In this paper, a comprehensive form of the range migration algorithm (RMA) is analytically derived for reconstructing the reflectivity function using synthetic aperture imaging techniques. Specifically, amplitude compensation, in addition to the typical phase compensation, is included in the development of the matched filter of the RMA, with the result herein referred to as the amplitude compensated RMA (AC-RMA). To illustrate the improvements offered by the AC-RMA, simulation and measurement (at Ka-band, 26.5 - 40 GHz) are performed to reconstruct the reflectivity function of a target using both RMA and AC-RMA algorithms. The results prove that the AC-RMA is a robust algorithm that can successfully reconstruct the reflectivity function of a target with higher accuracy, regardless of its dielectric properties, including scenarios with low contrast between the dielectric properties of the background and target in the presence of noise. This approach is also independent of the bandwidth of the imaging system and is applicable to multilayer media as well. In addition, while the formulation of the AC-RMA is more complicated than the traditional (phase compensation only) RMA, the processing time necessary for images created with the AC-RMA is just 1.2 times greater than that of the traditional RMA processing time.
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