Concise fractional Fourier transform based on a non-uniform order searching method for estimating physical parameters from Newton’s rings

Newton’s ring pattern is very common in interferometry. By analyzing it, the physical parameters can be estimated, such as the curvature radius and the rings’ center. However, parameter estimation from large images using fractional Fourier transform (FRFT) consumes considerable time. A concise FRFT based on a non-uniform order searching method is proposed to reduce the computational time without decreasing the accuracy. Experimental results show that the time of the proposed method is about 2.7 s, which is about 1/600 of that of the traditional FRFT-based method and 1/5 of that of the Fast FRFT-based method when processing 960 × 960 pixel images.