A color rendering index (CRI) 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 (CIE), 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 (CCT). 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 Ra value, "CRI" being a general term and CIE Ra being the international standard color rendering index.

Numerically, the highest possible CIE Ra 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 (incandescent lamps are effectively black bodies), 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 Ra'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..Conference version of this article: CRI is not a good indicator for use in visual assessment of light sources, especially for sources below 5000 kelvin (K). (A verbatim re-publication of the 1974, second edition. Accompanying disk D008: Computer Program to Calculate CRIs. ) New standards, such as the IES TM-30, resolve these issues and have begun replacing the usage of CRI among professional lighting designers.Illuminating Engineering Society. 2018. IES Method for Evaluating Light Source Color Rendition, IES Technical Memorandum (TM) 30-18. 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 (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".

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 (SPD) in "representative" spectral bands, whereas their North American counterparts studied the colorimetric effect of the illuminants on reference objects.American approach is expounded in , and the European approach in , and . See for a historical overview.

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 (CCT), 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 (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 extant versions of CRI: the more commonly used Ra of (actually from 1974) and R96a 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 (e.g., 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.

Using the 2° standard observer, find the chromaticity co-ordinates of the test source in the CIE 1960 color space.Note that when CRI was designed in 1965, the most perceptually uniform chromaticity space was the CIE 1960 UCS, the CIE 1976 UCS not yet having been invented. Determine the correlated color temperature (CCT) of the test source by finding the closest point to the Planckian locus on the (u, v) 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 (DC) 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., Section 5.3: Tolerance for reference illuminant 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 (i.e., particular) CRI using the formula Per , and, as demonstrated in the 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 lights" boast CRIs approaching 100; e.g., Philips TL950 or . compares older products; compares newer ones.It appeared that could be negative (), and this was indeed calculated for some lamp test colors, especially TCS9 (strong red). Find the general CRI (Ra) 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 (uc,i, vc,i) for each sample. The mixed subscripts (t, i) 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 (leaf)

As specified in , the original test color samples (TCS) 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.See the CIE 1960 UCS diagram towards the end of the Example section. 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 ,TCS spectra in CSV form , Korea Research Institute of Standards and Science. and their approximate Munsell notations are listed aside.Munsell Renotation Data, Munsell Color Science Laboratory, Rochester Institute of Technology

R96a method

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 R96a method was developed. The committee was dissolved in 1999, releasing , but no firm recommendations, partly due to disagreements between researchers and manufacturers."Authors' response to SA Fotios and JA Lynes" in : "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."

The R96a 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 (since CIELAB is well-tested under D65).

It is conventional to use the original method; R96a should be explicitly mentioned if used.

New test color samples TCS01* TCS02* TCS03* TCS04* TCS05* TCS06* TCS07* TCS08* TCS09* TCS10* L* 40.9 61.1 81.6 72.0 55.7 51.7 30.0 51.0 68.7 63.9 a* 51.0 28.8 −4.2 −29.4 −43.4 −26.4 23.2 47.3 14.2 11.7 b* 26.3 57.9 80.3 58.9 35.6 −24.6 −49.6 −13.8 17.4 17.3

As discussed in , recommends the use of a ColorChecker chart owing to the obsolescence of the original samples, of which only metameric matches remain.X-Rite ColorChecker Chart. In addition to the eight ColorChart samples, two skin tone samples are defined (TCS09* and TCS10*). 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 (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 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 (CMFs) yields (X, Y, Z) = (109.2, 100.0, 38.9) (after normalizing for Y = 100). From this follow the xy chromaticity values:

The next step is to convert these chromaticities to the CIE 1960 UCS in order to be able to determine the CCT: