In Chapters 3 and 4, we showed how coherently illuminated optical systems naturally display the Fourier transform of a signal and how to use this information in spectrum-analysis applications. Optical spectrum analyzers are divided into several major architectural classes based on the variable of integration for the Fourier-transform operation. One architecture, described as *space integrating*, performs a Fourier transform with respect to a space variable. This is the natural mode of operation because lenses collect or integrate light over a given area. The second architecture, described as *time integrating*, performs a Fourier transform with respect to a time variable. The integration is achieved by collecting light on a photodetector array for a given time period. In some cases the two types are combined to form *hybrid* architectures. Both one- and two-dimensional Fourier transforms exist for all types of architectures.

In this chapter we concentrate our attention on one-dimensional power spectrum analyzers of the space integrating type. These systems are often called *instantaneous power spectrum analyzers* because the Fourier transform is computed for the signal history resident in the cell at every instant in time. Because the calculations are completed as soon as light has propagated to the Fourier-transform plane, generally in a few nanoseconds, the computation is essentially instantaneous. A photodetector array in ...

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