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Color Science
Robert M. Boynton
University of California, San Diego
I. Physical Basis of Perceived Color
II. CIE System of Color Specification
III. Color Rendering
IV. Global Surface Properties
V. Physical Basis of Surface Color
VI. Color Difference and Color Order
VII. Physiological Basis of Color Vision
GLOSSARY Color rendering General expression for the effect of a
light source on the color appearance of objects in com-
Chromaticity Ratios x, y, z of each of the tristimulus parison with their color appearance under a reference
values of a light to the sum of the three tristimulus val- light source.
ues X, Y , Z, these being the amounts of three primaries Color temperature Absolute temperature of a blackbody
required to match the color of the light. radiator having a chromaticity closest to that of a light
Chromaticity diagram Plane diagram formed by plot- source being specified.
ting one of the three chromaticity coordinates against Metamerism (1) Phenomenon whereby lights of differ-
another (usually y versus x). ent spectral power distributions appear to have the same
Color Characteristics of sensations elicited by light by color. (2) Degree to which a material appears to change
which a human observer can distinguish between two color when viewed under different illuminants.
structure-free patches of light of the same size and Optimal colors Stimuli that for a given chromaticity have
shape. the greatest luminous reflectance.
Colorant A substance, such as a dye or pigment, that Primaries (1) Additive: Any one of three lights in terms
modifies the color of objects or imparts color to other- of which a color is specified by giving the amount
wise achromatic objects. of each required to match it by combining the lights.
Colorimetry Measurement and specification of color. (2) Subtractive: Set of dyes or pigments that, when
Color matching Action of making a test color appear the mixed in various proportions, provides a gamut of
same as a reference color. colors.
Color order System of reference whereby the relation of Radiance Radiant flux per unit solid angle (intensity) per
one color to another can be perceived and the position of unit area of an element of an extended source or reflect-
that color can be established with respect to the universe ing surface in a specified direction.
of all colors. Reflectance Ratio of reflected to incident light.
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290 Color Science
Reflection Process by which incident flux leaves a surface match will, of course, occur if there is no physical differ-
or medium from the incident side, without change in ence between the fields, and in special cases color matches
wavelength. are also possible when substantial physical differences ex-
ist between the fields. An understanding of how this can
happen provides an opening to a scientific understanding
COLOR SCIENCE examines a fundamental aspect of of this subject.
human perception. It is based on experimental study un- Given an initial physical match, a difference in color
der controlled conditions susceptible to physical measure- can be introduced by either of two procedures, which are
ment. For a difference in color to be perceived between often carried out in combination. In the first instance, the
two surfaces, three conditions must be satisfied: (1) There radiance of one part of a homogeneous field is altered
must be an appropriate source of illumination, (2) the two without any change in its relative spectral distribution.
surfaces must not have identical spectral reflectances, and This produces an achromatic color difference. In the sec-
(3) an observer must be present to view them. This arti- ond case, the relative spectral distribution of one field is
cle is concerned with the relevant characteristics of lights, changed such that, for all possible relative radiances of the
surfaces, and human vision that conjoin to allow the per- two fields, no match is possible. This is called a chromatic
ception of object color. color difference.
When fields of different spectral distributions can be ad-
justed in relative radiance to eliminate all color difference,
I. PHYSICAL BASIS OF
the result is termed a metameric color match. In a color-
PERCEIVED COLOR
matching experiment, a test field is presented next to a
comparison field and the observer causes the two fields to
The physical basis of color exists in the interaction of light
match exactly by manipulating the radiances of so-called
with matter, both outside and inside the eye. The sensation
primaries provided to the comparison field. Such primaries
of color depends on physiological activity in the visual sys-
are said to be added; this can be accomplished by superpo-
tem that begins with the absorption of light in photorecep-
sition with a half-silvered mirror, by superimposed images
tors located in the retina of the eye and ends with patterns
projected onto a screen, by very rapid temporal alternation
of biochemical activity in the brain. Perceived color can be
of fields at a rate above the fusion frequency for vision,
described by the color names white, gray, black, yellow,
or by the use of pixels too small and closely packed to be
orange, brown, red, green, blue, purple, and pink. These
discriminated (as in color television). If the primaries are
11 basic color terms have unambiguous referents in all
suitably chosen (no one of them should be matched by any
fully developed languages. All of these names (as well as
possible mixture of the other two), a human observer with
combinations of these and many other less precisely used
normal color vision can uniquely match any test color by
nonbasic color terms) describe colors, but white, gray, and
adjusting the radiances of three monochromatic primaries.
black are excluded from the list of those called hues. Col-
To accomplish this, it sometimes proves necessary to shift
ors with hue are called chromatic colors; those without are
one of the primaries so that it is added to the color being
called achromatic colors.
matched; it is useful to treat this as a negative radiance
Although color terms are frequently used in reference
of that primary in the test field. The choice of exactly
to all three aspects of color (e.g., one may speak of a sen-
three primaries is by no means arbitrary: If only one or
sation of red, a red surface, or a red light), such usage is
two primaries are used, matches are generally impossible,
scientifically appropriate only when applied to the sensa-
whereas if four or more primaries are allowed, matches
tion; descriptions of lights and surfaces should be provided
are not uniquely determined.
in physical and geometrical language.
The result of the color-matching experiment can be rep-
resented mathematically as t(T ) = r(R) + g(G) + b(B),
meaning that t units of test field T produce a color that
II. CIE SYSTEM OF COLOR SPECIFICATION
is matched by an additive combination of r units of pri-
mary R, g units of primary G, and b units of primary
A. Basic Color-Matching Experiment
B, where one or two of the quantities r, g, or b may be
The most fundamental experiment in color science entails negative. Thus any color can be represented as a vector
the determination of whether two fields of light such as in R, G, B space. For small, centrally fixated fields, ex-
those that might be produced on a screen with two slide periment shows that the transitive, reflexive, linear, and
projectors, appear the same or different. If such fields are associative properties of algebra apply also to their empir-
abutted and the division between them disappears to form ical counterparts, so that color-matching equations can be
a single, homogeneous field, the fields are said to match. A manipulated to predict matches that would be made with a
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Color Science 291
change in the choice of primaries. These simple relations In the color-matching experiment, an observer is in ef-
break down for very low levels of illumination and also fect acting as an analog computer, solving three simulta-
with higher levels if the fields are large enough to permit neous equations by iteration, using his or her sensations as
significant contributions by rod photoreceptors or if the a guide. Although activity in the brain underlies the expe-
fields are so bright as to bleach a significant fraction of rience of color, the initial encoding of information related
cone photopigments, thus altering their action spectra. to wavelength is in terms of the ratios of excitations of
Matches are usually made by a method of adjustment, an three different classes of cone photoreceptors in the retina
iterative, trial-and-error procedure whereby the observer of the eye, whose spectral sensitivities overlap. Any two
manipulates three controls, each of which monotonically physical fields, whether of the same or different spectral
varies the radiance of one primary. Although such set- composition, whose images on the retina excite each of
tings at the match point may be somewhat more variable the three classes of cones in the same way will be indis-
than most purely physical measurements, reliable data re- criminable. The action spectra of the three classes of cones
sult from the means of several settings for each condition in the normal eye are such that no two wavelengths in the
tested. A more serious problem, which will not be treated spectrum produce exactly the same ratios of excitations
in this article, results from differences among observers. among them.
Although not great among those with normal color vi-
sion, such differences are by no means negligible. (For
B. Imaginary Primaries
those with abnormal color vision, they can be very large.)
To achieve a useful standardization—one that is unlikely Depending on the choice of primaries, many different sets
to apply exactly to any particular individual—averages of of color-matching functions are possible, all of which de-
normal observers are used, leading to the concept of a scribe the same color-matching behavior. Figure 1 shows
standard observer. experimental data for the primaries 435.8, 546.1, and
FIGURE 1 Experimental color-matching data for primaries at 435.8, 546.1, and 700.0 nm. [From Billmeyer, F. W.,
Jr., and Saltzmann, M. (1981). “Principles of Color Technology,” 2nd ed. Copyright ©1981 John Wiley & Sons, Inc.
Reprinted by permission of John Wiley & Sons, Inc.]
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292 Color Science
By simulating any of these sets of sensitivity func-
tions in three optically filtered photocells, it is possible
to remove the human observer from the system of color
measurement (colorimetry) and develop a purely physical
(though necessarily very limited) description of color, one
that can be implemented in automated colorimeters.
C. Chromaticity Diagram
A useful separation between the achromatic and chromatic
aspects of color was achieved in a system of colorimetry
adopted by the CIE in 1931. This was the first specifica-
tion of color to achieve international agreement; it remains
today the principal system used internationally for spec-
ifying colors quantitatively, without reference to a set of
actual samples.
The color-matching functions x¯ (λ), y¯ (λ), and z¯(λ) are
based on primaries selected and smoothed to force the
y¯ (λ) function to be proportional to the spectral luminous
efficiency function V (λ), which had been standardized a
decade earlier to define the quantity of “luminous flux”
in lumens per watt of radiant power. The x¯ (λ), y¯ (λ), and
z¯(λ) functions were then scaled to equate the areas under
FIGURE 2 Estimates of human cone action spectra (Ko¨nig fun- the curves, an operation that does not alter the predictions
damentals) derived by V. Smith and J. Pokorny. [From Wyszecki, they make about color matches.
G., and Stiles, W. S. (1982). “Color Science: Concepts and Meth-
To specify the color of a patch of light, one begins by
ods, Quantitative Data and Formulate,” 2nd ed. Copyright ©1982
integrating its spectral radiance distribution S(λ) in turn
John Wiley & Sons, Inc. Reprinted by permission of John Wiley &
with the three color-matching functions:
Sons, Inc.]
∫
X = k S(λ)x¯ (λ) dλ,
∫
700.0 nm. Depicted in Fig. 2 are current estimates of
Y = k S(λ)y¯ (λ) dλ,
the spectral sensitivities of the three types of cone pho-
toreceptors. These functions, which have been inferred ∫
from the data of psychophysical experiments of various
Z = k S(λ)z¯(λ) dλ.
kinds, agree reasonably well with direct microspectropho-
tometric measurements of the absorption spectra of outer
The values X, Y , and Z are called relative tristimulus
segments of human cone photoreceptors containing the
values; these are equal for any light having an equal-
photopigments that are the principal determinants of the
radiance spectrum. Tristimulus values permit the spec-
spectral sensitivity of the cones.
ification of color in terms of three variables that are
The cone spectral sensitivities may be regarded as color-
related to cone sensitivities rather than by continuous spec-
matching functions based on primaries that are said to be
tral radiance distributions, which do not. Like R, G, and B,
imaginary in the sense that, although calculations of color
the tristimulus values represent the coordinates of a three-
matches based on them are possible, they are not phys-
dimensional vector whose angle specifies chromatic color
ically realizable. To exist physically, each such primary
and whose length characterizes the amount of that color.
would uniquely excite only one type of cone, whereas
Chromaticity coordinates, which do not depend on the
real primaries always excite at least two types.
amount of a color, specify each of the tristimulus values
Another set of all-positive color-matching functions,
relative to their sum:
based on a different set of imaginary primaries, is given
in Fig. 3. This set, which makes very similar predictions x = X/(X + Y + Z);
about color matches as the cone sensitivity curves, was
y = Y (X + Y + Z);
adopted as a standard by the International Commission on
Illumination (CIE) in 1931. z = Z/(X + Y + Z)
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Color Science 293
FIGURE 3 Tristimulus values of the equal-energy spectrum of the 1931 CIE system of colorimetry. [From Billmeyer,
F. W., Jr., and Saltzmann, M. (1981). “Principles of Color Technology,” 2nd ed. Copyright ©1981 John Wiley & Sons,
Inc. Reprinted by permission of John Wiley & Sons, Inc.]
Given any two of these, the third is determined (e.g., z = mixture components. Another is that straight lines on one
1 − x − y). Therefore, full information about chromaticity such diagram translate into straight lines on any other re-
can be conveniently represented in a two-dimensional di- lated to it by a change of assumed primaries. The locations
agram, with y versus x having been chosen by the CIE for of the imaginary primaries X, Y , and Z are shown in Fig. 5,
this purpose. The resulting chromaticity diagram is shown where one sees that the triangle formed by them com-
in Fig. 4. If one wishes to specify the quantity of light as pletely encloses the domain of realizable colors. The lines
well, the Y tristimulus value can be given, allowing a color X–Y and X–Z of Fig. 5 form the coordinate axes of the CIE
to be fully specified as x, y, and Y , instead of X, Y , and Z. chromaticity diagram of Fig. 4. Conversely, the lines B–G
The manner in which the quantity of light Y is specified and B–R in Fig. 4 form the coordinate axes of the chro-
is determined by the normalization constant k. maticity diagram of Fig. 5. The uneven grid of nonoorthog-
Depending on the choice of primaries for determining onal lines in Fig. 4, forming various angles at their inter-
color-matching functions, many other chromaticity dia- sections, translates into the regular grid of evenly spaced,
grams are possible. For example, the set of color-matching orthogonal lines in Fig. 5. This illustrates that angles and
functions of Fig. 1 leads to the chromaticity diagram of areas have no instrinsic meaning in chromaticity diagrams.
Fig. 5. This so-called RGB system is seldom used. The CIE in 1964 adopted an alternative set of color-
◦
The affine geometry of chromaticity diagrams endows matching functions based on experiments with large (10 )
all of them with a number of useful properties. Most funda- fields. Their use is recommended for making predictions
◦
mental is that an additive mixture of any two lights will fall about color matches for fields subtending more than 4 at
along a straight line connecting the chromaticities of the the eye.
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294 Color Science
FIGURE 4 The XYZ chromaticity diagram showing the locations of the RGB primaries of Fig. 5 and the projection of
the rectilinear grid of that figure onto this one. [From LeGrand, Y. (1957). “Light, Colour, and Vision,” 2nd ed., Wiley
Interscience, New York.]
Table I lists values of the CIE color-matching func- very close to being one of the worst possible. This illu-
◦ ◦
tions for 2 and 10 fields at 10-nm wavelength values. minant consists mainly of the paired sodium lines that lie
◦ ◦
Tables for 1-nm wavelength values for 2 and 10 fields very close together (at 589.0 and 589.6 nm) in the “yel-
are available in Color Measurement, the second volume low” region of the spectrum; although some other spectral
in the series Optical Radiation Measurements, edited by lines are also represented, these are present at such low
F. Grum and C. J. Bartleson. relative radiances that low-pressure sodium lighting is for
practical purposes monochromatic.
For a surface that does not fluoresce, its spectral re-
III. COLOR RENDERING
flectance characteristics can modify the quantity and
geometry of incident monochromatic light, but not its
From an evolutionary viewpoint, it is not surprising that
wavelength. Viewed under separate monochromatic light
sunlight is an excellent source for color rendering. Its
sources of the same wavelength, any two surfaces with
strong, gap-free spectral irradiance distribution (Fig. 6) al-
arbitrarily chosen spectral distributions can be made to
lows the discrimination of a very large number of surface-
match, both physically and visually, by adjusting the rel-
color differences. Color appearance in sunlight provides
ative radiances of incident lights. Therefore, no chro-
the standard against which the adequacy of other sources
matic color differences can exist under monochromatic
for color rendering is often judged.
illumination.
The best sources for color rendering emit continuous
A. Best and Worst Artificial Sources
spectra throughout the visible region. Blackbody radia-
for Color Rendering
tion, which meets this criterion, is shown for three tem-
Of the light sources in common use today, low-pressure peratures in Fig. 7. These curves approximate those for
sodium is one of the poorest for color rendering, coming tungsten sources at these temperatures.
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Color Science 295
FIGURE 5 The RGB chromaticity diagram showing the locations of the XYZ primaries of Fig. 4. [From LeGrand, Y.
(1957). “Light, Colour, and Vision,” 2nd ed., Wiley Interscience, New York.]
B. Intermediate Quality C. Efficacy
of Fluorescent Lighting
The amount of visible light emitted by a source is mea-
Much of the radiant flux produced by incandescence sured in lumens, determined by integrating its radiant
emerges as infrared radiation at wavelengths longer than power output S(λ) with the spectral luminous efficiency
those visible; this is not true of fluorescent light, which is function V (λ). The latter, which is proportional to y¯ (λ),
more efficiently produced, accounting for its widespread peaks at ∼555 nm. Therefore, the theoretically most effi-
use. This light results from the electrical energizing of mer- cient light source would be monochromatic at this wave-
cury vapor, which emits ultraviolet radiation. Although it- length, with the associated inability to render chromatic
self invisible, this radiation elicits visible light by causing color differences. Efficacy does not include power lost
the fluorescence of phosphors suspended in a layer coating in the conversion from electrical input to radiant output,
the inside of a transparent tube. which may vary independently of the efficacy of the light
Fluorescent lamps emit energy at all visible wave- finally produced.
lengths, which is a good feature for color rendering, but
their spectra are punctuated by regions of much higher ra-
D. Correlated Color Temperature
diance whose spectral locations depend on the phosphors
chosen and the visible radiations of mercury vapor. Radi- A blackbody, or Planckian radiator, is a cavity within a
ant power distributions of six types of fluorescent lamps heated material from which heat cannot escape. No mat-
are shown in Fig. 8. ter what the material, the walls of the cavity exhibit a
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296 Color Science
TABLE I Spectral Tristimulus Values for Equal Spectral Power Source
a. CIE 1931 Standard Observer b. CIE 1964 Supplementary Observer
Wavelength Wavelength
(nanometer) x¯(λ) y¯ (λ) z¯(λ) (nanometer) x¯10(λ) y¯ 10(λ) z¯10(λ)
380 0.0014 0.0000 0.0065 380 0.0002 0.0000 0.0007
385 0.0022 0.0001 0.0105 385 0.0007 0.0001 0.0029
390 0.0042 0.0001 0.0201 390 0.0024 0.0003 0.0105
395 0.0076 0.0002 0.0362 395 0.0072 0.0008 0.0323
400 0.0143 0.0004 0.0679 400 0.0191 0.0020 0.0860
405 0.0232 0.0006 0.1102 405 0.0434 0.0045 0.1971
410 0.0435 0.0012 0.2074 410 0.0847 0.0088 0.3894
415 0.0776 0.0022 0.3713 415 0.1406 0.0145 0.6568
420 0.1344 0.0040 0.6456 420 0.2045 0.0214 0.9725
425 0.2148 0.0073 1.0391 425 0.2647 0.0295 1.2825
430 0.2839 0.0116 1.3856 430 0.3147 0.0387 1.5535
435 0.3285 0.0618 1.6230 435 0.3577 0.0496 1.7985
440 0.3483 0.0230 1.7471 440 0.3837 0.0621 1.9673
445 0.3481 0.0298 1.7826 445 0.3687 0.0747 2.0273
450 0.3362 0.0380 1.7721 450 0.3707 0.0895 1.9948
455 0.3187 0.0480 1.7441 455 0.3430 0.1063 1.9007
460 0.2908 0.0600 1.6692 460 0.3023 0.1282 1.7454
465 0.2511 0.0739 1.5281 465 0.2541 0.1528 1.5549
470 0.1954 0.0910 1.2876 470 0.1956 0.1852 1.3176
475 0.1421 0.1126 1.0419 475 0.1323 0.2199 1.0302
480 0.0956 0.1390 0.8130 480 0.0805 0.2536 0.7721
485 0.0580 0.1693 0.6162 485 0.0411 0.2977 0.5701
490 0.0320 0.2080 0.4652 490 0.0162 0.3391 0.4153
495 0.0147 0.2586 0.3533 495 0.0051 0.3954 0.3024
500 0.0049 0.3230 0.2720 500 0.0038 0.4608 0.2185
505 0.0024 0.4073 0.2123 505 0.0154 0.5314 0.1592
510 0.0093 0.5030 0.1582 510 0.0375 0.6067 0.1120
515 0.0291 0.6082 0.1117 515 0.0714 0.6857 0.0822
520 0.0633 0.7100 0.0782 520 0.1177 0.7618 0.0607
525 0.1096 0.7932 0.0573 525 0.1730 0.8233 0.0431
530 0.1655 0.8620 0.0422 530 0.2365 0.8752 0.0305
535 0.2257 0.9149 0.0298 535 0.3042 0.9238 0.0206
540 0.2904 0.9540 0.0203 540 0.3768 0.9620 0.0137
545 0.3597 0.9803 0.0134 545 0.4516 0.9822 0.0079
550 0.4334 0.9950 0.0087 550 0.5298 0.9918 0.0040
555 0.5121 1.0000 0.0057 555 0.6161 0.9991 0.0011
560 0.5945 0.9950 0.0039 560 0.7052 0.9973 0.0000
565 0.6784 0.9786 0.0027 565 0.7938 0.9824 0.0000
570 0.7621 0.9520 0.0021 570 0.8787 0.9556 0.0000
575 0.8425 0.9154 0.0018 575 0.9512 0.9152 0.0000
580 0.9163 0.8700 0.0017 580 1.0142 0.8689 0.0000
585 0.9786 0.8163 0.0014 585 1.0743 0.8526 0.0000
590 1.0263 0.7570 0.0011 590 1.1185 0.7774 0.0000
595 1.0567 0.6949 0.0010 595 1.1343 0.7204 0.0000
600 1.0622 0.6310 0.0008 600 1.1240 0.6583 0.0000
605 1.0456 0.5668 0.0006 605 1.0891 0.5939 0.0000
610 1.0026 0.5030 0.0003 610 1.0305 0.5280 0.0000
continues
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TABLE I (continued )
a. CIE 1931 Standard Observer b. CIE 1964 Supplementary Observer
Wavelength Wavelength
(nanometer) x¯(λ) y¯ (λ) z¯(λ) (nanometer) x¯10(λ) y¯ 10(λ) z¯10(λ)
615 0.9384 0.4412 0.0002 615 0.9507 0.4618 0.0000
620 0.8544 0.3810 0.0002 620 0.8563 0.3981 0.0000
625 0.7514 0.3210 0.0001 625 0.7549 0.3396 0.0000
630 0.6424 0.2650 0.0000 630 0.6475 0.2835 0.0000
635 0.5419 0.2170 0.0000 635 0.5351 0.2283 0.0000
640 0.4479 0.1750 0.0000 640 0.4316 0.1798 0.0000
645 0.3608 0.1382 0.0000 645 0.3437 0.1402 0.0000
650 0.2835 0.1070 0.0000 650 0.2683 0.1076 0.0000
655 0.2187 0.0816 0.0000 655 0.2043 0.0812 0.0000
660 0.1649 0.0610 0.0000 660 0.1526 0.0603 0.0000
665 0.1212 0.0446 0.0000 665 0.1122 0.0441 0.0000
670 0.0874 0.0320 0.0000 670 0.0813 0.0318 0.0000
675 0.0636 0.0232 0.0000 675 0.0579 0.0226 0.0000
680 0.0468 0.0170 0.0000 680 0.0409 0.0159 0.0000
685 0.0329 0.0119 0.0000 685 0.0286 0.0111 0.0000
690 0.0227 0.0082 0.0000 690 0.0199 0.0077 0.0000
695 0.0158 0.0057 0.0000 695 0.0318 0.0054 0.0000
700 0.0114 0.0041 0.0000 700 0.0096 0.0037 0.0000
705 0.0081 0.0029 0.0000 705 0.0066 0.0026 0.0000
710 0.0058 0.0021 0.0000 710 0.0046 0.0018 0.0000
715 0.0041 0.0015 0.0000 715 0.0031 0.0012 0.0000
720 0.0029 0.0010 0.0000 720 0.0022 0.0008 0.0000
725 0.0020 0.0007 0.0000 725 0.0015 0.0006 0.0000
730 0.0014 0.0005 0.0000 730 0.0010 0.0004 0.0000
735 0.0010 0.0004 0.0000 735 0.0007 0.0003 0.0000
740 0.0007 0.0002 0.0000 740 0.0005 0.0002 0.0000
745 0.0005 0.0002 0.0000 745 0.0004 0.0001 0.0000
750 0.0003 0.0001 0.0000 750 0.0003 0.0001 0.0000
755 0.0002 0.0001 0.0000 755 0.0001 0.0001 0.0000
760 0.0002 0.0001 0.0000 760 0.0001 0.0000 0.0000
765 0.0002 0.0001 0.0000 765 0.0001 0.0000 0.0000
770 0.0001 0.0000 0.0000 770 0.0001 0.0000 0.0000
775 0.0001 0.0000 0.0000 775 0.0000 0.0000 0.0000
780 0.0000 0.0000 0.0000 780 0.0000 0.0000 0.0000
Totals 21.3714 21.3711 21.3715 Totals 23.3294 23.3324 23.3343
characteristic spectral emission, which is a function of its perature, determined by calculating the chromaticity co-
temperature. The locus of the chromaticity coordinates ordinates of the source and then locating the point on the
corresponding to blackbody radiation, as a function of blackbody locus perceptually closest to these coordinates.
temperature, plots in the chromaticity diagram as a curved
line known as the Planckian locus (see Fig. 4). The spec-
E. Color-Rendering Index
tral distribution of light from sources with complex spectra
does not approximate that of a Planckian radiator. Never- The CIE has developed a system for attempting to specify
theless, it is convenient to have a single index by which the quality of color rendering supplied by any light source.
to characterize these other sources of artificial light. For The calculations are based on a set of reflecting sam-
this purpose the CIE has defined a correlated color tem- ples specified in terms of their reflectance functions. The
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The intermediate color-rendering properties of most flu-
orescent light sources are closer to the best than to the
worst. Mercury vapor and high-pressure sodium sources,
widely used for street lighting, have poor color-rendering
properties that fall between those of fluorescent and low-
pressure sodium illumination.
IV. GLOBAL SURFACE PROPERTIES
The term reflection characterizes any of a variety of phys-
ical processes by which less than 100% of the radiant
energy incident on a body at each wavelength is returned
without change of wavelength. Reflection is too compli-
cated for detailed specification at a molecular level for
most surfaces and wavelengths of light. For this reason and
because the molecular details are unimportant for many
practical purposes, methods have been devised for mea-
suring the spectral reflectance of a surface—the spectral
FIGURE 6 Spectral power distribution of typical daylight. [From
distribution of returned light relative to that which is in-
Billmeyer, F. W., Jr., and Saltzmann, M. (1981). “Principles of Color
Technology,” 2nd ed., Copyright ©1981 John Wiley & Sons, Inc. cident. Reflectance depends on the wavelength and angle
Reprinted by permission of John Wiley & Sons, Inc.] of incidence of the light, as well as the angle(s) at which
reflected light is measured.
calculations begin with the choice of a reference illumi-
A. Specular and Diffuse Reflectance
nant specified as a blackbody (or daylight) radiator having
a color temperature (or correlated color temperature) as A familiar example of specular reflectance is provided by
close as possible to the correlated color temperature of the a plane mirror, in which the angles of light incidence and
test illuminant; the choice of reference illuminant depends reflectance are equal. An ideal mirror reflects all incident
on the correlated color temperature of the test illuminant light nonselectively with wavelength. If free of dust and
(daylight is used as a reference above 5000 K). For each suitably framed, the surface of an even less than ideal real
of the samples, defined by their spectral reflectance func- mirror is not perceived at all; instead, the virtual image of
tions, the amount of color shift E introduced in going an object located physically in front of the mirror is seen
from reference to test illuminant is determined using the as if positioned behind.
CIELUV formula described in Section VIB. There are 14 Although specular reflectance seldom provides infor-
reference samples in all. A special color-rendering index mation about the color of a surface, there are exceptions.
Ri , peculiar to each sample, is calculated as 100–4.6 E. In particular, highly polished surfaces of metals such as
Most commonly a single-number index is calculated from gold, steel, silver, and copper reflect specularly. They also
the mean of a subset of eight special color-rendering in- reflect diffusely from within but do so selectively with
dices to provide a final value known as the general color- wavelength so that the specular reflection is seen to be
rendering index Ra. The factor 4.6 was chosen so that tinged with the color of the diffuse component. More of-
a standard warm white fluorescent lamp would have an ten, because highlights from most surfaces do not alter the
Ra of ∼50; tungsten-incadescent sources score very close spectral distribution of incident light, specular reflection
to 100. Table II gives Ra values for several commonly provides information about the color of the source of light
used artificial sources. Despite its official status, Ra is of rather than that of the surface.
limited value because of its many arbitrary features, espe- Diffuse reflectance, on the other hand, is typically selec-
cially its dependence on so limited a set of color samples. tive with wavelength, and for the normal observer under
It is most useful for distinguishing large differences in typical conditions of illumination it is the principal de-
color rendering, but not so useful for discriminating among terminant of the perceived color of a surface. A surface
sources of very high color-rendering properties. Individ- exhibiting perfectly diffuse reflectance returns all of the
ual values of Ri can be useful for determining the man- incident light with the distribution shown in Fig. 9, where
ner in which light sources differ in their color-rendering the luminance (intensity per unit area) of the reflected
properties. light decreases a cosine function of the angle of reflection
