適應性光學(adaptive optics system，AOS)是一種感知光線變化並補償雷射或光學系統相位變化的技術，以改變成像的品質，常被用於天文學、醫學、軍事等領域之中，也被廣泛使用在雷射加工上。
本論文以適應性光學概念為主軸，欲在光學系統中加入一主動式光學元件，藉以補償斜向入射光學系統中的誤差與加工中可能產生的光學像差(aberration)干擾，藉由可調變式聚焦鏡(deformable mirror，DM)的整合，在補償像差之餘更能主動調控聚焦能力。
本實驗同時與深度學習(deep learning，DL)整合，利用常見的波前感測器(Shack-Hartmann wavefront sensor，SHWS)所拍攝之光點圖作為輸入，分析光點圖所得之Zernike多項式其各項係數為輸出，建立SHWS分析模型。

The deformable mirror (DM) provides fast responsive modulation to the incident laser wavefront and effective compensation to the optical aberrations. Based on system design and power efficiency requirement for various applications, the laser is incident to DM with different angle instead of normal incidence. Due to the incident angle change and the coupling effect of DM channels, to identify the DM voltage vectors for generating individual Zernike mode is complicated and not intuitive. The present study proposes the deep learning neural network (DNN) to assist the DM identification and find the control vectors. We have successfully trained the SHWS analysis model and the model that maps individual oblique DM aberrations to the 15 Zernike modes. A DM with tip-tilt compensation is placed at angle of 45 degree with the optical axis so that the reflected laser power efficiency can be maximized due to no beam splitter is required. The remote focusing is achieved by adjusting the defocus term of Zernike polynomials. We have shown the defocus can be successfully performed in the adaptive optics system (AOS) with the combination of Zernike polynomials even if the DM is not orthogonal to the optical axis. The results are confirmed with home-made Shack-Hartmann wavefront sensor (SHWS).

1.H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
2.J. M. Beckers, “Adaptive optics for astronomy: principles, performance, and applications,” Annu. Rev. Astron. Astrophys. 31, 13–62 (1993).
3.P. Kern, “Adaptive optics prototype system for infrared astronomy, I: system description,” SPIE Proc. 1271, 243–251 (1990).
4.R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (CRC, 1998).
5.N. Ji, “Adaptive optical fluorescence microscopy,” Nat. Methods 14(4), 374–380 (2017).
6.M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light: Sci. Appl. 3(4), e165 (2014).
7.J.-H. Park, Z. Yu, K. Lee, P. Lai, and Y. Park, “Perspective: Wavefront shaping techniques for controlling multiple light scattering in biological tissues: Toward in vivo applications,” APL Photonics 3(10), 100901 (2018).
8.W. Zheng, Y. Wu, P. Winter, R. Fischer, D. Dalle Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14, 869–872 (2017).
9.Z. Qin, S. He, C. Yang, J. S.-Y. Yung, C. Chen, C. K.-S. Leung, K. Liu, and J. Y. Qu, “Adaptive optics two-photon microscopy enables near-diffraction-limited and functional retinal imaging in vivo,” Light Sci. Appl. 9, 79 (2020).
10.C. Rodríguez and N. Ji, “Adaptive optical microscopy for neurobiology,” Curr. Opin. Neurobiol. 50, 83–91 (2018).
11.L. Kong and M. Cui, “In vivo neuroimaging through the highly scattering tissue via iterative multi-photon adaptive compensation technique,” Opt. Express 23(5), 6145–6150 (2015).
12.Y. Wang, H. Xu, D. Li, R. Wang, C. Jin, X. Yin, S. Gao, Q. Mu, L. Xuan, and Z. Cao, “Performance analysis of an adaptive optics system for free-space optics communication through atmospheric turbulence,” Sci. Rep. 8, 1124 (2018).
13.M. Negro, M. Quintavalla, J. Mocci, A. G. Ciriolo, M. Devetta, R. Muradore, S. Stagira, C. Vozzi, and S. Bonora, “Fast stabilization of a high-energy ultrafast OPA with adaptive lenses,” Sci. Rep. 8, 4–9 (2018).
14.M. Jenne, D. Flamm, T. Ouaj, J. Hellstern, J. Kleiner, D. Grossmann, M. Koschig, M. Kaiser, M. Kumkar, and S. Nolte, “High-quality tailored-edge cleaving using aberration-corrected Bessel-like beams,” Opt. Lett. 43(13), 3164–3167 (2018).
15.G.-L. Roth, S. Rung, C. Esen, and R. Hellmann, “Microchannels inside bulk PMMA generated by femtosecond laser using adaptive beam shaping,” Opt. Express 28(4), 5801–5811 (2020).
16.P. S. Salter and M. J. Booth, “Adaptive optics in laser processing,” Light: Sci. Appl. 8(1), 110 (2019).
17.B. C. Platt and R. V. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
18.R. Irwan and R. G. Lane, “Analysis of optimal centroid estimation applied to Shack–Hartmann sensing,” Appl. Opt. 38, 6737–6743 (1999).
19.S.-H. Baik, S.-K. Park, C.-J. Kim, and B. Cha, “A center detection algorithm for Shack–Hartmann wavefront sensor,” Opt. Las. Technol. 39(2), 262–267 (2007).
20.W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980).
21.G.-M. Dai, “Modal wavefront reconstruction with Zernike polynomials and Karhunen-Loève functions,” J. Opt. Soc. Am. A 13, 1218–1225 (1996).
22.B. F. Grewe, F. F. Voigt, M. van ’t Hoff, and F. Helmchen, “Fast two-layer two-photon imaging of neuronal cell populations using an electrically tunable lens,” Biomed. Opt. Express 2(7), 2035–2046 (2011).
23.H. Ren, D. Fox, P. A. Anderson, B. Wu, and S.-T. Wu, “Tunable-focus liquid lens controlled using a servo motor,” Opt. Express 14(18), 8031–8036 (2006).
24.A. Mermillod-Blondin, E. McLeod, and C. B. Arnold, “High-speed varifocal imaging with a tunable acoustic gradient index of refraction lens,” Opt. Lett. 33(18), 2146–2148 (2008).
25.M. Duocastella, G. Vicidomini, and A. Diaspro, “Simultaneous multiplane confocal microscopy using acoustic tunable lenses,” Opt. Express 22(16), 19293–19301 (2014).
26.G. D. Love, “Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator,” Appl. Opt. 36(7), 1517–1524 (1997).
27.G. D. Love, J. V. Major, and A. Purvis, “Liquid-crystal prisms for tip-tilt adaptive optics,” Opt. Lett. 19(15), 1170–1172 (1994).
28.O. Kazasidis, S. Verpoort, and U. Wittrock, “Sensor for dynamic focus control of a deformable mirror,” Appl. Opt. 59, 5625-5630 (2020).
29.W. J. Shain, N. A. Vickers, B. B. Goldberg, T. Bifano, and J. Mertz, “Extended depth-of-field microscopy with a high-speed deformable mirror,” Opt. Lett. 42, 995–998 (2017).
30.A. Jewel, V. Akondi, and B. Vohnsen, “A direct comparison between a MEMS deformable mirror and a liquid crystal spatial light modulator in signal-based wavefront sensing,” J. Eur. Opt. Soc. 8 (2013).
31.A. Krizhevsky, I. Sutskever and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” Commun. Acm, vol. 60, no. 6, pp. 84-90, Jun. 2017.
32.S. S. Yadav and S. M. Jadhav, “Deep convolutional neural network based medical image classification for disease diagnosis,” J Big Data 6, 113 (2019).
33.C. Li, A. Moatti, X. Zhang, H. T. Ghashghaei, and A. Greenabum, “Deep learning-based autofocus method enhances image quality in light-sheet fluorescence microscopy,” Biomed. Opt. Express 12(8), 5214–5226 (2021).
34.L. Salmela, N. Tsipinakis, A. Foi, C. Billet, J. M. Dudley, and G. Genty, “Predicting ultrafast nonlinear dynamics in fibre optics with a recurrent neural network,” Nat. Mach. Intell. 3(4), 344–354 (2021).
35.H. Guo, N. Korablinova, Q. Ren, and J. Bille, “Wavefront reconstruction with artificial neural networks,” Opt. Express 14, 6456-6462 (2006).
36.L. Hu, S. Hu, W. Gong, and K. Si, “Learning-based Shack-Hartmann wavefront sensor for high-order aberration detection,” Opt. Express 27, 33504-33517 (2019).
37.F. J. de C. Juez, F. S. Lasheras, N. Roqueñí, and J. Osborn, “An ANN-Based Smart Tomographic Reconstructor in a Dynamic Environment,” Sensors 12, 8895–8911 (2012).
38.Thorlabs, introduction of Deformable Mirrors, from:https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=5056
39.Thorlabs, UV-Enhanced Aluminum Mirrors reflectance, from:https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=12393
40.M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press,1970).
41.S. S. Niu, J. X. Shen, C. Liang, and B. M. Li, “Human eye aberration measurement and correction based on micro adaptive optics system,” IEEE Eng. Med. Biol. 3, 1023-1207 (2009).
42.S. Bosch, S. Vallmitjana, A. Marzoa, J. Arines, and E. Acosta, “Using Shack-Hartmann wavefront sensors and Zernike coefficients for beam characterisation: numerical procedures”, Optical Methods for Inspection, Characterization, and Imaging of Biomaterials III 10333, 1033318 (2017).
43.V. Ye. Zavalova, and A. V. Kudryashov, “Shack-Hartmann wavefront sensor for laser beam analyses”, Proc. SPIE 4493, 277-282 (2002).
44.A. Yen, “Straightforward path to Zernike polynomials”, JM3 20(02), 020501 (2021).
45.L. Zhu, P. C. Sun, D. U. Bartsch, W. R. Freeman, and Y. Fainman, “Wave-front generation of Zernike polynomial modes with a micromachined membrane deformable mirror”, Appl. Opt. 38, 6019-6026 (1999).
46.L. Zhu, P. C. Sun, D. U. Bartsch, W. R. Freeman, and Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation”, Appl. Opt. 38, 168-176 (1999).
47.V. Lakshminarayanan, and A. Fleck, “Zernike polynomials: a guide”, J. Mod. Opt. 58(7), 545-561 (2010).
48.AMATEUR TELESCOPE OPTICS:https://www.telescope-optics.net/zernike_expansion_schemes.htm
49.Edmund optics, specification of micro-lens array #64-482, from:https://www.edmundoptics.com.tw/p/microlens-array-10-x-10mm-500mum-pitch-05deg-divergence/19194/
50.Basler, specification of CMOS camera acA2040-90um, from:https://www.baslerweb.com/en/products/cameras/area-scan-cameras/ace/aca2040-90um/
51.AMATEUR TELESCOPE OPTICS:https://www.telescope-optics.net/monochromatic_eye_aberrations.htm
52.Unice, specification of objevtive MOS-3, from:https://www.unice-eo.com/en/product/image-testing-components_1630/microscopy_2816/international-standard-microscope-objectives-1805/mso-3-1665539994_15382
53.Basler, specification of CMOS camera daA2500-14um, from:https://www.baslerweb.com/en/products/cameras/area-scan-cameras/dart/daa2500-14um-cs-mount/
54.B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (John Wiley & Sons, Inc., 2019).
55.E. Hecht, Optics, 5th ed. (Pearson, 2016).
56.I. Miyamoto and H. Maruo, “Effects of misalignment in focusing CO2 laser beam by parabolic mirror,” ICALEO 1993, 341–349 (1993).
57.AWS, introduction of Deep learning, from:https://aws.amazon.com/tw/what-is/deep-learning/
58.Medium, introduction of CNN, from:https://chih-sheng-huang821.medium.com/卷積神經網路-convolutional-neural-network-cnn-卷積運算-池化運算-856330c2b703
59.Cupoy, introduction of max pooling, from:https://www.cupoy.com/qa/club/ai_tw
60.796t, introduction of GAP, from:https://www.796t.com/content/1547374354.html
61.D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv:1412.6980v9 (2014).
62.K. You, M. Long, J.Wang, M. I. Jordan, “How does learning rate decay help modern neural networks?,” arXiv:1908.01878v2 (2019).
63.Medium, introduction of MLP, from:https://medium.com/手寫筆記/learn-multilayer-perceptron-with-tensorflow-e73062ff0844
64.Medium, introduction of dropout layer, from:https://medium.com/手寫筆記/使用-tensorflow-了解-dropout-bf64a6785431