View source for Color rendering index

{{Short description|Measure of ability of a light source to reproduce colors in comparison with a standard light source}}
{{use American English|date=January 2022}}
{{use mdy dates|date=September 2020|cs1-dates=ly}}
[[File:Simple spectroscope.jpg|thumb|upright=1.35|right|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.]]
[[File:AmbientLED.png|thumb|upright=1.35|right|Color rendering index shown as color accuracy]]

A '''color rendering index''' ('''CRI''') is a quantitative measure of the ability of a [[light source]] to reveal the [[color]]s of various objects faithfully in comparison with a natural or standard light source.

''[[Color rendering]]'', as defined by the [[International Commission on Illumination]] (CIE), is the effect of an [[Light#Light sources|illuminant]] on the color appearance of objects by conscious or subconscious comparison with their color appearance under a reference or [[standard illuminant]].<ref>{{cite web |url=http://www.cie.co.at/publ/abst/17-4-89.html |title=CIE 17.4-1987 International Lighting Vocabulary |access-date=2008-02-19 |archive-url=https://web.archive.org/web/20100227034508/http://www.cie.co.at/publ/abst/17-4-89.html |archive-date=2010-02-27 }}</ref>

The CRI of a light source does not indicate the apparent color of the light source; that information is given by the [[Color temperature|correlated color temperature (CCT)]]. The CRI is determined by the light source's [[spectrum]]. An [[incandescent lamp]] has a [[continuous spectrum]], a [[fluorescent lamp]] has a discrete [[Emission spectrum|line spectrum]]; implying that the incandescent lamp has the higher CRI.

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.

Numerically, the highest possible CIE R<sub>a</sub> value is 100 and would only be given to a source whose [[spectrum]] is identical to [[Solar spectrum|the spectrum of daylight]], very close to that of a [[black body]] (incandescent lamps are effectively black bodies), dropping to negative values for some light sources. [[Low-pressure sodium light]]ing has a negative CRI; [[fluorescent light]]s range from about 50 for the basic types, up to about 98 for the best multi-phosphor type. Typical white-color [[LEDs]] have a CRI of 80 or more, while some manufacturers claim that their LEDs achieve a CRI of up to 98.<ref>{{Cite web |url=http://www.ledengin.com/files/products/LZC/LZC-00GW00.pdf |title=LZC-00GW00 Data Sheet |date=March 16, 2015 |website=ledengin.com |publisher=LED ENGIN |archive-url=https://web.archive.org/web/20170105235216/http://www.ledengin.com/files/products/LZC/LZC-00GW00.pdf |archive-date=January 5, 2017 }}</ref>

CIE R<sub>a</sub>'s ability to predict color appearance has been criticized in favor of measures based on [[color appearance model]]s, such as [[CIECAM02]] and for [[daylight]] simulators, the CIE [[metamerism index]].<ref>{{citation |first2=János |last2=Schanda |first1=Norbert |last1=Sándor |journal=Lighting Research and Technology |volume=38 |issue=3 |title=Visual colour rendering based on colour difference evaluations |date=September 1, 2006 |pages=225–239 |doi=10.1191/1365782806lrt168oa }}.<br />Conference version of this article:<br />{{citation |first2=János |last2=Schanda |first1=Norbert |last1=Sándor |title=Visual colour-rendering experiments |journal=AIC Colour '05: 10th Congress of the International Colour Association |year=2005 |pages=511–514 |url=http://www.knt.vein.hu/staff/schandaj/SJCV-Publ-2005/521.pdf |archive-url=https://web.archive.org/web/20110721114551/http://www.knt.vein.hu/staff/schandaj/SJCV-Publ-2005/521.pdf |archive-date=2011-07-21}}</ref> CRI is not a good indicator for use in visual assessment of light sources, especially for sources below 5000&nbsp;[[kelvin]] (K).<ref>{{citation
 | last1 = Guo
 | first1= Xin
 | last2 = Houser
 | first2= Kevin W.
 | year = 2004
 | title = A review of colour rendering indices and their application to commercial light sources
 | journal = Lighting Research and Technology
 | volume = 36
 | issue = 3
 | pages = 183–199
 | doi = 10.1191/1365782804li112oa
 }}</ref><ref name="CIE1995">{{citation
 |author       = CIE
 |series       = Publication 13.3
 |year         = 1995
 |url          = http://www.cie.co.at/publ/abst/13-3-95.html
 |title        = Method of Measuring and Specifying Colour Rendering Properties of Light Sources
 |isbn         = 978-3-900734-57-2
 |publisher    = Commission Internationale de l'Eclairage
 |location     = Vienna
 |access-date  = 2008-01-19
 |archive-url  = https://web.archive.org/web/20080103162323/http://www.cie.co.at/publ/abst/13-3-95.html
 |archive-date = 2008-01-03
 }}
 (A verbatim re-publication of the 1974, second edition. Accompanying disk [http://www.cie.co.at/publ/abst/d008.html D008: Computer Program to Calculate CRIs]. {{Webarchive|url=https://web.archive.org/web/20080327023340/http://www.cie.co.at/publ/abst/d008.html |date=2008-03-27 }})</ref> New standards, such as the [[IES TM-30]], resolve these issues and have begun replacing the usage of CRI among professional lighting designers.<ref>Illuminating Engineering Society. 2018. ''IES Method for Evaluating Light Source Color Rendition, IES Technical Memorandum (TM) 30-18''.</ref> However, CRI is still common among household lighting products.

==History==

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 [[Illumination (image)|illumination]] 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".<ref>{{cite book |author=P. J. Bouma |year=1948 |title=''Physical aspects of colour; an introduction to the scientific study of colour stimuli and colour sensations'' |publisher=(Eindhoven: Philips Gloeilampenfabrieken (Philips Industries) Technical and Scientific Literature Dept.)}}</ref>

Around the middle of the 20th century, color scientists took an interest in assessing the ability of [[artificial light]]s to accurately reproduce colors. European researchers attempted to describe illuminants by measuring the [[spectral power distribution]] (SPD) in "representative" spectral bands, whereas their North American counterparts studied the [[colorimetric]] effect of the illuminants on reference objects.<ref>American approach is expounded in {{harvtxt|Nickerson|1960}}, and the European approach in {{harvtxt|Barnes|1957}}, and {{harvtxt|Crawford|1959}}. See {{harvtxt|Schanda|Sándor|2003}} for a historical overview.</ref>

The [[International Commission on Illumination|CIE]] assembled a committee to study the matter and accepted the proposal to use the latter approach, which has the virtue of not needing [[spectrophotometry]], with a set of [[Munsell color system|Munsell]] 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, [[CIE 1964 color space|CIEUVW]]. In 1931, the CIE adopted the first formal system of [[colorimetry]], which is based on the trichromatic nature of the [[human visual system]].<ref name="Color rendering: Beyond pride and prejudice - Rea - 2010 - Color Research &amp; Application - Wiley Online Library" >{{cite journal |last1=Rea |first1=M. S. |last2=Freyssinier |first2=J. P. |title=Color rendering: Beyond pride and prejudice |journal=Color Research and Application |year=2010 |volume=35 |issue=6 |pages=401–409 |doi=10.1002/col.20562}}</ref><ref>{{cite magazine |title=Background |magazine=Guide to Light and Color in Retail Merchandising |volume=8 |issue=1 |date=March 2010 |page=5 |publisher=Alliance for Solid-State Illumination Systems and Technologies |url= http://www.lrc.rpi.edu/programs/solidstate/assist/pdf/AR-ColorGuideforRetailLighting-March2010.pdf}}</ref> CRI is based upon this system of colorimetry.<ref>{{cite web |last1=Rea |first1=M. |last2=Deng |first2=L. |last3=Wolsey |first3=R. |date=2004 |work=NLPIP Lighting Answers |title=Light Sources and Color |location=Troy, NY |publisher=Rensselaer Polytechnic Institute |url=http://www.lrc.rpi.edu/nlpip/publicationDetails.asp?id=901&type=2 |access-date=2010-06-17 |archive-url= https://web.archive.org/web/20100611200908/http://www.lrc.rpi.edu/nlpip/publicationDetails.asp?id=901&type=2 |archive-date=2010-06-11 }}</ref>

To deal with the problem of having to compare light sources of different correlated color temperatures (CCT), the CIE settled on using a reference [[black body]] with the same color temperature for lamps with a CCT of under 5000&nbsp;K, or a phase of CIE [[standard illuminant]] 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 [[chromatic adaptation transform]]. There are two extent versions of CRI: the more commonly used R<sub>a</sub> of {{harvtxt|CIE|1995}} (actually from 1974) and R96<sub>a</sub> of {{harvtxt|CIE|1999}}.

==Test method==

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&nbsp;K, and a phase of daylight otherwise (e.g., [[CIE Standard Illuminant D65|D65]]). [[Chromatic adaptation]] should be performed so that like quantities are compared.  The ''Test Method'' (also called ''Test Sample Method'' or ''Test Color Method'') needs only [[colorimetric]], rather than [[spectrophotometric]], information.<ref name="CIE1995"/><ref>
{{citation
 |title=Color rendering of light sources: CIE method of specification and its application
 |first1=Dorothy
 |last1=Nickerson
 |first2=Charles W.
 |last2=Jerome
 |journal=Illuminating Engineering
 |date=April 1965
 |pages=262–271
 |volume=60
 |issue=4
 |publisher=[[Illuminating Engineering Society of North America|IESNA]]
 }}</ref>

[[File:CIE 1960 UCS.png|thumb|CIE 1960 UCS. Planckian locus and co-ordinates of several illuminants shown in illustration below.]] 
[[File:Planckian-locus.png|thumb|(''u'', ''v'') chromaticity diagram with several CIE illuminants]]

# Using the [[CIE 1931 color space#CIE standard observer|2° standard observer]], find the [[chromaticity]] co-ordinates of the test source in the [[CIE 1960 color space]].<ref>Note that when CRI was designed in 1965, the most perceptually uniform chromaticity space was the [[CIE 1960 color space|CIE 1960 UCS]], the [[CIELUV|CIE 1976 UCS]] not yet having been invented.</ref>
# Determine the [[correlated color temperature]] (CCT) of the test source by finding the closest point to the [[Planckian locus]] on the (''u'',&nbsp;''v'') chromaticity diagram.
# If the test source has a CCT < 5000&nbsp;K, use a black body for reference, otherwise use CIE [[standard illuminant]] D. Both sources should have the same CCT.
# 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.<ref>{{harv|CIE|1995}}, [http://resodance.com/ali/CRI_prob.html Section 5.3: Tolerance for reference illuminant]</ref> <math>\text{DC} = \Delta_{uv} = \sqrt{(u_r - u_t)^2 + (v_r - v_t)^2}.</math>
# Illuminate the first eight standard samples, from the fifteen listed below, alternately using both sources.
# Using the 2° standard observer, find the co-ordinates of the light reflected by each sample in the [[CIE 1964 color space]].
# Chromatically adapt each sample by a [[Chromatic adaptation#Von Kries transform|Von Kries transform]].
# For each sample, calculate the [[Euclidean distance]] <math>\Delta E_i</math> between the pair of co-ordinates.
# Calculate the special (i.e., particular) CRI using the formula <math>R_i = 100 - 4.6 \Delta E_i</math><ref>Per {{harvtxt|Schanda|Sándor|2003}}, {{harvtxt|Schanda|2002}} and, as demonstrated in the [[#Example|Example]] section, the coefficient was chosen as 4.6 so that the CRI of the CIE [[standard illuminant]] F4, an obsolete "warm white" calcium halophosphate [[fluorescent lamp]] would be 51. Today's fluorescent "[[full-spectrum light]]s" boast CRIs approaching 100; e.g., [http://www.truesun.com/philips_TL950.php Philips TL950] {{webarchive|url=https://web.archive.org/web/20071012085113/http://www.truesun.com/philips_TL950.php |date=2007-10-12 }} or {{patent|EP|1184893}}. {{harvtxt|Thornton|1972}} compares older products; {{harvtxt|Guo|Houser|2004}} compares newer ones.</ref><ref>It appeared that <math>R_i</math> could be negative (<math>\Delta E_i \ge 22</math>), and this was indeed calculated for some lamp test colors, especially TCS9 (strong red).</ref>
# Find the general CRI (R<sub>a</sub>) by calculating the [[arithmetic mean]] of the special CRIs.

Note that the last three steps are equivalent to finding the mean [[color difference]], <math>\Delta \bar{E}_{UVW}</math> and using that to calculate <math>R_a</math>:

<math display="block">R_a = 100 - 4.6 \Delta \bar{E}_{UVW}.</math>

===Chromatic adaptation===
[[File:CIE CRI TCS under FL4.svg|thumb|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)]]

{{harvtxt|CIE|1995}} uses this von Kries chromatic transform equation to find the [[corresponding color]] (''u''<sub>''c'',''i''</sub>,&nbsp;''v''<sub>''c'',''i''</sub>) for each sample. The mixed subscripts (''t'',&nbsp;''i'') refer to the [[inner product]] of the test illuminant spectrum and the spectral reflexivity of sample ''i'':

<math display="block">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}},</math>

<math display="block">v_{c,i} = \frac{5.520}{16.518 + 1.481 (c_r/c_t) c_{t,i} - (d_r/d_t) d_{t,i}},</math>

<math display="block">c = (4.0 - u - 10.0 v) / v,</math>

<math display="block">d = (1.708 v - 1.481 u + 0.404) / v,</math>

where subscripts ''r'' and ''t'' refer to reference and test light sources respectively.

===Test color samples===

{| class="wikitable floatleft"
|-
! Name
! Appr. Munsell
! Appearance under daylight
! Swatch
|-
| TCS01
| 7,5 R 6/4
| Light greyish red
| style="background:#e8a7b0;" |
|-
| TCS02
| 5 Y 6/4
| Dark greyish yellow
| style="background:#ccb184;" |
|-
| TCS03
| 5 GY 6/8
| Strong yellow green
| style="background:#abc161;" |
|-
| TCS04
| 2,5 G 6/6
| Moderate yellowish green
| style="background:#6fc59f;" |
|-
| TCS05
| 10 BG 6/4
| Light bluish green
| style="background:#7fc2df;" |
|-
| TCS06
| 5 PB 6/8
| Light blue
| style="background:#8fb6ff;" |
|-
| TCS07
| 2,5 P 6/8
| Light violet
| style="background:#cca5ff;" |
|-
| TCS08
| 10 P 6/8
| Light reddish purple
| style="background:#eea3ef;" |
|-
| TCS09
| 4,5 R 4/13
| Strong red
| style="background:#e9214c;" |
|-
| TCS10
| 5 Y 8/10
| Strong yellow
| style="background:#fff456;" |
|-
| TCS11
| 4,5 G 5/8
| Strong green
| style="background:#0cac8a;" |
|-
| TCS12
| 3 PB 3/11
| Strong blue
| style="background:#005bc0;" |
|-
| TCS13
| 5 YR 8/4
| Light yellowish pink 
| style="background:#ffe8da;" |
|-
| TCS14
| 5 GY 4/4
| Moderate olive green ([[leaf]])
| style="background:#6c7d4f;" |
|}

As specified in {{harvtxt|CIE|1995}}, the original test color samples (TCS) are taken from an early edition of the [[Farnsworth-Munsell 100 hue test|Munsell]] Atlas. The first eight samples, a subset of the eighteen proposed in {{harvtxt|Nickerson|1960}}, are relatively low saturated colors and are evenly distributed over the complete range of hues.<ref>See the CIE 1960 UCS diagram towards the end of the [[#Example|Example]] section.</ref> These eight samples are employed to calculate the general color rendering index <math>R_a</math>. 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 {{harvtxt|CIE|2004}},<ref>[http://photometry.kriss.re.kr/wiki/img_auth.php/4/47/CIE_TCS.csv TCS spectra in CSV form] {{webarchive|url=https://web.archive.org/web/20090211042805/http://photometry.kriss.re.kr/wiki/img_auth.php/4/47/CIE_TCS.csv |date=2009-02-11 }}, Korea Research Institute of Standards and Science.</ref> and their approximate Munsell notations are listed aside.<ref>[https://www.rit.edu/science/munsell-color-science-lab-educational-resources#munsell-renotation-data Munsell Renotation Data], ''Munsell Color Science Laboratory'', [[Rochester Institute of Technology]]</ref>

[[File:CIE CRI TCS SPDs.svg|300px|right]]
{{-}}

==R96<sub>a</sub> method==
[[File:CIE CRI TCS chromaticities.svg|300px|right]]

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 {{harvtxt|CIE|1999}}, but no firm recommendations, partly due to disagreements between researchers and manufacturers.<ref>"Authors' response to SA Fotios and JA Lynes" in {{harvtxt|Sándor|Schanda|2005}}: "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."{{failed verification|date=September 2020}}</ref>

The R96<sub>a</sub> method has a few distinguishing features:{{sfnp|Bodrogi|2004|p=11|loc=Past research to improve the CRI}}

* [[#New test color samples|A new set of test color samples]]
* Six reference illuminants: D65, D50, [[black bodies]] of 4200 K, 3450 K, 2950 K, and 2700 K.
* A new chromatic adaptation transform: CIECAT94.
* Color difference evaluation in CIELAB.
* Adaptation of all colors to [[CIE Standard Illuminant D65|D65]] (since CIELAB is well-tested under D65).

It is conventional to use the original method; R96<sub>a</sub> should be explicitly mentioned if used.

===New test color samples===
{| class="wikitable floatright" border="1"
|-
! 
! TCS01<sup>*</sup>
! TCS02<sup>*</sup>
! TCS03<sup>*</sup>
! TCS04<sup>*</sup>
! TCS05<sup>*</sup>
! TCS06<sup>*</sup>
! TCS07<sup>*</sup>
! TCS08<sup>*</sup>
! TCS09<sup>*</sup>
! TCS10<sup>*</sup>
|-
| L<sup>*</sup> || 40.9 || 61.1 || 81.6 || 72.0 || 55.7 || 51.7 || 30.0 || 51.0 || 68.7 || 63.9
|-
| a<sup>*</sup> || 51.0 || 28.8 || −4.2 || −29.4 || −43.4 || −26.4 || 23.2 || 47.3 || 14.2 || 11.7
|-
| b<sup>*</sup> || 26.3 || 57.9 || 80.3 || 58.9 || 35.6 || −24.6 || −49.6 || −13.8 || 17.4 || 17.3
|- 
| style="height:25px;" |
| style="background:#ad3139;" |
| style="background:#d17e27;" |
| style="background:#e0cb08;" |
| style="background:#92be38;" |
| style="background:#369842;" |
| style="background:#0089a5;" |
| style="background:#413c95;" |
| style="background:#bb5593;" |
| style="background:#c99e89;" |
| style="background:#b7837d;" |
|}

As discussed in {{harvtxt|Sándor|Schanda|2005}}, {{harvtxt|CIE|1999}} recommends the use of a [[ColorChecker]] chart owing to the obsolescence of the original samples, of which only [[Metamerism (color)|metameric]] matches remain.<ref>[http://www.xrite.com/product_overview.aspx?ID=820&Action=Library X-Rite ColorChecker Chart].</ref> 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, {{harvtxt|Hung|2002}} has determined that the patches in {{harvtxt|CIE|1995}} give better correlations for any color difference than the ColorChecker chart, whose samples are not equally distributed in a uniform color space.

== Example ==
{{missing information|section|Can we briefly do a R96<sub>a</sub> too?|date=November 2021}}
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&nbsp;nm increments {{harvtxt|CIE|2004}}, so it is suggested to use interpolation up to the resolution of the illuminant's spectrophotometry.

Starting with the SPD, let us verify that the CRI of reference illuminant F4 is 51. The first step is to determine the [[tristimulus value]]s using the 1931 standard observer. Calculation of the [[inner product]] of the SPD with the standard observer's color matching functions (CMFs) yields (''X'',&nbsp;''Y'',&nbsp;''Z'') = (109.2,&nbsp;100.0,&nbsp;38.9) (after normalizing for ''Y''&nbsp;= 100). From this follow the ''xy'' chromaticity values:

[[Image:CIE 1960 UCS, FL4.svg|thumb|right|upright=0.8|The tight isotherms are from 2935&nbsp;K to 2945&nbsp;K. FL4 marked with a cross.]]

<math display="block">x = \frac{109.2}{109.2 + 100.0 + 38.9} = 0.4402,</math>

<math display="block">y = \frac{100}{109.2 + 100.0 + 38.9} = 0.4031.</math>

The next step is to convert these chromaticities to the [[CIE 1960 color space|CIE 1960 UCS]] in order to be able to determine the CCT:

<math display="block">u = \frac{4 \times 0.4402}{-2 \times 0.4402 + 12 \times 0.4031 + 3} = 0.2531,</math>

<math display="block">v = \frac{6 \times 0.4031}{-2 \times 0.4402 + 12 \times 0.4031 + 3} = 0.3477.</math>

[[Image:CIE illuminant F4 and a blackbody of 2938K.svg|thumb|Relative SPD of FL4 and a [[black body]] of equal CCT. Not normalized.]]

Examining the CIE 1960 UCS reveals this point to be closest to 2938&nbsp;K on the Planckian locus, which has a coordinate of (0.2528,&nbsp;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:

<math display="block">\begin{align}
 \text{DC} &= \sqrt{(0.2531 - 0.2528)^2 + (0.3477 - 0.3484)^2} \\
           &= 8.12 \times 10^{-4} < 5.4 \times 10^{-3}.
\end{align}</math>

We can verify the CCT by using [[Color temperature#Approximation|McCamy's approximation algorithm]] to estimate the CCT from the ''xy'' chromaticities:

<math display="block">\text{CCT}_\text{est.} = -449 n^3 + 3525 n^2 - 6823.3 n + 5520.33,</math>

where <math>n = \frac{x - 0.3320}{y - 0.1858}</math>.

Substituting <math>(x, y) = (0.4402, 0.4031)</math> yields ''n''&nbsp;= 0.4979 and CCT<sub>est.</sub>&nbsp;= 2941&nbsp;K, which is close enough. ([[Color temperature#Robertson's method|Robertson's method]] can be used for greater precision, but we will be content with 2940&nbsp;K in order to replicate published results.) Since 2940&nbsp;< 5000, we select a Planckian radiator of 2940&nbsp;K as the reference illuminant.

The next step is to determine the values of the test color samples under each illuminant in the [[CIE 1964 color space|CIEUVW color space]]. 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 ''u'',&nbsp;''v'' coordinates of the reference illuminant as white point):

{| class="wikitable"
|-
! colspan = 2 | Illuminant || TCS1 || TCS2 || TCS3 || TCS4 || TCS5 || TCS6 || TCS7 || TCS8
|-
! rowspan = 3 | Reference
! U
| 39.22 || 17.06 || −13.94 || −40.83 || −35.55 || −23.37 || 16.43 || 44.64
|-
! V
| 2.65 || 9.00 || 14.97 || 7.88 || −2.86 || −13.94 || −12.17 || −8.01
|-
! W
| 62.84 || 61.08 || 61.10 || 58.11 || 59.16 || 58.29 || 60.47 || 63.77
|-
! rowspan = 3 | CIE FL4
! U
| 26.56 || 10.71 || −14.06 || −27.45 || −22.74 || −13.99 || 9.61 || 25.52
|-
! V
| 3.91 || 11.14 || 17.06 || 9.42 || −3.40 || −17.40 || −15.71 || -10.23
|-
! W
| 63.10 || 61.78 || 62.30 || 57.54 || 58.46 || 56.45 || 59.11 || 61.69
|-
! rowspan = 3 | CIE FL4<br />(CAT)
! U
| 26.34 || 10.45 || −14.36 || −27.78 || −23.10 || −14.33 || 9.37 || 25.33
|-
! V
| 4.34 || 11.42 || 17.26 || 9.81 || −2.70 || −16.44 || −14.82 || −9.47
|-
! W
| 63.10 || 61.78 || 62.30 || 57.54 || 58.46 || 56.45 || 59.11 || 61.69
|}

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 <math>R_i = 100 - 4.6 \Delta E_{UVW}</math>.

{| class="wikitable"
|-
! || TCS1 || TCS2 || TCS3 || TCS4 || TCS5 || TCS6 || TCS7 || TCS8
|-
! <math>\Delta E_{UVW}</math> 
| 12.99 || 7.07 || 2.63 || 13.20 || 12.47 || 9.56 || 7.66 || 19.48
|-
! R<sub>i</sub>
| 40.2 || 67.5 || 87.9 || 39.3 || 42.6 || 56.0 || 64.8 || 10.4
|}

Finally, the general color rendering index is the mean of the special CRIs: 51.

[[File:CIE CRI TCS under FL4.svg|thumb|upright=2.8|center|The cyan circles indicate the TCS under the ''reference'' illuminant. The short, black, vectors indicate the TCS under the ''test'' 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]]).]]

== Typical values ==
{{unreferenced section|date=November 2021}}
{| class="wikitable" style="float:right; margin:5px;"
|-
! Light source
! CCT (K)
! CRI R<sub>a</sub>
|-
| [[Sodium-vapor lamp#Low-pressure sodium|Low-pressure sodium]] (LPS/SOX)
| 1800
| −44
|-
| Clear [[Mercury-vapor lamp|mercury-vapor]]
| 6410
| 17
|-
| [[Sodium-vapor lamp#High-pressure sodium|High-pressure sodium]] (HPS/SON)
| 2100
| 24
|-
| Coated mercury-vapor
| 3600
| 49
|-
| Halophosphate warm-white [[Fluorescent lamp|fluorescent]]
| 2940
| 51
|-
| Halophosphate cool-white fluorescent
| 4230
| 64
|-
| Tri-phosphor warm-white fluorescent
| 2940
| 73
|-
| Halophosphate cool-daylight fluorescent
| 6430
| 76
|-
| [[w:Sodium-vapor lamp|"White" SON]]
| 2700
| 82
|-
| Standard [[LED]] Lamp
| 2700–5000
| 83
|-
| Quartz [[Metal-halide lamp|metal halide]]
| 4200
| 85
|-
| Tri-phosphor cool-white [[Fluorescent lamp|fluorescent]]
| 4080
| 89
|-
| High-CRI [[LED]] lamp (blue LED)
| 2700–5000
| 95
|-
| [[Ceramic discharge metal-halide lamp]]
| 5400
| 96
|-
| Ultra-high-CRI [[LED]] lamp (violet LED)
| 2700–5000
| 99
|-
| [[Incandescent light bulb|Incandescent]]/[[Halogen lamp|halogen]] bulb
| 3200
| 100
|}

A reference source, such as [[black-body radiation]], is defined as having a CRI of 100. This is why [[incandescent lamp]]s have that rating, as they are, in effect, almost black-body radiators.<ref>{{Cite web |last=Fixtures |first=Access |date=2017-01-26 |title=CRI: What Is the Color Rendering Index? Is It Accurate? |url=https://www.accessfixtures.com/color-rendering-index/ |access-date=2022-03-13 |website=Access Fixtures |language=en-US}}</ref> The best possible faithfulness to a reference is specified by CRI&nbsp;= 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.

== Special value: R9 ==

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.

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&nbsp;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.

R9 value, TCS&nbsp;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.<ref>{{cite web |url=https://www.mmsvideolight.com/why-r9-is-important-for-high-cri-lighting/ |title=Why R9 is important for High CRI Lighting? }}{{Dead link|date=March 2022 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>

== Criticism ==
{{missing information|section|CRI penalization of "pleasantly inaccurate" colorfulness-enhancing light &ndash; an important point in CQS and TM-30|date=November 2021}} 
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 [[Light-emitting diode|LED]]s. Another problem is that the CRI is discontinuous at 5000&nbsp;K,<ref>"Authors' response to SA Fotios and JA Lynes" in {{harvtxt|Sándor|Schanda|2005}}: "It is quite obvious that just at 5000&nbsp;K, where the reference illuminant has to be changed, the present system shows discontinuity."{{failed verification|date=September 2020}}</ref> because the chromaticity of the reference moves from the [[Planckian locus]] to the [[Standard illuminant#Illuminant series D|CIE daylight locus]]. {{harvtxt|Davis|Ohno|2006}} identify several other issues, which they address in their [[color quality scale]] (CQS):
* The color space in which the color distance is calculated (CIEUVW) is obsolete and nonuniform. Use [[CIELAB]] or [[CIELUV]] instead.
* The chromatic adaptation transform used ([[Von Kries transform]]) is inadequate. Use [[CIECAM02#Chromatic adaptation|CMCCAT2000]] or [[CIECAM02|CIECAT02]] instead.
* 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 [[root-mean-square deviation]] instead.
* 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 ∆''E''<sub>''i''</sub>, while in general a saturated color is experienced as being more attractive.
* A negative CRI is difficult to interpret. Normalize the scale from 0 to 100 using the formula <math>R_\text{out} = 10 \ln \left[\exp(R_\text{in}/10) + 1\right]</math>.
* The CRI cannot be calculated for light sources that do not have a CCT (non-white light).
* 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).
* The samples are not saturated enough to pose difficulty for reproduction.
* 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 [[gamut]] area of the polygon formed by the fifteen samples in CIELAB for 6500&nbsp;K to the gamut area for the test source. 6500&nbsp;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.

=== Alternatives ===
{{main|Color rendering#Scales}}
{{update|section|inaccurate=yes|date=November 2021}}
{{harvtxt|CIE|2007}} "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".<ref>[http://www.cie.co.at/div1/ActReps/D1ActivityReport08.pdf CIE Activity Report. Division 1: Vision and Color]. {{Webarchive|url=https://web.archive.org/web/20110706091259/http://www.cie.co.at/div1/ActReps/D1ActivityReport08.pdf|date=2011-07-06}}, p. 21, January 2008.</ref>

For a comprehensive review of alternative color rendering indexes see {{harvtxt|Guo|Houser|2004}}.

{{harvtxt|Smet|2011}} 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<ref>Smet K. A. G., Ryckaert W. R., Pointer M. R., Deconinck G., Hanselaer P. Colour Appearance Rating of Familiar Real Objects. Colour Research and Application 2011; 36(3):192–200.</ref>) correlated best for preference (''r''&nbsp;= 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 ''p''&nbsp;< 0.0001.<ref>Smet K. A. G., Ryckaert W. R., Pointer M. R., Deconinck G., Hanselaer P. [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&org= Correlation between color quality metric predictions and visual appreciation of light sources].</ref>

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.).<ref>{{cite journal |last1=Dangol |first1=R |last2=Islam |first2=M |last3=LiSc |first3=M Hyvärinen |last4=Bhusal |first4=P |last5=Puolakka |first5=M |last6=Halonen |first6=L |title=Subjective preferences and colour quality metrics of LED light sources |journal=Lighting Research & Technology |date=December 2013 |volume=45 |issue=6 |pages=666–688 |doi=10.1177/1477153512471520 }}</ref> They carried out further experiments in real offices evaluating various spectra generated for combination existing and proposed color rendering metrics.<ref>{{cite journal|last1=Dangol|first1=R|last2=Islam|first2=MS|last3=Hyvärinen|first3=M|last4=Bhushal|first4=P|last5=Puolakka|first5=M|last6=Halonen|first6=L|year=2015|title=User acceptance studies for LED office lighting: Preference, naturalness and colourfulness|journal=Lighting Research & Technology|volume=47|pages=36–53|doi=10.1177/1477153513514424 }}</ref><ref>{{cite journal|last1=Islam|first1=MS|last2=Dangol|first2=R|last3=Hyvärinen|first3=M|last4=Bhusal|first4=P|last5=Puolakka|first5=M|last6=Halonen|first6=L|year=2013|title=User acceptance studies for LED office lighting: Lamp spectrum, spatial brightness and illuminance|journal=Lighting Research & Technology|volume=47|pages=54–79|doi=10.1177/1477153513514425 }}</ref><ref>{{cite journal|last1=Baniya|first1=R. R.|last2=Dangol|first2=R.|last3=Bhusal|first3=P.|last4=Wilm|first4=A.|last5=Baur|first5=E.|last6=Puolakka|first6=M.|last7=Halonen|first7=L.|year=2015|title=User-acceptance studies for simplified light-emitting diode spectra|journal=Lighting Research and Technology|volume=47|issue=2|pages=177–191|doi=10.1177/1477153513515264 }}</ref>

Due to the criticisms of CRI many researchers have developed alternative metrics, though relatively few of them have had wide adoption.

==== Gamut area index (GAI) ====
Developed in 2010 by Rea and Freyssinier, the gamut area index (GAI) is an attempt to improve over the flaws found in the CRI.<ref>{{cite journal | last1 = Rea | first1 = M. S. | last2 = Freysinnier-Nova | first2 = J. P. | year = 2008| title = Color rendering: A tale of two metrics | journal = Color Research and Application | volume = 33 | issue = 3| pages = 192–202 | doi = 10.1002/col.20399 }}</ref> 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.<ref name="Color rendering: Beyond pride and prejudice - Rea - 2010 - Color Research & Application - Wiley Online Library" /> 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.<ref>{{cite magazine |title=Light Levels |publisher=Alliance for Solid-State Illumination Systems and Technologies |magazine=Guide to Light and Color in Retail Merchandising |volume=8 |issue=1 |page=12 |date=March 2010 |url= http://www.lrc.rpi.edu/programs/solidstate/assist/pdf/AR-ColorGuideforRetailLighting-March2010.pdf |access-date=2020-09-14}}</ref><ref>{{cite magazine |title=Color Rendering |publisher=Alliance for Solid-State Illumination Systems and Technologies |magazine=Recommendations for Specifying Color Properties of Light Sources for Retail Merchandising |volume=8 |issue=2 |date=March 2010 |page=6 |access-date=2020-09-14 |url= http://www.lrc.rpi.edu/programs/solidstate/assist/pdf/AR-SpecifyColorRec-March2010.pdf}}</ref>

==== Color quality scale (CQS) ====
{{Further|Color quality scale}}
{{harvtxt|Pousset|Obein|Razet|2010}} 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.

== Film and video high-CRI LED lighting ==
{{Further|High-CRI LED lighting}}
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 [[Academy of Motion Picture Arts and Sciences]] scientific staff.<ref>
{{cite web
 | url = http://www.oscars.org/science-technology/sci-tech-projects/solid-state-lighting-report
 | title = Solid State Lighting Report
 | date = September 3, 2014
 }}</ref>

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.<ref>
{{cite web
 | url = https://tech.ebu.ch/tlci-2012
 | title = EBU Technology & Innovation - Television Lighting Consistency Index 2012
 | date = May 31, 2016
 }}</ref>  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.<ref>{{cite web
 | url = http://www.gtc.org.uk/tlci-results.aspx
 | title = The Guild of Television Cameramen: TLCI Results
 | access-date = 2014-08-28
 | archive-url = https://web.archive.org/web/20140903072219/http://www.gtc.org.uk/tlci-results.aspx
 | archive-date = 2014-09-03
 }}</ref> Some manufacturers say that their products have TLCI values of up to 99.<ref>
{{cite web
 | url = https://www.yujiintl.com/film-lighting.html
 | title = High TLCI LEDs for Film and Photography
 }}</ref>

== References ==
{{Reflist}}

== Sources ==
<!-- Harvard citations used. Please do not correct "colour" to color in the references and quotes. -->
* {{citation |series=Publication 135/2|year=1999|url=http://cie.kee.hu/newcie/publ/abst/135-99.html|title=Colour rendering (TC 1-33 closing remarks) |website=Commission internationale de l'éclairage |access-date=2008-07-16 |archive-url=https://web.archive.org/web/20080922013149/http://cie.kee.hu/newcie/publ/abst/135-99.html|archive-date=2008-09-22 |ref={{harvid|CIE|1999}}}}
* {{citation |title=CIE Colorimetric and Colour Rendering Tables |website=Commission internationale de l'éclairage |year=2004  |url=http://www.cie.co.at/publ/abst/d002.html |access-date=2008-02-16 |archive-url=https://web.archive.org/web/20080305120337/http://www.cie.co.at/publ/abst/d002.html|archive-date=2008-03-05 |ref={{harvid|CIE|2004}}}}
* {{citation |series=Publication 177:2007|year=2007|url=http://www.slg.ch/pdf/publikation177.pdf |title=Colour rendering of white LED light sources |publisher=CIE Central Bureau |location=Vienna |via=Schweizer Licht Gesellschaft |isbn=978-3-901906-57-2 |ref={{harvid|CIE|2007}}}}{{Dead link|date=January 2019 |bot=InternetArchiveBot |fix-attempted=yes }}. Carried out by TC 1-69: color Rendering of White Light Sources.
* {{citation|title=Band Systems for Appraisal of Color Rendition|journal=[[JOSA]]|volume=47|issue=12|date=December 1957|first=Bentley T.|last=Barnes|pages=1124–1129|doi=10.1364/JOSA.47.001124|bibcode=1957JOSA...47.1124B}}
* {{citation|first=Peter|last=Bodrogi|contribution=Colour rendering: past, present(2004), and future |year=2004|title=CIE Expert Symposium on LED Light Sources|pages=10–12 |url=http://cie2.nist.gov/LED_Sympo_2004/CIE_LED_symp04_prog_abstr.pdf|access-date=2008-07-18|archive-url=https://web.archive.org/web/20110721055141/http://cie2.nist.gov/LED_Sympo_2004/CIE_LED_symp04_prog_abstr.pdf|archive-date=2011-07-21}}
* {{citation|title=Measurement of color rendering tolerances|first=Brian Hewson|last=Crawford|journal=[[JOSA]]|date=December 1959|volume=49|issue=12|pages=1147–1156|doi=10.1364/JOSA.49.001147|bibcode=1959JOSA...49.1147C}}
* {{citation|url=http://physics.nist.gov/Divisions/Div844/facilities/vision/color.html |first1=Wendy |last1=Davis |first2=Yoshi |last2=Ohno |date=December 2006 |title=Color Rendering of Light Sources |publisher=[[NIST]] |archive-url=https://web.archive.org/web/20090825230627/http://physics.nist.gov/Divisions/Div844/facilities/vision/color.html |archive-date=August 25, 2009 }}
* {{cite conference |mode=cs2 |chapter=Sensitivity metamerism index digital still camera |volume=4922 |title=Proceedings of the SPIE: Color Science and Imaging Technologies |editor=Dazun Zhao |editor2=Ming R. Luo |editor3=Kiyoharu Aizawa |date=September 2002 |pages=1–14 |doi=10.1117/12.483116 |first=Po-Chieh |last=Hung |bibcode=2002SPIE.4922....1H}}
* {{citation|title=Light sources and color rendering|first=Dorothy|last=Nickerson|journal=[[JOSA]]|date=January 1960|volume=50|issue=1|pages=57–69|doi=10.1364/JOSA.50.000057|bibcode=1960JOSA...50...57N}}
* {{cite conference |title=Optical metrology for LEDs and solid state lighting |last=Ohno |first=Yoshi |series=Fifth Symposium Optics in Industry |year=2006 |book-title=Proceedings of SPIE: Fifth Symposium Optics in Industry |volume=6046 |pages=604625-1–604625-8 |editor=E. Rosas |editor2=R. Cardoso |editor3=J.C. Bermudez |editor4=O. Barbosa-Garcia |url=http://www.nist.gov/manuscript-publication-search.cfm?pub_id=840989 |doi=10.1117/12.674617 |bibcode=2006SPIE.6046E..25O}}
* {{citation|first1=Nicolas|last1=Pousset|first2=Gael|last2=Obein|first3=Annick|last3=Razet|title=Visual experiment on LED lighting quality with color quality scale colored samples|journal=Proceedings of CIE 2010: Lighting Quality and Energy Efficiency, Vienna, Austria|year=2010|pages=722–729 |url=http://nicolas.pousset.pagesperso-orange.fr/Recherche/Article/CQS.pdf}}
* {{citation|first=János|last=Schanda|contribution=The concept of colour rendering revisited|title=First European Conference on Color in Graphics Imaging and Vision|location=Poitiers, France|date=April 2–5, 2002 |url=http://www.knt.vein.hu/staff/schandaj/SJCV-Publ-2005/462.pdf|archive-url=https://web.archive.org/web/20110721113839/http://www.knt.vein.hu/staff/schandaj/SJCV-Publ-2005/462.pdf |archive-date=July 21, 2011}}
* {{cite conference |first1=János |last1=Schanda |first2=Norbert |last2=Sándor |year=2003 |title=Colour rendering, past – present – future |pages=76–85 |conference=International Lighting and Colour Conference, Cape Town, South Africa, Nov 2–5, 2003}}
* {{citation|first=William A.|last=Thornton|title=Color-Rendering Capability of Commercial Lamps|journal=[[Applied Optics]]|year=1972|volume=11|issue=5|pages=1078–1086|doi=10.1364/AO.11.001078|pmid=20119099|bibcode=1972ApOpt..11.1078T}}
* {{citation|first=K.A.G.|last=Smet|title=Correlation between color quality metric predictions and visual appreciation of light sources|journal=[[Optics Express]]|year=2011|volume=19|issue=9|pages=8151–8166 |doi=10.1364/oe.19.008151|pmid=21643065|bibcode=2011OExpr..19.8151S|doi-access=free}}
* {{citation|first1=R.|last1=Dangol|first2=M.|last2=Islam|first3=M.|last3=Hyvärinen|first4=P.|last4=Bhusal |first5=M.|last5=Puolakka|first6=L.|last6=Halonen|title=Subjective preferences and colour quality metrics of LED light sources |journal=Lighting Research and Technology|volume=45|issue=6|pages=666–688|date=December 2013 |issn=1477-1535|doi=10.1177/1477153512471520 }}
* {{citation|first1=M.S.|last1=Islam|first2=R.|last2=Dangol|first3=M.|last3=Hyvärinen|first4=P.|last4=Bhusal |first5=M.|last5=Puolakka|first6=L.|last6=Halonen|title=User preferences for LED lighting in terms of light spectrum |journal=Lighting Research and Technology|volume=45|issue=6|pages=641–665|date=December 2013 |issn=1477-1535|doi=10.1177/1477153513475913 }}
* {{cite journal |last1=Baniya |first1=R.R. |last2=Dangol |first2=R. |last3=Bhusal |first3=P. |last4=Wilm |first4=A. |last5=Baur |first5=E. |last6=Puolakka |first6=M. |last7=Halonen |first7=L. |year=2015| title=User-acceptance studies for simplified light-emitting diode spectra |journal=Lighting Research and Technology |volume=47 |issue=2| pages=177–191 |doi= 10.1177/1477153513515264 }}
* {{cite journal |last1=Dangol |first1=R. |last2=Islam |first2=M. |last3=Hyvärinen |first3=M. |last4=Bhusal |first4=P. |last5=Puolakka |first5=M. |last6=Halonen |first6=L. |year=2015| title=User acceptance studies for LED office lighting: Preference, naturalness and colourfulness |journal=Lighting Research and Technology |volume=47 |issue=1| pages=36–53 |doi= 10.1177/1477153513514424 }}
* {{cite journal |last1=Islam |first1=M. |last2=Dangol |first2=R. |last3=Hyvärinen |first3=M. |last4=Bhusal |first4=P. |last5=Puolakka |first5=M. |last6=Halonen |first6=L. |year=2013| title=User acceptance studies for LED office lighting: lamp spectrum, spatial brightness and illuminance level |journal=Lighting Research and Technology |volume=47 |issue=1| pages=54–79 |doi= 10.1177/1477153513514425 }}

==External links==
* [http://www.lrc.rpi.edu/programs/nlpip/lightinganswers/lightsources/appendixb1.asp MATLAB script for calculating measures of light source color], [[Rensselaer Polytechnic Institute]], 2004.
* [https://web.archive.org/web/20071109105911/http://www.lightinglab.fi/teaching/217/CRI_calculation.xls Excel spreadsheet with a cornucopia of data], Lighting Laboratory of the [[Helsinki University of Technology]] (Note: Cell contents in both sheets are password protected. It may be possible to unlock the individual worksheets using AAAAAAABABB/)
* [http://stacks.iop.org/0026-1394/46/704 Uncertainty evaluation for measurement of LED colour<!-- Should be Colour not Colour, it's part of an article title, do not "correct" it--> , Metrologia]
* [http://www1.eere.energy.gov/buildings/ssl/cri_leds.html Color Rendering Index and LEDs], [http://www.eere.energy.gov/ United States Department of Energy, Office of Energy Efficiency and Renewable Energy (EERE)][bad link]
* [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]
* [http://www.edaphic.com.au/knowledge-base/articles/light-articles/ What is the difference between CRI and CQS?] {{Webarchive|url=https://web.archive.org/web/20150718064746/http://www.edaphic.com.au/knowledge-base/articles/light-articles/ |date=2015-07-18  }}, Edaphic Scientific Knowledge Base
* [https://www.lumens.com/light-bulb-facts/color-rendering-index.html Understanding color rendering index for lighting], Lumens

{{DEFAULTSORT:Color Rendering Index}}
[[Category:Color|rendering index]]
[[Category:Lighting]]