本論文提出兩種同時量測主軸和線性雙折射性系統的創新設計，並採用圓偏光儀架構及共路徑電光調變旋光外差干涉技術。成功地改進過去發展量測系統之低精度、受限的量測範圍、煩瑣的訊號處理、架構複雜及不能同時量測等缺點，經實驗證實具有實用價值。

　　第一套的新型旋光外差干涉儀有僅據有單一訊號且直接容易的訊號處理、簡潔的共路徑光學架構、主軸量測範圍高至 、相位延遲量測範圍高至 及不受光強擾動的影響等特點；而第二套同時量測系統由於利用兩個相位鎖住擷取的訊號處理方式，使得主軸和相位延遲量測具有高精度和解析度，而相位延遲量測範圍更可高至 ，經實驗證實此干涉儀不受光強擾動且具有不錯的重覆性及穩定性。設計上有經由光路之特殊安排以消除非偏極分光鏡之反射相位延遲對相位擷取準確性的影響，及使用相位補償器來降低分光鏡之傳輸相位延遲的影響，有效地降低非線性誤差及提高量測精度等特點。

　　In this paper, two novel measurement systems designed for simultaneously measuring the principal axis and phase retardation of the linear birefringent materials are proposed. They are based on circular polariscope and common-path electro-optic modulated circular heterodyne technique. The defects as low precision, limited dynamic range, tedious signal processing, high complexity, or the inability to simultaneously measure the principal axis and phase retardation in previous measurement systems are improved successfully.

　　The first novel circular heterodyne interferometer has the advantages of a straightforward signal processing operation on a single photodetector, a simple compact common-path optical configuration, the dynamic range of the principal axis angle measurement is up to and that of phase retardation measurement is up to , and is not influenced by the intensity variation. The second novel measurement system is capable of simultaneously measuring the principal axis and phase retardation with high accuracy and resolution by means of a simple two phase-locked extractions technique. Moreover, the dynamic range of the phase retardation measurement is up to . This interferometer is not influenced by the intensity variation and has good repeatability and stability via experimental validation. There are two unique advantages in this system. One advantage is using the appropriate arrangement of optical path to eliminate the influence caused by the reflection phase retardation effect of nonpolarized beam splitter on the accuracy of phase-locked extraction. The other one is using a phase compensator to suppress the transmission phase retardation effect in the beam splitter, thereby alleviating the non-linearity error and enhancing the precision of the measuring performance

Azzam, R. M. A. and Mahmoud, F. A., “Symmetrically coated pellicle beam splitters for dual quarter-wave retardation in reflection and transmission,” Appl. Opt., Vol. 41, pp. 235-238, 2002.

Azzam., R. M. A. and Bashara, N. M., Ellipsometry and polarized light, Elsevier Science, New York, 1989.

Bitou, Y., “Polarization mixing error reduction in a two-beam Interferometer,” Opt. Rev., Vol. 9, pp. 227-229, 2002.

Bobroff, N., “Recent advances in displacement measuring interferometry,” Meas. Sci. Tech., Vol. 4, pp. 907-926, 1993.

Cameron, B. D. and Cóte, G. L., “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Transactions on Biomedical Engineering, Vol. 44, No. 12, pp. 1221-1227, 1997.

Chiu, M. H., Chen, C. D., and Su, D. C., “Method for determining the fast axis and phase retardation of a wave plate,” J. Opt. Soc. Am. A, Vol. 13, pp. 1924-1929, 1996.

Dally, J. W. and Riley, W. F., Experimental stress analysis, McGraw-Hill, 1999.

Feng, C. M., Huang, Y. C., Chang, J. G., Chang, M., and Chou, C., “A true phase sensitive optical heterodyne polarimeter on glucose concentration measurement,” Opt. Commun., Vol. 141, pp. 314-321, 1997.

Freitas, J. M. De and Player, M. A., “Importance of rotational beam alignment in the generation of second harmonic errors in laser heterodyne interferometry,” Meas. Sci. Tech., Vol. 4, pp. 1173-1176, 1993.

Gary, L. Cloud., Optical methods of engineering analysis,
Cambridge, 1994.

Gazalet, M. G., Ravez, M., Haine, F., Bruneel C., and Bridoux E., “Acousto-optic low frequency shifter,” Appl. Opt., Vol. 33, pp. 1293-1298, 1994.

Gelmini, E., Minomi, U., and Docchio, F., “Tunable, double-wavelength heterodyne detection interferometer for absolute distance measurement,” Opt. Lett., Vol. 19, pp. 213-215,
1994.

Hariharan, P., Optical interfeometry, Academic Press, 1983.
Haus, H. A., Waves and fields in optoelectronics, Prientice-Hall, Inc., Englewood Cliffs, New Jersey, Ch. 12, 1984.

Hecht, Optics, Addision-Wesley, 3rd ed., Ch. 8, pp. 330-340, 1998.

Hou, W. and Wilkening, G., “Investigation and compensation of nonlinearity of heterodyne interferometers,” Prec. Eng., Vol. 14, No. 2, pp. 91-98, 1992.

Hu, H. Z., “Polarization heterodyne interferometry using a simple rotating analyzer. 1: Theory and error analysis,” Appl. Opt., Vol. 22, pp. 2052-2056, 1983.

Huang, Y. C., Chou, C., and Chang, M. “Direct measurement of refractive indices ( ne, no ) of a linear birefringent retardation plate,” Opt. Commun., Vol. 133, pp. 11-16,
1997.

Kemp, J. C., “Piezo-optical birefringence modulators: new use for a long known effect,” J. Opt. Sci. Am., Vol. 59, pp. 950-954, 1969.

Kothiyal, M. P. and Delisle, C., “Optical frequency shifter for heterodyne interferometry using coumterrotating wave plates,” Opt. Lett., Vol. 9, pp. 319-321, 1984.

Kurzynowski, P. and Wozniak, W. A., “Phase retardation measurement in simple and reverse senarmont compensators without calibrated quarter wave plates,” Optik, Vol. 113, pp. 51-53, 2002.

Lin, D., Jiang, H., and Yin, C., “Analysis of nonlinearity in a high-resolution grating interferometer,” Opics & Laser Technology, Vol. 32, pp. 95-99, 2000.

Lin, J. Y. and Su, D. C., “A new type of optical heterodyne polarimeter,” Meas. Sci. Tech., Vol. 14, pp. 55-58, 2003.

Lin, Y., Zhou, Z., and Wang, R., “Optical heterodyne measurement of the phase retardation of a quarter-wave plate,” Appl. Opt., Vol. 13, pp. 553-555, 1988.

Lo, Y. L. and Hsu, P. F., “Birefringence measurements by an electro-optic modulator using a new heterodyne scheme,” SPIE, Opt. Eng., Vol. 41, No. 11, pp. 2764-2767, 2002.

Lo, Y. L., Lai, C. H., Lin, J. F., and Hsu, P. F., “Simultaneous absolute measurements of principal angle and phase retardation with a new common-path heterodyne interferometer,” Appl. Opt., Vol. 43, pp. 2013-2022, 2004.

Mackey, J. R., Salari, E., and Tin, P., “Optical material stress measurement system using two orthogonally polarized sinusoidally intensity-modulated semiconductor lasers,” Meas. Sci. Tech., Vol. 13, pp. 179-185, 2002.

Nishida, Y. and Yamanaka, M., “Development of a two-dimensional birefringence distribution measurement system in laser-diode pumped solid-state laser material,” Rev. Sci. Instrum., Vol. 72, pp. 2387-2391, 2001.

Ohkubo, S. and Umeda, N., “Near-field scanning optical microscope based on fast birefringence measurements,” Sens. and Mater., Vol. 13, No. 8, pp. 433-443, 2001.

Rochford, K. B., Rose, A. H., and Wang, C. M., “NIST study investigates retardance uncertainty,” Laser Focus World, pp. 223-227, 1997.

Rosenbluth, A. E. and Bobroff, N., “Optical sources of nonlinearity in heterodyne interferometers,” Prec. Eng., Vol. 12, No. 1, pp. 7-11, 1990.

Serreze, H. B. and Goldner, R. B., “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum., Vol. 45, pp. 1613-1614, 1974.

Shindo, Y. and Hanabusa, H., “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun., Vol. 24, pp. 240-244, 1983.

Shurcliff, W. A., Polarized light, Harvard U. Press, Cambridge, Mass., 1962.

Su, D. C., Chiu, M. H., and Chen, C. D., “Simple two frequency laser,” Prec. Eng., Vol. 18, pp. 161-163, 1996.

Suits, J. C., “Magneto-optical rotation and ellipticity measurements with a spinning analyzer,” Rev. Sci. Instrum., Vol. 42, pp. 19-22, 1971.

Suzuki, T. and Hioki, R., “Translation of light frequency by moving grating,” J. Opt. Soc. Am., Vol. 57, pp. 1551, 1967.

Takasaki, H., Umeda, N., and Tsukiji, M., “Stabilized transverse Zeeman laser as a new light source for optical measurement,” Appl. Opt., Vol. 19, pp. 435-441, 1980.

Teng, H. K., Chou, C., and Chang, H. F., “Polarization-shifting interferometry on two-dimensional linear birefringent parameters measurement,” Opt. Commun., Vol. 224, pp. 197-204, 2003.

Theocaris, P. S. and Gdoutos, E. E., Matrix theory of photoelasticity, Springer-Verlag, Berlin Heidelberg, Ch. 7, 1979.

Villèle, G. D. and Loriette, V., “Birefringence imagining with imperfect benches: application to large-scale birefringence measurements,” Appl. Opt., Vol. 39, pp. 3864-3874, 2000.

Wang, B. and Oakberg, T. C., “A new instrument for measuring both the magnitude and angle of low level linear birefringence,” Rev. Sci. Instrum., Vol. 70, pp. 3847-
3854, 1999.

Wang, B., “Linear birefringence measurement instrument using two photoelastic modulators,” SPIE, Opt. Eng., Vol. 41, No. 5, pp. 981-987, 2002.

Wickramasingle, H. K., Laser heterodyne probes, Optical Metrology, NATO ASI series, 1987.

Wu, C. M. and Su, C. S., “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Tech., Vol. 7, pp. 62-68, 1996.

Xie, Y. and Wu, Y. Z., “Elliptical polarization and nonorthogonality of stabilized Zeeman laser output,” Appl. Opt., Vol. 28, pp. 2043-2046, 1989.

Xie, Y. and Wu, Y. Z., “Zeeman laser interferometer errors for high-precision measurements,” Appl. Opt., Vol. 31, pp. 881-884, 1992.

Yariv, A. and Yeh, P., Optical waves in crystal, John Wiley＆Sons, Inc., Ch. 4, 1984.

Zandman, F., Redner, S., and Dally, J. W., Photoelastic coating, Society for Experimental Stress Analysis, Ch. 2, 1977.

Zhao, H. and Zhang, G., “Nonlinear error by orientation and elliptical polarization in two-beam interferometer,” Opt. Eng., Vol. 41, pp. 3204-3208, 2002.

Zhu, Y., Koyama, T., Takada, T., and Murooka, Y., “Two-dimensional measurement technique for birefringence vector distributions: measurement principle,” Appl. Opt., Vol. 38, pp. 2225-2231, 1999.

Zhu, Y., Koyama, T., Takada, T., Murooka, Y., and Otsuka T., “Two-dimensional measurement technique for birefringence vector distributions: data processing and experimental verification,” Appl. Opt., Vol. 38, pp. 2216-2224, 1999.

林俊佑，以外差干涉術測量葡萄糖溶液之偏極折射率及濃度，國立交通大學光電工程研究所碩士論文，2000.

邱銘宏，共光程外差干涉儀的原理與其應用之研究，國立交通大學光電工程研究所博士論文，1997.

李朱育，外差干涉術在量測s-與p-偏光間相位差變化的應用，國立交通大學光電工程研究所博士論文，1998.

徐彬峰，新型共路外差干涉量測系統之研發，國立成功大學機械工程研究所碩士論文，2002.

殷純永，民國84年，光電精密儀器設計，機械工業出版社，大陸.

郭彥珍，邱宗明，李信，激光偏振干涉光路的非線性分析計算，計量學報，Vol. 16, No. 4, Oct. 1995.

陳應誠，電光晶體調制外差式干涉儀與其非線性誤差之消減，國立清華大學物理研究所碩士論文，1995.

游展汶，以旋光外差干涉術測量雙折射晶體之尋常光及非尋常光折射率，國立交通大學光電工程研究所碩士論文，2000.

趙慧洁，外差干涉儀頻率混疊誤差分析，計量學報，Vol. 20, No.3, July 1999.

賴俊豪，新型共路外差干涉儀於同時量測主軸方向和雙折射特性之研究與應用，國立成功大學機械工程研究所碩士論文，2003.