適應性光學(adaptive optics，AO)是一種透過控制波前修正元件，以即時修正光束在傳播過程中因環境擾動、介質折射率變化或系統誤差所造成波前畸變之技術，進而提升光束品質、成像解析度與聚焦效果。此技術已廣泛應用於天文觀測、光通信、組織顯微成像以及高精度雷射加工等領域。本論文選用可調變聚焦鏡(deformable mirror，DM)作為波前修正元件，並以Shack-Hartmann波前感測器(Shack-Hartmann wavefront sensor，SHWS)量測波前變化，再透過Zernike多項式作為數學模型描述光學像差組成。
在傳統AO系統中，通常使光束垂直入射DM，並搭配分光鏡(beam splitter)完成光路分離。然而，分光鏡不僅會增加光學系統配置複雜度，也會造成額外能量損耗，對於高功率雷射或能量效率要求較高之應用將產生明顯限制。因此，本研究採用45度斜向入射DM之光路架構，取代傳統垂直入射搭配分光鏡的設計，以降低光學元件造成之能量損失，並簡化整體系統架構。然而，斜向入射會使DM膜面變形與波前響應之間的對應關係更加複雜，進而引入額外的非線性與模態耦合效應，使傳統鑑別方法[張家源2.1]在建模精度與可辨識項數上受到限制。
為改善上述問題，本論文導入深度學習(deep learning)技術，建立深度神經網路(deep neural network，DNN)模型，以學習SHWS量測資訊、Zernike像差模態與DM驅動電壓之間的非線性映射關係。首先建立以SHWS影像為輸入之Zernike係數預測模型，直接預測前15項Zernike係數，以簡化傳統重心演算法、斜率計算與擬反矩陣求解之流程。接著進一步建立用於DM控制之DNN模型，透過聚焦點位移矩陣預測對應之DM驅動電壓，使系統能夠在斜向入射架構下完成較高階像差之鑑別與補償。實驗結果顯示，相較於傳統鑑別方法，本研究所提出之DNN鑑別方法可提升DM控制之可辨識範圍，並將Zernike可建模項數由原本8項拓展至15項。
此外為滿足即時補償需求，本研究透過LabVIEW搭配Python Node[張家源3.1]建構跨平台控制介面，整合SHWS影像擷取、Zernike係數計算、Python模型推論、GPU加速角頻譜法模擬以及DM電壓輸出。由單次閉迴路迭代時間分析可知，整體流程約需33.958 ms，對應更新率約為29.45 Hz，顯示此系統已具備即時補償之基本能力。最後，本研究進一步以熱源與風流作為動態干擾，驗證系統於時變像差條件下之補償效果。結果顯示，所建立之斜向入射DM鑑別與閉迴路控制系統能有效降低熱干擾造成之波前畸變，並改善聚焦點品質，證明本方法應用於即時光學像差補償具有可行性。

Adaptive optics (AO) is a real-time wavefront correction technique used to improve beam quality, imaging resolution, and focusing performance. In this study, a deformable mirror (DM) and a Shack-Hartmann wavefront sensor (SHWS) are used to measure and correct optical aberrations, which are described by Zernike polynomials. To reduce energy loss and simplify the system, this study adopts a 45-degree oblique-incidence DM configuration instead of the conventional beam-splitter-based structure. However, oblique incidence introduces nonlinear wavefront responses and modal coupling, limiting the performance of the traditional three-step identification method. Therefore, a deep neural network (DNN)-based method is proposed to identify Zernike aberrations and predict the corresponding DM driving voltages. Experimental results show that the identifiable Zernike terms are extended from 8 to 15. A real-time closed-loop control system is further implemented through LabVIEW Python Node, integrating SHWS image acquisition, model inference, GPU-accelerated simulation, and DM voltage output. The system achieves a closed-loop iteration time of 33.958 ms, corresponding to 29.45 Hz. Dynamic thermal disturbance experiments confirm that the proposed system can effectively reduce wavefront distortion and improve focal spot quality.

1.R. Davies and M. Kasper, “Adaptive optics for astronomy,” Annu. Rev. Astron. Astrophys. 50, 305–351 (2012).
2.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).
3.M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light Sci. Appl. 3, e165 (2014).
4.R. D. Simmonds, P. S. Salter, A. Jesacher, and M. J. Booth, “Three dimensional laser microfabrication in diamond using a dual adaptive optics system,” Opt. Express 19(24), 24122–24128 (2011).
5.A. Jesacher and M. J. Booth, “Parallel direct laser writing in three dimensions with spatially dependent aberration correction,” Opt. Express 18(20), 21090–21099 (2010).
6.M. Najafabadi et al., “Deep learning applications and challenges in big data analytics,” J. Big Data 2, 1 (2015).
7.D. Shen, G. Wu, and H. I. Suk, “Deep learning in medical image analysis,” Annu. Rev. Biomed. Eng. 19, 221–248 (2017).
8.S. Revay and M. Teschke, “Multiclass language identification using deep learning on spectral images of audio signals,” arXiv preprint arXiv:1905.04348 (2019).
9.S. A. Ramakrishna et al., “A dissipative quantum mechanical beam-splitter,” Opt. Express 2, 29–34 (1998).
10.P. S. Salter and M. J. Booth, “Adaptive optics in laser processing,” Light Sci. Appl. 8, 110 (2019).
11.L. Zhu et al., “Wavefront generation of Zernike polynomial modes with a micromachined membrane deformable mirror,” Appl. Opt. 38(28), 6019–6026 (1999).
12.L. Zhu et al., “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38(1), 168–176 (1999).
13.Z. Xu, P. Yang, K. Hu, B. Xu, and H. Li, “Deep learning control model for adaptive optics systems,” Appl. Opt. 58, 1998–2009 (2019).
14.W.-S. Huang, C.-W. Hsu, F.-C. Hsu, C.-Y. Lin, and S.-J. Chen, “Model predictive control-based adaptive optics system with deep-learning Shack-Hartmann wavefront sensor,” Proc. SPIE 12624, 126241C (2023).
15.A. J. del Águila-Carrasco et al., “The effect of aberrations on objectively assessed image quality and depth of focus,” J. Vis. 17, 2 (2017).
16.B. C. Platt and R. V. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
17.W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980).
18.R. G. Lane and M. Tallon, “Wave-front reconstruction using a Shack-Hartmann sensor,” Appl. Opt. 31, 6902–6908 (1992).
19.J. W. Cha, J. Ballesta, and P. T. C. So, “Shack-Hartmann wavefront-sensor-based adaptive optics system for multiphoton microscopy,” J. Biomed. Opt. 15, 046022 (2010).
20.J. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994).
21.Basler AG. (n.d.). CCD vs. CMOS: Differences between the sensors. Retrieved May 12, 2026, from https://www.baslerweb.com/en-us/learning/ccd-cmos/
22.IDS Imaging Development Systems GmbH. (n.d.). UI-3370CP-M-GL Rev. 2. Retrieved May 12, 2026, from https://en.ids-imaging.com/store/ui-3370cp-rev-2.html
23.Basler AG. (n.d.). ace acA2040 90μm – USB 3.0 camera. Retrieved May 12, 2026, from https://www.baslerweb.com/en-us/shop/aca2040-90um/
24.Edmund Optics Inc. (n.d.). Microlens Array 10×10 mm, 500 μm Pitch, 0.5° Divergence. Retrieved May 12, 2026, from https://www.edmundoptics.com/p/microlens-array-10-x-10mm-500mum-pitch-05deg-divergence/19194/
25.B. Pathak and B. R. Boruah, “Zonal wavefront sensing with enhanced spatial resolution,” Opt. Lett. 41(23), 5600–5603 (2016).
26.V. N. Mahajan, “Zernike circle polynomials and optical aberrations of systems with circular pupils,” Appl. Opt. 33(34), 8121–8124 (1994).
27.F. Zernike, “Diffraction theory of the knife-edge test and its improved form, the phase-contrast method,” Mon. Not. R. Astron. Soc. 94, 377–384 (1934).
28.X. Cheng, A. Bradley, S. Ravikumar, and L. N. Thibos, “Visual impact of Zernike and Seidel forms of monochromatic aberrations,” Optom. Vis. Sci. 87, 300–312 (2010).
29.R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
30.J. Alda and G. D. Boreman, “Zernike-based matrix model of deformable mirrors: optimization of aperture size,” Appl. Opt. 32, 2431–2438 (1993).
31. J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, Vol. 11, 28–39 (1992).
32.N. Kuo and T. Chao, “Zernike polynomials and their applications,” J. Opt. 24(12), 123001 (2022).
33.Boston Micromachines Corp. (n.d.). Standard Deformable Mirrors. Retrieved May 12, 2026, from https://bostonmicromachines.com/products/deformable-mirrors/standard-deformable-mirrors/
34.Thorlabs Inc. (n.d.). Piezoelectric Deformable Mirrors. Retrieved May 12, 2026, from https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=5056
35.Thorlabs Inc. (n.d.). UV Enhanced Aluminum Mirrors. Retrieved May 12, 2026, from https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=12393
36.Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
37.D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representations by back-propagating errors,” Nature 323, 533–536 (1986).
38.Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86, 2278–2324 (1998).
39.A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” in Advances in Neural Information Processing Systems 25, 1097–1105 (2012).
40.J. L. Elman, “Finding structure in time,” Cogn. Sci. 14, 179–211 (1990).
41.A. Graves, A. Mohamed, and G. Hinton, “Speech recognition with deep recurrent neural networks,” in Proc. IEEE Int. Conf. Acoust. Speech Signal Process., 6645–6649 (2013).
42.M. Abadi et al., “TensorFlow: a system for large-scale machine learning,” in Proc. 12th USENIX Symp. Operating Systems Design and Implementation, 265–283 (2016).
43.CHTseng. (2017, July 24). Neural Networks (一). Retrieved May 12, 2026, from https://chtseng.wordpress.com/2017/07/24/neural-networks-%E4%B8%80/
44.Jadon, S. (2018). Introduction to Different Activation Functions for Deep Learning. Medium. Retrieved May 12, 2026, from
https://medium.com/@shrutijadon/survey-on-activation-functions-for-deep-learning-9689331ba092
45.Huang, T. (2018, March 27). 卷積神經網路(Convolutional neural network, CNN) — CNN運算流程. Retrieved May 12, 2026, from https://chih-sheng-huang821.medium.com/%E5%8D%B7%E7%A9%8D%E7%A5%9E%E7%B6%93%E7%B6%B2%E8%B7%AF-convolutional-neural-network-cnn-cnn%E9%81%8B%E7%AE%97%E6%B5%81%E7%A8%8B-ecaec240a631
46.TensorFlow. (2024, August 15). Better performance with tf.function. Retrieved May 12, 2026, from https://www.tensorflow.org/guide/function
47.J. T. Yang et al., “Remote focusing with dynamic aberration elimination by model-based adaptive optics,” Opt. Laser Technol. 169, 110126 (2024).
48.G. F. Franklin, J. D. Powell, and M. L. Workman, Digital Control of Dynamic Systems, 3rd ed. (Ellis-Kagle Press, 1998).
49.Thorlabs Inc. (n.d.). DMP40/M-F01 40-Actuator Piezo Deformable Mirror, Tip-Tilt Actuation, UV-Enhanced Aluminum, M4 and M6 Taps. Retrieved May 12, 2026, from https://www.thorlabs.com/piezoelectric-deformable-mirrors?pn=DMP40%2FMF01&aID=f867c26bca47a5393e030f3d9871a648&aC=1&aE=1&aN=1&tabName=Graphs
50.J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
51.Thorlabs. (2021). Piezoelectric Deformable Mirror DMP40 Operation Manual (Version 2.8). Retrieved May 12, 2026, from https://www.thorlabs.com/item/DMP40_MF01?aID=f867c26bca47a5393e030f3d9871a648&aC=1
52.Thorlabs, Inc. (n.d.). MEMS-Based Deformable Mirrors. Retrieved May 12, 2026, from https://www.thorlabs.com/mems-based-deformable-mirrors?tabName=Overview