本論文研發出利用液晶(liquid crystal device，LCD)移相干涉術(phase-shift interferometry，PSI)來偵測光波前的適應性光學(adaptive optics)系統，可用來即時修正因外來擾動所造成之像差。它主要包含三個部份：波前感測器(wavefront sensor，WFS)、波前修正器(wavefront corrector)與補償控制器(reconstruction controller)。
　　文中提出Mach-Zehnder之徑向剪切式(radial shear)干涉術架構成功地動態偵測波前，此方式在光路設計上可避免Sagnac架構波前耦合問題。LCD經由一精準相位校正方式與瞬間向列驅動方法，可正確快速地於5ms內完成三步PSI動作，並搭配光二極體陣列(photodiode array，PA)來量測干涉光強，可即時偵測重建波前相位變化情形。此干涉式波前偵測器之相位資訊即時回饋至嵌入式(embedded)數位訊號處理器(digital signal processor，DSP)，經由比例積分微分(proportional-integral-derivative，PID)控制法則計算出控制訊號，再經由可調變聚焦鏡(deformable mirror，DM)來動態修正波前。目前，整體適應性光學系統於五個輸出入通道下，控制迴圈速度可達30Hz以上。於數Hz熱干擾下，雜訊可被抑制20dB以上，穩態相位標準差低於0.02π rms，而輸出光的Strehl ratio可從0.5大幅升至0.9，明顯增加輸出光之聚焦效率，降低因外來干擾所造成之像差問題。

An adaptive optics system with liquid crystal device (LCD) phase-shift interferometry (PSI) has been developed to compensate aberration in real time. The adaptive optics system consists of three main components: wavefront sensor, wavefront corrector, and reconstruction controller.
In this thesis, a Mach-Zehnder radial shearing interferometer has successfully detected the dynamic wavefront. Unlike the Sagnac setup, the Mach-Zehnder interferometer can avoid the coupling effect between the measurement wavefront and reference wavefront from the interferometry system.
To measure the variation of wavefront in real time, we use the LCD to rapidly and precisely achieve PSI within 5ms based on a precise phase calibration and overdriving method, and photodiode array (PA) to record the three interference patterns. The wavefront signals are transmitted to the embedded digital signal processor (DSP) based on the proportional-integral-derivative (PID) control rule to generate the control signals which will be sent to DM. Thus, the aberration of the wavefront are corrected dynamically.
The developed multichannel adaptive optics system has the bandwidth of the control loop up to 30Hz. The experimental results to control several Hertz thermal turbulence demonstrate that the steady state error of the wavefront phase was under 0.02π rms and the signal-to-noise ratio improvement is better than 20dB. Also, the Strehl ratio of the focusing spot can be increased from 0.5 to 0.9.

[1] E. Hecht, Optics. 4th ed. Addison Wesley (2002).
[2] R.K. Tyson, Principles of Adaptive Optics. 2nd ed. Academic (1998).
[3] H.B. Rosenstock and J.H. Hancock, “Light propagation through a moving gas,” Appl. Opt. 10, 1299-1307 (1971).
[4] F.G. Gebhardt, “High power laser propagation,” Appl. Opt. 15, 1479-1493 (1976).
[5] R.K. Tyson, “Adaptive optics and ground-to-space laser communications” Appl. Opt. 35, 3640-3646 (1996).
[6] E.J. Fernndez, I. Iglesias, and P. Artal, “Closed-loop adaptive optics in the human eye,” Opt. Lett. 26, 746-748 (2001).
[7] D.C.L Cheung, T.H. Barnes, A.R.D Somervell, and T.G. Haskell, “Aberration correction using a multi-segment mirror with feedback
interferometry,” Opt. Lasers Eng. 41, 113-125 (2004).
[8] D.C.L Cheung, T.H. Barnes, T.G. Haskell, “Feedback
interferometry with membrane mirror for adaptive optics,” Opt. Commun. 218, 33-41 (2003).
[9] T. Shirai, “Liquid-crystal adaptive optics based on feedback interferometry for high-resolution retinal imaging,” Appl. Opt. 41, 4013-4023 (2002).
[10] T. Shirai, T.H. Barnes, and T.G. Haskell, “Adaptive wave-front correction by means of all-optical feedback interferometry,” Opt. Lett. 25, 773-775 (2000).
[11] H.W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229 (1953).
[12] L.C. Bradley and J. Herrmann, “Phase compensation for thermal blooming,” Appl. Opt. 13, 331-334 (1974).
[13] M.C. Roggemann and B. Welsh, Image Through Turbulence. CRC Press (1996).
[14] F.G. Smith ed., Atmospheric Propagation of Radiation. SPIE (1993).
[15] D.L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–61 (1982).
[16] J.-P. Gaffard and G. Ledanois, “Adaptive optical transfer function modeling,” Proc. SPIE 1542, 34-45 (1991).
[17] D.M. Alloin and J.-M. Mariotti ed., Adaptive Optics for Astronomy. Kluwer Academic (1994).
[18] S.R. Restaino, W. Junor, and N. Duric ed., Catching the Perfect Wave: Adaptive Optics and Interferometry in the 21st Century Astronomical Society of the Pacific Conference (1999).
[19] F. Roddier ed., Adaptive Optics in Astronmy. Cambridge University Press (1999).
[20] G.D. Boreman and C. Dainty, “Zernike expansions for non-Kolmogorov turbulence,” J. Opt. Soc. Am. A. 13, 517 (1996).
[21] R.R. Parenti and R.J. Sasiela, “Laser-guide-star systems for astronomical applications,” J. Opt. Soc. Am. A 11, 288–309 (1994).
[22] A.T. Young, “Seeing: Its cause and cure,” Astrophys. J. 189, 587–604 (1974).
[23] L.M. Frantz, A.A. Sawchuk, and W. von der Ohe, “Optical phase measurement in real time,” Appl. Opt. 18, 3301-3306 (1979).
[24] D. Malacara ed., Optical Shop Testing. Wiley (1992).
[25] S.-K. Park, S.-H. Baik, C.-J. Kim, and S.W. Ra, “A study on a fast measuring technique of wavefront using a Shack–Hartmann sensor,” Optics & Laser Technology 34, 687-694 (2002).
[26] http://www.meadowlark.com/
[27] 張智強，適應性光學之系統鑑別，中央大學機械工程所碩士論文，2004。
[28] http://www.agiloptics.com/
[29] R.J. Noll, “Zernike polinomials and atmospheric turbulence, ” J. Opt. Soc. Am. 66, 207-211 (1976).
[30] D. Li, H. Chen, and Z. Chen, “Simple algorithms of wavefront reconstruction for cyclic radial shearing interferometer, ” Opt. Eng. 41, 1893-1898 (2002).
[31] J.Y. Wang and D.E. Silva, “Wave-front interpretation with Zernike polynomials, ” Appl. Opt. 19, 1510-1518 (1980).
[32] J. Herrmann, ‘‘Phase variance and Strehl ratio in adaptive optics, ” J. Opt. Soc. A 9, 2257–2258(1992).