Extended shift-rotation method for absolute interferometric testing of a spherical surface with pixel-level spatial resolution

An improved shift-rotation method for the absolute testing of spherical surfaces is developed to obtain pixel-level spatial resolution and a low noise propagation ratio. The absolute testing process includes multiple rotational tests and two lateral shifting tests with large shifts. A wavefront reconstruction algorithm based on subaperture division and least squares fitting is proposed to reconstruct the surface figure of the test optics. Numerical simulation results show that the method reveals high-frequency figures missed in the traditional Zernike-based shift-rotation method. The algorithm error is lower than 0.4%, and the noise propagation ratio can be reduced by 70% using large shifts. The absolute testing of spherical optics is carried out to verify this method. One spherical surface was tested with the presented absolute testing method and the method using a point diffraction interferometer. The difference of the measurement results based on the two methods showed that the testing uncertainty reached 0.19 nm root mean square (RMS), which indicated that the presented method has potential subnanometer testing uncertainty.