Self-calibrated subaperture stitching test of hyper-hemispheres using latitude and longitude coordinates

Limited by the f-number of the transmission sphere, it is impossible to test the whole surface of a hyper-hemisphere using a standard interferometer directly. This paper presents an extension of the subaperture stitching test method to hyper hemispheres. The stitching algorithm is based on the coordinate mapping from local measurement frame to a global frame, and overlapping correspondence is calculated by virtue of coordinates of latitude and longitude. The reference surface error is represented by Zernike polynomials and self-calibrated during the stitching to achieve higher accuracy. Then the stitched surface error distribution is presented by map projection. To realize accessibility to the whole surface of a hyper-hemisphere, we also propose a design for the subaperture test platform, according to the subaperture lattice design. Finally, a hemisphere and a full sphere are tested and figured, respectively, to validate the method and the experimental setup.