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为获得与单口径望远镜相当的空间分辨率, 使成像系统成像质量达到或接近衍射极限, 拼接主镜式望远镜的分块子镜应确保实现共相位拼接, 本文针对拼接主镜式望远镜高精度平移(piston)误差检测问题, 提出了一种基于卷积神经网络的高精度平移误差检测方法. 通过在成像系统的出瞳面上设置具有离散孔的光阑, 构建了对平移误差极为敏感的点扩散函数图像数据集, 根据此数据集的特点搭建了具有高性能的网络模型, 并测试得到网络的最佳检测范围. 仿真结果表明, 在略小于一个波长的捕获范围内, 单个网络能够准确地输出一个或多个分块子镜的平移误差; 应用于六子镜成像系统时, 平移误差检测精度达0.0013λ RMS (root mean square), 并且方法对残余倾斜(tip-tilt)误差、波前像差、CCD噪声、光源带宽具有良好的鲁棒性. 该方法简单快速, 可广泛应用于分块镜系统的平移误差检测.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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图 2 不同平移误差对应的PSF图像样本 (a) p = 0; (b) p= 0.3λ
Fig. 2. PSF image samples corresponding to different piston errors: (a) p = 0; (b) p = 0.3λ.
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]
Fig. 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
Fig. 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
Fig. 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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