本論文提出一種新式的位移量測技術並結合軟體解相技術開發出一套精密位移量測系統－弦波相位調制光柵干涉儀。
在21世紀中精密位移量測的技術在各項產業中扮演著不可或缺的角色，尤其是在半導體產業上，半導體製程技術已達數個奈米，故檢測技術的解析度也須提升至數奈米甚至次奈米才能滿足半導體產業的需求，因此本文將使用光學技術開發一套精密位移量測系統。
本論文使用弦波相位調制的技術將頻差引入相位內形成外差光源，再以光柵繞射後的正一階光與部分被光柵反射形成繞射的零階反射光經反射鏡再次反射經過光柵繞射的負一階光干涉，當反射鏡移動時，位移訊號會存在於干涉訊號中，而後以自行開發的軟體鎖相放大技術解出位移訊號。由於傳統的外差干涉儀需使用到大量的偏振元件，但偏振元件因製程上的缺陷容易引入量測上的非線性誤差，另外在解相作業需使用類比電路鎖相放大器，該儀器體積大且成本高，而弦波相位調制光柵干涉儀以非常簡單的架構即可達到高解析度的位移量測，只需要使用雷射、一個架設於位移平台的光柵、反射鏡與光檢測器即可量測位移，解相的部分以軟體解相技術取代了傳統的電路鎖相放大器，可大幅降低量測系統成本與縮小量測系統的體積。本論文所提出的弦波相位調制光柵干涉儀的量測解析度約為2 nm，靈敏度為1.14°/nm，量測速度為2.85 μm/s。

In this study, a high-precision displacement measurement system: sinusoidal phase modulation grating interferometer, is developed by integrating heterodyne grating interferometry and digital lock-in technique.
In the 21st century, high-precision displacement measurement technology plays an important role in a wide range of industries, especially in the industry of semiconductor. Currently, production of semiconductor has achieved nanoscale dimensions, therefore it is essential that measurement system attains nanometer or even sub-nanometer resolution, in order to meet the demand of semiconductor industry. Thus, this study presents a high-precision displacement measurement system developed using optical technology.
The measurement system utilizes sinusoidal phase modulation as heterodyne light source, which is passed through a grating to generate 1st order light by diffraction and 0th order light by reflection. A mirror is used to direct the 0th order light to the grating so that -1st order light can be generated by diffraction. As the mirror moves, displacement signals are stored within the interferometry signals, and the relative phase can be retrieved using digital lock-in technique. Conventional heterodyne grating interferometry requires many polarizing elements, nevertheless fabrication flaws of polarizing elements increase the chances of nonlinear inaccuracies during measurement. Furthermore, conventional method requires analogue lock-in amplifier, which is big in volume and expensive, in order to extract signal from a noisy environment. In contrast, the sinusoidal phase modulation grating interferometer presented in this study is able to achieve high resolution in displacement measurement with a simple set-up. Displacement measurement can be performed by utilizing a laser, a grating fixed on moving stage, a mirror and a photodetector. This system uses digital lock-in technique, eliminating the need for a conventional lock-in amplifier, and thus reducing the measurement cost and size of measurement system in a great scale. The sinusoidal phase modulation grating interferometer proposed in this study is able to achieve resolution of 2 nm and sensitivity of 1.14 ˚/nm with measurement speed at 2.85 μm/s.

[1]. H. Marutama, S. Inoue, T. Mitsuyama. M. Ohmi. and M. Haruna, “Low-coherence interferometer system for the simultaneous measurement of refractive index and thickness,” App. Opt. 41(7), 1315-1322, (2002).
[2]. S. D. Nicola, P. Ferraoro, A. Finizio, G. Pesce and G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Comm. 118(5), 491-494, (1995).
[3]. M.H. chiu, J. Y. Lee and D. C. Su, “Refractive-index measurement base on the effects of total internal reflection and the uses of heterodyne interferometry,” App. Opt. 36(13), 2936-2939, (1997)
[4]. M.H. chiu, J. Y. Lee and D. C. Su, “Complex refractive-index measurement base on Frensnel’s equations and the uses of heterodyne interferometry,” App. Opt. 38(19), 4407- 4410 (1999).
[5]. S. Hosoe, “Laser interferometric system for displacement measurement with high precision,” Manotechnology 2(2), 88-95 (1991).
[6]. Y. Jourlin, J. Jay and O. Parriaux, “Compact diffractive interferometric displacement sensor in reflection,” Precision Eng. 26(1), 1-6 (2002).
[7]. O. G. Helleso, P. Benech and R. Rimet, “Interferometric displacement sensor made by integrated optics on glass,” Sensors and actuators A 47(1), 478-481 (1995).
[8]. T. Kubota, M. Nara, and T. Yoshino, “Interferometer for measuring displacement and distance,” Opt. Letters 12(5), 310-312 (1987).
[9]. H. Chen, S. Shen, and M. Bao, “Over-range capacity of a piezoresistive,” Sensors and Actuators 58, 197-201 (1997)
[10]. S. Yan, G. Wang, C. Lin and Y. Luo, “Displacement measurement by Single-grating heterodyne Interferometry,” Conference on Lasers and Electro-Optics Pacific Rim (2015)
[11]. J. Guo, Z. Zhu, and W. Deng, “Small-angle measurement based on surface-plasmonresonance and the use of magneto-optical modulation,” App. Opt. 38(31), 6550-6555 (1999).
[12]. J. Jin, L. Zhao, and S. Xu “High-precision rotation angle measurement method based on monocular vision,” Opt. Soc. 31(7),1401-1407 (2014).
[13]. S. T. Lin, K. T. Lin and W. J. Syu, “Angular interferometer using calcite prism and rotating analyzer,” Opt. Commun. 277(2), 251-255 (2007).
[14]. M. Lkram and G. Hussian, “Michelson interferometer for precision angle measurement,” App. Opt. 38(1) (1999).
[15]. P. Shi and E. Stijns, “New optical method for measuring small-angle rotations,” App. Opt. Vol 27(20), (1988).
[16]. W. Gao, Precision Nanometrology, Springer Verlag (2010).
[17]. 潘同宣，「疊紋自動準直儀系統」，國立中央大學，碩士論文，民國102年。
[18]. N. B. Yim, C. I, Eom and S. W. Kim “Dual mode phase measurement for optical heterodyne interferometry,” Sci. Tehnol. 11, 1131-1137 (2000).
[19]. 徐力弘，「類合成波長研製」，國立虎尾科技大學，計畫編號 NSC102-2221-E150-053 民國102年。
[20]. V. Mandryka, H. Buchner, G. Jager, “Design aspects in the development of a standing-wave interferometer,” Opt. Metrology in Production Engng. 5457 (2004).
[21]. C. Zhang and X. Wang, “Sinusoidal phase-modulating laser diode interferometer for measuring angular displacement,” Opt. Eng. 43, 3008-3013 (2004).
[22]. W. H. Sevenson, “Optical Frequency shifting by mean of a rotating diffraction grating,” App. Opt. 9(3) (1970).
[23]. S. Yan, G. Wang, C. Lin and Y. Luo, “Displacement measurement by Single-grating heterodyne Interferometry,” Conference on Lasers and Electro-Optics Pacific Rim (2015).
[24]. J. Y. Lee, H. Y. Chen, C. C. Hsu and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sensors and Actuators, 137(1) (2007).
[25]. 吳維庭，「準共光程外差光柵干涉術之研究」，國立中央大學，碩士論文，民國97年。
[26]. H.L. Hsieh, J.Y. Lee, W.T. Wu, J.C. Chen, R. Deturche, G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Journal of Measurement Science and Technology, 21(11) 1–9 (2010).
[27]. J. Y. Lee and M. P. Lu, “Optical heterodyne grating shearing interferometry for long-range positioning applications,” Opt. Commun. 284 857-862, (2011).
[28]. http://forums.ni.com/t5/LabVIEW/NI-virtual-Lock-In-Amplifier-problem/td-p/2628661.
[29]. K. J. Gasvilk, “optical metrology”, Third Edition, John Wiley & Sons, (2000).
[30]. P. Zeeman, “The effect of magnetization on the nature of light emitted by a substance”, Sensors and Actuators, 55 (1897).
[31]. S. O. Kasap, “Optoelectronics and photonics”, Prentice Hall, New Jersey, 2001.
[32]. R. Roy, P. A. Schulz and A. Walther, “Acousto-optic modulator as an electronically selectable unidirectional device in a ring laser,” Opt. lett.. 9 (1992).
[33]. Bennett and A. Charles, “Principles of physical optics,” (2008).
[34]. O. Sasaki, and Okazaki, H., “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25(18), 3137-3140 (1986).
[35]. O. Sasaki, and K. Takahashi, “Sinusoidal phase modulating interferometer using optical fibers for displacement measurement,” Appl. Opt. 27(19), 4139-4142 (1988).
[36]. T. Suzuki and O. Sasaki, S. Takayama and T. Maruyama, “Real-time displacement measurement using synchronous detection in a sinusoidal phase modulating interferometer,” Opt. Eng. 32(5), 1033-1037 (1993).
[37]. Y. L. Lo and T.C. Yu, “A polarimetric glucose sensor using a liquid-crystal polarization modulator driven by a sinusoidal signal,” Opt. Commun. 259(1), 40-48 (2006).
[38]. Stanford Research System, Model SR850 DSP Lock-In Amplifier (1992).
[39]. Moffat, R. J., “Describing the uncertainties in experimental results,” Exp. Therm. Fluid Sci. 1(1), 3-17 (1988).