Radius of curvature measurement based on iterative correlation coefficient matching strategy with a single-shot interferogram.

• This strategy only uses a single interferogram, which will reduce data acquisition requirements and improve measurement efficiency. • Based on the theoretical analysis of the optical propagation path in the experimental system, a simple method is derived to correct the retrace error and established a matching model. • Simulation and experimental results show that our method not only has high-accuracy of measuring small ROC, but also performs well in the measurement of large ROC. We proposed an iterative correlation coefficient matching strategy for the high-precision measurement of the radius of curvature (ROC), which only needs a single-frame interferogram. This strategy includes two parts: one is to obtain an initial ROC by using the relationship between the ROC and the diameter of the dark ring; other is to further solve a high-precision value by an iterative method. In the iterative part, we simulated a series of interference patterns with each ROC in the setting range, and calculated the correlation coefficient between the each simulated interferogram and the measured interferogram, and searched the maximum of the correlation coefficient that would be used to confirm a new ROC in the next iteration. When the calculated ROCs in the adjacent iterations meet the termination condition, the high-accuracy ROC can be solved. The feasibility of our proposed method has been verified by simulations and experiments. The errors of the test mirrors with the ROC of 101.6 mm and 1000 mm are 0.013% and 0.024% in experiments, respectively. This research provides a simple and feasible method for realizing the high-precision ROC measurement. [ABSTRACT FROM AUTHOR]