Abstract

Assume that an image acquired from a diffraction- limited system using partially coherent illumination is processed by a linear postdetection filter having a desired transfer function. The processing performed by an imaging system followed by a linear filter can be described by a bilinear transfer function. The problem is to design an equivalent system consisting of an apodized imaging system followed by a short-length finite impulse response (FIR) filter that has a bilinear transfer function that closely approximates the bilinear transfer function of the diffraction-limited imaging system followed by the ideal linear filter. The complexity of the postdetection filter is reduced since the FIR filter is presumably easier to implement than the ideal linear filter. Alternatively, a high-order FIR implementation of the ideal linear filter can be replaced by a lower-order implementation without loss of performance. Assuming that the coherence of the illumination is fixed, the problem reduces to finding the pupil screen of the imaging system and the weights of the FIR filter that result in the best approximation to the desired bilinear transfer function. The problem is solved using nonlinear parameter optimization techniques. The design of several equivalent systems is presented.

© 1987 Optical Society of America