Acta Photonica Sinica, Volume. 48, Issue 12, 1212004(2019)

Nonlinear Optimization Method for Reconstruction of the Off-axis Aspherical Surface by Profile Measurement

Wei-zheng LEI1,1,2,2,3,3, Lü-jun YUAN1,1,2,2、*, Yan KANG1,1,2,2, and Zhi-de SU1,1,2,2
Author Affiliations
  • 1Nanjing Institute of Astronomical Optics & Technology, National Astronomical Observatories, Chinese Academy of Sciences, Nanjing 210042, China
  • 2CAS Key Laboratory of Astronomical Optics & Technology, Nanjing Institute of Astronomical Optics & Technology, Nanjing 210042, China
  • 3University of Chinese Academy of Sciences, Beijing 100049, China
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    Profile measurement plays an important role in aspherical mirror testing. However, the coordinate deflection and shift will lead to errors in result. In this paper, the analytical mathematic formula for misalignment error is presented. The measurement results are optimized by numerical differentiation method and nonlinear optimization algorithm based on least square method and the influence of these errors is eliminated. This method can effectively reconstruct the off-axis aspherical surface with systematic error. After four times polishing of the 570 mm off-axis aspherical mirror, the surface PV and RMS are decreased from 34.80 μm to 13.83 μm, and from 3.28 μm to 1.89 μm, respectively. For further comparison, the 220 mm×96 mm off-axis rectangle-shaped mirror is measured and proved that this method has strong applicability and generality for special shape mirror.

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    Wei-zheng LEI, Lü-jun YUAN, Yan KANG, Zhi-de SU. Nonlinear Optimization Method for Reconstruction of the Off-axis Aspherical Surface by Profile Measurement[J]. Acta Photonica Sinica, 2019, 48(12): 1212004

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    Paper Information

    Received: Jun. 28, 2019

    Accepted: Sep. 4, 2019

    Published Online: Mar. 17, 2020

    The Author Email: YUAN Lü-jun (ljyuan@niaot.ac.cn)

    DOI:10.3788/gzxb20194812.1212004

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