CINXE.COM
Representations of world coordinates in FITS | Astronomy & Astrophysics (A&A)
<!DOCTYPE html> <html xml:lang="en-gb" lang="en-gb" dir="ltr"> <head> <meta name="viewport" content="width=device-width, initial-scale=1.0, shrink-to-fit=no"> <base href="https://www.aanda.org/component/article" /> <meta http-equiv="content-type" content="text/html; charset=utf-8" /> <meta name="keywords" content="Astronomy & Astrophysics, A&A, ESO, EDP Sciences" /> <meta name="robots" content="index, follow, noarchive" /> <meta name="description" content="Astronomy & Astrophysics (A&A) is an international journal which publishes papers on all aspects of astronomy and astrophysics" /> <title>Representations of world coordinates in FITS | Astronomy & Astrophysics (A&A)</title> <link rel="stylesheet" href="/libraries/jquery/jquery.multiselect.css" type="text/css" /> <link rel="stylesheet" href="/libraries/jquery/jquery.qtip/jquery.qtip.min.css" type="text/css" /> <link rel="stylesheet" href="/libraries/jquery/jquery.magnific-popup.css" type="text/css" /> <link rel="stylesheet" href="https://ajax.googleapis.com/ajax/libs/jqueryui/1.12.0/themes/smoothness/jquery-ui.css" type="text/css" /> <link rel="stylesheet" href="/templates/template1/css/com_article.css" type="text/css" /> <link rel="stylesheet" href="/templates/template1/css/com_article_hljs_github.min.css" type="text/css" /> <link rel="stylesheet" href="/templates/template1/css/mod_article_bookmarking.css" type="text/css" /> <link rel="stylesheet" href="/templates/template1/css/mod_article_purchase.css" type="text/css" /> <link rel="stylesheet" href="/templates/template1/css/mod_solr.css" type="text/css" /> <script src="https://ajax.googleapis.com/ajax/libs/jquery/3.3.1/jquery.min.js" type="text/javascript"></script> <script src="/plugins/system/jqueryeasy/jquerynoconflict.js" type="text/javascript"></script> <script src="https://ajax.googleapis.com/ajax/libs/jqueryui/1.12.0/jquery-ui.min.js" type="text/javascript"></script> <script src="/libraries/jquery/jquery.multiselect.min.js" type="text/javascript"></script> <script src="/libraries/jquery/jquery.magnific-popup.min.js" type="text/javascript"></script> <script src="/libraries/jquery/jquery.qtip/jquery.qtip.min.js" type="text/javascript"></script> <script src="https://www.aanda.org/components/com_article/assets/js/highlight/highlight.min.js" type="text/javascript"></script> <script src="https://www.aanda.org/components/com_article/assets/js/article.js" type="text/javascript"></script> <script src="https://www.aanda.org/components/com_article/assets/js/highlight/highlight.js" type="text/javascript"></script> <script src="https://www.googletagmanager.com/gtag/js?id=G-S2LKMZBHJL" type="text/javascript"></script> <script src="/modules/mod_article_bookmarking/assets/js/bookmarking.js" type="text/javascript"></script> <script src="/libraries/jquery/jquery.autocomplete.js" type="text/javascript"></script> <script type="text/javascript"> var ARTICLE_CLICK_VIEW = "Click to view fullscreen"; var ARTICLE_CLICK_HIDE = "Click anywhere to hide the fullscreen overlay"; var ARTICLE_CLICK_MOVIE = "Click to play the movie"; var COM_ARTICLE_DISPLAY_EQUATION_AS = "Display equations as"; var COM_ARTICLE_COPY_IN_CLIPBOARD = "LaTeX copied in clipboard!"; const MATHML_DISPLAY = "disabled"; window.dataLayer = window.dataLayer || []; function gtag() {dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-S2LKMZBHJL', { 'edpsname': 'aa', 'site_name': 'Astronomy & Astrophysics (A&A)', 'plateform': 'journal', 'plateform_type': 'edp', 'server_host': 'ovh-canada' });gtag('config', 'G-T2TE0Y7XE9', { 'edpsname': 'aa', 'site_name': 'Astronomy & Astrophysics (A&A)', 'plateform': 'journal', 'plateform_type': 'edp', 'server_host': 'ovh-canada' });gtag('config', 'user_properties', { 'edpsname': 'aa', 'site_name': 'Astronomy & Astrophysics (A&A)', 'plateform': 'journal', 'plateform_type': 'edp', 'server_host': 'ovh-canada' }); </script> <link title="schema(PRISM)" rel="schema.prism" href="http://prismstandard.org/namespaces/1.2/basic/"> <meta name="citation_journal_title" content="Astronomy & Astrophysics"> <meta name="citation_journal_abbrev" content="A&A"> <meta name="citation_publisher" content="EDP Sciences"> <meta name="citation_author" content="E. W. Greisen"> <meta name="citation_author_institution" content="National Radio Astronomy Observatory, PO Box O, Socorro, NM 87801-0387, USA"> <meta name="citation_author" content="M. R. Calabretta"> <meta name="citation_author_institution" content="Australia Telescope National Facility, PO Box 76, Epping, NSW 1710, Australia"> <meta name="citation_title" content="Representations of world coordinates in FITS"> <meta name="citation_online_date" content="2002/11/18"> <meta name="citation_publication_date" content="2002/12/01"> <meta name="citation_volume" content="395"> <meta name="citation_issue" content="3"> <meta name="citation_firstpage" content="1061"> <meta name="citation_lastpage" content="1075"> <meta name="citation_doi" content="10.1051/0004-6361:20021326"> <meta name="citation_bibcode" content="2002A%26A...395.1061G"> <meta name="citation_abstract_html_url" content="https://www.aanda.org/articles/aa/abs/2002/45/aah3859/aah3859.html"> <meta name="citation_pdf_url" content="https://www.aanda.org/articles/aa/pdf/2002/45/aah3859.pdf"> <meta name="citation_issn" content="0004-6361"> <meta name="citation_issn" content="1432-0746"> <meta name="citation_language" content="en"> <meta name="citation_keyword" content="methods: data analysis"> <meta name="citation_keyword" content="techniques: image processing"> <meta name="citation_keyword" content="astronomical data bases: miscellaneous"> <meta name="citation_article_type" content="Research Article"> <meta name="citation_abstract" lang="en" content="The initial descriptions of the FITS format provided a simplified method for describing the physical coordinate values of the image pixels, but deliberately did not specify any of the detailed conventions required to convey the complexities of actual image coordinates. Building on conventions in wide use within astronomy, this paper proposes general extensions to the original methods for describing the world coordinates of FITS data. In subsequent papers, we apply these general conventions to the methods by which spherical coordinates may be projected onto a two-dimensional plane and to frequency/wavelength/velocity coordinates."> <meta name="citation_reference" content="Adobe Systems, Inc. 1999, PostScript Language Reference Manual, Third ed. (Addison-Wesley Publishing Company, Inc.), Reading, Massachusetts (see especially pages 293-296)"> <meta name="citation_reference" content="citation_author=M. R. Calabretta;citation_author=E. W. Greisen;citation_publication_date=2002;citation_journal_title=A&A;citation_volume=395;citation_firstpage=1077;"> <meta name="citation_reference" content="Calabretta, M. R., et al. 2003, Representations of distortions in FITS world coordinate systems, in preparation, Paper IV"> <meta name="citation_reference" content="citation_author=W. D. Cotton;citation_author=D. Tody;citation_author=W. D. Pence;citation_publication_date=1995;citation_journal_title=A&AS;citation_volume=113;citation_firstpage=159;"> <meta name="citation_reference" content="citation_author=A. Einstein;citation_publication_date=1905;citation_journal_title=Ann. Physik;citation_volume=17;citation_firstpage=891;"> <meta name="citation_reference" content="George, I. M., & Angelini, L. 1995, Specification of Physical Units within OGIP FITS files, OGIP Memo OGIP/93-001, NASA Goddard Space Flight Center, Greenbelt, Maryland,http://www.cv.nrao.edu/fits/wcs/OGIP93_001.ps"> <meta name="citation_reference" content="citation_author=E. W. Greisen;citation_author=R. H. Harten;citation_publication_date=1981;citation_journal_title=A&AS;citation_volume=44;citation_firstpage=371;"> <meta name="citation_reference" content="Greisen, E. W. 1983, Non-linear Coordinate Systems in AIPS, AIPS Memo No. 27, National Radio Astronomy Observatory, Charlottesville, Virginia, November,http://www.cv.nrao.edu/fits/wcs/aips27.ps"> <meta name="citation_reference" content="Greisen, E. W. 1986, Additional Non-linear Coordinates, AIPS Memo No. 46, National Radio Astronomy Observatory, Charlottesville, Virginia, May 20,http://www.cv.nrao.edu/fits/wcs/aips46.ps"> <meta name="citation_reference" content="Greisen, E. W., Valdes, F. G., Calabretta, M. R., & Allen, S. L. 2003, A&A, in preparation, Paper III"> <meta name="citation_reference" content="citation_author=P. Grosb酶l;citation_author=R. H. Harten;citation_author=E. W. Greisen;citation_author=D. C. Wells;citation_publication_date=1988;citation_journal_title=A&AS;citation_volume=73;citation_firstpage=359;"> <meta name="citation_reference" content="citation_author=R. J. Hanisch;citation_author=A. Farris;citation_author=E. W. Greisen;citation_publication_date=2001;citation_journal_title=A&A;citation_volume=376;citation_firstpage=359;"> <meta name="citation_reference" content="Hanisch, R. J., & Wells, D. C. 1988, World Coordinate Systems Representations Within the FITS Format, draft based on notes from a meeting sponsored by the National Aeronautics and Space Administration, Code EZ, held in Charlottesville, Virginia, January 1988. Located at http://www.cv.nrao.edu/fits/wcs/wcs88.ps.Z"> <meta name="citation_reference" content="citation_author=R. H. Harten;citation_author=P. Grosb酶l;citation_author=E. W. Greisen;citation_author=D. C. Wells;citation_publication_date=1988;citation_journal_title=A&AS;citation_volume=73;citation_firstpage=365;"> <meta name="citation_reference" content="IAU Inf. Bull. 1983, No. 49, 14"> <meta name="citation_reference" content="McNally, D. (ed.) 1988, Transactions of the IAU, Proceedings of the Twentieth General Assembly (Dordrecht: Kluwer)"> <meta name="citation_reference" content="Ochsenbein, F., Paul, N., & Kuin, M. 1996, Standards for Astronomical Catalogues, Version 1.5,http://vizier.u-strasbg.fr/doc/catstd.htx"> <meta name="citation_reference" content="citation_author=J. D. Ponz;citation_author=R. W. Thompson;citation_author=J. R. Mu帽oz;citation_publication_date=1994;citation_journal_title=A&AS;citation_volume=105;citation_firstpage=53;"> <meta name="citation_reference" content="citation_author=D. C. Wells;citation_author=E. W. Greisen;citation_author=R. H. Harten;citation_publication_date=1981;citation_journal_title=A&AS;citation_volume=44;citation_firstpage=363;"> <meta name="prism.copyright" content="漏 ESO, 2002"> <meta name="prism.publicationName" content="Astronomy & Astrophysics"> <meta name="prism.coverDisplayDate" content="December I 2002"> <meta name="prism.volume" content="395"> <meta name="prism.number" content="3"> <meta name="prism.section" content="Numerical methods and codes"> <meta name="prism.startingPage" content="1061"> <meta name="prism.endingPage" content="1075"> <meta name="prism.issn" content="0004-6361"> <meta name="prism.eIssn" content="1432-0746"> <meta name="prism.doi" content="10.1051/0004-6361:20021326"> <meta name="prism.keyword" content="methods: data analysis"> <meta name="prism.keyword" content="techniques: image processing"> <meta name="prism.keyword" content="astronomical data bases: miscellaneous"> <meta name="prism.url" content="https://www.aanda.org/articles/aa/abs/2002/45/aah3859/aah3859.html"> <meta name="citation_fulltext_world_readable" content=""> <link href="/templates/template1/images/aa/favicon.ico" rel="shortcut icon" type="image/vnd.microsoft.icon" /> <link rel="preconnect" href="https://fonts.googleapis.com"> <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin> <link href="https://fonts.googleapis.com/css2?family=Crimson+Text&family=Open+Sans:wght@400;600&display=swap" rel="stylesheet"> <link href="/templates/source/css/article.css" rel="stylesheet" type="text/css"/> <link href="/templates/template1/css/cookie.css" rel="stylesheet" type="text/css"/> <link href="/templates/template1/css/commun_v3.css" rel="stylesheet" type="text/css"/> <link href="/templates/template1/css/template1.css" rel="stylesheet" type="text/css"/> <link href="/templates/source/css/flags25.css" rel="stylesheet" type="text/css"/> <link href="/templates/template1/css/aa.css" rel="stylesheet" type="text/css"/> <link href="/templates/source/js/mmenu2/dist/css/jquery.mmenu.all.css" rel="stylesheet" type="text/css"/> <!--[if IE]> <link rel="stylesheet" href="/templates/template1/css/ie.css" type="text/css" /> <script src="/templates/template1/html5-ie.js"></script> <![endif]--> </head> <body id="com_article" class="aa marketing "> <div id="journal-webpage"> <header> <div class="header-edp"> <div class="wrap "> <div class="logo-edp"> <a href="https://www.edpsciences.org" target="_blank"><img src="/templates/source/images/logos/logo_edp_105.svg" alt="EDP Sciences logo"></a> </div> <nav class="edp-nav"> <ul> <li><a href="https://publications.edpsciences.org/">Journals</a></li> <li><a href="https://www.edpsciences.org/en/books">Books</a></li> <li><a href="https://www.webofconferences.org/">Conferences</a></li> </ul> </nav> <div class="header_cart"> <a href="#" class="cart-box" id="cart-info" title="Display your shopping cart"> <span class="ico ico-cart"></span> <span class="cart-counter hidden">0</span> </a> </div> <div class="reg_info auth"> <div class="btn-nav"> <span class="ico16 white subs"></span><span>Subscriber Authentication Point </span> <nav class="user"> <ul> <li> <a href="/component/authenticate/?task=login"> Sign in with login/password </a> </li> <li> <a href="/component/authenticate/?task=access"> Your subscription </a> </li> </ul> </nav> </div> </div> <div class="reg_info account"> <div class="btn-nav"> <span class="ico16 white login"></span> <span class="reg_info-user">EDPS Account</span> <nav class="user"> <ul> <li><a href="/component/services/">Login</a></li> </ul> </nav> </div> </div> <div class="clear"></div> </div> </div> <div class="header-nav"> <div class="wrap"> <a href="/" class="logo" title="Journal homepage"><img src="/templates/template1/images/aa/logo_aa.svg" alt="Astronomy & Astrophysics (A&A)"></a> <nav class="menu"> <ul class="menu"> <li class="item-122"><a href="/component/issues/?task=all&Itemid=122" >All volumes</a></li><li class="item-443"><a href="/for-authors" >For authors</a></li></ul> </nav> <div class="custom search default"> <span class="ico ico-search" title="Display the search engine">Search</span> </div> <a href="#menu-mobile" class="nav-mobile-link">Menu</a> </div> <nav id="menu-mobile"> <ul class="menu"> <li class="item-145 deeper parent"><span class="separator">About A&A</span> <ul><li class="item-137"><a href="/about-aa/aims-and-scope" >Aims and scope</a></li><li class="item-143"><a href="/about-aa/history" >History</a></li><li class="item-136"><a href="/about-aa/editors-of-aa" >Editors of A&A</a></li><li class="item-140"><a href="/about-aa/board-of-directors" >Board of Directors</a></li><li class="item-138"><a href="/about-aa/indexed-in" >Indexed in</a></li><li class="item-139"><a href="/about-aa/copyright" >Copyright</a></li><li class="item-162"><a href="/images/stories/leaflet/aa_leaflet.pdf" target="_blank" >A&A leaflet (PDF)</a></li><li class="item-530"><a href="https://www.edpsciences.org/images/stories/librarians/EDP-AA-S2O.pdf" target="_blank" >A&A S2O leaflet (PDF)</a></li><li class="item-197"><a href="/about-aa/masthead" >Masthead</a></li></ul></li><li class="item-424 deeper parent"><span class="separator">Browse articles</span> <ul><li class="item-427"><a href="/component/issues/?task=all" >All volumes</a></li><li class="item-429"><a href="/component/list/?task=topic" >Special issues</a></li><li class="item-432"><a href="/component/forthcoming/" >Forthcoming</a></li><li class="item-435"><a href="/highlights" >Highlights</a></li><li class="item-221"><a href="/2024-press-releases" >Press releases</a></li><li class="item-533"><a href="/component/issues/?task=images" >Featured images</a></li></ul></li><li class="item-396 deeper parent"><a href="/for-authors" >For authors</a><ul><li class="item-161 deeper parent"><span class="separator">Author information</span> <ul><li class="item-186"><a href="/for-authors/author-information/paper-organization" >Paper organization</a></li><li class="item-232"><a href="/for-authors/author-information/news-from-the-editorial-office" >News from the Editorial Office</a></li><li class="item-192"><a href="/for-authors/author-information/page-charges" >Page charges</a></li><li class="item-173"><a href="/for-authors/author-information/acceptance-stage" >Acceptance stage</a></li><li class="item-159"><a href="/for-authors/author-information/production-stage" >Production stage</a></li><li class="item-233"><a href="/for-authors/author-information/copyright" >Copyright</a></li><li class="item-231"><a href="/for-authors/author-information/open-access" >Open Access</a></li><li class="item-196"><a href="/doc_journal/instructions/aadoc.pdf" target="_blank" >Author's guide (PDF)</a></li></ul></li><li class="item-189 deeper parent"><span class="separator">Language editing</span> <ul><li class="item-502"><a href="/for-authors/language-editing/1-introduction" >1. Introduction</a></li><li class="item-472"><a href="/for-authors/language-editing/2-main-guidelines" >2. Main guidelines for A&A style</a></li><li class="item-475"><a href="/for-authors/language-editing/3-general-structure" >3. General structure</a></li><li class="item-478"><a href="/for-authors/language-editing/4-uk-versus-us-spelling-and-grammar" >4. UK versus US spelling and grammar</a></li><li class="item-481"><a href="/for-authors/language-editing/5-punctuation-and-style-concerns-regarding-equations-figures-tables-and-footnotes" >5. Punctuation and style concerns regarding equations, figures, tables, and footnotes</a></li><li class="item-484"><a href="/for-authors/language-editing/6-verb-tenses" >6. Verb tenses</a></li><li class="item-487"><a href="/for-authors/language-editing/7-general-hyphenation-guide" >7. General hyphenation guide</a></li><li class="item-490"><a href="/for-authors/language-editing/8-common-editing-issues" >8. Common editing issues</a></li><li class="item-493"><a href="/for-authors/language-editing/9-measurements-and-their-descriptions" >9. Measurements and their descriptions</a></li><li class="item-496"><a href="/for-authors/language-editing/10-suggested-resources-for-more-tips-on-language-editing-in-the-sciences" >10. Suggested resources for more tips on language editing in the sciences</a></li><li class="item-499"><a href="/images/stories/author/EnglishGuide-2021.pdf" target="_blank" >Full Guide (PDF file)</a></li></ul></li><li class="item-178 deeper parent"><span class="separator">LaTeX issues</span> <ul><li class="item-370"><a href="/for-authors/latex-issues/texnical-background-information" >TeXnical background information </a></li><li class="item-369"><a href="/for-authors/latex-issues/the-preamble-of-your-tex-file" >The preamble of your TEX file</a></li><li class="item-371"><a href="/for-authors/latex-issues/the-manuscript-header" >The manuscript header</a></li><li class="item-391"><a href="/for-authors/latex-issues/including-author-names-using-non-roman-alphabets" >Including author names using non-Roman alphabets</a></li><li class="item-372"><a href="/for-authors/latex-issues/the-main-text" >The main text</a></li><li class="item-373"><a href="/for-authors/latex-issues/figures" >Figures</a></li><li class="item-374"><a href="/for-authors/latex-issues/tables" >Tables</a></li><li class="item-375"><a href="/for-authors/latex-issues/multi-media" >Multimedia </a></li><li class="item-376"><a href="/for-authors/latex-issues/references" >References </a></li><li class="item-377"><a href="/for-authors/latex-issues/typography" >Typography</a></li><li class="item-378"><a href="/for-authors/latex-issues/appendices" >Appendices </a></li><li class="item-380"><a href="/for-authors/latex-issues/astronomical-objects-linking-to-databases" >Astronomical objects: linking to databases </a></li><li class="item-381"><a href="/for-authors/latex-issues/latex-examples" >LaTeX examples</a></li><li class="item-466"><a href="/for-authors/latex-issues/information-files" >Information files</a></li></ul></li><li class="item-456"><a href="https://writingstudio.aws.edpsciences.org/login" target="_blank" >Writing studio</a></li><li class="item-459"><a href="/for-authors/submit-an-article" >Submit an article</a></li></ul></li><li class="item-440"><a href="/component/journal_price/" >Subscriber information</a></li><li class="item-514"><a href="/subscribe-to-open-faqs" >Subscribe to Open (S2O) FAQs</a></li><li class="item-437"><a href="/component/services/" >Reader's services</a></li><li class="item-127"><a href="/news" >News</a></li></ul> </nav> </div> <div id="search" class="hidden"> <div class="wrap-search"> <form action="/component/solr/?task=quick_search" method="post"> <div class="wrap"> <div class="inputs"> <input type="text" name="q" /> <button type="submit" value="search"> <span class="ico ico-search" title="Search"></span> </button> </div> <div class="s_volume_page"> <a href="/component/searcharticle/?by=vol-page">Access by volume/page</a> </div> <div class="advanced"><a href="/component/solr/">Advanced Search</a></div> </div> </form> </div> </div> <script type="text/javascript"> jQuery(function ($) { var source = function (request, callback) { var term = request.term; $.ajax({ url: '/index.php', dataType: 'json', method: 'GET', data: { option: 'com_solr', task: 'auto_complete', query: term }, success: function (data) { var suggestions = []; try { data.suggest.default[term].suggestions.forEach(function (s) { suggestions.push(s.term)}) } catch (e) { } callback(suggestions); }, error: function (err) { callback([]); } }); }; $('#search').find('input[name=q]').autocomplete({ source: source }); }); </script> <div class="header-cover"> <div class="wrap"> </div> </div> </header> <main class="aa" id="main"> <!--div class="wrap"> <p>Message placeholder</p> </div--> <div class="wrap" > <div class="breadcrumbs"> <a href="/" class="pathway">Home</a> <img src="/media/system/images/arrow.png" alt="" /> <a href="/component/issues/" class="pathway">All issues</a> <img src="/media/system/images/arrow.png" alt="" /> <a href="/articles/aa/abs/2002/45/contents/contents.html" class="pathway">Volume 395 / No 3 (December I 2002)</a> <img src="/media/system/images/arrow.png" alt="" /> <a href="/articles/aa/abs/2002/45/aah3859/aah3859.html" class="pathway">A&A, 395 3 (2002) 1061-1075</a> <img src="/media/system/images/arrow.png" alt="" /> <span>Abstract</span></div> <div id="content" class="id- full"> <div> <nav class="nav-article nav-buttons"> <ul class="menu"> <li class="item-145 deeper parent"><span class="separator">About A&A</span> <ul><li class="item-137"><a href="/about-aa/aims-and-scope" >Aims and scope</a></li><li class="item-143"><a href="/about-aa/history" >History</a></li><li class="item-136"><a href="/about-aa/editors-of-aa" >Editors of A&A</a></li><li class="item-140"><a href="/about-aa/board-of-directors" >Board of Directors</a></li><li class="item-138"><a href="/about-aa/indexed-in" >Indexed in</a></li><li class="item-139"><a href="/about-aa/copyright" >Copyright</a></li><li class="item-162"><a href="/images/stories/leaflet/aa_leaflet.pdf" target="_blank" >A&A leaflet (PDF)</a></li><li class="item-530"><a href="https://www.edpsciences.org/images/stories/librarians/EDP-AA-S2O.pdf" target="_blank" >A&A S2O leaflet (PDF)</a></li><li class="item-197"><a href="/about-aa/masthead" >Masthead</a></li></ul></li><li class="item-424 deeper parent"><span class="separator">Browse articles</span> <ul><li class="item-427"><a href="/component/issues/?task=all" >All volumes</a></li><li class="item-429"><a href="/component/list/?task=topic" >Special issues</a></li><li class="item-432"><a href="/component/forthcoming/" >Forthcoming</a></li><li class="item-435"><a href="/highlights" >Highlights</a></li><li class="item-221"><a href="/2024-press-releases" >Press releases</a></li><li class="item-533"><a href="/component/issues/?task=images" >Featured images</a></li></ul></li><li class="item-396 deeper parent"><a href="/for-authors" >For authors</a><ul><li class="item-161 deeper parent"><span class="separator">Author information</span> <ul><li class="item-186"><a href="/for-authors/author-information/paper-organization" >Paper organization</a></li><li class="item-232"><a href="/for-authors/author-information/news-from-the-editorial-office" >News from the Editorial Office</a></li><li class="item-192"><a href="/for-authors/author-information/page-charges" >Page charges</a></li><li class="item-173"><a href="/for-authors/author-information/acceptance-stage" >Acceptance stage</a></li><li class="item-159"><a href="/for-authors/author-information/production-stage" >Production stage</a></li><li class="item-233"><a href="/for-authors/author-information/copyright" >Copyright</a></li><li class="item-231"><a href="/for-authors/author-information/open-access" >Open Access</a></li><li class="item-196"><a href="/doc_journal/instructions/aadoc.pdf" target="_blank" >Author's guide (PDF)</a></li></ul></li><li class="item-189 deeper parent"><span class="separator">Language editing</span> <ul><li class="item-502"><a href="/for-authors/language-editing/1-introduction" >1. Introduction</a></li><li class="item-472"><a href="/for-authors/language-editing/2-main-guidelines" >2. Main guidelines for A&A style</a></li><li class="item-475"><a href="/for-authors/language-editing/3-general-structure" >3. General structure</a></li><li class="item-478"><a href="/for-authors/language-editing/4-uk-versus-us-spelling-and-grammar" >4. UK versus US spelling and grammar</a></li><li class="item-481"><a href="/for-authors/language-editing/5-punctuation-and-style-concerns-regarding-equations-figures-tables-and-footnotes" >5. Punctuation and style concerns regarding equations, figures, tables, and footnotes</a></li><li class="item-484"><a href="/for-authors/language-editing/6-verb-tenses" >6. Verb tenses</a></li><li class="item-487"><a href="/for-authors/language-editing/7-general-hyphenation-guide" >7. General hyphenation guide</a></li><li class="item-490"><a href="/for-authors/language-editing/8-common-editing-issues" >8. Common editing issues</a></li><li class="item-493"><a href="/for-authors/language-editing/9-measurements-and-their-descriptions" >9. Measurements and their descriptions</a></li><li class="item-496"><a href="/for-authors/language-editing/10-suggested-resources-for-more-tips-on-language-editing-in-the-sciences" >10. Suggested resources for more tips on language editing in the sciences</a></li><li class="item-499"><a href="/images/stories/author/EnglishGuide-2021.pdf" target="_blank" >Full Guide (PDF file)</a></li></ul></li><li class="item-178 deeper parent"><span class="separator">LaTeX issues</span> <ul><li class="item-370"><a href="/for-authors/latex-issues/texnical-background-information" >TeXnical background information </a></li><li class="item-369"><a href="/for-authors/latex-issues/the-preamble-of-your-tex-file" >The preamble of your TEX file</a></li><li class="item-371"><a href="/for-authors/latex-issues/the-manuscript-header" >The manuscript header</a></li><li class="item-391"><a href="/for-authors/latex-issues/including-author-names-using-non-roman-alphabets" >Including author names using non-Roman alphabets</a></li><li class="item-372"><a href="/for-authors/latex-issues/the-main-text" >The main text</a></li><li class="item-373"><a href="/for-authors/latex-issues/figures" >Figures</a></li><li class="item-374"><a href="/for-authors/latex-issues/tables" >Tables</a></li><li class="item-375"><a href="/for-authors/latex-issues/multi-media" >Multimedia </a></li><li class="item-376"><a href="/for-authors/latex-issues/references" >References </a></li><li class="item-377"><a href="/for-authors/latex-issues/typography" >Typography</a></li><li class="item-378"><a href="/for-authors/latex-issues/appendices" >Appendices </a></li><li class="item-380"><a href="/for-authors/latex-issues/astronomical-objects-linking-to-databases" >Astronomical objects: linking to databases </a></li><li class="item-381"><a href="/for-authors/latex-issues/latex-examples" >LaTeX examples</a></li><li class="item-466"><a href="/for-authors/latex-issues/information-files" >Information files</a></li></ul></li><li class="item-456"><a href="https://writingstudio.aws.edpsciences.org/login" target="_blank" >Writing studio</a></li><li class="item-459"><a href="/for-authors/submit-an-article" >Submit an article</a></li></ul></li><li class="item-440"><a href="/component/journal_price/" >Subscriber information</a></li><li class="item-514"><a href="/subscribe-to-open-faqs" >Subscribe to Open (S2O) FAQs</a></li><li class="item-437"><a href="/component/services/" >Reader's services</a></li><li class="item-127"><a href="/news" >News</a></li></ul> </nav> <div id="system-message-container"> </div> <div class="flexme flexme-article"> <div class="article-content"> <div> <div class="special_article green">Free Access</div> </div> <div class="summary " > <table> <tr> <th valign="top"> Issue </th> <td width="10"></td> <td> <div> A&A </div> <div><strong>Volume </strong>395, Number <strong>3</strong>, December I 2002 </div> </td> <tr><td colspan="3" ></td></tr> <tr><td colspan="3" class="sep_issue"></td></tr> </tr> <tr> <th> Page(s) </th> <td></td> <td>1061 - 1075</td> </tr> <tr> <th>Section</th> <td></td> <td>Numerical methods and codes</td> </tr> <tr> <th>DOI</th> <td></td> <td> <a href="https://doi.org/10.1051/0004-6361:20021326"> https://doi.org/10.1051/0004-6361:20021326 </a> </td> </tr> <tr> <th>Published online</th> <td></td> <td> 18 November 2002 </td> </tr> </table> </div> <div id="article"> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"> <div id="contenu-min"> <div id="head">A&A 395, 1061-1075 (2002)<h2 class="title">Representations of world coordinates in FITS</h2> <div class="article-authors"><p class="bold"><span id="aah3859-author-1" data-url="/component/author/?dkey=10.1051/0004-6361:20021326&n=1" class="author">E. W. Greisen</span><sup>1</sup> and <span id="aah3859-author-2" data-url="/component/author/?dkey=10.1051/0004-6361:20021326&n=2" class="author">M. R. Calabretta</span><sup>2</sup></p></div> <p class="aff"> <sup>1</sup> National Radio Astronomy Observatory, PO Box O, Socorro, NM 87801-0387, USA <br> <sup>2</sup> Australia Telescope National Facility, PO Box 76, Epping, NSW 1710, Australia <br></p> <p class="corresp">Corresponding author: E. W. Greisen, egreisen@nrao.edu </p> <p class="history"><span class="bold">Received: </span> 24 July 2002 <br><span class="bold">Accepted: </span> 9 September 2002 </p> <p class="bold"><a name="abs"></a>Abstract</p> <p>The initial descriptions of the FITS format provided a simplified method for describing the physical coordinate values of the image pixels, but deliberately did not specify any of the detailed conventions required to convey the complexities of actual image coordinates. Building on conventions in wide use within astronomy, this paper proposes general extensions to the original methods for describing the world coordinates of FITS data. In subsequent papers, we apply these general conventions to the methods by which spherical coordinates may be projected onto a two-dimensional plane and to frequency/wavelength/velocity coordinates. </p> <div class="kword"><p><span class="bold">Key words: </span>methods: data analysis / techniques: image processing / astronomical data bases: miscellaneous</p></div> </div> <p><i>© ESO, 2002</i></p> </div> </div> <div id="metrics-tabs" data-doi="10.1051/0004-6361:20021326" data-edps_ref="aah3859"> <nav class="toolbar"> <button class="toolbar-item" id="metrics-siq">Current usage metrics</button> <button class="toolbar-item" id="info">About article metrics</button> <button class="toolbar-item" id="return">Return to article</button> </nav> <div class="panel" data-for="metrics-siq"> </div> <div class="panel" data-for="metrics-alm"></div> <div class="panel" data-for="info"> <p>Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.</p> <p>Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.</p> <div class="msg msg-info"> <span class="ico ico-info"></span> <div> <p>Initial download of the metrics may take a while.</p> </div> </div> </div> </div> <script type="text/javascript" src="/templates/source/js/metrics-tab.js"></script> </div> <nav class="article"> <div class="module_title"> <a href="/">Homepage</a> </div> <div class="nav-section"><div class="title_toc"> <ul class="menu browse"> <li class="item-452"><a class=" link-volumes" href="/component/issues/?task=all" >All volumes</a></li><li class="item-453"><a href="/component/list/?task=topic" >Special issues</a></li><li class="item-451"><a class=" link-forth" href="/component/forthcoming/" >Forthcoming articles</a></li><li class="item-448"><a class=" link-pr" href="/2022-press-releases" >Press releases</a></li></ul> <a href="/articles/aa/abs/2002/45/contents/contents.html">Table of Contents</a></div></div> <div class="nav-section files"> <h2>Article contents</h2><div class="article_doc"><ul><li><a href="/articles/aa/abs/2002/45/aah3859/aah3859.html" title="Abstract" class="current">Abstract</a></li><li><a href="/articles/aa/full/2002/45/aah3859/aah3859.html" title="Full HTML">Full HTML</a></li><li><a href="/articles/aa/pdf/2002/45/aah3859.pdf" title="PDF (246 KB)">PDF (246 KB)</a></li><li><a href="/articles/aa/ref/2002/45/aah3859/aah3859.html" title="References">References</a></li></ul> </div> </div> <div class="nav-section databases"> <h2>Database links</h2><div class="article_doc"><ul><li><a href="https://ui.adsabs.harvard.edu/#abs/2002A%26A...395.1061G" title="Article abstracts available on the Astrophysics Data System" class="related-database-link" target="_blank">NASA ADS Abstract Service</a></li></ul> </div> </div> <div class="nav-section stats"><h2>Metrics</h2><script type='text/javascript' src='https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js'></script><ul><li><a id="show-metrics">Show article metrics</a></li><li class="altmetrics"><div class='altmetric-embed' data-doi="10.1051/0004-6361:20021326" data-hide-no-mentions="true"></div></li></ul> </div> <div class="nav-section servs"><h2>Services</h2><ul><li><strong>Articles citing this article</strong><br /><div style="margin-left:8px"><a href="https://www.aanda.org/component/citedby/?task=crossref&doi=10.1051/0004-6361:20021326">CrossRef (160)</a></div></li><li><strong>Same authors</strong><br /><div style="margin-left:8px">- <a href="https://www.aanda.org/component/solr/?task=authors&tool=google&dkey=10.1051/0004-6361:20021326" target="_blank">Google Scholar</a></div><div style="margin-left:8px">- <a href="https://www.aanda.org/component/solr/?task=authors&tool=ads&dkey=10.1051/0004-6361:20021326" target="_blank">NASA ADS</a></div><div style="margin-left:8px">- <a href="https://www.aanda.org/component/solr/?task=authors&dkey=10.1051/0004-6361:20021326" target="_blank">EDP Sciences database</a></div></li><div class="separator"></div><li><a href="https://www.aanda.org/component/recommend/?type=article&dkey=10.1051/0004-6361:20021326">Recommend this article</a></li><li><a href="https://www.aanda.org/component/kindle/?dkey=10.1051/0004-6361:20021326" title="Send this article to my Kindle">Send to my Kindle</a></li><li><a href="https://www.aanda.org/component/makeref/?task=show&type=html&doi=10.1051/0004-6361:20021326">Download citation</a></li></ul> </div> <div class="nav-section related"> <h2>Related Articles</h2> <script type="text/javascript"> jQuery(function ($) { $(document).ready(function() { $('.nav-toggle').click(function() { var collapse_content_selector = $(this).attr('href'); var toggle_switch = $(this); $(collapse_content_selector).toggle(function() { if ($(this).css('display') == 'none') { toggle_switch.html('More'); } else { toggle_switch.html('Less'); } }); }); }); }); </script> <div class="articles"> <a href="https://www.aanda.org/articles/aa/abs/2006/14/aa4262-05/aa4262-05.html" class="title">Coordinate systems for solar image data</a> <br /> A&A 449, 791-803 (2006)<br /> <div class="separator"></div> <a href="https://www.aanda.org/articles/aa/abs/2006/05/aa3818-05/aa3818-05.html" class="title">Representations of spectral coordinates in FITS</a> <br /> A&A 446, 747-771 (2006)<br /> <div class="separator"></div> <a href="https://www.aanda.org/articles/aa/abs/2010/16/aa15362-10/aa15362-10.html" class="title">Definition of the Flexible Image Transport System (FITS), version 3.0</a> <br /> A&A 524, A42 (2010)<br /> <div class="separator"></div> </div> <div id="searchmlt" class="articles" style="display:none"> <div class="separator"></div> <a href="https://www.aanda.org/articles/aa/abs/2002/45/aah3860/aah3860.html" class="title">Representations of celestial coordinates in FITS</a> <br /> A&A 395, 1077-1122 (2002)<br /> <div class="separator"></div> <a href="https://www.aanda.org/articles/aa/abs/2001/34/aah2901/aah2901.html" class="title">Definition of the Flexible Image Transport System (FITS)</a> <br /> A&A 376, 359-380 (2001)<br /> <div class="separator"></div> </div> </ul> <button href="#searchmlt" class="nav-toggle">More</button> </div> <div class="nav-section bookmark"> <h2>Bookmarking</h2> <ul> <li> <a href="https://www.facebook.com/share.php?u=https://doi.org/10.1051/0004-6361:20021326" onclick="return fbs_click('https://doi.org/10.1051/0004-6361:20021326', 'Representations of world coordinates in FITS');" title="Share on Facebook" target="_blank" onclick="_gaq.push(['_trackPageview', '/bookmarking/Facebook/Representations of world coordinates in FITS']);"> <span class="ico ico-s ico-facebook"></span> </a> </li> <li> <a title="Share on Twitter" href="https://twitter.com/intent/tweet?text=Representations of world coordinates in FITS.%20https://doi.org/10.1051/0004-6361:20021326%20via%20@AandA_journal" class="twitter-share-button" data-count="none" target="_blank" onclick="_gaq.push(['_trackPageview', '/bookmarking/Twitter/Representations of world coordinates in FITS']);"> <span class="ico ico-s ico-twitter"></span> </a> </li> <li> <a title="Share on LinkedIn" href="https://www.linkedin.com/shareArticle?mini=true&url=https://doi.org/10.1051/0004-6361:20021326" onclick="_gaq.push(['_trackPageview', '/bookmarking/LinkedIn/Representations of world coordinates in FITS']);"> <span class="ico ico-s ico-linkedin"></span> </a> </li> <li> <a title="Share on Sina Weibo" href="https://service.weibo.com/share/share.php?title=Representations of world coordinates in FITS&url=https://doi.org/10.1051/0004-6361:20021326" target="_blank" onclick="_gaq.push(['_trackPageview', '/bookmarking/Weibo/Representations of world coordinates in FITS']);"> <span class="ico ico-s ico-sinaweibo"></span> </a> </li> <li> <a title="Add this article to your Mendeley library" href="https://www.mendeley.com/import/?doi=10.1051/0004-6361:20021326" onclick="_gaq.push(['_trackPageview', '/bookmarking/Mendeley/Representations of world coordinates in FITS']);"> <span class="ico ico-s ico-mendeley"></span> <svg class="share-icon-svg" viewBox="0 0 32 32" xmlns="https://www.w3.org/2000/svg"> <title>Mendeley</title> <path class="share-icon-svg-mendeley" d="M0 0h32v32H0z"/> <path class="share-icon-svg" d="M25.9 19.14a2.85 2.85 0 0 1 .1.86 2.64 2.64 0 0 1-.2.8 1.82 1.82 0 0 1-.42.67 2.1 2.1 0 0 1-.64.42 1.65 1.65 0 0 1-1.65-.2 2 2 0 0 1-.88-1.53 2.57 2.57 0 0 1 0-.6 3.24 3.24 0 0 1 .15-.57 3.17 3.17 0 0 0 .14-.37 1.42 1.42 0 0 0 .07-.4 1.58 1.58 0 0 0-.1-.7 1.52 1.52 0 0 0-.4-.53 1.67 1.67 0 0 0-.36-.28 2.94 2.94 0 0 0-.4-.2 3.58 3.58 0 0 0-2.44 0l-.34.18a1.65 1.65 0 0 0-.3.2 1.42 1.42 0 0 0-.47.68 1.6 1.6 0 0 0 0 .83 1.22 1.22 0 0 0 .16.44 2.18 2.18 0 0 1 .2 1.47 2.07 2.07 0 0 1-.77 1.25 1.62 1.62 0 0 1-.56.3 2.48 2.48 0 0 1-.62.13h-.48a1.54 1.54 0 0 1-.48-.12 2.2 2.2 0 0 1-.84-.64 2.17 2.17 0 0 1-.42-1 1.7 1.7 0 0 1 0-.7 2.58 2.58 0 0 1 .22-.66 1.8 1.8 0 0 0 .18-.56 1.56 1.56 0 0 0 0-.6 1.15 1.15 0 0 0-.15-.37 1.68 1.68 0 0 0-.32-.33 2.4 2.4 0 0 0-.42-.3 1.8 1.8 0 0 0-.46-.2 3.8 3.8 0 0 0-1.28-.18 3.3 3.3 0 0 0-1.26.32.84.84 0 0 0-.22.12l-.24.16a1.54 1.54 0 0 0-.53.73 1.6 1.6 0 0 0 0 .93 1.47 1.47 0 0 0 .06.23 1.84 1.84 0 0 0 .1.24 2.33 2.33 0 0 1 .17.9 2.55 2.55 0 0 1-.2.94 1.94 1.94 0 0 1-.74.85 1.7 1.7 0 0 1-1 .26 1.57 1.57 0 0 1-.7-.2 2.45 2.45 0 0 1-.6-.48 1.6 1.6 0 0 1-.33-.56 2.94 2.94 0 0 1-.23-.62 3 3 0 0 1 0-.55 2.06 2.06 0 0 1 .1-.54 1.2 1.2 0 0 1 .12-.35 1.37 1.37 0 0 1 .22-.28l.3-.28a2 2 0 0 1 .36-.22 1.82 1.82 0 0 1 .4-.15 1.4 1.4 0 0 1 .44 0 1.27 1.27 0 0 0 .35 0 1.17 1.17 0 0 0 .32-.1.94.94 0 0 0 .38-.28 1.06 1.06 0 0 0 .2-.4 1.3 1.3 0 0 0 .14-.42 3.4 3.4 0 0 0 0-.44v-.24q0-.37-.06-.73t-.1-.7a.12.12 0 0 0 0-.08.12.12 0 0 1 0-.08 2.6 2.6 0 0 1-.18-.9 4.14 4.14 0 0 1 0-.63 4.26 4.26 0 0 1 .1-.63 3.45 3.45 0 0 1 .8-1.35 2.83 2.83 0 0 1 1.3-.74 2.57 2.57 0 0 1 1.7.12 2.9 2.9 0 0 1 1.35 1.15l.12.18.14.18.33.3.32.34a1 1 0 0 0 .27.22 1.2 1.2 0 0 0 .33.13 1.17 1.17 0 0 0 .5 0 1.15 1.15 0 0 0 .46-.22l.23-.2.2-.23.27-.3.26-.3v-.14a3.08 3.08 0 0 1 .88-.92 2.7 2.7 0 0 1 3.2.13A2.93 2.93 0 0 1 23 12.63a4.53 4.53 0 0 1 0 .9 3.67 3.67 0 0 1-.17.86 1.9 1.9 0 0 0-.06.28v.28a5.7 5.7 0 0 0-.08.66 5.8 5.8 0 0 0 0 .66 1.65 1.65 0 0 0 0 .24v.24a1.3 1.3 0 0 0 .33.66 1.13 1.13 0 0 0 .63.3h.38a1.88 1.88 0 0 1 1.07.27 1.66 1.66 0 0 1 .8 1.17zM16 17.68a1.73 1.73 0 0 0 1.44-.68 2.25 2.25 0 0 0 .56-1.43 2.18 2.18 0 0 0-.6-1.5 1.83 1.83 0 0 0-1.4-.63 1.8 1.8 0 0 0-1.4.63 2.16 2.16 0 0 0-.56 1.5A2.3 2.3 0 0 0 14.6 17a1.7 1.7 0 0 0 1.4.68z"/> </svg> </a> </li> </ul> </div> <div class="nav-section account"> <ul> <li> <a href="/component/services/"><span class="ico ico-account"></span> Reader's services</a> </li> <li> <a href="/component/services/?label=toc_email"><span class="ico ico-alert"></span> Email-alert</a> </li> </ul> </div> </nav> </div> <div class="clear"></div> </div> </div> </main> <footer> <div class="footer-journal"> <div class="wrap"> <div class="footer-infos"> <h3>Astronomy & Astrophysics (A&A)</h3> <div class="flexme flexme3"> <div class="c13"> <p> Editor-in-Chief: T. Forveille<br /> Letters Editor-in-Chief: J. Alves<br /> Managing Editor: D. Elbaz <br /> </p> </div> <div class="c13"> <p>ISSN: 0004-6361 ; e-ISSN: 1432-0746<br /> Frequency: 12 volumes per year<br /> Published by: EDP Sciences<br /> </p> </div> <div class="c13"> <p> © The European Southern Observatory (<a target="_blank" href="http://www.eso.org/">ESO</a>) </p> </div> </div> </div> <div class="footer-social"> <ul class="ico-social"> <li><a class="twitter" title="Follow us on twitter" target="_blank" href="https://twitter.com/AandA_journal"></a></li> <li><a class="facebook" title="Follow us on Facebook" target="_blank" href="https://www.facebook.com/Astronomy-Astrophysics-192738067986000/"></a></li> <!--li><a class="linkedin" title="Follow us on LinkedIn" target="_blank" href="https://www.linkedin.com/company/edp-sciences"></a></li--> <!--li><a class="google" title="Follow us on Google+" target="_blank" href="https://plus.google.com/+EdpsciencesOrg"></a></li--> <li><a class="rss" title="Acc茅der aux flux RSS" href="/component/rsslist/?task=journal"></a></li> <li><a class="alert" title="Alerte courriel" href="/component/services/?label=toc_email"></a></li> </ul> </div> </div> </div> <div> </div> <div class="footer-edp"> <div class="wrap"> <a href="https://www.edpsciences.org/" target="_blank" title="EDP Sciences website"><img src="/templates/source/images/logos/logo_edp_fff.svg" alt="EDP Sciences"></a> <ul class="menu"> <li class="item-175"><a href="/mentions-legales" >Mentions l茅gales</a></li><li class="item-174"><a href="https://www.edpsciences.org/en/contact-us/contact-form?subject=Astronomy%20%26%20Astrophysics&contactid=5" >Contacts</a></li><li class="item-442"><a href="https://www.edpsciences.org/en/privacy-policy" target="_blank" >Privacy policy</a></li></ul> </div> </div> <div class="footer-ptf"> <div class="wrap"> <div class="position-footer-ptf"></div> <div class="link-vfp"><a href="https://www.vision4press.org" target="_blank">A Vision4Press website</a></div> </div> </div> </footer> </div> <script src="/templates/source/js/mmenu2/dist/js/jquery.mmenu.all.min.js"></script> <script src="/templates/template1/js/script.js"></script> <span class="translations" data-name="separator_and" data-value="and"></span> <span class="translations" data-name="select_all" data-value="Select all"></span> <span class="translations" data-name="unselect_all" data-value="Unselect all"></span> <span class="translations" data-name="show_short_summary" data-value="Show short summary"></span> <span class="translations" data-name="hide_short_summary" data-value="Hide short summary"></span> <span class="translations" data-name="cookie_text" data-value="By using this website, you agree that EDP Sciences may store web audience measurement cookies and, on some pages, cookies from social networks. <a href='/component/cookie_policy/'>More information and setup</a>"></span> <span class="translations" data-name="cookie_close" data-value="Click to close this notification"></span> <span class="translations" data-name="cookie_close_btn" data-value="OK"></span> <span class="translations" data-name="loading" data-value="Loading author..."></span> <span class="translations" data-name="view_fullscreen" data-value="Click to view fullscreen"></span> <span class="translations" data-name="hide_fullscreen" data-value="Click anywhere to hide the fullscreen overlay"></span> <span class="translations" data-name="play_movie" data-value="Click to play the movie"></span> <span class="translations" data-name="cookie_is_mobile" data-value=""></span> <span class="translations" data-name="add_to_cart" data-value="Add to cart"></span> <span class="translations" data-name="remove_from_cart" data-value="Remove from cart"></span> <span class="translations" data-name="loading_cart" data-value="Loading..."></span> <span class="translations" data-name="empty_cart" data-value="Your cart is empty"></span> <span class="translations" data-name="terms_agreeement" data-value="You must agree the Purchase Agreement Terms and Conditions."></span> <span class="translations" data-name="makeref_url" data-value="/component/makeref/?task=show&type=html&doi="></span> <span class="translations" data-name="set_cart_article_status_url" data-value="/component/services/?task=set_cart_article_status"></span> <span class="translations" data-name="get_shopping_cart_url" data-value="/component/services/?task=get_shopping_cart_list"></span> <span class="translations" data-name="clear_shopping_cart_url" data-value="/component/services/?task=clear_shopping_cart"></span> <span class="translations" data-name="get_billing_url" data-value="/component/services/?label=ppv&task=get_billing"></span> <span class="translations" data-name="authors_url" data-value="/component/article/?task=get_authors"></span> <span id="google_analytics" data-host="ovh-canada" data-domain="www.aanda.org" data-t1="UA-39520934-1" data-t2="UA-5187131-2" class="hidden"></span> <div id="wait" style="display:none"></div> <script src="/templates/source/js/cookie.js"></script> <script src="/templates/source/js/common.js"></script> </body> </html>