適應性光學系統(adaptive optics system，AOS)主要包含三個部分：波前感測器(wavefront sensor)、波前修正器(wavefront corrector)與補償控制器(reconstruction controller)。本論文主要以自製的Shack-Hartmann波前感測器(Shack-Hartmann wavefront sensor，SHWS)，搭配影像解碼器電路使感測系統達到30 Hz的速度，再利用現場可編程輯閘陣列(field programmable gate array，FPGA)接收資訊、演算法的運算並控制可調變聚焦鏡(deformable mirror，DM)。控制系統採用32通道DM來做為波前修正元件以補償波前相位干擾，實現基於FPGA之SHWS應用於適應性光學系統，可即時補償外來干擾所造成的像差。
SHWS、影像解碼器電路和FPGA所組成的系統主要是為了讓適應性光學系統達到即時修正，不須透過電腦，透過電腦會因多重任務執行的設計，會使得在高速時發生控制迴圈無法保持穩定，而本論文發展的系統是靠著硬體時脈在運行，所以可以維持固定速度。自製SHWS的前端的波前感測部分是使用Shack-Hartmann架構，藉由感光耦合元件(CCD)上的聚焦光點位置得到波前資訊，並以Zernike模型重建波前，使用多通道輸入及多通道輸出(multichannel-input-multichannel-output，MIMO)系統鑑別的動作先得到系統的狀態模型，利用linear-quadratic-integral (LQI)的控制概念與系統模型設計出所要的控制器，此適應性光學系統速度已到達30 Hz，並降低外來干擾所造成之像差，可以將受干擾輸出光的Strehl ratio提升1.75倍，有效的提高輸出雷射光的聚焦效率。

An adaptive optics system (AOS) consists of three main components: wavefront sensor, wavefront corrector, and reconstruction controller. This thesis has developed a Shack-Hartmann wavefront sensor (SHWS) that can achieve 30 Hz frame rate via a video decoder circuit. Moreover, a 32-channel deformable mirror (DM) is used to compensate the phase distortion from external disturbances. A field programmable gate array (FPGA)-based Shack-Hartmann wavefront sensor has been setup for AOS, and it can compensate the optical aberration from surrounding environment in real time.
The overall system of the wavefront sensor is composed of a lab-made SHWS, a video decoder circuit, and a FPGA-based control model. A FPGA-based control model not a CPU base, the AOS can achieve a real-time compensation. Due to the multitasking operation system of a CPU-based PC Window system, the timer of the control loop will be unstable at a speed higher than 10 Hz. The lab-made wavefront sensing system depends on the hardware clock of the FPGA, so it can maintain a fixed speed easily. The frontend of the wavefront sensing system is based the Shack-Hartmann configuration. The wavefront information is obtained by positioning the focal spots on a charge coupled device camera, and then uses a Zernike model to remodel the wavefront information. The system between the DM and the SHWS is identified by a multichannel-input-multichannel-output (MIMO) state-space system identification algorithm, and then the controller is designed by a linear-quadratic-integral (LQI) controller via the identified system model. Currently, the lab-made AOS can reduce the aberrations caused by external disturbances at control loop of 30 Hz and the Strehl ratio of focusing spot is increased up to 1.75 times.

[1] R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, 1998).
[2] P. Kern, “Adaptive optics prototype system for infrared astronomy. I. System description,” SPIE Proc. 1271, 243-251 (1990).
[3] J. Porter, H. Queener, J. Lin, K. Thorn, and A. A. S. Awwal, Adaptive Optics for Vision Science: Principles, Practices, Design, and Applications (Wiley, 2006).
[4] A. Greenaway and J. Burnett, Industrial and Medical Applications of Adaptive Optics (IOP, 2004).
[5] R. K. Tyson, “Bit-error rate for free-space adaptive optics laser communications,” J. Opt. Soc. Am. A 19, 753-758 (2002).
[6] H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229-236 (1953).
[7] N. Hubin and L. Noethe, “Active optics, adaptive optics, and laser guide stars,” Sci. 262, 1390-1394 (1993).
[8] G. Goodno, H. Komine, S. McNaught, S. Weiss, S. Redmond, W. Long, R. Simpson, E. Cheung, D. Howland, P. Epp, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers ,” Opt. Lett. 31, 1247-1249 (2006).
[9] E. J. Fernandez, I. Iglesias, and P. Artal, “Closed-loop adaptive optics in the human eye,” Opt. Lett. 26, 746-748 (2001).
[10] B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, S573-S577 (2001).
[11] J. Schwiegerling and D. R. Neal, “Historical development of the Shack- Hartmann wavefront sensor,” in Legends in Applied Optics, R. Shannon, R. Shack, J. E. Harvey, and R. B. Hooker eds. SPIE (2005)
[12] B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 7th ed. (Wiley, 2007).
[13] D. Malacara, Optical Shop Testing (Wiley, 1992).
[14] M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1970).
[15] 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).
[16] 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).
[17] http://www.ni.com
[18] C. Curatu, G. Curatu, and J. Rolland, “Fundamental and specific steps in Shack-Hartmann wavefront sensor design,” SPIE Proc. 6288, 6201-6300 (2006).
[19] C. Li, M. Xia, Z. Liu, D. Li, and L. Xuan, “Optimization for high precision Shack-Hartmann wavefront sensor,” Opt. Commun. 282, 4333-4338 (2009).
[20] D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” SPIE Proc. 4779, 148-160 (2002).
[21] G.-M. Dai, “Model wave-front reconstruction with Zernike polynomials and Karhunen-Loève functions,” J. Opt. Soc. Am. 13, 1218-1225 (1996).
[22] 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).
[23] http://www.edmundoptics.com
[24] http://www.analog.com/en/index.html
[25] E. J. Fernández and P. Artal, “Membrane deformable mirror for adaptive optics: performance limits in visual optics,” Opt. Express 11, 1056-1069 (2003).
[26] J. B. Stewart, A. Diouf, Y. Zhou, and T. Bifano, “Open-loop control of a MEMS deformable mirror for large-amplitude wavefront control,” J. Opt. Soc. Am. A 24, 3827-3833 (2007).
[27] B. Wang and M. J. Booth, “Optimum deformable mirror modes for sensorless adaptive optics,” Opt. Commun. 282, 4467-4474 (2009).
[28] P. V. Overschee and B. D. Moor, “N4SID: subspace algorithms for the identification of combined deterministic and stochastic systems,” Automatica 30, 75-93 (1994).
[29] http://www.mathworks.com/help/toolbox/control/ref/lqi.html
[30] J.-N. Juang and M. Q. Phan, Identification and Control of Mechanical Systems (Cambridge University Press, 2001).
[31] R. N. Paschall and D. J. Anderson, “Linear quadratic Gaussian control of a deformable mirror adaptive optics system with time-delayed measurements,” Appl. Opt. 32, 6347-6358 (1993).
[32] J. Herrmann, “Phase variance and Strehl ratio in adaptive optics,” J. Opt. Soc. Am. A 9, 2257-2258 (1992).