A two-dimensional (2D) model for describing the imaging of ocean waves by an along-track interferometric synthetic aperture radar (AT-INSAR) is derived. It includes the modulation of the normalized radar cross section by the long waves, velocity bunching, and azimuthal image smear due to orbital acceleration associated with long waves and due to the orbital velocity spread within the AT-INSAR resolution cell (parameterized by the scene coherence time). By applying the Monte-Carlo method, AT-INSAR amplitude and phase image spectra are calculated for different sea states and radar configurations. The Monte-Carlo simulations show that velocity bunching affects the AT-INSAR imaging mechanism of ocean waves, and that a unimodal ocean wave spectrum may be mapped into a bimodal AT-INSAR phase image spectrum due to an interference between the velocity term and the velocity bunching term in the AT-INSAR imaging model. It is shown that the AT-INSAR imaging mechanism of ocean waves depends on the ratio of the scene coherence time and the time separation between the observations by the two antennas. If this ratio is larger than one, the AT-INSAR phase image spectra are distorted. Furthermore, the simulations show that the AT-INSAR phase image spectrum is quite insensitive to the ocean wave-radar modulation transfer function. Comparing AT-INSAR with conventional SAR imaging of ocean waves, the authors find that the azimuthal cut-off in AT-INSAR phase image spectra is shifted toward higher wavenumbers than in conventional SAR image spectra. This implies that AT-INSAR can resolve shorter azimuthal wavenumbers than conventional SAR. Thus the authors conclude that AT-INSAR phase images are better suited for measuring ocean waves spectra than conventional SAR images.
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