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

The problem of obtaining quantitative data on spatial ocean wave spectra fr om the images of the ocean surface by either regular SAR or along-track int erferometric SAR (INSAR) is studied. The dominant mechanism which allows im aging of ocean waves by SAR/INSAR is the so-called velocity bunching. This mechanism is essentially nonlinear, The theoretical analysis of SAR/INSAR i magery of the ocean surface due to velocity bunching is performed, and nonl inear solutions of the SAR/INSAR images of monochromatic waves and of the s pectra of these images are obtained, Analytic expressions are presented her e which allow to simulate accurately both SAR and INSAR images of waves wit h 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 whi ch is related to the velocity bunching mechanism, it is shown that for comp lex INSAR, the degree of nonlinearity depends also on separation time betwe en the two antennas. The results of the present study indicate that in addi tion to the prevailing practice to consider the phase component of the INSA R image, an analysis of the imaginary part of the complex INSAR map of the ocean surface may provide some supplementary information, beneficial, in pa rticular, for rough sea.