TABLE OF CONTENTS In this chapter we will consider a representative set of applications of optical signal processing to radar. Among these radar signal processing applications we will discuss the use of optics in determining the ambiguity function, which is a mathematical transformation that expresses the tradeoff between time and frequency resolution in the measurement of objects using modulated waveforms. A particular class of waveforms of interest in high-range-resolution radar and synthetic aperture radar SAR) are frequency-coded waveforms, especially chirp waveforms. In fact, one of the earliest and most popular applications of Fourier optics has been to SAR imaging. We will discuss this extensively.
In radar signal processing (and, for that matter, sonar) an active sensor operates by transmitting a particular waveform and reflecting it from an object or distribution of objects. After receiving the reflected signal the waveform is processed in a way to recover range to the object (or a distribution of ranges), as well as range rate (or velocity) in many instances. Simple signal theory would say that the range to a single object (e.g., point scatterer) could be measured to arbitrary accuracy with a sufficiently fast risetime pulse for sufficient signal-to-noise ratio. In practice, however, pulses do not have arbitrarily short risetimes and there may be more than one scatterer. In this case, the ability to resolve two or more scatterers is directly related to pulse width. The narrower the pulse width, the finer the range resolution. Given a transmitted waveform defined by
