Fourier analysis is a ubiquitous tool that has found application to diverse areas of physics and engineering. This book deals with its applications in optics, and in particular with its applications to diffraction, imaging, optical data processing, holography and optical communications.

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In high precision holographic imagery of weak objects of small angular subtense, electronic detection and digital image formation have distinct advantages. Experiments with a vidicon detector and a PDP-6 computer have yielded reconstructed images of good quality with computation times of five minutes.

Over the past two decades, there have been various studies on the distributions of the DCT coefficients for images. However, they have concentrated only on fitting the empirical data from some standard pictures with a variety of well-known statistical distributions, and then comparing their goodness of fit. The Laplacian distribution is the dominant choice balancing simplicity of the model and fidelity to the empirical data. Yet, to the best of our knowledge, there has been no mathematical justification as to what gives rise to this distribution. We offer a rigorous mathematical analysis using a doubly stochastic model of the images, which not only provides the theoretical explanations necessary, but also leads to insights about various other observations from the literature. This model also allows us to investigate how certain changes in the image statistics could affect the DCT coefficient distributions.

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