High-precision radius of curvature interferometry method with axial error compensation algorithm

Radius of curvature measurement by interferometry is a well known technique, but it is sensitive to some error sources. The major errors such as Abbe error and null cavity errors limit its high-precision radius measurement application. We have conducted theoretical analysis on the principle of Abbe error formation and the linear relationship between the tested sphere near the null positions and relative displacement, and established an axial error compensation model. The results show that there is a linear relationship between the power near the null position and the position offset of the tested sphere, and the slope of the fitted line is consistent with the theoretical value. With this compensation model, the experimental results show that the radius of curvature with compensation has improved the repeatability by nearly8times, and the reproducibility is approximately 2 ppm.