## Abstract

The information capacity of four Kodak films is computed. The results lie in the range from one to six million bits per square centimeter—the Panatomic-X film having the largest information capacity, and the Royal-X film the least. The basic formula for the information capacity of a photographic film involves the Wiener spectrum of the granularity and the sine-wave response; data adequate for the calculation of these functions were published in 1958. The results obtained hold only if messages recorded on the film are coded in an optimal way. No optimal methods of coding are known, but methods that are close to optimal have been developed. It is known that when optimal coding is employed, nearly every message looks just like a grainy film. After the problem is formulated in mathematical terms, the chief mathematical problem is that of selecting the optimum set of messages; this is done with the help of the calculus of variations.

A photographic film is a peak-limited recording channel: the density is limited in both directions. The theory of information capacity is not yet adequately developed for such channels; the calculation is actually based on the existing formulas for mean-square-limited channels; at the end of the calculation an *ad hoc* correction is made to take account of the peak limiting.

Photographic films are nonlinear in at least two different ways: the noise (granularity) depends on the signal, and the output (density) is a nonlinear function of the input (exposure). It is shown that the first nonlinearity may be unloaded on the second, so that only the input–output nonlinearity remains.

© 1961 Optical Society of America

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