Principles of Modern Radar - Volume 2 1891121537

212 CHAPTER 6 Spotlight Synthetic Aperture Radarsimplifying mathematical assumptions. The principle underlying all synthetic apertureimaging is that of using measurements of a reflected wave field to infer the structure ofthe distribution of scatterers that created it.To gain an intuitive understanding of what SAR processing does, imagine a stonedropped into a still pond at an unknown location. If we could measure the waves all aroundthe pond as they reach its edge, it seems reasonable to expect that we could determinethe location and amplitude of the initial disturbance given that we know how fast waterwaves propagate. Not surprisingly, if we measure the waves only at a portion of the pond’sedge then we diminish our ability to infer the initial disturbance. The connection to SARis the principle that cross-range resolution is proportional to the angular interval overwhich the target is observed. It then becomes simple to compare the resolution achievableby spotlight, stripmap, and inverse SAR collections, as all of these modes function bymeasuring radar reflections through some angular interval.SAR belongs to a rather distinguished family of imaging techniques that has garneredseveral Nobel Prizes. For example, Martin Ryle and Antony Hewish won the 1974 prizefor Physics for applying aperture synthesis to radio astronomy. Also, the 1979 prizefor Medicine was awarded to Allan Cormack and Godfrey Hounsfield for their work incomputer-assisted tomography. We see that SAR imaging techniques are in good company,and it is the author’s opinion that their beauty makes them well worth learning.6.1.1 OrganizationIn the interest of pragmatism, we narrowly focus on Fourier-domain image reconstructionbased on the assumption that spherical radio waves incident upon the scene can beapproximated as being locally planar. This approach leads to the polar format algorithm(PFA), which is the most common method of creating spotlight SAR imagery. It is alsoa good framework for understanding advanced applications such as interferometry andcoherent change detection. These are covered in Chapter 8. The objective of this chapter isto discuss spotlight SAR imaging as it is usually encountered in practice. The presentationis succinct, as the extant literature provides a number of superb discussions for readersinterested in more details regarding specific topics (e.g., [3,4] and [5]).We begin with a brief discussion of the Fourier transform and its properties followedby a description of the SAR data collection geometry. The radar sampling constraints inrange and cross-range are then derived, along with the achievable image resolution. Thediscussion then turns to image reconstruction using the polar format algorithm and thetools used for evaluating image quality. The chapter concludes with a look at the imagedegradation caused by common phase error effects and two common autofocus algorithmsused to correct these effects.6.1.2 Key PointsThe key points discussed in this chapter include the following:• A great deal of SAR imaging can be understood in terms of basic signal processingideas, such as the Fourier transform and the Shannon–Nyquist sampling theorem.• SAR collections are subject to sampling constraints dictated both by the signal contentand the imaging geometry.• PFA is the most common spotlight SAR reconstruction algorithm, applied when the radiationincident on the scene can be modeled using planar wavefronts. Other approachesare needed for near-field imaging, such as backprojection or the ω-k algorithm.