Research On Performance Of The Subaperture Stitching Algorithm For Optical Surfaces

The subaperture stitching interferometry can extend the vertical dynamic range, while enhancing the lateral resolution. Hence it becomes an effective alternative to get full-aperture surface error of large aperture or large relative aperture optics. And it is expected to get high-middle frequency errors which reveal the details. The stitching algorithm pieces subaperture data together for full-aperture data. It is the key of subaperture stitching interferometry. Its performance directly determines the measurement accuracy. Therefore, research on the algorithm performance is important for improvement of the measurement algorithm and promotion of the subaperture stitching interferometry to practices.Three typical optical surfaces are used, i.e., the SiC folding mirror, the large spherical surface and the parabolic surface, to study the performance of two stitching algorithms, based on experiments and simulations. The main contents include:1. The basic model for simultaneous stitching of more than two subapertures is built according to minimization of overlapping inconsistency. It is a large sparse linear least-square problem, and can be solved with conventional algorithms. Then the iterative algorithm for subaperture stitching is introduced briefly. It is compared with the basic algorithm from the principle point of view.2. The overlapping calculation subproblem in the iterative algorithm is introduced to automatically determine the overlapping correspondence for the basic algorithm. Ball constraints are imposed on the optimization variables to guarantee the local validity of linearization, which is important for correct stitching. Using experimental data of the three surfaces, methods for accuracy evaluation for the iterative algorithm are proposed. The cross test with the full-aperture measurement, the residual error analysis of the overlapping area, and the high-pass filter give conclusion that the stitched results with the iterative algorithm are reliable.3. Furthermore, a lot of simulations are accomplished with the three tested surfaces. The variance analysis with non-repetitive dual factor test is adopted to comparatively study the performance of the basic algorithm and the iterative one. The effects of each factor on the stitching accuracy are analyzed. The results show that the iterative algorithm is less sensitive to the alignment error of subapertures, leading to more reliable measurement results. Moreover, it applies to flats, spheres and aspheres. Finally the influence of the weights in the iterative algorithm is also discussed through simulations.The thorough performance of the iterative stitching algorithm is revealed through theoretical analysis, cross test and statistical simulations. It is helpful to improve the algorithm (e.g., properly choose the weights) and develop the subaperture stitching platform (e.g., specify the mechanical precision which determines the initial configurations).