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Synthetic aperture radar (SAR) is an example of a computed imaging system that is capable of synthesizing imagery having extraordinary resolution. This is accomplished by coherently processing radar returns collected from many different spatial locations. SAR has many cousins, including computer tomography, magnetic resonance imaging, holography, interferometric radio astronomy, and x-ray crystallography. Each of these systems acquires partial Fourier data and then employs sophisticated digital processing techniques to form 2-D, 3-D, and 4-D images. In this talk, we first provide a brief overview of Fourier-based computed imaging and then focus on the application of SAR to radar astronomy. Conventional radar imaging has been used to map the radar reflectivity of the Moon, interior planets, and asteroids, employing range-Doppler techniques. Although this form of processing has proven highly successful over the years, it is problematic for extremely fine-resolution applications. During the data collection interval (typically several minutes), the object's rotation may cause scatterers to migrate through range-Doppler resolution cells. In addition, during extended observation times, the apparent rotation rate of the object may change, and the Doppler cell boundaries may actually move. Both situations contribute to spatially-varying smearing in the image when using conventional processing on high-resolution data. To overcome this problem, we propose the application of imaging algorithms from spotlight-mode SAR. When viewed in a tomographic context, this form of processing recognizes that each range-bin datum (after range compression) represents a superposition of the reflectivity of all illuminated scatterers at that range; this is approximately a linear projection. From the projection-slice theorem, the Fourier transform of each returned signal gives a slice of the 2-D Fourier transform of the reflectivity for a 2-D surface. Collecting data from many angles, as the object rotates, provides Fourier data on a nearly polar grid. Simple polar-to-Cartesian interpolation, followed by a 2-D FFT, produces the high-resolution image. We show results of applying such processing to Lunar data acquired at Arecibo Observatory and demonstrate that the SAR-based processing method is superior to conventional range-Doppler processing. Some of our more recent work is focused on imaging of 3-D objects having unknown and possibly highly irregular shapes. This work is motivated by the problem of imaging asteroids.
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