Abstract

Given a signal s(t), which is the convolution of a known signal f(f) with an unknown signal g(f), there is often the need to extract g(f). It is easily shown that in the frequency domain the Fourier transform of g(f) may be obtained by dividing the cross-spectral density of s(t) and f(f) by the power spectral density of f(t). Results are presented of experiments designed to obtain both the cross-spectral density and power spectral density optically using acoustooptic systems and, using a liquid crystal light valve as a programmable mask in the Fourier plane, to achieve the deconvolution of the signals in real time. Using digitally generated input signals, the results are compared to theory. The degree of success is found to be limited by the spatial resolution and dynamic range of the light valve.

© 1988 Optical Society of America