Analysis of the Spherical Earth Surface Effect in Spaceborne High-Orbit Synthetic Aperture Radar Imaging

‍ Spaceborne high-orbit Synthetic Aperture Radar （SAR）， with its short revisit period and large range mapping capability， has attracted widespread attention worldwide owing to its unique advantages in both military and civilian applications. However， the imaging geometry of high-orbit SAR is more complex. Under the same resolution condition， the synthetic aperture time of high-orbit SAR is much longer than that of low-Earth-orbit SAR. In this case， the assumption that the radar moves in a straight line is no longer applicable， and the longer synthetic aperture time makes the orbital bending effect more obvious. Additionally， general SAR imaging algorithms are based on the assumption of flat ground， while high-orbit SAR has wide beam coverage. The drop of the surface height in the beam irradiation area cannot be ignored， which makes the plane surface hypothesis no longer applicable， and the influence of the spherical earth surface effect on the imaging must be considered. To analyze the influence of the spherical surface effect on high-orbit SAR imaging， the geometric distortion and defocusing in imaging are studied in detail from two aspects： simple linear trajectory and more realistic curved trajectory. First， assuming that the radar moved in a straight line in a short time， the position mapping relationship between the imaging plane and the curved surface was obtained by detailed analysis of the range-Doppler relationship between the real target point on the surface of the earth and the pixels in the two-dimensional imaging domain， and the echo of the two was reversely deduced based on the mapping relationship. When imaging the SAR in straight track by echo analysis， the focusing was clear and defocusing did not occur. Then， in the case of a curved trajectory， the geometric distortion caused by the spherical surface effect of high-orbit SAR was also solved by the range-Doppler relationship. Additionally， based on the analysis of the distance history of the real target on the spherical surface and the corresponding pixels in the plane found based on the mapping relationship， it was found that additional defocusing would occur in the imaging under the case of curved trajectory. For this defocusing phenomenon， the Taylor expansion of the two distance-histories was performed in this study. By comparing the Taylor series of the two processes， the quadratic phase error of the two echoes was obtained， and the error phase was positively correlated with the width of the imaging scene. The defocusing would become more obvious with the increase of synthetic aperture time and the expansion of the imaging scene， with significant spatial variability. The effective focusing radius is given by the phase error. Finally， the mapping relationship between the spherical surface and the imaging plane and the imaging defocusing characteristics are verified by simulation experiments. In this study， the imaging geometry distortion caused by the surface bending effect is solved， and the secondary phase error of the radar echo when the radar is running on the curved track is obtained， which causes imaging defocusing. This study provides convenience for the subsequent research of compensation imaging algorithms based on the phase error， which solves the defocusing problem caused by the curved orbit and spherical surface of the Earth.