An analysis of gradient-induced distortion in ATI-SAR imagery of surface currents

This paper summarizes an analysis of gradient-induced distortions in the surface current estimates generated by along-track interferometric SAR (ATI-SAR) systems. In the presence of spatial current gradients, an effect akin to velocity bunching can cause distortion in the measured current profiles. This distortion is caused by variation in the azimuthal displacement induced by the current itself. Up to a point, these distortions can be removed by a straightforward, spatial remapping of the interferogram pixels based upon their phase values. However, there is a critical current gradient beyond which the true surface current field is not recoverable. This mechanism is compounded in dual-beam ATI-SAR systems designed to estimate the surface current vector using only a single aircraft pass. In such systems, interferograms from two squinted beams, one squinted forward of broadside and the other squinted aft by the same amount, are combined to measure the full surface current vector. However, when the current vector does not bisect the angle between the two beams, the along-track component of the current induces unequal azimuthal displacements in the fore- and aft-squinted interferograms. As a result, the two interferograms will not be spatially registered, in that corresponding pixels in the fore- and aft-interferograms will be related to currents at spatially distinct points on the water surface. Additional vector distortions will, therefore, occur in and around the gradient region. These effects are explored through an approximate, linear analysis as well as through an ATI-SAR model that accounts for nonlinearity and finite spatial resolution, using the current gradients present in rivers as an example.