# Color rendering index: Map

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The color rendering index (CRI) (sometimes called color rendition index), is a quantitative measure of the ability of a light source to reproduce the colors of various objects faithfully in comparison with an ideal or natural light source. Light sources with a high CRI are desirable in color-critical applications such as photography and cinematography. It is defined by the International Commission on Illumination as follows:
Color rendering: Effect of an illuminant on the color appearance of objects by conscious or subconscious comparison with their color appearance under a reference illuminant

Note that the CRI by itself does not indicate what the color temperature of the reference light source is; therefore, it is customary to also cite the correlated color temperature (CCT).

According to , CRI is being deprecated in favor of measures based on color appearance models, such as CIECAM02 and, for daylight simulators, the CIE Metamerism Index. and note that CRI is not a good indicator for use in visual assessment, especially for sources below 5000 K.

A newer version of the CRI has been developed (R96a), but it has not replaced the better-known Ra (general color rendering index).

## History

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.

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.

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.

## 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. Specified in and republished in , the Test Method (also called Test Sample Method or Test Color Method) needs only colorimetric, rather than spectrophotometric, information.
CIE 1960 UCS.
Planckian locus and co-ordinates of several illuminants shown in illustration below.
1. Using the 2° standard observer, find the chromaticity co-ordinates of the test source in the CIE 1960 color space.
2. 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.
3. If the test source has a CCT<5000&NBSP;K, use="" a="" black="" body="" for="" reference,="" otherwise="" CIE="" standard illuminant D. Both sources should have the same CCT.
4. Ensure that the chromaticity distance (DC) of the test source to the Planckian locus is under 5.4E-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. DC={\Delta}_{uv}=\sqrt{(u_r-u_t)^2+(v_r-v_t)^2}
5. Illuminate the first eight standard samples, from the fifteen listed below, alternately using both sources.
6. Using the 2° standard observer, find the chromaticity co-ordinates of the light reflected by each sample in the CIE 1964 color space.
7. Chromatically adapt each sample by a von Kries transform.
8. For each sample, calculate the Euclidean distance \Delta E_i between the pair of co-ordinates.
9. Calculate the special (i.e., particular) CRI using the formula R_i=100-4.6 \Delta E_iIt appeared that R_i could be negative (\Delta E_i ≥ 22), and this was indeed calculated for some lamp test colors, especially TCS9 (strong red).
10. 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, \Delta \bar{E}_{UVW} and using that to calculate R_a:

R_a=100-4.6 \Delta \bar{E}_{UVW}

Chromatic adaptation of TCSs lit by CIE FL4 (short, black vectors, to indicate before and after) to a black body of 2940K (cyan circles).
 uses this von Kries chromatic transform equation to find the corresponding color (uc,i,vc,i) for sample i:


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}}

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

c=\left(4.0-u-10.0v \right)/v

d=\left(1.708v-1.481u+0.404\right)/v

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 greyish red
TCS02 5 Y 6/4 Dark greyish 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 (skin)
TCS14 5 GY 4/4 Moderate olive green (leaf)
TCS15 1 YR 6/4 Asian skin

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. These eight samples are employed to calculate the general color rendering index R_a. The last seven samples provide supplementary information about the color rendering properties of the light source; the first four for high saturation, and the last three as representatives of well-known objects. The reflectance spectra of these samples may be found in , and their approximate Munsell notations are listed aside.

## 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.

The R96a method has a few distinguishing features:

• A new set of test color samples
• Six reference illuminants: D65, D50, black bodies of 4200K, 3450K, 2950K, and 2700K.
• 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 Macbeth (now X-Rite) color 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 (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 Macbeth chart, whose samples are not equally distributed in a uniform color space.

## Example

The CRI can also be theoretically derived from the 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 5nm 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 tight isotherms are from 2935K–2945K.
FL4 marked with a cross.

x=\frac{109.2}{109.2+100.0+38.9}=0.4402

y=\frac{100}{109.2+100.0+38.9}=0.4031

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

u=\frac{4 \times 0.4402}{-2 \times 0.4402 + 12 \times 0.4031 + 3}=0.2531

v=\frac{6 \times 0.4031}{-2 \times 0.4402 + 12 \times 0.4031 + 3}=0.3477

Examining the CIE 1960 UCS reveals this point to be closest to 2938 K on the Planckian locus, which has a co-ordinate of (0.2528, 0.3484). The distance of the test point to the locus is under the limit (5.4E-3), so we can continue the procedure, assured of a meaningful result:

\begin{align} DC&=\sqrt{ (0.2531-0.2528)^2+(0.3477-0.3484)^2 } \\& =8.12 \times 10^{-4} 5.4 \times 10^{-3} \end{align}

We can verify the CCT by using McCamy's approximation algorithm to estimate the CCT from the xy chromaticities:

CCT_{est.} = -449 n^3 + 3525 n^2 - 6823.3 n + 5520.33, where n=\frac{x-0.3320}{y-0.1858}.

Substituting (x,y)=(0.4402,0.4031) yields n=0.4979 and CCTest. = 2941 K, which is close enough. (Robertson's method can be used for greater precision, but we will be content with 2940 K [sic] in order to replicate published results.) 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 Reference U V W CIE FL4 U V TCS1 TCS2 TCS3 TCS4 TCS5 TCS6 TCS7 TCS8 39.22 17.06 -13.94 -40.83 -35.55 -23.37 16.43 44.64 2.65 9.00 14.97 7.88 -2.86 -13.94 -12.17 -8.01 62.84 61.08 61.10 58.11 59.16 58.29 60.47 63.77 26.56 10.71 -14.06 -27.45 -22.74 -13.99 9.61 25.52 3.91 11.14 17.06 9.42 -3.40 -17.40 -15.71 10.23 63.10 61.78 62.30 57.54 58.46 56.45 59.11 61.69 26.34 10.45 -14.36 -27.78 -23.10 -14.33 9.37 25.33 4.34 11.42 17.26 9.81 -2.70 -16.44 -14.82 -9.47 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 R_i=100-4.6 \Delta E_{UVW}.

 \Delta E_{UVW} Ri TCS1 TCS2 TCS3 TCS4 TCS5 TCS6 TCS7 TCS8 12.99 7.07 2.63 13.20 12.47 9.56 7.66 19.48 40.2 67.5 87.9 39.3 42.6 56.0 64.8 10.4

Finally, the general color rendering index is mean of the special CRI's: 51.

[[Image:CIE CRI TCS under FL4.svg|thumb|600px|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

Light source CCT (K) CRI
Low Pressure Sodium (LPS/SOX) 1800 ~5
Clear Mercury-vapor 6410 17
High Pressure Sodium (HPS/SON) 2100 24
Coated Mercury-vapor 3600 49
Halophosphate Warm White Fluorescent 2940 51
Halophosphate Cool White fluorescent 4230 64
Tri-phosphor Warm White Fluorescent 2940 73
Halophosphate Cool Daylight Fluorescent 6430 76
"White" SON 2700 82
Quartz Metal Halide 4200 85
Tri-phosphor Cool White fluorescent 4080 89
Ceramic Metal Halide 5400 96
Incandescent/Halogen Light Bulb 3200 100

A reference source, such as black body radiation, is defined as having a CRI of 100. This is why incandescent lamps have that rating, as they are, in effect, almost black body radiators. The best possible faithfulness to a reference is specified by a CRI of one hundred, while the very poorest is specified by a CRI of 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 (see next section).

## Criticism and resolution

 and others have criticised 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 LEDs. Another problem is that the CRI is discontinuous at 5000 K, because the chromaticity of the reference moves from the Planckian locus to the CIE Daylight Locus.  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.
• 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 ∆Ei, 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 R_{out}=10 \ln \left[\exp(R_{in}/10)+1\right]
• The CRI can not 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 K to the gamut area for the test source. 6500 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.

 "reviews the applicability of the CIE colour 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 colour 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."

For a comprehensive review of alternative color rendering indices see .

## Footnotes

1. CIE 17.4| International Lighting Vocabulary,
2. American approach is expounded in , and the European approach in , and . See for a historical overview.
3. 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.
4. , Section 5.3: Tolerance for reference illuminant
5. 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.
6. See the CIE 1960 UCS diagram towards the end of the Example section.
7. TCS spectra in CSV form, Korea Research Institute of Standards and Science.
8. Munsell Renotation Data, Munsell Color Science Laboratory, Rochester Institute of Technology
9. "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.
10. See "Past research to improve the CRI" in
11. X-Rite ColorChecker Chart.
12. "Authors’ response to SA Fotios and JA Lynes" in : It is quite obvious that just at 5000 K, where the reference illuminant has to be changed, the present system shows discontinuity.'
13. CIE Activity Report. Division 1: Vision and Color, pg.21, January 2008.