By analyzing Newton's rings, often encountered in interferometry, using fractional Fourier transform (FRFT), we can estimate the physical parameters, such as the curvature radius of the spherical surface and the rings' center. However, parameter estimation from large images using FRFT consumes considerable time. We introduce an improved method that resamples the image before applying FRFT. Because Newton's rings are sparse in the FRFT domain, this method reduces the computational time without decreasing the accuracy. Experimental results show that compared to traditional FRFT-based algorithms, this method can estimate parameters in about 1.3 s when processing 1920×1080 pixel images.