NATIONAL BUREAU OF STANDARDS REPORT

3773

DETERMINATION OF COLOR OF MAXIMUM CONTRAST

By

Deane B. Judd

To

Aerial Reconnaissance Laboratory

Wright Air Development Center

Wright-Patterson Air Force Base

Department of the Air Force

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
U. S. DEPARTMENT OF COMMERCE

Sinclair V* ceks. Secretary NATIONAL B1 REAP OF STANDARDS

A. \ . Aslin, Director

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NATIONAL BUREAU OF STANDARDS REPORT

H&3 PROJECT NIBS REPORT

0201-20-2325 November 12, 1954 3773

DETERMINATION OF COLOR OF MAXIMUM CONTRAST

By

Deane B. Judd

Photometry and Colorimetry Section

Optics and Metrology Division

To

Aerial Reconnaissance Laboratory

Wright Air Development Center

Wright-Patterson Air Force Base

Department of the Air Force

Contract No. AF 33

6 16 ) 52-21

E. 0. No. R677-34(H) SA-10

<NBS>

U. S. DEPARTMENT OF COMMERCE

NATIONAL OUREAU OF STANDARDS

The publication, rep

unless permission Is 25,D,C. Such pern

cal ly prepared If th

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST) on October 9, 2015

n part, is prohibited

indards, Washington

lort has been speclfiport for Its own use,

PREFACE

This is one of a series of reports prepared under

National Bureau of Standards Project No. 0201-20-2325,

“Color Reconnaissance Studies 11

. This project is financed

by the Aerial Reconnaissance Laboratory. Wright Air Development Center, Wright-Patterson Air Force Base, Ohio (Air

Force Contract No. AF 33 ( 616 ) 52-21) ; and it is coordinated

with Air Force Contract No. AF 33(6lb)-2o2 (Suppl. Agreement S3 ( 54-583 ) ) under Dr. Hugh T. O'Neill, O'Neill

Associates, Annapolis, Maryland, who supplies all requests

for studies, and all specimens and materials for spectrophotometric and colorimetric analyses, except those directly

requested or supplied by the Optics Division and others at

the Wright Air Development Center.

The present report resulted from one of Dr. O'Neill's

work requests, which was assigned an Oral Work Request

Serial Number; WADC-24/53

H. J. Keegan, Project Leader

DETERMINATION OF COLOR

OF MAXIMUM CONTRAST

By

De ane B „ J udd

1. A formula for calculating for any given color

whose chromaticity coordinates are known, the chromaticity coordinates of that color (producible from photographic film such as Kodachrome of Ansco color) which

will give the greatest contrast to the eye (including

nonspectral colors )„

2 0 Are two such colors calculated according to

this formula properly or conventionally called "Complementary colors®9 .,?

3o A formula for calculating how much greater is

the contrast between the darker complementary color and

black than with its lighter complementary color. Also

the name for the darker complementary color and white.

II. INTRODUCTION

The basic information required for problems 1 and

3 is a method of predicting reliably from the fundamental

specifications of the two colors what the magnitude of the

color contrast or difference, visually appraised, will be.

There have been a number of such formulas derived and

verified within about a factor of 2 for various specific

observing conditions; see formulas 28, 29, 30, 31? 32,

33, 3^, and 35 given by Judd (1952) 1 *

* Figures in brackets indicate the index reference at the

end of this report.

Formulas 28 and 29 apply only to color differences

involving a change of Munsell hue by 10 steps or less.

For problem 1, involving the largest possible color difference between some one color and some member of a
.

.

.

.

.
specified color gamut, these formulas are not applicable,

but may be replaced for specimens of large angular subtense by the Godlove (1951) formula:

A E = ^2C 1C 2 (1 - cos 3 o6° AH) + (AC ) 2 + (>AV) 2]

1/2

(1)

where AE is the predicted magnitude of the color difference,

visually appraised between two colors specified by Munsell

renotations, Ej V^/C^ and H2 V2/C 2 , aH = Ii]_ - H2 , AV = - V2 5 AC = Cf - Co. The unit for AE predicted

in this way has the size of one Munsell chroma step or

one fourth of a value step, To obtain the prediction in NBS

units multiply by 5 ° 0 , The other formulas cited (30 to 35) are applicable

to all color differences of whatever size between samples

of large angular extent* If the two colors are specified

by tristimulus values, X, Y, Z, in the 1931 CIE system,

formula 34 is recommended (Adams, 1942 PTl ; Nickerson and

stuitz, 1944 Kl).

’

AE = 50 ^

( 0.23 AVy ) 2

+ [A(Vx

.V

y

)]

2

+ [0.4 A(V2-V

y )3 2

1

1 /2

( 2 ) where Vx , V , Vz are functions, respectively, of X, Y, Z

given by Nickerson (1950) and Judd (1952) L5j , The predictions are given in NBS units (Judd, 1939) L6J

If one of the two colors whose contrast must be evaluated subtends an angle of the order of 0 , 1°, blue-yellow

differences evaluated by 0„4 a (Vz-V ) are found to be of

negligible importance. This phenomenon is .known as smallfield tritanopia (Judd, 1949 L7D ; Wright, 19}+9 [8] j Middleton, 1949 LSQ)* For this angular condition, the constant, 0,4, should be changed to zero. If, furthermore, the

angular extent of one of the colors is of the order of 0 , 01 °,

all chromatic differences come to be of negligible importance,

and the formula reduces simply to a factor multiplied by

AV r

c All of these phenomena can be represented by a generalized formula:

A E = 50^(1^ aVy ) 2 + [kr

A (Vx

-V

y ) j

2 + [kb A(Vz -V

y )3

2

f- 1/z

(3)

where k-,

, k

r and k^ are functions of the angular size of the

smallerof the two colors. These functions are not precisely

known but have values approximating those given in Table 1.

- 3

-

Table 1, Approximate values of the lightness constant,

k.,, the red-green constant, k , and the blueyellow constant, kg, in the generalized Adams

chromatic-value formula for size of color difference, visually appreciated.

Size of

field,

degrees

Lightness

constant

k

l

Red-green

constant

k

r

Blue -yellow

constant

kb

10 0.23 1.0 0.4

1 .20 .9 .3

0.1 IV) • 5 .0

0.01 .02 .0 .0

f.w. Problem 1

To solve the problem requires a method of trial and

error by means of the applicable formula (1, 2, or 3).

One method would involve computation of the color

difference between the given color and a succession of colors chosen from the extremes of the color gamut defined by

the three primary dyes of the system being studied (JSodachrome, Ansco color, or whatever special system may be devised). By making perhaps 10 such calculations a color

from the ganut not contrasting from the given color by

significantly less than the maximum might be found. Similarly, by a succession of applications' of this method, the

special system yielding a maximum out of a group of special

systenE might be found.

Another method depends on the property, held by

formulas 1, 2, and 3 in common, that a space array of colors is possible such that the distance between the locations

of any two colors is proportional to the color difference,

S, between them computed by formula. By this method a space diagram of the limiting colors of the gamut being

studied would be made, that is, the shell enclosing the

colors in this space would be defined by a sufficient number of points. Then, the point within the shell corresponding to the given color would be located in this

space diagram, and trial radii extending from this point

until they cut the shell would be drawn. The longest such

radius would identify the desired color of maximum contrast.

IV o Problem 2

It may now be noted that if the shell had a perfectly spherical shape with the black-white axis passing

through the center, the color contrasting maximally from

a given non-neutral color would necessarily be an exact

complementary; that is, would give by additive mixture in

suitable proportions the chromatic ity of the source . If,

indeed, the shape of the shell is any figure of revolution

about the black-white axis of the color solid generated by

the applicable formula, this same conclusion would hold,

except that more than one complementary color might be

found to have maximal contrast. However, there is no

three-dye color gamut having such a shell, and it seems,

in fact, impossible to imagine how to devise a three -dspc

system whose gamut would have a shell of such shape. The

answer to problem 2 is, therefore, that the color found to

be maximally in contrast with any given color will only by

chance be an exact complementary of that color. Many such

pairs will be found approximately complementary, and some

may be found that differ from the complementary by as much

as one -half of the hue circuit; that is, are of the same

rather than opposite hues. An example of this extreme deviation from complementarism is a reddish gray. The primary

red of the three-dye system will usually contrast more

strongly with the reddish gray than any other member of

the color gamut, and therefore by more than any complementary of the reddish gray.

V. Proble m 3

This problem is the easiest of the three. It may be

solved by direct use of the applicable formula (1, 2, or 3 )

VI. reference.

[l] D. Bo Judd, Color in Business, Science, and

Industry, pp. 256 - 265, New York, John Wiley &

Sons, 1952

Science, and

I. H. Godlove, Improved color-difference formula

with application to the perceptibility of fadings, J. Optical Soc. Am. ^1, 760; 195-f

E. Q. Adams, X-Z planes in the 1931 Id system

of colorimetry, J. Optical Soc. Am. 32 , 168;

19^2

- 5

-

D. Nickerson and K. F. Stultz, Color Tolerance

Specification, J. Optical Soc. Am. it, 550; 19^4.

D. Nickerson, Tables for use in computing small

color differences, Am. Dyestuff Reptr., ^9, 541

(Aug. 21, 1950). See also, D. B. Judd, Reference 1 (above), p. 268, and Appendix Tables A,

B, and C.

D. B. Judd, Specification of uniform color tolerances for textiles, Textile Research, 9 253, 2925

1939. See also, D, B. Judd, Specification of color

tolerances at the National Bureau of Standards,

Am. J. Psychol., t[2, 4l3 ; 1939.

D. B. Judd, Response functions for types of vision

according to the Mttller theory, J. Research NBS,

42, 1; 1949, RP1946.

W. D. Wright, Les courbes de melange des couleurs

enregistrees sur la fov6a sous de tres petits

champs visuels, Rev. optique, 28. 174; 1949.

W. S. K. Middleton and M. C. Holmes, The apparent

colors of surfaces of small subtense - A preliminary report, J. Optical Soc. Am., 3^, 582;

1949.

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