MATHEMATICAL MODEL FOR PHOTOGRAPHIC EXPOSURE AND ITS EXPERIMENTAL VERIFICATION

Based on parallelism of the reciprocity law failure curves at different wavelengths, lambda, and on the linear relationship between the slopes of intensity scale characteristic curves at different lambda and t values, a mathematical model of the photographic exposure problem is set up. This model is based on a generalized functional equation of the characteristic curve first derived by A. Van Kreveld and L. S. Ornstein. This equation contains four auxiliary subfunctions, which govern the reciprocity law failure and the changes in the shape of the characteristic curve with wavelength and exposure time. Specific forms are given to these subfunctions as used in the generalized equation of the characteristic curve. Experimental results ona specific emulsion are presented to illustrate how well the results on the real emulsion agree with the mathematical model.