Application Of Phase Retrieval To The Measurement Of Aspheric Surfaces

Modern technology meets serious challenge in the manufacture and measurement of aspheric optics which are being used widely in optical systems. Because the accuracy and efficiency of manufacture much depends on the optical measurement technology, in-situ test with high accuracy is very useful to aspheric optics manufacture,especially to those with large aperture. Since it has advantages of simplicity, vibration insensitivity, broad testing range and capability of quantitative calculation, phase retrieval is promising to realize in-situ test of aspheric optics. This thesis is dedicated to applying phase retrieval to problems in aspheric optical metrology. Beginning with the phase retrieval theory, it presents theoretical and experimental study on the in-situ test problems for aspheres, combined with the characteristics of aspheres and computer technology. The major research efforts include the following points.1. Some common problems in wave-front metrology are investigated from the view of classical phase retrieval. In view of the existence of ambiguity solutions in phase retrieval, some steps are taken to ensure the uniqueness of the testing result. Those include iterative computations back and forth between two defocus positions and constructing an irreducibility support to enhance restriction on solutions. The number of sampling points is defined theoretically using two-dimensional sampling theorem and space-bandwidth product invariability, and the limits of measurement are analyzed. According to the geometric optics model of wave-front curvature and intensity distributions, some principles about how to select the defocus positions are presented.2. Under-sampled phase retrieval algorithm is presented to expand the f-number of measurement range. This approach arrives at correct solution by virtue of sub-pixel ideal and nonlinear alternating optimization technique. Super solution intensities close to the focus are reconstructed from intensities away from the focus by sub-pixel phase retrieval algorithm. Then super solution intensities and phases are alternating optimized. An experiment is presented to investigate the validity of this method.3. A high dynamic range algorithm is described and demonstrated, which retrieves the figure errors beyond one wavelength after the rough polish process. Parameter algorithm and point-by-point algorithm are combined in this algorithm to reconstruct the figure error from outline to details. The low frequency part of the figure error is obtained by parameter algorithm firstly, and treated as a known wave-front phase in the followed point-by-point GS algorithm. And the latter is used to retrieve the high frequency part of the figure error.4. The phase retrieval method that tests aspheric mirror without auxiliary optics has been developed and demonstrated experimentally. Based on the primary principle of aspheric testing without auxiliary optics, the relationship between tested wave-front aberrations and figure errors is identified. In order to process large-scale data, a stitching method is proposed to calculate the light field produced by aspheres. Due to significant departure from the spherical surface, the intensities are usually saturated which will lead to phase retrieval failure. In order to overcome the effect from saturation, multi-pictures of the same scene with various exposure times are fused and the error in this process is analyzed. Based on the understanding of the caustic region produced by aspheric surfaces, the valid areas of intensities are defined. An aspheric phase retrieval algorithm is then presented. In addition, the light point and test point are proposed to be placed at paraxial conjugate positions properly selected to reduce system aberrations in the test. Phase retrieval tests are performed with a hyperboloid mirror and a paraboloid mirror at in-situ status. The retrieval results are then compared with the stitching and auto-collimating interference tests respectively, which verified the validity of the phase retrieval test.5. The phase retrieval testing system for off-axis aspheres based on Hindle test has been designed. The problem of phase retrieval for non-axial symmetry wave-front is translated into general spherical wave-front retrieval based on equivalent diffraction model. Adjustment in the test is reduced to moving light point along the direction of coordinate axes of tested mirror, and the displacement errors are separated using linear model about misalignment gradients for each degree of freedom. An experiment about off-axis ellipsoid testing is conducted. The phase retrieval test result is compared with measurements by interferometer and compensator. The agreement demonstrates this approach is feasible and realistic for off-axis ellipsoid test.