Another important characteristic of a white light source is its ability to show (i. e. render) the true colors of physical objects, e. g. fruits, plants, or toys, that are being illuminated by the source. The ability to render the colors of an object is measured in terms of the color-rendering index or CRI (Wyszecki and Stiles, 1982, 2000; MacAdam, 1993; Berger-Schunn, 1994; CIE, 1995). It is
a measure of the ability of the illuminant (i. e. a white illumination source) to faithfully render the colors of physical objects illuminated by the source.

Figure 19.3 shows an example of a physical object (here a painting by the impressionist Auguste Renoir) under illumination with a high-CRI source and with a low-CRI source. Colors appear richer and more vivid under illumination with a high-CRI source. Whereas high color rendering is important in locations such as museums, homes, and offices, it is less so in locations such as streets and parking lots. Finally, the color-rendering index is irrelevant for white light

Fig. 19.3. Artwork entitled “Fleurs dans un vase” illuminated with

(a) high-CRI source and (b) low-CRI source (Auguste Renoir, French im­pressionist, 1841-1919).

The color-rendering ability of a test light source (to be abbreviated as test source) is evaluated by comparing it with the color-rendering ability of a reference light source (to be abbreviated as reference source). For the calculation of the CRI, the reference source is chosen as follows (CIE, 1995): (i) If the chromaticity point of the test source is located on the planckian locus, the reference source is a planckian black-body radiator with the same color temperature as the test source. (ii) If the chromaticity point of the test source is located off the planckian locus, the reference source is a planckian black-body radiator with the same correlated color temperature as the test source. (iii) Alternatively, one of the standardized CIE illuminants (e. g. Illuminant D65) can be used as a reference source (CIE, 1995). Ideally, the test source and the reference source have the same chromaticity coordinates and luminous flux.

By convention, the planckian black-body reference source is assumed to have perfect color - rendering properties and thus its color-rendering index is CRI = 100. This convention was agreed upon because natural daylight closely resembles a planckian black-body source and thus rightfully deserves to be established as the standard reference source. Illuminants other than the reference source necessarily have a color-rendering index lower than 100. Because the CRI depends sensitively on the choice of the reference source, the selection of the reference source is
of critical importance when calculating the CRIs of test sources.

Because the emission spectrum of an incandescent lamp closely follows that of a planckian black-body radiator, such lamps have the highest possible CRI and thus the best color-rendering properties of all artificial light sources. Incandescent quartz-halogen lamps are used in locations where color rendering is of prime importance, such as in museums, art galleries, and clothing shops. The drawback of quartz-halogen lamps is high power consumption.

In addition to the test source and the reference source, test-color samples are instrumental in determining the CRI of a test source. Test-color samples could be derived from real objects, e. g. fruit, flowers, wood, furniture, and clothes. However, in the interest of international standardization, a specific set of 14 test-color samples has been agreed upon for the purpose of determining the CRI. These 14 test-color samples are a subset of a larger collection of test-color samples initially introduced by Albert H. Munsell, a professor who taught at Rochester Institute of Technology (Rochester, NY) in the late 1800s and early 1900s (Munsell, 1905; 2005; Billmeyer, 1987; Long and Luke, 2001). Munsell introduced a color notation - the Munsell color system - which is a notation for defining a very wide range of colors.

The CRI calculation has been discussed in detail by Wyszecki and Stiles (1982; 2000) and by CIE (1995). The CIE general CRI is an average calculated according to

(19.9)

where the CRI; are the special CRIs for a set of eight test-color samples. The special color - rendering indices are calculated according to

(19.10)

CRI,- = 100 - 4.6 AE*

where AE* represents the quantitative color change that occurs when a test-color sample is illuminated with, first, the reference illumination source (“reference source”), and subsequently with the test illumination source (“test source”). The special color-rendering indices are calculated in such a way that they have a value of 100 if there is no difference in color appearance. The quantitative color change, AE*, plays a key role in the calculation of the CRI and the determination of AE* will be discussed in detail in the two subsequent sections where we will differentiate between on-planckian-locus and off-planckian-locus test sources.

At the time Eq. (19.10) was established, the pre-factor 4.6 had been chosen in such a way
that the general CRI equals 60 when a “standard warm white” fluorescent lamp was used as a test source and a planckian black-body radiator was used as a reference source. Current fluorescent light sources have higher CRIs, typically in the range 60-85 (Kendall and Scholand, 2001).

The test-color samples mentioned above are defined in terms of their spectral reflectivity. The reflectivity curves of eight internationally agreed-upon test-color samples are shown in Fig. 19.4. The numerical values of the reflectivity of the eight test-color samples are listed in Appendix 19.1. The general color-rendering index is calculated from these eight test-color samples (/ = 1-8).

In addition to the test-color samples (with numbers 1-8) used to calculate the general color rendering index, six supplemental test-color samples (with numbers 9-14) are used to further assess the color rendering capabilities of test sources. These supplemental test-color samples have the following colors: 9 - strong red; 10 - strong yellow; 11 - strong green; 12 - strong purplish blue; 13 - complexion of white person; 14 - leaf of tree. The reflectivity spectra and the numerical values of the reflectivity of the supplemental test-color samples are given in Fig. 19.5 and in Appendix 19.2, respectively. Inspection of the reflectivity curves reveals that the colors of the test-color samples 9-14 have particularly strong colors with relatively narrow peaks. CRI9 to CRI14 are referred to as the special color-rendering indices 9—14.

The meaning of chromaticity difference of a test and a reference illumination source and the rendered colors of a test-color sample, when illuminated with the test and reference illumination sources, is illustrated in Fig. 19.6. In the example shown in the figure, the test source is located slightly off the planckian locus. The reference source is a planckian source with the least possible distance from the test-source chromaticity point. As a result, the color temperature of the reference source is equal to the correlated color temperature of the test source. The four chromaticity points shown in Fig. 19.6 enter the calculation of the CRI.

Note, however, that the term “color” as used by the CIE, is not equal to “chromaticity”. The broad CIE definition for color includes hue, saturation, and additionally, brightness (for light) or lightness (for physical objects). Whereas hue and saturation are fully defined by location in the chromaticity coordinate system, brightness and lightness are not. To allow for a graphical representation of object lightness (or source brightness) a third axis could be added to the chromaticity diagram, as done for illustrative purposes in Fig. 19.7. The color difference of a physical object when illuminated with, first, a reference source, and subsequently with a test source, thus consists of the chromaticity difference and the lightness difference, as represented by the geometrical distance of the two points shown in Fig. 19.7. The reader is cautioned that the representation shown in Fig. 19.7 is for educational purposes and not a standardized CIE representation.

Fig. 19.6. Chromaticity differ­ence resulting from the illumi­nation of an object with a ref­erence and a test light source. In the CIE 1976 u v' uniform chromaticity diagram, the chromaticity difference is di­rectly proportional to the geo­metric distance. The reference light source is located on the planckian locus at the corre­lated color temperature of the test light source.

//'-chromaticity coordinate

A uniform color space (CIE, 1986) is motivated by the need for a quantitative color space that includes chromaticity and brightness/lightness. This uniform color space provides direct proportionality between color difference and geometrical distance. Thus color differences can be directly related to geometric distances between two points in the uniform color space. The CIE has introduced two three-dimensional uniform color spaces, namely the (L*, u*, v*) and (L*, a*, b*) spaces (CIE, 1986; Wyszecki and Stiles, 2000). For our purposes, it will be sufficient to consider the (L*, u*, v*) uniform color space and we will therefore restrict our considerations to this space. The CIE (L*, u*, v*) uniform color space is a three-dimensional space with cartesian coordinates, two coordinates being associated primarily with the chromaticity (u*, v*), and the third coordinate, L*, representing the brightness (of a source) or lightness (of a physical object). The uniform color space is particularly suited to quantify color differences.

As an example and to become familiar with the CIE (L*, u*, v*) color space, we consider a test-color sample i illuminated with a white reference source. The coordinates, L*, u*, and v*, which give the color difference between object color and reference-source color, are defined as

L*lret = 1160W, i /YKf)1/3 - 16 (19.11a)

u*lref = 13 L*(uref, i - uref) (19.11b)

v* Iref = 13L*(vref, i - vref) (19.11c)

where Yref, i, uref, i, and vref, i describe the color stimulus of the test-color sample i when illuminated with the reference source, and Yref, uref, and vref describe the color stimulus of the white reference illuminant.

Next consider the test-color sample illuminated with a white test source. The coordinates, L*, u*, and v*, which give the color difference between object color and test-source color, are then given by

L*Lt = 1>6(Ytest, i /Y, eS,)1/3 - 16 (19.12a)

u*ltest = 13L*(utest, i - utest) (19.12b)

v*ltest = 13L*(vtest, i - vtest) (19.12c)

where 7test, i, utest, i, and vtest, i describe the color stimulus of the test-color sample i when illuminated with the test source, and 7test, utest, and vtest describe the color of the white test illuminant.

The difference in color between the two points located in the (L*, u*, v*) space given by Eqs. (19.11) and (19.12) is equal to the euclidean distance between the points, that is

AE * = V (AL*)2 + (Au*)2 + (Av*)2 (19.13)

where

AL * = L *L t - L *1 , (19.14a)

Itest Iref v '

Au * = u *|test - u *|ref (19.14b)

Av * = v * . . - v * _ . (19.14c)

test ref

The calculation of the CRI will be detailed in the two subsequent sections.

Table 19.1. General color-rendering indices (CRIs) of different light sources. (a) Using sunlight as reference source. (b) Using incandescent light with the same correlated color temperature as the reference source. (c) Using Illuminant D65 as the reference source (some data after Kendall and Scholand, 2001). Light source Color-rendering index Sunlight 100 (a) Quartz halogen W filament incandescent light 100 (b) W filament incandescent light 100 (b) Fluorescent light 60-95 (b) Trichromatic white LED 60-95 (b, c) Tetrachromatic white LED 70-95 (b, c) Phosphor-based LED 55-95 (b, c) Broadened dichromatic white LED 10-60 (b, c) Hg vapor light coated with phosphor 50 (b) Hg vapor light 33 (b) Low and high-pressure Na vapor light 10 and 22 (b) Green monochromatic light -50 (c)

An overview of the general color-rendering indices of common light sources is given in

Table 19.1. The table includes several types of LED sources including dichromatic white LEDs, trichromatic white LEDs, and phosphor-based white LEDs. A CRI between 90 and 100 is suitable for virtually all illumination applications. A CRI between 70 and 90 is suitable for many standard illumination applications. Light sources with a CRI below 70 are considered to be of lower quality.

19.2 Color-rendering index for planckian-locus illumination sources The following calculation gives the value of the quantity AE*, which, according to Eq. (19.10), is needed to determine the CRI of a test source. The calculation is suited for test sources that are located on the planckian locus or extremely close to the planckian locus. The calculation described here follows Wyszecki and Stiles (1982, 2000) and CIE (1995). AE*, which is the difference in appearance of a test-color sample when illuminated with the test and reference sources, is calculated according to

	* AE*	- V (AL*)2	+ (Au*)2
- L - Lref	- teL* CD t -	116 ( YreW v Yref	1/3 " 16 J
* - uref	* - utest -	13Lref ( uref, i	- uref ) -
II v a * 1-4	1 v e t -	13Lref ( vref, i	1 f vre 1

where

116

*

(19.15)

( y 'N'1/3 Ytest,/ v Yref J

(19.16) (19.17) (19.18)

- 16

Av* and

v

6Y

and

(19.19)

u —

v -

X + 15Y + 3Z

X + 15Y + 3Z

Note that u and v are calculated from the tristimulus values of the reference source spectrum (subscript “ref”), from the reference source spectrum reflected off the test-color samples (subscript “ref, i ”), and from the test source spectrum reflected off the test-color samples (subscript “test, i ”).

When calculating the CRI using the equations given above, the chromaticity coordinates and

luminous flux of the test and reference sources should be identical in order to get the highest possible CRI for the test source. That is, the conditions utest = uref, vtest = vref, and 7test = 7ref should be satisfied.

The calculation of the color-rendering index in terms of Eqs. (19.9)-( 19.19) illustrates that it is calculated from the ability of a test source to render the chromaticity of physical objects (taken into account by Au* and Av*) but also from the ability of the test source to render the lightnesses of the physical objects (taken into account by AL*). The CRI calculation is based on the premise that the reference source renders the true chromaticity and lightness, i. e. the true color, of physical objects.

The choice of the numerical prefactors in Eqs. (19.16)-( 19.19) is somewhat arbitrary. These prefactors have been determined in extensive experiments with human subjects. Evidence exists, however, that the current prefactors may not be optimal (Wyszecki and Stiles, 1982, 2000).

19.3 Color-rendering index for non-planckian-locus illumination sources The following calculation of AEi* is suited for test sources that are located off the planckian locus. The calculation described here follows the procedure developed by CIE (1995) and takes into account the adaptive color shift that follows from the human ability of chromatic adaptation.

Chromatic adaptation is the well-known ability of humans to adapt to certain illumination environments without a substantial loss of color perception. For example, the yellow illumination sources used in semiconductor clean rooms provide a low-quality light. Such yellow sources do not contain short-wavelength light (violet, blue and cyan) and they are located clearly off the planckian locus. However, after having adapted to the clean-room illumination conditions (which typically takes several tens of minutes), colors appear quite natural, certainly much more natural than before the chromatic adaptation.

When calculating the CRI for off-planckian-locus sources according to the method described in the previous section, the CRI is very low. However, such low CRI values are not supported by experiments with human subjects: Due to chromatic adaptation, colors can appear vivid and natural, even for illumination sources slightly off the planckian locus. To overcome this discrepancy and to allow for a more realistic calculation of the CRI, the CIE (1995) introduced an alternative method to calculate the CRI. This alternative method takes into account the human ability of chromatic adaptation by introducing an adaptive color shift of the test source towards the planckian reference source.

As a rule of thumb, the pleasantness and quality of white illumination sources decreases rapidly if the chromaticity point of the illumination source deviates from the planckian locus by a distance greater than 0.01 in the x, y chromaticity system. This corresponds to the distance of about 4 MacAdam ellipses, a standard employed by the lighting industry (Duggal, 2005). Note however, that the 0.01-rule-of-thumb is a necessary but not a sufficient condition for high quality of illumination sources.

The calculation starts with the uniform chromaticity coordinates of the reference and test sources and the chromaticity coordinates of the test-color samples when illuminated with the reference and test sources, i. e. (uref, Vref), (utest, Vtest), (ttrefi Vf), and («test, i, Vtest, i).

To account for the adaptive color shift, the (u, v) coordinates of (uref, vref), (utest, vtest), and (utestji, vtest, i) are transformed into (c, d) coordinates using the formulae

(19.20)

c = (4 - u - 10 v) / v

(19.21)

d = (1.708 V + 0.404 - 1.481 u) / V.

Note that these two equations correspond to six equations when transforming (uref, vref), (utest, Vtest), and (utest,/, Vtest,/) into (cref, dref), (ctest, dtest), and (ctesti dtest, i), respectively. Subsequently the adaptive-color-shifted chromaticity coordinates of the test-color samples are calculated according to

10.872 + 0.404 ^ ctesti - 4 ^ d

test, i

d

** u test, i

test

test

(19.22)

d

ref

d

16.518 + 1.481 c c test

test, i

test, i

d

test

5.520

** Vtest, i

(19.23)

d

ref

d

16.518 + 1.481 c c test

test, i

test, i

d

test

Correspondingly, the adaptive-color-shifted chromaticity coordinates of the test source are calculated according to

(19.24)

u

= uref

test

10.872 + 0.404 cref - 4 dref 16.518 + 1.481 cref - dref

16.518 + 1.481 cref — dref

^test

The values of utest*r and vtest*r are the chromaticity coordinates of the light source to be tested after the adaptive color shift has been performed (note that utest*r = uref and vtest*r = vref). Finally the color difference is calculated in terms of the uniform color space coordinates

yj (AL**)2 + (Au**)2 + (Av**)

2

AE* -

(19.26)

where

25(Yref, i )

25(Ytest, i )

1/3

1/3

AL - Lref, i Ltest, i

(19.27)

- 17

- 17

(19.28)

Au - uref utest - 13Lref, i (uref, i uref) 13 Ltest, i (utest, i utesty

)

A * Av

(19.29)

- vref v*est

test, i vtest

- 13Lref, i (vref, i vref) 13Ltest, i(v

Note that the calculation requires that Yref = Ytest = 100 (CIE, 1995). Using the calculated values of AE*, the general CRI is calculated using Eqs. (19.9) and (19.10). The special CRI for i = 9 to 14 may be of interest for a complete assessment of the color rendering properties of an illumination source.