This invention relates to a method and apparatus for reproducing the color of blended colorants on an electronic display.
The most accurate ways of computing color formulation are either very difficult to use, or computationally impractical. The most successful simple mathematical theory for predicting the color of mixtures is the Kubelka-Munk Model. For some applications, the model is overly simplistic. The Kubelka-Munk Model assumes light falls exactly perpendicular onto a perfectly flat media containing the colorants. The colorants must be perfectly mixed into the substrate media, and the resulting colored substrate must be isotropic. The index of refraction of the media and colorants is assumed to be the same as air, so internal and external specular reflection and refraction are ignored.
Assume these conditions are met, and the substrate is optically thick. In this case, Kubelka-Munk Theory predicts the following simple relationship: K/S=(1-R).sup.2 /2R. K and S are physical properties of the colored media. R is the measured color. The relationship expressed by the equation holds at each wavelength of light in the visible spectral band. R denotes the fraction of light reflected by the sample. K and S are light absorption and light scattering coefficients of the colorant mixture, respectively. It is more convenient to deal with K/S rather than R. This is because the physical properties of a mixture (K and S) are, to a good approximation, proportional to the physical properties of each colorant in the mixture, namely the corresponding coefficients K.sub.i and S.sub.i of colorant i. The proportionality constants are component concentrations C.sub.i. Therefore, for simple colorant formulation calculations, one assumes for N colorants that K=K.sub.1 C.sub.1 +K.sub.2 C.sub.2 +. . . K.sub.N C.sub.N and S=S.sub.1 C.sub.1 +S.sub.2 C.sub.2 +. . . S.sub.N C.sub.N. As before, these equations hold at each wavelength of light. By inverting the earlier formula (K/S=(1-R).sup.2 /2R) that connects K/S to R, and by using the above equations connecting K and S to K.sub.i and S.sub.i, a connection is obtained between colorant concentrations C.sub.i and measured color R. Values of absorption and scattering coefficients of colorants are typically extracted from least squares calculations involving sample color measurements.
For applications requiring a high degree of accuracy, this simple Kubelka-Munk Theory must be modified. Corrections for substrate surface reflection, internal refraction, and colorant interactions are necessary. Sometimes it is necessary to extend spectral measurements into the ultraviolet to deal with colorant fluorescence. The texture of some targets (e.g., textiles) have a gloss that cannot be easily subtracted by measurement or compensated for by mathematical modeling. This means computed values for K.sub.i and S.sub.i must be cautiously interpreted, and perhaps further modified, before subsequent colorant formulation predictions are accurate.
In computer aided design (CAD), visual feedback is desirable during color formulation. One way to do this is to simulate a product on an electronic display. Performing Kubelka-Munk calculations, with the corrections noted above, involves a great deal of computation. Spectral data at many wavelengths must be stored on computer. Color measurements are traditionally made with spectrophotometers. These devices are relatively expensive and require uncommon technical expertise to operate. The usual way of converting spectral data into color coordinates appropriate for electronic display involves complex nonlinear equations. Computer aided design is one example of an application where color precision requirements are less demanding than, say, textile dye formulation. The present invention solves these problems, in a manner not disclosed in the known prior art, for less demanding applications.