On the optimality and exactness of wavenumber-domain SAR data processing

Derives the wavenumber-domain SAR processing algorithm within a Hilbert-space framework. The derivation of the algorithm is motivated from geometrical considerations and the resulting image formation procedure is seen to be optimal. A new derivation of the algorithm, using a direct approximation of an exact Fourier identity, is given. The exact formulation is shown to be equivalent to previous derivations with appropriate approximations. Then, an approximate derivation of the algorithm is given which uses the principle of stationary phase to approximate the Fourier transforms. Fortunately, the approximations are exceedingly good for typical SAR imaging scenarios. Requirements on sampling for discrete implementation of the algorithm are discussed and the resolution achievable using this algorithm is shown to agree with that obtainable in a comparable spotlight scenario