On the cross spectrum between individual-look synthetic aperture radar images of ocean waves

Cross spectra of individual-look synthetic aperture radar (SAR) images of the ocean surface are used to retrieve ocean wave spectra. A quasilinear transform is derived that relates ocean wave spectra to SAR image cross spectra. Furthermore, Monte Carlo simulations are also carried out for those cases where quasilinear imaging does not apply. It is shown that, as the time separation between the individual-look SAR images increases (within a limit determined by the Doppler bandwidth of the original single-look complex SAR image), the spectral energy density of the imaginary part of the SAR image cross spectra increases, while the spectral energy density of the real part decreases. The integration time has a small effect on the SAR image cross spectra as long as the integration time is large compared to the scene coherence time. In order to retrieve ocean wave spectra from SAR data by using cross-spectral analysis techniques, the authors suggest calculating two SAR image cross spectra: one with a short time separation and one with a large one between the individual-look SAR images. The real part of the SAR image cross spectra calculated from individual-look SAR images with the short time separation is used for retrieving ocean wave spectra, which have a 180° ambiguity in wave propagation direction. The imaginary part of the SAR image cross spectra calculated from individual-look SAR images with the long time separation is used for removing this 180° ambiguity