Abstract

We describe a sensitive method for measuring the stress birefringence of an optical window that utilizes a phase-measuring Fizeau interferometer incorporating a variable retarder and a nonpolarizing beam splitter. When we test a material in an interferometer cavity, the wave front transmitted through the material is deviated by the surfaces, inhomogeneity, and birefringence of the material. Birefringence causes the transmitted wave front to have different optical path difference (OPD) profiles for the vertical and horizontal orientations of linear polarization. Subtracting these OPD profiles reveals the amount of phase difference between the fast and slow axes of the material. Hence, birefringence may be calculated. Phase-measurement techniques and a computer-controlled interferometer employing a variable liquid-crystal retarder provide a fully automated instrument for measuring stress birefringence. The theoretical derivation, discussion of the instrument, and experimental results are presented.

© 1992 Optical Society of America

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References

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  1. R. J. Meltzer, “Polarization,” in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, New York, 1980), Vol. 1, pp. 325–387.
  2. “Standard test method for analyzing stress in glass,” ASTM F218-68 (American Society for Testing and Materials, Philadelphia, Pa., 1989).
  3. S. R. M. Robertson, “Measuring birefringence properties using a wave plate and an analyzer,” Appl. Opt. 22, 2213–2216 (1983).
    [CrossRef] [PubMed]
  4. G. Birnbaum, E. Cory, K. Gow, “Interferometric null method for measuring stress-induced birefringence,” Appl. Opt. 13, 1660–1669 (1974).
    [CrossRef] [PubMed]
  5. S. E. Gilman, T. G. Baur, D. J. Gallagher, N. K. Shankar, “Properties of tunable nematic liquid crystal retarders,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 461–471 (1989).
  6. M. J. Schwartz, “Solving design problems with pellicles,” Electro-Opt. Syst. Design 2, 870–877 (1970).

1983 (1)

1974 (1)

1970 (1)

M. J. Schwartz, “Solving design problems with pellicles,” Electro-Opt. Syst. Design 2, 870–877 (1970).

Baur, T. G.

S. E. Gilman, T. G. Baur, D. J. Gallagher, N. K. Shankar, “Properties of tunable nematic liquid crystal retarders,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 461–471 (1989).

Birnbaum, G.

Cory, E.

Gallagher, D. J.

S. E. Gilman, T. G. Baur, D. J. Gallagher, N. K. Shankar, “Properties of tunable nematic liquid crystal retarders,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 461–471 (1989).

Gilman, S. E.

S. E. Gilman, T. G. Baur, D. J. Gallagher, N. K. Shankar, “Properties of tunable nematic liquid crystal retarders,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 461–471 (1989).

Gow, K.

Meltzer, R. J.

R. J. Meltzer, “Polarization,” in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, New York, 1980), Vol. 1, pp. 325–387.

Robertson, S. R. M.

Schwartz, M. J.

M. J. Schwartz, “Solving design problems with pellicles,” Electro-Opt. Syst. Design 2, 870–877 (1970).

Shankar, N. K.

S. E. Gilman, T. G. Baur, D. J. Gallagher, N. K. Shankar, “Properties of tunable nematic liquid crystal retarders,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 461–471 (1989).

Appl. Opt. (2)

Electro-Opt. Syst. Design (1)

M. J. Schwartz, “Solving design problems with pellicles,” Electro-Opt. Syst. Design 2, 870–877 (1970).

Other (3)

S. E. Gilman, T. G. Baur, D. J. Gallagher, N. K. Shankar, “Properties of tunable nematic liquid crystal retarders,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 461–471 (1989).

R. J. Meltzer, “Polarization,” in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, New York, 1980), Vol. 1, pp. 325–387.

“Standard test method for analyzing stress in glass,” ASTM F218-68 (American Society for Testing and Materials, Philadelphia, Pa., 1989).

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Figures (5)

Fig. 1
Fig. 1

(a) The principal directions of the stress in the cross section of the rod, which are either parallel or orthogonal to the radius. (b) For incident light linearly polarized in the vertical direction, the polarization remains unchanged in four orientations, V1, V2, H1, and H2.

Fig. 2
Fig. 2

Interference fringes have low contrast at the four 45° corners, obtained with a collimated beam linearly polarized in the vertical direction.

Fig. 3
Fig. 3

Schematic diagram of the polarization Fizeau interferometer and experimental setup: S1, S2, ends; R, return flat; T, transmission flat; B/S, beam splitter.

Fig. 4
Fig. 4

Birefringence measurement of a laser rod (0° azimuth orientation).

Fig. 5
Fig. 5

Birefringence measurement of a laser rod (90° azimuth orientation).

Equations (4)

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E ( r , θ ) = [ ( c 2 + s 2 cos ϕ ) + i ( - s 2 sin ϕ ) ( c s - c s cos ϕ ) + i ( c s sin ϕ ) ] ,
deformation ( r , θ ) = [ n e ( r ) - n o ( r ) ] τ sin 2 θ / λ ,
W ( x , y ) = M + B + S 1 + S 2 + R + T ,
n e ( r ) - n o ( r ) = [ W 2 ( r ) - W 1 ( r ) ] λ / 2 τ .

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