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By analyzing Newton’s rings, often encountered in interferometry, the parameters of spherical surfaces such as the rings’ center and the curvature radius can be estimated. First, the classical convolutional neural networks, visual geometry group (VGG) network and U-Net, are applied to parameter estimation of Newton’s rings. After these models are trained, the rings’ center and curvature radius can be obtained simultaneously. Compared with previous analysis methods of Newton’s rings, it is shown that the proposed method has higher precision, better immunity to noise, and lower time consumption. For a Newton’s rings pattern of 640 × 480 pixels comprising − 5 d B Gaussian noise or 60% salt-and-pepper noise, the parameters can be estimated by the VGG model in 0.01 s, the error of the rings’ center is less than one pixel, and the error of curvature radius is lower than 0.5%.

Analysis of closed-fringe patterns with quadratic phase that are often encountered plays an important role in optical interferometry. But because the frequency spectra of the two exponential signals that compose closed-fringe patterns overlap in the Fourier domain while one is clearly distinct from the other in the fractional Fourier domain, fractional Fourier transform (FRFT) is a useful method for analyzing the images to provide parameter estimation. However, when the fringe pattern has varying background and/or modulation due to non-uniform illumination, parameter estimation accuracy based on FRFT is affected, which lacks theoretical justification. Thus, the impact of varying background and/or modulation on the FRFT is studied with theoretic analysis and presented in this paper. Key factors that contribute to the optimal results are discussed when employing three kinds of fringe normalization methods to eliminate the impact. Here, the fringe pattern is first processed by the normalization technique. Then the cosine-only term is used to estimate parameter by use of the FRFT-based method. Physical quantities are then obtained by parameter estimation. In comparison with our previous method based on FRFT, more accurate results are achieved. The feasibility and applicability of the proposed approach are demonstrated using simulation and experimental results.

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.