適應性光學(adaptive optics，AO)一直是近年來許多研究重點發展之對象，已經在天文學研究、雷射加工、和生物觀測等領域上有顯著的成效，於生物樣本的觀察中，遙控調焦更是未來趨勢的潛力。
本論文根據現有的AO成果，將其作進一步的應用：與現場可程式邏輯閘陣列(field-programmable gate array，FPGA)做結合，並以常見的波前感測器(Shack-Hartmann wavefront sensor，SHWS)作為閉迴路校正之感測器，使用Zernike運算式的初階和高階項為波前分析背景，將系統干擾由32通道之可調變式聚焦鏡(deformable mirror，DM)消除，並希望以此結果延伸應用，發展基於適應性光學的軸向掃描等技術。在調焦掃描應用上，以特定像差：散焦(defocus aberration)，作為遙控調焦的關鍵變因，在消除系統干擾的同時，控制聚焦位置，實現校正與遙控調焦並存之成效，其成果於幾何光學之計算後，與調控之散焦像差十分相近於線性關係。本實驗最後以另一DM輸出光學靜態干擾和常見之熱能干擾影響系統，展現於低頻率干擾組合下，仍能將補償與軸向掃描技術結合之可能性。

Remote focusing by using deformable mirror (DM) performs fast and responsive axial scanning ability. To maintain the laser focusing quality, the optical aberrations can be corrected simultaneously by DM. A model-based adaptive optics (AO) is adopted to solve the DM channel coupling effect and reduce the control complexity. A Shack-Hartmann wavefront sensor (SHWS) estimates and decomposes the aberrations to Zernike polynomials. According to the feedback of Zernike coefficients to AO system, the proposed independent closed-loop controller for each Zernike mode shows rapid response to the command vector of the desired wavefront. The command vector consists of the desired coefficient value of defocus mode for remote focusing while other Zernike modes keep zero indicating aberration free. The proposed remote focusing with model-based AO shows rapid convergence to track the desired axial position and eliminates the present aberrations to more than 10 dB signal-to-noise ratio (SNR). Moreover, the low-frequency thermal disturbance in system is eliminated experimentally while the accurate laser focus quality and position remain steady.

1. R. K. Tyson, Principles of Adaptive Optics, (CRC, 1998).
2. J. Liang, D. R. Williams, and D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics”, J. Opt. Soc. Am. A 14(11), 2884 (1997).
3. M. Neitz, J. Carroll, A. Renner, H. Knau, J. Werner, and J. Neitz, “Variety of genotypes in males diagnosed as dichromatic on a conventional clinical anomaloscope”, Vis. Neurosci. 21(3), 205-216 (2004).
4. J. Winderickx, E. Sanocki, D. T. Lindsey, D. Y. Teller, A. G. Motulsky, and S. S. Deeb, “Defective colour vision associated with a missense mutation in the human green visual pigment gene”, Nat. Genet. 1(4), 251-256 (1992).
5. C. Yuodelis, and A. Hendrickson, “A qualitative and quantitative analysis of the human fovea during development”, Vis. Res. 26(6), 847-855 (1986).
6. P. Godara, A. M. Dubis, A. Roorda, J. L. Duncan, and J. Carroll, “Adaptive Optics Retinal Imaging: Emerging Clinical Applications”, Optom. Vis. Sci. 87(12), 930-941 (2010).
7. C. Rodríguez, and N. Ji, “Adaptive optical microscopy for neurobiology”, Curr. Opin. 50, 83-91 (2018).
8. P. Rajaeipour, A. Dorn, K. Banerjee, H. Zappe, and Ç. Ataman, “Fully refractive adaptive optics fluorescence microscope using an optofluidic wavefront modulator”, Opt. Express 28, 9944-9956 (2020).
9. X. Tao, O. Azucena, M. Fu, Y. Zuo, D. C. Chen, and J. Kubby, “Adaptive optics microscopy with direct wavefront sensing using fluorescent protein guide stars”, Opt. Lett. 36, 3389-3391 (2011).
10. C. Ahn, B. Hwang, K. Nam, H. Jin, T. Woo, and J. H. Park, “Overcoming the penetration depth limit in optical microscopy: Adaptive optics and wavefront shaping”, J. Innov. Opt. Health Sci. 12(04), 1930002 (2019).
11. T. Dumur, S. Duncan, K. Graumann, S. Desset, R. S. Randall, O. M. Scheid, D. Prodanov, C. Tatout, and C. Baroux, “Probing the 3D architecture of the plant nucleus with microscopy approaches: challenges and solutions”, Nucleus 10(1), 181-212 (2019).
12. M. E. Siemons, N. A. K. Hanemaaijer, M. H. P. Kole, and L. C. Kapitein, “Robust adaptive optics for localization microscopy deep in complex tissue”, Nat. Commun. 12(1), 1-9 (2021).
13. B. Platt, and R. Shack, “History and principles of Shack-Hartmann wavefront sensing”, J. Refract. Surg. 17(5), s573 (2001).
14. J. Pfund, N. Lindlein, and J. Schwider, “Dynamic range expansion of a Shack–Hartmann sensor by use of a modified unwrapping algorithm”, Opt. Lett. 23, 995-997 (1998).
15. N. Lindlein, J. Pfund, and J. Schwider, “Algorithm for expanding the dynamic range of a Shack-Hartmann sensor by using a spatial light modulator array”, Opt. Eng. 40(5), 837 (2001).
16. 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).
17. R. W. Duffner, and R. Q. Fugate, The Adaptive Optics Revolution: A History, (University of New Mexico Press, 2009).
18. H. W. Babcock, “The possibility of compensating astronomical seeing”, Publ. Astron. Soc. Pac. 65, 229 (1953).
19. D. P. Greenwood, “Bandwidth specification for adaptive optics systems*”, J. Opt. Soc. Am. 67, 390-393 (1977).
20. F. Roddier, “Curvature sensing and compensation: a new concept in adaptive optics”, Appl. Opt. 27, 1223-1225 (1988).
21. Y. Ata, and Ol. Korotkova, “Adaptive optics correction in natural turbulent waters”, J. Opt. Soc. Am. A 38, 587-594 (2021).
22. Y. Zheng, J. Chen, C. Wu, W. Gong, and K. Si, “Adaptive optics for structured illumination microscopy based on deep learning”, Cytometry A 99(6), 622-631 (2021).
23. S. W. Paine, and J. R. Fienup, “Machine learning for improved image-based wavefront sensing,” Opt. Lett. 43, 1235-1238 (2018).
24. 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)
25. W. Denk, J. Strickler, and W. Webb, “Two-photon laser scanning fluorescence microscopy”, Science 248(4951), 73-76 (1990).
26. T. A. Pologruto, B. L. Sabatini, and K. Svoboda, “ScanImage: Flexible software for operating laser scanning microscopes”, Biomed. Eng. Online 2(1), 13(2003).
27. K. Dobek, “Motionless microscopy with tunable thermal lens”, Opt. Express 26, 3892-3902 (2018).
28. K. F. Tehrani, C. V. Latchoumane, W. M. Southern, E. G. Pendleton, A. Maslesa, L. Karumbaiah, J. A. Call, and L. J. Mortensen, “Five-dimensional two-photon volumetric microscopy of in-vivo dynamic activities using liquid lens remote focusing”, Biomed. Opt. Express 10, 3591-3604 (2019).
29. B. W. Hendriks, S. Kuiper, and M. A. J. V. As, T. W. Tukker, “Electrowetting-Based Variable-Focus Lens for Miniature Systems”, Opt. Rev. 12(3), 255-259 (2005).
30. R. Marks, D. L. Mathine, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Astigmatism and defocus wavefront correction via Zernike modes produced with fluidic lenses”, Appl. Opt. 48, 3580-3587 (2009).
31. L. Liu, L. Li, Z. Zhao, Y. Wang, “A remote laser focusing system with spatial light modulator”, Comput. Commun. 154, 92-98 (2020).
32. H. Jiang, C. Wang, B. Wei, W. Gan, D. Cai, and M. Cui, “Long-range remote focusing by image-plane aberration correction”, Opt. Express 28, 34008-34014 (2020).
33. M. Žurauskas, O. Barnstedt, M. Frade-Rodriguez, S. Waddell, and M. J. Booth, “Rapid adaptive remote focusing microscope for sensing of volumetric neural activity”, Biomed. Opt. Express 8, 4369-4379 (2017).
34. E. J. Botcherby, R. Juškaitis, M. J. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy”, Opt. Commun. 281(4), 880-887 (2008).
35. A. V. Kudryashov, A. L. Rukosuev, A. N. Nikitin, I. V. Galaktionov, and J. V. Sheldakova, “Real-time 1.5 kHz adaptive optical system to correct for atmospheric turbulence”, Opt. Express 28, 37546-37552 (2020)
36. S. Hu, B. Xu, X. Zhang, J. Hou, J. Wu, and W. Jiang, “Double-deformable-mirror adaptive optics system for phase compensation”, Appl. Opt. 45, 2638-2642 (2006)
37. Y. Yang, W. Chen, J. L. Fan, and N. Ji, “Adaptive optics enables aberration-free single-objective remote focusing for two-photon fluorescence microscopy”, Biomed. Opt. Express 12, 354-366 (2021)
38. T. Chakraborty, B. Chen, S. Daetwyler, B.-J. Chang, O. Vanderpoorten, E. Sapoznik, C. F. Kaminski, T. P. J. Knowles, K. M. Dean, and R. Fiolka, “Converting lateral scanning into axial focusing to speed up three-dimensional microscopy”, Light: Sci. Appl. 9, 165 (2020).
39. W. H. Southwell, “Wave-front estimation from wave-front slope measurements”, J. Opt. Soc. Am. 70, 998-1006 (1980).
40. 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).
41. V. Ye. Zavalova, and A. V. Kudryashov, “Shack-Hartmann wavefront sensor for laser beam analyses”, Proc. SPIE 4493, 277-282 (2002).
42. A. Yen, “Straightforward path to Zernike polynomials”, JM3 20(02), 020501 (2021).
43. 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).
44. 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).
45. V. Lakshminarayanan, and A. Fleck, “Zernike polynomials: a guide”, J. Mod. Opt. 58(7), 545-561 (2010).
46. Edmund optics, specification of micro-lens array #64-482,from: https://www.edmundoptics.com/p/microlens-array-10-x-10mm-500mum-pitch-05deg-divergence/19194/.
47. STEMMER IMAGING, introduction of CameraLink, from: https://www.stemmer-imaging.com/en-gb/knowledge-base/cameralink/?choose-site=active
48. WIKIPEDIA, introduction of CameraLink, from: https://en.wikipedia.org/wiki/Camera_Link
49. NI, introduction of the advantages and disadvantages of various types of cameras, from: https://knowledge.ni.com/KnowledgeArticleDetails?id=kA00Z0000019LNhSAM&l=zh-TW
50. WIKIPEDIA, introduction of FPGA, from: https://en.wikipedia.org/wiki/Field-programmable_gate_array
51. HUA NAN SHEN NEWS, introduction of FPGA, from: https://events.entrust.com.tw/news/FPGA-478
52. HardwareBee, introduction of the difference between FPGA and CPU, from: https://hardwarebee.com/fpga-vs-cpu-difference/
53. Basler, specification of acA2040-90um, from: https://www.baslerweb.com/en/products/cameras/area-scan-cameras/ace/aca2040-90um/
54. RP PHOTONICS, introduction of Deformable Mirrors, from: https://www.rp-photonics.com/deformable_mirrors.html
55. Thorlabs, introduction of Deformable Mirrors, from:
https://www.Thorlabs.com/newgrouppage9.cfm?objectgroup_id=3258
56. ACTIVE OPTICAL SYSTEMS, specification of deformable mirrors, from: https://aos-llc.com/membrane-dms/
57. DIGILENT, specification of Pmod DA2-12bit D/A outputs, from:
https://digilent.com/shop/pmod-da2-two-12-bit-d-a-outputs/
58. K. Okamura, and T. Kobayashi, “Octave-spanning carrier-envelope phase stabilized visible pulse with sub-3-fs pulse duration”, Opt. Lett. 36, 226-228 (2011).
59. J. Garduño-Mejía, A. H. Greenaway, and D. T. Reid, “Programmable spectral phase control of femtosecond pulses by use of adaptive optics and real-time pulse measurement”, J. Opt. Soc. Am. B 21, 833-843 (2004).
60. J. Garduño-Mejía, A. H. Greenaway, and D. T. Reid, “Designer femtosecond pulses using adaptive optics”, Opt. Express 11, 2030-2040 (2003).
61. Flexible Optical B.V. OKO TECH, specification of linear deformable mirror, from: http://www.okotech.com/images/pdfs/typical-MMDM30-39.pdf
62. ANALOG DEVICES, specification of AD5380, from: https://www.analog.com/media/en/technical-documentation/data-sheets/ad5380.pdf
63. Basler, specification of acA2040-180km, from: https://www.baslerweb.com/en/products/cameras/area-scan-cameras/ace/aca2040-180km/
64. OPM, introduction of MO-14X, from: https://www.opmount.com.tw/cht/Product_list3/270.html
65. Basler, specification of daA2500-14um, from: https://www.baslerweb.com/en/products/cameras/area-scan-cameras/dart/daa2500-14um-cs-mount/
66. WIKIPEDIA, introduction of PID controller, from: https://en.wikipedia.org/wiki/PID_controller
67. NI, introduction of PID controller, from: https://www.ni.com/zh-tw/innovations/white-papers/06/pid-theory-explained.html
68. G.F. Franklin, J.D. Powell and M. Workman, Digital Control of Dynamic Systems, (Reading:Addison Wesley Longman, 1997).
69. Y. C. Wu, J. C. Chang, and C. Y. Chang, “Adaptive optics for dynamic aberration compensation using parallel model-based controllers based on a field programmable gate array”, Opt. Express 29, 21129-21142 (2021).
70. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, (John Wiley & Sons Inc., 1991).