Editing Color rendering index (section)

==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=October 12, 2007 }} 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 grayish red
| style="background:#e8a7b0;" |
|-
| TCS02
| 5 Y 6/4
| Dark grayish 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=February 11, 2009 }}, 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]]
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