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704 COLOR SENSITOMETRY
Modified Conversion Equations
A second complication arises from the fact that the absorption of radiant energy in an actual film sample cannot be entirely accounted for by the absorption of the yellow, magenta and cyan dye images. Additional radiation losses occur in the film base and in non-image "stain" as well as by reflection. To a first approximation, errors from these losses can be corrected by the addition of small constant terms to the transformation equations, which then assume the form : Y = an DB + ai2 D0 + ai3 DR + au,
M = 021 DB + 022 DG + 023 DR + «24,
C = a3i DB + a32 D0 + a3s DR + a34.
The values of these constant terms can be determined by trial. Since the equivalent neutral densities of gray samples are equal to their luminous densities, gray samples offer an accurate means of trial. Their measured densities are compared with their computed equivalent neutral density values. The computation equations are then altered by addition of the constants required to minimize errors. This empirical method of determining the additive constants au, a24 and a34 also provides a first-order correction for the departures shown by actual materials from the theoretical relationships discussed under Density as a Function of Dye Concentration, above.
Further improvement in the calculation of analytical densities might be achieved by the use of nonlinear transformations, but the added computing burden would make it difficult for such a procedure to compete in utility with the direct measurement of analytical densi
Computing Devices
The large-scale use of computed analytical densities in color sensitometry is dependent on rapid and economical procedures for the solution of the linear transformation equations which have been discussed. Standard desk calculators with provision for accumulative multiplication are well suited to this task. Alternatively, it is possible to use electrical networks for the solution of these equations. In the latter type of instrument, the values of DR, Do and DB are put in as shaft rotations, and this operation could, in principle, be directly performed by the integral densitometer in cases where the integral densities themselves are of no interest. In situations where only few data are to be handled and the required precision is not high, nomographs may be used to advantage.