Topography sensing by polarimetric SAR: theoretical basis and application using orthogonal-pass AIRSAR data

The authors have recently proposed an algorithm to derive topographical information from polarimetric SAR data. The algorithm is based on empirical comparisons between the terrain local slope angle and the corresponding changes in the relative position of the co-pol polarimetric signature maximum, and was supported by some preliminary theoretical analysis. Also the algorithm has been validated experimentally using data sets acquired over different geographical areas, over different types of natural targets (forest, bare soil) and using different digital elevation models as reference system. This paper presents some theoretical considerations on the scattering mechanisms which underpin the phenomenological aspects of the topography sensing method. A simplified closed form approximation to the relationship between the co-pol maximum shift and the measured covariance matrix elements is introduced. This step highlights the major contributions to the co-pol maximum shift and suggests an interpretation in terms of the azimuthal symmetry properties of the target. Covariance matrices generated from experimental or modelling data can then be used as input variables to establish the relationship between the true and estimated terrain tilt angle. An example of the theoretical analysis relative to the influence of the incidence angle on the estimator error for a slightly rough surface is reported. From the algorithm's application point of view a new technique is finally demonstrated, whereby using two pass orthogonal acquisition data the elevation surface can be generated as a solution of a Poisson type differential equation with only one tie-point.