Abstract

A simple formula for computing fadings or other color differences from Munsell notations has been derived from one simple assumption. Experimental data for the relative visual magnitudes of the Munsell “value” and chroma steps have been incorporated into the formula. It has been tested with several sets of experimental data and found valid even for some large differences. A table of constants facilitates quick application. The formula has been applied to the computation of the color differences of a great many dyes changing in concentration only, for example, from 2 percent to 0.5 percent. This change is known in the textile industry as “on-tone” fading. The user of dyed fabrics dislikes changes of hue more than equally perceptible changes in saturation or lightness, so that acceptability and perceptibility are not identical; hence, the importance of on-tone fading. For the 2–0.5 percent case, hue change as a function of hue of the stronger dyeing gave a well-defined curve. Maximum hue changes occur at 2R and 8YR, with zero change between. The total change is lowest for yellows (explaining why dyers find it most difficult to judge their fastnesses) and highest in the blues. Other published formulas yield the reverse of this fact. The question whether fastness is in large part a matter of perceptibility of changes was examined. The graphs of perceptibility and of average light-fastness ratings, both as a function of hue, show little resemblance, indicating that the fastness ratings are not primarily due to mere concentration change.

© 1951 Optical Society of America

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References

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  1. I. H. Godlove, J. Opt. Soc. Am. 30, 658 (1940).
  2. I. H. Godlove, J. Opt. Soc. Am. 41, 396 (1951).
    [Crossref] [PubMed]
  3. A. C. Hardy, J. Opt. Soc. Am. 28, 360 (1938); J. L. Michaelson, ibid., 365.
    [Crossref]
  4. H. R. Davidson and L. W. Imm, J. Opt. Soc. Am. 39, 942 (1949).
    [Crossref]
  5. Newhall, Nickerson, and Judd, J. Opt. Soc. Am. 33, 385 (1943).
    [Crossref]
  6. I. A. Balinkin, Bull. Am. Ceram. Soc. 20, 392 (1941); Am. J. Psychol. 52, 428 (1939).
  7. Dorothy Nickerson, J. Opt. Soc. Am. 21, 650 (1931); J. Opt. Soc. Am. 25, 253 (1935); Textile Research 6, 505 (1936); Am. Dyestuff Rptr. 33, 252 (1944).
  8. B. R. Bellamy and S. M. Newhall, J. Opt. Soc. Am. 32, 465 (1942).
    [Crossref]
  9. D. Nickerson, see reference 7; also Am. Dyestuff Rptr. 39, 541 (August21, 1950).
  10. H. R. Davidson, J. Opt. Soc. Am. (to be published).
  11. D. Nickerson and K. F. Stultz, J. Opt. Soc. Am. 34, 550 (1944).
    [Crossref]
  12. I. H. Godlove, Am. Dyestuff Rptr. 40 (Sept.3, 1951).
  13. I. H. Godlove, Am. Dyestuff Rptr. (July9, 1951).
  14. White, Vickerstaff, and Waters, Proc. Phys. Soc. (London) 55, 1 (1943); E. Waters, J. Soc. Dyers Colourists 59, 261 (1943).
    [Crossref]

1951 (3)

I. H. Godlove, Am. Dyestuff Rptr. 40 (Sept.3, 1951).

I. H. Godlove, Am. Dyestuff Rptr. (July9, 1951).

I. H. Godlove, J. Opt. Soc. Am. 41, 396 (1951).
[Crossref] [PubMed]

1949 (1)

1944 (1)

1943 (2)

Newhall, Nickerson, and Judd, J. Opt. Soc. Am. 33, 385 (1943).
[Crossref]

White, Vickerstaff, and Waters, Proc. Phys. Soc. (London) 55, 1 (1943); E. Waters, J. Soc. Dyers Colourists 59, 261 (1943).
[Crossref]

1942 (1)

1941 (1)

I. A. Balinkin, Bull. Am. Ceram. Soc. 20, 392 (1941); Am. J. Psychol. 52, 428 (1939).

1940 (1)

I. H. Godlove, J. Opt. Soc. Am. 30, 658 (1940).

1938 (1)

1931 (1)

Dorothy Nickerson, J. Opt. Soc. Am. 21, 650 (1931); J. Opt. Soc. Am. 25, 253 (1935); Textile Research 6, 505 (1936); Am. Dyestuff Rptr. 33, 252 (1944).

Balinkin, I. A.

I. A. Balinkin, Bull. Am. Ceram. Soc. 20, 392 (1941); Am. J. Psychol. 52, 428 (1939).

Bellamy, B. R.

Davidson, H. R.

H. R. Davidson and L. W. Imm, J. Opt. Soc. Am. 39, 942 (1949).
[Crossref]

H. R. Davidson, J. Opt. Soc. Am. (to be published).

Godlove, I. H.

I. H. Godlove, Am. Dyestuff Rptr. 40 (Sept.3, 1951).

I. H. Godlove, Am. Dyestuff Rptr. (July9, 1951).

I. H. Godlove, J. Opt. Soc. Am. 41, 396 (1951).
[Crossref] [PubMed]

I. H. Godlove, J. Opt. Soc. Am. 30, 658 (1940).

Hardy, A. C.

Imm, L. W.

Judd,

Newhall,

Newhall, S. M.

Nickerson,

Nickerson, D.

D. Nickerson and K. F. Stultz, J. Opt. Soc. Am. 34, 550 (1944).
[Crossref]

D. Nickerson, see reference 7; also Am. Dyestuff Rptr. 39, 541 (August21, 1950).

Nickerson, Dorothy

Dorothy Nickerson, J. Opt. Soc. Am. 21, 650 (1931); J. Opt. Soc. Am. 25, 253 (1935); Textile Research 6, 505 (1936); Am. Dyestuff Rptr. 33, 252 (1944).

Stultz, K. F.

Vickerstaff,

White, Vickerstaff, and Waters, Proc. Phys. Soc. (London) 55, 1 (1943); E. Waters, J. Soc. Dyers Colourists 59, 261 (1943).
[Crossref]

Waters,

White, Vickerstaff, and Waters, Proc. Phys. Soc. (London) 55, 1 (1943); E. Waters, J. Soc. Dyers Colourists 59, 261 (1943).
[Crossref]

White,

White, Vickerstaff, and Waters, Proc. Phys. Soc. (London) 55, 1 (1943); E. Waters, J. Soc. Dyers Colourists 59, 261 (1943).
[Crossref]

Am. Dyestuff Rptr. (2)

I. H. Godlove, Am. Dyestuff Rptr. 40 (Sept.3, 1951).

I. H. Godlove, Am. Dyestuff Rptr. (July9, 1951).

Bull. Am. Ceram. Soc. (1)

I. A. Balinkin, Bull. Am. Ceram. Soc. 20, 392 (1941); Am. J. Psychol. 52, 428 (1939).

J. Opt. Soc. Am. (8)

Proc. Phys. Soc. (London) (1)

White, Vickerstaff, and Waters, Proc. Phys. Soc. (London) 55, 1 (1943); E. Waters, J. Soc. Dyers Colourists 59, 261 (1943).
[Crossref]

Other (2)

D. Nickerson, see reference 7; also Am. Dyestuff Rptr. 39, 541 (August21, 1950).

H. R. Davidson, J. Opt. Soc. Am. (to be published).

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Figures (7)

Fig. 1
Fig. 1

Hue change as a function of original hue of the 2 percent dyeing, when changing to 0.5 percent. Here the “perceptibility” is assumed proportional to chroma, with chroma 10 taken as standard chroma, so that weighting of Munsell hue change is by one-tenth the original chroma. The positive direction was taken as an increase in Munsell hue number (as red to yellow); a decrease was taken as negative. The Munsell hue is indicated by initials for the hue names, e.g., GY for green-yellow. The hue order is that traditional in the textile industry, the order of hues obtained from an absorption band moving from the ultraviolet across the visible spectrum. The chroma legend is given above. Note that many of the large deviations from the “best” curve are for low chromas.

Fig. 2
Fig. 2

Derivation of the new color-difference formula or index. The desired color-difference index I or fading is the difference between colors represented by points P1 and P2, whose chromas are C1 and C2, whose Munsell “values” are V1 and V2, and whose hue difference is Δα. For the derivation, see the text.

Fig. 3
Fig. 3

The total color change or “perceptibility” is a function of original hue of the 2 percent dyeing, when changing to 0.5 percent. Whether the dyeing is of single dyes on wool or cotton or of a mixture on wool is indicated in the legend above. The hue scale is as indicated under Fig. 1. The magnitudes of the perceptibility I4 are taken from column 11 of Table I.

Fig. 4
Fig. 4

Rejectability as a function of original hue of the 2 percent dyeing, when changing to 0.5 percent. The remarks on hue are the same as those of Figs. 1 and 3. Wool, cotton, or mixture dyeings are indicated as in Fig. 3. The “rejectability,” or negative aspect of “acceptability,” depends upon weighting by 5 the hue component of the total color change, and is taken from column 12 of Table I.

Fig. 5
Fig. 5

“Perceptibility” and rejectability of the 2 percent dyeing “on-tone” fadings, taken from Figs. 3 and 4 and repeated here. Note that the arbitrary weighting of hue by a factor of 5 has considerably altered the computed color-change or fading only in narrow hue ranges at the left of the diagram. See the text for comments on the hue ranges involved.

Fig. 6
Fig. 6

The Nickerson “Index of Fading” IN. Remarks on the hue scale and textile fiber dyed are as in previous figures. The data are for the “on-tone” fading from 2 to 0.5 percent concentration on the fiber. Note the relative constancy of the indices, taken from the last column of Table I. Note that the fading index for many yellows is equal to or greater than that for blues (PB), the reverse of the facts as seen by our observers.

Fig. 7
Fig. 7

Average light fastness ratings in 50 hue ranges as a function of hue for strong and for weak dyeings. Here cotton and wool are considered together. The points are plotted at the center of a 2-step (Munsell) hue range. The reliability of the data is taken as parallel to the number of cases averaged, these being indicated as follows: ■, 15–24 cases; ▲, 11–24 cases; ●, 6–10 cases; ○, 3–5 cases; △, 2–3 cases; and □ only one case. For comparison, in the upper row near the horizontal center, the maxima and minima and zero-axis crossing points of Fig. 1 are shown by +, −, and ×, respectively. Similar data from Fig. 3 are shown for “perceptibility” from Fig. 3 (lower row).

Tables (8)

Tables Icon

Table I * “On-tone fading” (concentration change only) 2 to 0.5 percent. In each pair, the upper figures refer to the 0.5 percent dyeing, the lower figures to the 2 percent dyeing or to the pair together. In column 1, C refers to cotton, W refers to wool, and M to a mixture.

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Table II Values of ϕ(H)=1−cos3.6°ΔH.

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Table III(a) Munsell “5/5” colors.

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Table III(b) Color-differences between Munsell “5/5” colors and neutral gray and between successive “5/5” colors.

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Table IV Davidson’s colors.

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Table V Balinkin’s tile colors.

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Table VI(a) Visual estimates determining magnitude of “n” in Eq. (13). Here the total perceptual difference, made up chiefly of chroma difference (columns “b” in Table VI(b), was taken as the unit color difference; then the relative magnitude of the other total difference, consisting largely of “value” difference (columns “a”), was estimated. Hue differences are small or nil.

Tables Icon

Table VI(b) Ratio of magnitudes of “value” step and chroma step calculations of total difference in each pair by formula (Eqs. (12) and (13)).

Equations (13)

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I 2 P 1 ¯ P 2 2 ¯ = d 2 + ( Δ V ) 2
I 2 = C 1 2 + C 2 2 - 2 C 1 C 2 cos ( Δ α ) + ( Δ V ) 2 .
I 2 = C 1 2 + C 2 2 - 2 C 1 C 2 + 2 C 1 C 2 - 2 C 1 C 2 cos ( Δ α ) + ( Δ V ) 2 ,
I 2 = ( Δ C ) 2 + 2 C 1 C 2 [ 1 - cos ( Δ α ) ] + ( Δ V ) 2 .
Δ α = 3.6 ° Δ H , whence
I 2 = ( Δ C ) 2 + 2 C 1 C 2 [ 1 - cos 3.6 ° Δ H ] + ( Δ V ) 2 .
1 step of V = 2 steps of C = 3 steps of H ( at C = 5 ) ,
1 step of V = 8 steps of C = 22 steps of H ( at C = 6 ) .
1 step of V = 4.3 steps of C 4 steps of C .
I 4 2 = 2 C 1 C 2 ϕ ( H ) + ( Δ C ) 2 + ( 4 Δ V ) 2 ,
I 4 = [ 2 C 1 C 2 ϕ H + ( Δ C ) 2 + ( 4 Δ V ) 2 ] 1 2 ,
ϕ ( H ) = 1 - cos 3.6 ° Δ H .
I = { ( Δ C ) 2 + 2 C 1 C 2 ϕ ( H ) + ( n Δ V ) 2 } 1 2 ,