Improved FRFT-based method for estimating the physical parameters from Newton's rings

Newton's rings are often encountered in interferometry, and in analyzing them, we can estimate the physical parameters, such as curvature radius and the rings’ center. The fractional Fourier transform (FRFT) is capable of estimating these physical parameters from the rings despite noise and obstacles, but there is still a small deviation between the estimated coordinates of the rings' center and the actual values. The least-squares fitting method is popularly used for its accuracy but it is easily affected by the initial values. Nevertheless, with the estimated results from the FRFT, it is easy to meet the requirements of initial values. In this paper, the proposed method combines the advantages of the fractional Fourier transform (FRFT) with the least-squares fitting method in analyzing Newton's rings fringe patterns. Its performance is assessed by analyzing simulated and actual Newton's rings images. The experimental results show that the proposed method is capable of estimating the parameters in the presence of noise and obstacles. Under the same conditions, the estimation results are better than those obtained with the original FRFT-based method, especially for the rings’ center. Some applications are shown to illustrate that the improved FRFT-based method is an important technique for interferometric measurements.