Optimization of sparse subaperture array model for stitching detection of plane wavefront

Luo Qian; Wu Shibin; Wang Lihua; Yang Wei; Fan Bin

doi:10.12086/oee.2018.170638

Article navigation > Opto-Electronic Engineering > 2018 Vol. 45 > No. 5 > 170638

Next Article Previous Article

Luo Qian, Wu Shibin, Wang Lihua, et al. Optimization of sparse subaperture array model for stitching detection of plane wavefront[J]. Opto-Electronic Engineering, 2018, 45(5): 170638. doi: 10.12086/oee.2018.170638

Citation:

Luo Qian, Wu Shibin, Wang Lihua, et al. Optimization of sparse subaperture array model for stitching detection of plane wavefront[J]. Opto-Electronic Engineering, 2018, 45(5): 170638. doi: 10.12086/oee.2018.170638

Optimization of sparse subaperture array model for stitching detection of plane wavefront

1.
Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China

Fund Project: Supported by Key Project of the National Key Research and Development Plan for Earth Observation and Navigation (2016YFB0500200)

More Information

Corresponding author: Luo Qian, E-mail: luoqian_yy@163.com

Received Date 20 November 2017

Revised Date 16 January 2018

Published Date 01 May 2018

Abstract

Abstract

The sparse subaperture stitching, the accuracy of which is closely related to the arrangement, number and size of subapertures, is one of the main methods of quality testing for large aperture optical systems. A mathematical model was established to deduce the relation curve between the subaperture number k and fill factor M when the value of k ranges from one to infinity. As a result, the optimal arrangement layout, consisting of seven sparse subapertures, was obtained for the detection systems below 1.5 m. Autocollimation interference detection of Φ200 mm validated the rationality of the arrangement.
- sparse subaperture /
- mathematical modeling /
- stitching detection /
- wavefront reconstruction /
- interferometry

FullText(HTML)

References

[1]	侯溪, 伍凡, 杨力, 等.子孔径拼接干涉测试技术现状及发展趋势[J].光学与光电技术, 2005, 3(3): 50–53. Google Scholar Hou X, Wu F, Yang L, et al. Status and development trend of sub-aperture stitching interferometric testing technique[J]. Optics & Optoelectronic Technology, 2005, 3(3): 50–53. Google Scholar
[2]	Sj dahl M, Oreb B F. Stitching interferometric measurement data for inspection of large optical components[J]. Optical Engineering, 2002, 41(2): 403–408. doi: 10.1117/1.1430727 CrossRef Google Scholar
[3]	Kim C J. Polynomial fit of interferograms[J]. Applied Optics, 1982, 21(24): 4521–4525. doi: 10.1364/AO.21.004521 CrossRef Google Scholar
[4]	He Y, Wang Z X, Wang Q, et al. Testing the large aperture optical components by the sub-aperture stitching interferometer [J]. Proceedings of SPIE, 2007, 6624: 66240D. Google Scholar
[5]	Xu X D, Shen Z X, Tong G D, et al. Sparse subaperture stitching method for measuring large aperture planar optics[J]. Optical Engineering, 2016, 55(2): 024103. doi: 10.1117/1.OE.55.2.024103 CrossRef Google Scholar
[6]	闫锋涛, 范斌, 侯溪, 等.稀疏子孔径采样检测大口径光学器件[J].强激光与粒子束, 2011, 23(12): 3193–3196. Google Scholar Yan F T, Fan B, Hou X, et al. Large-aperture mirror test using sparse sub-aperture sampling[J]. High Power Laser and Particle Beams, 2011, 23(12): 3193–3196. Google Scholar
[7]	Chow W W, Lawrence G N. Method for subaperture testing interferogram reduction[J]. Optics Letters, 1983, 8(9): 468–470. doi: 10.1364/OL.8.000468 CrossRef Google Scholar
[8]	王琰, 伏瑞敏, 廖志波.基于稀疏孔径的波前重构算法[J].航天返回与遥感, 2015, 36(5): 51–59. Google Scholar Wang Y, Fu R M, Liao Z B. Wavefront reconstruction algorithm based on sparse aperture[J]. Spacecraft Recovery & Remote Sensing, 2015, 36(5): 51–59. Google Scholar
[9]	Chen S Y, Dai Y F, Li S Y, et al. Error reductions for stitching test of large optical flats[J]. Optics & Laser Technology, 2012, 44(5): 1543–1550. Google Scholar
[10]	Smith G A, Burge J H. Subaperture stitching surface errors due to noise[J]. Proceedings of SPIE, 2015, 9575: 95750W. doi: 10.1117/12.2188085 CrossRef Google Scholar
[11]	Hill J M, Salinari P. The large binocular telescope project[J]. Proceedings of SPIE, 2000, 5489: 603–614. Google Scholar
[12]	Chung S J, Miller D W, De Weck O L. Design and implementation of sparse aperture imaging systems[J]. Proceeding of SPIE, 2002, 4849: 181–192. doi: 10.1117/12.460077 CrossRef Google Scholar

Overview

Overview

Overview: The sparse subaperture stitching is one of the main methods of quality detection for large and oversized aperture optical systems. Tradition methods using parallel light pipe and plane mirror autocollimation have some limitations, and they are difficult to realize full-caliber high-precision wavefront aberration detection. The sparse subaperture stitching is based on the principle of interference autocollimation, and the system contains three parts, including interferometer, optical system to be measured and a plane mirror. Unlike overlapping subaperture stitching, a plurality of small aperture plane mirror structure according to the arrangement of a certain composition sparse aperture can replace a large flat mirror. Each subaperture wavefront information was used to reconstruct the full aperture wavefront by stitching algorithm to achieve the required accuracy. The precision of stitching algorithm is closely related to the arrangement, number and size of subaperture, and the coverage ratio of the subapertures in the whole region is represented by the filling factor M. Therefore the better M, the better the precision of stitching algorithm. In this paper, a mathematical model was established to deduce the relation curve between the subaperture number k and fill factor M when the value of k ranges from one to infinite. Though the relation curve between the subaperture number k and fill factor M, the maximum value of fill factor M=0.77778 was obtained when k equals to 7. As a result, the coverage ratio of the subapertures in the whole region is the largest, which collects most of the information. Seven sparse subapertures, which is the optimal layout diagram for the detection systems below 1.5 m was selected. Multiple subapertures ranging from 4 to 9 were stitching and detected, respectively. After stitching, the data were processed by removing tilt The data of the stitching wavefront and the full aperture test data were subtracted, and the residual error was compared. The obtained RMS is 0.0391λ and the direct detection RMS is 0.038λ when sampling the wavefront data with seven subapertures. The relative error is 2%. The residual wavefront RMS between stitching and direct detection is 0.0092λ. Compared with other subaperture, the reconstructed full-aperture wavefront is the most consistent with directly detected full-aperture wavefront, which verifies the rationality of the mathematical model. That is to say, self-collimation interference detection of Φ200 mm demonstrates the rationality of the arrangement.