Scene size limits for polar format algorithm

Synthetic aperture radar (SAR) is a form of remote sensing where coherent radar echoes transmitted from a moving platform are processed to form an image of a scene, usually on the ground. There are several algorithms that have been developed with varying levels of complexity and accuracy. In applications with large scene size requirements, the choice of image formation algorithm is important. Exact imaging algorithms like the back-projection algorithm (BPA) can form large images without errors, but they are computationally expensive. Another well-known algorithm is the polar format algorithm (PFA), which is significantly faster than BPA, but it uses approximations that cause image errors in large scenes. In this paper, we evaluate the scene size limitations of the PFA in terms of image defocus. This is caused by residual quadratic phase errors that arise due to approximations in the algorithm. We derive this residual quadratic phase error using a Taylor series expansion in the slow time dimension. Then, we derive simplified expressions for image defocus for two flight paths: circular and linear. We also use the Taylor series expansion to derive accurate corrections for image distortion caused by PFA. These distortion corrections are used in conjunction with the residual quadratic phase errors to derive accurate scene size limitations that are notably different from the circular regions of focus determined in earlier works.