FITTING THE PHOTOGRAPHIC CHARACTERISTIC CURVE - A FUNCTIONAL-EQUATIONAPPROACH

An outline is given of the mechanisms underlying the basic photographi c characteristic curve, that is the plot of density vs the logarithm o f exposure, an introduction to the idea of symmetry as it relates to s uch curves, and a discussion of the reasons for the departure from str ict symmetry exhibited by practical photographic systems. An account i s also given of the mathematical expression of these considerations, i nitially for the case of symmetrical curves in terms of so-called func tional equations and then more generally for asymmetrical cases, inclu ding the derivation of the appropriate parameters for process control purposes. As an aid to actual curve fitting, some of the properties of the asymmetrical curve are also derived. Finally, an account is given of some further generalizations to the basic photographic functional equation which allows some consideration of multilayer modelling.