The Fourier transform is key to using the full processing power of optical systems. Although the Fourier-transform relationship was discovered in the early 1800’s, strong connections between it and signal processing were not made until the early 1950’s. The application of these concepts in optical systems is often direct and elegant because a coherently illuminated optical system produces the Fourier transform of a signal as a physical light distribution, as we showed in Chapter 3. Spectrum analysis is thereby easily achieved by measuring the light intensity as a function of spatial frequency, as discussed in Chapter 4.

In this chapter, we consider signal-processing systems in which a spatial filter directly modifies the Fourier transform of a signal to produce a desired operation, such as pattern recognition. We begin by reviewing some fundamental results from signal processing and communication theory which we use extensively throughout the remainder of this book. Special attention is given to matched filtering as an important tool in pattern-recognition and signal-detection applications. We discuss methods for constructing various types of spatial filters and their applications. The spatial carrier method for constructing filters whose magnitude and phase response are arbitrary is the central theme of the chapter. We often draw analogies between techniques used in optical signal processing and equivalent methods used in communication systems ...

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