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Color rendering index - Wikipedia

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class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Example"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Example</span> </div> </a> <ul id="toc-Example-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Typical_values" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Typical_values"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Typical values</span> </div> </a> <ul id="toc-Typical_values-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Special_value:_R9" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Special_value:_R9"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Special value: R9</span> </div> </a> <ul id="toc-Special_value:_R9-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Criticism" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Criticism"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Criticism</span> </div> </a> <button aria-controls="toc-Criticism-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 Criticism subsection</span> </button> <ul id="toc-Criticism-sublist" class="vector-toc-list"> <li id="toc-Alternatives" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Alternatives"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Alternatives</span> </div> </a> <ul id="toc-Alternatives-sublist" class="vector-toc-list"> <li id="toc-Gamut_area_index_(GAI)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Gamut_area_index_(GAI)"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1.1</span> <span>Gamut area index (GAI)</span> </div> </a> <ul id="toc-Gamut_area_index_(GAI)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Color_quality_scale_(CQS)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Color_quality_scale_(CQS)"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1.2</span> <span>Color quality scale (CQS)</span> </div> </a> <ul id="toc-Color_quality_scale_(CQS)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Film_and_video_high-CRI_LED_lighting" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Film_and_video_high-CRI_LED_lighting"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Film and video high-CRI LED lighting</span> </div> </a> <ul id="toc-Film_and_video_high-CRI_LED_lighting-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">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-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">11</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Color rendering index</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 20 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-20" 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">20 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/%D9%85%D9%82%D9%8A%D8%A7%D8%B3_%D8%A7%D9%84%D8%AA%D8%AC%D8%B3%D9%8A%D8%AF_%D8%A7%D9%84%D9%84%D9%88%D9%86%D9%8A" title="مقياس التجسيد اللوني – Arabic" lang="ar" hreflang="ar" data-title="مقياس التجسيد اللوني" 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/%C3%8Dndex_de_reproducci%C3%B3_crom%C3%A0tica" title="Índex de reproducció cromàtica – Catalan" lang="ca" hreflang="ca" data-title="Índex de reproducció cromàtica" 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/Index_pod%C3%A1n%C3%AD_barev" title="Index podání barev – Czech" lang="cs" hreflang="cs" data-title="Index podání barev" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Farvegengivelsesindeks" title="Farvegengivelsesindeks – Danish" lang="da" hreflang="da" data-title="Farvegengivelsesindeks" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Farbwiedergabeindex" title="Farbwiedergabeindex – German" lang="de" hreflang="de" data-title="Farbwiedergabeindex" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%8Dndice_de_reproducci%C3%B3n_crom%C3%A1tica" title="Índice de reproducción cromática – Spanish" lang="es" hreflang="es" data-title="Índice de reproducción cromática" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B4%D9%86%D8%A7%D8%B3%D9%87_%D9%86%D9%85%D9%88%D8%AF_%D8%B1%D9%86%DA%AF" title="شناسه نمود رنگ – Persian" lang="fa" hreflang="fa" data-title="شناسه نمود رنگ" 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/Indice_de_rendu_des_couleurs" title="Indice de rendu des couleurs – French" lang="fr" hreflang="fr" data-title="Indice de rendu des couleurs" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Indeks_sesuaian_warna" title="Indeks sesuaian warna – Indonesian" lang="id" hreflang="id" data-title="Indeks sesuaian warna" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Indice_di_resa_cromatica" title="Indice di resa cromatica – Italian" lang="it" hreflang="it" data-title="Indice di resa cromatica" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Kleurweergave-index" title="Kleurweergave-index – Dutch" lang="nl" hreflang="nl" data-title="Kleurweergave-index" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Ra-indeks" title="Ra-indeks – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Ra-indeks" 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/Wsp%C3%B3%C5%82czynnik_oddawania_barw" title="Współczynnik oddawania barw – Polish" lang="pl" hreflang="pl" data-title="Współczynnik oddawania barw" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%98%D0%BD%D0%B4%D0%B5%D0%BA%D1%81_%D1%86%D0%B2%D0%B5%D1%82%D0%BE%D0%BF%D0%B5%D1%80%D0%B5%D0%B4%D0%B0%D1%87%D0%B8" title="Индекс цветопередачи – Russian" lang="ru" hreflang="ru" data-title="Индекс цветопередачи" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Color_rendering_index" title="Color rendering index – Simple English" lang="en-simple" hreflang="en-simple" data-title="Color rendering index" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/V%C3%A4rintoistoindeksi" title="Värintoistoindeksi – Finnish" lang="fi" hreflang="fi" data-title="Värintoistoindeksi" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Ra_(ljus)" title="Ra (ljus) – Swedish" lang="sv" hreflang="sv" data-title="Ra (ljus)" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%86%D0%BD%D0%B4%D0%B5%D0%BA%D1%81_%D0%BF%D0%B5%D1%80%D0%B5%D0%B4%D0%B0%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F_%D0%BA%D0%BE%D0%BB%D1%8C%D0%BE%D1%80%D1%83" title="Індекс передавання кольору – Ukrainian" lang="uk" hreflang="uk" data-title="Індекс передавання кольору" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ch%E1%BB%89_s%E1%BB%91_ho%C3%A0n_m%C3%A0u" title="Chỉ số hoàn màu – Vietnamese" lang="vi" hreflang="vi" data-title="Chỉ số hoàn màu" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%BC%94%E8%89%B2%E6%80%A7%E6%8C%87%E6%95%B8" 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<div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Measure of ability of a light source to reproduce colors in comparison with a standard light source</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Simple_spectroscope.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Simple_spectroscope.jpg/300px-Simple_spectroscope.jpg" decoding="async" width="300" height="478" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Simple_spectroscope.jpg/450px-Simple_spectroscope.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Simple_spectroscope.jpg/600px-Simple_spectroscope.jpg 2x" data-file-width="2000" data-file-height="3185" /></a><figcaption>Emitted light spectrum determines the CRI of the lamp. An incandescent lamp (middle image) has a continuous spectrum and therefore a higher CRI than a fluorescent lamp (lower image). The top image shows the setup of the demonstration from above.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:AmbientLED.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/AmbientLED.png/300px-AmbientLED.png" decoding="async" width="300" height="415" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/AmbientLED.png/450px-AmbientLED.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/58/AmbientLED.png/600px-AmbientLED.png 2x" data-file-width="978" data-file-height="1354" /></a><figcaption>Color rendering index shown as color accuracy</figcaption></figure> <p>A <b>color rendering index</b> (<b>CRI</b>) is a quantitative measure of the ability of a <a href="/wiki/Light_source" class="mw-redirect" title="Light source">light source</a> to reveal the <a href="/wiki/Color" title="Color">colors</a> of various objects faithfully in comparison with a natural or standard light source. </p><p><i><a href="/wiki/Color_rendering" title="Color rendering">Color rendering</a></i>, as defined by the <a href="/wiki/International_Commission_on_Illumination" title="International Commission on Illumination">International Commission on Illumination</a> (CIE), is the effect of an <a href="/wiki/Light#Light_sources" title="Light">illuminant</a> on the color appearance of objects by conscious or subconscious comparison with their color appearance under a reference or <a href="/wiki/Standard_illuminant" title="Standard illuminant">standard illuminant</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup> </p><p>The CRI of a light source does not indicate the apparent color of the light source; that information is given by the <a href="/wiki/Color_temperature" title="Color temperature">correlated color temperature (CCT)</a>. The CRI is determined by the light source's <a href="/wiki/Spectrum" title="Spectrum">spectrum</a>. An <a href="/wiki/Incandescent_lamp" class="mw-redirect" title="Incandescent lamp">incandescent lamp</a> has a <a href="/wiki/Continuous_spectrum" class="mw-redirect" title="Continuous spectrum">continuous spectrum</a>, a <a href="/wiki/Fluorescent_lamp" title="Fluorescent lamp">fluorescent lamp</a> has a discrete <a href="/wiki/Emission_spectrum" title="Emission spectrum">line spectrum</a>; implying that the incandescent lamp has the higher CRI. </p><p>The value often quoted as "CRI" on commercially available lighting products is properly called the CIE R<sub>a</sub> value, "CRI" being a general term and CIE R<sub>a</sub> being the international standard color rendering index. </p><p>Numerically, the highest possible CIE R<sub>a</sub> value is 100 and would only be given to a source whose <a href="/wiki/Spectrum" title="Spectrum">spectrum</a> is identical to <a href="/wiki/Solar_spectrum" class="mw-redirect" title="Solar spectrum">the spectrum of daylight</a>, very close to that of a <a href="/wiki/Black_body" title="Black body">black body</a> (incandescent lamps are effectively black bodies), dropping to negative values for some light sources. <a href="/wiki/Low-pressure_sodium_light" class="mw-redirect" title="Low-pressure sodium light">Low-pressure sodium lighting</a> has a negative CRI; <a href="/wiki/Fluorescent_light" class="mw-redirect" title="Fluorescent light">fluorescent lights</a> range from about 50 for the basic types, up to about 98 for the best multi-phosphor type. Typical white-color <a href="/wiki/LEDs" class="mw-redirect" title="LEDs">LEDs</a> have a CRI of 80 or more, while some manufacturers claim that their LEDs achieve a CRI of up to 98.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">&#91;</span>2<span class="cite-bracket">&#93;</span></a></sup> </p><p>CIE R<sub>a</sub>'s ability to predict color appearance has been criticized in favor of measures based on <a href="/wiki/Color_appearance_model" title="Color appearance model">color appearance models</a>, such as <a href="/wiki/CIECAM02" title="CIECAM02">CIECAM02</a> and for <a href="/wiki/Daylight" title="Daylight">daylight</a> simulators, the CIE <a href="/wiki/Metamerism_index" class="mw-redirect" title="Metamerism index">metamerism index</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">&#91;</span>3<span class="cite-bracket">&#93;</span></a></sup> CRI is not a good indicator for use in visual assessment of light sources, especially for sources below 5000&#160;<a href="/wiki/Kelvin" title="Kelvin">kelvin</a> (K).<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">&#91;</span>4<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-CIE1995_5-0" class="reference"><a href="#cite_note-CIE1995-5"><span class="cite-bracket">&#91;</span>5<span class="cite-bracket">&#93;</span></a></sup> New standards, such as the <a href="/wiki/IES_TM-30" class="mw-redirect" title="IES TM-30">IES TM-30</a>, resolve these issues and have begun replacing the usage of CRI among professional lighting designers.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">&#91;</span>6<span class="cite-bracket">&#93;</span></a></sup> However, CRI is still common among household lighting products. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_rendering_index&amp;action=edit&amp;section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Researchers use daylight as the benchmark to which to compare color rendering of electric lights. In 1948, daylight was described as the ideal source of <a href="/wiki/Illumination_(image)" title="Illumination (image)">illumination</a> for good color rendering because "it (daylight) displays (1) a great variety of colors, (2) makes it easy to distinguish slight shades of color, and (3) the colors of objects around us obviously look natural".<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">&#91;</span>7<span class="cite-bracket">&#93;</span></a></sup> </p><p>Around the middle of the 20th century, color scientists took an interest in assessing the ability of <a href="/wiki/Artificial_light" class="mw-redirect" title="Artificial light">artificial lights</a> to accurately reproduce colors. European researchers attempted to describe illuminants by measuring the <a href="/wiki/Spectral_power_distribution" title="Spectral power distribution">spectral power distribution</a> (SPD) in "representative" spectral bands, whereas their North American counterparts studied the <a href="/wiki/Colorimetric" class="mw-redirect" title="Colorimetric">colorimetric</a> effect of the illuminants on reference objects.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">&#91;</span>8<span class="cite-bracket">&#93;</span></a></sup> </p><p>The <a href="/wiki/International_Commission_on_Illumination" title="International Commission on Illumination">CIE</a> assembled a committee to study the matter and accepted the proposal to use the latter approach, which has the virtue of not needing <a href="/wiki/Spectrophotometry" title="Spectrophotometry">spectrophotometry</a>, with a set of <a href="/wiki/Munsell_color_system" title="Munsell color system">Munsell</a> samples. Eight samples of varying hue would be alternately lit with two illuminants, and the color appearance compared. Since no color appearance model existed at the time, it was decided to base the evaluation on color differences in a suitable color space, <a href="/wiki/CIE_1964_color_space" title="CIE 1964 color space">CIEUVW</a>. In 1931, the CIE adopted the first formal system of <a href="/wiki/Colorimetry" title="Colorimetry">colorimetry</a>, which is based on the trichromatic nature of the <a href="/wiki/Human_visual_system" class="mw-redirect" title="Human visual system">human visual system</a>.<sup id="cite_ref-Color_rendering:_Beyond_pride_and_prejudice_-_Rea_-_2010_-_Color_Research_&amp;_Application_-_Wiley_Online_Library_9-0" class="reference"><a href="#cite_note-Color_rendering:_Beyond_pride_and_prejudice_-_Rea_-_2010_-_Color_Research_&amp;_Application_-_Wiley_Online_Library-9"><span class="cite-bracket">&#91;</span>9<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">&#91;</span>10<span class="cite-bracket">&#93;</span></a></sup> CRI is based upon this system of colorimetry.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">&#91;</span>11<span class="cite-bracket">&#93;</span></a></sup> </p><p>To deal with the problem of having to compare light sources of different correlated color temperatures (CCT), the CIE settled on using a reference <a href="/wiki/Black_body" title="Black body">black body</a> with the same color temperature for lamps with a CCT of under 5000&#160;K, or a phase of CIE <a href="/wiki/Standard_illuminant" title="Standard illuminant">standard illuminant</a> D (daylight) otherwise. This presented a continuous range of color temperatures to choose a reference from. Any chromaticity difference between the source and reference illuminants were to be abridged with a von Kries-type <a href="/wiki/Chromatic_adaptation_transform" class="mw-redirect" title="Chromatic adaptation transform">chromatic adaptation transform</a>. There are two extent versions of CRI: the more commonly used R<sub>a</sub> of <a href="#CITEREFCIE1995">CIE (1995)</a> (actually from 1974) and R96<sub>a</sub> of <a href="#CITEREFCIE1999">CIE (1999)</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Test_method">Test method</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_rendering_index&amp;action=edit&amp;section=2" title="Edit section: Test method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The CRI is calculated by comparing the color rendering of the test source to that of a "perfect" source, which is a black body radiator for sources with correlated color temperatures under 5000&#160;K, and a phase of daylight otherwise (e.g., <a href="/wiki/CIE_Standard_Illuminant_D65" class="mw-redirect" title="CIE Standard Illuminant D65">D65</a>). <a href="/wiki/Chromatic_adaptation" title="Chromatic adaptation">Chromatic adaptation</a> should be performed so that like quantities are compared. The <i>Test Method</i> (also called <i>Test Sample Method</i> or <i>Test Color Method</i>) needs only <a href="/wiki/Colorimetric" class="mw-redirect" title="Colorimetric">colorimetric</a>, rather than <a href="/wiki/Spectrophotometric" class="mw-redirect" title="Spectrophotometric">spectrophotometric</a>, information.<sup id="cite_ref-CIE1995_5-1" class="reference"><a href="#cite_note-CIE1995-5"><span class="cite-bracket">&#91;</span>5<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">&#91;</span>12<span class="cite-bracket">&#93;</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:CIE_1960_UCS.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/CIE_1960_UCS.png/220px-CIE_1960_UCS.png" decoding="async" width="220" height="152" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/CIE_1960_UCS.png/330px-CIE_1960_UCS.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a1/CIE_1960_UCS.png/440px-CIE_1960_UCS.png 2x" data-file-width="2130" data-file-height="1467" /></a><figcaption>CIE 1960 UCS. Planckian locus and co-ordinates of several illuminants shown in illustration below.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Planckian-locus.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Planckian-locus.png/220px-Planckian-locus.png" decoding="async" width="220" height="98" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Planckian-locus.png/330px-Planckian-locus.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Planckian-locus.png/440px-Planckian-locus.png 2x" data-file-width="1334" data-file-height="597" /></a><figcaption>(<i>u</i>, <i>v</i>) chromaticity diagram with several CIE illuminants</figcaption></figure> <ol><li>Using the <a href="/wiki/CIE_1931_color_space#CIE_standard_observer" title="CIE 1931 color space">2° standard observer</a>, find the <a href="/wiki/Chromaticity" title="Chromaticity">chromaticity</a> co-ordinates of the test source in the <a href="/wiki/CIE_1960_color_space" title="CIE 1960 color space">CIE 1960 color space</a>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">&#91;</span>13<span class="cite-bracket">&#93;</span></a></sup></li> <li>Determine the <a href="/wiki/Correlated_color_temperature" title="Correlated color temperature">correlated color temperature</a> (CCT) of the test source by finding the closest point to the <a href="/wiki/Planckian_locus" title="Planckian locus">Planckian locus</a> on the (<i>u</i>,&#160;<i>v</i>) chromaticity diagram.</li> <li>If the test source has a CCT &lt; 5000&#160;K, use a black body for reference, otherwise use CIE <a href="/wiki/Standard_illuminant" title="Standard illuminant">standard illuminant</a> D. Both sources should have the same CCT.</li> <li>Ensure that the chromaticity distance (DC) of the test source to the Planckian locus is under 5.4×10<sup>−3</sup> in the CIE 1960 UCS. This ensures the meaningfulness of the result, as the CRI is only defined for light sources that are approximately white.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">&#91;</span>14<span class="cite-bracket">&#93;</span></a></sup> <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 {\text{DC}}=\Delta _{uv}={\sqrt {(u_{r}-u_{t})^{2}+(v_{r}-v_{t})^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>DC</mtext> </mrow> <mo>=</mo> <msub> <mi mathvariant="normal">&#x0394;<!-- Δ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> <mi>v</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>&#x2212;<!-- − --></mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>&#x2212;<!-- − --></mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{DC}}=\Delta _{uv}={\sqrt {(u_{r}-u_{t})^{2}+(v_{r}-v_{t})^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0282bcf23b2e99dd540e2bffdbc003cb89af6366" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:39.289ex; height:4.843ex;" alt="{\displaystyle {\text{DC}}=\Delta _{uv}={\sqrt {(u_{r}-u_{t})^{2}+(v_{r}-v_{t})^{2}}}.}"></span></li> <li>Illuminate the first eight standard samples, from the fifteen listed below, alternately using both sources.</li> <li>Using the 2° standard observer, find the co-ordinates of the light reflected by each sample in the <a href="/wiki/CIE_1964_color_space" title="CIE 1964 color space">CIE 1964 color space</a>.</li> <li>Chromatically adapt each sample by a <a href="/wiki/Chromatic_adaptation#Von_Kries_transform" title="Chromatic adaptation">Von Kries transform</a>.</li> <li>For each sample, calculate the <a href="/wiki/Euclidean_distance" title="Euclidean distance">Euclidean distance</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 \Delta E_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">&#x0394;<!-- Δ --></mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa40fa108e21d148e5a39c6202cf9a2ee69cb1cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.451ex; height:2.509ex;" alt="{\displaystyle \Delta E_{i}}"></span> between the pair of co-ordinates.</li> <li>Calculate the special (i.e., particular) CRI using the formula <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{i}=100-4.6\Delta E_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>100</mn> <mo>&#x2212;<!-- − --></mo> <mn>4.6</mn> <mi mathvariant="normal">&#x0394;<!-- Δ --></mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{i}=100-4.6\Delta E_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae5a68a11fd1c054f53f24a57d5c8aaa5d183c50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.412ex; height:2.509ex;" alt="{\displaystyle R_{i}=100-4.6\Delta E_{i}}"></span><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">&#91;</span>15<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">&#91;</span>16<span class="cite-bracket">&#93;</span></a></sup></li> <li>Find the general CRI (R<sub>a</sub>) by calculating the <a href="/wiki/Arithmetic_mean" title="Arithmetic mean">arithmetic mean</a> of the special CRIs.</li></ol> <p>Note that the last three steps are equivalent to finding the mean <a href="/wiki/Color_difference" title="Color difference">color difference</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 \Delta {\bar {E}}_{UVW}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">&#x0394;<!-- Δ --></mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">&#x00AF;<!-- ¯ --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>U</mi> <mi>V</mi> <mi>W</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta {\bar {E}}_{UVW}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/287de1848ddb2963d11558d5e147b1cb5068d5aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.19ex; height:2.843ex;" alt="{\displaystyle \Delta {\bar {E}}_{UVW}}"></span> and using that to calculate <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5799fce3a0226ed0ddc26ea365f7e0a492958601" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.866ex; height:2.509ex;" alt="{\displaystyle R_{a}}"></span>: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{a}=100-4.6\Delta {\bar {E}}_{UVW}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>100</mn> <mo>&#x2212;<!-- − --></mo> <mn>4.6</mn> <mi mathvariant="normal">&#x0394;<!-- Δ --></mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">&#x00AF;<!-- ¯ --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>U</mi> <mi>V</mi> <mi>W</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{a}=100-4.6\Delta {\bar {E}}_{UVW}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66af31c557141a96a2513a62377c0ff003b65904" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.101ex; height:2.843ex;" alt="{\displaystyle R_{a}=100-4.6\Delta {\bar {E}}_{UVW}.}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Chromatic_adaptation">Chromatic adaptation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_rendering_index&amp;action=edit&amp;section=3" title="Edit section: Chromatic adaptation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:CIE_CRI_TCS_under_FL4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/CIE_CRI_TCS_under_FL4.svg/220px-CIE_CRI_TCS_under_FL4.svg.png" decoding="async" width="220" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/CIE_CRI_TCS_under_FL4.svg/330px-CIE_CRI_TCS_under_FL4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/CIE_CRI_TCS_under_FL4.svg/440px-CIE_CRI_TCS_under_FL4.svg.png 2x" data-file-width="851" data-file-height="392" /></a><figcaption>Chromatic adaptation of TCSs lit by CIE FL4 (short, black vectors, to indicate before and after) to a black body of 2940 K (cyan circles)</figcaption></figure> <p><a href="#CITEREFCIE1995">CIE (1995)</a> uses this von Kries chromatic transform equation to find the <a href="/w/index.php?title=Corresponding_color&amp;action=edit&amp;redlink=1" class="new" title="Corresponding color (page does not exist)">corresponding color</a> (<i>u</i><sub><i>c</i>,<i>i</i></sub>,&#160;<i>v</i><sub><i>c</i>,<i>i</i></sub>) for each sample. The mixed subscripts (<i>t</i>,&#160;<i>i</i>) refer to the <a href="/wiki/Inner_product" class="mw-redirect" title="Inner product">inner product</a> of the test illuminant spectrum and the spectral reflexivity of sample <i>i</i>: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{c,i}={\frac {10.872+0.404(c_{r}/c_{t})c_{t,i}-4(d_{r}/d_{t})d_{t,i}}{16.518+1.481(c_{r}/c_{t})c_{t,i}-(d_{r}/d_{t})d_{t,i}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>10.872</mn> <mo>+</mo> <mn>0.404</mn> <mo stretchy="false">(</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>&#x2212;<!-- − --></mo> <mn>4</mn> <mo stretchy="false">(</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mn>16.518</mn> <mo>+</mo> <mn>1.481</mn> <mo stretchy="false">(</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>&#x2212;<!-- − --></mo> <mo stretchy="false">(</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{c,i}={\frac {10.872+0.404(c_{r}/c_{t})c_{t,i}-4(d_{r}/d_{t})d_{t,i}}{16.518+1.481(c_{r}/c_{t})c_{t,i}-(d_{r}/d_{t})d_{t,i}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d50c46f085f97a012e191c58ec43b239f8dd77a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:46.371ex; height:6.509ex;" alt="{\displaystyle u_{c,i}={\frac {10.872+0.404(c_{r}/c_{t})c_{t,i}-4(d_{r}/d_{t})d_{t,i}}{16.518+1.481(c_{r}/c_{t})c_{t,i}-(d_{r}/d_{t})d_{t,i}}},}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{c,i}={\frac {5.520}{16.518+1.481(c_{r}/c_{t})c_{t,i}-(d_{r}/d_{t})d_{t,i}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5.520</mn> <mrow> <mn>16.518</mn> <mo>+</mo> <mn>1.481</mn> <mo stretchy="false">(</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>&#x2212;<!-- − --></mo> <mo stretchy="false">(</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{c,i}={\frac {5.520}{16.518+1.481(c_{r}/c_{t})c_{t,i}-(d_{r}/d_{t})d_{t,i}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37b41188c764d32f0001fc27d6c103665217a66f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:45.006ex; height:6.009ex;" alt="{\displaystyle v_{c,i}={\frac {5.520}{16.518+1.481(c_{r}/c_{t})c_{t,i}-(d_{r}/d_{t})d_{t,i}}},}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c=(4.0-u-10.0v)/v,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mn>4.0</mn> <mo>&#x2212;<!-- − --></mo> <mi>u</mi> <mo>&#x2212;<!-- − --></mo> <mn>10.0</mn> <mi>v</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>v</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c=(4.0-u-10.0v)/v,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/243cb2a74028cdb2eeaad7e9e8a5a4f9d6889b9d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.096ex; height:2.843ex;" alt="{\displaystyle c=(4.0-u-10.0v)/v,}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d=(1.708v-1.481u+0.404)/v,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1.708</mn> <mi>v</mi> <mo>&#x2212;<!-- − --></mo> <mn>1.481</mn> <mi>u</mi> <mo>+</mo> <mn>0.404</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>v</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d=(1.708v-1.481u+0.404)/v,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c863bdf7967c7e7bb060d2b89d31ad2005f909bd" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:33.089ex; height:2.843ex;" alt="{\displaystyle d=(1.708v-1.481u+0.404)/v,}"></span> </p><p>where subscripts <i>r</i> and <i>t</i> refer to reference and test light sources respectively. </p> <div class="mw-heading mw-heading3"><h3 id="Test_color_samples">Test color samples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_rendering_index&amp;action=edit&amp;section=4" title="Edit section: Test color samples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable floatleft"> <tbody><tr> <th>Name </th> <th>Appr. Munsell </th> <th>Appearance under daylight </th> <th>Swatch </th></tr> <tr> <td>TCS01 </td> <td>7,5 R 6/4 </td> <td>Light greyish red </td> <td style="background:#e8a7b0;"> </td></tr> <tr> <td>TCS02 </td> <td>5 Y 6/4 </td> <td>Dark greyish yellow </td> <td style="background:#ccb184;"> </td></tr> <tr> <td>TCS03 </td> <td>5 GY 6/8 </td> <td>Strong yellow green </td> <td style="background:#abc161;"> </td></tr> <tr> <td>TCS04 </td> <td>2,5 G 6/6 </td> <td>Moderate yellowish green </td> <td style="background:#6fc59f;"> </td></tr> <tr> <td>TCS05 </td> <td>10 BG 6/4 </td> <td>Light bluish green </td> <td style="background:#7fc2df;"> </td></tr> <tr> <td>TCS06 </td> <td>5 PB 6/8 </td> <td>Light blue </td> <td style="background:#8fb6ff;"> </td></tr> <tr> <td>TCS07 </td> <td>2,5 P 6/8 </td> <td>Light violet </td> <td style="background:#cca5ff;"> </td></tr> <tr> <td>TCS08 </td> <td>10 P 6/8 </td> <td>Light reddish purple </td> <td style="background:#eea3ef;"> </td></tr> <tr> <td>TCS09 </td> <td>4,5 R 4/13 </td> <td>Strong red </td> <td style="background:#e9214c;"> </td></tr> <tr> <td>TCS10 </td> <td>5 Y 8/10 </td> <td>Strong yellow </td> <td style="background:#fff456;"> </td></tr> <tr> <td>TCS11 </td> <td>4,5 G 5/8 </td> <td>Strong green </td> <td style="background:#0cac8a;"> </td></tr> <tr> <td>TCS12 </td> <td>3 PB 3/11 </td> <td>Strong blue </td> <td style="background:#005bc0;"> </td></tr> <tr> <td>TCS13 </td> <td>5 YR 8/4 </td> <td>Light yellowish pink </td> <td style="background:#ffe8da;"> </td></tr> <tr> <td>TCS14 </td> <td>5 GY 4/4 </td> <td>Moderate olive green (<a href="/wiki/Leaf" title="Leaf">leaf</a>) </td> <td style="background:#6c7d4f;"> </td></tr></tbody></table> <p>As specified in <a href="#CITEREFCIE1995">CIE (1995)</a>, the original test color samples (TCS) are taken from an early edition of the <a href="/wiki/Farnsworth-Munsell_100_hue_test" class="mw-redirect" title="Farnsworth-Munsell 100 hue test">Munsell</a> Atlas. The first eight samples, a subset of the eighteen proposed in <a href="#CITEREFNickerson1960">Nickerson (1960)</a>, are relatively low saturated colors and are evenly distributed over the complete range of hues.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">&#91;</span>17<span class="cite-bracket">&#93;</span></a></sup> These eight samples are employed to calculate the general color rendering index <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5799fce3a0226ed0ddc26ea365f7e0a492958601" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.866ex; height:2.509ex;" alt="{\displaystyle R_{a}}"></span>. The last six samples provide supplementary information about the color rendering properties of the light source; the first four for high saturation, and the last two as representatives of well-known objects. The reflectance spectra of these samples may be found in <a href="#CITEREFCIE2004">CIE (2004)</a>,<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">&#91;</span>18<span class="cite-bracket">&#93;</span></a></sup> and their approximate Munsell notations are listed aside.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">&#91;</span>19<span class="cite-bracket">&#93;</span></a></sup> </p> <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/File:CIE_CRI_TCS_SPDs.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/CIE_CRI_TCS_SPDs.svg/300px-CIE_CRI_TCS_SPDs.svg.png" decoding="async" width="300" height="205" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/CIE_CRI_TCS_SPDs.svg/450px-CIE_CRI_TCS_SPDs.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d7/CIE_CRI_TCS_SPDs.svg/600px-CIE_CRI_TCS_SPDs.svg.png 2x" data-file-width="537" data-file-height="367" /></a><figcaption></figcaption></figure> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading2"><h2 id="R96a_method">R96<sub>a</sub> method</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_rendering_index&amp;action=edit&amp;section=5" title="Edit section: R96a method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/File:CIE_CRI_TCS_chromaticities.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/CIE_CRI_TCS_chromaticities.svg/300px-CIE_CRI_TCS_chromaticities.svg.png" decoding="async" width="300" height="237" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/CIE_CRI_TCS_chromaticities.svg/450px-CIE_CRI_TCS_chromaticities.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/36/CIE_CRI_TCS_chromaticities.svg/600px-CIE_CRI_TCS_chromaticities.svg.png 2x" data-file-width="461" data-file-height="364" /></a><figcaption></figcaption></figure> <p>In the CIE's 1991 Quadrennial Meeting, Technical Committee 1-33 (Color Rendering) was assembled to work on updating the color rendering method, as a result of which the R96<sub>a</sub> method was developed. The committee was dissolved in 1999, releasing <a href="#CITEREFCIE1999">CIE (1999)</a>, but no firm recommendations, partly due to disagreements between researchers and manufacturers.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">&#91;</span>20<span class="cite-bracket">&#93;</span></a></sup> </p><p>The R96<sub>a</sub> method has a few distinguishing features:<sup id="cite_ref-FOOTNOTEBodrogi200411Past_research_to_improve_the_CRI_21-0" class="reference"><a href="#cite_note-FOOTNOTEBodrogi200411Past_research_to_improve_the_CRI-21"><span class="cite-bracket">&#91;</span>21<span class="cite-bracket">&#93;</span></a></sup> </p> <ul><li><a href="#New_test_color_samples">A new set of test color samples</a></li> <li>Six reference illuminants: D65, D50, black bodies of 4200 K, 3450 K, 2950 K, and 2700 K.</li> <li>A new chromatic adaptation transform: CIECAT94.</li> <li>Color difference evaluation in CIELAB.</li> <li>Adaptation of all colors to <a href="/wiki/CIE_Standard_Illuminant_D65" class="mw-redirect" title="CIE Standard Illuminant D65">D65</a> (since CIELAB is well-tested under D65).</li></ul> <p>It is conventional to use the original method; R96<sub>a</sub> should be explicitly mentioned if used. </p> <div class="mw-heading mw-heading3"><h3 id="New_test_color_samples">New test color samples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_rendering_index&amp;action=edit&amp;section=6" title="Edit section: New test color samples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable floatright" border="1"> <tbody><tr> <th> </th> <th>TCS01<sup>*</sup> </th> <th>TCS02<sup>*</sup> </th> <th>TCS03<sup>*</sup> </th> <th>TCS04<sup>*</sup> </th> <th>TCS05<sup>*</sup> </th> <th>TCS06<sup>*</sup> </th> <th>TCS07<sup>*</sup> </th> <th>TCS08<sup>*</sup> </th> <th>TCS09<sup>*</sup> </th> <th>TCS10<sup>*</sup> </th></tr> <tr> <td>L<sup>*</sup></td> <td>40.9</td> <td>61.1</td> <td>81.6</td> <td>72.0</td> <td>55.7</td> <td>51.7</td> <td>30.0</td> <td>51.0</td> <td>68.7</td> <td>63.9 </td></tr> <tr> <td>a<sup>*</sup></td> <td>51.0</td> <td>28.8</td> <td>−4.2</td> <td>−29.4</td> <td>−43.4</td> <td>−26.4</td> <td>23.2</td> <td>47.3</td> <td>14.2</td> <td>11.7 </td></tr> <tr> <td>b<sup>*</sup></td> <td>26.3</td> <td>57.9</td> <td>80.3</td> <td>58.9</td> <td>35.6</td> <td>−24.6</td> <td>−49.6</td> <td>−13.8</td> <td>17.4</td> <td>17.3 </td></tr> <tr> <td style="height:25px;"> </td> <td style="background:#ad3139;"> </td> <td style="background:#d17e27;"> </td> <td style="background:#e0cb08;"> </td> <td style="background:#92be38;"> </td> <td style="background:#369842;"> </td> <td style="background:#0089a5;"> </td> <td style="background:#413c95;"> </td> <td style="background:#bb5593;"> </td> <td style="background:#c99e89;"> </td> <td style="background:#b7837d;"> </td></tr></tbody></table> <p>As discussed in <a href="#CITEREFSándorSchanda2005">Sándor &amp; Schanda (2005)</a>, <a href="#CITEREFCIE1999">CIE (1999)</a> recommends the use of a <a href="/wiki/ColorChecker" title="ColorChecker">ColorChecker</a> chart owing to the obsolescence of the original samples, of which only <a href="/wiki/Metamerism_(color)" title="Metamerism (color)">metameric</a> matches remain.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">&#91;</span>22<span class="cite-bracket">&#93;</span></a></sup> In addition to the eight ColorChart samples, two skin tone samples are defined (TCS09<sup>*</sup> and TCS10<sup>*</sup>). Accordingly, the updated general CRI is averaged over ten samples, not eight as before. Nevertheless, <a href="#CITEREFHung2002">Hung (2002)</a> has determined that the patches in <a href="#CITEREFCIE1995">CIE (1995)</a> give better correlations for any color difference than the ColorChecker chart, whose samples are not equally distributed in a uniform color space. </p> <div class="mw-heading mw-heading2"><h2 id="Example">Example</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_rendering_index&amp;action=edit&amp;section=7" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Missing_information plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Wiki_letter_w.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/44px-Wiki_letter_w.svg.png" decoding="async" width="44" height="44" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/66px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/88px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>is missing information</b> about Can we briefly do a R96<sub>a</sub> too?.<span class="hide-when-compact"> Please expand the section to include this information. Further details may exist on the <a href="/wiki/Talk:Color_rendering_index" title="Talk:Color rendering index">talk page</a>.</span> <span class="date-container"><i>(<span class="date">November 2021</span>)</i></span></div></td></tr></tbody></table> <p>The CRI can also be theoretically derived from the spectral power distribution (SPD) of the illuminant and samples, since physical copies of the original color samples are difficult to find. In this method, care should be taken to use a sampling resolution fine enough to capture spikes in the SPD. The SPDs of the standard test colors are tabulated in 5&#160;nm increments <a href="#CITEREFCIE2004">CIE (2004)</a>, so it is suggested to use interpolation up to the resolution of the illuminant's spectrophotometry. </p><p>Starting with the SPD, let us verify that the CRI of reference illuminant F4 is 51. The first step is to determine the <a href="/wiki/Tristimulus_value" class="mw-redirect" title="Tristimulus value">tristimulus values</a> using the 1931 standard observer. Calculation of the <a href="/wiki/Inner_product" class="mw-redirect" title="Inner product">inner product</a> of the SPD with the standard observer's color matching functions (CMFs) yields (<i>X</i>,&#160;<i>Y</i>,&#160;<i>Z</i>) = (109.2,&#160;100.0,&#160;38.9) (after normalizing for <i>Y</i>&#160;= 100). From this follow the <i>xy</i> chromaticity values: </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:CIE_1960_UCS,_FL4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/CIE_1960_UCS%2C_FL4.svg/180px-CIE_1960_UCS%2C_FL4.svg.png" decoding="async" width="180" height="258" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/CIE_1960_UCS%2C_FL4.svg/270px-CIE_1960_UCS%2C_FL4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/CIE_1960_UCS%2C_FL4.svg/360px-CIE_1960_UCS%2C_FL4.svg.png 2x" data-file-width="276" data-file-height="395" /></a><figcaption>The tight isotherms are from 2935&#160;K to 2945&#160;K. FL4 marked with a cross.</figcaption></figure> <p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x={\frac {109.2}{109.2+100.0+38.9}}=0.4402,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>109.2</mn> <mrow> <mn>109.2</mn> <mo>+</mo> <mn>100.0</mn> <mo>+</mo> <mn>38.9</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0.4402</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x={\frac {109.2}{109.2+100.0+38.9}}=0.4402,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d83c9ade320a0947bf36f6041c2dbcb7e325e292" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:35.877ex; height:5.343ex;" alt="{\displaystyle x={\frac {109.2}{109.2+100.0+38.9}}=0.4402,}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y={\frac {100}{109.2+100.0+38.9}}=0.4031.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>100</mn> <mrow> <mn>109.2</mn> <mo>+</mo> <mn>100.0</mn> <mo>+</mo> <mn>38.9</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0.4031.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y={\frac {100}{109.2+100.0+38.9}}=0.4031.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14bb8fe4dc1bef35aa955df1d497be5c3ea392f4" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:35.703ex; height:5.343ex;" alt="{\displaystyle y={\frac {100}{109.2+100.0+38.9}}=0.4031.}"></span> </p><p>The next step is to convert these chromaticities to the <a href="/wiki/CIE_1960_color_space" title="CIE 1960 color space">CIE 1960 UCS</a> in order to be able to determine the CCT: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u={\frac {4\times 0.4402}{-2\times 0.4402+12\times 0.4031+3}}=0.2531,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mo>&#x00D7;<!-- × --></mo> <mn>0.4402</mn> </mrow> <mrow> <mo>&#x2212;<!-- − --></mo> <mn>2</mn> <mo>&#x00D7;<!-- × --></mo> <mn>0.4402</mn> <mo>+</mo> <mn>12</mn> <mo>&#x00D7;<!-- × --></mo> <mn>0.4031</mn> <mo>+</mo> <mn>3</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0.2531</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u={\frac {4\times 0.4402}{-2\times 0.4402+12\times 0.4031+3}}=0.2531,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fdffc331bce0730e5684749ce47687880ab76d0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:46.206ex; height:5.343ex;" alt="{\displaystyle u={\frac {4\times 0.4402}{-2\times 0.4402+12\times 0.4031+3}}=0.2531,}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v={\frac {6\times 0.4031}{-2\times 0.4402+12\times 0.4031+3}}=0.3477.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mo>&#x00D7;<!-- × --></mo> <mn>0.4031</mn> </mrow> <mrow> <mo>&#x2212;<!-- − --></mo> <mn>2</mn> <mo>&#x00D7;<!-- × --></mo> <mn>0.4402</mn> <mo>+</mo> <mn>12</mn> <mo>&#x00D7;<!-- × --></mo> <mn>0.4031</mn> <mo>+</mo> <mn>3</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0.3477.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v={\frac {6\times 0.4031}{-2\times 0.4402+12\times 0.4031+3}}=0.3477.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3332c38f5d62543a18530097e4ee131570fdd59" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:46.004ex; height:5.343ex;" alt="{\displaystyle v={\frac {6\times 0.4031}{-2\times 0.4402+12\times 0.4031+3}}=0.3477.}"></span> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:CIE_illuminant_F4_and_a_blackbody_of_2938K.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/CIE_illuminant_F4_and_a_blackbody_of_2938K.svg/220px-CIE_illuminant_F4_and_a_blackbody_of_2938K.svg.png" decoding="async" width="220" height="177" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/CIE_illuminant_F4_and_a_blackbody_of_2938K.svg/330px-CIE_illuminant_F4_and_a_blackbody_of_2938K.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7f/CIE_illuminant_F4_and_a_blackbody_of_2938K.svg/440px-CIE_illuminant_F4_and_a_blackbody_of_2938K.svg.png 2x" data-file-width="348" data-file-height="280" /></a><figcaption>Relative SPD of FL4 and a black body of equal CCT. Not normalized.</figcaption></figure> <p>Examining the CIE 1960 UCS reveals this point to be closest to 2938&#160;K on the Planckian locus, which has a coordinate of (0.2528,&#160;0.3484). The distance of the test point to the locus is under the limit (5.4×10<sup>−3</sup>), so we can continue the procedure, assured of a meaningful result: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}{\text{DC}}&amp;={\sqrt {(0.2531-0.2528)^{2}+(0.3477-0.3484)^{2}}}\\&amp;=8.12\times 10^{-4}&lt;5.4\times 10^{-3}.\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="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>DC</mtext> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <mn>0.2531</mn> <mo>&#x2212;<!-- − --></mo> <mn>0.2528</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mn>0.3477</mn> <mo>&#x2212;<!-- − --></mo> <mn>0.3484</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>8.12</mn> <mo>&#x00D7;<!-- × --></mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>&#x2212;<!-- − --></mo> <mn>4</mn> </mrow> </msup> <mo>&lt;</mo> <mn>5.4</mn> <mo>&#x00D7;<!-- × --></mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>&#x2212;<!-- − --></mo> <mn>3</mn> </mrow> </msup> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\text{DC}}&amp;={\sqrt {(0.2531-0.2528)^{2}+(0.3477-0.3484)^{2}}}\\&amp;=8.12\times 10^{-4}&lt;5.4\times 10^{-3}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3064ee501aea25858d7b5cc2263a02493ff0268d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.505ex; width:49.712ex; height:8.176ex;" alt="{\displaystyle {\begin{aligned}{\text{DC}}&amp;={\sqrt {(0.2531-0.2528)^{2}+(0.3477-0.3484)^{2}}}\\&amp;=8.12\times 10^{-4}&lt;5.4\times 10^{-3}.\end{aligned}}}"></span> </p><p>We can verify the CCT by using <a href="/wiki/Color_temperature#Approximation" title="Color temperature">McCamy's approximation algorithm</a> to estimate the CCT from the <i>xy</i> chromaticities: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{CCT}}_{\text{est.}}=-449n^{3}+3525n^{2}-6823.3n+5520.33,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>CCT</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>est.</mtext> </mrow> </msub> <mo>=</mo> <mo>&#x2212;<!-- − --></mo> <mn>449</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mn>3525</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>&#x2212;<!-- − --></mo> <mn>6823.3</mn> <mi>n</mi> <mo>+</mo> <mn>5520.33</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{CCT}}_{\text{est.}}=-449n^{3}+3525n^{2}-6823.3n+5520.33,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9c4de0e9be41c90eaba864dd78ebbe48f2f9d60" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:50.327ex; height:3.009ex;" alt="{\displaystyle {\text{CCT}}_{\text{est.}}=-449n^{3}+3525n^{2}-6823.3n+5520.33,}"></span> </p><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 n={\frac {x-0.3320}{y-0.1858}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mo>&#x2212;<!-- − --></mo> <mn>0.3320</mn> </mrow> <mrow> <mi>y</mi> <mo>&#x2212;<!-- − --></mo> <mn>0.1858</mn> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n={\frac {x-0.3320}{y-0.1858}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2574d6d000b458ee71083d2cfa956b6b489db99f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.959ex; height:5.676ex;" alt="{\displaystyle n={\frac {x-0.3320}{y-0.1858}}}"></span>. </p><p>Substituting <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,y)=(0.4402,0.4031)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mn>0.4402</mn> <mo>,</mo> <mn>0.4031</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x,y)=(0.4402,0.4031)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6af3996b1bc0821472615915d47394e7912e146f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.188ex; height:2.843ex;" alt="{\displaystyle (x,y)=(0.4402,0.4031)}"></span> yields <i>n</i>&#160;= 0.4979 and CCT<sub>est.</sub>&#160;= 2941&#160;K, which is close enough. (<a href="/wiki/Color_temperature#Robertson&#39;s_method" title="Color temperature">Robertson's method</a> can be used for greater precision, but we will be content with 2940&#160;K in order to replicate published results.) Since 2940&#160;&lt; 5000, we select a Planckian radiator of 2940&#160;K as the reference illuminant. </p><p>The next step is to determine the values of the test color samples under each illuminant in the <a href="/wiki/CIE_1964_color_space" title="CIE 1964 color space">CIEUVW color space</a>. This is done by integrating the product of the CMF with the SPDs of the illuminant and the sample, then converting from CIEXYZ to CIEUVW (with the <i>u</i>,&#160;<i>v</i> coordinates of the reference illuminant as white point): </p> <table class="wikitable"> <tbody><tr> <th colspan="2">Illuminant</th> <th>TCS1</th> <th>TCS2</th> <th>TCS3</th> <th>TCS4</th> <th>TCS5</th> <th>TCS6</th> <th>TCS7</th> <th>TCS8 </th></tr> <tr> <th rowspan="3">Reference </th> <th>U </th> <td>39.22</td> <td>17.06</td> <td>−13.94</td> <td>−40.83</td> <td>−35.55</td> <td>−23.37</td> <td>16.43</td> <td>44.64 </td></tr> <tr> <th>V </th> <td>2.65</td> <td>9.00</td> <td>14.97</td> <td>7.88</td> <td>−2.86</td> <td>−13.94</td> <td>−12.17</td> <td>−8.01 </td></tr> <tr> <th>W </th> <td>62.84</td> <td>61.08</td> <td>61.10</td> <td>58.11</td> <td>59.16</td> <td>58.29</td> <td>60.47</td> <td>63.77 </td></tr> <tr> <th rowspan="3">CIE FL4 </th> <th>U </th> <td>26.56</td> <td>10.71</td> <td>−14.06</td> <td>−27.45</td> <td>−22.74</td> <td>−13.99</td> <td>9.61</td> <td>25.52 </td></tr> <tr> <th>V </th> <td>3.91</td> <td>11.14</td> <td>17.06</td> <td>9.42</td> <td>−3.40</td> <td>−17.40</td> <td>−15.71</td> <td>-10.23 </td></tr> <tr> <th>W </th> <td>63.10</td> <td>61.78</td> <td>62.30</td> <td>57.54</td> <td>58.46</td> <td>56.45</td> <td>59.11</td> <td>61.69 </td></tr> <tr> <th rowspan="3">CIE FL4<br />(CAT) </th> <th>U </th> <td>26.34</td> <td>10.45</td> <td>−14.36</td> <td>−27.78</td> <td>−23.10</td> <td>−14.33</td> <td>9.37</td> <td>25.33 </td></tr> <tr> <th>V </th> <td>4.34</td> <td>11.42</td> <td>17.26</td> <td>9.81</td> <td>−2.70</td> <td>−16.44</td> <td>−14.82</td> <td>−9.47 </td></tr> <tr> <th>W </th> <td>63.10</td> <td>61.78</td> <td>62.30</td> <td>57.54</td> <td>58.46</td> <td>56.45</td> <td>59.11</td> <td>61.69 </td></tr></tbody></table> <p>From this we can calculate the color difference between the chromatically adapted samples (labeled "CAT") and those illuminated by the reference. (The Euclidean metric is used to calculate the color difference in CIEUVW.) The special CRI is simply <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{i}=100-4.6\Delta E_{UVW}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>100</mn> <mo>&#x2212;<!-- − --></mo> <mn>4.6</mn> <mi mathvariant="normal">&#x0394;<!-- Δ --></mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>U</mi> <mi>V</mi> <mi>W</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{i}=100-4.6\Delta E_{UVW}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7dd0f74c8d6b8ad4e37d849b463e9c87134905d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:23.091ex; height:2.509ex;" alt="{\displaystyle R_{i}=100-4.6\Delta E_{UVW}}"></span>. </p> <table class="wikitable"> <tbody><tr> <th></th> <th>TCS1</th> <th>TCS2</th> <th>TCS3</th> <th>TCS4</th> <th>TCS5</th> <th>TCS6</th> <th>TCS7</th> <th>TCS8 </th></tr> <tr> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E_{UVW}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">&#x0394;<!-- Δ --></mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>U</mi> <mi>V</mi> <mi>W</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E_{UVW}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/991fc84d6c13d316484d89593e76c56a79729565" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.13ex; height:2.509ex;" alt="{\displaystyle \Delta E_{UVW}}"></span> </th> <td>12.99</td> <td>7.07</td> <td>2.63</td> <td>13.20</td> <td>12.47</td> <td>9.56</td> <td>7.66</td> <td>19.48 </td></tr> <tr> <th>R<sub>i</sub> </th> <td>40.2</td> <td>67.5</td> <td>87.9</td> <td>39.3</td> <td>42.6</td> <td>56.0</td> <td>64.8</td> <td>10.4 </td></tr></tbody></table> <p>Finally, the general color rendering index is the mean of the special CRIs: 51. </p> <figure class="mw-default-size mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:CIE_CRI_TCS_under_FL4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/CIE_CRI_TCS_under_FL4.svg/620px-CIE_CRI_TCS_under_FL4.svg.png" decoding="async" width="620" height="286" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/CIE_CRI_TCS_under_FL4.svg/930px-CIE_CRI_TCS_under_FL4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/CIE_CRI_TCS_under_FL4.svg/1240px-CIE_CRI_TCS_under_FL4.svg.png 2x" data-file-width="851" data-file-height="392" /></a><figcaption>The cyan circles indicate the TCS under the <i>reference</i> illuminant. The short, black, vectors indicate the TCS under the <i>test</i> illuminant, before and after chromatic adaptation transformation (CAT). (The vectors are short because the white points are close.) The post-CAT end of the vector lies NW, mirroring the chromaticity vector between the reference and test illuminants. The special CRIs are reflected in the length of the dotted lines linking the chromaticities of the samples under the reference and chromatically adapted test illuminants, respectively. Short distances, as in the case of TCS3, result in a high special CRI (87.9), whereas long distances, as in the case of TCS8, result in a low special CRI (10.4). In simpler terms, TCS3 reproduces better under FL4 than does TCS8 (relative to a black body).</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Typical_values">Typical values</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_rendering_index&amp;action=edit&amp;section=8" title="Edit section: Typical values"><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/Color_rendering_index" title="Special:EditPage/Color rendering index">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">November 2021</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> <table class="wikitable" style="float:right; margin:5px;"> <tbody><tr> <th>Light source </th> <th>CCT (K) </th> <th>CRI R<sub>a</sub> </th></tr> <tr> <td><a href="/wiki/Sodium-vapor_lamp#Low-pressure_sodium" title="Sodium-vapor lamp">Low-pressure sodium</a> (LPS/SOX) </td> <td>1800 </td> <td>−44 </td></tr> <tr> <td>Clear <a href="/wiki/Mercury-vapor_lamp" title="Mercury-vapor lamp">mercury-vapor</a> </td> <td>6410 </td> <td>17 </td></tr> <tr> <td><a href="/wiki/Sodium-vapor_lamp#High-pressure_sodium" title="Sodium-vapor lamp">High-pressure sodium</a> (HPS/SON) </td> <td>2100 </td> <td>24 </td></tr> <tr> <td>Coated mercury-vapor </td> <td>3600 </td> <td>49 </td></tr> <tr> <td>Halophosphate warm-white <a href="/wiki/Fluorescent_lamp" title="Fluorescent lamp">fluorescent</a> </td> <td>2940 </td> <td>51 </td></tr> <tr> <td>Halophosphate cool-white fluorescent </td> <td>4230 </td> <td>64 </td></tr> <tr> <td>Tri-phosphor warm-white fluorescent </td> <td>2940 </td> <td>73 </td></tr> <tr> <td>Halophosphate cool-daylight fluorescent </td> <td>6430 </td> <td>76 </td></tr> <tr> <td><a href="/wiki/Sodium-vapor_lamp" title="Sodium-vapor lamp">"White" SON</a> </td> <td>2700 </td> <td>82 </td></tr> <tr> <td>Standard <a href="/wiki/LED" class="mw-redirect" title="LED">LED</a> Lamp </td> <td>2700–5000 </td> <td>83 </td></tr> <tr> <td>Quartz <a href="/wiki/Metal-halide_lamp" title="Metal-halide lamp">metal halide</a> </td> <td>4200 </td> <td>85 </td></tr> <tr> <td>Tri-phosphor cool-white <a href="/wiki/Fluorescent_lamp" title="Fluorescent lamp">fluorescent</a> </td> <td>4080 </td> <td>89 </td></tr> <tr> <td>High-CRI <a href="/wiki/LED" class="mw-redirect" title="LED">LED</a> lamp (blue LED) </td> <td>2700–5000 </td> <td>95 </td></tr> <tr> <td><a href="/wiki/Ceramic_discharge_metal-halide_lamp" class="mw-redirect" title="Ceramic discharge metal-halide lamp">Ceramic discharge metal-halide lamp</a> </td> <td>5400 </td> <td>96 </td></tr> <tr> <td>Ultra-high-CRI <a href="/wiki/LED" class="mw-redirect" title="LED">LED</a> lamp (violet LED) </td> <td>2700–5000 </td> <td>99 </td></tr> <tr> <td><a href="/wiki/Incandescent_light_bulb" title="Incandescent light bulb">Incandescent</a>/<a href="/wiki/Halogen_lamp" title="Halogen lamp">halogen</a> bulb </td> <td>3200 </td> <td>100 </td></tr></tbody></table> <p>A reference source, such as blackbody radiation, is defined as having a CRI of 100. This is why <a href="/wiki/Incandescent_lamp" class="mw-redirect" title="Incandescent lamp">incandescent lamps</a> have that rating, as they are, in effect, almost blackbody radiators.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">&#91;</span>23<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">&#91;</span>24<span class="cite-bracket">&#93;</span></a></sup> The best possible faithfulness to a reference is specified by CRI&#160;= 100, while the very poorest is specified by a CRI below zero. A high CRI by itself does not imply a good rendition of color, because the reference itself may have an imbalanced SPD if it has an extreme color temperature. </p> <div class="mw-heading mw-heading2"><h2 id="Special_value:_R9">Special value: R9</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_rendering_index&amp;action=edit&amp;section=9" title="Edit section: Special value: R9"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>R<sub>a</sub> is the average value of R1–R8; other values from R9 to R15 are not used in the calculation of R<sub>a</sub>, including R9 "saturated red", R13 "skin color (light)", and R15 "skin color (medium)", which are all difficult colors to faithfully reproduce. R9 is a vital index in high-CRI lighting, as many applications require red lights, such as film and video lighting, medical lighting, art lighting, etc. However, in the general CRI (R<sub>a</sub>) calculation R9 is not included. </p><p>R9 is one of the numbers of R<sub>i</sub> refers to test color samples (TCS), which is one score in extended CRI. It is the number rates the light source's color revealing ability towards TCS&#160;09. And it describes the specific ability of light to accurately reproduce the red color of objects. Many lights manufacturers or retailers do not point out the score of R9, while it is a vital value to evaluate the color rendition performance for film and video lighting, as well as any applications that need high CRI value. So, generally, it is regarded as a supplement of color rendering index when evaluating a high-CRI light source. </p><p>R9 value, TCS&#160;09, or in other words, the red color is the key color for many lighting applications, such as film and video lighting, textile printing, image printing, skin tone, medical lighting, and so on. Besides, many other objects which are not in red color, but actually consists of different colors including red color. For instance, the skin tone is impacted by the blood under the skin, which means that the skin tone also includes red color, although it looks much like close to white or light yellow. So, if the R9 value is not good enough, the skin tone under this light will be more paleness or even greenish in your eyes or cameras.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">&#91;</span>25<span class="cite-bracket">&#93;</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Criticism">Criticism</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_rendering_index&amp;action=edit&amp;section=10" title="Edit section: Criticism"><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-Missing_information plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Wiki_letter_w.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/44px-Wiki_letter_w.svg.png" decoding="async" width="44" height="44" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/66px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/88px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>is missing information</b> about CRI penalization of "pleasantly inaccurate" colorfulness-enhancing light &#8211; an important point in CQS and TM-30.<span class="hide-when-compact"> Please expand the section to include this information. Further details may exist on the <a href="/wiki/Talk:Color_rendering_index" title="Talk:Color rendering index">talk page</a>.</span> <span class="date-container"><i>(<span class="date">November 2021</span>)</i></span></div></td></tr></tbody></table> <p>Ohno and others have criticized CRI for not always correlating well with subjective color rendering quality in practice, particularly for light sources with spiky emission spectra such as fluorescent lamps or white <a href="/wiki/Light-emitting_diode" title="Light-emitting diode">LEDs</a>. Another problem is that the CRI is discontinuous at 5000&#160;K,<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">&#91;</span>26<span class="cite-bracket">&#93;</span></a></sup> because the chromaticity of the reference moves from the <a href="/wiki/Planckian_locus" title="Planckian locus">Planckian locus</a> to the <a href="/wiki/Standard_illuminant#Illuminant_series_D" title="Standard illuminant">CIE daylight locus</a>. <a href="#CITEREFDavisOhno2006">Davis &amp; Ohno (2006)</a> identify several other issues, which they address in their <a href="/wiki/Color_quality_scale" title="Color quality scale">color quality scale</a> (CQS): </p> <ul><li>The color space in which the color distance is calculated (CIEUVW) is obsolete and nonuniform. Use <a href="/wiki/CIELAB" class="mw-redirect" title="CIELAB">CIELAB</a> or <a href="/wiki/CIELUV" title="CIELUV">CIELUV</a> instead.</li> <li>The chromatic adaptation transform used (<a href="/wiki/Von_Kries_transform" class="mw-redirect" title="Von Kries transform">Von Kries transform</a>) is inadequate. Use <a href="/wiki/CIECAM02#Chromatic_adaptation" title="CIECAM02">CMCCAT2000</a> or <a href="/wiki/CIECAM02" title="CIECAM02">CIECAT02</a> instead.</li> <li>Calculating the arithmetic mean of the errors diminishes the contribution of any single large deviation. Two light sources with similar CRI may perform significantly differently if one has a particularly low special CRI in a spectral band that is important for the application. Use the <a href="/wiki/Root-mean-square_deviation" class="mw-redirect" title="Root-mean-square deviation">root-mean-square deviation</a> instead.</li> <li>The metric is not perceptual; all errors are equally weighted, whereas humans favor certain errors over others. A color can be more saturated or less saturated without a change in the numerical value of ∆<i>E</i><sub><i>i</i></sub>, while in general a saturated color is experienced as being more attractive.</li> <li>A negative CRI is difficult to interpret. Normalize the scale from 0 to 100 using the formula <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\text{out}}=10\ln \left[\exp(R_{\text{in}}/10)+1\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>out</mtext> </mrow> </msub> <mo>=</mo> <mn>10</mn> <mi>ln</mi> <mo>&#x2061;<!-- ⁡ --></mo> <mrow> <mo>[</mo> <mrow> <mi>exp</mi> <mo>&#x2061;<!-- ⁡ --></mo> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>in</mtext> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>10</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1</mn> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\text{out}}=10\ln \left[\exp(R_{\text{in}}/10)+1\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99fc5eac38293353d6dd7eb4c9ead08747873de0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:29.635ex; height:2.843ex;" alt="{\displaystyle R_{\text{out}}=10\ln \left[\exp(R_{\text{in}}/10)+1\right]}"></span>.</li> <li>The CRI cannot be calculated for light sources that do not have a CCT (non-white light).</li> <li>Eight samples are not enough since manufacturers can optimize the emission spectra of their lamps to reproduce them faithfully, but otherwise perform poorly. Use more samples (they suggest fifteen for CQS).</li> <li>The samples are not saturated enough to pose difficulty for reproduction.</li> <li>CRI merely measures the faithfulness of any illuminant to an ideal source with the same CCT, but the ideal source itself may not render colors well if it has an extreme color temperature, due to a lack of energy at either short or long wavelengths (i.e., it may be excessively blue or red). Weight the result by the ratio of the <a href="/wiki/Gamut" title="Gamut">gamut</a> area of the polygon formed by the fifteen samples in CIELAB for 6500&#160;K to the gamut area for the test source. 6500&#160;K is chosen for reference since it has a relatively even distribution of energy over the visible spectrum and hence high gamut area. This normalizes the multiplication factor.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Alternatives">Alternatives</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_rendering_index&amp;action=edit&amp;section=11" title="Edit section: Alternatives"><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/Color_rendering#Scales" title="Color rendering">Color rendering §&#160;Scales</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Update plainlinks metadata ambox ambox-content ambox-Update" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Ambox_current_red.svg/42px-Ambox_current_red.svg.png" decoding="async" width="42" height="34" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Ambox_current_red.svg/63px-Ambox_current_red.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/98/Ambox_current_red.svg/84px-Ambox_current_red.svg.png 2x" data-file-width="360" data-file-height="290" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section's <b><a href="/wiki/Wikipedia:Accuracy_dispute" title="Wikipedia:Accuracy dispute">factual accuracy</a> may be compromised due to out-of-date information</b>.<span class="hide-when-compact"> Please help update this article to reflect recent events or newly available information.</span> <span class="date-container"><i>(<span class="date">November 2021</span>)</i></span></div></td></tr></tbody></table> <p><a href="#CITEREFCIE2007">CIE (2007)</a> "reviews the applicability of the CIE color rendering index to white LED light sources based on the results of visual experiments". Chaired by Davis, CIE TC 1-69(C) is currently investigating "new methods for assessing the color rendition properties of white-light sources used for illumination, including solid-state light sources, with the goal of recommending new assessment procedures [...] by March, 2010".<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">&#91;</span>27<span class="cite-bracket">&#93;</span></a></sup> </p><p>For a comprehensive review of alternative color rendering indexes see <a href="#CITEREFGuoHouser2004">Guo &amp; Houser (2004)</a>. </p><p><a href="#CITEREFSmet2011">Smet (2011)</a> reviewed several alternative quality metrics and compared their performance based on visual data obtained in nine psychophysical experiments. It was found that a geometric mean of the GAI index and the CIE Ra correlated best with naturalness (r=0.85), while a color quality metric based on memory colors (MCRI<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">&#91;</span>28<span class="cite-bracket">&#93;</span></a></sup>) correlated best for preference (<i>r</i>&#160;= 0.88). The differences in performance of these metrics with the other tested metrics (CIE Ra; CRI-CAM02UCS; CQS; RCRI; GAI; geomean (GAI, CIE Ra); CSA; Judd Flattery; Thornton CPI; MCRI) were found to be statistically significant with <i>p</i>&#160;&lt; 0.0001.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">&#91;</span>29<span class="cite-bracket">&#93;</span></a></sup> </p><p>Dangol, et al., performed psychophysical experiments and concluded that people's judgments of naturalness and overall preference could not be predicted with a single measure, but required the joint use of a fidelity-based measure (e.g., Qp) and a gamut-based measure (e.g., Qg or GAI.).<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">&#91;</span>30<span class="cite-bracket">&#93;</span></a></sup> They carried out further experiments in real offices evaluating various spectra generated for combination existing and proposed color rendering metrics.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">&#91;</span>31<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">&#91;</span>32<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">&#91;</span>33<span class="cite-bracket">&#93;</span></a></sup> </p><p>Due to the criticisms of CRI many researchers have developed alternative metrics, though relatively few of them have had wide adoption. </p> <div class="mw-heading mw-heading4"><h4 id="Gamut_area_index_(GAI)"><span id="Gamut_area_index_.28GAI.29"></span>Gamut area index (GAI)</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_rendering_index&amp;action=edit&amp;section=12" title="Edit section: Gamut area index (GAI)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Developed in 2010 by Rea and Freyssinier, the gamut area index (GAI) is an attempt to improve over the flaws found in the CRI.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">&#91;</span>34<span class="cite-bracket">&#93;</span></a></sup> They have shown that the GAI is better than the CRI at predicting color discrimination on standardized Farnsworth-Munsell 100 Hue Tests and that GAI is predictive of color saturation.<sup id="cite_ref-Color_rendering:_Beyond_pride_and_prejudice_-_Rea_-_2010_-_Color_Research_&amp;_Application_-_Wiley_Online_Library_9-1" class="reference"><a href="#cite_note-Color_rendering:_Beyond_pride_and_prejudice_-_Rea_-_2010_-_Color_Research_&amp;_Application_-_Wiley_Online_Library-9"><span class="cite-bracket">&#91;</span>9<span class="cite-bracket">&#93;</span></a></sup> Proponents of using GAI claim that, when used in conjunction with CRI, this method of evaluating color rendering is preferred by test subjects over light sources that have high values of only one measure. Researchers recommend a lower and an upper limit to GAI. Use of LED technology has called for a new way to evaluate color rendering because of the unique spectrum of light created by these technologies. Preliminary tests have shown that the combination of GAI and CRI used together is a preferred method for evaluating color rendering.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">&#91;</span>35<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">&#91;</span>36<span class="cite-bracket">&#93;</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Color_quality_scale_(CQS)"><span id="Color_quality_scale_.28CQS.29"></span>Color quality scale (CQS)</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_rendering_index&amp;action=edit&amp;section=13" title="Edit section: Color quality scale (CQS)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Color_quality_scale" title="Color quality scale">Color quality scale</a></div> <p><a href="#CITEREFPoussetObeinRazet2010">Pousset, Obein &amp; Razet (2010)</a> developed a psychophysical experiment in order to evaluate light quality of LED lightings. It is based on colored samples used in the "color quality scale". Predictions of the CQS and results from visual measurements were compared. </p> <div class="mw-heading mw-heading2"><h2 id="Film_and_video_high-CRI_LED_lighting">Film and video high-CRI LED lighting</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_rendering_index&amp;action=edit&amp;section=14" title="Edit section: Film and video high-CRI LED lighting"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/High-CRI_LED_lighting" title="High-CRI LED lighting">High-CRI LED lighting</a></div> <p>Problems have been encountered attempting to use LED lighting on film and video sets. The color spectra of LED lighting primary colors does not match the expected color wavelength bandpasses of film emulsions and digital sensors. As a result, color rendition can be completely unpredictable in optical prints, transfers to digital media from film (DIs), and video camera recordings. This phenomenon with respect to motion picture film has been documented in an LED lighting evaluation series of tests produced by the <a href="/wiki/Academy_of_Motion_Picture_Arts_and_Sciences" title="Academy of Motion Picture Arts and Sciences">Academy of Motion Picture Arts and Sciences</a> scientific staff.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">&#91;</span>37<span class="cite-bracket">&#93;</span></a></sup> </p><p>To that end, various other metrics such as the TLCI (television lighting consistency index) have been developed to replace the human observer with a camera observer.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">&#91;</span>38<span class="cite-bracket">&#93;</span></a></sup> Similar to the CRI, the metric measures quality of a light source as it would appear on camera on a scale from 0 to 100.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">&#91;</span>39<span class="cite-bracket">&#93;</span></a></sup> Some manufacturers say that their products have TLCI values of up to 99.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">&#91;</span>40<span class="cite-bracket">&#93;</span></a></sup> </p> <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=Color_rendering_index&amp;action=edit&amp;section=15" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100227034508/http://www.cie.co.at/publ/abst/17-4-89.html">"CIE 17.4-1987 International Lighting Vocabulary"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.cie.co.at/publ/abst/17-4-89.html">the original</a> on 2010-02-27<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-02-19</span></span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=unknown&amp;rft.btitle=CIE+17.4-1987+International+Lighting+Vocabulary&amp;rft_id=http%3A%2F%2Fwww.cie.co.at%2Fpubl%2Fabst%2F17-4-89.html&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20170105235216/http://www.ledengin.com/files/products/LZC/LZC-00GW00.pdf">"LZC-00GW00 Data Sheet"</a> <span class="cs1-format">(PDF)</span>. <i>ledengin.com</i>. LED ENGIN. March 16, 2015. Archived from <a rel="nofollow" class="external text" href="http://www.ledengin.com/files/products/LZC/LZC-00GW00.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2017-01-05.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=ledengin.com&amp;rft.atitle=LZC-00GW00+Data+Sheet&amp;rft.date=2015-03-16&amp;rft_id=http%3A%2F%2Fwww.ledengin.com%2Ffiles%2Fproducts%2FLZC%2FLZC-00GW00.pdf&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSándorSchanda2006" class="citation cs2">Sándor, Norbert; Schanda, János (September 1, 2006), "Visual colour rendering based on colour difference evaluations", <i>Lighting Research and Technology</i>, <b>38</b> (3): 225–239, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1191%2F1365782806lrt168oa">10.1191/1365782806lrt168oa</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a>&#160;<a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:109858508">109858508</a></cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Lighting+Research+and+Technology&amp;rft.atitle=Visual+colour+rendering+based+on+colour+difference+evaluations&amp;rft.volume=38&amp;rft.issue=3&amp;rft.pages=225-239&amp;rft.date=2006-09-01&amp;rft_id=info%3Adoi%2F10.1191%2F1365782806lrt168oa&amp;rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A109858508%23id-name%3DS2CID&amp;rft.aulast=S%C3%A1ndor&amp;rft.aufirst=Norbert&amp;rft.au=Schanda%2C+J%C3%A1nos&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" class="Z3988"></span>.<br />Conference version of this article:<br /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSándorSchanda2005" class="citation cs2">Sándor, Norbert; Schanda, János (2005), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110721114551/http://www.knt.vein.hu/staff/schandaj/SJCV-Publ-2005/521.pdf">"Visual colour-rendering experiments"</a> <span class="cs1-format">(PDF)</span>, <i>AIC Colour '05: 10th Congress of the International Colour Association</i>: 511–514, archived from <a rel="nofollow" class="external text" href="http://www.knt.vein.hu/staff/schandaj/SJCV-Publ-2005/521.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2011-07-21</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=AIC+Colour+%2705%3A+10th+Congress+of+the+International+Colour+Association&amp;rft.atitle=Visual+colour-rendering+experiments&amp;rft.pages=511-514&amp;rft.date=2005&amp;rft.aulast=S%C3%A1ndor&amp;rft.aufirst=Norbert&amp;rft.au=Schanda%2C+J%C3%A1nos&amp;rft_id=http%3A%2F%2Fwww.knt.vein.hu%2Fstaff%2Fschandaj%2FSJCV-Publ-2005%2F521.pdf&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGuoHouser2004" class="citation cs2">Guo, Xin; Houser, Kevin W. (2004), "A review of colour rendering indices and their application to commercial light sources", <i>Lighting Research and Technology</i>, <b>36</b> (3): 183–199, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1191%2F1365782804li112oa">10.1191/1365782804li112oa</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a>&#160;<a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:109227871">109227871</a></cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Lighting+Research+and+Technology&amp;rft.atitle=A+review+of+colour+rendering+indices+and+their+application+to+commercial+light+sources&amp;rft.volume=36&amp;rft.issue=3&amp;rft.pages=183-199&amp;rft.date=2004&amp;rft_id=info%3Adoi%2F10.1191%2F1365782804li112oa&amp;rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A109227871%23id-name%3DS2CID&amp;rft.aulast=Guo&amp;rft.aufirst=Xin&amp;rft.au=Houser%2C+Kevin+W.&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" class="Z3988"></span></span> </li> <li id="cite_note-CIE1995-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-CIE1995_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-CIE1995_5-1"><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="CITEREFCIE1995" class="citation cs2">CIE (1995), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080103162323/http://www.cie.co.at/publ/abst/13-3-95.html"><i>Method of Measuring and Specifying Colour Rendering Properties of Light Sources</i></a>, Publication 13.3, Vienna: Commission Internationale de l'Eclairage, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a>&#160;<a href="/wiki/Special:BookSources/978-3-900734-57-2" title="Special:BookSources/978-3-900734-57-2"><bdi>978-3-900734-57-2</bdi></a>, archived from <a rel="nofollow" class="external text" href="http://www.cie.co.at/publ/abst/13-3-95.html">the original</a> on 2008-01-03<span class="reference-accessdate">, retrieved <span class="nowrap">2008-01-19</span></span></cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=Method+of+Measuring+and+Specifying+Colour+Rendering+Properties+of+Light+Sources&amp;rft.place=Vienna&amp;rft.series=Publication+13.3&amp;rft.pub=Commission+Internationale+de+l%27Eclairage&amp;rft.date=1995&amp;rft.isbn=978-3-900734-57-2&amp;rft.au=CIE&amp;rft_id=http%3A%2F%2Fwww.cie.co.at%2Fpubl%2Fabst%2F13-3-95.html&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" class="Z3988"></span> (A verbatim re-publication of the 1974, second edition. Accompanying disk <a rel="nofollow" class="external text" href="http://www.cie.co.at/publ/abst/d008.html">D008: Computer Program to Calculate CRIs</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080327023340/http://www.cie.co.at/publ/abst/d008.html">Archived</a> 2008-03-27 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>)</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">Illuminating Engineering Society. 2018. <i>IES Method for Evaluating Light Source Color Rendition, IES Technical Memorandum (TM) 30-18</i>.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP._J._Bouma1948" class="citation book cs1">P. J. Bouma (1948). <i><span></span></i>Physical aspects of colour; an introduction to the scientific study of colour stimuli and colour sensations<i><span></span></i>. (Eindhoven: Philips Gloeilampenfabrieken (Philips Industries) Technical and Scientific Literature Dept.).</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=Physical+aspects+of+colour%3B+an+introduction+to+the+scientific+study+of+colour+stimuli+and+colour+sensations&amp;rft.pub=%28Eindhoven%3A+Philips+Gloeilampenfabrieken+%28Philips+Industries%29+Technical+and+Scientific+Literature+Dept.%29&amp;rft.date=1948&amp;rft.au=P.+J.+Bouma&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" 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">American approach is expounded in <a href="#CITEREFNickerson1960">Nickerson (1960)</a>, and the European approach in <a href="#CITEREFBarnes1957">Barnes (1957)</a>, and <a href="#CITEREFCrawford1959">Crawford (1959)</a>. See <a href="#CITEREFSchandaSándor2003">Schanda &amp; Sándor (2003)</a> for a historical overview.</span> </li> <li id="cite_note-Color_rendering:_Beyond_pride_and_prejudice_-_Rea_-_2010_-_Color_Research_&amp;_Application_-_Wiley_Online_Library-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-Color_rendering:_Beyond_pride_and_prejudice_-_Rea_-_2010_-_Color_Research_&amp;_Application_-_Wiley_Online_Library_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Color_rendering:_Beyond_pride_and_prejudice_-_Rea_-_2010_-_Color_Research_&amp;_Application_-_Wiley_Online_Library_9-1"><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="CITEREFReaFreyssinier2010" class="citation journal cs1">Rea, M. S.; Freyssinier, J. P. (2010). "Color rendering: Beyond pride and prejudice". <i>Color Research and Application</i>. <b>35</b> (6): 401–409. <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.20562">10.1002/col.20562</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Color+Research+and+Application&amp;rft.atitle=Color+rendering%3A+Beyond+pride+and+prejudice&amp;rft.volume=35&amp;rft.issue=6&amp;rft.pages=401-409&amp;rft.date=2010&amp;rft_id=info%3Adoi%2F10.1002%2Fcol.20562&amp;rft.aulast=Rea&amp;rft.aufirst=M.+S.&amp;rft.au=Freyssinier%2C+J.+P.&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation magazine cs1"><a rel="nofollow" class="external text" href="http://www.lrc.rpi.edu/programs/solidstate/assist/pdf/AR-ColorGuideforRetailLighting-March2010.pdf">"Background"</a> <span class="cs1-format">(PDF)</span>. <i>Guide to Light and Color in Retail Merchandising</i>. Vol.&#160;8, no.&#160;1. Alliance for Solid-State Illumination Systems and Technologies. March 2010. p.&#160;5.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Guide+to+Light+and+Color+in+Retail+Merchandising&amp;rft.atitle=Background&amp;rft.volume=8&amp;rft.issue=1&amp;rft.pages=5&amp;rft.date=2010-03&amp;rft_id=http%3A%2F%2Fwww.lrc.rpi.edu%2Fprograms%2Fsolidstate%2Fassist%2Fpdf%2FAR-ColorGuideforRetailLighting-March2010.pdf&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" 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 id="CITEREFReaDengWolsey2004" class="citation web cs1">Rea, M.; Deng, L.; Wolsey, R. (2004). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100611200908/http://www.lrc.rpi.edu/nlpip/publicationDetails.asp?id=901&amp;type=2">"Light Sources and Color"</a>. <i>NLPIP Lighting Answers</i>. Troy, NY: Rensselaer Polytechnic Institute. Archived from <a rel="nofollow" class="external text" href="http://www.lrc.rpi.edu/nlpip/publicationDetails.asp?id=901&amp;type=2">the original</a> on 2010-06-11<span class="reference-accessdate">. Retrieved <span class="nowrap">2010-06-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=NLPIP+Lighting+Answers&amp;rft.atitle=Light+Sources+and+Color&amp;rft.date=2004&amp;rft.aulast=Rea&amp;rft.aufirst=M.&amp;rft.au=Deng%2C+L.&amp;rft.au=Wolsey%2C+R.&amp;rft_id=http%3A%2F%2Fwww.lrc.rpi.edu%2Fnlpip%2FpublicationDetails.asp%3Fid%3D901%26type%3D2&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNickersonJerome1965" class="citation cs2">Nickerson, Dorothy; Jerome, Charles W. (April 1965), "Color rendering of light sources: CIE method of specification and its application", <i>Illuminating Engineering</i>, <b>60</b> (4), <a href="/wiki/Illuminating_Engineering_Society_of_North_America" class="mw-redirect" title="Illuminating Engineering Society of North America">IESNA</a>: 262–271</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Illuminating+Engineering&amp;rft.atitle=Color+rendering+of+light+sources%3A+CIE+method+of+specification+and+its+application&amp;rft.volume=60&amp;rft.issue=4&amp;rft.pages=262-271&amp;rft.date=1965-04&amp;rft.aulast=Nickerson&amp;rft.aufirst=Dorothy&amp;rft.au=Jerome%2C+Charles+W.&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">Note that when CRI was designed in 1965, the most perceptually uniform chromaticity space was the <a href="/wiki/CIE_1960_color_space" title="CIE 1960 color space">CIE 1960 UCS</a>, the <a href="/wiki/CIELUV" title="CIELUV">CIE 1976 UCS</a> not yet having been invented.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">(<a href="#CITEREFCIE1995">CIE 1995</a>), <a rel="nofollow" class="external text" href="http://resodance.com/ali/CRI_prob.html">Section 5.3: Tolerance for reference illuminant</a></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">Per <a href="#CITEREFSchandaSándor2003">Schanda &amp; Sándor (2003)</a>, <a href="#CITEREFSchanda2002">Schanda (2002)</a> and, as demonstrated in the <a href="#Example">Example</a> section, the coefficient was chosen as 4.6 so that the CRI of the CIE <a href="/wiki/Standard_illuminant" title="Standard illuminant">standard illuminant</a> F4, an obsolete "warm white" calcium halophosphate <a href="/wiki/Fluorescent_lamp" title="Fluorescent lamp">fluorescent lamp</a> would be 51. Today's fluorescent "<a href="/wiki/Full-spectrum_light" title="Full-spectrum light">full-spectrum lights</a>" boast CRIs approaching 100; e.g., <a rel="nofollow" class="external text" href="http://www.truesun.com/philips_TL950.php">Philips TL950</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20071012085113/http://www.truesun.com/philips_TL950.php">Archived</a> 2007-10-12 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> or <style data-mw-deduplicate="TemplateStyles:r1041539562">.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}</style><span class="citation patent"><a rel="nofollow" class="external text" href="https://worldwide.espacenet.com/textdoc?DB=EPODOC&amp;IDX=EP1184893">EP 1184893</a></span><span class="Z3988" title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Apatent&amp;rft.number=1184893&amp;rft.cc=EP&amp;rft.title="><span style="display: none;">&#160;</span></span>. <a href="#CITEREFThornton1972">Thornton (1972)</a> compares older products; <a href="#CITEREFGuoHouser2004">Guo &amp; Houser (2004)</a> compares newer ones.</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text">It appeared that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db421291be9d0103404ced7495b363437b67b6b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.564ex; height:2.509ex;" alt="{\displaystyle R_{i}}"></span> could be negative (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E_{i}\geq 22}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">&#x0394;<!-- Δ --></mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>&#x2265;<!-- ≥ --></mo> <mn>22</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E_{i}\geq 22}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b64ccfb2a2f49e62b6b091d267f06bd6de0bfd3c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.874ex; height:2.509ex;" alt="{\displaystyle \Delta E_{i}\geq 22}"></span>), and this was indeed calculated for some lamp test colors, especially TCS9 (strong red).</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">See the CIE 1960 UCS diagram towards the end of the <a href="#Example">Example</a> section.</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://photometry.kriss.re.kr/wiki/img_auth.php/4/47/CIE_TCS.csv">TCS spectra in CSV form</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090211042805/http://photometry.kriss.re.kr/wiki/img_auth.php/4/47/CIE_TCS.csv">Archived</a> 2009-02-11 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, Korea Research Institute of Standards and Science.</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.rit.edu/science/munsell-color-science-lab-educational-resources#munsell-renotation-data">Munsell Renotation Data</a>, <i>Munsell Color Science Laboratory</i>, <a href="/wiki/Rochester_Institute_of_Technology" title="Rochester Institute of Technology">Rochester Institute of Technology</a></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text">"Authors' response to SA Fotios and JA Lynes" in <a href="#CITEREFSándorSchanda2005">Sándor &amp; Schanda (2005)</a>: "The main message of our investigations is an answer to the lamp industry, who still use the colour rendering index and the lamp efficacy as parameters for optimizing their lamp spectra, and have turned down the work of CIE TC 1-33 by stating that there are not enough visual experiments showing the shortcomings of the CIE colour rendering calculation method."<sup class="noprint Inline-Template" style="white-space:nowrap;">&#91;<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="The material near this tag failed verification of its source citation(s). (September 2020)">failed verification</span></a></i>&#93;</sup></span> </li> <li id="cite_note-FOOTNOTEBodrogi200411Past_research_to_improve_the_CRI-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBodrogi200411Past_research_to_improve_the_CRI_21-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBodrogi2004">Bodrogi (2004)</a>, p.&#160;11, Past research to improve the CRI.</span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.xrite.com/product_overview.aspx?ID=820&amp;Action=Library">X-Rite ColorChecker Chart</a>.</span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.sciencedirect.com/topics/engineering/blackbody-radiator">"Blackbody Radiator - an overview | ScienceDirect Topics"</a>. <i>www.sciencedirect.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-03-13</span></span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=www.sciencedirect.com&amp;rft.atitle=Blackbody+Radiator+-+an+overview+%7C+ScienceDirect+Topics&amp;rft_id=https%3A%2F%2Fwww.sciencedirect.com%2Ftopics%2Fengineering%2Fblackbody-radiator&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFixtures2017" class="citation web cs1">Fixtures, Access (January 26, 2017). <a rel="nofollow" class="external text" href="https://www.accessfixtures.com/color-rendering-index/">"CRI: What Is the Color Rendering Index? Is It Accurate?"</a>. <i>Access Fixtures</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-03-13</span></span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=Access+Fixtures&amp;rft.atitle=CRI%3A+What+Is+the+Color+Rendering+Index%3F+Is+It+Accurate%3F&amp;rft.date=2017-01-26&amp;rft.aulast=Fixtures&amp;rft.aufirst=Access&amp;rft_id=https%3A%2F%2Fwww.accessfixtures.com%2Fcolor-rendering-index%2F&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mmsvideolight.com/why-r9-is-important-for-high-cri-lighting/">"Why R9 is important for High CRI Lighting?"</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=unknown&amp;rft.btitle=Why+R9+is+important+for+High+CRI+Lighting%3F&amp;rft_id=https%3A%2F%2Fwww.mmsvideolight.com%2Fwhy-r9-is-important-for-high-cri-lighting%2F&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" class="Z3988"></span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">&#91;<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title="&#160;Dead link tagged March 2022">permanent dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">&#8205;</span>&#93;</span></sup></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text">"Authors' response to SA Fotios and JA Lynes" in <a href="#CITEREFSándorSchanda2005">Sándor &amp; Schanda (2005)</a>: "It is quite obvious that just at 5000&#160;K, where the reference illuminant has to be changed, the present system shows discontinuity."<sup class="noprint Inline-Template" style="white-space:nowrap;">&#91;<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="The material near this tag failed verification of its source citation(s). (September 2020)">failed verification</span></a></i>&#93;</sup></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"><a rel="nofollow" class="external text" href="http://www.cie.co.at/div1/ActReps/D1ActivityReport08.pdf">CIE Activity Report. Division 1: Vision and Color</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110706091259/http://www.cie.co.at/div1/ActReps/D1ActivityReport08.pdf">Archived</a> 2011-07-06 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, p.&#160;21, January 2008.</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">Smet K.&#160;A.&#160;G., Ryckaert W.&#160;R., Pointer M.&#160;R., Deconinck G., Hanselaer P. Colour Appearance Rating of Familiar Real Objects. Colour Research and Application 2011; 36(3):192–200.</span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text">Smet K.&#160;A.&#160;G., Ryckaert W.&#160;R., Pointer M.&#160;R., Deconinck G., Hanselaer P. <a rel="nofollow" class="external text" href="http://www.opticsinfobase.org/view_article.cfm?gotourl=http%3A%2F%2Fwww.opticsinfobase.org%2FDirectPDFAccess%2F3AAAA211-C63E-79CC-4E0A0772E17419BA_212731.pdf%3Fda%3D1%26id%3D212731%26seq%3D0%26mobile%3Dno&amp;org=">Correlation between color quality metric predictions and visual appreciation of light sources</a>.</span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDangolIslamHyvärinenBhusal2013" class="citation cs2">Dangol, R.; Islam, M.; Hyvärinen, M.; Bhusal, P.; Puolakka, M.; Halonen, L. 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May 31, 2016.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=unknown&amp;rft.btitle=EBU+Technology+%26+Innovation+-+Television+Lighting+Consistency+Index+2012&amp;rft.date=2016-05-31&amp;rft_id=https%3A%2F%2Ftech.ebu.ch%2Ftlci-2012&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" class="Z3988"></span></span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"><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/20140903072219/http://www.gtc.org.uk/tlci-results.aspx">"The Guild of Television Cameramen: TLCI Results"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.gtc.org.uk/tlci-results.aspx">the original</a> on 2014-09-03<span class="reference-accessdate">. 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Carried out by TC 1-69: color Rendering of White Light Sources.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBarnes1957" class="citation cs2">Barnes, Bentley T. 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(2013). <a rel="nofollow" class="external text" href="http://lrt.sagepub.com/content/47/1/54">"User acceptance studies for LED office lighting: lamp spectrum, spatial brightness and illuminance level"</a>. <i>Lighting Research and Technology</i>. <b>47</b> (1): 54–79. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F1477153513514425">10.1177/1477153513514425</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a>&#160;<a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:109592929">109592929</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Lighting+Research+and+Technology&amp;rft.atitle=User+acceptance+studies+for+LED+office+lighting%3A+lamp+spectrum%2C+spatial+brightness+and+illuminance+level&amp;rft.volume=47&amp;rft.issue=1&amp;rft.pages=54-79&amp;rft.date=2013&amp;rft_id=info%3Adoi%2F10.1177%2F1477153513514425&amp;rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A109592929%23id-name%3DS2CID&amp;rft.aulast=Islam&amp;rft.aufirst=M.&amp;rft.au=Dangol%2C+R.&amp;rft.au=Hyv%C3%A4rinen%2C+M.&amp;rft.au=Bhusal%2C+P.&amp;rft.au=Puolakka%2C+M.&amp;rft.au=Halonen%2C+L.&amp;rft_id=http%3A%2F%2Flrt.sagepub.com%2Fcontent%2F47%2F1%2F54&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+rendering+index" class="Z3988"></span></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=Color_rendering_index&amp;action=edit&amp;section=17" 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.lrc.rpi.edu/programs/nlpip/lightinganswers/lightsources/appendixb1.asp">MATLAB script for calculating measures of light source color</a>, <a href="/wiki/Rensselaer_Polytechnic_Institute" title="Rensselaer Polytechnic Institute">Rensselaer Polytechnic Institute</a>, 2004.</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20071109105911/http://www.lightinglab.fi/teaching/217/CRI_calculation.xls">Excel spreadsheet with a cornucopia of data</a>, Lighting Laboratory of the <a href="/wiki/Helsinki_University_of_Technology" title="Helsinki University of Technology">Helsinki University of Technology</a> (Note: Cell contents in both sheets are password protected. It may be possible to unlock the individual worksheets using AAAAAAABABB/)</li> <li><a rel="nofollow" class="external text" href="http://stacks.iop.org/0026-1394/46/704">Uncertainty evaluation for measurement of LED colour , Metrologia</a></li> <li><a rel="nofollow" class="external text" href="http://www1.eere.energy.gov/buildings/ssl/cri_leds.html">Color Rendering Index and LEDs</a>, <a rel="nofollow" class="external text" href="http://www.eere.energy.gov/">United States Department of Energy, Office of Energy Efficiency and Renewable Energy (EERE)</a>[bad link]</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110718171338/http://www.lrc.rpi.edu/programs/solidstate/assist/recommends/lightcolor.asp">Alliance for Solid State Illumination Systems and Technologies, Color Rendering</a></li> <li><a rel="nofollow" class="external text" href="http://www.edaphic.com.au/knowledge-base/articles/light-articles/">What is the difference between CRI and CQS?</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150718064746/http://www.edaphic.com.au/knowledge-base/articles/light-articles/">Archived</a> 2015-07-18 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, Edaphic Scientific Knowledge Base</li> <li><a rel="nofollow" class="external text" href="https://www.lumens.com/light-bulb-facts/color-rendering-index.html">Understanding color rendering index for lighting</a>, Lumens</li></ul> <!-- NewPP limit report Parsed by mw‐web.codfw.main‐6b7f745dd4‐7hjck Cached time: 20241125133629 Cache expiry: 2592000 Reduced expiry: false Complications: [vary‐revision‐sha1, show‐toc] CPU time usage: 0.905 seconds Real time usage: 1.182 seconds Preprocessor visited node count: 5165/1000000 Post‐expand include size: 124116/2097152 bytes Template argument size: 6294/2097152 bytes Highest expansion depth: 17/100 Expensive parser function count: 12/500 Unstrip recursion depth: 1/20 Unstrip post‐expand size: 152648/5000000 bytes Lua time usage: 0.545/10.000 seconds Lua memory usage: 7875020/52428800 bytes Number of Wikibase entities loaded: 0/400 --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 914.040 1 -total 43.06% 393.559 1 Template:Reflist 15.42% 140.936 20 Template:Citation 14.98% 136.964 10 Template:Cite_web 14.24% 130.119 27 Template:Harvtxt 8.36% 76.377 1 Template:Short_description 8.01% 73.227 8 Template:Cite_journal 7.60% 69.480 4 Template:Ambox 6.52% 59.571 2 Template:Missing_information 5.43% 49.653 2 Template:Pagetype --> <!-- Saved in parser cache with key enwiki:pcache:1324664:|#|:idhash:canonical and timestamp 20241125133629 and revision id 1234582073. 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