Subaperture stitching testing for fine flat mirrors with large apertures using an orthonormal polynomial fitting algorithm

Interferometry, which measures the difference between a reference surface and a test surface, is widely used in high-precision testing. Usually the reference surface is considered as perfect and the surface errors there can be ignored during the testing. Considering the interferometry for fine optics with large apertures where the error of the reference surface is non-ignorable, we propose a stitching algorithm based on an orthonormal polynomial fitting method that can be used to accomplish the testing of both the reference surface and the surface under test simultaneously. To evaluate the accuracy of the above algorithm, the performance of the proposed method was analyzed by testing the tertiary mirror for the Thirty-Meter Telescope project (TMT project) and utilizing the algorithm in the simulation. Further, a practical experiment was implemented to demonstrate the practicability of the proposed method.