Abstract
As with the colors of light, the colors of objects are relative, not absolute. Objects perceived to be as different as yellow and blue can have exactly the same chromaticities, when one is illuminated with a phase of daylight that has a higher correlated color temperature than the light that illuminates the other. The perceptions do not correspond in any absolute way to the chromaticities. The perceptions correspond, rather, to the locations of the chromaticities relative to the chromaticities of the illuminating lights. This is the basis of the practice in colorimetry of determining dominant wavelength by extending the straight line drawn from the illuminant point through the chromaticity (x, y) point of the sample when the latter is computed by use of the spectral distribution of the illuminant.
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References
Use of the 1976 CIE Luv formula, rather than the color-difference formula recommended by the CIE in 1964, would give substantially the same color-rendering indices. The 1976 CIE Luv formula will be given and discussed in Sect. 8.1.
Further information on the Kubelka and Munk theory and applications is in D. B. Judd, G. Wyszecki: Color in Business, Science, and Industry, 3rd ed. (Wiley, New York 1975) pp. 420–460. For applications, see Rolf G. Kuehni: Computer Colorant Formulation (D. C. Heath, Lexington, MA 1975).
To avoid confusion with the other curves in Figs. 7.14, 15, trace the curve of interest on a piece of translucent paper. Include the left and right boundary lines for 400 and 700 nm. Mark on the 400 nm line the location of the horizontal stroke labeled with the number of the curve traced. Place the tracing over the curve for the Monastral Blue with the 400 and 700 nm lines coincident, and slide the tracing up or down until the right-hand portion of the traced curve is as nearly as possible coincident with the curve for the pigment. If the traced curve does not nearly fit the right-hand end of the pigment curve, try fitting it to the curve for Monastral Green or Carbon Black. When the right-hand end of the traced curve nearly fits one of the pigment curves, make a note of the name of that pigment and record the location of the horizontal stroke (on the 400 nm boundary) on the concentration scale on the pigment-curve chart. That is the ratio of the concentration of the pigment in the mixture represented by the curve for the pigment alone. For example, if the stroke on the tracing is at 0.4 on the scale of the curve for 2% Monastral Blue, then the amount of Monastral Blue in the mixture is 0.4 × 2% = 0.8%. To subtract the contributions of that pigment from the values of K/S for the mixture, tape the tracing to the pigment curve with the right-hand ends of the curves coincident and also the 400 and 700 nm lines. At every 20 nm (or 10 nm where changes are rapid), measure the separations between the traced curve and the pigment curve. At each of those wavelengths, find the value of the scale that is at that distance below 1. Subtract that value from 1. Find the distance from 1 on the concentration scale to the result of that subtraction. Mark a point at that distance above the traced curve at the corresponding wavelength. Draw a curve through the points thus determined. Try to fit the pigment curves for Monastral Scarlet, Monastral Red, Bon Red and Molybdate Orange to the resulting curve. Using the pigment curve that fits best, determinejts concentration in the mixture in the manner explained previously. Subtract its contributions to K/S in the way explained above. The curve obtained represents K/S for the yellow constituent of the mixture. Find which of Medium Chrome Yellow or Dalmar Yellow best fits that curve. Determine its concentration in the mixture by the method described previously.
An apparent exception, to the effect that the chromaticity of the net change need not be coincident with O if the change of mass is zero, is fallacious because the change of mass is the denominator of the expression for each of its chromaticity coordinates. If the net change of Y is other than zero when the net change of m is zero, the chromaticity coordinate y of the change is infinite. The moment of the change, which then seems indeterminate, is merely the net change of Y. If that is other than zero, the y coordinate of the modified color is different than that of the original color, because the numerator of that fraction is changed, whereas its denominator is not changed.
Tables of data from which Figs. 7.23–25 were prepared are in D. L. MacAdam: Maximum visual efficiencies of colored materials. J. Opt. Soc. Am. 25, 361–367(1935).
To determine the transition wavelengths for a desired dominant wavelength and maximum reflectance (or transmittance) R, draw a horizontal line in Fig. 7.27 through the dominant wavelength indicated on the left-hand margin. Through the points where that line intersects the two curves for R, draw vertical lines. They indicate the transition wavelengths on the horizontal axis. If a purple is desired, substitute the complementary wavelength in place of the dominant wavelength in the foregoing instructions. Short-end optimal colors have the dominant wavelengths indicated by the intersections of the R curves with the left-hand margin. The single transition wavelength for each is indicated by the intersection of the corresponding horizontal line with the other curve labelled with that same value of R. Long-end optimal colors have the dominant wavelengths indicated by the intersections of the R curves with the right-hand axis. The transitional wavelength for each is indicated by the intersection of the corresponding horizontal line with the other curve labelled with the same value of R.
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© 1981 Springer-Verlag Berlin Heidelberg
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MacAdam, D.L. (1981). Colors of Objects. In: Color Measurement. Springer Series in Optical Sciences, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13508-2_7
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DOI: https://doi.org/10.1007/978-3-662-13508-2_7
Publisher Name: Springer, Berlin, Heidelberg
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