Abstract

There is described in the present paper a method, discovered empirically, for computing the approximate number of “least perceptible differences” between any two colors of the same brightness whose specifications are available. This method has been stated in simple form as an empirical relation; it is shown to be in substantial agreement with extant sensibility data of the following types: (1) the least wave-length difference perceptible in the pure spectrum as a function of wave length (Steindler, Jones); (2) the least dominant-wave-length difference perceptible at constant purity as a function of purity (Watson, Tyndall); (3) the least purity difference perceptible at constant dominant wave length as a function of purity (Donath); (4) the least purity difference perceptible near zero purity as a function of dominant wave length (Priest, Brickwedde), and (5) the least color-temperature difference perceptible as a function of color temperature (Priest). A mixture diagram is included showing colors specified by their trilinear coordinates and by the dominant wave length and purity of their stimuli. From this diagram the number of “least perceptible differences” separating any two colors of the same brightness may be read with a degree of certainty indicated by the comparisons here presented.

The empirical relation was originally expressed in terms of distribution (“sensation,” “excitation”) curves which suggest a three-components theory of vision (Young-Helmholtz); but it has been re-expressed in terms of curves which suggest an opponent-colors theory (Hering). Since this re-expression is nearly as convenient as the original expression, it is concluded that such success as has been demonstrated for the empirical relation can not be used as an argument for either form of theory; rather is a theory suggested which is more complex than either, such as that of G. E. Müller.

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Figures (11)

Fig. 1
Fig. 1

The (r, g)-diagram whose use is suggested by the empirical relation (1a). The point representing the chromaticity of any color specified by the dominant wave length and colorimetric purity of its stimulus may be easily found from this diagram because of the loci of constant dominant wave length and constant purity which appear on it. If the empirical relation (1a) were an exact expression of the facts, the chromaticity difference between any two colors represented by points on this diagram, (r1, g1), (r2, g2), would be accurately proportional to the absolute value of (r1r2), or to the absolute value of (g1g2), whichever absolute value is the greater.

Fig. 2
Fig. 2

A replot of the mixture diagram of Fig. 1 with a change of origin and scale and a rotation of the axes through an angle of 45°. This diagram may be made to serve all the purposes of the (r, g)-diagram of Fig. 1 with but little change in convenience. Since this diagram refers to distribution curves which suggest an opponent-colors hypothesis (Hering) rather than the three-components hypothesis (Young-Helmholtz) suggested by the mixture diagram of Fig. 1, it is concluded that the limited justification of the empirical relation (1a) demonstrated in the present paper can not be used as an argument in favor of either of these hypotheses as opposed to the other.

Fig. 3
Fig. 3

Least wave-length difference perceptible in the spectrum. Experimental results from various observers are compared with results computed from the O. S. A. “excitation” curves (Table 1) by means of the empirical relation (1a). The ordinates are (0.0074/K)(dλ/dE); see p. 88.

Fig. 4
Fig. 4

Sensibility to wave-length change as affected by the addition of white light. Certain of Watson’s experimental results are compared with results computed from the O. S. A. “excitation” curves (Table 1) according to the empirical relation (1a).

Fig. 5
Fig. 5

Sensibility to wave-length change as affected by the addition of white light. Some of the experimental results by Tyndall and Watson are compared with results computed from the O. S. A. “excitation” curves (Table 1) by means of the empirical relation (1a).

Fig. 6
Fig. 6

Sensibility to purity-change at constant dominant wave length as a function of purity. The experimental results by Donath from rotating disks have been expressed in terms of colorimetric purity by means of relation (11a). With these are compared results computed from the O. S. A. “excitation” curves (Table 1) by means of the empirical relation (1a).

Fig. 7
Fig. 7

Sensibility to purity-change at constant dominant wave length as a function of purity. Additional experimental results by Donath are compared with results computed from the O. S. A. “excitation” curves (Table 1) by means of the empirical relation (1a).

Fig. 8
Fig. 8

Sensibility to purity-change at constant dominant wave length as a function of purity. The remainder of Donath’s experimental results are compared with results computed by means of the empirical relation (1a). Note that the purities in this case are less than zero; that is, the colors dealt with are non-spectral or purple colors.

Fig. 9
Fig. 9

Least purity-difference perceptible near zero purity as a function of dominant wave length. Experimental results by Priest and Brickwedde are compared to results computed from the O. S. A. “excitation” curves (Table 1) by means of the empirical relation (1a).

Fig. 10
Fig. 10

Least color-temperature difference perceptible as a function of color temperature. Results according to Priest’s empirical, spectral-centroid relation are compared with results computed from the O. S. A. “excitation” curves (Table 1) by means of the empirical relation (1a). A simple function (θ2) discovered by Davis to be a close representation of Priest’s empirical spectral-centroid relation is also shown.

Fig. 11
Fig. 11

Sensibility to change in Lovibond red on the 35Y+NR locus. Experimental results by three observers (Walker, Brown, Judd) are compared with results computed from the O. S. A. “excitation” curves (Table 1) by means of the empirical relation (1a).

Tables (5)

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Table 1 Trilinear coordinates (r, g, b) corresponding to various values of dominant wave length and purity; O.S.A. “excitations” extrapolated, Abbot-Priest sun as basic stimulus.

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Table 2 Value of K for monocular observation of a small field.

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Table 3 Value of K for binocular observation of a large field.

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Table 4 Saturation sensibility at three colors: Saturated violet-blue, saturated orange-red, and pale violet. Illumination: Abbot-Priest sunlight. Observer: DBJ.

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Table 5 Comparison of the subjective mean determined by Jacobsohn’s experimental method with the saturation mean from relation (1a).

Equations (21)

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K Δ E = | c 1 - c 2 | .
K d E = d c .
K d E d q = d c d q , or d q d E = K ( d c / d q )
c = S ( 1 - p ) / p + C 3 S ( 1 - p ) / p + 1
p = S ( d R / d λ - d G / d λ ) - ( R - G ) ( d S / d λ ) ( S - 1 3 ) ( d R / d λ - d G / d λ ) - ( R - G ) ( d S / d λ ) .
c = s c ( 1 - P ) / P + c c 3 s c ( 1 - P ) / P + 1
p = p c P .
( d Λ / d E ) p = K / ( d c / d Λ ) p
d λ / d E = K / ( d C / d λ ) p = 1
( d Λ / d E ) p ( d Λ / d E ) p = 1 = ( d C / d λ ) p = 1 ( d c / d Λ ) p
( d Λ / d E ) p ( d Λ / d E ) p = 1 = [ 3 S ( 1 - p ) + p ] 2 ( d C / d λ ) p { [ 3 S ( 1 - p ) + p ] ( d C / d λ ) + ( 1 - p ) ( 1 - 3 C ) ( d S / d λ ) }
( d p / d E ) Λ = K [ 3 S ( 1 - p ) + p ] 2 S ( 3 C - 1 ) .
( d p / d E ) Λ = p c ( d P / d E ) .
( d p / d E ) Λ , p 1 = K / S ( 3 C - 1 ) .
( d p / d E ) Λ , p 0 = 9 K S / ( 3 C - 1 ) .
d θ / d E = K ( d θ / d c ) = K ( d θ / d r )
d N / d E = K ( d N / d c ) = K ( d N / d r ) .
χ 1.00 ρ + 1.00 γ - 2.00 β ψ 3.00 ρ - 3.00 γ ζ - 3.94 ρ + 2.06 γ + 2.06 β }
x = 50 ( r + g - 2 3 ) y = 50 ( r - g ) } .
| r 1 - r 2 | = | x 1 - x 2 + y 1 - y 2 | / 100 | g 1 - g 2 | = | x 1 - x 2 + y 2 - y 1 | / 100.
K Δ E = ( | x 1 - x 2 | + | y 1 - y 2 | ) / 100.