The scattering of light within paper can affect the color of a halftone image. Because of scattering, a photon may enter and emerge from the paper in different regions of the halftone microstructure. The microstructure of a halftone print consists of a number of dots of ink of varying color and size. The color of the halftone image is the partitive mixture of the colors of the microstructure—the colors of the dots, the colors of the dot overlaps, and the color of the bare paper. In the present study the tristimulus values of the color of a halftone print are calculated in terms of the halftone microstructure. The analysis includes the effects of the scattering of light within the paper, an effect known as optical dot gain or the Yule–Nielsen effect. The tristimulus values are expressed as the trace of the product of two matrices—one a matrix that expresses the different colors of the microstructure that contribute to the partitive mixture and is a function of the ink transmittances and the paper reflectance and the other a matrix that expresses the amount of each color that contributes. The relative amount of each color is equal to the probability of the scattering process that gives rise to that color. These probabilities are calculated in terms of the dot shapes and sizes and in terms of the photon migration in the paper. As a result of the scattering, several “new” colors contribute to the partitive mixture.
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