Spectral signal to clutter and thermal noise properties of ocean wave imaging synthetic aperture radars

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Abstract
The high wavenumber detection cut-off is determined above which the spectrum of ocean waves imaged by a synthetic aperture radar (SAR) is lost in the background noise spectrum consisting of the clutter noise associated with the Rayleigh statistics of the backscattering surface and the thermal noise originating in the SAR system itself. For given power, the maximum detection cut-off wavenumber is attained if the SAR resolution is chosen such that the clutter and noise spectra are equal at the cut-off wavenumber. Assuming a constant modulation transfer function relating the image modulation and wave slope spectra, the cut-off wavenumber is in this case proportional to (ρaρg)−1/2, where ρa and ρg represent the full bandwidth (single look) azimuthal and ground range resolutions, respectively. The same proportionality holds (but with a cut-off wavenumber increased by a factor √2) for a clutter limited cut-off, the normal operating condition of an SAR. To first order, incoherent multilook averaging has no influence on the signal-to-background detection cut-off wavenumber, provided the reduced Nyquist cut-off wavenumber resulting from the reduced multilook spatial resolution remains greater than the signal-to-background cut-off wavenumber. Estimates of the detection cut-off wave-numbers are given for the Seasat SAR and the SAR proposed for the European Remote Sensing Satellite ERS-1.