Theoretical analysis and verification of time variation of background ionosphere on geosynchronous SAR imaging

Geosynchronous synthetic aperture radar (SAR) (GEO SAR) has the characteristic of long integration time; thus, the time-freezing model assumption of background ionosphere for traditional low Earth orbit (LEO) SAR no longer holds in GEO SAR. Furthermore, the background ionosphere variation within the integration time cannot be omitted either. In this letter, the variation of total electron content within integration time is analyzed and described in detail by using polynomial approximation, and a new GEO SAR signal model influenced by background ionosphere is also proposed. In view of this novel model, the analytical expression of image shift and defocusing phase error are derived in the first place. Then, a quantitative analysis for the image shift and image defocusing in the range and azimuth directions is conducted, and the performance bounds of time-varying parameters of background ionosphere effects on focusing are obtained. Finally, the U.S. Total Electron Content measured data are used to verify the theoretical results of background ionosphere effects on GEO SAR focusing.