Perturbation Amplitude Effects of Polynomial plus Power Law Errors on Refraction Autofocus

Recent investigations have generated methods that apply automatic correction in synthetic aperture radar (SAR) image data of the scene defocus artifacts that are induced via refraction of radar pulses in the intervening atmospheric. In particular, spatial variations of the physical parameters in the atmosphere can cause bending and delay effects in the propagation of radar pulses. Therefore, radar motion in a SAR collection can yield difficult scenarios due the differences in bending and delay effects from one radar pulse to the next. This methodology applies a signal theoretic model for the estimation of the bending and delay errors that arise for a given pulse to the next along the synthetic aperture. Specifically, this approach applies two-dimensional maximum likelihood techniques [1] in order to estimate and compensate for the error due to the bending effects, as modeled by the elevation angle θ 1 in Figure 1 , and the pulse path length delay, as shown via the variable s 1 . These autofocus methods compensate for the deleterious defocus effects of atmospheric bending and delay of the radar pulses. These techniques are an extension of Phase Gradient Autofocus (PGA) methods [2] that are used to focus SAR imagery for unknown motions of the moving radar platform.