CIE 1931 color space

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vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Meaning_of_X,_Y_and_Z"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Meaning of <i>X</i>, <i>Y</i> and <i>Z</i></span> </div> </a> <ul id="toc-Meaning_of_X,_Y_and_Z-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-CIE_standard_observer" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#CIE_standard_observer"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>CIE standard observer</span> </div> </a> <button aria-controls="toc-CIE_standard_observer-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 CIE standard observer subsection</span> </button> <ul id="toc-CIE_standard_observer-sublist" class="vector-toc-list"> <li id="toc-Color_matching_functions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Color_matching_functions"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Color matching functions</span> </div> </a> <ul id="toc-Color_matching_functions-sublist" class="vector-toc-list"> <li id="toc-Analytical_approximation" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Analytical_approximation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Analytical approximation</span> </div> </a> <ul id="toc-Analytical_approximation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Computing_XYZ_from_spectral_data" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Computing_XYZ_from_spectral_data"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Computing XYZ from spectral data</span> </div> </a> <ul id="toc-Computing_XYZ_from_spectral_data-sublist" class="vector-toc-list"> <li id="toc-Emissive_case" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Emissive_case"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1</span> <span>Emissive case</span> </div> </a> <ul id="toc-Emissive_case-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reflective_and_transmissive_cases" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Reflective_and_transmissive_cases"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.2</span> <span>Reflective and transmissive cases</span> </div> </a> <ul id="toc-Reflective_and_transmissive_cases-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-CIE_xy_chromaticity_diagram_and_the_CIE_xyY_color_space" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#CIE_xy_chromaticity_diagram_and_the_CIE_xyY_color_space"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>CIE xy <span><span>chromaticity diagram</span></span> and the CIE xyY color space</span> </div> </a> <button aria-controls="toc-CIE_xy_chromaticity_diagram_and_the_CIE_xyY_color_space-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 CIE xy <span><span>chromaticity diagram</span></span> and the CIE xyY color space subsection</span> </button> <ul id="toc-CIE_xy_chromaticity_diagram_and_the_CIE_xyY_color_space-sublist" class="vector-toc-list"> <li id="toc-Mixing_colors_specified_with_the_CIE_xy_chromaticity_diagram" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mixing_colors_specified_with_the_CIE_xy_chromaticity_diagram"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Mixing colors specified with the CIE xy chromaticity diagram</span> </div> </a> <ul id="toc-Mixing_colors_specified_with_the_CIE_xy_chromaticity_diagram-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Definition_of_the_CIE_XYZ_color_space" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definition_of_the_CIE_XYZ_color_space"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Definition of the CIE XYZ color space</span> </div> </a> <button aria-controls="toc-Definition_of_the_CIE_XYZ_color_space-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 Definition of the CIE XYZ color space subsection</span> </button> <ul id="toc-Definition_of_the_CIE_XYZ_color_space-sublist" class="vector-toc-list"> <li id="toc-CIE_RGB_color_space" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#CIE_RGB_color_space"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>CIE RGB color space</span> </div> </a> <ul id="toc-CIE_RGB_color_space-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Grassmann's_Laws" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Grassmann's_Laws"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Grassmann's Laws</span> </div> </a> <ul id="toc-Grassmann's_Laws-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Construction_of_the_CIE_XYZ_color_space_from_the_Wright–Guild_data" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Construction_of_the_CIE_XYZ_color_space_from_the_Wright–Guild_data"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Construction of the CIE XYZ color space from the Wright–Guild data</span> </div> </a> <ul id="toc-Construction_of_the_CIE_XYZ_color_space_from_the_Wright–Guild_data-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Subsequent_refinements" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Subsequent_refinements"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Subsequent refinements</span> </div> </a> <ul id="toc-Subsequent_refinements-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</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 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</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 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class="firstHeading mw-first-heading"><span class="mw-page-title-main">CIE 1931 color space</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 18 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-18" 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">18 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%84%D9%81%D8%B6%D8%A7%D8%A1_%D8%A7%D9%84%D9%84%D9%88%D9%86%D9%8A_%D8%B3%D9%8A_%D8%A2%D9%8A_%D8%A5%D9%8A_1931" title="الفضاء اللوني سي آي إي 1931 – Arabic" lang="ar" hreflang="ar" data-title="الفضاء اللوني سي آي إي 1931" 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/CIE_1931_XYZ" title="CIE 1931 XYZ – Catalan" lang="ca" hreflang="ca" data-title="CIE 1931 XYZ" 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/CIE_XYZ" title="CIE XYZ – Czech" lang="cs" hreflang="cs" data-title="CIE XYZ" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/CIE-Normvalenzsystem" title="CIE-Normvalenzsystem – German" lang="de" hreflang="de" data-title="CIE-Normvalenzsystem" 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/CIE_1931" title="CIE 1931 – Estonian" lang="et" hreflang="et" data-title="CIE 1931" 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/Espacio_de_color_CIE_1931" title="Espacio de color CIE 1931 – Spanish" lang="es" hreflang="es" data-title="Espacio de color CIE 1931" 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/%D9%81%D8%B6%D8%A7%DB%8C_%D8%B1%D9%86%DA%AF_%D8%B3%DB%8C%E2%80%8C%D8%A2%DB%8C%E2%80%8C%D8%A7%DB%8C%DB%8C_%DB%B1%DB%B9%DB%B3%DB%B1" title="فضای رنگ سی‌آی‌ایی ۱۹۳۱ – Persian" lang="fa" hreflang="fa" data-title="فضای رنگ سی‌آی‌ایی ۱۹۳۱" 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/CIE_XYZ" title="CIE XYZ – French" lang="fr" hreflang="fr" data-title="CIE XYZ" 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/CIE_1931_XYZ" title="CIE 1931 XYZ – Galician" lang="gl" hreflang="gl" data-title="CIE 1931 XYZ" 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/CIE_1931_%EC%83%89_%EA%B3%B5%EA%B0%84" title="CIE 1931 색 공간 – Korean" lang="ko" hreflang="ko" data-title="CIE 1931 색 공간" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/CIE_1931_prostor_boja" title="CIE 1931 prostor boja – Croatian" lang="hr" hreflang="hr" data-title="CIE 1931 prostor boja" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/CIE_XYZ" title="CIE XYZ – Italian" lang="it" hreflang="it" data-title="CIE XYZ" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/CIE_1931_%E8%89%B2%E7%A9%BA%E9%96%93" title="CIE 1931 色空間 – Japanese" lang="ja" hreflang="ja" data-title="CIE 1931 色空間" 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/CIE_1931" title="CIE 1931 – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="CIE 1931" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/CIEXYZ" title="CIEXYZ – Polish" lang="pl" hreflang="pl" data-title="CIEXYZ" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/CIE_1931_XYZ_-v%C3%A4riavaruus" title="CIE 1931 XYZ -väriavaruus – Finnish" lang="fi" hreflang="fi" data-title="CIE 1931 XYZ -väriavaruus" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B3%DB%8C_%D8%A2%D8%A6%DB%8C_%D8%A7%DB%8C_%D8%B1%D9%86%DA%AF%D9%88%DA%BA_%DA%A9%DB%8C_%D8%AC%DA%AF%DB%81" title="سی آئی ای رنگوں کی جگہ – Urdu" lang="ur" hreflang="ur" data-title="سی آئی ای رنگوں کی جگہ" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/CIE_1931%E8%89%B2%E5%BD%A9%E7%A9%BA%E9%97%B4" title="CIE 1931色彩空间 – Chinese" lang="zh" hreflang="zh" data-title="CIE 1931色彩空间" 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 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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">Color space defined by the CIE in 1931</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 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.ambox{display:none!important}}</style><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/CIE_1931_color_space" title="Special:EditPage/CIE 1931 color space">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=%22CIE+1931+color+space%22">"CIE 1931 color space"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22CIE+1931+color+space%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22CIE+1931+color+space%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=%22CIE+1931+color+space%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22CIE+1931+color+space%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22CIE+1931+color+space%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">May 2019</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> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:CIE1931xy_CIERGB.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/CIE1931xy_CIERGB.svg/325px-CIE1931xy_CIERGB.svg.png" decoding="async" width="325" height="345" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/CIE1931xy_CIERGB.svg/488px-CIE1931xy_CIERGB.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/CIE1931xy_CIERGB.svg/650px-CIE1931xy_CIERGB.svg.png 2x" data-file-width="495" data-file-height="526" /></a><figcaption>Gamut of the CIE RGB primaries and location of primaries on the CIE 1931 <i>xy</i> chromaticity diagram</figcaption></figure><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:CIE1931_RGBCMF.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/CIE1931_RGBCMF.svg/325px-CIE1931_RGBCMF.svg.png" decoding="async" width="325" height="206" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/CIE1931_RGBCMF.svg/488px-CIE1931_RGBCMF.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/CIE1931_RGBCMF.svg/650px-CIE1931_RGBCMF.svg.png 2x" data-file-width="1325" data-file-height="840" /></a><figcaption>The CIE 1931 RGB color matching functions normalized to equal areas under the curves. Multiplying the red and green curves by 72.0962 and 1.3791 respectively yields the actual color matching functions. The color matching functions are proportional to the intensities of primaries needed to match the monochromatic test color at the wavelength shown on the horizontal scale.</figcaption></figure> <p>In 1931 the <a href="/wiki/International_Commission_on_Illumination" title="International Commission on Illumination">International Commission on Illumination</a> (CIE) published the <b>CIE 1931 color spaces</b> which define the relationship between the <a href="/wiki/Visible_spectrum" title="Visible spectrum">visible spectrum</a> and the visual sensation of specific colors by human <a href="/wiki/Color_vision" title="Color vision">color vision</a>.<sup id="cite_ref-cie1931_1-0" class="reference"><a href="#cite_note-cie1931-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><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> The CIE color spaces are mathematical models that create a "standard observer", which attempts to predict the perception of unique hues of color. These <a href="/wiki/Color_space" title="Color space">color spaces</a> are essential tools that provide the foundation for measuring color for industry, including inks, dyes, and paints, illumination, color imaging, etc. The CIE color spaces contributed to the development of color television, the creation of instruments for maintaining consistent color in manufacturing processes, and other methods of <a href="/wiki/Color_management" title="Color management">color management</a>. </p><p>The initials <b>CIE</b> come from the French name <a href="/wiki/International_Commission_on_Illumination" title="International Commission on Illumination">"Commission Internationale de l'éclairage"</a>, which has maintained and developed many of the standards in use today relating to <a href="/wiki/Colorimetry" title="Colorimetry">colorimetry</a>. The CIE color spaces were created using data from a series of experiments, where human test subjects adjusted red, green, and blue <a href="/wiki/Primary_colors" class="mw-redirect" title="Primary colors">primary colors</a> to find a visual match to a second, pure color. The original experiments were conducted in the mid 1920s by <a href="/w/index.php?title=William_David_Wright&action=edit&redlink=1" class="new" title="William David Wright (page does not exist)">William David Wright</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://ja.wikipedia.org/wiki/%E3%82%A6%E3%82%A3%E3%83%AA%E3%82%A2%E3%83%A0%E3%83%BB%E3%83%87%E3%83%93%E3%83%83%E3%83%89%E3%83%BB%E3%83%A9%E3%82%A4%E3%83%88" class="extiw" title="ja:ウィリアム・デビッド・ライト">ja</a>]</span> using ten observers<sup id="cite_ref-wright_3-0" class="reference"><a href="#cite_note-wright-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> and John Guild using seven observers.<sup id="cite_ref-guild_4-0" class="reference"><a href="#cite_note-guild-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The experimental results were combined, creating the CIE RGB color space. The CIE XYZ color space was derived from CIE RGB in an effort to simplify the math. </p><p>The CIE 1931 XYZ color space is still widely used, even though it is not perceptually uniform in relation to human vision. In 1976 the CIE published the <a href="/wiki/CIELUV" title="CIELUV">CIELUV</a> and <a href="/wiki/CIELAB" class="mw-redirect" title="CIELAB">CIELAB</a> color spaces, which are derived from XYZ, and are intended to provide more uniform predictions relative to human perception. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Background:_the_human_eye_and_tristimulus_values">Background: the human eye and tristimulus values</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=1" title="Edit section: Background: the human eye and tristimulus values"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Cones_SMJ2_E.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Cones_SMJ2_E.svg/200px-Cones_SMJ2_E.svg.png" decoding="async" width="200" height="151" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Cones_SMJ2_E.svg/300px-Cones_SMJ2_E.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Cones_SMJ2_E.svg/400px-Cones_SMJ2_E.svg.png 2x" data-file-width="287" data-file-height="217" /></a><figcaption>The normalized <a href="/wiki/Spectral_sensitivity" title="Spectral sensitivity">spectral sensitivity</a> of human <a href="/wiki/Cone_cell" title="Cone cell">cone cells</a> of short-, middle- and long-wavelength types</figcaption></figure> <p>The <a href="/wiki/Human_eye" title="Human eye">human eye</a> with normal vision has three kinds of <a href="/wiki/Cone_cell" title="Cone cell">cone cells</a> that sense light, having peaks of <a href="/wiki/Spectral_sensitivity" title="Spectral sensitivity">spectral sensitivity</a> in short ("S", <span class="nowrap">420 nm</span> – <span class="nowrap">440 nm</span>), medium ("M", <span class="nowrap">530 nm</span> – <span class="nowrap">540 nm</span>), and long ("L", <span class="nowrap">560 nm</span> – <span class="nowrap">580 nm</span>) wavelengths. These cone cells underlie human color perception in conditions of medium and high brightness; in very dim light <a href="/wiki/Color_vision" title="Color vision">color vision</a> diminishes, and the low-brightness, monochromatic "night vision" receptors, denominated "<a href="/wiki/Rod_cell" title="Rod cell">rod cells</a>", become effective. Thus, three parameters corresponding to levels of stimulus of the three kinds of cone cells, in principle describe any human color sensation. Weighting a total light power spectrum by the individual spectral sensitivities of the three kinds of cone cells renders three effective values of <a href="/wiki/Stimulus_(physiology)" title="Stimulus (physiology)">stimulus</a>; these three values compose a tristimulus specification of the objective color of the light spectrum. The three parameters, denoted "S", "M", and "L", are indicated using a <a href="/wiki/3-dimensional" class="mw-redirect" title="3-dimensional">3-dimensional</a> space denominated the "<a href="/wiki/LMS_color_space" title="LMS color space">LMS color space</a>", which is one of many color spaces devised to quantify human <a href="/wiki/Color_vision" title="Color vision">color vision</a>. </p><p>A color space maps a range of physically produced colors from mixed light, <a href="/wiki/Pigment" title="Pigment">pigments</a>, etc. to an objective description of color sensations registered in the human eye, typically in terms of tristimulus values, but not usually in the <a href="/wiki/LMS_color_space" title="LMS color space">LMS color space</a> defined by the spectral sensitivities of the <a href="/wiki/Cone_cell" title="Cone cell">cone cells</a>. The <b>tristimulus values</b> associated with a color space can be conceptualized as amounts of three <a href="/wiki/Primary_color" title="Primary color">primary colors</a> in a tri-chromatic, <a href="/wiki/Additive_color" title="Additive color">additive</a> <a href="/wiki/Color_model" title="Color model">color model</a>. In some color spaces, including the LMS and XYZ spaces, the primary colors used are not real colors in the sense that they cannot be generated in any light spectrum. </p><p>The CIE XYZ color space encompasses all color sensations that are visible to a person with average eyesight. That is why CIE XYZ tristimulus values are a device-invariant representation of color.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> It serves as a standard reference against which many other color spaces are defined. A set of color-matching functions, like the spectral sensitivity curves of the <a href="/wiki/LMS_color_space" title="LMS color space">LMS color space</a>, but not restricted to non-negative sensitivities, associates physically produced light spectra with specific tristimulus values. </p><p>Consider two light sources composed of different mixtures of various wavelengths. Such light sources may appear to be the same color; this effect is called "<a href="/wiki/Metamerism_(color)" title="Metamerism (color)">metamerism</a>." Such light sources have the same apparent color to an observer when they produce the same tristimulus values, regardless of the <a href="/wiki/Spectral_power_distribution" title="Spectral power distribution">spectral power distributions</a> of the sources. </p><p>Most wavelengths stimulate two or all three kinds of <a href="/wiki/Cone_cell" title="Cone cell">cone cell</a> because the spectral sensitivity curves of the three kinds overlap. Certain tristimulus values are thus physically impossible: e.g. LMS tristimulus values that are non-zero for the M component and zero for both the L and S components. Furthermore pure spectral colors would, in any normal trichromatic additive color space, e.g., the <a href="/wiki/RGB_color_spaces" title="RGB color spaces">RGB color spaces</a>, imply negative values for at least one of the three <a href="/wiki/Primary_color" title="Primary color">primaries</a> because the <a href="/wiki/Chromaticity" title="Chromaticity">chromaticity</a> would be outside the <a href="/wiki/Color_triangle" title="Color triangle">color triangle</a> defined by the primary colors. To avoid these negative RGB values, and to have one component that describes the perceived <a href="/wiki/Brightness" title="Brightness">brightness</a>, "imaginary" primary colors and corresponding color-matching functions were formulated. The CIE 1931 color space defines the resulting tristimulus values, in which they are denoted by "X", "Y", and "Z".<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> In XYZ space, all combinations of non-negative coordinates are meaningful, but many, such as the primary locations [1, 0, 0], [0, 1, 0], and [0, 0, 1], correspond to <a href="/wiki/Imaginary_color" class="mw-redirect" title="Imaginary color">imaginary colors</a> outside the space of possible LMS coordinates; imaginary colors do not correspond to any spectral distribution of wavelengths and therefore have no physical reality. </p> <div class="mw-heading mw-heading2"><h2 id="Meaning_of_X,_Y_and_Z"><span id="Meaning_of_X.2C_Y_and_Z"></span>Meaning of <i>X</i>, <i>Y</i> and <i>Z</i></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=2" title="Edit section: Meaning of X, Y and Z"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Comparison_between_CIE_luminosity_function_and_M_cone_response.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Comparison_between_CIE_luminosity_function_and_M_cone_response.svg/260px-Comparison_between_CIE_luminosity_function_and_M_cone_response.svg.png" decoding="async" width="260" height="158" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Comparison_between_CIE_luminosity_function_and_M_cone_response.svg/390px-Comparison_between_CIE_luminosity_function_and_M_cone_response.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Comparison_between_CIE_luminosity_function_and_M_cone_response.svg/520px-Comparison_between_CIE_luminosity_function_and_M_cone_response.svg.png 2x" data-file-width="446" data-file-height="271" /></a><figcaption>A comparison between a typical normalized M cone's spectral sensitivity and the CIE 1931 <a href="/wiki/Luminosity_function" class="mw-redirect" title="Luminosity function">luminosity function</a> for a standard observer in <a href="/wiki/Photopic_vision" title="Photopic vision">photopic vision</a></figcaption></figure> <p>In the CIE 1931 model, <i>Y</i> is the <a href="/wiki/Luminance" title="Luminance">luminance</a>, <i>Z</i> is quasi-equal to blue (of CIE RGB), and <i>X</i> is a mix of the three CIE RGB curves chosen to be nonnegative (see <a href="#Definition_of_the_CIE_XYZ_color_space">§ Definition of the CIE XYZ color space</a>). Setting <i>Y</i> as luminance has the useful result that for any given <i>Y</i> value, the XZ plane will contain all possible <a href="/wiki/Chromaticity" title="Chromaticity">chromaticities</a> at that luminance. </p><p>The unit of the tristimulus values <span class="texhtml"><i>X</i></span>, <span class="texhtml"><i>Y</i></span>, and <span class="texhtml"><i>Z</i></span> is often arbitrarily chosen so that <span class="texhtml"><i>Y</i> = 1</span> or <span class="texhtml"><i>Y</i> = 100</span> is the brightest white that a color display supports. In this case, the Y value is known as the <a href="/wiki/Relative_luminance" title="Relative luminance">relative luminance</a>. The corresponding whitepoint values for <span class="texhtml"><i>X</i></span> and <span class="texhtml"><i>Z</i></span> can then be inferred using the <a href="/wiki/Standard_illuminant" title="Standard illuminant">standard illuminants</a>. </p><p>Since the XYZ values are defined much earlier than the characterization of cone cells in the 1950s (by <a href="/wiki/Ragnar_Granit" title="Ragnar Granit">Ragnar Granit</a>),<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> the physiological meaning of these values are known only much later. The Hunt-Pointer-Estevez matrix from the 1980s relates XYZ with LMS.<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> When inverted, it shows how the three cone responses add up to XYZ functions: </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 {\begin{bmatrix}X\\Y\\Z\end{bmatrix}}=\left[{\begin{aligned}1&.910\,20\!\!\!&\!\!-1&.112\,12\!\!\!&\!\!0&.201\,91\\0&.370\,95\!\!\!&\!\!0&.629\,05\!\!\!&\!\!0&\\0&\!\!\!&\!\!0&\!\!\!&\!\!1&.000\,00\end{aligned}}\right]{\begin{bmatrix}L\\M\\S\end{bmatrix}}_{\rm {HPE}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>X</mi> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mo>=</mo> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>.910</mn> <mspace width="thinmathspace" /> <mn>20</mn> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> </mtd> <mtd> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mo>−</mo> <mn>1</mn> </mtd> <mtd> <mn>.112</mn> <mspace width="thinmathspace" /> <mn>12</mn> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> </mtd> <mtd> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mn>0</mn> </mtd> <mtd> <mn>.201</mn> <mspace width="thinmathspace" /> <mn>91</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>.370</mn> <mspace width="thinmathspace" /> <mn>95</mn> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> </mtd> <mtd> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mn>0</mn> </mtd> <mtd> <mn>.629</mn> <mspace width="thinmathspace" /> <mn>05</mn> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> </mtd> <mtd> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mn>0</mn> </mtd> <mtd /> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> </mtd> <mtd> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mn>0</mn> </mtd> <mtd> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> </mtd> <mtd> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mn>1</mn> </mtd> <mtd> <mn>.000</mn> <mspace width="thinmathspace" /> <mn>00</mn> </mtd> </mtr> </mtable> </mrow> <mo>]</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>L</mi> </mtd> </mtr> <mtr> <mtd> <mi>M</mi> </mtd> </mtr> <mtr> <mtd> <mi>S</mi> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">E</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}X\\Y\\Z\end{bmatrix}}=\left[{\begin{aligned}1&.910\,20\!\!\!&\!\!-1&.112\,12\!\!\!&\!\!0&.201\,91\\0&.370\,95\!\!\!&\!\!0&.629\,05\!\!\!&\!\!0&\\0&\!\!\!&\!\!0&\!\!\!&\!\!1&.000\,00\end{aligned}}\right]{\begin{bmatrix}L\\M\\S\end{bmatrix}}_{\rm {HPE}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a15573a77cd48decc68aada921e4ff01a6d24e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:54.421ex; height:9.343ex;" alt="{\displaystyle {\begin{bmatrix}X\\Y\\Z\end{bmatrix}}=\left[{\begin{aligned}1&.910\,20\!\!\!&\!\!-1&.112\,12\!\!\!&\!\!0&.201\,91\\0&.370\,95\!\!\!&\!\!0&.629\,05\!\!\!&\!\!0&\\0&\!\!\!&\!\!0&\!\!\!&\!\!1&.000\,00\end{aligned}}\right]{\begin{bmatrix}L\\M\\S\end{bmatrix}}_{\rm {HPE}}}"></span></dd></dl> <p>In other words, the Z value is solely made up of the S cone response, the Y value a mix of L and M responses, and X value a mix of all three. This fact makes XYZ values analogous to, but different from, the LMS cone responses of the human eye. </p> <div class="mw-heading mw-heading2"><h2 id="CIE_standard_observer">CIE standard observer</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=3" title="Edit section: CIE standard observer"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Due to the distribution of cones in the eye, the tristimulus values depend on the observer's <a href="/wiki/Field_of_view" title="Field of view">field of view</a>. To eliminate this variable, the CIE defined a color-mapping function called the <b>standard (colorimetric) observer</b>, to represent an average human's chromatic response within a 2° arc inside the <a href="/wiki/Fovea_centralis" title="Fovea centralis">fovea</a>. This angle was chosen owing to the belief that the color-sensitive cones resided within a 2° arc of the fovea. Thus the <i>CIE 1931 Standard Observer</i> function is also known as the <i>CIE 1931 2° Standard Observer</i>. A more modern but less-used alternative is the <i>CIE 1964 10° Standard Observer</i>, which is derived from the work of Stiles and Burch,<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> and Speranskaya.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>For the 10° experiments, the observers were instructed to ignore the central 2° spot. The 1964 Supplementary Standard Observer function is recommended when dealing with more than about a 4° field of view. Both standard observer functions are discretized at <span class="nowrap">5 nm</span> wavelength intervals from <span class="nowrap">380 nm</span> to <span class="nowrap">780 nm</span> and distributed by the <a href="/wiki/International_Commission_on_Illumination" title="International Commission on Illumination">CIE</a>.<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> All corresponding values have been calculated from experimentally obtained data using <a href="/wiki/Interpolation" title="Interpolation">interpolation</a>. The standard observer is characterized by three <i>color matching functions</i>. </p><p>There is also a <span class="nowrap">1 nm</span>-interval dataset of CIE 1931 and CIE 1964 provided by Wyszecki 1982.<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> A CIE publication in 1986 appears also to have a 1 nm dataset, probably using the same data.<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> Like the regular <span class="nowrap">5 nm</span> dataset, this dataset is also derived from interpolation. </p><p>The derivation of the CIE standard observer from color matching experiments is given <a href="#Construction_of_the_CIE_XYZ_color_space_from_the_Wright–Guild_data">below</a>, after the description of the CIE RGB space. </p> <div class="mw-heading mw-heading3"><h3 id="Color_matching_functions">Color matching functions</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=4" title="Edit section: Color matching functions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:CIE_1931_XYZ_Color_Matching_Functions.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/CIE_1931_XYZ_Color_Matching_Functions.svg/325px-CIE_1931_XYZ_Color_Matching_Functions.svg.png" decoding="async" width="325" height="197" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/CIE_1931_XYZ_Color_Matching_Functions.svg/488px-CIE_1931_XYZ_Color_Matching_Functions.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8f/CIE_1931_XYZ_Color_Matching_Functions.svg/650px-CIE_1931_XYZ_Color_Matching_Functions.svg.png 2x" data-file-width="446" data-file-height="271" /></a><figcaption>The CIE XYZ standard observer color matching functions</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:CIE1931_RGBCMF.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/CIE1931_RGBCMF.svg/325px-CIE1931_RGBCMF.svg.png" decoding="async" width="325" height="206" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/CIE1931_RGBCMF.svg/488px-CIE1931_RGBCMF.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/CIE1931_RGBCMF.svg/650px-CIE1931_RGBCMF.svg.png 2x" data-file-width="1325" data-file-height="840" /></a><figcaption>The normalized CIE RGB color matching functions</figcaption></figure> <p>The CIE's <b>color matching functions</b> <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 {\overline {x}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {x}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c66d9bb9f712fc5f55bfb7b48777e09320bd56d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.609ex; height:2.843ex;" alt="{\displaystyle {\overline {x}}(\lambda )}"></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 {\overline {y}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>y</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {y}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57dbc1311b7e980c1730d667434ba28cb95dc4d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.446ex; height:2.843ex;" alt="{\displaystyle {\overline {y}}(\lambda )}"></span> 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 {\overline {z}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>z</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {z}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8bd6d3420325c2bc24a30246e0756012932a85b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.372ex; height:2.843ex;" alt="{\displaystyle {\overline {z}}(\lambda )}"></span> are the numerical description of the chromatic response of the <i>observer</i> (described above). They can be thought of as the spectral sensitivity curves of three linear light detectors yielding the CIE tristimulus values <i>X</i>, <i>Y</i> and <i>Z</i>. Collectively, these three functions describe the CIE standard observer.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Analytical_approximation">Analytical approximation</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=5" title="Edit section: Analytical approximation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Table lookup can become impractical for some computational tasks. Instead of referring to the published table, the CIE XYZ color matching functions can be approximated by a sum of <a href="/wiki/Gaussian_function" title="Gaussian function">Gaussian functions</a>, as follows:<sup id="cite_ref-approx_15-0" class="reference"><a href="#cite_note-approx-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>Let <i>g</i>(<i>x</i>) denote a piecewise-Gaussian function, defined 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 g(x;\mu ,\tau _{1},\tau _{2})={\begin{cases}\exp {\bigl (}{-\tau _{1}^{2}(x-\mu )^{2}/2}{\bigr )},&x<\mu ,\\[2mu]\exp {\bigl (}{-\tau _{2}^{2}(x-\mu )^{2}/2}{\bigr )},&x\geq \mu .\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>;</mo> <mi>μ</mi> <mo>,</mo> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing="0.311em 0.2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mi>exp</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <msubsup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>μ</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>,</mo> </mtd> <mtd> <mi>x</mi> <mo><</mo> <mi>μ</mi> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>exp</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <msubsup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>μ</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>,</mo> </mtd> <mtd> <mi>x</mi> <mo>≥</mo> <mi>μ</mi> <mo>.</mo> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g(x;\mu ,\tau _{1},\tau _{2})={\begin{cases}\exp {\bigl (}{-\tau _{1}^{2}(x-\mu )^{2}/2}{\bigr )},&x<\mu ,\\[2mu]\exp {\bigl (}{-\tau _{2}^{2}(x-\mu )^{2}/2}{\bigr )},&x\geq \mu .\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d659cba95a7eb9b93001347d1ae97e432f0bda77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:49.018ex; height:7.509ex;" alt="{\displaystyle g(x;\mu ,\tau _{1},\tau _{2})={\begin{cases}\exp {\bigl (}{-\tau _{1}^{2}(x-\mu )^{2}/2}{\bigr )},&x<\mu ,\\[2mu]\exp {\bigl (}{-\tau _{2}^{2}(x-\mu )^{2}/2}{\bigr )},&x\geq \mu .\end{cases}}}"></span></dd></dl> <p>That is, <i>g</i>(<i>x</i>) resembles a bell curve with its peak at <span class="texhtml"><i>x</i> = <i>μ</i></span>, a spread/standard deviation of <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 1/\tau _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/\tau _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fca30e1c28fd674ea2e65f0580b7082e970711a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.395ex; height:2.843ex;" alt="{\displaystyle 1/\tau _{1}}"></span> to the left of the mean, and spread of <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 1/\tau _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/\tau _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c27beb71bab0bf698a8edc2d3ede921df9c94bdd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.395ex; height:2.843ex;" alt="{\displaystyle 1/\tau _{2}}"></span> to the right of the mean. With the wavelength <i>λ</i> measured in <a href="/wiki/Nanometre" title="Nanometre">nanometers</a>, we then approximate the 1931 color matching functions: </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 {\begin{aligned}{\overline {x}}(\lambda )&=1.056\,g(\lambda ;599.8,0.0264,0.0323)+0.362\,g(\lambda ;442.0,0.0624,0.0374)\\[2mu]&\quad -0.065\,g(\lambda ;501.1,0.0490,0.0382),\\[5mu]{\overline {y}}(\lambda )&=0.821\,g(\lambda ;568.8,0.0213,0.0247)+0.286\,g(\lambda ;530.9,0.0613,0.0322),\\[5mu]{\overline {z}}(\lambda )&=1.217\,g(\lambda ;437.0,0.0845,0.0278)+0.681\,g(\lambda ;459.0,0.0385,0.0725).\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.411em 0.578em 0.578em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>1.056</mn> <mspace width="thinmathspace" /> <mi>g</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo>;</mo> <mn>599.8</mn> <mo>,</mo> <mn>0.0264</mn> <mo>,</mo> <mn>0.0323</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>0.362</mn> <mspace width="thinmathspace" /> <mi>g</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo>;</mo> <mn>442.0</mn> <mo>,</mo> <mn>0.0624</mn> <mo>,</mo> <mn>0.0374</mn> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mspace width="1em" /> <mo>−</mo> <mn>0.065</mn> <mspace width="thinmathspace" /> <mi>g</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo>;</mo> <mn>501.1</mn> <mo>,</mo> <mn>0.0490</mn> <mo>,</mo> <mn>0.0382</mn> <mo stretchy="false">)</mo> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>y</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>0.821</mn> <mspace width="thinmathspace" /> <mi>g</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo>;</mo> <mn>568.8</mn> <mo>,</mo> <mn>0.0213</mn> <mo>,</mo> <mn>0.0247</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>0.286</mn> <mspace width="thinmathspace" /> <mi>g</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo>;</mo> <mn>530.9</mn> <mo>,</mo> <mn>0.0613</mn> <mo>,</mo> <mn>0.0322</mn> <mo stretchy="false">)</mo> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>z</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>1.217</mn> <mspace width="thinmathspace" /> <mi>g</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo>;</mo> <mn>437.0</mn> <mo>,</mo> <mn>0.0845</mn> <mo>,</mo> <mn>0.0278</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>0.681</mn> <mspace width="thinmathspace" /> <mi>g</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo>;</mo> <mn>459.0</mn> <mo>,</mo> <mn>0.0385</mn> <mo>,</mo> <mn>0.0725</mn> <mo stretchy="false">)</mo> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\overline {x}}(\lambda )&=1.056\,g(\lambda ;599.8,0.0264,0.0323)+0.362\,g(\lambda ;442.0,0.0624,0.0374)\\[2mu]&\quad -0.065\,g(\lambda ;501.1,0.0490,0.0382),\\[5mu]{\overline {y}}(\lambda )&=0.821\,g(\lambda ;568.8,0.0213,0.0247)+0.286\,g(\lambda ;530.9,0.0613,0.0322),\\[5mu]{\overline {z}}(\lambda )&=1.217\,g(\lambda ;437.0,0.0845,0.0278)+0.681\,g(\lambda ;459.0,0.0385,0.0725).\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132034f55fb9788049fdaa5ed7be69b9bfbd4723" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.338ex; width:74.508ex; height:13.843ex;" alt="{\displaystyle {\begin{aligned}{\overline {x}}(\lambda )&=1.056\,g(\lambda ;599.8,0.0264,0.0323)+0.362\,g(\lambda ;442.0,0.0624,0.0374)\\[2mu]&\quad -0.065\,g(\lambda ;501.1,0.0490,0.0382),\\[5mu]{\overline {y}}(\lambda )&=0.821\,g(\lambda ;568.8,0.0213,0.0247)+0.286\,g(\lambda ;530.9,0.0613,0.0322),\\[5mu]{\overline {z}}(\lambda )&=1.217\,g(\lambda ;437.0,0.0845,0.0278)+0.681\,g(\lambda ;459.0,0.0385,0.0725).\end{aligned}}}"></span></dd></dl> <p>The squared differences between the above approximation and the measured CIE <i>xyz</i> color matching functions is less than the within-observer variance encountered in the experimental measurements used to form the CIE standards. It is also possible to use fewer gaussian functions, with one gaussian for each "lobe". CIE 1964 fits well with a one-lobe function.<sup id="cite_ref-approx_15-1" class="reference"><a href="#cite_note-approx-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>The CIE XYZ color matching functions are nonnegative, and lead to nonnegative XYZ coordinates for all real colors (that is, for nonnegative light spectra). Other observers, such as for the CIE RGB space or other <a href="/wiki/RGB_color_spaces" title="RGB color spaces">RGB color spaces</a>, are defined by other sets of three color-matching functions, not generally nonnegative, and lead to tristimulus values in those other spaces, which may include negative coordinates for some real colors. </p> <div class="mw-heading mw-heading3"><h3 id="Computing_XYZ_from_spectral_data">Computing XYZ from spectral data</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=6" title="Edit section: Computing XYZ from spectral data"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Emissive_case">Emissive case</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=7" title="Edit section: Emissive case"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The tristimulus values for a color with a <a href="/wiki/Spectral_radiance" title="Spectral radiance">spectral radiance</a> <i>L</i><sub>e,Ω,λ</sub> are given in terms of the standard observer 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 {\begin{aligned}X&=\int _{\lambda }L_{\mathrm {e} ,\Omega ,\lambda }(\lambda )\,{\overline {x}}(\lambda )\,d\lambda ,\\[6mu]Y&=\int _{\lambda }L_{\mathrm {e} ,\Omega ,\lambda }(\lambda )\,{\overline {y}}(\lambda )\,d\lambda ,\\[6mu]Z&=\int _{\lambda }L_{\mathrm {e} ,\Omega ,\lambda }(\lambda )\,{\overline {z}}(\lambda )\,d\lambda .\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.633em 0.633em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> </msub> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mo>,</mo> <mi mathvariant="normal">Ω</mi> <mo>,</mo> <mi>λ</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>λ</mi> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> </msub> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mo>,</mo> <mi mathvariant="normal">Ω</mi> <mo>,</mo> <mi>λ</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>y</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>λ</mi> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> </msub> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mo>,</mo> <mi mathvariant="normal">Ω</mi> <mo>,</mo> <mi>λ</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>z</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>λ</mi> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}X&=\int _{\lambda }L_{\mathrm {e} ,\Omega ,\lambda }(\lambda )\,{\overline {x}}(\lambda )\,d\lambda ,\\[6mu]Y&=\int _{\lambda }L_{\mathrm {e} ,\Omega ,\lambda }(\lambda )\,{\overline {y}}(\lambda )\,d\lambda ,\\[6mu]Z&=\int _{\lambda }L_{\mathrm {e} ,\Omega ,\lambda }(\lambda )\,{\overline {z}}(\lambda )\,d\lambda .\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f62d8f94207fbbf4909ab58734898c6fcae324d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -9.005ex; width:26.071ex; height:19.176ex;" alt="{\displaystyle {\begin{aligned}X&=\int _{\lambda }L_{\mathrm {e} ,\Omega ,\lambda }(\lambda )\,{\overline {x}}(\lambda )\,d\lambda ,\\[6mu]Y&=\int _{\lambda }L_{\mathrm {e} ,\Omega ,\lambda }(\lambda )\,{\overline {y}}(\lambda )\,d\lambda ,\\[6mu]Z&=\int _{\lambda }L_{\mathrm {e} ,\Omega ,\lambda }(\lambda )\,{\overline {z}}(\lambda )\,d\lambda .\end{aligned}}}"></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 \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span> is the wavelength of the equivalent <a href="/wiki/Monochromatic" class="mw-redirect" title="Monochromatic">monochromatic</a> light (measured in <a href="/wiki/Nanometers" class="mw-redirect" title="Nanometers">nanometers</a>), and customary limits of the integral are <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 \lambda \in [380,780]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>380</mn> <mo>,</mo> <mn>780</mn> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda \in [380,780]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a2085e55423178ed3ce092367c2038d1af45d83" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.498ex; height:2.843ex;" alt="{\displaystyle \lambda \in [380,780]}"></span>. </p><p>The values of <i>X</i>, <i>Y</i>, and <i>Z</i> are bounded if the radiance spectrum <i>L</i><sub>e,Ω,λ</sub> is bounded. </p> <div class="mw-heading mw-heading4"><h4 id="Reflective_and_transmissive_cases">Reflective and transmissive cases</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=8" title="Edit section: Reflective and transmissive cases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The reflective and transmissive cases are very similar to the emissive case, with a few differences. The spectral radiance <i>L</i><sub>e,Ω,λ</sub> is replaced by the spectral <a href="/wiki/Reflectance" title="Reflectance">reflectance</a> (or <a href="/wiki/Transmittance" title="Transmittance">transmittance</a>) <i>S(λ)</i> of the object being measured, multiplied by the spectral power distribution of the illuminant <i>I(λ)</i>. </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 {\begin{aligned}X&={\frac {K}{N}}\int _{\lambda }S(\lambda )\,I(\lambda )\,{\overline {x}}(\lambda )\,d\lambda ,\\[8mu]Y&={\frac {K}{N}}\int _{\lambda }S(\lambda )\,I(\lambda )\,{\overline {y}}(\lambda )\,d\lambda ,\\[8mu]Z&={\frac {K}{N}}\int _{\lambda }S(\lambda )\,I(\lambda )\,{\overline {z}}(\lambda )\,d\lambda ,\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.744em 0.744em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>K</mi> <mi>N</mi> </mfrac> </mrow> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> </msub> <mi>S</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>I</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>λ</mi> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>K</mi> <mi>N</mi> </mfrac> </mrow> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> </msub> <mi>S</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>I</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>y</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>λ</mi> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>K</mi> <mi>N</mi> </mfrac> </mrow> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> </msub> <mi>S</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>I</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>z</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>λ</mi> <mo>,</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}X&={\frac {K}{N}}\int _{\lambda }S(\lambda )\,I(\lambda )\,{\overline {x}}(\lambda )\,d\lambda ,\\[8mu]Y&={\frac {K}{N}}\int _{\lambda }S(\lambda )\,I(\lambda )\,{\overline {y}}(\lambda )\,d\lambda ,\\[8mu]Z&={\frac {K}{N}}\int _{\lambda }S(\lambda )\,I(\lambda )\,{\overline {z}}(\lambda )\,d\lambda ,\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c448fc8038f4d343e3efefd50cdeba2154a14f59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -9.338ex; width:29.978ex; height:19.843ex;" alt="{\displaystyle {\begin{aligned}X&={\frac {K}{N}}\int _{\lambda }S(\lambda )\,I(\lambda )\,{\overline {x}}(\lambda )\,d\lambda ,\\[8mu]Y&={\frac {K}{N}}\int _{\lambda }S(\lambda )\,I(\lambda )\,{\overline {y}}(\lambda )\,d\lambda ,\\[8mu]Z&={\frac {K}{N}}\int _{\lambda }S(\lambda )\,I(\lambda )\,{\overline {z}}(\lambda )\,d\lambda ,\end{aligned}}}"></span></dd></dl> <p>where </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 N=\int _{\lambda }I(\lambda )\,{\overline {y}}(\lambda )\,d\lambda ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> </msub> <mi>I</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>y</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>λ</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=\int _{\lambda }I(\lambda )\,{\overline {y}}(\lambda )\,d\lambda ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd496237d2e34f25e11b5f49cf2a344645679454" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:20.806ex; height:5.676ex;" alt="{\displaystyle N=\int _{\lambda }I(\lambda )\,{\overline {y}}(\lambda )\,d\lambda ,}"></span></dd></dl> <p><i>K</i> is a scaling factor (usually 1 or 100), 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 \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span> is the wavelength of the equivalent <a href="/wiki/Monochromatic" class="mw-redirect" title="Monochromatic">monochromatic</a> light (measured in <a href="/wiki/Nanometers" class="mw-redirect" title="Nanometers">nanometers</a>), and the standard limits of the integral are <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 \lambda \in [380,780]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>380</mn> <mo>,</mo> <mn>780</mn> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda \in [380,780]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a2085e55423178ed3ce092367c2038d1af45d83" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.498ex; height:2.843ex;" alt="{\displaystyle \lambda \in [380,780]}"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="CIE_xy_chromaticity_diagram_and_the_CIE_xyY_color_space">CIE xy <style data-mw-deduplicate="TemplateStyles:r1238216509">.mw-parser-output .vanchor>:target~.vanchor-text{background-color:#b1d2ff}@media screen{html.skin-theme-clientpref-night .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}</style><span class="vanchor"><span id="chromaticity_diagram"></span><span class="vanchor-text">chromaticity diagram</span></span> and the CIE xyY color space</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=9" title="Edit section: CIE xy chromaticity diagram and the CIE xyY color space"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" 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 section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/CIE_1931_color_space" title="Special:EditPage/CIE 1931 color space">improve this section</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 <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">October 2015</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> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:CIE1931xy_blank.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/CIE1931xy_blank.svg/300px-CIE1931xy_blank.svg.png" decoding="async" width="300" height="319" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/CIE1931xy_blank.svg/450px-CIE1931xy_blank.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/CIE1931xy_blank.svg/600px-CIE1931xy_blank.svg.png 2x" data-file-width="495" data-file-height="526" /></a><figcaption>The CIE 1931 color space chromaticity diagram. The outer curved boundary is the spectral (or monochromatic) locus, with wavelengths shown in nanometers. The colors your screen displays in this image are specified using <a href="/wiki/SRGB" title="SRGB">sRGB</a>, so the colors outside the sRGB <a href="/wiki/Gamut" title="Gamut">gamut</a> are not displayed properly. Depending on the <a href="/wiki/Color_space" title="Color space">color space</a> and calibration of your display device, the sRGB colors may not be displayed properly either. This diagram displays the maximally saturated bright colors that can be produced by a <a href="/wiki/Computer_monitor" title="Computer monitor">computer monitor</a> or <a href="/wiki/Television_set" title="Television set">television set</a>.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:CIE-1931_diagram_in_LAB_space.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/CIE-1931_diagram_in_LAB_space.svg/300px-CIE-1931_diagram_in_LAB_space.svg.png" decoding="async" width="300" height="312" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/CIE-1931_diagram_in_LAB_space.svg/450px-CIE-1931_diagram_in_LAB_space.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/CIE-1931_diagram_in_LAB_space.svg/600px-CIE-1931_diagram_in_LAB_space.svg.png 2x" data-file-width="469" data-file-height="487" /></a><figcaption>The CIE 1931 color space chromaticity diagram rendered in terms of the colors of lower saturation and value than those displayed in the diagram above that can be produced by <a href="/wiki/Pigment" title="Pigment">pigments</a>, such as those used in <a href="/wiki/Printing" title="Printing">printing</a>. The color names are from the <a href="/wiki/Munsell_color_system" title="Munsell color system">Munsell color system</a>. The solid curve with dots on it, through the middle, is the <a href="/wiki/Planckian_locus" title="Planckian locus">Planckian locus</a>, with the dots corresponding to a few select <a href="/wiki/Black-body_radiation" title="Black-body radiation">black-body</a> temperatures that are indicated just above the x-axis.</figcaption></figure> <p>Since the <a href="/wiki/Human_eye" title="Human eye">human eye</a> has <a href="/wiki/Cone_cell#Types" title="Cone cell">three types</a> of color sensors that respond to different ranges of <a href="/wiki/Wavelength" title="Wavelength">wavelengths</a>, a full plot of all visible colors is a three-dimensional figure. However, the concept of color can be divided into two parts: brightness and <a href="/wiki/Chromaticity" title="Chromaticity">chromaticity</a>. For example, the color white is a bright color, while the color grey is considered to be a less bright version of that same white. In other words, the chromaticity of white and grey are the same while their brightness differs. </p><p>The CIE XYZ color space was deliberately designed so that the <i>Y</i> parameter is also a measure of the <a href="/wiki/Luminance" title="Luminance">luminance</a> of a color. The chromaticity is then specified by the two derived parameters <i>x</i> and <i>y</i>, two of the three normalized values being functions of all three <a href="#Tristimulus_values">tristimulus values</a> <i>X</i>, <i>Y</i>, and <i>Z</i>: <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><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag needs further explanation. (September 2021)">further explanation needed</span></a></i>]</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 {\begin{aligned}x&={\frac {X}{X+Y+Z}}\\[5mu]y&={\frac {Y}{X+Y+Z}}\\[5mu]z&={\frac {Z}{X+Y+Z}}=1-x-y\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.578em 0.578em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>x</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>X</mi> <mrow> <mi>X</mi> <mo>+</mo> <mi>Y</mi> <mo>+</mo> <mi>Z</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>Y</mi> <mrow> <mi>X</mi> <mo>+</mo> <mi>Y</mi> <mo>+</mo> <mi>Z</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>Z</mi> <mrow> <mi>X</mi> <mo>+</mo> <mi>Y</mi> <mo>+</mo> <mi>Z</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mi>x</mi> <mo>−</mo> <mi>y</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}x&={\frac {X}{X+Y+Z}}\\[5mu]y&={\frac {Y}{X+Y+Z}}\\[5mu]z&={\frac {Z}{X+Y+Z}}=1-x-y\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/873561ef50950673969394936959aced38d64188" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.241ex; margin-bottom: -0.263ex; width:29.557ex; height:18.176ex;" alt="{\displaystyle {\begin{aligned}x&={\frac {X}{X+Y+Z}}\\[5mu]y&={\frac {Y}{X+Y+Z}}\\[5mu]z&={\frac {Z}{X+Y+Z}}=1-x-y\end{aligned}}}"></span></dd></dl> <p>That is, because each tristimulus parameter, <i>X</i>, <i>Y</i>, <i>Z</i>, is divided by the sum of all three, the resulting values, <i>x</i>, <i>y</i>, <i>z</i>, each represent a proportion of the whole and so their sum must be equal to one. Therefore, the value <i>z</i> can be deduced by knowing <i>x</i> and <i>y</i>, and consequently the latter two values are sufficient for describing the chromaticity of any color. </p><p>The derived color space specified by <i>x</i>, <i>y</i>, and <i>Y</i> is known as the CIE xyY color space and is widely used to specify colors in practice. </p><p>The <i>X</i> and <i>Z</i> tristimulus values can be calculated back from the chromaticity values <i>x</i> and <i>y</i> and the <i>Y</i> tristimulus value: <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> </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 {\begin{aligned}X&={\frac {Y}{y}}x,\\[5mu]Z&={\frac {Y}{y}}(1-x-y).\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.578em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>Y</mi> <mi>y</mi> </mfrac> </mrow> <mi>x</mi> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>Y</mi> <mi>y</mi> </mfrac> </mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>x</mi> <mo>−</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}X&={\frac {Y}{y}}x,\\[5mu]Z&={\frac {Y}{y}}(1-x-y).\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f438636eedf7bdbe729e512052e76e1f6addaca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.505ex; width:20.224ex; height:12.176ex;" alt="{\displaystyle {\begin{aligned}X&={\frac {Y}{y}}x,\\[5mu]Z&={\frac {Y}{y}}(1-x-y).\end{aligned}}}"></span></dd></dl> <p>The figure on the right shows the related chromaticity diagram. The outer curved boundary is the <i>spectral locus</i>, with wavelengths shown in nanometers. The chromaticity diagram is a tool to specify how the human eye will experience light with a given spectrum. It cannot specify colors of objects (or printing inks), since the chromaticity observed while looking at an object depends on the light source as well. </p><p>Mathematically the colors of the chromaticity diagram occupy a region of the <a href="/wiki/Projective_plane" title="Projective plane">real projective plane</a>. </p><p>The chromaticity diagram illustrates a number of interesting properties of the CIE XYZ color space: </p> <ul><li>The diagram represents all of the chromaticities visible to the average person. These are shown in color and this region is called the <a href="/wiki/Gamut" title="Gamut">gamut</a> of human vision. The gamut of all visible chromaticities on the CIE plot is the tongue-shaped or horseshoe-shaped figure shown in color. The curved edge of the gamut is called the <i>spectral locus</i> and corresponds to monochromatic light (each point representing a pure hue of a single wavelength), with wavelengths listed in nanometers. The straight edge on the lower part of the gamut is called the <a href="/wiki/Line_of_purples" title="Line of purples">line of purples</a>. These colors, although they are on the border of the gamut, have no counterpart in monochromatic light. Less saturated colors appear in the interior of the figure with white at the center.</li> <li>It is seen that all visible chromaticities correspond to non-negative values of <i>x</i>, <i>y</i>, and <i>z</i> (and therefore to non-negative values of <i>X</i>, <i>Y</i>, and <i>Z</i>).</li> <li>If one chooses any two points of color on the chromaticity diagram, then all the colors that lie in a straight line between the two points can be formed by mixing these two colors. It follows that the gamut of colors must be <a href="/wiki/Convex_set" title="Convex set">convex</a> in shape. All colors that can be formed by mixing three sources are found inside the triangle formed by the source points on the chromaticity diagram (and so on for multiple sources).</li> <li>An equal mixture of two equally bright colors will not generally lie on the midpoint of that <a href="/wiki/Line_segment" title="Line segment">line segment</a>. In more general terms, a distance on the CIE xy chromaticity diagram does not correspond to the degree of difference between two colors. In the early 1940s, <a href="/wiki/David_MacAdam" title="David MacAdam">David MacAdam</a> studied the nature of visual sensitivity to <a href="/wiki/Color_difference" title="Color difference">color differences</a>, and summarized his results in the concept of a <a href="/wiki/MacAdam_ellipse" title="MacAdam ellipse">MacAdam ellipse</a>. Based on the work of MacAdam, the <a href="/wiki/CIE_1960_color_space" title="CIE 1960 color space">CIE 1960</a>, <a href="/wiki/CIE_1964_color_space" title="CIE 1964 color space">CIE 1964</a>, and <a href="/wiki/CIELUV" title="CIELUV">CIE 1976</a> color spaces were developed, with the goal of achieving perceptual uniformity (have an equal distance in the color space correspond to equal differences in color). Although they were a distinct improvement over the CIE 1931 system, they were not completely free of distortion.</li> <li>It can be seen that, given three real sources, these sources cannot cover the gamut of human vision. Geometrically stated, there are no three points within the gamut that form a triangle that includes the entire gamut; or more simply, the gamut of human vision is not a triangle.</li> <li>Light with a <a href="/wiki/Standard_illuminant#Illuminant_E" title="Standard illuminant">flat power spectrum</a> in terms of wavelength (equal power in every <span class="nowrap">1 nm</span> interval) corresponds to the point <span class="nowrap">(<i>x</i>, <i>y</i>) = (1/3, 1/3)</span>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Mixing_colors_specified_with_the_CIE_xy_chromaticity_diagram">Mixing colors specified with the CIE xy chromaticity diagram</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=10" title="Edit section: Mixing colors specified with the CIE xy chromaticity diagram"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When two or more colors are additively mixed, the x and y chromaticity coordinates of the resulting color (x<sub>mix</sub>,y<sub>mix</sub>) may be calculated from the chromaticities of the mixture components (x<sub>1</sub>,y<sub>1</sub>; x<sub>2</sub>,y<sub>2</sub>; …; x<sub>n</sub>,y<sub>n</sub>) and their corresponding luminances (L<sub>1</sub>, L<sub>2</sub>, …, L<sub>n</sub>) with the following formulas:<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> </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 x_{\mathrm {mix} }={\frac {{\dfrac {x_{1}}{y_{1}}}L_{1}+{\dfrac {x_{2}}{y_{2}}}L_{2}+\dots +{\dfrac {x_{n}}{y_{n}}}L_{n}}{{\dfrac {L_{1}}{y_{1}}}+{\dfrac {L_{2}}{y_{2}}}+\dots +{\dfrac {L_{n}}{y_{n}}}}}\quad ,\quad y_{\mathrm {mix} }={\frac {L_{1}+L_{2}+\dots +L_{n}}{{\dfrac {L_{1}}{y_{1}}}+{\dfrac {L_{2}}{y_{2}}}+\dots +{\dfrac {L_{n}}{y_{n}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mstyle> </mrow> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mstyle> </mrow> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mstyle> </mrow> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mstyle> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mstyle> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mstyle> </mrow> </mrow> </mfrac> </mrow> <mspace width="1em" /> <mo>,</mo> <mspace width="1em" /> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mstyle> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mstyle> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mstyle> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{\mathrm {mix} }={\frac {{\dfrac {x_{1}}{y_{1}}}L_{1}+{\dfrac {x_{2}}{y_{2}}}L_{2}+\dots +{\dfrac {x_{n}}{y_{n}}}L_{n}}{{\dfrac {L_{1}}{y_{1}}}+{\dfrac {L_{2}}{y_{2}}}+\dots +{\dfrac {L_{n}}{y_{n}}}}}\quad ,\quad y_{\mathrm {mix} }={\frac {L_{1}+L_{2}+\dots +L_{n}}{{\dfrac {L_{1}}{y_{1}}}+{\dfrac {L_{2}}{y_{2}}}+\dots +{\dfrac {L_{n}}{y_{n}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d050f0c91f9ee3ab6c8d8a662d20e2a0345fb784" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.505ex; width:72.843ex; height:11.676ex;" alt="{\displaystyle x_{\mathrm {mix} }={\frac {{\dfrac {x_{1}}{y_{1}}}L_{1}+{\dfrac {x_{2}}{y_{2}}}L_{2}+\dots +{\dfrac {x_{n}}{y_{n}}}L_{n}}{{\dfrac {L_{1}}{y_{1}}}+{\dfrac {L_{2}}{y_{2}}}+\dots +{\dfrac {L_{n}}{y_{n}}}}}\quad ,\quad y_{\mathrm {mix} }={\frac {L_{1}+L_{2}+\dots +L_{n}}{{\dfrac {L_{1}}{y_{1}}}+{\dfrac {L_{2}}{y_{2}}}+\dots +{\dfrac {L_{n}}{y_{n}}}}}}"></span></dd></dl> <p>These formulas can be derived from the previously presented definitions of x and y chromaticity coordinates by taking advantage of the fact that the tristimulus values X, Y, and Z of the individual mixture components are directly additive. In place of the luminance values (L<sub>1</sub>, L<sub>2</sub>, etc.) one can alternatively use any other photometric quantity that is directly proportional to the tristimulus value Y (naturally meaning that Y itself can also be used as well). </p><p>As already mentioned, when two colors are mixed, the resulting color x<sub>mix</sub>, y<sub>mix</sub> will lie on the straight line segment that connects these colors on the CIE xy chromaticity diagram. To calculate the mixing ratio of the component colors x<sub>1</sub>,y<sub>1</sub> and x<sub>2</sub>,y<sub>2</sub> that results in a certain x<sub>mix</sub>,y<sub>mix</sub> on this line segment, one can use the formula </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 {L_{1}}{L_{2}}}={\frac {y_{1}\left(x_{2}-x_{\mathrm {mix} }\right)}{y_{2}\left(x_{\mathrm {mix} }-x_{1}\right)}}={\frac {y_{1}\left(y_{2}-y_{\mathrm {mix} }\right)}{y_{2}\left(y_{\mathrm {mix} }-y_{1}\right)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {L_{1}}{L_{2}}}={\frac {y_{1}\left(x_{2}-x_{\mathrm {mix} }\right)}{y_{2}\left(x_{\mathrm {mix} }-x_{1}\right)}}={\frac {y_{1}\left(y_{2}-y_{\mathrm {mix} }\right)}{y_{2}\left(y_{\mathrm {mix} }-y_{1}\right)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/034d1581a2e6ea9b18ccba650b00546ef8646a38" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:38.702ex; height:6.509ex;" alt="{\displaystyle {\frac {L_{1}}{L_{2}}}={\frac {y_{1}\left(x_{2}-x_{\mathrm {mix} }\right)}{y_{2}\left(x_{\mathrm {mix} }-x_{1}\right)}}={\frac {y_{1}\left(y_{2}-y_{\mathrm {mix} }\right)}{y_{2}\left(y_{\mathrm {mix} }-y_{1}\right)}}}"></span></dd></dl> <p>where L<sub>1</sub> is the luminance of color x<sub>1</sub>,y<sub>1</sub> and L<sub>2</sub> the luminance of color x<sub>2</sub>,y<sub>2</sub>. Because y<sub>mix</sub> is unambiguously determined by x<sub>mix</sub> and vice versa, knowing just one or the other of them is enough for calculating the mixing ratio. In accordance with the remarks concerning the formulas for x<sub>mix</sub> and y<sub>mix</sub>, the mixing ratio L<sub>1</sub>/L<sub>2</sub> may well be expressed in terms of other photometric quantities than luminance. </p> <div class="mw-heading mw-heading2"><h2 id="Definition_of_the_CIE_XYZ_color_space">Definition of the CIE XYZ color space</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=11" title="Edit section: Definition of the CIE XYZ color space"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="CIE_RGB_color_space">CIE RGB color space</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=12" title="Edit section: CIE RGB color space"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The first step in developing the CIE XYZ color space is the measurement of the CIE RGB color space. The CIE RGB color space is one of many <a href="/wiki/RGB_color_spaces" title="RGB color spaces">RGB color spaces</a>, distinguished by a particular set of monochromatic (single-wavelength) <a href="/wiki/Primary_color" title="Primary color">primary colors</a>. </p><p>In the 1920s, two independent experiments on human color perception were conducted by W. David Wright<sup id="cite_ref-wright_3-1" class="reference"><a href="#cite_note-wright-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> with ten observers, and John Guild<sup id="cite_ref-guild_4-1" class="reference"><a href="#cite_note-guild-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> with seven observers. Their results laid the foundation for the trichromatic CIE XYZ color space specification. </p><p>The experiments were conducted by using a circular split screen (a bipartite field) 2 degrees in diameter, which is the angular size of the human fovea. On one side a test color was projected while on the other an observer-adjustable color was projected. The adjustable color was a mixture of the three monochromatic primary colors, each with adjustable brightness. The observer would alter the brightness of each of the three primary beams until a match to the test color was observed. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:CIE1931xy_CIERGB.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/CIE1931xy_CIERGB.svg/325px-CIE1931xy_CIERGB.svg.png" decoding="async" width="325" height="345" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/CIE1931xy_CIERGB.svg/488px-CIE1931xy_CIERGB.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/CIE1931xy_CIERGB.svg/650px-CIE1931xy_CIERGB.svg.png 2x" data-file-width="495" data-file-height="526" /></a><figcaption>Gamut of the CIE RGB primaries and location of primaries on the CIE 1931 <i>xy</i> chromaticity diagram</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:CIE1931_RGBCMF2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/CIE1931_RGBCMF2.png/325px-CIE1931_RGBCMF2.png" decoding="async" width="325" height="244" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/CIE1931_RGBCMF2.png/488px-CIE1931_RGBCMF2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/CIE1931_RGBCMF2.png/650px-CIE1931_RGBCMF2.png 2x" data-file-width="1300" data-file-height="975" /></a><figcaption>The normalized CIE RGB color matching functions, with primary wavelengths indicated</figcaption></figure> <p>If the test color were simply a monochromatic color at wavelength λ, and if it could be matched by a combination of the three primaries at relative 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 {\bar {r}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {r}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69fdbe5280b72127fb8cb3667a43203939fe9b91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.456ex; height:2.843ex;" alt="{\displaystyle {\bar {r}}(\lambda )}"></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 {\bar {g}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>g</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {g}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd543e51a3a670859645e5b7b4a78b081ac90250" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.396ex; height:2.843ex;" alt="{\displaystyle {\bar {g}}(\lambda )}"></span>, 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 {\bar {b}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {b}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c542ca0623da96c1f5c34608f19b929f4966f90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.327ex; height:3.009ex;" alt="{\displaystyle {\bar {b}}(\lambda )}"></span> respectively, then a tabulation of these values at various λ will estimate three functions of wavelength. These are the RGB color-matching functions. Any spectral distribution can be thought of as a combination of a number of monochromatic sources at varying intensities, so that (by <a href="/wiki/Grassmann%27s_laws_(color_science)" title="Grassmann's laws (color science)">Grassmann's laws</a>) integrating the color matching functions with that spectral distribution will yield the intensities of the three primaries necessary to match it. The problem is that the three primaries can only produce colors which lie withinin their gamut - the triangle in color space formed by the primaries, which never touches the monochromatic locus nor the <a href="/wiki/Line_of_purples" title="Line of purples">purple line</a> except at the three primaries. In other words, there is no monochromatic source that can be matched by a combination of the three primaries, except at the wavelengths of the three primaries themselves. However, by adding one of the primaries to the monochromatic test color, the test color can be brought into the RGB gamut, allowing a match to be made. Adding a primary to the monochromatic test color is effectively the same as subtracting it from the adjustable color, which of course cannot be done since it is impossible to have a negative intensity for any of the primaries. </p><p>For wavelengths between the blue and green primaries, some red primary must be added to allow matching, resulting in negative values of <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 {\bar {r}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {r}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69fdbe5280b72127fb8cb3667a43203939fe9b91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.456ex; height:2.843ex;" alt="{\displaystyle {\bar {r}}(\lambda )}"></span>. Likewise, between the green and red primaries, some blue must be added 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 {\bar {b}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {b}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c542ca0623da96c1f5c34608f19b929f4966f90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.327ex; height:3.009ex;" alt="{\displaystyle {\bar {b}}(\lambda )}"></span> will be negative. For wavelengths below the wavelength of the blue primary, or above the wavelength of the red primary, some green must be added 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 {\bar {g}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>g</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {g}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd543e51a3a670859645e5b7b4a78b081ac90250" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.396ex; height:2.843ex;" alt="{\displaystyle {\bar {g}}(\lambda )}"></span> will be negative. In each case, the remaining two color matching functions will be positive. It can be seen that the deviation of the RGB gamut from the complete gamut is rather small except between the blue and green primaries at 435.8 and 546.1 nm. In this wavelength band, rather large amounts of the red primary needed to be added to the test color, and it is in this band that the red color matching function has rather large negative values. In their regions of negative values, the green and blue matching functions have rather small negative values. </p><p>Although Wright and Guild's experiments were carried out using various primaries at various intensities, and although they used a number of different observers, all of their results were summarized by the standardized CIE RGB color matching functions <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 {\overline {r}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {r}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132681d5c7554f61def2898cdb71881d0f7b3d12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.328ex; height:2.843ex;" alt="{\displaystyle {\overline {r}}(\lambda )}"></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 {\overline {g}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>g</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {g}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd95637c6efb283e30f73d9f8e0cd5165daa88b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.4ex; height:2.843ex;" alt="{\displaystyle {\overline {g}}(\lambda )}"></span>, 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 {\overline {b}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {b}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a30007776e3ac900c6a818572f5f93c201abeaf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.277ex; height:3.509ex;" alt="{\displaystyle {\overline {b}}(\lambda )}"></span>, obtained using three monochromatic primaries at standardized wavelengths of <span class="nowrap">700 nm</span> (red), <span class="nowrap">546.1 nm</span> (green) and <span class="nowrap">435.8 nm</span> (blue). The (un-normalized) color matching functions are the amounts of primaries needed to match the monochromatic test primary. These functions are shown in the plot on the right (CIE 1931). <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 {\overline {r}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {r}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132681d5c7554f61def2898cdb71881d0f7b3d12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.328ex; height:2.843ex;" alt="{\displaystyle {\overline {r}}(\lambda )}"></span> 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 {\overline {g}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>g</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {g}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd95637c6efb283e30f73d9f8e0cd5165daa88b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.4ex; height:2.843ex;" alt="{\displaystyle {\overline {g}}(\lambda )}"></span> are zero at <span class="nowrap">435.8 nm</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 {\overline {r}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {r}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132681d5c7554f61def2898cdb71881d0f7b3d12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.328ex; height:2.843ex;" alt="{\displaystyle {\overline {r}}(\lambda )}"></span> 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 {\overline {b}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {b}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a30007776e3ac900c6a818572f5f93c201abeaf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.277ex; height:3.509ex;" alt="{\displaystyle {\overline {b}}(\lambda )}"></span> are zero at <span class="nowrap">546.1 nm</span> 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 {\overline {g}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>g</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {g}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd95637c6efb283e30f73d9f8e0cd5165daa88b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.4ex; height:2.843ex;" alt="{\displaystyle {\overline {g}}(\lambda )}"></span> 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 {\overline {b}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {b}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a30007776e3ac900c6a818572f5f93c201abeaf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.277ex; height:3.509ex;" alt="{\displaystyle {\overline {b}}(\lambda )}"></span> are zero at <span class="nowrap">700 nm</span>, since in these cases the test color is one of the primaries. The primaries with wavelengths <span class="nowrap">546.1 nm</span> and <span class="nowrap">435.8 nm</span> were chosen because they are easily reproducible monochromatic lines of a mercury vapor discharge. The <span class="nowrap">700 nm</span> wavelength, which in 1931 was difficult to reproduce as a monochromatic beam, was chosen because the eye's perception of color is rather unchanging at this wavelength, and therefore small errors in wavelength of this primary would have little effect on the results. </p><p>The color matching functions and primaries were settled upon by a CIE special commission after considerable deliberation.<sup id="cite_ref-fairman_19-0" class="reference"><a href="#cite_note-fairman-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> The cut-offs at the short- and long-wavelength side of the diagram are chosen somewhat arbitrarily; the human eye can actually see light with wavelengths up to about <span class="nowrap">810 nm</span>, but with a sensitivity that is many thousand times lower than for green light. These color matching functions define what is known as the "1931 CIE standard observer". Rather than specify the brightness of each primary, the curves are normalized to have constant area beneath them. This area is fixed to a particular value by specifying that </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 \int _{0}^{\infty }{\overline {r}}(\lambda )\,d\lambda =\int _{0}^{\infty }{\overline {g}}(\lambda )\,d\lambda =\int _{0}^{\infty }{\overline {b}}(\lambda )\,d\lambda .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>λ</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>g</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>λ</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>λ</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{0}^{\infty }{\overline {r}}(\lambda )\,d\lambda =\int _{0}^{\infty }{\overline {g}}(\lambda )\,d\lambda =\int _{0}^{\infty }{\overline {b}}(\lambda )\,d\lambda .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65e0a23cd865ce60f4d8aeef56451560065dddfe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:42.904ex; height:5.843ex;" alt="{\displaystyle \int _{0}^{\infty }{\overline {r}}(\lambda )\,d\lambda =\int _{0}^{\infty }{\overline {g}}(\lambda )\,d\lambda =\int _{0}^{\infty }{\overline {b}}(\lambda )\,d\lambda .}"></span></dd></dl> <p>The resulting normalized color matching functions are then scaled in the r:g:b ratio of 1:4.5907:0.0601 for source <a href="/wiki/Luminance" title="Luminance">luminance</a> and 72.0962:1.3791:1 for source <a href="/wiki/Radiance" title="Radiance">radiance</a> to reproduce the true color matching functions. By proposing that the primaries be standardized, the CIE established an international system of objective color notation. </p><p>Given these scaled color matching functions, the RGB <a href="/wiki/Tristimulus" class="mw-redirect" title="Tristimulus">tristimulus</a> values for a color with a <a href="/wiki/Spectral_power_distribution" title="Spectral power distribution">spectral power distribution</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 S(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c5186313c3051d5c2af725d546ad7245ba1b2b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.664ex; height:2.843ex;" alt="{\displaystyle S(\lambda )}"></span> would then be 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 {\begin{aligned}R&=\int _{0}^{\infty }S(\lambda )\,{\overline {r}}(\lambda )\,d\lambda ,\\[6mu]G&=\int _{0}^{\infty }S(\lambda )\,{\overline {g}}(\lambda )\,d\lambda ,\\[6mu]B&=\int _{0}^{\infty }S(\lambda )\,{\overline {b}}(\lambda )\,d\lambda .\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.633em 0.633em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>R</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mi>S</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>λ</mi> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>G</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mi>S</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>g</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>λ</mi> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>B</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mi>S</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>λ</mi> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}R&=\int _{0}^{\infty }S(\lambda )\,{\overline {r}}(\lambda )\,d\lambda ,\\[6mu]G&=\int _{0}^{\infty }S(\lambda )\,{\overline {g}}(\lambda )\,d\lambda ,\\[6mu]B&=\int _{0}^{\infty }S(\lambda )\,{\overline {b}}(\lambda )\,d\lambda .\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bffdfda00945dd919f6b1ef6cc18313e090b231" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.961ex; margin-bottom: -0.21ex; width:23.459ex; height:19.509ex;" alt="{\displaystyle {\begin{aligned}R&=\int _{0}^{\infty }S(\lambda )\,{\overline {r}}(\lambda )\,d\lambda ,\\[6mu]G&=\int _{0}^{\infty }S(\lambda )\,{\overline {g}}(\lambda )\,d\lambda ,\\[6mu]B&=\int _{0}^{\infty }S(\lambda )\,{\overline {b}}(\lambda )\,d\lambda .\end{aligned}}}"></span></dd></dl> <p>These are all <a href="/wiki/Inner_products" class="mw-redirect" title="Inner products">inner products</a> and can be thought of as a projection of an infinite-dimensional spectrum to a <a href="/wiki/Hilbert_space" title="Hilbert space">three-dimensional color</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Grassmann's_Laws"><span id="Grassmann.27s_Laws"></span>Grassmann's Laws</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=13" title="Edit section: Grassmann's Laws"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <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">Main article: <a href="/wiki/Grassmann%27s_laws_(color_science)" title="Grassmann's laws (color science)">Grassmann's laws (color science)</a></div> <p>One might ask: "Why is it possible that Wright and Guild's results can be summarized using different primaries and different intensities from those actually used?" One might also ask: "What about the case when the test colors being matched are not monochromatic?" The answer to both of these questions lies in the (near) linearity of human color perception. This linearity is expressed in Grassmann's laws of color. </p><p>The CIE RGB space can be used to define chromaticity in the usual way: The chromaticity coordinates are <i>r</i>, <i>g</i> and <i>b</i> where: </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 {\begin{aligned}r&={\frac {R}{R+G+B}},\\[5mu]g&={\frac {G}{R+G+B}},\\[5mu]b&={\frac {B}{R+G+B}}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.578em 0.578em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>r</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>R</mi> <mrow> <mi>R</mi> <mo>+</mo> <mi>G</mi> <mo>+</mo> <mi>B</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>g</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>G</mi> <mrow> <mi>R</mi> <mo>+</mo> <mi>G</mi> <mo>+</mo> <mi>B</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>b</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>B</mi> <mrow> <mi>R</mi> <mo>+</mo> <mi>G</mi> <mo>+</mo> <mi>B</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}r&={\frac {R}{R+G+B}},\\[5mu]g&={\frac {G}{R+G+B}},\\[5mu]b&={\frac {B}{R+G+B}}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15cfc20b09a52c5f725cead93f5671c6564ed4a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.344ex; margin-bottom: -0.328ex; width:17.484ex; height:18.509ex;" alt="{\displaystyle {\begin{aligned}r&={\frac {R}{R+G+B}},\\[5mu]g&={\frac {G}{R+G+B}},\\[5mu]b&={\frac {B}{R+G+B}}.\end{aligned}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Construction_of_the_CIE_XYZ_color_space_from_the_Wright–Guild_data"><span id="Construction_of_the_CIE_XYZ_color_space_from_the_Wright.E2.80.93Guild_data"></span>Construction of the CIE XYZ color space from the Wright–Guild data</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=14" title="Edit section: Construction of the CIE XYZ color space from the Wright–Guild data"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:308px;max-width:308px"><div class="trow"><div class="tsingle" style="width:152px;max-width:152px"><div class="thumbimage"><span typeof="mw:File"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/SRGB_gamut_within_CIEXYZ_color_space_mesh.webm/150px-seek%3D0-SRGB_gamut_within_CIEXYZ_color_space_mesh.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="150" height="150" data-durationhint="8" data-mwtitle="SRGB_gamut_within_CIEXYZ_color_space_mesh.webm" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2b/SRGB_gamut_within_CIEXYZ_color_space_mesh.webm/SRGB_gamut_within_CIEXYZ_color_space_mesh.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="480" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/2/2b/SRGB_gamut_within_CIEXYZ_color_space_mesh.webm" type="video/webm; codecs="vp9"" data-width="512" data-height="512" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2b/SRGB_gamut_within_CIEXYZ_color_space_mesh.webm/SRGB_gamut_within_CIEXYZ_color_space_mesh.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="240" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2b/SRGB_gamut_within_CIEXYZ_color_space_mesh.webm/SRGB_gamut_within_CIEXYZ_color_space_mesh.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="360" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2b/SRGB_gamut_within_CIEXYZ_color_space_mesh.webm/SRGB_gamut_within_CIEXYZ_color_space_mesh.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="360" data-height="360" /></video></span></span></div></div><div class="tsingle" style="width:152px;max-width:152px"><div class="thumbimage"><span typeof="mw:File"><span><video id="mwe_player_1" poster="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Visible_gamut_within_CIEXYZ_color_space_D65_whitepoint_mesh.webm/150px-seek%3D0-Visible_gamut_within_CIEXYZ_color_space_D65_whitepoint_mesh.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="150" height="150" data-durationhint="8" data-mwtitle="Visible_gamut_within_CIEXYZ_color_space_D65_whitepoint_mesh.webm" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/3/34/Visible_gamut_within_CIEXYZ_color_space_D65_whitepoint_mesh.webm/Visible_gamut_within_CIEXYZ_color_space_D65_whitepoint_mesh.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="480" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/3/34/Visible_gamut_within_CIEXYZ_color_space_D65_whitepoint_mesh.webm" type="video/webm; codecs="vp9"" data-width="512" data-height="512" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/3/34/Visible_gamut_within_CIEXYZ_color_space_D65_whitepoint_mesh.webm/Visible_gamut_within_CIEXYZ_color_space_D65_whitepoint_mesh.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="240" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/3/34/Visible_gamut_within_CIEXYZ_color_space_D65_whitepoint_mesh.webm/Visible_gamut_within_CIEXYZ_color_space_D65_whitepoint_mesh.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="360" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/3/34/Visible_gamut_within_CIEXYZ_color_space_D65_whitepoint_mesh.webm/Visible_gamut_within_CIEXYZ_color_space_D65_whitepoint_mesh.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="360" data-height="360" /></video></span></span></div></div></div><div class="trow" style="display:flex"><div class="thumbcaption">The <a href="/wiki/SRGB" title="SRGB">sRGB</a> gamut (<i>left</i>) and visible gamut under D65 illumination (<i>right</i>) projected within the CIEXYZ color space. <i>X</i> and <i>Z</i> are the horizontal axes; <i>Y</i> is the vertical axis.</div></div></div></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237032888/mw-parser-output/.tmulti"><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:308px;max-width:308px"><div class="trow"><div class="tsingle" style="width:152px;max-width:152px"><div class="thumbimage"><span typeof="mw:File"><span><video id="mwe_player_2" poster="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/SRGB_gamut_within_CIExyY_color_space_mesh.webm/150px-seek%3D0-SRGB_gamut_within_CIExyY_color_space_mesh.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="150" height="150" data-durationhint="8" data-mwtitle="SRGB_gamut_within_CIExyY_color_space_mesh.webm" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/c/c2/SRGB_gamut_within_CIExyY_color_space_mesh.webm/SRGB_gamut_within_CIExyY_color_space_mesh.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="480" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/c/c2/SRGB_gamut_within_CIExyY_color_space_mesh.webm" type="video/webm; codecs="vp9"" data-width="512" data-height="512" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/c/c2/SRGB_gamut_within_CIExyY_color_space_mesh.webm/SRGB_gamut_within_CIExyY_color_space_mesh.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="240" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/c/c2/SRGB_gamut_within_CIExyY_color_space_mesh.webm/SRGB_gamut_within_CIExyY_color_space_mesh.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="360" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/c/c2/SRGB_gamut_within_CIExyY_color_space_mesh.webm/SRGB_gamut_within_CIExyY_color_space_mesh.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="360" data-height="360" /></video></span></span></div></div><div class="tsingle" style="width:152px;max-width:152px"><div class="thumbimage"><span typeof="mw:File"><span><video id="mwe_player_3" poster="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Visible_gamut_within_CIExyY_color_space_D65_whitepoint_mesh.webm/150px-seek%3D0-Visible_gamut_within_CIExyY_color_space_D65_whitepoint_mesh.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="150" height="150" data-durationhint="8" data-mwtitle="Visible_gamut_within_CIExyY_color_space_D65_whitepoint_mesh.webm" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/6d/Visible_gamut_within_CIExyY_color_space_D65_whitepoint_mesh.webm/Visible_gamut_within_CIExyY_color_space_D65_whitepoint_mesh.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="480" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/6/6d/Visible_gamut_within_CIExyY_color_space_D65_whitepoint_mesh.webm" type="video/webm; codecs="vp9"" data-width="512" data-height="512" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/6d/Visible_gamut_within_CIExyY_color_space_D65_whitepoint_mesh.webm/Visible_gamut_within_CIExyY_color_space_D65_whitepoint_mesh.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="240" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/6d/Visible_gamut_within_CIExyY_color_space_D65_whitepoint_mesh.webm/Visible_gamut_within_CIExyY_color_space_D65_whitepoint_mesh.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="360" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/6d/Visible_gamut_within_CIExyY_color_space_D65_whitepoint_mesh.webm/Visible_gamut_within_CIExyY_color_space_D65_whitepoint_mesh.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="360" data-height="360" /></video></span></span></div></div></div><div class="trow" style="display:flex"><div class="thumbcaption">The <a href="/wiki/SRGB" title="SRGB">sRGB</a> gamut (<i>left</i>) and visible gamut under D65 illumination (<i>right</i>) projected within the CIExyY color space. <i>x</i> and <i>y</i> are the horizontal axes; <i>Y</i> is the vertical axis.</div></div></div></div> <p>Having developed an RGB model of human vision using the CIE RGB matching functions, the members of the special commission wished to develop another color space that would relate to the CIE RGB color space. It was assumed that Grassmann's law held, and the new space would be related to the CIE RGB space by a linear transformation. The new space would be defined in terms of three new color matching functions <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 {\overline {x}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {x}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c66d9bb9f712fc5f55bfb7b48777e09320bd56d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.609ex; height:2.843ex;" alt="{\displaystyle {\overline {x}}(\lambda )}"></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 {\overline {y}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>y</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {y}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57dbc1311b7e980c1730d667434ba28cb95dc4d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.446ex; height:2.843ex;" alt="{\displaystyle {\overline {y}}(\lambda )}"></span>, 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 {\overline {z}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>z</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {z}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8bd6d3420325c2bc24a30246e0756012932a85b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.372ex; height:2.843ex;" alt="{\displaystyle {\overline {z}}(\lambda )}"></span> as described above. The new color space would be chosen to have the following desirable properties: </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:CIE1931_rgxy.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/CIE1931_rgxy.png/325px-CIE1931_rgxy.png" decoding="async" width="325" height="325" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/CIE1931_rgxy.png/488px-CIE1931_rgxy.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/16/CIE1931_rgxy.png/650px-CIE1931_rgxy.png 2x" data-file-width="1260" data-file-height="1260" /></a><figcaption>Diagram in CIE <i>rg</i> chromaticity space showing the construction of the triangle specifying the CIE XYZ color space. The triangle C<sub>b</sub>-C<sub>g</sub>-C<sub>r</sub> is just the <span class="nowrap"><i>xy</i> = (0, 0), (0, 1), (1, 0)</span> triangle in CIE <i>xy</i> chromaticity space. The line connecting C<sub>b</sub> and C<sub>r</sub> is the alychne. The spectral locus passes through <span class="nowrap"><i>rg</i> = (0, 0)</span> at <span class="nowrap">435.8 nm</span>, through <span class="nowrap"><i>rg</i> = (0, 1)</span> at <span class="nowrap">546.1 nm</span> and through <span class="nowrap"><i>rg</i> = (1, 0)</span> at <span class="nowrap">700 nm</span>. Also, the equal energy point (E) is at <span class="nowrap"><i>rg</i> = <i>xy</i> = (1/3, 1/3)</span>.</figcaption></figure> <ol><li>The new color matching functions were to be everywhere greater than or equal to zero. In 1931, computations were done by hand or slide rule, and the specification of positive values was a useful computational simplification.</li> <li>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 {\overline {y}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>y</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {y}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57dbc1311b7e980c1730d667434ba28cb95dc4d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.446ex; height:2.843ex;" alt="{\displaystyle {\overline {y}}(\lambda )}"></span> color matching function would be exactly equal to the <a href="/wiki/Luminosity_function" class="mw-redirect" title="Luminosity function">photopic luminous efficiency function</a> <i>V</i>(<i>λ</i>) for the "CIE standard photopic observer".<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> The luminance function describes the variation of perceived brightness with wavelength. The fact that the luminance function could be constructed by a linear combination of the RGB color matching functions was not guaranteed by any means but might be expected to be nearly true due to the near-linear nature of human sight. Again, the main reason for this requirement was computational simplification.</li> <li>For the constant energy <a href="/wiki/White_point" title="White point">white point</a>, it was required that <span class="nowrap"><i>x</i> = <i>y</i> = <i>z</i> = 1/3</span>.</li> <li>By virtue of the definition of <a href="/wiki/Chromaticity" title="Chromaticity">chromaticity</a> and the requirement of positive values of <i>x</i> and <i>y</i>, it can be seen that the gamut of all colors will lie inside the triangle [1, 0], [0, 0], [0, 1]. It was required that the gamut fill this space practically completely.</li> <li>It was found that 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 {\overline {z}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>z</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {z}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8bd6d3420325c2bc24a30246e0756012932a85b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.372ex; height:2.843ex;" alt="{\displaystyle {\overline {z}}(\lambda )}"></span> color matching function could be set to zero above <span class="nowrap">650 nm</span> while remaining within the bounds of experimental error. For computational simplicity, it was specified that this would be so.</li></ol> <p>In geometrical terms, choosing the new color space amounts to choosing a new triangle in <i>rg</i> chromaticity space. In the figure above-right, the <i>rg</i> chromaticity coordinates are shown on the two axes in black, along with the gamut of the 1931 standard observer. Shown in red are the CIE <i>xy</i> chromaticity axes which were determined by the above requirements. The requirement that the XYZ coordinates be non-negative means that the triangle formed by C<sub>r</sub>, C<sub>g</sub>, C<sub>b</sub> must encompass the entire gamut of the standard observer. The line connecting C<sub>r</sub> and C<sub>b</sub> is fixed by the requirement that 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 {\overline {y}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>y</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {y}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57dbc1311b7e980c1730d667434ba28cb95dc4d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.446ex; height:2.843ex;" alt="{\displaystyle {\overline {y}}(\lambda )}"></span> function be equal to the luminance function. This line is the line of zero luminance, and is called the alychne. The requirement that 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 {\overline {z}}(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>z</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {z}}(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8bd6d3420325c2bc24a30246e0756012932a85b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.372ex; height:2.843ex;" alt="{\displaystyle {\overline {z}}(\lambda )}"></span> function be zero above <span class="nowrap">650 nm</span> means that the line connecting C<sub>g</sub> and C<sub>r</sub> must be tangent to the gamut in the region of K<sub>r</sub>. This defines the location of point C<sub>r</sub>. The requirement that the equal energy point be defined by <span class="nowrap"><i>x</i> = <i>y</i> = 1/3</span> puts a restriction on the line joining C<sub>b</sub> and C<sub>g</sub>, and finally, the requirement that the gamut fill the space puts a second restriction on this line to be very close to the gamut in the green region, which specifies the location of C<sub>g</sub> and C<sub>b</sub>. The above described transformation is a linear transformation from the CIE RGB space to XYZ space. The standardized transformation settled upon by the CIE special commission was as follows: </p><p>The numbers in the conversion matrix below are exact, with the number of digits specified in CIE standards.<sup id="cite_ref-fairman_19-1" class="reference"><a href="#cite_note-fairman-19"><span class="cite-bracket">[</span>19<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 {\begin{aligned}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}&={\begin{bmatrix}b_{11}&b_{12}&b_{13}\\b_{21}&b_{22}&b_{23}\\b_{31}&b_{32}&b_{33}\end{bmatrix}}{\begin{bmatrix}R\\G\\B\end{bmatrix}}\\[10mu]&={\begin{bmatrix}0.490\,00&0.310\,00&0.200\,00\\0.176\,97&0.812\,40&0.010\,63\\0.000\,00&0.010\,00&0.990\,00\end{bmatrix}}{\begin{bmatrix}R\\G\\B\end{bmatrix}}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.856em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>X</mi> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>11</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>13</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>22</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>23</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>31</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>32</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>33</mn> </mrow> </msub> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>R</mi> </mtd> </mtr> <mtr> <mtd> <mi>G</mi> </mtd> </mtr> <mtr> <mtd> <mi>B</mi> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0.490</mn> <mspace width="thinmathspace" /> <mn>00</mn> </mtd> <mtd> <mn>0.310</mn> <mspace width="thinmathspace" /> <mn>00</mn> </mtd> <mtd> <mn>0.200</mn> <mspace width="thinmathspace" /> <mn>00</mn> </mtd> </mtr> <mtr> <mtd> <mn>0.176</mn> <mspace width="thinmathspace" /> <mn>97</mn> </mtd> <mtd> <mn>0.812</mn> <mspace width="thinmathspace" /> <mn>40</mn> </mtd> <mtd> <mn>0.010</mn> <mspace width="thinmathspace" /> <mn>63</mn> </mtd> </mtr> <mtr> <mtd> <mn>0.000</mn> <mspace width="thinmathspace" /> <mn>00</mn> </mtd> <mtd> <mn>0.010</mn> <mspace width="thinmathspace" /> <mn>00</mn> </mtd> <mtd> <mn>0.990</mn> <mspace width="thinmathspace" /> <mn>00</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>R</mi> </mtd> </mtr> <mtr> <mtd> <mi>G</mi> </mtd> </mtr> <mtr> <mtd> <mi>B</mi> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}&={\begin{bmatrix}b_{11}&b_{12}&b_{13}\\b_{21}&b_{22}&b_{23}\\b_{31}&b_{32}&b_{33}\end{bmatrix}}{\begin{bmatrix}R\\G\\B\end{bmatrix}}\\[10mu]&={\begin{bmatrix}0.490\,00&0.310\,00&0.200\,00\\0.176\,97&0.812\,40&0.010\,63\\0.000\,00&0.010\,00&0.990\,00\end{bmatrix}}{\begin{bmatrix}R\\G\\B\end{bmatrix}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3bd2edf319df55b2d5b83193a952791eabcd3164" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -9.505ex; width:47.884ex; height:20.176ex;" alt="{\displaystyle {\begin{aligned}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}&={\begin{bmatrix}b_{11}&b_{12}&b_{13}\\b_{21}&b_{22}&b_{23}\\b_{31}&b_{32}&b_{33}\end{bmatrix}}{\begin{bmatrix}R\\G\\B\end{bmatrix}}\\[10mu]&={\begin{bmatrix}0.490\,00&0.310\,00&0.200\,00\\0.176\,97&0.812\,40&0.010\,63\\0.000\,00&0.010\,00&0.990\,00\end{bmatrix}}{\begin{bmatrix}R\\G\\B\end{bmatrix}}\end{aligned}}}"></span></dd></dl> <p>The above matrix is balanced for the equi-energy stimulus: it has coordinates (1,1,1) in both RGB and XYZ coordinates. </p><p>While the above matrix is exactly specified in standards, the inverse is left unspecified so that it can be approximated to machine precision to reduce round-trip rounding errors. Its values can be computed precisely using rational numbers: </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 {\begin{bmatrix}R\\G\\B\end{bmatrix}}={\frac {1}{3400850}}{\begin{bmatrix}8041697&-3049000&-1591847\\-1752003&4851000&301853\\17697&-49000&3432153\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>R</mi> </mtd> </mtr> <mtr> <mtd> <mi>G</mi> </mtd> </mtr> <mtr> <mtd> <mi>B</mi> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3400850</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>8041697</mn> </mtd> <mtd> <mo>−</mo> <mn>3049000</mn> </mtd> <mtd> <mo>−</mo> <mn>1591847</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>1752003</mn> </mtd> <mtd> <mn>4851000</mn> </mtd> <mtd> <mn>301853</mn> </mtd> </mtr> <mtr> <mtd> <mn>17697</mn> </mtd> <mtd> <mo>−</mo> <mn>49000</mn> </mtd> <mtd> <mn>3432153</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>X</mi> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}R\\G\\B\end{bmatrix}}={\frac {1}{3400850}}{\begin{bmatrix}8041697&-3049000&-1591847\\-1752003&4851000&301853\\17697&-49000&3432153\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13c530eef0e80e79ac50fa37b1cf790c7c0eb75d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:61.916ex; height:9.176ex;" alt="{\displaystyle {\begin{bmatrix}R\\G\\B\end{bmatrix}}={\frac {1}{3400850}}{\begin{bmatrix}8041697&-3049000&-1591847\\-1752003&4851000&301853\\17697&-49000&3432153\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}}"></span></dd></dl> <p>Which has these approximate values: </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 {\begin{bmatrix}R\\G\\B\end{bmatrix}}\approx {\begin{bmatrix}2.364\,61385&-0.896\,54057&-0.468\,07328\\-0.515\,16621&1.426\,4081&0.088\,7581\\0.005\,2037&-0.014\,40816&1.009\,20446\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>R</mi> </mtd> </mtr> <mtr> <mtd> <mi>G</mi> </mtd> </mtr> <mtr> <mtd> <mi>B</mi> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>2.364</mn> <mspace width="thinmathspace" /> <mn>61385</mn> </mtd> <mtd> <mo>−</mo> <mn>0.896</mn> <mspace width="thinmathspace" /> <mn>54057</mn> </mtd> <mtd> <mo>−</mo> <mn>0.468</mn> <mspace width="thinmathspace" /> <mn>07328</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>0.515</mn> <mspace width="thinmathspace" /> <mn>16621</mn> </mtd> <mtd> <mn>1.426</mn> <mspace width="thinmathspace" /> <mn>4081</mn> </mtd> <mtd> <mn>0.088</mn> <mspace width="thinmathspace" /> <mn>7581</mn> </mtd> </mtr> <mtr> <mtd> <mn>0.005</mn> <mspace width="thinmathspace" /> <mn>2037</mn> </mtd> <mtd> <mo>−</mo> <mn>0.014</mn> <mspace width="thinmathspace" /> <mn>40816</mn> </mtd> <mtd> <mn>1.009</mn> <mspace width="thinmathspace" /> <mn>20446</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>X</mi> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}R\\G\\B\end{bmatrix}}\approx {\begin{bmatrix}2.364\,61385&-0.896\,54057&-0.468\,07328\\-0.515\,16621&1.426\,4081&0.088\,7581\\0.005\,2037&-0.014\,40816&1.009\,20446\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62965c10812bf101e39a5cc6aebdbd2decf88aca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:63.019ex; height:9.176ex;" alt="{\displaystyle {\begin{bmatrix}R\\G\\B\end{bmatrix}}\approx {\begin{bmatrix}2.364\,61385&-0.896\,54057&-0.468\,07328\\-0.515\,16621&1.426\,4081&0.088\,7581\\0.005\,2037&-0.014\,40816&1.009\,20446\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}}"></span></dd></dl> <p>The XYZ primaries will have XYZ coordinates [1,0,0], [0,1,0], and [0,0,1] in XYZ space, so the columns of the inverse matrix above specify the XYZ primaries ( Cr, Cg and Cb) in RGB space. Dividing each column by its sum will give the coordinates of the XYZ primaries in rgb space which yields: </p> <dl><dd>Cr = {1.27496, -0.27777, 0.00280576}</dd> <dd>Cg = {-1.7393, 2.76726, -0.0279521}</dd> <dd>Cb = {-0.743104, 0.140911, 1.60219}</dd></dl> <p>The r and g coordinates of the XYZ primaries are indicated in the rg chromaticity space diagram above. </p><p>The integrals of the XYZ color matching functions must all be equal by requirement 3 above, and this is set by the integral of the photopic luminous efficiency function by requirement 2 above. The tabulated sensitivity curves have a certain amount of arbitrariness in them. The shapes of the individual <i>X</i>, <i>Y</i> and <i>Z</i> sensitivity curves can be measured with a reasonable accuracy. However, the overall luminosity curve (which in fact is a weighted sum of these three curves) is subjective, since it involves asking a test person whether two light sources have the same brightness, even if they are in completely different colors. Along the same lines, the relative magnitudes of the <i>X</i>, <i>Y</i>, and <i>Z</i> curves are arbitrary. Furthermore, one could define a valid color space with an <i>X</i> sensitivity curve that has twice the amplitude. This new color space would have a different shape. The sensitivity curves in the CIE 1931 and 1964 XYZ color spaces are scaled to have equal areas under the curves. </p> <div class="mw-heading mw-heading2"><h2 id="Subsequent_refinements">Subsequent refinements<span class="anchor" id="Similar_color_spaces"></span><span class="anchor" id="Other_observers"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=15" title="Edit section: Subsequent refinements"><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:XYZ_color_matching_functions,_CIE_1931_and_Stockman_%26_Sharpe_2006.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/XYZ_color_matching_functions%2C_CIE_1931_and_Stockman_%26_Sharpe_2006.jpg/220px-XYZ_color_matching_functions%2C_CIE_1931_and_Stockman_%26_Sharpe_2006.jpg" decoding="async" width="220" height="132" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/XYZ_color_matching_functions%2C_CIE_1931_and_Stockman_%26_Sharpe_2006.jpg/330px-XYZ_color_matching_functions%2C_CIE_1931_and_Stockman_%26_Sharpe_2006.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/XYZ_color_matching_functions%2C_CIE_1931_and_Stockman_%26_Sharpe_2006.jpg/440px-XYZ_color_matching_functions%2C_CIE_1931_and_Stockman_%26_Sharpe_2006.jpg 2x" data-file-width="983" data-file-height="592" /></a><figcaption>XYZ color matching functions, CIE 1931 and Stockman & Sharpe 2006 (CIE 170-2)</figcaption></figure> <p>A few other XYZ-style color-matching functions have been available, correcting for known issues in the original 1931 color space. These functions imply their own XYZ-like and xyY-like color spaces.<sup id="cite_ref-Intro_21-0" class="reference"><a href="#cite_note-Intro-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <dl><dt>Judd and Vos corrections for the 2° CMF</dt> <dd>The most serious problem with the 1931 CIE XYZ color matching functions is the error in the photopic Y (or <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 V(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b6def6cd8f362fe0e921a3ab1b1df61b838a5e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.952ex; height:2.843ex;" alt="{\displaystyle V(\lambda )}"></span> function on the blue end of the spectrum.<sup id="cite_ref-Stockman2019_22-0" class="reference"><a href="#cite_note-Stockman2019-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> The Judd (1951) and its following Vos (1978)<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> corrections sought to correct for the issue without deviating from the original methodology.<sup id="cite_ref-Intro_21-1" class="reference"><a href="#cite_note-Intro-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup></dd> <dt>CIE 1964 X<sub>10</sub>Y<sub>10</sub>Z<sub>10</sub></dt> <dd>X<sub>10</sub>Y<sub>10</sub>Z<sub>10</sub> (also written XYZ<sub>10</sub> and analogously for the following) is the XYZ-style color space defined using the CIE 1964 10° observer CMFs.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> The 3 CMFs are mainly derived from Stiles and Burch's RGB color-matching functions,<sup id="cite_ref-Stiles&Burch1959_25-0" class="reference"><a href="#cite_note-Stiles&Burch1959-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> which unlike the Wright–Guild functions (and the subsequent Judd–Vos corrections) are "directly measured", freeing them from the reconstruction errors of the 1931 functions.<sup id="cite_ref-Intro_21-2" class="reference"><a href="#cite_note-Intro-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup></dd> <dd>Stiles and Burch also published a set of 2° RGB color-matching functions; however, no XYZ space derived from them has been formally recognized by the CIE.<sup id="cite_ref-Intro_21-3" class="reference"><a href="#cite_note-Intro-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup></dd> <dt>CIE 170-2 X<sub>F</sub>Y<sub>F</sub>Z<sub>F</sub></dt> <dd>X<sub>F</sub>Y<sub>F</sub>Z<sub>F</sub> is the XYZ-style color space defined using the Stockman & Sharpe (2000) physiological 2° observer, which is in turn a linear combination of the <a href="/wiki/LMS_color_space" title="LMS color space">LMS cone response functions</a>.<sup id="cite_ref-cie170.2_26-0" class="reference"><a href="#cite_note-cie170.2-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> The CMF data, along with the physiological 10° dataset, is available from the Colour & Vision Research laboratory of <a href="/wiki/University_College_London" title="University College London">University College London</a> down to 0.1 nm resolution.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup></dd> <dt>CIE 170-2 X<sub>F,10</sub>Y<sub>F,10</sub>Z<sub>F,10</sub></dt> <dd>This space is based on the Stockman & Sharpe (2000) physiological 10° observer.<sup id="cite_ref-cie170.2_26-1" class="reference"><a href="#cite_note-cie170.2-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></dd></dl> <p>According to <a href="/wiki/Konica_Minolta" title="Konica Minolta">Konica Minolta</a>, the older CIE 1931 CMF exhibits metamerism failure (failure to predict when colors appear the same) for <a href="/wiki/Wide_color_gamut" class="mw-redirect" title="Wide color gamut">wide color gamut</a> displays containing narrowband emitters like <a href="/wiki/OLED" title="OLED">OLED</a>, whereas the 2015 XYZ<sub>F</sub> CMF is not affected.<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> Older <a href="/wiki/Sony" title="Sony">Sony</a> manuals recommend using the Judd-Vos correction by applying an offset to the <a href="/wiki/White_point" title="White point">white point</a> depending on the display technology used. </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=CIE_1931_color_space&action=edit&section=16" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Trichromacy" title="Trichromacy">Trichromacy</a></li> <li><a href="/wiki/Impossible_color" title="Impossible color">Impossible color</a></li> <li><a href="/wiki/CIELAB_color_space" title="CIELAB color space">CIELAB color space</a></li> <li><a href="/wiki/Standard_illuminant" title="Standard illuminant">Standard illuminant</a>, the definition of white point used by CIE and commonly shown in color space diagrams as E, D50 or <a href="/wiki/Illuminant_D65" class="mw-redirect" title="Illuminant D65">D65</a></li></ul> <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=CIE_1931_color_space&action=edit&section=17" 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-cie1931-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-cie1931_1-0">^</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 id="CITEREFCIE1932" class="citation book cs1"><a href="/wiki/International_Commission_on_Illumination" title="International Commission on Illumination">CIE</a> (1932). <i>Commission internationale de l'Eclairage proceedings, 1931</i>. Cambridge: <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Commission+internationale+de+l%27Eclairage+proceedings%2C+1931&rft.place=Cambridge&rft.pub=Cambridge+University+Press&rft.date=1932&rft.au=CIE&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmithGuild1931–32" class="citation journal cs1 cs1-prop-year-range-abbreviated">Smith, Thomas; Guild, John (1931–32). "The C.I.E. colorimetric standards and their use". <i>Transactions of the Optical Society</i>. <b>33</b> (3): 73–134. <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/1931TrOS...33...73S">1931TrOS...33...73S</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%2F1475-4878%2F33%2F3%2F301">10.1088/1475-4878/33/3/301</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Transactions+of+the+Optical+Society&rft.atitle=The+C.I.E.+colorimetric+standards+and+their+use&rft.volume=33&rft.issue=3&rft.pages=73-134&rft.date=1931%2F1932&rft_id=info%3Adoi%2F10.1088%2F1475-4878%2F33%2F3%2F301&rft_id=info%3Abibcode%2F1931TrOS...33...73S&rft.aulast=Smith&rft.aufirst=Thomas&rft.au=Guild%2C+John&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" class="Z3988"></span></span> </li> <li id="cite_note-wright-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-wright_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-wright_3-1"><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="CITEREFWright1928" class="citation journal cs1">Wright, William David (1928). "A re-determination of the trichromatic coefficients of the spectral colors". <i>Transactions of the Optical Society</i>. <b>30</b> (4): 141–164. <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%2F1475-4878%2F30%2F4%2F301">10.1088/1475-4878/30/4/301</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Transactions+of+the+Optical+Society&rft.atitle=A+re-determination+of+the+trichromatic+coefficients+of+the+spectral+colors&rft.volume=30&rft.issue=4&rft.pages=141-164&rft.date=1928&rft_id=info%3Adoi%2F10.1088%2F1475-4878%2F30%2F4%2F301&rft.aulast=Wright&rft.aufirst=William+David&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" class="Z3988"></span></span> </li> <li id="cite_note-guild-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-guild_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-guild_4-1"><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="CITEREFGuild1932" class="citation journal cs1">Guild, J. (1932). <a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsta.1932.0005">"The colorimetric properties of the spectrum"</a>. <i><a href="/wiki/Philosophical_Transactions_of_the_Royal_Society_A" title="Philosophical Transactions of the Royal Society A">Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character</a></i>. <b>230</b> (681–693): 149–187. <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/1932RSPTA.230..149G">1932RSPTA.230..149G</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/10.1098%2Frsta.1932.0005">10.1098/rsta.1932.0005</a></span>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/91229">91229</a>. <q>The trichromatic coefficients for [Wright's] ten observers agreed so closely with those of the seven observers examined at the National Physical Laboratory as to indicate that both groups must give results approximating more closely to 'normal' than might have been expected from the size of either group</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions+of+the+Royal+Society+of+London.+Series+A%2C+Containing+Papers+of+a+Mathematical+or+Physical+Character&rft.atitle=The+colorimetric+properties+of+the+spectrum&rft.volume=230&rft.issue=681%E2%80%93693&rft.pages=149-187&rft.date=1932&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F91229%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1098%2Frsta.1932.0005&rft_id=info%3Abibcode%2F1932RSPTA.230..149G&rft.aulast=Guild&rft.aufirst=J.&rft_id=https%3A%2F%2Fdoi.org%2F10.1098%252Frsta.1932.0005&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</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.youtube.com/watch?v=d74gJxUdsq8">"- YouTube"</a>. <i><a href="/wiki/YouTube" title="YouTube">YouTube</a></i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160317005216/https://www.youtube.com/watch?v=d74gJxUdsq8">Archived</a> from the original on 2016-03-17<span class="reference-accessdate">. Retrieved <span class="nowrap">2015-10-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=YouTube&rft.atitle=-+YouTube&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3Dd74gJxUdsq8&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" class="Z3988"></span> Tristimulus Value of Color: Device Independent Color Representation</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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHunt1998" class="citation book cs1">Hunt, R. W. (1998). <i>Measuring Colour</i> (3rd ed.). England: Fountain Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-86343-387-1" title="Special:BookSources/0-86343-387-1"><bdi>0-86343-387-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Measuring+Colour&rft.place=England&rft.edition=3rd&rft.pub=Fountain+Press&rft.date=1998&rft.isbn=0-86343-387-1&rft.aulast=Hunt&rft.aufirst=R.+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" class="Z3988"></span>. See pgs. 39–46 for the basis in the physiology of the <a href="/wiki/Human_eye" title="Human eye">human eye</a> of tripartite color models, and 54–7 for chromaticity coordinates.</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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.japi.org/w29454/ragnar-granit-sensory-structure-of-retina-and-vision">"Ragnar Granit - Sensory Structure of Retina and Vision"</a>. <i>www.japi.org</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.japi.org&rft.atitle=Ragnar+Granit+-+Sensory+Structure+of+Retina+and+Vision&rft_id=https%3A%2F%2Fwww.japi.org%2Fw29454%2Fragnar-granit-sensory-structure-of-retina-and-vision&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" 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="CITEREFSchanda2007" class="citation book cs1">Schanda, János, ed. (2007-07-27). <i>Colorimetry</i>. p. 305. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F9780470175637">10.1002/9780470175637</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780470175637" title="Special:BookSources/9780470175637"><bdi>9780470175637</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Colorimetry&rft.pages=305&rft.date=2007-07-27&rft_id=info%3Adoi%2F10.1002%2F9780470175637&rft.isbn=9780470175637&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" 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="CITEREFStilesBirch1959" class="citation journal cs1">Stiles, W. 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I. (1959). "Determination of spectrum color co-ordinates for twenty seven normal observers". <i>Optics and Spectroscopy</i>. <b>7</b>: 424–428.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Optics+and+Spectroscopy&rft.atitle=Determination+of+spectrum+color+co-ordinates+for+twenty+seven+normal+observers&rft.volume=7&rft.pages=424-428&rft.date=1959&rft.aulast=Speranskaya&rft.aufirst=N.+I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" 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://web.archive.org/web/20170828183922/http://www.cie.co.at/index.php/LEFTMENUE/DOWNLOADS">"CIE Free Documents for Download"</a>. 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"NPL colour-matching investigation: final report". <i>Optica Acta</i>. <b>6</b> (1). <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/1959AcOpt...6....1S">1959AcOpt...6....1S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F713826267">10.1080/713826267</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Optica+Acta&rft.atitle=NPL+colour-matching+investigation%3A+final+report&rft.volume=6&rft.issue=1&rft.date=1959&rft_id=info%3Adoi%2F10.1080%2F713826267&rft_id=info%3Abibcode%2F1959AcOpt...6....1S&rft.aulast=Stiles&rft.aufirst=WS&rft.au=Burch%2C+JM&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" class="Z3988"></span></span> </li> <li id="cite_note-cie170.2-26"><span class="mw-cite-backlink">^ <a href="#cite_ref-cie170.2_26-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-cie170.2_26-1"><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 class="citation book cs1"><a rel="nofollow" class="external text" href="https://cie.co.at/publications/fundamental-chromaticity-diagram-physiological-axes-part-2-spectral-luminous-efficiency"><i>CIE 170-2:2015: Fundamental Chromaticity Diagram with Physiological Axes – Part 2: Spectral Luminous Efficiency Functions and Chromaticity Diagrams</i></a>. CIE. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-902842-05-3" title="Special:BookSources/978-3-902842-05-3"><bdi>978-3-902842-05-3</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20231119023239/https://cie.co.at/publications/fundamental-chromaticity-diagram-physiological-axes-part-2-spectral-luminous-efficiency">Archived</a> from the original on Nov 19, 2023.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=CIE+170-2%3A2015%3A+Fundamental+Chromaticity+Diagram+with+Physiological+Axes+%E2%80%93+Part+2%3A+Spectral+Luminous+Efficiency+Functions+and+Chromaticity+Diagrams&rft.pub=CIE&rft.isbn=978-3-902842-05-3&rft_id=https%3A%2F%2Fcie.co.at%2Fpublications%2Ffundamental-chromaticity-diagram-physiological-axes-part-2-spectral-luminous-efficiency&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</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="http://cvrl.ucl.ac.uk/ciexyzpr.htm">"CIE functions"</a>. <i>Colour & Vision Research Laboratory</i>. Institute of Ophthalmology, University College London. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20231119023223/http://cvrl.ucl.ac.uk/ciexyzpr.htm">Archived</a> from the original on Nov 19, 2023.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Colour+%26+Vision+Research+Laboratory&rft.atitle=CIE+functions&rft_id=http%3A%2F%2Fcvrl.ucl.ac.uk%2Fciexyzpr.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://sensing.konicaminolta.asia/wp-content/uploads/2018/09/Resolving_Display_Color_Matching_Issue.pdf">"Resolving Display Color Matching Issue"</a> <span class="cs1-format">(PDF)</span>. <i>KONICA MINOLTA</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=KONICA+MINOLTA&rft.atitle=Resolving+Display+Color+Matching+Issue&rft_id=https%3A%2F%2Fsensing.konicaminolta.asia%2Fwp-content%2Fuploads%2F2018%2F09%2FResolving_Display_Color_Matching_Issue.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=CIE_1931_color_space&action=edit&section=18" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBroadbent2004" class="citation journal cs1">Broadbent, Arthur D. (August 2004). "A critical review of the development of the CIE1931 RGB color-matching functions". <i>Color Research & Application</i>. <b>29</b> (4): 267–272. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fcol.20020">10.1002/col.20020</a>. <q>This article describes the development of the CIE1931 chromaticity coordinates and color-matching functions starting from the initial experimental data of W. D. Wright and J. Guild. Sufficient information is given to allow the reader to reproduce and verify the results obtained at each stage of the calculations and to analyze critically the procedures used. Unfortunately, some of the information required for the coordinate transformations was never published and the appended tables provide likely versions of that missing data.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Color+Research+%26+Application&rft.atitle=A+critical+review+of+the+development+of+the+CIE1931+RGB+color-matching+functions&rft.volume=29&rft.issue=4&rft.pages=267-272&rft.date=2004-08&rft_id=info%3Adoi%2F10.1002%2Fcol.20020&rft.aulast=Broadbent&rft.aufirst=Arthur+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTrezona2001" class="citation journal cs1">Trezona, Pat W. (2001). "Derivation of the 1964 CIE 10° XYZ Colour-Matching Functions and Their Applicability in Photometry". <i>Color Research and Application</i>. <b>26</b> (1): 67–75. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F1520-6378%28200102%2926%3A1%3C67%3A%3AAID-COL7%3E3.0.CO%3B2-4">10.1002/1520-6378(200102)26:1<67::AID-COL7>3.0.CO;2-4</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Color+Research+and+Application&rft.atitle=Derivation+of+the+1964+CIE+10%C2%B0+XYZ+Colour-Matching+Functions+and+Their+Applicability+in+Photometry&rft.volume=26&rft.issue=1&rft.pages=67-75&rft.date=2001&rft_id=info%3Adoi%2F10.1002%2F1520-6378%28200102%2926%3A1%3C67%3A%3AAID-COL7%3E3.0.CO%3B2-4&rft.aulast=Trezona&rft.aufirst=Pat+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWright2007" class="citation book cs1">Wright, William David (2007). "Golden Jubilee of Colour in the CIE—The Historical and Experimental Background to the 1931 CIE System of Colorimetry". In Schanda, János (ed.). <i>Colorimetry</i>. Wiley Interscience. pp. 9–24. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F9780470175637.ch2">10.1002/9780470175637.ch2</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-470-04904-4" title="Special:BookSources/978-0-470-04904-4"><bdi>978-0-470-04904-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Golden+Jubilee+of+Colour+in+the+CIE%E2%80%94The+Historical+and+Experimental+Background+to+the+1931+CIE+System+of+Colorimetry&rft.btitle=Colorimetry&rft.pages=9-24&rft.pub=Wiley+Interscience&rft.date=2007&rft_id=info%3Adoi%2F10.1002%2F9780470175637.ch2&rft.isbn=978-0-470-04904-4&rft.aulast=Wright&rft.aufirst=William+David&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACIE+1931+color+space" class="Z3988"></span> (originally published by the <a href="/wiki/Society_of_Dyers_and_Colourists" title="Society of Dyers and Colourists">Society of Dyers and Colourists</a>, Bradford, 1981.)</li></ul> <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=CIE_1931_color_space&action=edit&section=19" 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.techmind.org/colour/">Introduction to Colour Science</a>, William Andrew Steer.</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20080416044228/http://www.efg2.com/Lab/Graphics/Colors/Chromaticity.htm">efg's Color Chromaticity Diagrams Lab Report</a> and <a rel="nofollow" class="external text" href="https://web.archive.org/web/20061031155046/http://www.efg2.com/Lab/Graphics/Colors/Chromaticity.ZIP">Delphi source</a></li> <li><a rel="nofollow" class="external text" href="http://docs-hoffmann.de/ciexyz29082000.pdf">CIE Color Space</a>, Gernot Hoffmann</li> <li><a rel="nofollow" class="external text" href="http://cvrl.ioo.ucl.ac.uk/index.htm">Annotated downloadable data tables</a>, Andrew Stockman and Lindsay T. Sharpe.</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20080708200746/http://www.cis.rit.edu/mcsl/research/1931.php">Calculation from the original experimental data of the CIE 1931 RGB standard observer spectral chromaticity co-ordinates and color matching functions</a></li> <li><a rel="nofollow" class="external text" href="http://isp.uv.es/code/visioncolor/colorlab.html">Colorlab</a> MATLAB toolbox for color science computation and accurate color reproduction (by Jesus Malo and Maria Jose Luque, Universitat de Valencia). It includes CIE standard tristimulus colorimetry and transformations to a number of non-linear color appearance models (CIE Lab, CIE CAM, etc.).</li> <li><a rel="nofollow" class="external text" href="http://www2.konicaminolta.eu/eu/Measuring/pcc/en/index.html">Precise color communication</a> A Look at the Past and Future of LED Binning</li> <li><a rel="nofollow" class="external autonumber" href="https://www.lumenpulse.com/knowledge/led-binning?unit=metric">[1]</a> Measuring Color in a world of light</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 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href="/wiki/ICAM_(color_appearance_model)" title="ICAM (color appearance model)">iCAM</a></li> <li><a href="/wiki/CAM16" class="mw-redirect" title="CAM16">CAM16</a></li> <li><a href="/w/index.php?title=CIECAM16&action=edit&redlink=1" class="new" title="CIECAM16 (page does not exist)">CIECAM16</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/International_Commission_on_Illumination" title="International Commission on Illumination">CIE</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">XYZ (1931)</a></li> <li><a class="mw-selflink-fragment" href="#CIE_RGB_color_space">RGB (1931)</a></li> <li><a href="/wiki/CIE_1960_color_space" title="CIE 1960 color space">YUV (1960)</a></li> <li><a href="/wiki/CIE_1964_color_space" title="CIE 1964 color space">UVW (1964)</a></li> <li><a href="/wiki/CIELAB_color_space" title="CIELAB color space">CIELAB (1976)</a></li> <li><a href="/wiki/CIELUV" title="CIELUV">CIELUV (1976)</a></li> <li><a href="/wiki/CIECAM02" title="CIECAM02">CIECAM02</a></li> <li><a href="/w/index.php?title=CIECAM16&action=edit&redlink=1" class="new" title="CIECAM16 (page does not exist)">CIECAM16</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/RGB_color_model" title="RGB color model">RGB</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/RGB_color_spaces" title="RGB color spaces">RGB color spaces</a></li> <li><a href="/wiki/SRGB" title="SRGB">sRGB</a></li> <li><a href="/wiki/Rg_chromaticity" title="Rg chromaticity">rg chromaticity</a></li> <li><a href="/wiki/Adobe_RGB_color_space" title="Adobe RGB color space">Adobe</a></li> <li><a href="/wiki/Wide-gamut_RGB_color_space" title="Wide-gamut RGB color space">Wide-gamut</a></li> <li><a href="/wiki/ProPhoto_RGB_color_space" title="ProPhoto RGB color space">ProPhoto</a></li> <li><a href="/wiki/ScRGB" title="ScRGB">scRGB</a></li> <li><a href="/wiki/DCI-P3" title="DCI-P3">DCI-P3</a></li> <li><a href="/wiki/Rec._601" title="Rec. 601">Rec. 601</a></li> <li><a href="/wiki/NTSC#SMPTE_C" title="NTSC">SMPTE 240M/"C"</a></li> <li><a href="/wiki/Rec._709" title="Rec. 709">Rec. 709</a></li> <li><a href="/wiki/Rec._2020" title="Rec. 2020">Rec. 2020</a></li> <li><a href="/wiki/Rec._2100" title="Rec. 2100">Rec. 2100</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Y%E2%80%B2UV" title="Y′UV">Y′UV</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Y%E2%80%B2UV" title="Y′UV">YUV</a> <ul><li><a href="/wiki/PAL" title="PAL">PAL</a></li></ul></li> <li><a href="/wiki/YDbDr" title="YDbDr">YDbDr</a> <ul><li><a href="/wiki/SECAM" title="SECAM">SECAM</a></li></ul></li> <li><a href="/wiki/YIQ" title="YIQ">YIQ</a> <ul><li><a href="/wiki/NTSC" title="NTSC">NTSC</a></li></ul></li> <li><a href="/wiki/YCbCr" title="YCbCr">YCbCr</a> <ul><li><a href="/wiki/Rec._601" title="Rec. 601">Rec. 601</a></li> <li><a href="/wiki/Rec._709" title="Rec. 709">Rec. 709</a></li> <li><a href="/wiki/Rec._2020" title="Rec. 2020">Rec. 2020</a></li> <li><a href="/wiki/Rec._2100" title="Rec. 2100">Rec. 2100</a></li></ul></li> <li><a href="/wiki/ICtCp" title="ICtCp">ICtCp</a> <ul><li><a href="/wiki/Rec._2100" title="Rec. 2100">Rec. 2100</a></li></ul></li> <li><a href="/wiki/YPbPr" title="YPbPr">YPbPr</a> <ul><li><a href="/wiki/Multiplexed_Analogue_Components" title="Multiplexed Analogue Components">MAC</a></li></ul></li> <li><a href="/wiki/XvYCC" title="XvYCC">xvYCC</a></li> <li><a href="/wiki/YCoCg" title="YCoCg">YCoCg</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/CcMmYK_color_model" title="CcMmYK color model">CcMmYK</a></li> <li><a href="/wiki/CMYK_color_model" title="CMYK color model">CMYK</a></li> <li><a href="/wiki/ColorADD" title="ColorADD">ColorADD</a></li> <li><a href="/wiki/Coloroid" title="Coloroid">Coloroid</a></li> <li><a href="/wiki/LMS_color_space" title="LMS color space">LMS</a></li> <li><a href="/wiki/Hexachrome" title="Hexachrome">Hexachrome</a></li> <li><a href="/wiki/HSL_and_HSV" title="HSL and HSV">HSL, HSV</a></li> <li><a href="/wiki/HCL_color_space" title="HCL color space">HCL</a></li> <li><a href="/wiki/Impossible_color" title="Impossible color">Imaginary color</a></li> <li><a href="/wiki/Oklab_color_space" title="Oklab color space">Oklab</a></li> <li><a href="/wiki/OSA-UCS" title="OSA-UCS">OSA-UCS</a></li> <li><a href="/wiki/Practical_Color_Coordinate_System" title="Practical Color Coordinate System">PCCS</a></li> <li><a href="/wiki/RG_color_models" title="RG color models">RG</a></li> <li><a href="/wiki/RYB_color_model" title="RYB color model">RYB</a></li> <li><a href="/wiki/HWB_color_model" title="HWB color model">HWB</a></li> <li><a href="/wiki/YJK" title="YJK">YJK</a></li> <li><a href="/wiki/TSL_color_space" title="TSL color space">TSL</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Color systems<br />and standards</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Academy_Color_Encoding_System" title="Academy Color Encoding System">ACES</a></li> <li><a href="/wiki/News_Media_Alliance" title="News Media Alliance">ANPA</a></li> <li><a href="/wiki/Colour_Index_International" title="Colour Index International">Colour Index International</a> <ul><li><a href="/wiki/List_of_dyes" title="List of dyes">CI list of dyes</a></li></ul></li> <li><a href="/wiki/DIC_Corporation" title="DIC Corporation">DIC</a></li> <li><a href="/wiki/Federal_Standard_595" title="Federal Standard 595">Federal Standard 595</a></li> <li><a href="/wiki/HKS_(colour_system)" title="HKS (colour system)">HKS</a></li> <li><a href="/wiki/ICC_profile" title="ICC profile">ICC profile</a></li> <li><a href="/wiki/ISCC%E2%80%93NBS_system" title="ISCC–NBS system">ISCC–NBS</a></li> <li><a href="/wiki/Munsell_color_system" title="Munsell color system">Munsell</a></li> <li><a href="/wiki/Natural_Color_System" title="Natural Color System">NCS</a></li> <li><a href="/wiki/Ostwald_color_system" title="Ostwald color system">Ostwald</a></li> <li><a href="/wiki/Pantone" title="Pantone">Pantone</a></li> <li><a href="/wiki/RAL_colour_standard" title="RAL colour standard">RAL</a> <ul><li><a href="/wiki/List_of_RAL_colors" class="mw-redirect" title="List of RAL colors">list</a></li></ul></li> <li><a href="/w/index.php?title=JIS_Z8102&action=edit&redlink=1" class="new" title="JIS Z8102 (page does not exist)">JIS Z8102</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://ja.wikipedia.org/wiki/JIS%E6%85%A3%E7%94%A8%E8%89%B2%E5%90%8D" class="extiw" title="ja:JIS慣用色名">ja</a>]</span></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>For the vision capacities of organisms or machines, see <span class="noviewer" typeof="mw:File"><span title="Template"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/16px-Symbol_template_class_pink.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/23px-Symbol_template_class_pink.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/31px-Symbol_template_class_pink.svg.png 2x" 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CIE 1931 color space - Wikipedia