本論文是在探討製造和分析光學編碼器。使用了兩個飛秒雷射在Invar合金上製造最佳且精確的反射光柵。在兩種制度下用不同的雷射參數製作了幾個光柵：固定的重複率和固定的平均雷射功率。通過確定衍射點的功率來測量衍射光柵的效率，並且通過改進的Littrow配置設置來測量Talbot圖像的圖像處理以及光柵的節距。這顯示了Talbot圖像設置有能力成為光學編碼器生產線中光柵的在線NDT測試機器。改進Littrow間距測量裝置的方法可以消除安裝誤差高達0.03º。
光路被引入以使衍射光柵的階數發生干涉，並且根據該光路，已經設計和製造了M編碼器。不同行程和不同安裝情況下的測量結果表明，製作光柵的總誤差，安裝誤差，環境，信號處理和電路的誤差小於±195nm / 100mm。 M編碼器的安裝公差和尺寸與市場上的其他編碼器兼容。

This thesis is discussing fabricating and analyzing optical encoder. Two femtosecond lasers have been used for fabricating optimal and precise reflecting grating on the Invar alloy. Several gratings were made with different laser parameters in two regimes: constant repetition rates and constant average laser power. The efficiency of diffraction gratings is measured in an off-plane configuration by determining the power of diffracted points, image processing of Talbot image and also the pitch of gratings has been measured by an improved Littrow configuration setup. It has been shown that Talbot image setup has capability to be an online NDT test machine for grating in the optical encoder fabrication line. The method of improving Littrow pitch measuring setup could remove the error of installation up to 0.03º.
An optical path has been introduced for making interference between orders of diffraction grating and according to this optical path, M-encoder has been designed and fabricated. The result of measurement in different traveling distances and in different installation situations has been showed that the total error of fabricating grating, installing error, environment, signal processing and circuits is less than ±195nm /100mm. The installation tolerance and size of M-encoder is compatible to the other encoders in the market.

1. Y.G. Wang, W. Tong. A high resolution DIC technique for measuring small thermal expansion of _lm specimens. Optics and Lasers in Engineering. 2013, 51(1), 3033.
2. Dornfeld, A. David, Helu, M. Moneer. Precision manufacturing. Springer; 2008. DOI:10.1007/978-0-387-68208-2-11
3. Y. Samsonov. Potentiality of Optical Diffraction Grating Technology in the Fabrication of Miniaturized Multicapillary Chromatographic and Electrophoresis Columns. Journal of Chromatographic Science. 2001; 39: 445-449.
4. P. Laporta, M. Marano, L. Pallaro, S. Taccheo. Amplitude and frequency stabilisation of a TmHo:YAG laser for coherent lidar applications at 2.1 m. Optics and Lasers in Engineering. 2002; 37(5):447-457.
5. W. YAN, W. CHEN, C. LIPPOLD, H. XU. Heat-Transfer Behavior of Mold Fluxes for Continuous Casting of Invar Alloy. Metallurgical and Materials Transactions B. 2013; 44(6):1466-1477.
6. S. Nihtianov, A. Luque. Smart Sensors and MEMS: Intelligent Devices and Microsystems for Industrial Applications. Woodhead Publishing; 2014.
7. J. Yang, R.Wang, W. Liu, Y. Sun, X. Zhu. Investigation of microstructuring CuInGaSe2 thin _lms with ultrashort laser pulses. Journal of Physics D-Applied Physics. 2009;42:21.
8. F. D'Amatoa, M. De Rosab. Tunable diode lasers and two-tone frequency modulation spectroscopy applied to atmospheric gas analysis. Optics and Lasers in Engineering. 2002; 37(5):533-551.
9. J. Zheng, C. Zhou, B. Wang, and J. Feng. Beam splitting of low-contrast binary gratings under second Bragg angle incidence. JOSA A.230 2008;25(5):1075-1083.
10. Soocheol Kim, Jaehyun Hwang, Jung Heo, Suho Ryu, Donghak Lee, Sang-Hoon Kim, Seung Jae Oh, and Chulmin Joo. Spectrally encoded slit confocal microscopy using a wavelength-swept laser. J. Biomed. Opt. 2015;20(3):036016.
11. Yuji Matsuzoe, Kazuhiro Koizumi, Tetsuya Saitoh, and Toru Yoshizawa. Optimizing design of high-resolution optical encoder using a point-source light-emitting diode with slits. Opt. Eng. 2004;44(1):013609.
12. http://www.renishaw.com/en/tonic-relm-linear-encoder-system{10236.
13. H. Wanga, H. Xiea,Y. Lib, P. Fangc, X. Daia, L. Wua, M. Tanga. Fabrication of high temperature moir grating and its application. Optics and Lasers in Engineering. 2013; 54:255262.
14. Y. Chen, J. Chu, J. Jang, C. Hsieh, Y. Yang, C. Li, Y. Chen and J. Jeng.Replication of nano/micro-scale features using bulk metallic glass mold prepared by femtosecond laser and imprint processes. Journal of Micromechanics and Microengineering. 2013;23:035030. doi:10.1088/0960-1317/23/3/035030
15. Guo Ping Wang, Yongxiang Yi, and Weihua Lin. Tunable and omnidirectional photonic bandgap properties of one-dimensional photonic crystals fabricated by holography. JOSA B. 2004; 21(3):554-561.250 doi:10.1364/JOSAB.21.000554
16. T. Kohoutek, M. Hughes, J. Orava, M. Mastumoto, T. Misumi, H. Kawashima, T. Suzuki, and Y. Ohishi. Direct laser writing of relief diffraction gratings into a bulk chalcogenide glass. JOSA B. 2012; 29(10): 2779-2786.
17. E. Gamaly, A. Rode, B. Luther-Davies and V. Tikhonchuk. Ablation of solids by femtosecond lasers: Ablation mechanism and ablation thresholds for metals and dielectrics. Phys. Plasmas. 2002; 9:949. http://dx.doi.org/10.1063/1.1447555
18. S. Eaton, H. Zhang, P. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Arai. Heat accumulation e_ects in femtosecond laser-written waveguides with variable repetition rate. Optics Express. 2005; 13(12):4708-4716.
19. Z. Li, , P. Li, J. Fan, R. Fang, D. Zhang. Energy accumulation effect and parameter optimization for fabricating of high-uniform and large-area period surface structures induced by femtosecond pulsed lase. Optics and Lasers in Engineering. 2010; 48 (1): 6468. doi:10.1016/j.optlaseng.2009.07.017
20. Seea, T.L., Liua, B. Z., Liua, H., Lib, L., Chippendalec, J., Cheethamc, S., Dilworthc, S., “Effect of geometry measurements on characteristics of femtosecond laser ablation of HR4 nickel alloy,” Optics and Lasers in Engineering, Vol. 64, pp. 71–78, 2015.
21. Eaton,S., Zhang, H., Herman, P., Yoshino, F., Shah, L., Bovatsek, J., and Arai, A., “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Optics Express, Vol. 13, No. 12, pp. 4708-4716, 2015.
22. Crespo, D., Alonso, J., Morlanes, T., and Bernabeu, E., “Optical encoder based on the Lau effect,” Optical Engineering, Vol. 39, pp. 817–824, 2000.
23. Sanchez-Brea, L. M. Torcal-Milla„ F. J., and Bernabeu, E., “Continuous self-imaging regime with a double grating mask,” Applied Optics, Vol. 48, No. 30, pp. 5722-5727, 2009. doi:10.1364/AO.48.005722
24. Heidenhain Co. 2015. Exposed Linear Encoders catalogue of Heidenhain. Accessed September 2. http://www.heidenhain.com/en_US/products-and-applications/linear-encoders/exposed-linear-encoders/
25. Ye, G. Y., Liu, H. Z., Fan, S. J., Li, X., Yu, H. Y., Lei, B., Shi, Y. S., Yin, and Lu,B. H. , “A theoretical investigation of generalized grating imaging and its application to optical encoders,” Optics Communications, Vol. 354, pp. 21–27, 2015.
26. Kao, C. F., and Lu, S. H., “Reflective-type optical encoder based on fractional Talbot selfimage effect using phase grating,” In Proceeding of SPIE, Vol. 7544 No. 75440N, 2010. doi: 10.1117/12.886238.
27. Kao, C. F., and Lu, M. H., “Optical encoder based on the fractional Talbot effect,” Optics Communications, Vol. 250, pp. 16-23, 2005.
28. Liu, L., “Talbot and Lau effects on incident beams of arbitrary wavefront and their use,” Applied Optics, Vol. 28, pp. 4668–4678, 1989. doi:10.1364/AO.29.004337.
29. Ariel Lutenberg, Fernando Perez-Quintián, and María A. Rebollo Optical encoder based on a nondiffractive beam , Applied Optics, Vol. 47, Issue 13, pp. 2201-2206 (2008)\
30. Lucas García-Rodríguez, José Alonso, and Eusebio Bernabéu, Grating pseudo-imaging with polychromatic and finite extension sources, Optics Express, Vol. 12,Issue 11,pp. 2529-2541 (2004).
31. Leslie L. Deck, Peter J. de Groot, Michael Schroeder, Interferometric encoder systems, US20110255096 A1, Zygo Corporation.
32. Luo, H. X., Zhou, C. H., Zou, H., and Lu, Y. Q, “Talbot-SNOM method for non-contact evaluation of high-density gratings,” Optics Communications, Vol. 248, pp. 97–103, 2005. doi:10.1016/j.optcom.2004.12.004.
33. Guerineau, N., Harchaoui, B., and Primot, J., “Talbot experiment re-examined: demonstration of an achromatic and continuous self-imaging regime,” Optics Communications, Vol. 180, pp. 199–203, 2000.
34. Wei, W. A., Zhou, C. H., Dai, E. W., and Bai, B., “Talbot effect under illumination of double femtosecond laser pulses,” Optik, Vol. 120, pp. 625–629, 2009. doi:10.1016/j.ijleo.2008.02.014.
35. Wei, W. A., Zhou,C. H., Dai, E. W., and Liu, W. J., “Experimental study of the Talbot effect under femtosecond laser illumination,” Optics Communications, Vol. 260, pp. 415–419, 2006. doi:10.1016/j.optcom.2005.11.021
36. Liu, Q. A., and Ohba, R. J., “The effect of arbitrary small discrepancy between normal directions of grating planes in Talbot interferometry,” Optics Communications, Vol. 170, pp. 193–199, 1999.
37. Liu, Q. A., and Ohba, R. J., “A simple real-time method for checking parallelism between the two gratings in Talbot interferometry,” Optics Communications, Vol. 175, pp. 19–26, 2007. doi:10.1016/S0030-4018(99)00757-9.
38. Teng, S. Y., Wang, J. H., Zhang, W., and Cui, Y. W., “Talbot effect of the defective grating in deep Fresnel region,” Optics Communications, Vol. 336, pp. 213–223, 2014. doi:10.1016/j.optcom.2014.10.013.
39. JSM-6700 Field Emission SEM Users Manual. JOEL ltd. 2000. P2-2.
40. Ala’a F. Eftaiha, Sophie M.K. Brunet and Matthew F. Paige, A comparison of atomic force microscopy, confocal fluorescence microscopy and Brewster angle microscopy for characterizing mixed monolayer surfactant films. Current Microscopy Contributions to Advances in Science and Technology, 2012 FORMATEX pp1438.
41. Fabio Frassetto, Paolo Villoresi, and Luca Poletto, Optical concept of a compressor for XUV pulses in the attosecond domain, Optics Express, Vol. 16, Issue 9, pp. 6652-6667, 2008.
42. Kun Xiao, Lina Wang, “Analysis and Error Compensation of Electric Sine/Cosine Encoder”, The 9th International Conference on Electronic Measurement & Instruments, pp. 1-87, ICME 2009.
43. W.J. Wu, C.K. Lee, and C.T. Hsieh, “ Signal Processing Algorithm for Doppler Effect Based Manometer Positioning Systems.” Jpn. J. Appl. Phys. Vol 38, pp. 1725-1729, 1999.