Sub-aperture stitching method to measure aspherical mirror in phase retrieval

A sub-aperture stitching method to measure aspherical mirror in phase retrieval is presented. Analytical expressions for the gradient of a squared-error metric with respect to the object and sub-aperture parameters are obtained. Then we give the sub-aperture stitching algorithm in phase retrieval to measure aspherical mirror. The validity of it has been proved in simulation by us. The influence of misalignment in this algorithm is shown and the corresponding method to align is supplied. Using this sub-aperture stitching method we have arranged an experimental setup to test an aspheric mirror with 640 mm vertex radius and 206 mm clear aperture. In this experiment, the optical path has been perfectly aligned using foregoing alignment method. The good agreement between the results of sub-aperture stitching and the corresponding interferometer results indicates the correction of the sub-aperture stitching approach and the corresponding aligning method.