## Two-dimensional measurement technique for birefringence vector distributions: measurement principle

Applied Optics, Vol. 38, Issue 11, pp. 2225-2231 (1999)

http://dx.doi.org/10.1364/AO.38.002225

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### Abstract

The two-dimensional measurement principle for a birefringence vector distribution in transparent materials is analyzed. The system nonuniformity that results from the system components makes the two-dimensional measurement principle quite different from that of a point-measurement method, and the measurement principle requires a two-dimensional analysis. A pulsed optical phase modulation is employed to simplify the two-dimensional mathematical analysis. As a result, concepts are proposed of the system function that characterizes the system nonuniformity that results from the system components and of the intrinsic function that is related to the birefringence vector distribution in a birefringent sample. The influence of the system nonuniformity on the two-dimensional measurement is eliminated by measurement of the intrinsic function, whereas its two values allow for the mathematical separation of the birefringence vector components. The effectiveness of the two-dimensional analysis is illustrated by measurement of a birefringence vector distribution, which is induced by an internal stress distribution in a poly(methyl methacrylate) plate, owing to the photoelastic effect.

© 1999 Optical Society of America

**OCIS Codes**

(260.1440) Physical optics : Birefringence

**History**

Original Manuscript: June 5, 1998

Revised Manuscript: December 1, 1998

Published: April 10, 1999

**Citation**

Yongchang Zhu, Takehiro Koyama, Tatsuo Takada, and Yoshihiro Murooka, "Two-dimensional measurement technique for birefringence vector distributions: measurement principle," Appl. Opt. **38**, 2225-2231 (1999)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-11-2225

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### References

- J. Tsuji, M. Nishida, K. Kawada, “The basis for photoelastic stress analysis,” in Experimental Methods Using Photoelastic Effect (Japanese Nikkan Kougyo, Tokyo, 1965), pp. 51–170 (in Japanese).
- J. W. Dally, W. F. Riley, “Theory of photo-elasticity,” in Experimental Stress Analysis (McGraw-Hill, New York, 1978), pp. 406–446.
- M. Zahn, T. Takada, S. Voldman, “Kerr electro-optic field mapping measurement in water using parallel cylindrical electrodes,” J. Appl. Phys. 54, 4749–4761 (1983). [CrossRef]
- N. O’Flaherty, N. Kiyomoto, I. Srahama, Y. Machida, “A system for high sensitive measurement of birefringence using a photo-elastic modulator and its applications,” in Electro-Optic and Magneto-Optic Materials II, H. Dammann, ed., Proc. SPIE1274, 122–131 (1990). [CrossRef]
- H. Sato, M. Yamaguchi, A. Yoshimoto, T. Takada, “High sensitive measurement system of birefringence using optical phase modulator and two Faraday rotators,” Jpn. J. Soc. Mater. Eng. Res. 4, 22–34 (1991). [CrossRef]
- M. Takayama, T. Takada, T. Yoshino, “Stress distribution using high sensitive birefringence measurement system,” Jpn. J. Nondestructive Tests 44, 249–252 (1995).
- M. Ohmi, M. Akatsuka, K. Ishikawa, K. Naito, Y. Yonezawa, Y. Nishida, M. Yamanaka, Y. Izawa, S. Nakai, “High-sensitivity two-dimensional thermal- and mechanical-stress-induced birefringence measurements in a Nd:YAG rod,” Appl. Opt. 33, 6368–6372 (1994). [CrossRef] [PubMed]
- Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994). [CrossRef]
- U. Gafvert, A. Jaksts, C. Tornkvist, L. Walfridsson, “Electrical field distribution in transformer oil,” IEEE Trans. Electr. Insul. 27, 647–660 (1992). [CrossRef]
- K. Tanaka, T. Takada, “Measurement of the 2-dimensional electric field vector in dielectric liquid,” IEEE Trans. Dieletr. Electr. Insul. 1, 747–753 (1994). [CrossRef]
- R. M. A. Azzam, N. M. Bashara, “Propagation of polarized light through polarizing optical systems,” in Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), pp. 66–152.
- Y. C. Zhu, T. Takada, D. M. Tu, “An optical measurement technique for studying residual surface charge distribution,” J. Phys. D 28, 1468–1477 (1995). [CrossRef]
- Y. C. Zhu, T. Takada, “A 2-dimensional Kerr-effect technique for electric field distribution in liquid dielectrics,” IEEE Trans. Dielectr. Electr. Insul. 4, 748–757 (1997). [CrossRef]
- T. Kawasaki, Y. Hirata, T. Takada, T. Maeno, “Visualization and quantification technique of latent electric charge image using Pockels effect, high-sensitive measurement using image lock-in amplifier,” Trans. IEE Jpn. 113-C, 1114–1120 (1993).
- Y. C. Zhu, T. Koyama, T. Takada, Y. Murooka, “Two-dimensional measurement technique for birefringence vector distributions: data processing and experiment verification,” Appl. Opt. 38, 2216–2224 (1999). [CrossRef]

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