SAR imaging of ocean waves: Theory

Abstract

We present a formalism for deriving the image of a scene and apply it to the case of an ocean-wave surface. For a dominant wave, the optimum image is obtained when the matched filter of the radar processor is adjusted in proportion to the azimuth component of the wave phase velocity. In the specular scattering approximation, the orbital velocity effects introduce a phase perturbation term of the form \Psi(k_{l}\cdotr - \omega_{l}t ) where \Psi is a function of the wave height, depression angle, and the ocean wave vector k_{l} and orbital frequency \omega_{l} . This term does not introduce any significant degradations in the wave image. The presence of more than one dominant wave component results in azimuth-resolution degradation dependent on the orbital phase velocity magnitudes and direction. Wave-wave interactions, resulting in the advection of each ocean-wave component by the orbital velocity variations of the other waves, introduce a phase perturbation of the form [\Psi(k_{l}\cdotr - \omega_{l}t)]t into the SAR imaging integral. This leads to a degradation in the azimuthal resolution and is significant only when U_{ol}(R/v_{a}), U_{ol} the orbital velocity and R and v_{a} the radar platform range and velocity, is greater than the resolution cell width. Published calculations, showing that velocity bunching is a primary mechanism for the modulations in images of azimuthally traveling waves, evaluate the SAR imaging integral for an orbital velocity phase perturbation of the form \Psi(k_{l}\cdotr - \omega_{l}t) , and their conclusions are a consequence only of the mathematical approximations used. An exact evaluation of the integral does not yield the azimuth image modulations predicted. Data are presented to show a) the dependence of focusing on the azimuth component of the wave phase velocity, b) image degradation of azimuthally traveling waves as a function of integration time, c) autocorrelations of scans across a wave imaged from different viewing angles of the SAR, d) scans across the spectra, in the azimuth wave-vector direction, of two different azimuthally traveling waves of different periods, to illustrate the dependence of image distortions on wave period, and e) dependence of the ratio of the energy in a SAR wave image spectrum peak and the zero spectrum component on the reported significant wave height for data taken during the SEASAT experiment.