Impulse Response Function for Ultra-wideband SAR

Abstract:
A new impulse response function (IRF) for ultra-wideband synthetic-aperture radar (SAR) is derived based on an analytical Fourier transform pair. The latter corresponds in 2D frequency domain to a triangular area with constant amplitude, zero amplitude otherwise, which is used to model the SAR IRF. We show that the IRF reduces to a 2D sinc function for small aperture angles and that it is a good approximation for SAR up to about 10deg of aperture angle. This IRF also generates the characteristic crossed sidelobe arms of ultra-wideband SAR from two rotated and interfering sinc functions. For aperture angles greater than about 10deg, the IRF is constructed by superposition of adjacent triangles next to each other in frequency domain. The IRF for ultra-wideband SAR corresponding to an annulus sector is thus given by an infinite series of such triangular regions, but only a few terms are necessary for typical ultra-wideband SAR systems. About one term per 10deg of aperture angle gives an accurate result.