Shape measurement of stressed mirror based on stereoscopic phase measuring deflectometry

Chen Zhenyi; Zhao Wenchuan; Zhang Qican; Han Yu; Liu Yuankun

doi:10.12086/oee.2020.190435

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Chen Z Y, Zhao W C, Zhang Q C, et al. Shape measurement of stressed mirror based on stereoscopic phase measuring deflectometry[J]. Opto-Electron Eng, 2020, 47(8): 190435. doi: 10.12086/oee.2020.190435

Citation:

Chen Z Y, Zhao W C, Zhang Q C, et al. Shape measurement of stressed mirror based on stereoscopic phase measuring deflectometry[J]. Opto-Electron Eng, 2020, 47(8): 190435. doi: 10.12086/oee.2020.190435

Shape measurement of stressed mirror based on stereoscopic phase measuring deflectometry

1.
School of Electronics and Information Engineering, Sichuan University, Chengdu, Sichuan 610065, China
2.
Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China

Fund Project: Supported by National Natural Science Foundation of China (61675141, 61505216) and The Youth Innovation Promotion Association, Chinese Academy of Sciences

More Information

Corresponding author: Zhang Qican, E-mail:zqc@scu.edu.cn

Received Date 23 July 2019

Revised Date 22 October 2019

Published Date 01 August 2020

Abstract

Abstract

Stressed polishing technology transforms aspheric fabrication into spherical fabrication by applying predetermined loads on the surface of the mirror. The key to achieve high precision of stressed polishing is to test the surface deformation with high precision. Stereoscopic phase measuring deflectometry was used to test the surface topography and the deformation of stressed mirror. After obtained unwrapped phase distribution, and combined with normal consistency constraint and gradient integral algorithm, the height distribution was finally obtained. Composition of systematic errors were simulated. Also, the errors were calibrated and removed by N-step averaging method in this system, which improved the measuring precision. In this paper, the surface topography and the deformation of a stressed mirror with a diameter of 320 mm, spherical radius of 5200 mm were measured. The measuring results were consistent with the corresponding result of CMM and finite element simulation, indicating that this proposed method is on the level of micron in terms of accuracy and more suitable for the test of stressed mirror compared with interferometer and CMM.
- optical testing /
- stereoscopic phase measuring deflectometry /
- systematic error /
- stressed mirror polishing

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References

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Overview

Overview

Overview: Stressed polishing technology was firstly proposed by Jerry E.Nelson in 1980, considered as an effective method of aspheric fabrication. According to the calculated results of elastic mechanics, this method exerts an external force on the mirror to form a deformation which opposite to the desired deformation from spherical surface to off-axis aspheric surface. Under the state of deformation, the mirror is polished into sphere surface. After removing the external force, the required off-axis aspheric surface can be obtained. Because aspheric fabrication is converted to spherical fabrication, tools with large diameter can be used and efficiency is greatly improved.

The key to achieve high precision of stressed polishing is to test the deformation of mirror with high precision. However, the main methods of surface measurement nowadays are interferometer and CMM. If interferometer is used, its dynamic range can only support the detection below micron deformation. If CMM is used, probe may scratch the mirror surface, and the detection tempo is very slow. Furthermore, interferometer and CMM are both expensive and complex equipments.

So, aimed at stressed polishing above micron deformation, stereoscopic phase measuring deflectometry was used to test its surface topography and deformation. It is low cost and convenient technique and only screen, camera, and computer were needed when implemented. More importantly, characteristics such as high dynamic range, full-field three-dimensional measurement and excellent performance in medium and high frequency were brought in, which are very suitable for the test of stressed mirror.

When measuring, firstly calculating the unwrapped phase distribution through CCD cameras, then calculating the height of a specific point on the measured surface using normal consistency constraint, and finally the full-field height distribution was obtained by Southwell gradient integral algorithm. To improve the measuring accuracy, composition of systematic errors were simulated, proved that it mainly includes low-order non-rotational symmetry items. According to simulating results, errors were calibrated and removed by N-step averaging method to get a absolute surface topography.

In this paper, the absolute surface topography and the deformation of a stressed mirror with a diameter of 320 mm, spherical radius of 5200 mm were measured. The measuring results were consistent with the corresponding result of CMM and finite element simulation, indicating that this proposed method is on the level of micron in terms of accuracy and more suitable for the test of stressed mirror compared with interferometer and CMM.