Simplified radar mapping equations for terrain correction of space-borne SAR images

Correction of a space-borne Synthetic Aperture Radar (SAR) image for the effects of terrain distortion requires the use of mapping equations that relate the coordinates of a scatterer in three dimensions to its position in the twodimensional image. These mapping equations are complicated since they take into account the curved geometry of the Earth's surface, and since they must be evaluated of the order of 10 to 100 million times in the course of correcting a typical SAR image, the complexity is a disadvantage. In this paper we derive two approximations, one quadratic and one linear, to the mapping equation, and evaluate their performance relative to the observational parameters of a variety of space-borne SAR systems and the range of topographic variation present in the scene. We show that the quadratic approximation is sufficiently accurate in virtually all circumstances likely to be encountered. In most cases the linear approximation is also valid, although it is unsuitable where the topographic variation is large and the near-swath incidence angle is small.