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In order to achieve the resolution comparable to the resolution of a monolithic primary mirror telescope and make the imaging quality of the imaging system reach or approach to the diffraction limit, the submirrors of the segments telescope should ensure co-phase splicing. To solve the problem of phase error detection, a high-precision piston error detection method is proposed based on convolutional neural network (CNN). By setting a mask with a sparse multi-subpupil configuration on the exit pupil of the imaging system, a point spread function (PSF) image dataset that is extremely sensitive to the piston error is constructed. According to the characteristics of this dataset, a high-performance CNN model is built. And the best detection range of CNN is tested. The simulation results show that a single network can accurately output the piston error of one or more submirrors in the capture range slightly less than one wavelength. When the single network is applied to the six-submirror imaging system, the detection precision of the piston error reaches an RMS value of 0.0013λ (here, RMS stands for root mean square). And the method has good robustness to residual tip-tilt error, wavefront aberration, and CCD noise, light source bandwidth. The method is simple and fast, and can be widely used to detect the piston error of the segments.
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Keywords:
- segmented telescopes /
- piston /
- CNN /
- PSF
[1] Hege E K, Beckers J M, Strittmatter P A, McCarthy D W 1985 Appl. Opt. 24 2565
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Luo Q, Huang L H, Gu N T, Li F, Rao C H 2012 Acta Phys. Sin. 61 069501
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Yan Z J, Chen X Y, Zheng L X, Ding Y Y, Zhu N H 2016 Acta Phys. Sin. 65 199501
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[4] 常军, 张正慧, 王蕊瑞 2011 物理学报 60 034218
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Chang J, Zhang Zh H, Wang R R 2011 Acta Phys. Sin. 60 034218
Google Scholar
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[8] Toni F 2010 Phys. Today. 63 26
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[9] Chanan G, Troy M, Dekens F, Michaels S, Nelson J, Mast T, Kirkman D 1998 Appl. Opt. 37 140
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[10] Shi F, Chanan G, Ohara C, Troy M, David C 2004 Appl. Opt. 43 4474
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[11] Li D, Xu S Y, Wang D, Yan D J 2019 Opt. Lett. 44 1170
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[12] Pizarro C, Arasa J, Laguarta F, Tomàs N 2002 Appl. Opt. 41 4562
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[13] Roddier F 1990 Appl. Opt. 29 1402
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[14] Dohlen K, Langlois M, Lanzoni P, Mazzanti S, Vigan A, Montoya L, Hernandez E, Reyes M, Surdej I, Yaitskova N 2006 Proc. SPIE 6267 626734
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[16] Pinna E, Esposito S, Puglisi A, Pieralli F, Myers R M, Busoni L, Tozzi A, Stefanini P 2006 Proc. SPIE 6267 62672Y
Google Scholar
[17] Wang S S, Zhu Q D, Zhao W R, Li L, Cao G R 2009 Chin. Opt. Lett. 07 1007
[18] Jiang A M, Wang S, Dong Z C, Xue J W, Wang J Y, Dai Y F 2018 Appl. Opt. 57 2736
Google Scholar
[19] Salinas-Luna J, Luna E, Salas L, Cruz-González I, Cornejo-Rodríguez A 2004 Opt. Express 12 3719
Google Scholar
[20] Vasishta G, Bootha A J, Colavitaa M M, Johnsona R L, Ligona E R, Moore J D, Palmera D L 2003 Proc. SPIE 4838 824
Google Scholar
[21] Booth J A, Adams M T, Ames G H, Fowler J R, Rakoczy J M 2000 Proc. SPIE 4003 176
Google Scholar
[22] 易红伟, 李英才, 樊超, 王矫 2008 光子学报 37 1373
Yi H W, Li Y C, Fan C, Wang J 2008 Acta Photon. Sin. 37 1373
[23] Dailos G R, Lara D G, Juan T S, Jose R M 2018 Opt. Lett. 43 4264
Google Scholar
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Google Scholar
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图 1 光阑子孔径分布
Figure 1. Sub-pupils distribution of the diaphragm.
图 2 不同平移误差对应的PSF图像样本 (a) p = 0; (b) p= 0.3λ
Figure 2. PSF image samples corresponding to different piston errors: (a) p = 0; (b) p = 0.3λ.
图 3 CNN网络结构
Figure 3. The network structure of CNN.
图 4 Mlpconv结构图
Figure 4. Structure diagram of Mlpconv.
图 5 不同检测范围时设定平移值对应的CNN预测误差分布图 (a) [–0.5λ, 0.5λ]; (b) [–0.49λ, 0.49λ]; (c) [–0.48λ, 0.48λ]
Figure 5. The distribution of CNN prediction errors corresponding to the piston value in different detection ranges: (a) [–0.5λ, 0.5λ] ; (b) [–0.49λ, 0.49λ] ; (c) [–0.48λ, 0.48λ].
图 6 六子镜成像系统 (a) 分块镜(六边形)和离散光阑孔(圆形); (b) PSF图像
Figure 6. Six submirror imaging system: (a) Segments (hexagons) and sparse subpupils (circles); (b) PSF image.
图 7 六子镜成像系统测试结果分布情况 (a) 子镜2; (b) 子镜3; (c) 子镜4; (d) 子镜5; (e) 子镜6
Figure 7. Distributions of errors over all the testing results for six submirror system: (a) Submirror 2; (b) submirror 3; (c) submirror 4; (d) submirror 5; (e) submirror 6.
表 1 不同检测范围时方法的检测精度
Table 1. Detection precision of the method in different detection ranges.
检测范围/λ ± 0.6 ± 0.5 ± 0.49 ± 0.48 ± 0.47 ± 0.46 ± 0.4 ± 0.35 精度/λ RMS 0.14 0.013 0.0065 0.0014 0.0017 0.0017 0.0014 0.0018 
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表 2 六子镜成像系统数据集划分情况
Table 2. Division of six submirror imaging system data set.
数据集 占比/% 样本形状 标签形状 训练集 80 (16000, 128, 128, 1) (16000, 5) 验证集 10 (2000, 128, 128, 1) (2000, 5) 测试集 10 (2000, 128, 128, 1) (2000, 5)
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表 3 不同倾斜值时方法的检测精度
Table 3. Detection precision of the method in different tip-tilt values.
倾斜值/λ RMS 0.004 0.04 0.1 0.2 0.3 0.4 精度/λ RMS 0.0015 0.0040 0.0095 0.012 0.023 0.041
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表 4 不同信噪比值时方法的检测精度
Table 4. Dtection precision of the method in different signal-to-noise ratio.
${R_{{\text{SN}}}}$/dB 50 45 40 35 30 25 精度/λ RMS 0.0033 0.0037 0.0058 0.0091 0.019 0.073
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表 5 不同像差时方法的检测精度
Table 5. Dtection precision of the method in different aberrations.
像差值/λ RMS 0.01 0.02 0.03 0.04 0.05 0.06 精度/λ RMS 0.0047 0.0095 0.014 0.019 0.024 0.032
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表 6 不同带宽时方法的检测精度
Table 6. Dtection precision of the method with different spectral widths.
带宽Δλ/nm 10–6 10–4 10–2 1 5 10 精度/λ RMS 0.0014 0.0015 0.0015 0.0023 0.0025 0.0028
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[1] Hege E K, Beckers J M, Strittmatter P A, McCarthy D W 1985 Appl. Opt. 24 2565
Google Scholar
[2] 罗群, 黄林海, 顾乃庭, 李斐, 饶长辉 2012 物理学报 61 069501
Google Scholar
Luo Q, Huang L H, Gu N T, Li F, Rao C H 2012 Acta Phys. Sin. 61 069501
Google Scholar
[3] 颜召军, 陈欣扬, 郑立新, 丁媛媛, 朱能鸿 2016 物理学报 65 199501
Google Scholar
Yan Z J, Chen X Y, Zheng L X, Ding Y Y, Zhu N H 2016 Acta Phys. Sin. 65 199501
Google Scholar
[4] 常军, 张正慧, 王蕊瑞 2011 物理学报 60 034218
Google Scholar
Chang J, Zhang Zh H, Wang R R 2011 Acta Phys. Sin. 60 034218
Google Scholar
[5] Platt B C, Shack R 2001 J. Refract. Surg. 17 S573
Google Scholar
[6] Harvey J E, Rockwell R A 1988 Opt. Eng. 27 762
Google Scholar
[7] Baron F, Cassaing F, Blanca A, Laubier D 2003 Opt. Eng. 4852 663
Google Scholar
[8] Toni F 2010 Phys. Today. 63 26
Google Scholar
[9] Chanan G, Troy M, Dekens F, Michaels S, Nelson J, Mast T, Kirkman D 1998 Appl. Opt. 37 140
Google Scholar
[10] Shi F, Chanan G, Ohara C, Troy M, David C 2004 Appl. Opt. 43 4474
Google Scholar
[11] Li D, Xu S Y, Wang D, Yan D J 2019 Opt. Lett. 44 1170
Google Scholar
[12] Pizarro C, Arasa J, Laguarta F, Tomàs N 2002 Appl. Opt. 41 4562
Google Scholar
[13] Roddier F 1990 Appl. Opt. 29 1402
Google Scholar
[14] Dohlen K, Langlois M, Lanzoni P, Mazzanti S, Vigan A, Montoya L, Hernandez E, Reyes M, Surdej I, Yaitskova N 2006 Proc. SPIE 6267 626734
Google Scholar
[15] Esposito S, Pinna E, Puglisi A, Tozzi A, Stefanini P 2005 Opt. Lett. 30 2572
Google Scholar
[16] Pinna E, Esposito S, Puglisi A, Pieralli F, Myers R M, Busoni L, Tozzi A, Stefanini P 2006 Proc. SPIE 6267 62672Y
Google Scholar
[17] Wang S S, Zhu Q D, Zhao W R, Li L, Cao G R 2009 Chin. Opt. Lett. 07 1007
[18] Jiang A M, Wang S, Dong Z C, Xue J W, Wang J Y, Dai Y F 2018 Appl. Opt. 57 2736
Google Scholar
[19] Salinas-Luna J, Luna E, Salas L, Cruz-González I, Cornejo-Rodríguez A 2004 Opt. Express 12 3719
Google Scholar
[20] Vasishta G, Bootha A J, Colavitaa M M, Johnsona R L, Ligona E R, Moore J D, Palmera D L 2003 Proc. SPIE 4838 824
Google Scholar
[21] Booth J A, Adams M T, Ames G H, Fowler J R, Rakoczy J M 2000 Proc. SPIE 4003 176
Google Scholar
[22] 易红伟, 李英才, 樊超, 王矫 2008 光子学报 37 1373
Yi H W, Li Y C, Fan C, Wang J 2008 Acta Photon. Sin. 37 1373
[23] Dailos G R, Lara D G, Juan T S, Jose R M 2018 Opt. Lett. 43 4264
Google Scholar
[24] Hui M, Li W Q, Liu M, Dong L Q, Kong L Q, Zhao Y J 2020 Appl. Opt. 59 771
Google Scholar
[25] Ma X F, Xie Z L, Ma H T, Xu Y J, Ren G, Liu Y 2019 Opt. Express 27 16058
Google Scholar
[26] Clampin M 2008 Proc. SPIE 41 254
Google Scholar
[27] Cheetham A C, Tuthill P G, Sivaramakrishnan A, Lloyd J P 2012 Opt. Express 20 29457
Google Scholar
[28] Cheetham A, Cvetojevic N, Norris B, Sivaramakrishnan A, Tuthill P 2014 Opt. Express 22 12924
Google Scholar
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