A nonlinear integral transform between ocean wave spectra and phase image spectra of a cross-track interferometric SAR

Due to motion of the ocean surface, the scatter elements on the ocean surface are mapped into an InSAR image with a shift in azimuth direction, which results in velocity bunching and thus nonlinearity in InSAR imaging of ocean waves. A simple InSAR phase model is proposed, where the phase is proportional to the ocean surface elevation with an azimuth shift. This azimuth shift is determined by the radial component of the orbital velocity of the scatter element and the velocity of platform as well as the range distance between platform and scatter element. Since both radial component of the orbital velocity and ocean surface elevation are related to the ocean wave spectra, a nonlinear integral transform between ocean wave spectra and InSAR phase image spectra is derived based on the simple phase model. The characteristic function method is applied in the derivation. This nonlinear integral transform can be used to analyze the nonlinear imaging mechanism, as well as to retrieve ocean wave spectra from InSAR phase image spectra