本論文主要探討液晶透鏡之電極對稱性對透鏡全息光學元件製作與性能之影響，液晶透鏡的電極結構使用單一與對稱成對圓孔電極兩種設計，其光學能力的評估則分別進行觀察相位延遲環、焦距與焦點等表徵。同時，液晶透鏡的相位延遲環與理想二次曲線方程式進行擬合並計算其出RMS數值，實驗結果顯示對稱成對圓孔電極的液晶透鏡具有較小的RMS值及較佳的焦點表現，而相位延遲環的完整程度在兩種電極結構的液晶透鏡皆具有理想的表現，且分別對應之最短焦距的皆是20公分左右，但對稱成對圓孔電極的液晶透鏡需要較高的電壓才能達到相同的焦距。由於單以液晶透鏡製作透鏡全息光學元件仍無法得到理想的菲涅爾區圖樣(Fresnel zone pattern)，因此採用液晶透鏡結合玻璃透鏡進行全息光學元件製作，實驗結果顯示使用對稱成對圓孔電極液晶透鏡的組合透鏡具有較佳的焦點表徵，且其全息干涉可以得到理想的菲涅爾區圖樣(Fresnel zone pattern)。將實驗製作完成之透鏡全息光學元件全相片進行焦點還原觀察與測量，結果顯示使用對稱成對圓孔電極液晶透鏡的組合透鏡其全息光學元件重建之焦點表現具有較集中的光點，顯示對稱成對圓孔電極液晶透鏡確實能有助於全息光學元件的性能改善。

This paper focuses on the application of liquid crystal lenses in recording holographic optical elements. The electrode structure of the liquid crystal lenses is modified from the original asymmetric single-hole design to a symmetric dual-hole configuration. The optical capabilities of the two different electrode structures are measured, and it is observed that the liquid crystal lens with symmetric dual-hole electrodes exhibits smaller RMS values and more concentrated focal light spots. However, when both types of liquid crystal lenses are individually used in recording holographic optical elements, satisfactory results in terms of Fresnel zone pattern are not achieved. Therefore, experiments are conducted by combining the two electrode structures of liquid crystal lenses with glass lenses. The results demonstrate that the combined lens using symmetric samples can reproduce more ideal light spots, indicating that the symmetric dual-hole electrode design indeed contributes to the recording of holographic optical elements.

[1] Mitov, M., Liquid‐Crystal Science from 1888 to 1922: Building a Revolution. ChemPhysChem, 2014. 15(7): p. 1245-1250.
[2] Blinov, L.M., Structure and properties of liquid crystals. Vol. 123. 2010: Springer Science & Business Media.
[3] Lin, H.-C., M.-S. Chen, and Y.-H. Lin, A review of electrically tunable focusing liquid crystal lenses. Transactions on electrical and electronic materials, 2011. 12(6): p. 234-240.
[4] Sato, S., Liquid-crystal lens-cells with variable focal length. Japanese Journal of Applied Physics, 1979. 18(9): p. 1679.
[5] Vanackere, T., et al., Improvement of liquid crystal tunable lenses with weakly conductive layers using multifrequency driving. Optics Letters, 2020. 45(4): p. 1001-1004.
[6] Wang, B., et al., Liquid crystal lens with spherical electrode. Japanese Journal of Applied Physics, 2002. 41(11A): p. L1232.
[7] Pishnyak, O., S. Sato, and O.D. Lavrentovich, Electrically tunable lens based on a dual-frequency nematic liquid crystal. Applied Optics, 2006. 45(19): p. 4576-4582.
[8] Lin, Y.-H., H.-S. Chen, and M.-S. Chen, Electrically tunable liquid crystal lenses and applications. Molecular Crystals and Liquid Crystals, 2014. 596(1): p. 12-21.
[9] Fowler, C. and E. Pateras, Liquid crystal lens review. Ophthalmic and Physiological Optics, 1990. 10(2): p. 186-194.
[10] Hsu, C.-J., J.-J. Jhang, and C.-Y. Huang, Large aperture liquid crystal lens with an imbedded floating ring electrode. Optics Express, 2016. 24(15): p. 16722-16731.
[11] Gabor, D., Theory of communication. Part 1: The analysis of information. Journal of the Institution of Electrical Engineers-part III: radio and communication engineering, 1946. 93(26): p. 429-441.
[12] Hong, K., et al., Full-color lens-array holographic optical element for three-dimensional optical see-through augmented reality. Optics letters, 2014. 39(1): p. 127-130.
[13] Maimone, A., A. Georgiou, and J.S. Kollin, Holographic near-eye displays for virtual and augmented reality. ACM Transactions on Graphics (Tog), 2017. 36(4): p. 1-16.
[14] Lehmann, O., Flüssige Kristalle sowie Plastizität von Kristallen im allgemeinen, molekulare Umlagerungen und Aggregatzustandsänderungen. 1904: Verlag von Wilhelm Engelmann.
[15] Trainer, N., Greener Synthesis of Poly-1, 3-Isobenzofurandione-4, 7-diphenyl. 2018.
[16] 劉瑞祥, 松本正一, and 角田市良, 液晶之基礎與應用. 國立編譯館.
[17] Yariv, A. and P. Yeh, Photonics: optical electronics in modern communications. 2007: Oxford university press.
[18] Yang, D.-K. and S.-T. Wu, Fundamentals of liquid crystal devices. 2014: John Wiley & Sons.
[19] Luckhurst, G., School of Chemistry, University of Southampton, UK SO17 1BJ Commentary on: On the Theory of Liquid Crystals, FC Frank, Discuss. Faraday Soc., 1958, 25, 19-28. 100 Years of Physical Chemistry, 2003: p. 225.
[20] Khoo, I.C., Nonlinear optics, active plasmonics and metamaterials with liquid crystals. Progress in Quantum Electronics, 2014. 38(2): p. 77-117.
[21] Ye, M., et al., Properties of variable-focus liquid crystal lens and its application in focusing system. Optical review, 2007. 14: p. 173-175.
[22] 張繼鴻, 發展一可用電壓調控焦距的液晶元件. 2003.
[23] Ye, M. and S. Sato, Optical properties of liquid crystal lens of any size. Japanese journal of applied physics, 2002. 41(5B): p. L571.
[24] Ren, H., et al., Liquid crystal lens with large focal length tunability and low operating voltage. Optics express, 2007. 15(18): p. 11328-11335.
[25] Choi, Y., et al., Fabrication of a focal length variable microlens array based on a nematic liquid crystal. Optical materials, 2003. 21(1-3): p. 643-646.
[26] Ye, M., B. Wang, and S. Sato, Driving of liquid crystal lens without disclination occurring by applying in-plane electric field. Japanese journal of applied physics, 2003. 42(8R): p. 5086.
[27] Kuo, C.-H., et al., Influence of pretilt angle on disclination lines of liquid crystal lens. Applied Optics, 2012. 51(19): p. 4269-4274.
[28] Hsu, C.J. and C.R. Sheu, Preventing occurrence of disclination lines in liquid crystal lenses with a large aperture by means of polymer stabilization. Optics express, 2011. 19(16): p. 14999-15008.
[29] 三宅和夫, RJ Collier, CB Burckhardt and LH Lin: Optical Holography, Academic Press, New York, 1971, 605日本物理学会誌, 1972. 27(5): p. 419-420.
[30] Wang, Q.-H., et al. Augmented reality 3D display system based on holographic optical element. in Advances in Display Technologies IX. 2019. SPIE.
[31] Zhang, H.-L., et al., Tabletop augmented reality 3D display system based on integral imaging. JOSA B, 2017. 34(5): p. B16-B21.