Spline based least squares integration for two-dimensional shape or wavefront reconstruction |
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| Institution: | 1. Brookhaven National Laboratory - NSLS II, 50 Rutherford Dr. Upton, NY 11973-5000, USA;2. School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, China;3. Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China;4. University of Chinese Academy of Sciences, Beijing 100049, China;5. Jiangsu Key Laboratory of Spectral Imaging & Intelligence Sense, Nanjing University of Science and Technology, Nanjing 210094, China;1. Nanjing University of Science and Technology, School of Electronic and Optical Engineering, Xiaolingwei 200#, Nanjing 210094, China;2. Nanjing University of Science and Technology, Jiangsu Key Laboratory of Spectral Imaging & Intelligence Sense, Xiaolingwei 200#, Nanjing 210094, China;1. School of Electronic and Optical Engineering, Nanjing University of Science and Technology, No. 200 Xiaolingwei Street, Nanjing, Jiangsu Province 210094, China;2. Jiangsu Key Laboratory of Spectral Imaging and Intelligent Sense, Nanjing, Jiangsu Province 210094, China;3. Smart Computational Imaging Laboratory (SCILab), Nanjing University of Science and Technology, Nanjing, Jiangsu Province 210094, China;1. School of Electronic and Optical Engineering, Nanjing University of Science and Technology, No.200 Xiaolingwei Street, Jiangsu Province 210094, China;2. Jiangsu Key Laboratory of Spectral Imaging & Intelligent Sense, Nanjing, Jiangsu Province 210094, China;3. Smart Computational Imaging Laboratory(SCIlab), Nanjing University of Science and Technology, Nanjing, Jiangsu Province 210094, China;1. School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China;2. Nanjing University of Science and Technology, Jiangsu Key Laboratory of Spectral Imaging & Intelligence Sense, Xiaolingwei 200#, Nanjing, 210094, China;1. Smart Computational Imaging Laboratory (SCILab), Nanjing University of Science and Technology, Nanjing, Jiangsu Province 210094, China;2. Jiangsu Key Laboratory of Spectral Imaging & Intelligent Sense, Nanjing University of Science and Technology, Nanjing, Jiangsu Province 210094, China |
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| Abstract: | In this work, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. The noise influence is studied by adding white Gaussian noise to the slope data. Experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement. |
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| Keywords: | Shape reconstruction from gradient Wavefront reconstruction Splines |
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