1994年，Liang首次將Hartmann Shack波前量測技術應用在自適應光學。近年來，這項技術廣泛的使用在人眼屈光手術(LASIK)上，其精準度是值得本文來研究與探討。
本文主要分成兩部份，第一部份是利用光學軟體來模擬Hartmann-Shack波前量測儀並且加入架設儀器容易產生的誤差源來分析和討論系統誤差。第二部份是自行架設Hartmann-Shack波前量測儀，利用透鏡和反射鏡取代人眼，光波經過透鏡系統和Hartmann-Shack波前量測儀將波前聚焦在CCD上，分析CCD上的影像計算出Zernike係數重建出波前。最後我們將Hartmann-Shack波前量測儀波前重建之結果與Zygo干涉儀量測結果比較，兩波前的誤差RMS為0.035λ，然而考慮tilt是架設儀器產生的像差，將x和y方向的tilt扣除，其誤差RMS降低為0.025λ。

The Hartmann-Shack wavefront measurement of adaptive optics was first brought up by Liang in 1994, and it was widely used in LASIK surgery recently. The accuracy of the Hartmann-Shack wavefront measurement technique was discussed in this research.
The analysis of Hartmann-Shack sensor errors was composed of two parts. The first part was simulted by software including man-made errors and system errors. The second part was the establishment of the whole system including HSS and one reflective mirror. The Hartmann-Shack sensor contained micro-lens array and CCD. In this setup, the light is reflected from the mirror, passing through the test lens and micro-lens array, and finally focused on CCD. We analyzed the images captured by CCD, calculated the Zernike coefficients and reconstructed to wavefront. The RMS error of the wavefront reconstructed by the system compared to Zygo interferometer was 0.035λ. Moreover, the RMS error can be reduced to 0.025λ after deducting the tilt aberration in the x and y directions.

[1]. MS. Smirnov "Measurement of the wave aberration of the human eye", Biophysics, 6 , pp.776-794, 1961.
[2]. M. Campbell, E. Harrison, and P. Simonet, "Psychophysical measurement of blur on the retina due to optical aberrations of the eye", Vision Res. 30, pp.1587-1602, 1990.
[3]. F. Berny and S. Slansky, "Wavefront determination resulting from Foucault test as applied to the human eye and visual instruments", Optical Instruments and Techniques, H. Dickson , ed. (Oriel, London), pp. 375-386, 1970.
[4]. L. N. Thibos, “Principles of Hartmann - Shack Aberrometry”, Journal of Refractive Surgery, 16, pp.563-565, 2000.
[5]. M. Troy, R. G. Dekany, G. Brack, B. R. Oppenheimer, E. E. Bloemhof, T. Trinh, F. G. Dekens, F. Shi, T. L. Hayward, and B. Brandl, “Palomar adaptive optics project: status and performance”, Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE 4007, 2000.
[6]. J. Liang, B. Grimm, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wavefront sensor”, J. Opt. Soc. Am. A, 11, pp.1949-1957, 1994.
[7]. V. N. Mahajan, Optical Imaging and Aberrations, SPIE, 1998.
[8]. 陳弘, “幾何光學”, 台灣東華書局股份有限公司, 1987.
[9]. Born & Wolf, “Principles of Optics”, pp.152~171, 1959.
[10]. D. Malacara, “Optical Shop Testing”, Wiley, New York, 1997.
[11]. J. R. Noll, “Zernike polynomials and atmospheric turbulence”, J. Opt. Soc. Am. A, 66, pp.207-211, 1976.
[12]. L. N. Thibos, “Handbook of Visual Optics, Draft Chapter on Standards for Reporting Aberrations of the Eye.”,1999
[13]. R. H. Hudgin, “Wave-front reconstruction for compensated imaging”, J. Opt. Soc. Am. 67, pp.375–378, 1977.
[14]. R. Cubalchini, “Modal wavefront estimation from phase derivative measurements”, J. Opt. Soc. Am. 69, pp. 972-977, 1979.
[15]. Daniel M. Topa, Inc, “Wavefront reconstruction for the Shack-Hartmann wavefront sensor”, Optical Design and Analysis Software II, Richard C. Juergens, Editor, Proceedings of SPIE, 4769, pp.101-115, 2002.
[16]. W. H. Southwell, “Wave-front estimation from wave-front slope measurements”, J. Opt. Soc. Am., 70, pp.988, 1980.
[17]. 陳志輝, 凌寧, 饒學軍, 王成, “人眼像差哈特曼測量儀的重複性測試”, Opo-Electronic Engineering, 31, pp.5-8, 2004.
[18]. W. H. Southwell, “Wavefront estimation from wavefront slope measurements”, J. Opt. Soc. Am. 70, pp. 998-1006 ,1980.
[19]. J. Liang, “A new method to precisely measure the wave aberrations of the human eye with a Hartmann-Shack wavefront sensor”, Ph.D. dissertation University of Heidelberg, Heidelberg, Germany, 1991.
[20]. P. M. Prieto, and F. Vargas-Martin, “Analysis of the performance of the Hartmann-Shack sensor in human eye”, J. Opt. Soc. Am. A, 17, pp. 1388-1398, 2000.
[21]. G. Cao, X. Yu, “Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object”, Optical Engineering, 33, pp.2331-2334, 1994.
[22]. R. Lrwan, R. G. Lane, “Analysis of optimal centroid estimation applied to Shack-Hartmann sensing”, Applied Optics, 38, pp.6737-6743, 1999.
[23]. M. A. Dam, “Measuring the centroid gain of a Shack–Hartmann quad-cell wavefront sensor by using slope discrepancy”, J. Opt. Soc. Am. A, 22, pp. 1509-1514, 2005.
[24]. 沈峰, 姜文漢, “提高Hartmann-Shack波前傳感器質心探測精度的值方法”, Opo-Electronic Engineering, 24, pp.1-8, 2004.
[25]. D. P. Salas-Peimbert, D. Malacara-Doblado, V. M. Duran-Ramirez, G. Trujillo-Schiaffino, and D. Malacara-Herandez, “Wave-front retrieval from Hartmann test data”, Applied Optics, 44, pp. 4228-4238, 2005.
[26]. L. Liang, D. R. Williams, ”Aberration and Retinal Image Quality of the Normal Human Eye”, J. Opt. Soc. Am. A, 14, pp. 2873-2883, 1997.
[27]. H. Hofer, L. Chen, G. Y. Yoon, B. Singer, Y.Yamauchi, and D. R.Williams, “Improvement in retinal image quality with dynamic correction of the eye’s aberrations”, Optics Express, 8, pp. 631-643, 2001.