In Chapter 8 we discussed acousto-optic power spectrum analyzers in which we use direct detection of the intensity of the light at the Fourier-transform plane. Detecting light intensities is sometimes restrictive because both the phase and the temporal frequency of the signal are lost. In this chapter we show how the range of signal processing operations can be expanded considerably by using heterodyne detection in which we add a reference wave, sometimes called the local oscillator, to the light distribution to be detected. The interference between the signal and reference waves produces an output signal that is linearly proportional to the input signal voltage so that magnitude, frequency, and phase information are preserved. More sophisticated signal-processing operations, based on heterodyne detection, are discussed in subsequent chapters.
Heterodyne detection is also used in holography, matched filtering, and synthetic aperture radar processing. In the first two instances the signals are functions of two or three spatial dimensions while, in the last instance, we perform heterodyne detection on the temporal radar returns, which are then recorded on film as a raster-scanned, two-dimensional spatial function. Leith and Upatnieks recognized that the angle between the interfering waves in the holographic process must be large enough to separate the desired terms from all others upon reconstruction. They applied the principles of communication ...