NUMERICAL RESTORATION OF OPTICAL OBJECTS OBSURED BY DIFFRACTION AND NOISE
UTAH STATE UNIV LOGAN ELECTRO-DYNAMICS LAB
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The problem considered is the restoration of incoherent optical objects which have been diffracted by an optical system and corrupted by detector and additive background noise. The approach in solving the problem is basically numerical and considers operating directly on the image and point spread function rather than the Fourier transform of these quantities. Special emphasis is placed on studying the effects of noise and the use of a priori information in the restoration process. Several optimum estimates of the object intensity distribution are considered. Based substantially on statistics which have been verified in practice, the Bayes, maximum a posteriori, maximum likelihood and mean square error estimates of the object intensity distribution are obtained. These statistical estimates are compared mathematically and in many cases numerically to other non-statistical estimates formulated from control theory and dynamic programming. Extensive numerical results have been obtained for the restoration of various one-dimensional objects in the presence of noise. Two monochromatic point sources in the presence of noise are shown to be resolved when separated by 15 of the Rayleigh criterion distance. Numerical results are also shown for the mean square error as a function of a priori information, the measuring scheme chosen, and diffraction.