近年隨半導體製造技術的精進，不僅晶片本身微縮，機械元件亦達到微米尺度。然而，伴隨而來的是這些元件變形量測及可靠度、壽命預估的問題。因此，本研究提出一改進原始電子光斑(Electronic Speckle Pattern Interferometry)干涉量測之光路設計，將面內、外電子光斑量測之光路結合並導入相平移法(Phase-Shifting)作為條紋相位提取及增進相位分佈(Wrapped Phase)影像品質之工具。而此二維變形量測光路設計僅需透過遮避方式切換面內、面外量測光路，藉此改善本二維變形量測工具之穩定、捷便性。
為了驗證此光路設計之可行、可靠性，本研究透過四點彎折試驗(Four-Point Bending)，量測一矽試片在承受純撓矩(Bending Moment)時面內、外變形情況。並將試片之量測結果比對有限元素法軟體ANSYS®之模擬結果，及尤拉-伯努利樑方程式(Euler–Bernoulli Beam Equation)之理論解。
此外，原始相關條紋的影像結果經過相平移法後仍存在許多非連續之斑點，故本研究引入一使用正、餘弦之原始相位影像平滑法，試圖將此噪點去除。最後為了得到連續之位移量分佈，利用影像品質引導相位重建演算法(Quality Guided Phase Unwrapping )將原始相位分佈展開成連續相位分佈。透過位移與相位之線性關係得到全域之面內、外位移量分佈圖。
結果顯示，本研究提出的以遮避式切換二維電子光斑量測光路量測到之變形分佈及位移量對比於模擬、理論結果，誤差皆在5%以下，且此實驗標準差皆在量測精度以下。因此證明本研究提出之電子光斑光路設計具精確與可行性。

As the progress of semiconductor manufacturing technology, even the mechanical components in MEMS (Micro Electro Mechanical System) are fairly small and shrink to micro-scale. Accompanied with the size reduction, how to measure the deformation of a package or a device becomes an issue. Therefore, this study proposes an improvement of the ESPI (Electronic Speckle Pattern Interferometry) light path design that switches between ESPI in-plane/out-of-plane measurement without moving and rotating any optical devices. And phase-shifting is built in the light path as the phase extraction method and phase map quality enhancement.
In order to verify the feasibility and reliability of the novel light path design, four-point bending test with silicon specimens is performed. Numerical results obtained by finite element software (ANSYS®) and the theoretical solution from Euler-Bernoulli beam equation is also brought in for affirmation. By comparing the three results with different methods, the 2D ESPI light path design can be validated.
However, there are still lots of singular points (noise) in the phase map acquired from phase-shifting, so the sine/cosine image smoothing algorithm is introduced in image post-processing. And the quality guided phase unwrapping algorithm is implemented for generating the continuous phase map. Because the linear relationship between continuous phase map and displacement map is established when light path is set, the whole in-plane/out-of-plane displacement map is obtained as the continuous phase map is obtained.
Compare the experiment results with FEM and theoretical results, the errors of all tests are lesser than 5%, and the standard variation is minor . It shows that the light path proposed in this study is feasible and stable.

[1] D. Gabor, "A New Microscope Principles," Nature, vol. 161 (4098), pp. 777-778, 1948.
[2] E. N. Leith and J. Upatnieks, "Wavefront Reconstruction with Diffused Illumination and Three-Dimensional Objects," J. Opt. Soc. Am., vol. 54, pp. 1295-1301, 1964.
[3] J. N. Butters and J. A. Leendertz, "A double exposure technique for speckle pattern interferometry," Journal of Physics E: Scientific Instruments, vol. 4, p. 277, 1971.
[4] C. Wykes, "De-correlation Effects in Speckle-pattern Interferometry," Optica Acta: International Journal of Optics, vol. 24, pp. 517 - 532, 1977.
[5] K. Creath, "Phase-shifting speckle interferometry," Applied Optics, vol. 24, pp. 3053-3058, 1985.
[6] F. Chen, W. D. Luo, M. Dale, A. Petniunas, P. Harwood, and G. M. Brown, "High-speed ESPI and related techniques: overview and its application in the automotive industry," Optics and Lasers in Engineering, vol. 40, pp. 459-485, 2003.
[7] C. Wykes, "Use of electronic speckle pattern interferometry/ESPI/ in the measurement of static and dynamic surface displacements," Optical Engineering, vol. 21, pp. 400-406, 1982.
[8] R. S. Hansen, "A compact ESPI system for displacement measurements of specular reflecting or optical rough surfaces," Optics and Lasers in Engineering, vol. 41, pp. 73-80, 2004.
[9] B. W. Lee, W. S. Jang, D. W. Kim, J. H. Jeong, J. W. Nah, K. W. Paik, and D. Kwon, "Application of electronic speckle-pattern interferometry to measure in-plane thermal displacement in flip-chip packages," Materials Science and Engineering A, vol. 380, pp. 231-236, 2004.
[10] D. C. Ghiglia, G. A. Mastin, and L. A. Romero, "Cellular-automata method for phase unwrapping," Journal of the Optical Society of America A, vol. 4, pp. 267-280, 1987.
[11] K. Qian, H. S. Seah, and A. Asundi, "Filtering the complex field in phase shifting interferometry," Optical Engineering, vol. 42, pp. 2792-2793, 2003.
[12] K. Qian, "Windowed Fourier Transform for Fringe Pattern Analysis: Addendum," Appl. Opt., vol. 43, pp. 3472-3473, 2004.
[13] K. Qian, S. Hock Soon, and A. Asundi, "A simple phase unwrapping approach based on filtering by windowed Fourier transform," Optics & Laser Technology, vol. 37, pp. 458-462, 2005.
[14] K. Qian, "Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations," Optics and Lasers in Engineering, vol. 45, pp. 304-317, 2007.
[15] K. Qian, "A simple phase unwrapping approach based on filtering by windowed Fourier transform: The phase near edges," Optics & Laser Technology, vol. 39, pp. 1364-1369, 2007.
[16] K. Qian, "On window size selection in the windowed Fourier ridges algorithm," Optics and Lasers in Engineering, vol. 45, pp. 1186-1192, 2007.
[17] K. Qian, N. L. T. Hoai, F. Lin, and S. S. Hock, "Comparative analysis on some filters for wrapped phase maps," Appl. Opt., vol. 46, pp. 7412-7418, 2007.
[18] K. Qian, "A simple phase unwrapping approach based on filtering by windowed Fourier transform: A note on the threshold selection," Optics & Laser Technology, vol. 40, pp. 1091-1098, 2008.
[19] B. Pan, K. Qian, H. Xie, and A. Asundi, "Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review," Measurement Science and Technology, vol. 20, p. 062001, 2009.
[20] K. Qian, W. Gao, and H. Wang, "Windowed Fourier-filtered and quality-guided phase-unwrapping algorithm," Appl. Opt., vol. 47, pp. 5420-5428, 2008.
[21] W. Gao, K. Qian, H. Wang, F. Lin, and H. S. Seah, "Parallel computing for fringe pattern processing: A multicore CPU approach in MATLAB® environment," Optics and Lasers in Engineering, vol. 47, pp. 1286-1292, 2009.
[22] W. Gao, N. T. T. Huyen, H. S. Loi, and K. Qian, "Real-time 2D parallel windowed Fourier transform for fringe pattern analysis using Graphics Processing Unit," Opt. Express, vol. 17, pp. 23147-23152, 2009.
[23] C. S. Yang, "Design and Construction of a 3D ESPI and Shearographic System," Master, Institute of Applied Mechanics, National Taiwan University, Taipei, 1999.
[24] EdmundOptics, "Understanding Spatial Filters," ed: EdmundOptics.
[25] R. S. Sirohi, Optical Methods of Measurement: Wholefield Techniques, 2 ed.: CRC Press, 2009.
[26] P. Carré, "Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures," Metrologia, vol. 2, p. 13, 1966.
[27] K. Qian, F. Shu, and X. Wu, "Determination of the best phase step of the Carré algorithm in phase shifting interferometry," Measurement Science and Technology, vol. 11, p. 1220, 2000.
[28] J. van Wingerden, H. J. Frankena, and C. Smorenburg, "Linear approximation for measurement errors in phase shifting interferometry," Appl. Opt., vol. 30, pp. 2718-2729, 1991.
[29] J. M. Gere, Mechanics of Materials: Brooks/Cole, 2004.
[30] C. C. Lee, " Investigation of Electromigration Characteristic in SnAg3.0Cu0.5 Flip Chip Interconnection and the External Mechanical Stress Impact of Al Thin Film," PhD, Department of Power Mechanical Engineering, National Tsing-Hua University, Hsinchu, 2007.
[31] ANSYS User's Manual: ANSYS Inc. Company.
[32] R. D. Cook, D. S. Markus, M. E. Plesha, and R. J. Witt, Concepts and Applications of Finite element Analysis. New York: John Wiley & Sons, Inc., 2002.
[33] A. McAndrew, An introduction to digital image processing with MATLAB: Thomson/Course Technology, 2004.
[34] D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software. New York: John Wiley & Sons, Inc., 1998.
[35] H. A. Aebischer and S. Waldner, "A simple and effective method for filtering speckle-interferometric phase fringe patterns," Optics Communications, vol. 162, pp. 205-210, 1999.
[36] Ben. (2008). 3D view of two argument inverse tangent.
[37] A. J. Jerri, "The Shannon sampling theorem—Its various extensions and applications: A tutorial review," Proceedings of the IEEE, vol. 65, pp. 1565-1596, 1977.
[38] K. Itoh, "Analysis of the phase unwrapping problem," Applied Optics, vol. 21, p. 2470, July 15 1982.
[39] R. Goldstein, H. Zebker, and C. Werner, "Satellite radar interferometry- Two-dimensional phase unwrapping," Radio Science, vol. 23, pp. 713-720, 1988.
[40] D. J. Bone, "Fourier fringe analysis: the two-dimensional phase unwrapping problem," Appl. Opt., vol. 30, pp. 3627-3632, 1991.
[41] J. A. Quiroga, A. González-Cano, and E. Bernabeu, "Phase-unwrapping algorithm based on an adaptive criterion," Appl. Opt., vol. 34, pp. 2560-2563, 1995.
[42] Y. Xu and C. Ai, "Simple and effective phase unwrapping technique," San Diego, CA, USA, 1993, pp. 254-263.
[43] M. D. Pritt, "Phase unwrapping by means of multigrid techniques for interferometric SAR," Geoscience and Remote Sensing, IEEE Transactions on, vol. 34, pp. 728-738, 1996.
[44] R. Jones and C. Wykes, Holographic and speckle interferometry: a discussion of the theory, practice and application of the techniques: Cambridge University Press, 1989.
[45] J. F. Orr and J. C. Shelton, Optical measurement methods in biomechanics: Chapman & Hall, 1996.
[46] T. Kreis, Handbook of holographic interferometry: optical and digital methods: Wiley-VCH, 2005.
[47] A. K. Dunn, H. Bolay, M. A. Moskowitz, and D. A. Boas, "Dynamic Imaging of Cerebral Blood Flow Using Laser Speckle," J Cereb Blood Flow Metab, vol. 21, pp. 195-201, 2001.
[48] S. Yuan, A. Devor, D. A. Boas, and A. K. Dunn, "Determination of optimal exposure time for imaging of blood flow changes with laser speckle contrast imaging," Appl. Opt., vol. 44, pp. 1823-1830, 2005.
[49] M. Madou, Fundamentals of Microfabrication: The Science of Miniaturization: CRC Press, 2002.
[50] S. K. Kaldor and I. C. Noyan, "Flexural loading of rectangular Si beams and plates," Materials Science and Engineering: A, vol. 399, pp. 64-71, 2005.