Interferometric measurement of the radius of curvature based on axial displacement from a confocal position and corresponding defocus wavefront

Abstract

The radius of curvature (R) is a fundamental parameter of spherical optical surfaces. The measurement range of the widely adopted traditional interferometric method is limited by the length of the precision linear guide rail carrying the measured surface from the cat’s eye to the confocal position, and the test result is vulnerable to airflow and vibration in the test environment. An interferometric method is proposed for the radius measurement of spherical surfaces based on a small axial moving distance and the corresponding defocus wavefront to eliminate the dependence on a long guide rail and extend the measuring range. To eliminate the influence of the test environment and calculate the R, a defocus transform algorithm is proposed to instantaneously measure the defocus wavefront from a single interferogram. Numerical simulations theoretically demonstrate that there is no limit to the measurement range of this method because only a short distance of the measured mirror must be moved. A spherical mirror with a radius of curvature of 101.6087 mm is experimentally tested, and the relative measurement error is 0.037%. This method can achieve high accuracy for optical shops and greatly increase the measurement range of the interferometric method without additional equipment.