A simple algorithm for the direct extraction of the two-dimensional surface image spectrum from the return signal of a synthetic aperture radar

Abstract A simple method is derived for 1the determination of the two-dimensional surface image spectrum from the return signal of a synthetic aperture radar (SAR) without explicitly producing an image. The algorithm is similar in structure to a two-dimensional Fourier transformation, but the transformed function also depends explicitly on the wavenumber components. The function consists of the quadratic product of the complex return signal amplitude and the time-delayed complex conjugate return signal, the time delays with respect to range and azimuth time being proportional to the corresponding wavenumber components in these directions. The algorithm appears to be sufficiently simple to be implemented in real time aboard a satellite. Because of the considerable data compression achieved in reducing the original image to its statistical variance spectrum, this opens the possibility of obtaining global surface-wave spectral data from satellites without the excessive costs of sophisticated telemetry and a ...