Topographic slope from the SAR interferometric phase gradient

A new algorithm for the direct calculation of topographic slope maps from synthetic aperture radar (SAR) interferograms is presented. The algorithm derives slope maps without first requiring the creation of a digital elevational model (DEM) from the interferogram, thus obviating the need for high SNR in the interferogram and altitude calibration points for the scene. SAR data useful for interferometry has been collected by the Active Microwave Imager on board the ERS-1 satellite, when it was in a short period repeat orbit. Two passes of the radar sensor form a cross-track interferometric baseline. For a point target at some position (x,y,h), the interferometric phase difference phi is proportional to the difference in path lengths for the two sensor positions to the scatterer. Given the phase difference as measured in the complex interferogram and an accurate baseline geometry, the position of the scatterer, most significantly the height h, can be determined through triangulation. The interferometric phase measurement however is known only modulo 2-pi, and hence it is necessary to determine the correct multiple of 2-pi to add to the phase at each point to obtain an estimate of the actual phase with respect to an absolute datum. This phase unwrapping process is required for creating DEM's, and is difficult or impossible for regions of low SNR or SAR image layover. The new algorithm described here derives slope maps without requiring phase unwrapping.