Color rendering index

A color rendering index is a quantitative measure of the ability of a light source to reveal the colors of various objects faithfully in comparison with a natural or standard light source.
Color rendering, as defined by the International Commission on Illumination, is the effect of an illuminant on the color appearance of objects by conscious or subconscious comparison with their color appearance under a reference or standard illuminant.
The CRI of a light source does not indicate the apparent color of the light source; that information is given by the correlated color temperature. The CRI is determined by the light source's spectrum. An incandescent lamp has a spectrum approximating that of a black body emitter, while a fluorescent lamp has an irregular emission spectrum with multiple relatively narrow peaks, which suggests that the incandescent lamp should have the higher CRI.
The value often quoted as "CRI" on commercially available lighting products is properly called the CIE R_a value, "CRI" being a general term and CIE R_a being the international standard color rendering index.
Numerically, the highest possible CIE R_a value is 100 and would only be given to a source whose spectrum is identical to the spectrum of daylight, very close to that of a black body, dropping to negative values for some light sources. Low-pressure sodium lighting has a negative CRI; fluorescent lights 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.
CIE R_a's ability to predict color appearance has been criticized in favor of measures based on color appearance models, such as CIECAM02 and for daylight simulators, the CIE metamerism index. CRI is not a good indicator for use in visual assessment of light sources, especially for sources below 5000 kelvin. New standards, such as the IES TM-30, resolve these issues and have begun replacing the usage of CRI among professional lighting designers. 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 for good color rendering because "it displays a great variety of colors, makes it easy to distinguish slight shades of color, and the colors of objects around us obviously look natural".
Around the middle of the 20th century, color scientists took an interest in assessing the ability of artificial lights to accurately reproduce colors. European researchers attempted to describe illuminants by measuring the spectral power distribution in "representative" spectral bands, whereas their North American counterparts studied the colorimetric effect of the illuminants on reference objects.
The 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 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, CIEUVW. In 1931, the CIE adopted the first formal system of colorimetry, which is based on the trichromatic nature of the human visual system. CRI is based upon this system of colorimetry.
To deal with the problem of having to compare light sources of different correlated color temperatures, the CIE settled on using a reference black body with the same color temperature for lamps with a CCT of under 5000 K, or a phase of CIE standard illuminant D 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 extant versions of CRI: the more commonly used R_a of and R96_a of.

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 K, and a phase of daylight otherwise. Chromatic adaptation should be performed so that like quantities are compared. The Test Method needs only colorimetric, rather than spectrophotometric, information.

Using the 2° standard observer, find the chromaticity co-ordinates of the test source in the CIE 1960 color space.
Determine the correlated color temperature of the test source by finding the closest point to the Planckian locus on the chromaticity diagram.
If the test source has a CCT < 5000 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 of the test source to the Planckian locus is under 5.4×10⁻³ 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.
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 Von Kries transform.
For each sample, calculate the Euclidean distance between the pair of co-ordinates.
Calculate the special CRI using the formula
Find the general CRI by calculating the arithmetic mean of the special CRIs.

Note that the last three steps are equivalent to finding the mean color difference, and using that to calculate :

Chromatic adaptation

uses this von Kries chromatic transform equation to find the corresponding color for each sample. The mixed subscripts refer to the inner product of the test illuminant spectrum and the spectral reflexivity of sample i:
where subscripts r and t refer to reference and test light sources respectively.

Test color samples

Name	Appr. Munsell	Appearance under daylight	Swatch
TCS01	7,5 R 6/4	Light grayish red
TCS02	5 Y 6/4	Dark grayish yellow
TCS03	5 GY 6/8	Strong yellow green
TCS04	2,5 G 6/6	Moderate yellowish green
TCS05	10 BG 6/4	Light bluish green
TCS06	5 PB 6/8	Light blue
TCS07	2,5 P 6/8	Light violet
TCS08	10 P 6/8	Light reddish purple
TCS09	4,5 R 4/13	Strong red
TCS10	5 Y 8/10	Strong yellow
TCS11	4,5 G 5/8	Strong green
TCS12	3 PB 3/11	Strong blue
TCS13	5 YR 8/4	Light yellowish pink
TCS14	5 GY 4/4	Moderate olive green

As specified in, the original test color samples are taken from an early edition of the Munsell Atlas. The first eight samples, a subset of the eighteen proposed in, are relatively low saturated colors and are evenly distributed over the complete range of hues. These eight samples are employed to calculate the general color rendering index. 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, and their approximate Munsell notations are listed aside.

R96_a method

In the CIE's 1991 Quadrennial Meeting, Technical Committee 1-33 was assembled to work on updating the color rendering method, as a result of which the R96_a method was developed. The committee was dissolved in 1999, releasing, but no firm recommendations, partly due to disagreements between researchers and manufacturers.
The R96_a method has a few distinguishing features:

[|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 D65.

It is conventional to use the original method; R96_a should be explicitly mentioned if used.

New test color samples

As discussed in, recommends the use of a ColorChecker chart owing to the obsolescence of the original samples, of which only metameric matches remain. In addition to the eight ColorChart samples, two skin tone samples are defined. Accordingly, the updated general CRI is averaged over ten samples, not eight as before. Nevertheless, has determined that the patches in give better correlations for any color difference than the ColorChecker chart, whose samples are not equally distributed in a uniform color space.

Example

The CRI can also be theoretically derived from the spectral power distribution 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 nm increments, 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 values using the 1931 standard observer. Calculation of the inner product of the SPD with the standard observer's color matching functions yields = . From this follow the xy chromaticity values:
Image:CIE 1960 UCS, FL4.svg|thumb|right|upright=0.8|The tight isotherms are from 2935 K to 2945 K. FL4 marked with a cross.
The next step is to convert these chromaticities to the CIE 1960 UCS in order to be able to determine the CCT:
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 K on the Planckian locus, which has a coordinate of. The distance of the test point to the locus is under the limit, so we can continue the procedure, assured of a meaningful result:
We can verify the CCT by using McCamy's approximation algorithm to estimate the CCT from the xy chromaticities:
where.
Substituting yields n = 0.4979 and CCT_est. = 2941 K, which is close enough. Since 2940 < 5000, we select a Planckian radiator of 2940 K as the reference illuminant.
The next step is to determine the values of the test color samples under each illuminant in the 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 :

Illuminant	Illuminant	TCS1	TCS2	TCS3	TCS4	TCS5	TCS6	TCS7	TCS8
Reference	U	39.22	17.06	−13.94	−40.83	−35.55	−23.37	16.43	44.64
Reference	V	2.65	9.00	14.97	7.88	−2.86	−13.94	−12.17	−8.01
Reference	W	62.84	61.08	61.10	58.11	59.16	58.29	60.47	63.77
CIE FL4	U	26.56	10.71	−14.06	−27.45	−22.74	−13.99	9.61	25.52
CIE FL4	V	3.91	11.14	17.06	9.42	−3.40	−17.40	−15.71	-10.23
CIE FL4	W	63.10	61.78	62.30	57.54	58.46	56.45	59.11	61.69
CIE FL4	U	26.34	10.45	−14.36	−27.78	−23.10	−14.33	9.37	25.33
CIE FL4	V	4.34	11.42	17.26	9.81	−2.70	−16.44	−14.82	−9.47
CIE FL4	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 and those illuminated by the reference. The special CRI is simply.

	TCS1	TCS2	TCS3	TCS4	TCS5	TCS6	TCS7	TCS8
	12.99	7.07	2.63	13.20	12.47	9.56	7.66	19.48
R_i	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.