Abstract

An object, illuminated by partially coherent light, is composed of a signal plus a noise transmittance. The problem is to design the pupil screen of the imaging system so that the detected image of the object is the minimum mean-square error estimate of the image of the signal transmittance. This problem is not linear but is bilinear, because of the input-output relationship between input transmittance and output intensity. This problem is solved using a nonlinear parameter optimization approach where the parameters to optimize are discrete samples of the magnitude and phase of the pupil. The improvement factor, which compares system performance relative to the performance of a diffraction-limited imaging system, is defined. The design of several optimal pupil screens is presented. These designs verify the validity of our design technique and demonstrate that both the optimal pupil screen and the improvement factor are a function of the statistics of the signal and noise and a function of the coherence of the object illumination. Our results also show that preprocessing is more effective for coherent systems than for incoherent systems.

© 1986 Optical Society of America