An exact analytic representation of a regular or interferometric SAR image of ocean swell

The problem of obtaining quantitative data on spatial ocean wave spectra from the images of the ocean surface by either regular SAR or along-track interferometric SAR (INSAR) is studied. The dominant mechanism which allows imaging of ocean waves by SAR/INSAR is the so-called velocity bunching. This mechanism is essentially nonlinear. The theoretical analysis of SAR/INSAR imagery of the ocean surface due to velocity bunching is performed, and nonlinear solutions of the SAR/INSAR images of monochromatic waves and of the spectra of these images are obtained. Analytic expressions are presented here which allow to simulate accurately both SAR and INSAR images of waves with arbitrary lengths, heights and propagation directions. It is demonstrated that a monochromatic wave expands in the SAR/INSAR images into an infinite number of harmonics. In addition to the nonlinearity parameters of SAR which is related to the velocity bunching mechanism, it is shown that for complex INSAR, the degree of nonlinearity depends also on separation time between the two antennas. The results of the present study indicate that in addition to the prevailing practice to consider the phase component of the INSAR image, an analysis of the imaginary part of the complex INSAR map of the ocean surface may provide some supplementary information, beneficial, in particular, for rough sea.