A New Quasi-Linear Integral Transform Between Ocean Wave Spectrum and Phase Spectrum of an XTI-SAR

Cross-Track Interferometric Synthetic Aperture Radar (XTI-SAR) can utilize variations in interferometric phase to measure sea surface velocity along radar radial direction and sea surface height, which can be used for ocean wave parameter inversion. However, research on the imaging mechanisms of XTI-SAR systems for ocean waves remains understudied, and there are still some problems in its perception. To further study the imaging mechanism of XTI-SAR measurement systems for ocean waves, this paper describes research based on the nonlinear integral transform model and the quasi-linear integral transform model derived by Bao in 1999, which relate the XTI-SAR ocean wave spectrum to the phase spectrum. Firstly, this work derived another quasi-linear integral transform model based on the nonlinear integral transform model, and also optimized the quasi-linear integral transform model derived by Bao. The optimized quasi-linear integral transform model eliminates the need for complex calculations of cross-correlation functions between sea surface height and radar radial orbital velocity components of ocean waves, as well as the radar line-of-sight velocity transfer function, while maintaining high integral transform accuracy. Secondly, based on two-dimensional sea surface simulations, we analyzed the differences between the quasi-linear integral transform models and the nonlinear integral transform model corresponding to different XTI-SAR system configurations and different sea states. The numerical simulation results show that, for the XTI-SAR system, in general, the difference between the quasi-linear integral transform model derived in this work and the nonlinear integral transform model is greater than that of the quasi-linear integral transform model derived by Bao. However, the difference between the optimized quasi-linear integral transform model and the nonlinear integral transform model in this study is smaller, and it is more convenient when transforming the ocean wave spectrum to the phase spectrum.