Measurement of aspheric surfaces using annular subaperture stitching interferometry based on an automatic positioning method: Theory and application

A simple and effective automatic positioning method (APM) is proposed for the application of annular subaperture stitching interferometry in the stage of precision polishing. In the testing process, a series of optical path difference (OPD) data of subaperture are obtained since the interferometer is shifted relative to the tested aspheric surface. These OPD data are analyzed by the APM to get the key stitching parameters (e.g., aspheric departure) without a precision motion system. The basic principles of the APM are described. The performance of the method is simulated in some pertinent cases. Finally, we study the applicability of the proposed method to subaperture stitching tests of a hyperbolic mirror. The stitching results agree with the full-aperture test results. It demonstrates the validity and practicability of the proposed algorithm.