Radius of curvature of spherical wave measurement based on vortex beam interference

We proposed a new method for the radius of curvature (ROC) of spherical wave measurement based on vortex beam interference and Fermat's spiral fitting, which can not only provide a large measurement range but also have high precision. Theoretical analysis showed that the maximum distribution of the interference light intensity is in accordance with the Fermat's spiral, and the spiral coefficient is proportional to the ROC of spherical wave. For a concave spherical mirror with a ROC of 899.89mm and a convex spherical lens with a ROC of 59.99mm, the average measurement error of five measurements are 0.080% and 0.083%, respectively. Controlled experiments showed that, our proposed method has a higher measurement accuracy and a larger measurement range than Newton's rings method, it has almost equal measurement accuracy for large and small ROC. This research provides a theoretical basis for the development of a ROC measurement system with large measurement range and high precision.