摘要
隨著科技的進步以及光電產業的迅速發展，各類型的光學產品，如數位相機、數位手機或是微型投影機等等，皆往輕薄，微小化的趨勢邁進，為了在此類精密光學中以不影響成像品質的條件下減輕重量和減少體積，遂發展出液態透鏡技術來提供變焦功能極為重要，為了使液態透鏡的技術發展完整，加速商業化的應用，如何快速、簡易、及低成本的檢測其系統，故而新檢測技術成為業界發展的重要關鍵。
在以往的非接觸式量測技術中，常使用干涉儀做為檢測的平台，但干涉儀需要較多的光學元件來提高量測品質，導致儀器整體的體積較大並且價格較昂貴，並且干涉儀在量測時易受震動及空氣擾動等環境影響，故本論文中採用夏克．哈特曼(Shack-Hartmann)波前量測儀來量測液態透鏡的自由曲面，因夏克．哈特曼波前量測儀是利用光點強度和位置的不同來判別不同的波前，故較不需要精密且複雜的光學元件，即可達到高精確度；而在波前還原的步驟中使用澤尼克多項式(Zernike Polynomials)由計算出不同的像差係數重建波前，得知待測物的光學特性，並配合光學分析軟體的模擬此量測系統與實驗數據做比較。

關鍵詞：自由曲面、液態透鏡、夏克．哈特曼波前量測儀、澤尼克多項式

ABSTRACT
With the fast advancement in technology and progress in optoelectronics industry, various optical products, such as digital cameras, cellphones and micro projectors, are following the trends of compactness and miniaturization. For the purposes of volume and weight reduction without sacrificing image qualities, liquid lens technology has been developed for achieving the important variable focus function. To further perfecting the liquid lens technology and expediting the commercial applications, new metrological technology for fast, simple and low cost inspection has become the most critical development in the industry.
In the traditional non-contact metrological technology, measurement platform based upon interferometry is commonly adopted. However, the system needs more precision optical components for maintaining the measurement quality so that bulky and less cost effective instruments are necessary. Furthermore, interferometer is very sensitive to vibrations and air turbulences in environment. Therefore, the free form interfaces in liquid lens has been measured with the help of Shack-Hartmann wavefront sensors in this thesis. Since the wavefront has been measured via the positional difference of focal point of Shack-Hartmann sensors, less precision and complicated optical components have been necessary for high accuracy in the measurements. In the restoration of wavefront data, Zernike Polyminomials have been adopted for calculation of the phase of light in terms of aberration coefficients. The optical characteristics of the liquid lens under test have been obtained for comparisons between the simulation results from optics analysis and experimental data.
Keywords: Free Surface, Liquid Lens, Shack-Hartmann Sensors

參考文獻
[1] D. R. Neal, D. J. Armstrong and W. Tim Turner, "Wavefront sensors for control and processing monitoring in optics manufacture", Proc. SPIE Volume 2993, pp.211 (1997).

[2] 季法文，「照相手機畫素持續升級 減少尺寸與自動對焦為大勢所趨」，新通訊元件雜誌，2006 年 8 月號 66 期（2006）。

[3] D. R. Neal, Copland, David A, James, Neal,” Shack-Hartmann wavefront sensor precision and accuracy, Proceedings of the SPIE, Volume 4779, pp. 148-160 (2002).

[4] D. R. Neal, J. Schwiegerling, “Historical Development of the Shack-Hartmann Wavefront Sensor” (2005)

[5] D. Malacara, ”Optical Shop Testing”, John Wiley (2007)

[6] J. Liang*, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor”, JOSAA Vol. 11, Issue 7, pp. 1949-1957 (1994)

[7] 林穎毅，「液體鏡片之發展現況」，光連，民國94年3月56期，頁42-45（2005）。

[8] S. Kuiper, B. H. W. Hendriks,” Variable-focus liquid lens for miniature cameras”, APPLIED PHYSICS LETTERS, Vol. 85, No. 7, pp.1128-1130 (2004).

[9] C. C. Cheng and J. A. Yeh, “Dielectrically actuated liquid lens”, Optics Express Vol. 15, pp.7140-7145 (2007).

[10] Hecht, Eugene,”Optics”, Addison-Wesley Pub. Co (1987)

[11] 葉玉堂，「幾何光學」，五南(2008)。

[12] V. N. Mahajan,” Optical Imaging and AberrationsPart I. Ray Geometrical Optics”, SPIE (1998).

[13] Dai, Guang-ming, “Wavefront optics for vision correction”, SPIE Press (2008).

[14] F. Zernike, Phsica, pp.1,689 (1934).

[15] M. Born and E. Wolf, “Principles of optics”, Cambridge University Press (1999).

[16] J. C. Wyant – Shack-Hartmann Patterns for Seidel Aberrations http://wyant.optics.arizona.edu/seidelHartmann/seidel.htm.

[17] R. R. Rammage, D. R. Neal, and R. J. Copland, ” Application of Shack-Hartmann wavefront sensing technology to transmissive optic metrology”, SPIE Proceedings Vol. 4779, pp.161-172 (2002).

[18] 蔡智偉，「介電式液態透鏡與光圈之研究」，國立清華大學碩博士論文(2010)。