This letter presents an improved polar format algorithm for nonlinear aperture and widefield spotlight synthetic aperture radar imaging. In the proposed algorithm, the chirp $z$ transform is used for uniform range resampling, while the fast Gaussian grid nonuniform fast Fourier transform is employed to focus the nonuniform samples in azimuth. Additionally, the space-variant postfiltering is incorporated for eliminating the geometric distortion and marginal defocusing effects induced by wavefront curvature. The effectiveness of the proposed algorithm is validated by simulation and real large scene Gotcha data set.