all within a certain bandwidth, or by using longer "<a href="/wiki/Chirp_pulse" class="mw-redirect" title="Chirp pulse">chirp pulses</a>" in which frequency varies (often linearly) with time within that bandwidth. The differing times at which echoes return allow points at different distances to be distinguished. </p><p>Image resolution of SAR in its range coordinate (expressed in image pixels per distance unit) is mainly proportional to the radio bandwidth of whatever type of pulse is used. In the cross-range coordinate, the similar resolution is mainly proportional to the bandwidth of the Doppler shift of the signal returns within the beamwidth. Since Doppler frequency depends on the angle of the scattering point's direction from the broadside direction, the Doppler bandwidth available within the beamwidth is the same at all ranges. Hence the theoretical spatial resolution limits in both image dimensions remain constant with variation of range. However, in practice, both the errors that accumulate with data-collection time and the particular techniques used in post-processing further limit cross-range resolution at long ranges. </p> <div class="mw-heading mw-heading4"><h4 id="Image_resolution_and_beamwidth">Image resolution and beamwidth</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=49" title="Edit section: Image resolution and beamwidth"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Antena_SAR_SAOCOM1A_en_sala_limpia_LIE_CETT_CONAE_Nov_2017.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Antena_SAR_SAOCOM1A_en_sala_limpia_LIE_CETT_CONAE_Nov_2017.jpg/260px-Antena_SAR_SAOCOM1A_en_sala_limpia_LIE_CETT_CONAE_Nov_2017.jpg" decoding="async" width="260" height="173" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Antena_SAR_SAOCOM1A_en_sala_limpia_LIE_CETT_CONAE_Nov_2017.jpg/390px-Antena_SAR_SAOCOM1A_en_sala_limpia_LIE_CETT_CONAE_Nov_2017.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Antena_SAR_SAOCOM1A_en_sala_limpia_LIE_CETT_CONAE_Nov_2017.jpg/520px-Antena_SAR_SAOCOM1A_en_sala_limpia_LIE_CETT_CONAE_Nov_2017.jpg 2x" data-file-width="5337" data-file-height="3558" /></a><figcaption>SAR antenna of the <a href="/wiki/SAOCOM" title="SAOCOM">SAOCOM</a> satellites.</figcaption></figure> <p>The total signal is that from a beamwidth-sized patch of the ground. To produce a beam that is narrow in the cross-range direction<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (October 2012)">clarification needed</span></a></i>]</sup>, <a href="/wiki/Diffraction" title="Diffraction">diffraction</a> effects require that the antenna be wide in that dimension. Therefore, the distinguishing, from each other, of co-range points simply by strengths of returns that persist for as long as they are within the beam width is difficult with aircraft-carryable antennas, because their beams can have linear widths only about two orders of magnitude (hundreds of times) smaller than the range. (Spacecraft-carryable ones can do 10 or more times better.) However, if both the amplitude and the phase of returns are recorded, then the portion of that multi-target return that was scattered radially from any smaller scene element can be extracted by phase-vector correlation of the total return with the form of the return expected from each such element. </p><p>The process can be thought of as combining the series of spatially distributed observations as if all had been made simultaneously with an antenna as long as the beamwidth and focused on that particular point. The "synthetic aperture" simulated at maximum system range by this process not only is longer than the real antenna, but, in practical applications, it is much longer than the radar aircraft, and tremendously longer than the radar spacecraft. </p><p>Although some references to SARs have characterized them as "radar telescopes", their actual optical analogy is the microscope, the detail in their images being smaller than the length of the synthetic aperture. In radar-engineering terms, while the target area is in the "<a href="/wiki/Far_field" class="mw-redirect" title="Far field">far field</a>" of the illuminating antenna, it is in the "near field" of the simulated one. Careful design and operation can accomplish resolution of items smaller than a millionth of the range, for example, 30 cm at 300 km, or about one foot at nearly 200 miles (320 km). </p> <div class="mw-heading mw-heading4"><h4 id="Pulse_transmission_and_reception">Pulse transmission and reception</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=50" title="Edit section: Pulse transmission and reception"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The conversion of return delay time to geometric range can be very accurate because of the natural constancy of the speed and direction of propagation of electromagnetic waves. However, for an aircraft flying through the never-uniform and never-quiescent atmosphere, the relating of pulse transmission and reception times to successive geometric positions of the antenna must be accompanied by constant adjusting of the return phases to account for sensed irregularities in the flight path. SAR's in spacecraft avoid that atmosphere problem, but still must make corrections for known antenna movements due to rotations of the spacecraft, even those that are reactions to movements of onboard machinery. Locating a SAR in a crewed space vehicle may require that the humans carefully remain motionless relative to the vehicle during data collection periods. </p><p>Returns from scatterers within the range extent of any image are spread over a matching time interval. The inter-pulse period must be long enough to allow farthest-range returns from any pulse to finish arriving before the nearest-range ones from the next pulse begin to appear, so that those do not overlap each other in time. On the other hand, the interpulse rate must be fast enough to provide sufficient samples for the desired across-range (or across-beam) resolution. When the radar is to be carried by a high-speed vehicle and is to image a large area at fine resolution, those conditions may clash, leading to what has been called SAR's ambiguity problem. The same considerations apply to "conventional" radars also, but this problem occurs significantly only when resolution is so fine as to be available only through SAR processes. Since the basis of the problem is the information-carrying capacity of the single signal-input channel provided by one antenna, the only solution is to use additional channels fed by additional antennas. The system then becomes a hybrid of a SAR and a phased array, sometimes being called a Vernier array. </p> <div class="mw-heading mw-heading3"><h3 id="Data_processing">Data processing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=51" title="Edit section: Data processing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Combining the series of observations requires significant computational resources, usually using <a href="/wiki/Fourier_transform" title="Fourier transform">Fourier transform</a> techniques. The high digital computing speed now available allows such processing to be done in near-real time on board a SAR aircraft. (There is necessarily a minimum time delay until all parts of the signal have been received.) The result is a map of radar reflectivity, including both amplitude and phase. </p> <div class="mw-heading mw-heading4"><h4 id="Amplitude_data">Amplitude data</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=52" title="Edit section: Amplitude data"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The amplitude information, when shown in a map-like display, gives information about ground cover in much the same way that a black-and-white photo does. Variations in processing may also be done in either vehicle-borne stations or ground stations for various purposes, so as to accentuate certain image features for detailed target-area analysis. </p> <div class="mw-heading mw-heading4"><h4 id="Phase_data">Phase data</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=53" title="Edit section: Phase data"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Although the phase information in an image is generally not made available to a human observer of an image display device, it can be preserved numerically, and sometimes allows certain additional features of targets to be recognized. </p> <div class="mw-heading mw-heading4"><h4 id="Coherence_speckle">Coherence speckle</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=54" title="Edit section: Coherence speckle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Unfortunately, the phase differences between adjacent image picture elements ("pixels") also produce random interference effects called "coherence <a href="/wiki/Speckle_noise" class="mw-redirect" title="Speckle noise">speckle</a>", which is a sort of graininess with dimensions on the order of the resolution, causing the concept of resolution to take on a subtly different meaning. This effect is the same as is apparent both visually and photographically in laser-illuminated optical scenes. The scale of that random speckle structure is governed by the size of the synthetic aperture in wavelengths, and cannot be finer than the system's resolution. Speckle structure can be subdued at the expense of resolution. </p> <div class="mw-heading mw-heading4"><h4 id="Optical_holography">Optical holography</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=55" title="Edit section: Optical holography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Before rapid digital computers were available, the data processing was done using an optical <a href="/wiki/Holography" title="Holography">holography</a> technique. The analog radar data were recorded as a holographic interference pattern on photographic film at a scale permitting the film to preserve the signal bandwidths (for example, 1:1,000,000 for a radar using a 0.6-meter wavelength). Then light using, for example, 0.6-micrometer waves (as from a <a href="/wiki/Helium%E2%80%93neon_laser" title="Helium–neon laser">helium–neon laser</a>) passing through the hologram could project a terrain image at a scale recordable on another film at reasonable processor focal distances of around a meter. This worked because both SAR and phased arrays are fundamentally similar to optical holography, but using microwaves instead of light waves. The "optical data-processors" developed for this radar purpose<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Leith_49-0" class="reference"><a href="#cite_note-Leith-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> were the first effective analog <a href="/wiki/Optical_computer" class="mw-redirect" title="Optical computer">optical computer</a> systems, and were, in fact, devised before the holographic technique was fully adapted to optical imaging. Because of the different sources of range and across-range signal structures in the radar signals, optical data-processors for SAR included not only both spherical and cylindrical lenses, but sometimes conical ones. </p> <div class="mw-heading mw-heading2"><h2 id="Image_appearance">Image appearance</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=56" title="Edit section: Image appearance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The following considerations apply also to real-aperture terrain-imaging radars, but are more consequential when resolution in range is matched to a cross-beam resolution that is available only from a SAR. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:25cm_resolution_SAR_image_of_downtown_Cleveland,_Ohio.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/25cm_resolution_SAR_image_of_downtown_Cleveland%2C_Ohio.jpg/220px-25cm_resolution_SAR_image_of_downtown_Cleveland%2C_Ohio.jpg" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/25cm_resolution_SAR_image_of_downtown_Cleveland%2C_Ohio.jpg/330px-25cm_resolution_SAR_image_of_downtown_Cleveland%2C_Ohio.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/45/25cm_resolution_SAR_image_of_downtown_Cleveland%2C_Ohio.jpg/440px-25cm_resolution_SAR_image_of_downtown_Cleveland%2C_Ohio.jpg 2x" data-file-width="18351" data-file-height="18350" /></a><figcaption>25cm resolution SAR image of downtown Cleveland, Ohio by <a href="/w/index.php?title=Umbra_Space&action=edit&redlink=1" class="new" title="Umbra Space (page does not exist)">Umbra</a></figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Range,_cross-range,_and_angles"><span id="Range.2C_cross-range.2C_and_angles"></span>Range, cross-range, and angles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=57" title="Edit section: Range, cross-range, and angles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The two dimensions of a radar image are range and cross-range. Radar images of limited patches of terrain can resemble oblique photographs, but not ones taken from the location of the radar. This is because the range coordinate in a radar image is perpendicular to the vertical-angle coordinate of an oblique photo. The apparent <a href="/wiki/Entrance_pupil" title="Entrance pupil">entrance-pupil</a> position (or <a href="/wiki/Camera_center" class="mw-redirect" title="Camera center">camera center</a>) for viewing such an image is therefore not as if at the radar, but as if at a point from which the viewer's line of sight is perpendicular to the slant-range direction connecting radar and target, with slant-range increasing from top to bottom of the image. </p><p>Because slant ranges to level terrain vary in vertical angle, each elevation of such terrain appears as a curved surface, specifically a <a href="/wiki/Hyperbolic_cosine" class="mw-redirect" title="Hyperbolic cosine">hyperbolic cosine</a> one. Verticals at various ranges are perpendiculars to those curves. The viewer's apparent looking directions are parallel to the curve's "hypcos" axis. Items directly beneath the radar appear as if optically viewed horizontally (i.e., from the side) and those at far ranges as if optically viewed from directly above. These curvatures are not evident unless large extents of near-range terrain, including steep slant ranges, are being viewed. </p> <div class="mw-heading mw-heading3"><h3 id="Visibility">Visibility</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=58" title="Edit section: Visibility"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When viewed as specified above, fine-resolution radar images of small areas can appear most nearly like familiar optical ones, for two reasons. The first reason is easily understood by imagining a flagpole in the scene. The slant-range to its upper end is less than that to its base. Therefore, the pole can appear correctly top-end up only when viewed in the above orientation. Secondly, the radar illumination then being downward, shadows are seen in their most-familiar "overhead-lighting" direction. </p><p>The image of the pole's top will overlay that of some terrain point which is on the same slant range arc but at a shorter horizontal range ("ground-range"). Images of scene surfaces which faced both the illumination and the apparent eyepoint will have geometries that resemble those of an optical scene viewed from that eyepoint. However, slopes facing the radar will be foreshortened and ones facing away from it will be lengthened from their horizontal (map) dimensions. The former will therefore be brightened and the latter dimmed. </p><p>Returns from slopes steeper than perpendicular to slant range will be overlaid on those of lower-elevation terrain at a nearer ground-range, both being visible but intermingled. This is especially the case for vertical surfaces like the walls of buildings. Another viewing inconvenience that arises when a surface is steeper than perpendicular to the slant range is that it is then illuminated on one face but "viewed" from the reverse face. Then one "sees", for example, the radar-facing wall of a building as if from the inside, while the building's interior and the rear wall (that nearest to, hence expected to be optically visible to, the viewer) have vanished, since they lack illumination, being in the shadow of the front wall and the roof. Some return from the roof may overlay that from the front wall, and both of those may overlay return from terrain in front of the building. The visible building shadow will include those of all illuminated items. Long shadows may exhibit blurred edges due to the illuminating antenna's movement during the "time exposure" needed to create the image. </p> <div class="mw-heading mw-heading3"><h3 id="Mirroring_artefacts_and_shadows">Mirroring artefacts and shadows</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=59" title="Edit section: Mirroring artefacts and shadows"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Surfaces that we usually consider rough will, if that roughness consists of relief less than the radar wavelength, behave as smooth mirrors, showing, beyond such a surface, additional images of items in front of it. Those mirror images will appear within the shadow of the mirroring surface, sometimes filling the entire shadow, thus preventing recognition of the shadow. </p><p>The direction of overlay of any scene point is not directly toward the radar, but toward that point of the SAR's current path direction that is nearest to the target point. If the SAR is "squinting" forward or aft away from the exactly broadside direction, then the illumination direction, and hence the shadow direction, will not be opposite to the overlay direction, but slanted to right or left from it. An image will appear with the correct projection geometry when viewed so that the overlay direction is vertical, the SAR's flight-path is above the image, and range increases somewhat downward. </p> <div class="mw-heading mw-heading3"><h3 id="Objects_in_motion">Objects in motion</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=60" title="Edit section: Objects in motion"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Objects in motion within a SAR scene alter the Doppler frequencies of the returns. Such objects therefore appear in the image at locations offset in the across-range direction by amounts proportional to the range-direction component of their velocity. Road vehicles may be depicted off the roadway and therefore not recognized as road traffic items. Trains appearing away from their tracks are more easily properly recognized by their length parallel to known trackage as well as by the absence of an equal length of railbed signature and of some adjacent terrain, both having been shadowed by the train. While images of moving vessels can be offset from the line of the earlier parts of their wakes, the more recent parts of the wake, which still partake of some of the vessel's motion, appear as curves connecting the vessel image to the relatively quiescent far-aft wake. In such identifiable cases, speed and direction of the moving items can be determined from the amounts of their offsets. The along-track component of a target's motion causes some defocus. Random motions such as that of wind-driven tree foliage, vehicles driven over rough terrain, or humans or other animals walking or running generally render those items not focusable, resulting in blurring or even effective invisibility. </p><p>These considerations, along with the speckle structure due to coherence, take some getting used to in order to correctly interpret SAR images. To assist in that, large collections of significant target signatures have been accumulated by performing many test flights over known terrains and cultural objects. </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=61" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="excerpt-block"><style data-mw-deduplicate="TemplateStyles:r1066933788">.mw-parser-output .excerpt-hat .mw-editsection-like{font-style:normal}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable dablink excerpt-hat selfref">This section is an excerpt from <a href="/wiki/History_of_synthetic-aperture_radar" title="History of synthetic-aperture radar">History of synthetic-aperture radar</a>.<span class="mw-editsection-like plainlinks"><span class="mw-editsection-bracket">[</span><a class="external text" href="https://en.wikipedia.org/w/index.php?title=History_of_synthetic-aperture_radar&action=edit">edit</a><span class="mw-editsection-bracket">]</span></span></div><div class="excerpt"> The <a href="/wiki/History_of_synthetic-aperture_radar" title="History of synthetic-aperture radar">history of synthetic-aperture radar</a> begins in 1951, with the invention of the technology by mathematician <a href="/wiki/Carl_A._Wiley" title="Carl A. Wiley">Carl A. Wiley</a>, and its development in the following decade. Initially developed for military use, the technology has since been applied in the field of <a href="/wiki/Planetary_science" title="Planetary science">planetary science</a>.</div></div> <div class="mw-heading mw-heading2"><h2 id="Relationship_to_phased_arrays">Relationship to phased arrays</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=62" title="Edit section: Relationship to phased arrays"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Phased_array" title="Phased array">Phased array</a></div> <p>A technique closely related to SAR uses an array (referred to as a "<a href="/wiki/Phased_array" title="Phased array">phased array</a>") of real antenna elements spatially distributed over either one or two dimensions perpendicular to the radar-range dimension. These physical arrays are truly synthetic ones, indeed being created by synthesis of a collection of subsidiary physical antennas. Their operation need not involve motion relative to targets. All elements of these arrays receive simultaneously in real time, and the signals passing through them can be individually subjected to controlled shifts of the phases of those signals. One result can be to respond most strongly to radiation received from a specific small scene area, focusing on that area to determine its contribution to the total signal received. The coherently detected set of signals received over the entire array aperture can be replicated in several data-processing channels and processed differently in each. The set of responses thus traced to different small scene areas can be displayed together as an image of the scene. </p><p>In comparison, a SAR's (commonly) single physical antenna element gathers signals at different positions at different times. When the radar is carried by an aircraft or an orbiting vehicle, those positions are functions of a single variable, distance along the vehicle's path, which is a single mathematical dimension (not necessarily the same as a linear geometric dimension). The signals are stored, thus becoming functions, no longer of time, but of recording locations along that dimension. When the stored signals are read out later and combined with specific phase shifts, the result is the same as if the recorded data had been gathered by an equally long and shaped phased array. What is thus synthesized is a set of signals equivalent to what could have been received simultaneously by such an actual large-aperture (in one dimension) phased array. The SAR simulates (rather than synthesizes) that long one-dimensional phased array. Although the term in the title of this article has thus been incorrectly derived, it is now firmly established by half a century of usage. </p><p>While operation of a phased array is readily understood as a completely geometric technique, the fact that a synthetic aperture system gathers its data as it (or its target) moves at some speed means that phases which varied with the distance traveled originally varied with time, hence constituted temporal frequencies. Temporal frequencies being the variables commonly used by radar engineers, their analyses of SAR systems are usually (and very productively) couched in such terms. In particular, the variation of phase during flight over the length of the synthetic aperture is seen as a sequence of <a href="/wiki/Doppler_effect" title="Doppler effect">Doppler</a> shifts of the received frequency from that of the transmitted frequency. Once the received data have been recorded and thus have become timeless, the SAR data-processing situation is also understandable as a special type of phased array, treatable as a completely geometric process. </p><p>The core of both the SAR and the phased array techniques is that the distances that radar waves travel to and back from each scene element consist of some integer number of wavelengths plus some fraction of a "final" wavelength. Those fractions cause differences between the phases of the re-radiation received at various SAR or array positions. Coherent detection is needed to capture the signal phase information in addition to the signal amplitude information. That type of detection requires finding the differences between the phases of the received signals and the simultaneous phase of a well-preserved sample of the transmitted illumination. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=63" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 20em;"> <ul><li><a href="/wiki/Alaska_Satellite_Facility" title="Alaska Satellite Facility">Alaska Satellite Facility</a></li> <li><a href="/wiki/Aperture_synthesis" title="Aperture synthesis">Aperture synthesis</a></li> <li><a href="/wiki/Beamforming" title="Beamforming">Beamforming</a></li> <li><a href="/wiki/Earth_observation_satellite" title="Earth observation satellite">Earth observation satellite</a></li> <li><a href="/wiki/High_Resolution_Wide_Swath_SAR_imaging" title="High Resolution Wide Swath SAR imaging">High Resolution Wide Swath SAR imaging</a></li> <li><a href="/wiki/Interferometric_synthetic_aperture_radar" class="mw-redirect" title="Interferometric synthetic aperture radar">Interferometric synthetic aperture radar</a> (InSAR)</li> <li><a href="/wiki/Inverse_synthetic_aperture_radar" class="mw-redirect" title="Inverse synthetic aperture radar">Inverse synthetic aperture radar</a> (ISAR)</li> <li><a href="/wiki/Magellan_probe" class="mw-redirect" title="Magellan probe">Magellan</a> space probe</li> <li><a href="/wiki/Pulse-Doppler_radar" title="Pulse-Doppler radar">Pulse-Doppler radar</a></li> <li><a href="/wiki/Radar_MASINT" title="Radar MASINT">Radar MASINT</a></li> <li><a href="/wiki/Remote_sensing" title="Remote sensing">Remote sensing</a></li> <li><a href="/wiki/SAR_Lupe" class="mw-redirect" title="SAR Lupe">SAR Lupe</a></li> <li><a href="/wiki/Seasat" title="Seasat">Seasat</a></li> <li><a href="/wiki/Sentinel-1" title="Sentinel-1">Sentinel-1</a></li> <li><a href="/wiki/Speckle_noise" class="mw-redirect" title="Speckle noise">Speckle noise</a></li> <li><a href="/wiki/Synthetic_aperture_sonar" class="mw-redirect" title="Synthetic aperture sonar">Synthetic aperture sonar</a></li> <li><a href="/wiki/Synthetic_Aperture_Ultrasound" class="mw-redirect" title="Synthetic Aperture Ultrasound">Synthetic Aperture Ultrasound</a></li> <li><a href="/wiki/Synthetic_array_heterodyne_detection" class="mw-redirect" title="Synthetic array heterodyne detection">Synthetic array heterodyne detection</a> (SAHD)</li> <li><a href="/wiki/Synthetically_thinned_aperture_radar" title="Synthetically thinned aperture radar">Synthetically thinned aperture radar</a></li> <li><a href="/wiki/TerraSAR-X" title="TerraSAR-X">TerraSAR-X</a></li> <li><a href="/wiki/Terrestrial_SAR_Interferometry" class="mw-redirect" title="Terrestrial SAR Interferometry">Terrestrial SAR Interferometry</a> (TInSAR)</li> <li><a href="/wiki/Very_long_baseline_interferometry" class="mw-redirect" title="Very long baseline interferometry">Very long baseline interferometry</a> (VLBI)</li> <li><a href="/wiki/Wave_radar" title="Wave radar">Wave radar</a></li></ul></div> <style data-mw-deduplicate="TemplateStyles:r1130092004">.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;justify-content:center;align-items:baseline}.mw-parser-output .portal-bar-bordered{padding:0 2em;background-color:#fdfdfd;border:1px solid #a2a9b1;clear:both;margin:1em auto 0}.mw-parser-output .portal-bar-related{font-size:100%;justify-content:flex-start}.mw-parser-output .portal-bar-unbordered{padding:0 1.7em;margin-left:0}.mw-parser-output .portal-bar-header{margin:0 1em 0 0.5em;flex:0 0 auto;min-height:24px}.mw-parser-output .portal-bar-content{display:flex;flex-flow:row wrap;flex:0 1 auto;padding:0.15em 0;column-gap:1em;align-items:baseline;margin:0;list-style:none}.mw-parser-output .portal-bar-content-related{margin:0;list-style:none}.mw-parser-output .portal-bar-item{display:inline-block;margin:0.15em 0.2em;min-height:24px;line-height:24px}@media screen and (max-width:768px){.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;flex-flow:column wrap;align-items:baseline}.mw-parser-output .portal-bar-header{text-align:center;flex:0;padding-left:0.5em;margin:0 auto}.mw-parser-output .portal-bar-related{font-size:100%;align-items:flex-start}.mw-parser-output .portal-bar-content{display:flex;flex-flow:row wrap;align-items:center;flex:0;column-gap:1em;border-top:1px solid #a2a9b1;margin:0 auto;list-style:none}.mw-parser-output .portal-bar-content-related{border-top:none;margin:0;list-style:none}}.mw-parser-output .navbox+link+.portal-bar,.mw-parser-output .navbox+style+.portal-bar,.mw-parser-output .navbox+link+.portal-bar-bordered,.mw-parser-output .navbox+style+.portal-bar-bordered,.mw-parser-output .sister-bar+link+.portal-bar,.mw-parser-output .sister-bar+style+.portal-bar,.mw-parser-output .portal-bar+.navbox-styles+.navbox,.mw-parser-output .portal-bar+.navbox-styles+.sister-bar{margin-top:-1px}</style><div class="portal-bar noprint metadata noviewer portal-bar-bordered" role="navigation" aria-label="Portals"><span class="portal-bar-header"><a href="/wiki/Wikipedia:Contents/Portals" title="Wikipedia:Contents/Portals">Portals</a>:</span><ul class="portal-bar-content"><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Aviacionavion.png/19px-Aviacionavion.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Aviacionavion.png/29px-Aviacionavion.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/68/Aviacionavion.png/38px-Aviacionavion.png 2x" data-file-width="1600" data-file-height="1600" /></span></span> </span><a href="/wiki/Portal:Aviation" title="Portal:Aviation">Aviation</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/RocketSunIcon.svg/19px-RocketSunIcon.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/RocketSunIcon.svg/29px-RocketSunIcon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/RocketSunIcon.svg/38px-RocketSunIcon.svg.png 2x" data-file-width="128" data-file-height="128" /></span></span> </span><a href="/wiki/Portal:Spaceflight" title="Portal:Spaceflight">Spaceflight</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/17px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="17" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/26px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/34px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span> </span><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics</a></li></ul></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=64" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Kirscht, Martin, and Carsten Rinke. "3D Reconstruction of Buildings and Vegetation from Synthetic Aperture Radar (SAR) Images." MVA. 1998.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">"Introduction to Airborne RADAR", G. W. Stimson, Chapter 1 (13 pp).</span> </li> <li id="cite_note-:2-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-:2_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:2_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:2_3-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:2_3-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text">Tomographic SAR. Gianfranco Fornaro. National Research Council (CNR). Institute for Electromagnetic Sensing of the Environment (IREA) Via Diocleziano, 328, I-80124 Napoli, ITALY</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Oliver, C. and Quegan, S. Understanding Synthetic Aperture Radar Images. Artech House, Boston, 1998.</span> </li> <li id="cite_note-:3-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-:3_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:3_5-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:3_5-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:3_5-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:3_5-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-:3_5-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-:3_5-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-:3_5-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-:3_5-8"><sup><i><b>i</b></i></sup></a> <a href="#cite_ref-:3_5-9"><sup><i><b>j</b></i></sup></a> <a href="#cite_ref-:3_5-10"><sup><i><b>k</b></i></sup></a> <a href="#cite_ref-:3_5-11"><sup><i><b>l</b></i></sup></a></span> <span class="reference-text">Synthetic Aperture Radar Imaging Using Spectral Estimation Techniques. Shivakumar Ramakrishnan, Vincent Demarcus, Jerome Le Ny, Neal Patwari, Joel Gussy. University of Michigan.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://sciengsustainability.blogspot.com/2017/02/bridge-monitoring-with-satellite-data.html">"Science Engineering & Sustainability: Bridge monitoring with satellite data SAR"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Science+Engineering+%26+Sustainability%3A+Bridge+monitoring+with+satellite+data+SAR&rft_id=https%3A%2F%2Fsciengsustainability.blogspot.com%2F2017%2F02%2Fbridge-monitoring-with-satellite-data.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWuZhangXiongZhang2023" class="citation journal cs1">Wu, Xuan; Zhang, Zhijie; Xiong, Shengqing; Zhang, Wanchang; Tang, Jiakui; Li, Zhenghao; An, Bangsheng; Li, Rui (12 April 2023). <a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Frs15082046">"A Near-Real-Time Flood Detection Method Based on Deep Learning and SAR Images"</a>. <i>Remote Sensing</i>. <b>15</b> (8): 2046. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2023RemS...15.2046W">2023RemS...15.2046W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Frs15082046">10.3390/rs15082046</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2072-4292">2072-4292</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Remote+Sensing&rft.atitle=A+Near-Real-Time+Flood+Detection+Method+Based+on+Deep+Learning+and+SAR+Images&rft.volume=15&rft.issue=8&rft.pages=2046&rft.date=2023-04-12&rft.issn=2072-4292&rft_id=info%3Adoi%2F10.3390%2Frs15082046&rft_id=info%3Abibcode%2F2023RemS...15.2046W&rft.aulast=Wu&rft.aufirst=Xuan&rft.au=Zhang%2C+Zhijie&rft.au=Xiong%2C+Shengqing&rft.au=Zhang%2C+Wanchang&rft.au=Tang%2C+Jiakui&rft.au=Li%2C+Zhenghao&rft.au=An%2C+Bangsheng&rft.au=Li%2C+Rui&rft_id=https%3A%2F%2Fdoi.org%2F10.3390%252Frs15082046&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGargFeinsteinTimnatBatchu2023" class="citation journal cs1">Garg, Shubhika; Feinstein, Ben; Timnat, Shahar; Batchu, Vishal; Dror, Gideon; Rosenthal, Adi Gerzi; Gulshan, Varun (7 November 2023). <a rel="nofollow" class="external text" href="https://doi.org/10.1017%2Feds.2023.34">"Cross-modal distillation for flood extent mapping"</a>. <i>Environmental Data Science</i>. <b>2</b>: e37. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2302.08180">2302.08180</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2023EnvDS...2E..37G">2023EnvDS...2E..37G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1017%2Feds.2023.34">10.1017/eds.2023.34</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2634-4602">2634-4602</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Environmental+Data+Science&rft.atitle=Cross-modal+distillation+for+flood+extent+mapping&rft.volume=2&rft.pages=e37&rft.date=2023-11-07&rft_id=info%3Aarxiv%2F2302.08180&rft.issn=2634-4602&rft_id=info%3Adoi%2F10.1017%2Feds.2023.34&rft_id=info%3Abibcode%2F2023EnvDS...2E..37G&rft.aulast=Garg&rft.aufirst=Shubhika&rft.au=Feinstein%2C+Ben&rft.au=Timnat%2C+Shahar&rft.au=Batchu%2C+Vishal&rft.au=Dror%2C+Gideon&rft.au=Rosenthal%2C+Adi+Gerzi&rft.au=Gulshan%2C+Varun&rft_id=https%3A%2F%2Fdoi.org%2F10.1017%252Feds.2023.34&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFA._Maity2016" class="citation arxiv cs1">A. Maity (2016). "Supervised Classification of RADARSAT-2 Polarimetric Data for Different Land Features". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1608.00501">1608.00501</a></span> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/cs.CV">cs.CV</a>].</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Supervised+Classification+of+RADARSAT-2+Polarimetric+Data+for+Different+Land+Features&rft.date=2016&rft_id=info%3Aarxiv%2F1608.00501&rft.au=A.+Maity&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-:4-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-:4_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:4_10-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:4_10-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMoreiraPrats-IraolaYounisKrieger2013" class="citation journal cs1">Moreira, Alberto; Prats-Iraola, Pau; Younis, Marwan; Krieger, Gerhard; Hajnsek, Irena; P. Papathanassiou, Konstantinos (2013). <a rel="nofollow" class="external text" href="https://elib.dlr.de/82313/1/SAR-Tutorial-March-2013.pdf">"A tutorial on synthetic aperture radar"</a> <span class="cs1-format">(PDF)</span>. <i>IEEE Geoscience and Remote Sensing Magazine</i>. <b>1</b> (1): <span class="nowrap">6–</span>43. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013IGRSM...1a...6M">2013IGRSM...1a...6M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FMGRS.2013.2248301">10.1109/MGRS.2013.2248301</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:7487291">7487291</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Geoscience+and+Remote+Sensing+Magazine&rft.atitle=A+tutorial+on+synthetic+aperture+radar&rft.volume=1&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E6-%3C%2Fspan%3E43&rft.date=2013&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A7487291%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FMGRS.2013.2248301&rft_id=info%3Abibcode%2F2013IGRSM...1a...6M&rft.aulast=Moreira&rft.aufirst=Alberto&rft.au=Prats-Iraola%2C+Pau&rft.au=Younis%2C+Marwan&rft.au=Krieger%2C+Gerhard&rft.au=Hajnsek%2C+Irena&rft.au=P.+Papathanassiou%2C+Konstantinos&rft_id=https%3A%2F%2Felib.dlr.de%2F82313%2F1%2FSAR-Tutorial-March-2013.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.lockheedmartin.com/en-us/news/features/history/sar.html">"Lockheed Martin: Synthetic Aperture Radar: "Round the Clock Reconnaissance"<span class="cs1-kern-right"></span>"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Lockheed+Martin%3A+Synthetic+Aperture+Radar%3A+%22Round+the+Clock+Reconnaissance%22&rft_id=https%3A%2F%2Fwww.lockheedmartin.com%2Fen-us%2Fnews%2Ffeatures%2Fhistory%2Fsar.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFColburn,_Robert2009" class="citation web cs1">Colburn, Robert (10 March 2009). <a rel="nofollow" class="external text" href="https://insight.ieeeusa.org/articles/your-engineering-heritage-synthetic-aperture-radar/">"Your Engineering Heritage: Synthetic Aperture Radar"</a>. <i>IEEE USA InSight</i>. IEEE.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=IEEE+USA+InSight&rft.atitle=Your+Engineering+Heritage%3A+Synthetic+Aperture+Radar&rft.date=2009-03-10&rft.au=Colburn%2C+Robert&rft_id=https%3A%2F%2Finsight.ieeeusa.org%2Farticles%2Fyour-engineering-heritage-synthetic-aperture-radar%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFR._BamlerP._Hartl1998" class="citation journal cs1">R. Bamler; P. Hartl (August 1998). "Synthetic aperture radar interferometry". <i>Inverse Problems</i>. <b>14</b> (4): <span class="nowrap">R1 –</span> <span class="nowrap">R54</span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1998InvPr..14R...1B">1998InvPr..14R...1B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0266-5611%2F14%2F4%2F001">10.1088/0266-5611/14/4/001</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:250827866">250827866</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Inverse+Problems&rft.atitle=Synthetic+aperture+radar+interferometry&rft.volume=14&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3ER1+-%3C%2Fspan%3E+%3Cspan+class%3D%22nowrap%22%3ER54%3C%2Fspan%3E&rft.date=1998-08&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A250827866%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F0266-5611%2F14%2F4%2F001&rft_id=info%3Abibcode%2F1998InvPr..14R...1B&rft.au=R.+Bamler&rft.au=P.+Hartl&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-:15-14"><span class="mw-cite-backlink">^ <a href="#cite_ref-:15_14-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:15_14-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">G. Fornaro, G. Franceschetti, "SAR Interferometry", Chapter IV in G. Franceschetti, R. Lanari, Synthetic Aperture Radar Processing, CRC-PRESS, Boca Raton, Marzo 1999.</span> </li> <li id="cite_note-:9-15"><span class="mw-cite-backlink">^ <a href="#cite_ref-:9_15-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:9_15-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFornaroPascazio2014" class="citation book cs1">Fornaro, Gianfranco; Pascazio, Vito (2014). "SAR Interferometry and Tomography: Theory and Applications". <i>Academic Press Library in Signal Processing: Volume 2 – Communications and Radar Signal Processing</i>. Vol. 2. pp. <span class="nowrap">1043–</span>1117. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FB978-0-12-396500-4.00020-X">10.1016/B978-0-12-396500-4.00020-X</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780123965004" title="Special:BookSources/9780123965004"><bdi>9780123965004</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=SAR+Interferometry+and+Tomography%3A+Theory+and+Applications&rft.btitle=Academic+Press+Library+in+Signal+Processing%3A+Volume+2+%E2%80%93+Communications+and+Radar+Signal+Processing&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1043-%3C%2Fspan%3E1117&rft.date=2014&rft_id=info%3Adoi%2F10.1016%2FB978-0-12-396500-4.00020-X&rft.isbn=9780123965004&rft.aulast=Fornaro&rft.aufirst=Gianfranco&rft.au=Pascazio%2C+Vito&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFReigberLombardiniVivianiNannini2015" class="citation book cs1">Reigber, Andreas; Lombardini, Fabrizio; Viviani, Federico; Nannini, Matteo; Martinez Del Hoyo, Antonio (2015). "Three-dimensional and higher-order imaging with tomographic SAR: Techniques, applications, issues". <i>2015 IEEE International Geoscience and Remote Sensing Symposium (IGARSS)</i>. pp. <span class="nowrap">2915–</span>2918. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FIGARSS.2015.7326425">10.1109/IGARSS.2015.7326425</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/11568%2F843638">11568/843638</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4799-7929-5" title="Special:BookSources/978-1-4799-7929-5"><bdi>978-1-4799-7929-5</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:9589219">9589219</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Three-dimensional+and+higher-order+imaging+with+tomographic+SAR%3A+Techniques%2C+applications%2C+issues&rft.btitle=2015+IEEE+International+Geoscience+and+Remote+Sensing+Symposium+%28IGARSS%29&rft.pages=%3Cspan+class%3D%22nowrap%22%3E2915-%3C%2Fspan%3E2918&rft.date=2015&rft_id=info%3Ahdl%2F11568%2F843638&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A9589219%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FIGARSS.2015.7326425&rft.isbn=978-1-4799-7929-5&rft.aulast=Reigber&rft.aufirst=Andreas&rft.au=Lombardini%2C+Fabrizio&rft.au=Viviani%2C+Federico&rft.au=Nannini%2C+Matteo&rft.au=Martinez+Del+Hoyo%2C+Antonio&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAllen" class="citation web cs1">Allen, Chris. <a rel="nofollow" class="external text" href="https://people.eecs.ku.edu/~callen58/826/826_SAR_Implementation_03.pptx">"Synthetic-Aperture Radar (SAR) Implementation"</a>. <i>EECS Department, University of Kansas</i><span class="reference-accessdate">. Retrieved <span class="nowrap">14 January</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=EECS+Department%2C+University+of+Kansas&rft.atitle=Synthetic-Aperture+Radar+%28SAR%29+Implementation&rft.aulast=Allen&rft.aufirst=Chris&rft_id=https%3A%2F%2Fpeople.eecs.ku.edu%2F~callen58%2F826%2F826_SAR_Implementation_03.pptx&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text">Xiaoxiang Zhu, "Spectral Estimation for Synthetic Aperture Radar Tomography", Earth Oriented Space Science and Technology – ESPACE, 19 September 2008.</span> </li> <li id="cite_note-:12-19"><span class="mw-cite-backlink">^ <a href="#cite_ref-:12_19-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:12_19-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDeGraaf1998" class="citation journal cs1">DeGraaf, S. R. (May 1998). "SAR Imaging via Modern 2-D Spectral Estimation Methods". <i>IEEE Transactions on Image Processing</i>. <b>7</b> (5): <span class="nowrap">729–</span>761. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1998ITIP....7..729D">1998ITIP....7..729D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F83.668029">10.1109/83.668029</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/18276288">18276288</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Image+Processing&rft.atitle=SAR+Imaging+via+Modern+2-D+Spectral+Estimation+Methods&rft.volume=7&rft.issue=5&rft.pages=%3Cspan+class%3D%22nowrap%22%3E729-%3C%2Fspan%3E761&rft.date=1998-05&rft_id=info%3Apmid%2F18276288&rft_id=info%3Adoi%2F10.1109%2F83.668029&rft_id=info%3Abibcode%2F1998ITIP....7..729D&rft.aulast=DeGraaf&rft.aufirst=S.+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFD._Rodriguez" class="citation journal cs1">D. Rodriguez. "A computational Kronecker-core array algebra SAR raw data generation modeling system". <i>Signals, Systems and Computers, 2001. Conference Record of the Thirty-Fifth Asilomar Conference on Year: 2001</i>. <b>1</b>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Signals%2C+Systems+and+Computers%2C+2001.+Conference+Record+of+the+Thirty-Fifth+Asilomar+Conference+on+Year%3A+2001&rft.atitle=A+computational+Kronecker-core+array+algebra+SAR+raw+data+generation+modeling+system&rft.volume=1&rft.au=D.+Rodriguez&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-:13-21"><span class="mw-cite-backlink">^ <a href="#cite_ref-:13_21-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:13_21-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFT._Gough1994" class="citation journal cs1">T. Gough, Peter (June 1994). "A Fast Spectral Estimation Algorithm Based on the FFT". <i>IEEE Transactions on Signal Processing</i>. <b>42</b> (6): <span class="nowrap">1317–</span>1322. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1994ITSP...42.1317G">1994ITSP...42.1317G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F78.286949">10.1109/78.286949</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Signal+Processing&rft.atitle=A+Fast+Spectral+Estimation+Algorithm+Based+on+the+FFT&rft.volume=42&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1317-%3C%2Fspan%3E1322&rft.date=1994-06&rft_id=info%3Adoi%2F10.1109%2F78.286949&rft_id=info%3Abibcode%2F1994ITSP...42.1317G&rft.aulast=T.+Gough&rft.aufirst=Peter&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-:10-22"><span class="mw-cite-backlink">^ <a href="#cite_ref-:10_22-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:10_22-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDatcuPopescuGavat2008" class="citation journal cs1">Datcu, Mihai; Popescu, Anca; Gavat, Inge (2008). "Complex SAR image characterization using space variant spectral analysis". <i>2008 IEEE Radar Conference</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=2008+IEEE+Radar+Conference&rft.atitle=Complex+SAR+image+characterization+using+space+variant+spectral+analysis&rft.date=2008&rft.aulast=Datcu&rft.aufirst=Mihai&rft.au=Popescu%2C+Anca&rft.au=Gavat%2C+Inge&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJ._Capo41969" class="citation journal cs1">J. Capo4 (August 1969). "High resolution frequency wave-number spectrum analysis". <i>Proceedings of the IEEE</i>. <b>57</b> (8): <span class="nowrap">1408–</span>1418. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FPROC.1969.7278">10.1109/PROC.1969.7278</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+IEEE&rft.atitle=High+resolution+frequency+wave-number+spectrum+analysis&rft.volume=57&rft.issue=8&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1408-%3C%2Fspan%3E1418&rft.date=1969-08&rft_id=info%3Adoi%2F10.1109%2FPROC.1969.7278&rft.au=J.+Capo4&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: CS1 maint: numeric names: authors list (<a href="/wiki/Category:CS1_maint:_numeric_names:_authors_list" title="Category:CS1 maint: numeric names: authors list">link</a>)</span></span> </li> <li id="cite_note-:5-24"><span class="mw-cite-backlink">^ <a href="#cite_ref-:5_24-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:5_24-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:5_24-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:5_24-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFA._JakobssonS._L._MarpleP._Stoica2000" class="citation journal cs1">A. Jakobsson; S. L. Marple; P. Stoica (2000). "Computationally efficient two-dimensional Capon spectrum analysis". <i>IEEE Transactions on Signal Processing</i>. <b>48</b> (9): <span class="nowrap">2651–</span>2661. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000ITSP...48.2651J">2000ITSP...48.2651J</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.7">10.1.1.41.7</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F78.863072">10.1109/78.863072</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Signal+Processing&rft.atitle=Computationally+efficient+two-dimensional+Capon+spectrum+analysis&rft.volume=48&rft.issue=9&rft.pages=%3Cspan+class%3D%22nowrap%22%3E2651-%3C%2Fspan%3E2661&rft.date=2000&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.41.7%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1109%2F78.863072&rft_id=info%3Abibcode%2F2000ITSP...48.2651J&rft.au=A.+Jakobsson&rft.au=S.+L.+Marple&rft.au=P.+Stoica&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFI._YildirimN._S._TezelI._ErerB._Yazgan" class="citation journal cs1">I. Yildirim; N. S. Tezel; I. Erer; B. Yazgan. "A comparison of non-parametric spectral estimators for SAR imaging". <i>Recent Advances in Space Technologies, 2003. RAST '03. International Conference on. Proceedings of Year: 2003</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Recent+Advances+in+Space+Technologies%2C+2003.+RAST+%2703.+International+Conference+on.+Proceedings+of+Year%3A+2003&rft.atitle=A+comparison+of+non-parametric+spectral+estimators+for+SAR+imaging&rft.au=I.+Yildirim&rft.au=N.+S.+Tezel&rft.au=I.+Erer&rft.au=B.+Yazgan&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text">"Iterative realization of the 2-D Capon method applied in SAR image processing", IET International Radar Conference 2015.</span> </li> <li id="cite_note-:6-27"><span class="mw-cite-backlink">^ <a href="#cite_ref-:6_27-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:6_27-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFR._AltyJakobssonG._Larsson" class="citation journal cs1">R. Alty, Stephen; Jakobsson, Andreas; G. Larsson, Erik. "Efficient implementation of the time-recursive Capon and APES spectral estimators". <i>Signal Processing Conference, 2004 12th European</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Signal+Processing+Conference%2C+2004+12th+European&rft.atitle=Efficient+implementation+of+the+time-recursive+Capon+and+APES+spectral+estimators&rft.aulast=R.+Alty&rft.aufirst=Stephen&rft.au=Jakobsson%2C+Andreas&rft.au=G.+Larsson%2C+Erik&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLiP._Stoica1996" class="citation journal cs1">Li, Jian; P. Stoica (1996). <a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F78.506612">"An adaptive filtering approach to spectral estimation and SAR imaging"</a>. <i>IEEE Transactions on Signal Processing</i>. <b>44</b> (6): <span class="nowrap">1469–</span>1484. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1996ITSP...44.1469L">1996ITSP...44.1469L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F78.506612">10.1109/78.506612</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Signal+Processing&rft.atitle=An+adaptive+filtering+approach+to+spectral+estimation+and+SAR+imaging&rft.volume=44&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1469-%3C%2Fspan%3E1484&rft.date=1996&rft_id=info%3Adoi%2F10.1109%2F78.506612&rft_id=info%3Abibcode%2F1996ITSP...44.1469L&rft.aulast=Li&rft.aufirst=Jian&rft.au=P.+Stoica&rft_id=https%3A%2F%2Fdoi.org%2F10.1109%252F78.506612&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLiE._G._LarssonP._Stoica2002" class="citation journal cs1">Li, Jian; E. G. Larsson; P. Stoica (2002). <a rel="nofollow" class="external text" href="https://doi.org/10.1109%2Ftsp.2002.1003059">"Amplitude spectrum estimation for two-dimensional gapped data"</a>. <i>IEEE Transactions on Signal Processing</i>. <b>50</b> (6): <span class="nowrap">1343–</span>1354. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002ITSP...50.1343L">2002ITSP...50.1343L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1109%2Ftsp.2002.1003059">10.1109/tsp.2002.1003059</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Signal+Processing&rft.atitle=Amplitude+spectrum+estimation+for+two-dimensional+gapped+data&rft.volume=50&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1343-%3C%2Fspan%3E1354&rft.date=2002&rft_id=info%3Adoi%2F10.1109%2Ftsp.2002.1003059&rft_id=info%3Abibcode%2F2002ITSP...50.1343L&rft.aulast=Li&rft.aufirst=Jian&rft.au=E.+G.+Larsson&rft.au=P.+Stoica&rft_id=https%3A%2F%2Fdoi.org%2F10.1109%252Ftsp.2002.1003059&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-:0-30"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_30-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_30-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:0_30-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:0_30-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:0_30-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMoreira" class="citation web cs1">Moreira, Alberto. <a rel="nofollow" class="external text" href="https://earth.esa.int/documents/10174/642943/6-LTC2013-SAR-Moreira.pdf">"Synthetic Aperture Radar: Principles and Applications"</a> <span class="cs1-format">(PDF)</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Synthetic+Aperture+Radar%3A+Principles+and+Applications&rft.aulast=Moreira&rft.aufirst=Alberto&rft_id=https%3A%2F%2Fearth.esa.int%2Fdocuments%2F10174%2F642943%2F6-LTC2013-SAR-Moreira.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-:1-31"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_31-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_31-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:1_31-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:1_31-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:1_31-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-:1_31-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDuersch" class="citation journal cs1">Duersch, Michael. "Backprojection for Synthetic Aperture Radar". <i>BYU ScholarsArchive</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=BYU+ScholarsArchive&rft.atitle=Backprojection+for+Synthetic+Aperture+Radar&rft.aulast=Duersch&rft.aufirst=Michael&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-:8-32"><span class="mw-cite-backlink">^ <a href="#cite_ref-:8_32-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:8_32-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZhuoChungsheng2011" class="citation book cs1">Zhuo, LI; Chungsheng, LI (2011). "Back projection algorithm for high resolution GEO-SAR image formation". <i>2011 IEEE International Geoscience and Remote Sensing Symposium</i>. pp. <span class="nowrap">336–</span>339. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FIGARSS.2011.6048967">10.1109/IGARSS.2011.6048967</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4577-1003-2" title="Special:BookSources/978-1-4577-1003-2"><bdi>978-1-4577-1003-2</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:37054346">37054346</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Back+projection+algorithm+for+high+resolution+GEO-SAR+image+formation&rft.btitle=2011+IEEE+International+Geoscience+and+Remote+Sensing+Symposium&rft.pages=%3Cspan+class%3D%22nowrap%22%3E336-%3C%2Fspan%3E339&rft.date=2011&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A37054346%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FIGARSS.2011.6048967&rft.isbn=978-1-4577-1003-2&rft.aulast=Zhuo&rft.aufirst=LI&rft.au=Chungsheng%2C+LI&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: </span><span class="cs1-visible-error citation-comment"><code class="cs1-code">|journal=</code> ignored (<a href="/wiki/Help:CS1_errors#periodical_ignored" title="Help:CS1 errors">help</a>)</span></span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFXiaolingChen" class="citation journal cs1">Xiaoling, Zhang; Chen, Cheng. "A new super-resolution 3D-SAR imaging method based on MUSIC algorithm". <i>2011 IEEE RadarCon (RADAR)</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=2011+IEEE+RadarCon+%28RADAR%29&rft.atitle=A+new+super-resolution+3D-SAR+imaging+method+based+on+MUSIC+algorithm&rft.aulast=Xiaoling&rft.aufirst=Zhang&rft.au=Chen%2C+Cheng&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFA._F._Yegulalp" class="citation journal cs1">A. F. Yegulalp. "Fast backprojection algorithm for synthetic aperture radar". <i>Radar Conference, 1999. The Record of the 1999 IEEE Year: 1999</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Radar+Conference%2C+1999.+The+Record+of+the+1999+IEEE+Year%3A+1999&rft.atitle=Fast+backprojection+algorithm+for+synthetic+aperture+radar&rft.au=A.+F.+Yegulalp&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text">Mark T. Crockett, "An Introduction to Synthetic Aperture Radar:A High-Resolution Alternative to Optical Imaging"</span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBauck2019" class="citation report cs1">Bauck, Jerald (19 October 2019). <a rel="nofollow" class="external text" href="https://engrxiv.org/preprint/view/698/1540">A Rationale for Backprojection in Spotlight Synthetic Aperture Radar Image Formation</a> (Report). <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.31224%2Fosf.io%2F5wv2d">10.31224/osf.io/5wv2d</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:243085005">243085005</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=report&rft.btitle=A+Rationale+for+Backprojection+in+Spotlight+Synthetic+Aperture+Radar+Image+Formation&rft.date=2019-10-19&rft_id=info%3Adoi%2F10.31224%2Fosf.io%2F5wv2d&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A243085005%23id-name%3DS2CID&rft.aulast=Bauck&rft.aufirst=Jerald&rft_id=https%3A%2F%2Fengrxiv.org%2Fpreprint%2Fview%2F698%2F1540&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text">C. Romero, High Resolution Simulation of Synthetic Aperture Radar Imaging. 2010. [Online]. Available: <a rel="nofollow" class="external free" href="http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1364&context=theses">http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1364&context=theses</a>. Accessed: 14 November 2016.</span> </li> <li id="cite_note-:7-38"><span class="mw-cite-backlink">^ <a href="#cite_ref-:7_38-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:7_38-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:7_38-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:7_38-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFY._YamaguchiT._MoriyamaM._IshidoH._Yamada2005" class="citation journal cs1">Y. Yamaguchi; T. Moriyama; M. Ishido; H. Yamada (2005). "Four-component scattering model for polarimetric SAR image decomposition". <i>IEEE Transactions on Geoscience and Remote Sensing</i>. <b>43</b> (8): 1699. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2005ITGRS..43.1699Y">2005ITGRS..43.1699Y</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTGRS.2005.852084">10.1109/TGRS.2005.852084</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:10094317">10094317</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Geoscience+and+Remote+Sensing&rft.atitle=Four-component+scattering+model+for+polarimetric+SAR+image+decomposition&rft.volume=43&rft.issue=8&rft.pages=1699&rft.date=2005&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A10094317%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FTGRS.2005.852084&rft_id=info%3Abibcode%2F2005ITGRS..43.1699Y&rft.au=Y.+Yamaguchi&rft.au=T.+Moriyama&rft.au=M.+Ishido&rft.au=H.+Yamada&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text">Woodhouse, H.I. 2009. Introduction to microwave remote sensing. CRC Press, Taylor & Fancis Group, Special Indian Edition.</span> </li> <li id="cite_note-:14-40"><span class="mw-cite-backlink">^ <a href="#cite_ref-:14_40-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:14_40-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:14_40-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFA._FreemanS._L._Durden1998" class="citation journal cs1">A. Freeman; S. L. Durden (May 1998). "A three-component scattering model for polarimetric SAR data". <i>IEEE Transactions on Geoscience and Remote Sensing</i>. <b>36</b> (3): <span class="nowrap">963–</span>973. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1998ITGRS..36..963F">1998ITGRS..36..963F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F36.673687">10.1109/36.673687</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Geoscience+and+Remote+Sensing&rft.atitle=A+three-component+scattering+model+for+polarimetric+SAR+data&rft.volume=36&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E963-%3C%2Fspan%3E973&rft.date=1998-05&rft_id=info%3Adoi%2F10.1109%2F36.673687&rft_id=info%3Abibcode%2F1998ITGRS..36..963F&rft.au=A.+Freeman&rft.au=S.+L.+Durden&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://earth.esa.int/documents/653194/656796/Polarimetric_Decompositions.pdf">"PolSARpro v6.0 (Biomass Edition) Toolbox"</a> <span class="cs1-format">(PDF)</span>. ESA<span class="reference-accessdate">. Retrieved <span class="nowrap">20 November</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=PolSARpro+v6.0+%28Biomass+Edition%29+Toolbox&rft.pub=ESA&rft_id=https%3A%2F%2Fearth.esa.int%2Fdocuments%2F653194%2F656796%2FPolarimetric_Decompositions.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1">"Gianfranco Fornaro; Diego Reale; Francesco Serafino,"Four-Dimensional SAR Imaging for Height Estimation and Monitoring of Single and Double Scatterers"<span class="cs1-kern-right"></span>". <i>IEEE Transactions on Geoscience and Remote Sensing</i>. <b>47</b> (1). 2009.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Geoscience+and+Remote+Sensing&rft.atitle=Gianfranco+Fornaro%3B+Diego+Reale%3B+Francesco+Serafino%2C%22Four-Dimensional+SAR+Imaging+for+Height+Estimation+and+Monitoring+of+Single+and+Double+Scatterers%22&rft.volume=47&rft.issue=1&rft.date=2009&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1">"Haijian Zhang; Wen Yang; Jiayu Chen; Hong Sun," Improved Classification of Polarimetric SAR Data Based on Four-component Scattering Model"<span class="cs1-kern-right"></span>". <i>2006 CIE International Conference on Radar</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=2006+CIE+International+Conference+on+Radar&rft.atitle=Haijian+Zhang%3B+Wen+Yang%3B+Jiayu+Chen%3B+Hong+Sun%2C%22+Improved+Classification+of+Polarimetric+SAR+Data+Based+on+Four-component+Scattering+Model%22&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBathkeShirzaeiWalter2011" class="citation journal cs1">Bathke, H.; Shirzaei, M.; Walter, T. R. (2011). <a rel="nofollow" class="external text" href="http://gfzpublic.gfz-potsdam.de/pubman/item/escidoc:243727">"Inflation and deflation at the steep-sided Llaima stratovolcano (Chile) detected by using InSAR"</a>. <i>Geophys. Res. Lett</i>. <b>38</b> (10): L10304. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011GeoRL..3810304B">2011GeoRL..3810304B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1029%2F2011GL047168">10.1029/2011GL047168</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Geophys.+Res.+Lett.&rft.atitle=Inflation+and+deflation+at+the+steep-sided+Llaima+stratovolcano+%28Chile%29+detected+by+using+InSAR&rft.volume=38&rft.issue=10&rft.pages=L10304&rft.date=2011&rft_id=info%3Adoi%2F10.1029%2F2011GL047168&rft_id=info%3Abibcode%2F2011GeoRL..3810304B&rft.aulast=Bathke&rft.aufirst=H.&rft.au=Shirzaei%2C+M.&rft.au=Walter%2C+T.+R.&rft_id=http%3A%2F%2Fgfzpublic.gfz-potsdam.de%2Fpubman%2Fitem%2Fescidoc%3A243727&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDawsonCumminsTregoningLeonard2008" class="citation journal cs1">Dawson, J.; Cummins, P.; Tregoning, P.; Leonard, M. (2008). "Shallow intraplate earthquakes in Western Australia observed by Interferometric Synthetic Aperture Radar". <i>J. Geophys. Res</i>. <b>113</b> (B11): B11408. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008JGRB..11311408D">2008JGRB..11311408D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1029%2F2008JB005807">10.1029/2008JB005807</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Geophys.+Res.&rft.atitle=Shallow+intraplate+earthquakes+in+Western+Australia+observed+by+Interferometric+Synthetic+Aperture+Radar&rft.volume=113&rft.issue=B11&rft.pages=B11408&rft.date=2008&rft_id=info%3Adoi%2F10.1029%2F2008JB005807&rft_id=info%3Abibcode%2F2008JGRB..11311408D&rft.aulast=Dawson&rft.aufirst=J.&rft.au=Cummins%2C+P.&rft.au=Tregoning%2C+P.&rft.au=Leonard%2C+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.iris.edu/hq/inclass/animation/volcano_monitoring_using_insar_to_see_changes_in_volcano_shape">"Volcano Monitoring: Using InSAR to see changes in volcano shape- Incorporated Research Institutions for Seismology"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Volcano+Monitoring%3A+Using+InSAR+to+see+changes+in+volcano+shape-+Incorporated+Research+Institutions+for+Seismology&rft_id=https%3A%2F%2Fwww.iris.edu%2Fhq%2Finclass%2Fanimation%2Fvolcano_monitoring_using_insar_to_see_changes_in_volcano_shape&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-:11-47"><span class="mw-cite-backlink">^ <a href="#cite_ref-:11_47-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:11_47-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:11_47-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLombardiniViviani2014" class="citation book cs1">Lombardini, Fabrizio; Viviani, Federico (2014). "Multidimensional SAR Tomography: Advances for Urban and Prospects for Forest/Ice Applications". <i>2014 11th European Radar Conference</i>. pp. <span class="nowrap">225–</span>228. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FEuRAD.2014.6991248">10.1109/EuRAD.2014.6991248</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-2-8748-7037-8" title="Special:BookSources/978-2-8748-7037-8"><bdi>978-2-8748-7037-8</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:37114379">37114379</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Multidimensional+SAR+Tomography%3A+Advances+for+Urban+and+Prospects+for+Forest%2FIce+Applications&rft.btitle=2014+11th+European+Radar+Conference&rft.pages=%3Cspan+class%3D%22nowrap%22%3E225-%3C%2Fspan%3E228&rft.date=2014&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A37114379%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FEuRAD.2014.6991248&rft.isbn=978-2-8748-7037-8&rft.aulast=Lombardini&rft.aufirst=Fabrizio&rft.au=Viviani%2C+Federico&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text">"Synthetic Aperture Radar", L. J. Cutrona, Chapter 23 (25 pp) of the McGraw Hill "Radar Handbook", 1970. (Written while optical data processing was still the only workable method, by the person who first led that development.)</span> </li> <li id="cite_note-Leith-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-Leith_49-0">^</a></b></span> <span class="reference-text">"A short history of the Optics Group of the Willow Run Laboratories", Emmett N. Leith, in <i>Trends in Optics: Research, Development, and Applications</i> (book), Anna Consortini, Academic Press, San Diego: 1996.</span> </li> <li id="cite_note-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-50">^</a></b></span> <span class="reference-text">"Sighted Automation and Fine Resolution Imaging", W. M. Brown, J. L. Walker, and W. R. Boario, IEEE Transactions on Aerospace and Electronic Systems, Vol. 40, No. 4, October 2004, pp 1426–1445.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=65" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCurlanderMcDonough" class="citation book cs1">Curlander, John C.; McDonough, Robert N. <i>Synthetic Aperture Radar: Systems and Signal Processing</i>. Remote Sensing and Image Processing. Wiley.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Synthetic+Aperture+Radar%3A+Systems+and+Signal+Processing&rft.series=Remote+Sensing+and+Image+Processing&rft.pub=Wiley&rft.aulast=Curlander&rft.aufirst=John+C.&rft.au=McDonough%2C+Robert+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGart2006" class="citation thesis cs1">Gart, Jason H (2006). <i>Electronics and Aerospace Industry in Cold War Arizona, 1945–1968: Motorola, Hughes Aircraft, Goodyear Aircraft</i> (Thesis). Arizona State University.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adissertation&rft.title=Electronics+and+Aerospace+Industry+in+Cold+War+Arizona%2C+1945%E2%80%931968%3A+Motorola%2C+Hughes+Aircraft%2C+Goodyear+Aircraft&rft.inst=Arizona+State+University&rft.date=2006&rft.aulast=Gart&rft.aufirst=Jason+H&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMoreiraPrats-IraolaYounisKrieger2013" class="citation journal cs1">Moreira, A.; Prats-Iraola, P.; Younis, M.; Krieger, G.; Hajnsek, I.; Papathanassiou, K. P. (2013). <a rel="nofollow" class="external text" href="https://elib.dlr.de/82313/1/SAR-Tutorial-March-2013.pdf">"A tutorial on synthetic aperture radar"</a> <span class="cs1-format">(PDF)</span>. <i>IEEE Geoscience and Remote Sensing Magazine</i>. <b>1</b> (1): <span class="nowrap">6–</span>43. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013IGRSM...1a...6M">2013IGRSM...1a...6M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FMGRS.2013.2248301">10.1109/MGRS.2013.2248301</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:7487291">7487291</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Geoscience+and+Remote+Sensing+Magazine&rft.atitle=A+tutorial+on+synthetic+aperture+radar&rft.volume=1&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E6-%3C%2Fspan%3E43&rft.date=2013&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A7487291%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FMGRS.2013.2248301&rft_id=info%3Abibcode%2F2013IGRSM...1a...6M&rft.aulast=Moreira&rft.aufirst=A.&rft.au=Prats-Iraola%2C+P.&rft.au=Younis%2C+M.&rft.au=Krieger%2C+G.&rft.au=Hajnsek%2C+I.&rft.au=Papathanassiou%2C+K.+P.&rft_id=https%3A%2F%2Felib.dlr.de%2F82313%2F1%2FSAR-Tutorial-March-2013.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWoodhouse2006" class="citation book cs1">Woodhouse, Iain H (2006). <i>Introduction to Microwave Remote Sensing</i>. CRC Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Microwave+Remote+Sensing&rft.pub=CRC+Press&rft.date=2006&rft.aulast=Woodhouse&rft.aufirst=Iain+H&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASynthetic-aperture+radar" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Synthetic-aperture_radar&action=edit&section=66" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.fas.org/irp/program/collect/isfar.htm">InSAR measurements from the Space Shuttle</a></li> <li><a rel="nofollow" class="external text" href="https://www.jpl.nasa.gov/radar/sircxsar/">Images from the Space Shuttle SAR instrument</a></li> <li><a rel="nofollow" class="external text" href="http://www.asf.alaska.edu/">The Alaska Satellite Facility</a> has numerous technical documents, including an introductory text on SAR theory and scientific applications</li> <li><a rel="nofollow" class="external text" href="http://www.syntheticapertureradar.com/">SAR Journal</a> SAR Journal tracks the Synthetic Aperture Radar (SAR) industry</li> <li><a rel="nofollow" class="external text" href="https://www.jpl.nasa.gov/releases/98/angkor98.html">NASA radar reveals hidden remains at ancient Angkor</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20141224003449/http://www.jpl.nasa.gov/releases/98/angkor98.html">Archived</a> 24 December 2014 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> – <a href="/wiki/Jet_Propulsion_Laboratory" title="Jet Propulsion Laboratory">Jet Propulsion Laboratory</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"></div><div role="navigation" class="navbox authority-control" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q740686#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/7504513-8">Germany</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Synthetic aperture radar"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85131656">United States</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Radar à antenne synthétique"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb119849437">France</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Radar à antenne synthétique"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb119849437">BnF data</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/01148112">Japan</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007555932405171">Israel</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Synthetic-aperture_radar&oldid=1259201286">https://en.wikipedia.org/w/index.php?title=Synthetic-aperture_radar&oldid=1259201286</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Category</a>: <ul><li><a href="/wiki/Category:Synthetic_aperture_radar" title="Category:Synthetic aperture radar">Synthetic aperture radar</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:CS1_maint:_numeric_names:_authors_list" title="Category:CS1 maint: numeric names: authors list">CS1 maint: numeric names: authors list</a></li><li><a href="/wiki/Category:CS1_errors:_periodical_ignored" title="Category:CS1 errors: periodical ignored">CS1 errors: periodical ignored</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Use_dmy_dates_from_October_2019" title="Category:Use dmy dates from October 2019">Use dmy dates from October 2019</a></li><li><a href="/wiki/Category:Articles_needing_additional_references_from_March_2012" title="Category:Articles needing additional references from March 2012">Articles needing additional references from March 2012</a></li><li><a href="/wiki/Category:All_articles_needing_additional_references" title="Category:All articles needing additional references">All articles needing additional references</a></li><li><a href="/wiki/Category:Wikipedia_articles_that_are_excessively_detailed_from_March_2012" title="Category:Wikipedia articles that are excessively detailed from March 2012">Wikipedia articles that are excessively detailed from March 2012</a></li><li><a href="/wiki/Category:All_articles_that_are_excessively_detailed" title="Category:All articles that are excessively detailed">All articles that are excessively detailed</a></li><li><a href="/wiki/Category:Wikipedia_articles_with_style_issues_from_March_2012" title="Category:Wikipedia articles with style issues from March 2012">Wikipedia articles with style issues from March 2012</a></li><li><a href="/wiki/Category:All_articles_with_style_issues" title="Category:All articles with style issues">All articles with style issues</a></li><li><a href="/wiki/Category:Wikipedia_articles_that_are_too_technical_from_November_2024" title="Category:Wikipedia articles that are too technical from November 2024">Wikipedia articles that are too technical from November 2024</a></li><li><a href="/wiki/Category:All_articles_that_are_too_technical" title="Category:All articles that are too technical">All articles that are too technical</a></li><li><a href="/wiki/Category:Articles_with_multiple_maintenance_issues" title="Category:Articles with multiple maintenance issues">Articles with multiple maintenance issues</a></li><li><a href="/wiki/Category:Wikipedia_articles_needing_clarification_from_October_2012" title="Category:Wikipedia articles needing clarification from October 2012">Wikipedia articles needing clarification from October 2012</a></li><li><a href="/wiki/Category:Articles_with_excerpts" title="Category:Articles with excerpts">Articles with excerpts</a></li><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 23 November 2024, at 22:38<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Synthetic-aperture_radar&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-78d9ddc6fb-9ncxx","wgBackendResponseTime":157,"wgPageParseReport":{"limitreport":{"cputime":"0.941","walltime":"1.389","ppvisitednodes":{"value":4293,"limit":1000000},"postexpandincludesize":{"value":144255,"limit":2097152},"templateargumentsize":{"value":17076,"limit":2097152},"expansiondepth":{"value":17,"limit":100},"expensivefunctioncount":{"value":19,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":177453,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 1004.066 1 -total"," 31.76% 318.902 1 Template:Reflist"," 17.50% 175.741 1 Template:Authority_control"," 13.67% 137.225 24 Template:Cite_journal"," 10.55% 105.938 1 Template:Multiple_issues"," 10.03% 100.714 7 Template:Cite_web"," 7.32% 73.459 1 Template:Short_description"," 6.89% 69.203 3 Template:Ambox"," 6.87% 69.007 1 Template:More_citations_needed"," 5.51% 55.339 1 Template:Excerpt"]},"scribunto":{"limitreport-timeusage":{"value":"0.568","limit":"10.000"},"limitreport-memusage":{"value":10228461,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-78d9ddc6fb-j295f","timestamp":"20250102124629","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Synthetic-aperture radar","url":"https:\/\/en.wikipedia.org\/wiki\/Synthetic-aperture_radar","sameAs":"http:\/\/www.wikidata.org\/entity\/Q740686","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q740686","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2004-05-10T04:31:22Z","dateModified":"2024-11-23T22:38:26Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/a\/a8\/TEIDE.JPG","headline":"form of radar which is used to create images of an object"}</script> </body> </html>