光碟片在高速旋轉及晃動下所產生的碟片傾斜，會使得碟片資訊層上讀取的雷射光點產生像差。像差會改變聚焦光點的強度分布情況，進而造成光感測器所偵測到反射光的訊號劣化，甚至錯誤的情況。隨著碟片儲存密度提高，碟片傾斜所造成訊號劣化的現象必須被深入研究及探討。
本篇論文主要架構在DVD的規格上，來模擬與分析碟片在三維空間中擺動時對聚焦誤差訊號的影響，並設法作補償。首先，我們將會提出建立數學模型相關的光學原理，並討論讀取頭中光學元件之間的光場轉換函數。接著，碟片傾斜角度所造成像差的理論將會被提出。而結合著切向傾斜（tangential tilt）和徑向傾斜（radial tilt）的三維傾斜角將會引入讀取頭數學模型中。由切向和徑向之兩軸為相互垂直的情況推論，三維傾斜角受到此兩方向之傾斜角的影響為互相獨立的，甚至在小角度的情況下是線性獨立的。因此，此三維傾斜角可以存在由這兩軸為正交基底而展開的向量空間中。換句話說，三維傾斜角大小為在此空間中的向量長度，而方向則與切向和徑向傾斜角大小有關。詳細幾何推論過程將在內文中呈現。在考慮不同傾角的情況下，聚焦訊號所受到的影響將會一一被模擬與分析，並建立其間之關係。因此可利用傾斜偵測器所得知的三維傾斜角，對讀取頭的聚焦誤差訊號以查表的方法來做補償。最後以一個碟片三維擺動的模型，對於僅作聚焦誤差訊號補償，以及預估下一時間之傾斜狀態而行聚焦誤差訊號補償等兩種不同控制方法進行比較。其中預測法引入一適應性增益值，由模擬結果可以看到此法有較好的表現。
本論文所模擬的數學模型是根據波動光學理論，並建立在MATLAB這個數學軟體中。

The optical disk tilt caused by the high-speed spin and vibration introduces the aberrations of the laser spot on the information layer. The aberrations will change the intensity distribution of the focused spot, and deteriorate the signal quality of the reflected light detected by the photo sensor, and then induce the mistake. Hence, with the increasing storage density of the disk, the phenomenon of the deteriorated signal caused by disk tilt should be discussed and studied thoroughly.This thesis is based on the DVD specification. In this thesis, we simulate and analyze the focus error signal affected by disk vibration in 3-dimensional space, and then try to compensate for this phenomenon. First, we propose the optical theory related to the mathematical model, and discuss the transfer function between the optical components in the system. Then, we propose the aberration theory resulted from the disk tilt. The 3-dimensional tilt angle composed of tangential tilt and radial tilt will be introduced into the mathematical model. Since the tangential and radial axes are perpendicular to each other, the effects of the 3-dimensional tilt angle resulted from these two tilt angles are independent, even are linear under small angle condition. Therefore the 3-dimensional tilt angle exits in the vector space constructed by the tangential and radial orthogonal bases. In other words, the magnitude of the 3-dimensional tilt angle is equal to the length of the vector in the space while the direction is relative to both the tangential and radial tilt angles. The detailed condition in geometric will be proposed in the content. The focus error influenced by different 3-dimensional tilt angles will be simulated and analyzed, and the relations will be established. The compensated method of looking up table will be used once we know the tilt angle from the tilt sensor. Finally, the performances of two focus servo control methods, one using the looking up table directly and the other using the tilt condition prediction beforehand, are compared while a 3-dimensional vibration model is built. It shows that the tilt condition prediction one works better.The mathematical model simulated in this thesis is based on the diffractive wave optics theory, and is built in the mathematical software, MATLAB.

[1] 徐桂香, “光碟讀取頭光路之數學模型”, 清華大學動力機械工程學系碩士論文, 民國90年6月.
[2] 陳信豪, “光碟機讀取頭光路系統像差對聚焦偵測之影響”, 清華大學動力機械工程學系碩士論文, 民國91年6月.
[3] 黃仁澤, “碟片晃動對光碟機讀取頭光強度及聚焦控制之影響分析”, 清華大學動力機械工程學系碩士論文, 民國92年6月.
[4] 黃仕臣,“碟片晃動對光碟機讀取資料之影響分析與補償” , 清華大學動力機械工程學系碩士論文, 民國93年6月.
[5] B.E.A.Saleh, M.C.Teich, “Fundamentals of Photonics”, New York: Wiley, 1991.
[6] “Optical Pick-Up Specifications for DVD/CD: HOP-1000”, Hitachi. Ltd., 1998.
[7] Miles V.Klein, Thomas E.Furtak, “Optics”, New York: Wiley, 1986.
[8] Frank L., Leno S., “Introduction to Optics”, Prentice Hall, Englewood Cliffs, 1993.
[9] Eugene Hecht, “Optics”, Addison Wesley Longman, third edition, 1998.
[10] C. Bartlett, D. Kay, M. Mansuripur, “Computer simulations of effects of disk tilt and lens tilt on push-pull tracking error signal in an optical disk drive”, Applied Optics, Vol. 36, pp. 8467-8473, 1997.
[11] Joseph Braat, “Analytical expressions for the aberration coefficients of a tilted plane parallel plate”, Applied Optics, Vol. 36, No. 32, pp. 8459-8466, 1997.
[12] “CD-ROM Learning Kit”, 太和科技, 初版, 民國87年1月
[13] “DVD specifications for Read-Only Disc”, Hitachi, Matsushita, Mitsubishi, Philips, Pioneer, Sony, Thomson, Toshiba, Time Warner, JVC, August 1996.

[14] Doh, T.-Y. Ma B.I., Choi B.H., Park I.S., Chung C.S., Lee Y.-H., Kim S.J., Shin D.H., “Radial tilt detection using one beam and its compensation in a high-density read only memory” Jpn. J. Appl Phys. Part 1, No.3B pp.1680-1683, Mar 2001
[15] Ryuichi Katayama, Shunichi Meguro, Yuichi Komatsu and Yutaka Yamanaka, “Radial and Tangential Tilt Detection for Rewritable Optical Disks”, Jpn. J. Appl. Phys. Vol. 40 (2001) pp. 1684–1693
[16] Ryuichi KATAYAMA, Shunichi MEGURO and Yuichi KOMATSU, “Land/Groove Signal and Differential Push-Pull Signal Detection for Optical Disks by an Improved 3-Beam Method”, Jpn. J. Appl. Phys. Vol. 38 (1999) pp. 1761–1767
[17] Wei-Hung Yeh, Lifeng Li, M. Mansuripur,” Vector Diffraction and Polarization Effects in an Optical Disk System”, Applied Optics, Vol. 37, No. 29, pp. 6983-6988, 1998
[18] Wei-Chih Liu and Marek W. Kowarz,” Vector diffraction from subwavelength optical disk structures: two-dimensional modeling of near-field profiles, far-field intensities, and detector signals from a DVD”, Applied Optics, Vol. 38, No. 17,pp. 3787-3797, 1999