Optical logarithmic filtering using inherent film nonlinearity.

Linear optical spatial filtering cannot be effectively applied to multiplied and convolved signals. One approach is to first perform a logarithmic transformation to produce a signal in additive form suitable for linear filtering processes [A. V. Oppenheim et al., Proc. IEEE 56, 1264 (1968)]. It was first suggested that a halftone screen be used to perform such a transformation [H. Kato and J. W. Goodman, Appl. Opt. 14, 1813 (1975)]. However, the maximum spatial resolution of this halftone screen technique is limited by the resolution of the screen. In this paper, we shall propose a different technique using the inherent film nonlinearity for the logarithmic transformation. Such a technique would enable the transformation of signals of very high spatial resolution, limited only by the resolution limit of the photographic film. This technique is applied to the spatial filtering and detection of signals in multiplicative noise. Experimental comparisons between linear and logarithmic filtering are presented.