Theoretical Feasibility Analysis of Fast Back-Projection Algorithm for Moon-Based SAR in Time Domain

Nowadays, the Earth observation based on the Moon has attracted attention from many researchers and relevant departments. There also exists a considerable amount of interest in monitoring large-scale and long-term geoscience phenomena using the Moon-based SAR (MBS). However, the Earth&rsquo:s observation from MBS has long transmission time, and the relative motion of MBS with its Earth ground target (EGT) is much different to the space-borne SAR, the above reasons indicate that the traditional stop-and-go model is no longer suitable for MBS in frequency domain imaging. Here a dual-path separate calculation method for single pulse is presented in this paper for a better match of a real scenario, and then the slant range is fitted to a high-order polynomial series. The MBS&rsquo:s location, the synthetic aperture time and other factors have effects on length of the dual- path and fit bias. Without thoroughly investigated phase de-correlation processing in frequency domain, and to avoid computational costs in traditional back-projection (BP) algorithm, the paper first proposes a fast back-projection (FBP) algorithm in time domain for MBS, a platform that has long transmission time and long synthetic aperture time. In the FBP algorithm, the original method, that projected echo on all pixels in the imaging area, is changed to projected echo on a centerline instead. A suitable interpolation for points on the centerline is adopted to reduce the projected error: the synthetic aperture length and imaging area are also divided into subsections to reduce computation cost. The formula indicates that the range error could be control once the product of sub-imaging area&rsquo:s length and sub-aperture&rsquo:s length stay constant. Through the theoretical analysis, the detailed range difference mainly at apogee, perigee, ascending, and descending nodes indicate the necessity to separately calculate the dual-path for MBS&rsquo:s single pulse transmission in Earth-Moon motion, with real ephemeris been adopted: then, the high-order polynomial fitting will better describe the motion trajectory. Lastly, the FBP algorithm proposed is simulated in a specific scenario under acceptable resolution, and the result shows show its feasibility for image compression.