Performance of the Polar Formatting Algorithm for SAR Image Formation on Wide Aperture Collections

In this paper we describe the performance of the well-known polar formatting algorithm (PFA) for formation of spotlight-mode synthetic aperture imagery from phase history data, under conditions of large-angle synthetic apertures. Such conditions typically occur when the SAR center frequency is low and/or the azimuthal resolution is is very high. Traditional wisdom states that PFA is not desirable for large aperture angles (say on the order of 60 degrees) because either: 1) the polar-toCartesian interpolation step is typically implemented as two separate one-dimensional filters and the resulting interpolation errors lead to unacceptable quality in the reconstructed image; or 2) the polar-to-Cartesian conversion is implemented as a fully two-dimensional interpolation and ends up consuming excessive computation time. Here we show that the traditional wisdom is incorrect, i.e., we show that the conventional polar-to-Cartesian interpolation implemented as two separable 1-D steps does yield acceptable image quality even for very wide-angle aperture collections. In addition, we dispell a second notion that PFA is inadequate in imaging scenarios wherein range curvature effects are significant. In fact, the defocus induced by range curvature in PFA in many situations can be corrected via post-filtering of the formed SAR image, and the calculation time for the refocus is quite reasonable. We will demonstrate these results by way of PFA formation of SAR imagery from synthetic target data and will contrast the PFA results with those from the CBP (convolution/back-projection) algorithm. CBP is often considered to be superior to PFA for wide-aperture or near-field imaging scenarios, because CBP avoids the step of 2-D interpolation of phase history data and also can be easily modified to account for curved wavefronts in the near-field scenario. The downside of CBP is that it is generally much less efficient computationally than PFA. Our conclusion is that PFA with post-filtering for correction of near-field effects is the algorithm of choice for many (but not all) practical spotlight-mode SAR imaging scenarios involving wide-angle synthetic apertures.