Efficient evaluation of fourier-based SAR focusing kernels

This letter addresses the efficient evaluation of Fourier-based kernels for synthetic aperture radar (SAR) image formation. The goal is to evaluate the quality of the focused impulse response function and the residual phase errors of the kernel without having to implement the processor itself nor perform a costly point-target simulation followed by the processing. The proposed methodology is convenient for situations where the assumption of a hyperbolic range history does not hold anymore, and hence, a compact analytic expression of the point target spectrum is not available. Examples where the hyperbolic range history does not apply include very high resolution spaceborne SAR imaging or bistatic SAR imaging. The approach first numerically computes the 2-D spectrum of a point target and then uses the transfer function of the focusing kernel to match it. The spectral support is then computed to adapt the spectrum to the output imaging geometry, so that the impulse response function (IRF) is finally obtained. The proposed approach is valid under the assumption of a large time-bandwidth product, as is usually the case for current air-and spaceborne SAR sensors. The methodology is validated by comparing the matched IRFs with the ones obtained using point-target simulations.