Abstract

A method for measuring the axial residual stress profile in optical fibers is presented. The axial stress profile on the fiber cross section is obtained from optical retardations of rays that travel laterally through the fiber. The retardations are measured for a number of fiber orientations by rotating the fiber through 180°. The stress profile is reconstructed by performing a numerical inversion of the data. This paper describes the principle, experimental setup, and measured stress profiles, as well as measurement errors and spatial resolution. It is shown that the nonaxisymmetrical stress profile can be nondestructively measured with high accuracy by using the method.

© 1986 Optical Society of America

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  1. K. Brugger, “Effect of thermal stress on refractive index in clad fibers,” Appl. Opt. 10, 437–438 (1971).
    [CrossRef] [PubMed]
  2. N. Shibata, K. Jinguji, M. Kawachi, J. Edahiro, “Nondestructive structure measurement of optical fiber preforms with photoelastic effect,” Jpn. J. Appl. Phys. 18, 1267–1273 (1979).
    [CrossRef]
  3. T. Abe, Y. Mitsunaga, H. Koga, “Axial residual stress measurement for silica optical fibers using a polariscope,” in Digest of the International Commission for Optics (Japan Society of Applied Physics, Sapporo, 1984), pp. 132–133.
  4. Y. Sasaki, K. Okamoto, T. Hosaka, N. Shibata, “Polarization-maintaining and absorption-reducing fibers,” in Digest of the Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper THCC6.
  5. T. Katsuyama, H. Matsumura, T. Suganuma, “Low-loss single-polarization fibers,” Electron. Lett. 17, 473–474 (1981).
    [CrossRef]
  6. T. Okoshi, K. Oyamada, M. Nishimura, H. Yokota, “Sidetunnel fiber: an approach to polarization-maintaining optical waveguiding scheme,” Electron. Lett. 18, 824–826 (1982).
    [CrossRef]
  7. N. Shibata, K. Okamoto, K. Suzuki, Y. Ishida, “Polarization-mode properties of elliptical-core fibers and stress-induced birefringent fibers,”J. Opt. Soc. Am. 73, 1792–1798 (1983).
    [CrossRef]
  8. P. L. Chu, T. Whitbread, “Measurement of stresses in optical fiber and preform,” Appl. Opt. 21, 4241–4245.
    [PubMed]
  9. S. P. Timoshenko, Theory of Elasticity (McGraw-Hill, New York, 1983), p. 468.
  10. T. F. Budinger, G. T. Gullberg, “Three-dimensional reconstruction in nuclear medicine emission imaging,”IEEE Trans. Nucl. Sci. NS-21, 2–20 (1974).
  11. L. A. Shepp, B. F. Logan, “The Fourier reconstruction of a head section,”IEEE Trans. Nucl. Sci. NS-21, 21–43 (1974).
  12. A. Klug, R. A. Crowther, “Three-dimensional image reconstruction from the viewpoint of information theory,” Nature 238, 435–440 (1972).
    [CrossRef]

1983 (1)

1982 (1)

T. Okoshi, K. Oyamada, M. Nishimura, H. Yokota, “Sidetunnel fiber: an approach to polarization-maintaining optical waveguiding scheme,” Electron. Lett. 18, 824–826 (1982).
[CrossRef]

1981 (1)

T. Katsuyama, H. Matsumura, T. Suganuma, “Low-loss single-polarization fibers,” Electron. Lett. 17, 473–474 (1981).
[CrossRef]

1979 (1)

N. Shibata, K. Jinguji, M. Kawachi, J. Edahiro, “Nondestructive structure measurement of optical fiber preforms with photoelastic effect,” Jpn. J. Appl. Phys. 18, 1267–1273 (1979).
[CrossRef]

1974 (2)

T. F. Budinger, G. T. Gullberg, “Three-dimensional reconstruction in nuclear medicine emission imaging,”IEEE Trans. Nucl. Sci. NS-21, 2–20 (1974).

L. A. Shepp, B. F. Logan, “The Fourier reconstruction of a head section,”IEEE Trans. Nucl. Sci. NS-21, 21–43 (1974).

1972 (1)

A. Klug, R. A. Crowther, “Three-dimensional image reconstruction from the viewpoint of information theory,” Nature 238, 435–440 (1972).
[CrossRef]

1971 (1)

Abe, T.

T. Abe, Y. Mitsunaga, H. Koga, “Axial residual stress measurement for silica optical fibers using a polariscope,” in Digest of the International Commission for Optics (Japan Society of Applied Physics, Sapporo, 1984), pp. 132–133.

Brugger, K.

Budinger, T. F.

T. F. Budinger, G. T. Gullberg, “Three-dimensional reconstruction in nuclear medicine emission imaging,”IEEE Trans. Nucl. Sci. NS-21, 2–20 (1974).

Chu, P. L.

Crowther, R. A.

A. Klug, R. A. Crowther, “Three-dimensional image reconstruction from the viewpoint of information theory,” Nature 238, 435–440 (1972).
[CrossRef]

Edahiro, J.

N. Shibata, K. Jinguji, M. Kawachi, J. Edahiro, “Nondestructive structure measurement of optical fiber preforms with photoelastic effect,” Jpn. J. Appl. Phys. 18, 1267–1273 (1979).
[CrossRef]

Gullberg, G. T.

T. F. Budinger, G. T. Gullberg, “Three-dimensional reconstruction in nuclear medicine emission imaging,”IEEE Trans. Nucl. Sci. NS-21, 2–20 (1974).

Hosaka, T.

Y. Sasaki, K. Okamoto, T. Hosaka, N. Shibata, “Polarization-maintaining and absorption-reducing fibers,” in Digest of the Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper THCC6.

Ishida, Y.

Jinguji, K.

N. Shibata, K. Jinguji, M. Kawachi, J. Edahiro, “Nondestructive structure measurement of optical fiber preforms with photoelastic effect,” Jpn. J. Appl. Phys. 18, 1267–1273 (1979).
[CrossRef]

Katsuyama, T.

T. Katsuyama, H. Matsumura, T. Suganuma, “Low-loss single-polarization fibers,” Electron. Lett. 17, 473–474 (1981).
[CrossRef]

Kawachi, M.

N. Shibata, K. Jinguji, M. Kawachi, J. Edahiro, “Nondestructive structure measurement of optical fiber preforms with photoelastic effect,” Jpn. J. Appl. Phys. 18, 1267–1273 (1979).
[CrossRef]

Klug, A.

A. Klug, R. A. Crowther, “Three-dimensional image reconstruction from the viewpoint of information theory,” Nature 238, 435–440 (1972).
[CrossRef]

Koga, H.

T. Abe, Y. Mitsunaga, H. Koga, “Axial residual stress measurement for silica optical fibers using a polariscope,” in Digest of the International Commission for Optics (Japan Society of Applied Physics, Sapporo, 1984), pp. 132–133.

Logan, B. F.

L. A. Shepp, B. F. Logan, “The Fourier reconstruction of a head section,”IEEE Trans. Nucl. Sci. NS-21, 21–43 (1974).

Matsumura, H.

T. Katsuyama, H. Matsumura, T. Suganuma, “Low-loss single-polarization fibers,” Electron. Lett. 17, 473–474 (1981).
[CrossRef]

Mitsunaga, Y.

T. Abe, Y. Mitsunaga, H. Koga, “Axial residual stress measurement for silica optical fibers using a polariscope,” in Digest of the International Commission for Optics (Japan Society of Applied Physics, Sapporo, 1984), pp. 132–133.

Nishimura, M.

T. Okoshi, K. Oyamada, M. Nishimura, H. Yokota, “Sidetunnel fiber: an approach to polarization-maintaining optical waveguiding scheme,” Electron. Lett. 18, 824–826 (1982).
[CrossRef]

Okamoto, K.

N. Shibata, K. Okamoto, K. Suzuki, Y. Ishida, “Polarization-mode properties of elliptical-core fibers and stress-induced birefringent fibers,”J. Opt. Soc. Am. 73, 1792–1798 (1983).
[CrossRef]

Y. Sasaki, K. Okamoto, T. Hosaka, N. Shibata, “Polarization-maintaining and absorption-reducing fibers,” in Digest of the Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper THCC6.

Okoshi, T.

T. Okoshi, K. Oyamada, M. Nishimura, H. Yokota, “Sidetunnel fiber: an approach to polarization-maintaining optical waveguiding scheme,” Electron. Lett. 18, 824–826 (1982).
[CrossRef]

Oyamada, K.

T. Okoshi, K. Oyamada, M. Nishimura, H. Yokota, “Sidetunnel fiber: an approach to polarization-maintaining optical waveguiding scheme,” Electron. Lett. 18, 824–826 (1982).
[CrossRef]

Sasaki, Y.

Y. Sasaki, K. Okamoto, T. Hosaka, N. Shibata, “Polarization-maintaining and absorption-reducing fibers,” in Digest of the Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper THCC6.

Shepp, L. A.

L. A. Shepp, B. F. Logan, “The Fourier reconstruction of a head section,”IEEE Trans. Nucl. Sci. NS-21, 21–43 (1974).

Shibata, N.

N. Shibata, K. Okamoto, K. Suzuki, Y. Ishida, “Polarization-mode properties of elliptical-core fibers and stress-induced birefringent fibers,”J. Opt. Soc. Am. 73, 1792–1798 (1983).
[CrossRef]

N. Shibata, K. Jinguji, M. Kawachi, J. Edahiro, “Nondestructive structure measurement of optical fiber preforms with photoelastic effect,” Jpn. J. Appl. Phys. 18, 1267–1273 (1979).
[CrossRef]

Y. Sasaki, K. Okamoto, T. Hosaka, N. Shibata, “Polarization-maintaining and absorption-reducing fibers,” in Digest of the Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper THCC6.

Suganuma, T.

T. Katsuyama, H. Matsumura, T. Suganuma, “Low-loss single-polarization fibers,” Electron. Lett. 17, 473–474 (1981).
[CrossRef]

Suzuki, K.

Timoshenko, S. P.

S. P. Timoshenko, Theory of Elasticity (McGraw-Hill, New York, 1983), p. 468.

Whitbread, T.

Yokota, H.

T. Okoshi, K. Oyamada, M. Nishimura, H. Yokota, “Sidetunnel fiber: an approach to polarization-maintaining optical waveguiding scheme,” Electron. Lett. 18, 824–826 (1982).
[CrossRef]

Appl. Opt. (2)

Electron. Lett. (2)

T. Katsuyama, H. Matsumura, T. Suganuma, “Low-loss single-polarization fibers,” Electron. Lett. 17, 473–474 (1981).
[CrossRef]

T. Okoshi, K. Oyamada, M. Nishimura, H. Yokota, “Sidetunnel fiber: an approach to polarization-maintaining optical waveguiding scheme,” Electron. Lett. 18, 824–826 (1982).
[CrossRef]

IEEE Trans. Nucl. Sci. (2)

T. F. Budinger, G. T. Gullberg, “Three-dimensional reconstruction in nuclear medicine emission imaging,”IEEE Trans. Nucl. Sci. NS-21, 2–20 (1974).

L. A. Shepp, B. F. Logan, “The Fourier reconstruction of a head section,”IEEE Trans. Nucl. Sci. NS-21, 21–43 (1974).

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (1)

N. Shibata, K. Jinguji, M. Kawachi, J. Edahiro, “Nondestructive structure measurement of optical fiber preforms with photoelastic effect,” Jpn. J. Appl. Phys. 18, 1267–1273 (1979).
[CrossRef]

Nature (1)

A. Klug, R. A. Crowther, “Three-dimensional image reconstruction from the viewpoint of information theory,” Nature 238, 435–440 (1972).
[CrossRef]

Other (3)

T. Abe, Y. Mitsunaga, H. Koga, “Axial residual stress measurement for silica optical fibers using a polariscope,” in Digest of the International Commission for Optics (Japan Society of Applied Physics, Sapporo, 1984), pp. 132–133.

Y. Sasaki, K. Okamoto, T. Hosaka, N. Shibata, “Polarization-maintaining and absorption-reducing fibers,” in Digest of the Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper THCC6.

S. P. Timoshenko, Theory of Elasticity (McGraw-Hill, New York, 1983), p. 468.

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Figures (9)

Fig. 1
Fig. 1

Coordinate systems.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

Reconstructed stress profiles in GI fiber by (a) the present method and by (b) the conventional method.

Fig. 4
Fig. 4

Measurement results for a PANDA fiber. (a) Photograph of cross-sectional area. (b) Three-dimensional plot of stress profile. (c) Stress profile represented by brightness.

Fig. 5
Fig. 5

Measurement results for an elliptical-jacket fiber. (a) Photograph of cross-sectional area. (b) Three-dimensional plot of stress profile. (c) Stress profile represented by brightness.

Fig. 6
Fig. 6

Measurement results for a side-tunnel fiber. (a) Photograph of cross-sectional area. (b) Three-dimensional plot of stress profile. (c) Stress profile represented by brightness.

Fig. 7
Fig. 7

Cross-sectional geometry of a PANDA fiber in computer simulation.

Fig. 8
Fig. 8

Three-dimensional plot of reconstructed stress profile with cross section shown in Fig. 7.

Fig. 9
Fig. 9

Stress errors by computer simulation for stress profile in Fig. 8.

Equations (20)

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R ( Y , θ ) = C - [ σ Z ( u , v ) - σ Y ( u , v ) ] d X ,
S σ Y ( u , v ) d X d Z = 0 ,
- σ Y ( u , v ) d X = 0.
R ( Y , θ ) = C - σ Z ( u , v ) d X .
σ Z ( u , v ) = 1 8 π 2 C 0 2 π [ - F ( ω , θ ) H ( ω ) exp ( i ω Y ) d ω ] d θ ,
F ( ω , θ ) = - R ( Y , θ ) exp ( - i ω Y ) d Y
H ( ω ) = | 2 W π sin ( π W 2 W ) | [ sin ( π ω / 2 W ) π ω / 2 W ] 2 ,
R ( Y ) = λ Φ ( Y ) / π .
e 1 = Δ R N / 4 M C a ,
N = 2 a / Δ Y .
M o p ( π / 2 ) N .
( u v ) = ( cos θ - sin θ sin θ cos θ ) ( X Y ) .
R ( Y , θ ) = C - σ Z ( X cos θ - Y sin θ , X sin θ + Y cos θ ) d X .
F ( ξ , η ) = C - - σ Z ( u , v ) exp [ - i ( ξ u + η v ) ] d u d v ,
F ( ω cos θ ¯ , ω sin θ ¯ ) = C - - σ Z ( u , v ) exp [ - i ω ( u cos θ ¯ + v sin θ ¯ ) ] d u d v = - [ C - σ Z ( X cos θ - Y sin θ , × X sin θ + Y cos θ ) d X ] exp ( - i ω Y ) d Y = - R ( Y , θ ) exp ( - i ω Y ) d Y .
C σ Z ( u , v ) = 1 4 π 2 - - F ( ξ , η ) exp [ i ( ξ u + η v ) ] d ξ d η .
C σ Z ( u , v ) = 1 8 π 2 0 2 π [ - F ( ω cos θ , ω sin θ ) ω exp ( i ω Y ) d ω ] d θ .
H ( ω ) = | 2 W π sin ( π ω 2 W ) | [ sin ( π ω / 2 W ) π ω / 2 W ] 2 ,
σ Z ( u , v ) = 1 8 π 2 C 0 2 π [ - F ( ω , θ ) H ( ω ) exp ( i ω Y ) d ω ] d θ ,
F ( ω , θ ) = - R ( Y , θ ) exp ( - i ω Y ) d Y .

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