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Our study investigated an object-detection method based on the faster region-based convolutional neural network (faster R-CNN). The method was designed to determine the center of either a concentric circle or concentric ellipse. Specifically, the central spot of the image (as the object region) can be marked by the bounding box when the circular or elliptical image is used as input data for the faster R-CNN model. The center point of the bounding box can then be calculated according to the coordinates of the upper left and lower right corners, that is, the center position of the concentric circle or concentric ellipse. It is important to determine the center coordinates when taking optical measurements, as the curvature radius of optical components can thus be obtained. The effectiveness of this method is demonstrated through simulation images. Furthermore, we can obtain the center coordinates of the actual Newton’s rings image using the above method; according to the coordinate transformation method, the curvature radius can be estimated based on the center.

Phase extraction from a single closed interferogram with a quadratic phase plays an important role in optical interferometry. Based on the energy of the interference images of this type is concentrated in a very narrow range around a point in the fractional Fourier transform (FRFT) domain under matched angle, the FRFT technique is a useful parameter estimator for the fringe pattern, but it has not been used to retrieve the desired phase from the fringe pattern. Thus, the parameter estimation approach based on FRFT is extended to the extract phase. The phase extraction can be done without using a phase unwrapping algorithm. Moreover, for ensuring both the estimation precision and speed, a coarse-to-fine searching strategy that includes a direct searching process implemented with a large step size and an iterative searching based on quasi-Newton method is presented in this paper to implement the FRFT method. The feasibility and applicability of the proposed approach are demonstrated using simulation and experimental results. The experimental results show that the proposed method is robust to noise and obstacles.