ENTROPY AND INFORMATION IN THE DESIGN AND ANALYSIS OF IMAGING SYSTEMS.

The main thrust of this dissertation is the application of statistics and information theory to design, analysis and estimation pertaining to image-forming systems. This study explores the application of Shannon's information in pupil design, the characterization of noise, and study of its behavior in a specific electro-optical system, and estimation of the degraded spread function in atmospherical imagery using the maximum entropy method. Our study shows that a pupil designed to maximize Shannon's information throughput is an apodizer, resulting in resolution and contrast enhancement when compared to the diffraction-limited case. The Strehl ratio is about 0.55. Investigation of statistical and spectral properties as a function of gray level in an electro-optical tracking system indicates that the noise is "white," having a wide band and a close-to-Gaussian distribution. Estimating the spread function via maximum entropy technique has revealed some remarkable results. Using an edge as the object, simulation studies predict a superior estimate in the mean squared error sense to those of the least squares in the presence of three types of noise (signal-dependent Gaussian and Poisson, and signal-independent Gaussian noise). Information theory, linear systems theory, sampling theory and more particularly, statistics and the Fast Fourier Transform are used to derive our results