Vertical autofocus for the phase screen in a turbulent ionosphere

Abstract

The performance of spaceborne synthetic aperture radars (SAR) is affected by the Earth's ionosphere. In particular, the ionospheric turbulence causes phase perturbations of the SAR signals, which may lead to image distortions. A convenient way to model those phase perturbations is by means of a phase screen. The latter is an infinitesimally thin layer positioned at a certain elevation above the Earth's surface. The radar signal acquires an instant perturbation once its trajectory intersects the screen. The trajectory is a ray between the antenna and the target, and the magnitude of the perturbation is equal to the screen density at the intersection point. The density is a bivariate function of the coordinates along the screen. The coordinates of a specific intersection point are determined by the ray itself, as well as the screen elevation. Thus, the magnitude of the phase perturbation explicitly depends on the screen elevation. Accordingly, to compensate for the resulting image distortions one should be able to determine the elevation of the screen. In the paper, we develop an algorithm of vertical autofocus that derives this elevation from the received SAR data, given a pair of point scatterers in the target area. The proposed algorithm exploits a modification of the coherent interferometric (CINT) imaging that was previously employed to reduce the effect of phase errors due to the trajectory uncertainty. In our analysis, we highlight the differences between this case and transionospheric propagation.