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 have derived a new nonlinear integral transform that relates the ocean wave spectrum to the AT-INSAR phase image spectrum. This integral transform is obtained from an approximation of the mapping integral that includes the radial 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. Under the assumption that the imaging is only weakly nonlinear, the nonlinear integral transform can be further simplified, In this case, the relationship between the AT-INSAR phase image spectrum and the ocean wave spectrum can be described by a linear transfer function.