Geometrical Approach To Subaperture Stitching Interferometry For Aspheric Surfaces

Aspheric optics are being used more and more widely in modern optical systems,due to their ability of correcting aberrations, enhancing the image quality, enlarging thefield of view and extending the range of e?ect, while reducing the weight and volume ofthe system. With the ever-increasing demands on system performances, large optics areadopted in high-energy laser weapons, laser fusion systems and space telescopes. Thetechnical requirements are more than traditional. More rigorous control of high-middlefrequency error is now demanded within the full aperture of the large-relative apertureoptics. Thereby surface quality within the full aperture and full band of frequency (allspatial frequency components of the wavefront in the e?ective aperture) becomes themain content of inspection of large optics. Whereas this problem has never been solved.The subaperture testing method seems to provide the answer. This thesis is dedicatedto solve the key problems in subaperture testing of aspheric surfaces. Unlike traditionalsubaperture stitching algorithms, the problems are formulated from the geometrical pointof view, combined with methods for workpiece localization, tolerance assessment and multi-view registration. The major research e?orts include the following points.1. A systematic introduction is first given to the theory of configuration space of sym-metric features and multi-features, which provides a mathematical background for theproblem of tolerance assessment and subaperture stitching. Then the mathematicalmodels and algorithms for tolerance assessment problem are proposed, in the form ofthe American standard ASME Y14.5.1M-1994. Several techniques are discussed toimprove the algorithm performances. Comparisons with other published algorithmsprove the validity and advantages of the proposed method.2. A geometrical approach is introduced to formulate the subaperture stitching problemmathematically. The problem is decomposed into a series of overlapping calculationsubproblems and geometrical parameter optimization subproblems. Actually it canbe viewed as generalized workpiece localization or multi-view registration problem.By virtue of the alternating optimization technique and the successive linearizationmethod, the problem is solved e?ciently, combined with sparse techniques, sequentialQR decomposition method and code vectorization skills. The model of the surface un-der test is utilized to simplify the overlapping calculation subproblem. Consequentlythe full aperture should be best localized with regard to the nominal surface. There-fore the algorithm is a combination of subaperture stitching algorithm and workpiecelocalization algorithm. As a major advantage, the algorithm is immune from fairlybig parameter (including the motion parameter) uncertainties. Thanks to it, preciseprior knowledge of the nulling and alignment motion is no longer required, nor arethe radii of best fit spheres. Simulations of subaperture stitching test of a large-scaleparaboloid surface verify the validity of the proposed algorithms. Stitching algorithm with the aid of fiducial marks is also developed to further compensate uncertaintyof the symmetric degrees of freedom. Subaperture stitching problem using a pla-nar interferometer is simpler than using a spherical interferometer, since the phase ismeasured with a plane datum. It can be considered as special case of the latter.3. Lattice is used here to mean the collection and arrangement of subapertures. Becauseof the varying curvature, lattice design is subtle and complicate for aspheric surfaces,especially for o?-axis subapertures. Methods are described for lattice design and cal-culation of the best fit sphere for each subaperture. The best fit sphere is determinedby minimizing the mean-squares aspheric deviations in the form of surface integral. Anumerical example is given to illustrate the procedure, and also verify the validity ofthe proposed methods. A prototype design of the subaperture stitching interferome-ter is presented based on the analysis of the degree-of-freedom. Requirements on theresolution, accuracy and stroke of the nulling and alignment motion are determinedby the robustness of the stitching algorithm against motion uncertainties, as well asthe sensitivity of sub-interferograms to motion errors.4. Major error sources in subaperture stitching interferometry are recognized. The prop-agation of uncertainty is discussed with the subaperture stitching algorithms. Undercertain assumptions, it can be explicitly formulated.5. Finally lattice design and subaperture stitching test are performed with a planar mir-ror and a paraboloid mirror respectively. The stitched full-aperture is then comparedwith the measured full-aperture, which verifies the validity of the subaperture testingexperimentally.