本論文主要目的是研究以液晶為介質的相位調制器應用在移相式數位全像術的性能。在此實驗當中，我們以Mach-Zehnder干涉儀為基本架構建立了一套系統，包含液晶的電壓-穿透率曲線測量與移相式數位全像術，透過此系統，能得到液晶之電壓-相位轉換曲線。

我們將CCD擷取的干涉條紋，運用四步演算法與Fresnel繞射積
分式，以電腦運算出物體的原始影像，並成功重建穿透式與反射式之物體。另外，我們也利用波板做為相位調制器應用於相同的實驗系統中，並比較波板與液晶相位調制之全像術結果。我們也觀察液晶元件對溫度變化的穩定性，從實驗結果發現，在溫度從室溫升高至60℃，從電壓-穿透率曲線來看，相位會隨著溫度的改變而有誤差產生，雖然液晶相位在溫度變化下，造成相同電壓下的相位不一致性，但是此現象對重建影像似乎影響不大，在實驗的溫度範圍內，相位誤差維持在±30°以內，這樣的結果與此液晶之溫度-折射率變化特性有關。

In this thesis, we mainly study optical characteristics of liquid crystal phase shifter used in phase-shifting digital holography. Our experimental setup is based on the Mach-Zehnder interferometer, which possesses two functions including voltage versus transmission (V-T) curve measurement of liquid crystal cells, and processes of phase-shifting digital holography. The relation between voltage and optical phase in the
LC cell can be calculated with V-T curve.

For processes of digital holography, a CCD camera caught the interference images with the four-step method in order to get amplitude and phase information of objects. According to Fresnel diffraction theory, we reconstructed the object images with both amplitude and phase information in the personal computer. We have successfully reconstructed object images with simulation and experiments. We also made comparisons between liquid crystal phase-shifter and mica wave plates used in digital holography. Due to liquid crystals is a temperature sensitive material, we also studied temperature effects on liquid crystal shifter used in digital holography. The experimental results show that reconstructed object images seem no significant difference when the LC cell is at a temperature range from room temperature to 60℃ although
refractive indices of liquid crystals have been changed. We have measured the phase difference about ±30° in this phase shifter when the temperature is at temperature range from room temperature to 60℃. The experimental results seem to be directly relative to characteristics of liquid crystal materials.

[1] 松本政一, 角田市良, 劉瑞祥譯, "液晶之基礎與應用", 國立
編譯館, 台北市 (1996).
[2] P. Yeh and C. Gu, “Optics of Liquid Crystal
Displays”, Wiley (1999).
[3] 張宗宏, "用全漏光導模光學量測對液晶盒極角錨定能之研
究", 國立成功大學碩士論文 (2007).
[4] P. Hariharan, “Basic Holography”, Cambridge (2002).
[5] 陳逸寧, "基礎雷射全像術", 全華科技圖書股份有限公司, 台
北市 (2005).
[6] J. W. Goodman, “Digital image formation from
electronically detected Holograms”, Applied Physics
Letters, vol. 11, num. 3 (1967).
[7] Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce,
and B. Javidi, “Three-Dimensional Imaging and
Processing Using Computational Holographic Imaging”,
Proceedings of the IEEE, vol. 94, 636-653 (2006).
[8] U. Schnars and W. Jueptner, “Digital Holography”,
Springer, 41-69 (2005).
[9] I. Yamaguchi and T. Zhang, “Phase-shifting digital
holography”, Optics Letters, vol. 22, 1268–1270
(1997).
[10] E. Tajahuerce, O. Matoba, and B. Javidi, “Shift-
invariant three-dimensional object recognition by
meas of digital holography”, Applied Optics, vol.
40, 3877-3886 (2001).
[11] Songcan Lai, Brian King, and Mark A. Neifeld, “Wave
front reconstruction by means of phase-shifting
digital in-line holography”, Optics Communications,
173, 155-160 (2000).
[12] I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno,
“Image formation in phase-shifting digital holography
and applications to microscopy”, Applied Optics,
vol. 40, no. 34, 6177-6186 (2001).
[13] 鄭作仲, "水平配向液晶盒純相位調制應用於移相式全像術之
研究", 國立成功大學碩士論文 (2008).
[14] http://upload.wikimedia.org/wikipedia/commons/5/54/
Huygens_principle.gif
[15] Ulf Shnars and Werner P. O. Juptner, “Digital
recording and reconstruction of holograms in hologram
interferometry and shearography”, Applied Optics,
vol. 33, no. 20 (1994).
[16] 李天嘉, "移相式數位全像術之研究", 聖約翰技術學院碩士論
文 (2004).
[17] J. W. Goodman, “Introduction to Fourier Optics”,
Third Edition, 63-96 (2005).
[18] E. Hecht, “Optics”, Fourth Edition, Addison Wesley
(2002).
[19] Jun Li, Sebastian Gauza, and Shin-Tson Wu,
“Temperature effect on liquid crystal refractive
indices”, Journal of Applied Physics, vol. 96, num.
1 (2004).