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In this chapter, we discuss some further methods that are useful in the analysis of linear optical systems. We will assume that the optical system is a stationary linear black box whose input/ˆ•output relationship is described by the convolution process in the space domain. The stationary linear optical system has the property that it is completely characterized by either its point spread function in the space domain or by the Fourier transform of its point spread function—the optical transfer function—in the frequency domain. We first discuss the sampling process whereby a given band-limited function is represented in terms of its values at a series of discrete sample points. The technique is described in both the space and spatial frequency domains. A space-bandwidth product is also discussed in terms of the sampled function, and a number of examples are given. Methods for describing statistical processes are introduced. These include ensemble and spatial averages, correlation functions, and the concept of spectral density. The use of these methods in linear system analysis is demonstrated by examples.
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