Absolute calibration of a spherical reference surface for a Fizeau interferometer with the shift-rotation method of iterative algorithm

Abstract

We present an absolute testing of a spherical reference surface of a Fizeau interferometer with the method of shift-rotation, which relies on the decomposition of the surface deviation into rotationally asymmetric and symmetric components. With a new procedure to measure the rotationally asymmetric component and an iterative algorithm to calculate the symmetric component, the method can calibrate the spherical reference surface with high accuracy. An experiment is presented to verify the validity of the absolute testing method. The reference surface deviation measured with the absolute testing method agrees well with that of random-ball-averaging testing method; the root mean square of the residual figure between them is ∼0.8 nm .