A new nonlinear integral transform relating ocean wave spectra to phase image spectra of an along-track interferometric synthetic aperture radar

The along-track interferometric synthetic aperture radar (AT-INSAR) has the potential to measure ocean surface currents and ocean surface waves. We ha ve derived a new nonlinear integral transform that relates the ocean wave s pectrum to the AT-INSAR phase image spectrum. This integral transform is ob tained from an approximation of the mapping integral that includes the radi al component of the velocity of the scatter elements and velocity bunching. However, it neglects the modulation of the normalized radar cross section by the long ocean waves, which has a small effect on the AT-INSAR phase. Un der the assumption that the imaging is only weakly nonlinear, the nonlinear integral transform can be further simplified, In this case, the relationsh ip between the AT-INSAR phase image spectrum and the ocean wave spectrum ca n be described by a linear transfer function.