Acta Photonica Sinica ›› 2019, Vol. 48 ›› Issue (12): 1212004-1212004.doi: 10.3788/gzxb20194812.1212004

• Instrumentation, Measurement and Metrology • Previous Articles     Next Articles

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

LEI Wei-zheng1,2,3, YUAN Lü-jun1,2, KANG Yan1,2, SU Zhi-de1,2   

  1. 1. Nanjing Institute of Astronomical Optics&Technology, National Astronomical Observatories, Chinese Academy of Sciences, Nanjing 210042, China;
    2. CAS Key Laboratory of Astronomical Optics&Technology, Nanjing Institute of Astronomical Optics&Technology, Nanjing 210042, China;
    3. University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2019-06-28 Published:2019-12-30
  • Supported by:
    The National Natural Science Foundation of China (No. 11603051)

Abstract: 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.

Key words: Off-axis aspherical surface, Profile measurement, Reconstruction of mirror surface, Nonlinear optimization, Mirror fabrication

CLC Number: