Abstract

The effects of off-focusing and beam deflection on polarimetric stress measurements of optical fibers are investigated. A simple method for reducing the distortion of the phase retardation caused by unwanted beam deflections in residual stress measurement is introduced. The method is examined numerically by ray-tracing techniques and experimentally by use of hollow silica fibers into which various index-matching liquids have been inserted. An autofocusing technique is introduced. The error in stress measurement reproducibility was determined to be less than 4%. We tested the absolute error in measured stress by applying incremental external tension and determined that it is less than 0.464 MPa.

© 2003 Optical Society of America

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References

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  1. P. L. Chu, T. Whitbread, “Stress transformation due to fusion splicing in optical fiber,” Electron. Lett. 20, 599–600 (1984).
    [CrossRef]
  2. T. Volotinen, M. Zimnol, M. Tomozawa, Y.-K. Lee, K. Raine, “Effect of mechanical striping and arc-fusion on the strength and aging of a spliced recoated optical fiber,” in Reliability of Photonics Materials and Structures, E. Suhir, M. Fukuda, C. R. Kurkjian, eds., Mater. Res. Soc. Symp. Proc.531, 163–168 (1998).
    [CrossRef]
  3. B. H. Kim, Y. Park, D. Y. Kim, U. C. Paek, W.-T. Han, “Effect of OH impurity on residual stress development in optical fiber,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 173–174, paper WA3.
  4. B. H. Kim, Y. Park, T.-J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, W.-T. Han, “Residual stress relaxation in core of optical fibers by CO2 laser irradiation,” Opt. Lett. 26, 1657–1659 (2001).
    [CrossRef]
  5. Y. Park, T.-J. Ahn, Y. H. Kim, W.-T. Han, U. C. Paek, D. Y. Kim, “Measurement method for profiling the residual stress and the strain-optic coefficient of an optical fiber,” Appl. Opt. 41, 21–26 (2002).
    [CrossRef] [PubMed]
  6. K. W. Raine, R. Feced, S. E. Kanellopoulos, V. A. Handerek, “Measurement of axial stress at high spatial resolution in ultraviolet-exposed fibers,” Appl. Opt. 38, 1086–1095 (1999).
    [CrossRef]
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    [CrossRef]
  9. Y. Park, U. C. Paek, D. Y. Kim, “Complete determination of the stress tensor of a polarization-maintaining fiber by photoelastic tomography,” Opt. Lett. 27, 1217–1219 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  13. R. Ditteon, ed., Modern Geometrical Optics (Wiley, New York, 1998).
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  18. Th. Rose, D. Spriegel, J.-R. Kropp, “Fast photoelastic stress determination application to monomode fibers and splices,” Meas. Sci. Technol. 4, 431–434 (1993).
    [CrossRef]
  19. M. Goldstein, T. H. Davies, “Glass fibers with oriented chain molecules,” J. Am. Ceram. Soc. 38, 223–226 (1955).
    [CrossRef]
  20. J. F. Stirling, “Frozen strains in glass fibers,” J. Soc. Glass Technol. 39, 134T–144T (1955).
  21. U. C. Paek, C. R. Kurkjian, “Calculation of cooling rate and induced stresses in drawing of optical fibers,” J. Am. Ceram. Soc. 58, 330–334 (1975).
    [CrossRef]

2002

2001

1999

1997

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329–1342 (1997).
[CrossRef]

1995

1993

Th. Rose, D. Spriegel, J.-R. Kropp, “Fast photoelastic stress determination application to monomode fibers and splices,” Meas. Sci. Technol. 4, 431–434 (1993).
[CrossRef]

1987

1986

1984

P. L. Chu, T. Whitbread, “Stress transformation due to fusion splicing in optical fiber,” Electron. Lett. 20, 599–600 (1984).
[CrossRef]

1982

1975

U. C. Paek, C. R. Kurkjian, “Calculation of cooling rate and induced stresses in drawing of optical fibers,” J. Am. Ceram. Soc. 58, 330–334 (1975).
[CrossRef]

1955

M. Goldstein, T. H. Davies, “Glass fibers with oriented chain molecules,” J. Am. Ceram. Soc. 38, 223–226 (1955).
[CrossRef]

J. F. Stirling, “Frozen strains in glass fibers,” J. Soc. Glass Technol. 39, 134T–144T (1955).

Abe, T.

Ahn, T.-J.

Bachmann, P. K.

Bayon, J. F.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329–1342 (1997).
[CrossRef]

Bernage, P.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329–1342 (1997).
[CrossRef]

Chu, P. L.

P. L. Chu, T. Whitbread, “Stress transformation due to fusion splicing in optical fiber,” Electron. Lett. 20, 599–600 (1984).
[CrossRef]

P. L. Chu, T. Whitbread, “Measurement of stresses in optical fibers and preforms,” Appl. Opt. 21, 4241–4245 (1982).
[CrossRef] [PubMed]

Chung, Y.

Cordier, P.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329–1342 (1997).
[CrossRef]

Davies, T. H.

M. Goldstein, T. H. Davies, “Glass fibers with oriented chain molecules,” J. Am. Ceram. Soc. 38, 223–226 (1955).
[CrossRef]

Delevaque, E.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329–1342 (1997).
[CrossRef]

Dong, L.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329–1342 (1997).
[CrossRef]

Douay, M.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329–1342 (1997).
[CrossRef]

Feced, R.

Fonjallaz, P. Y.

Goldstein, M.

M. Goldstein, T. H. Davies, “Glass fibers with oriented chain molecules,” J. Am. Ceram. Soc. 38, 223–226 (1955).
[CrossRef]

Goodier, J. N.

S. P. Timoshenko, J. N. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1970), pp. 65–68.

Han, W.-T.

Y. Park, T.-J. Ahn, Y. H. Kim, W.-T. Han, U. C. Paek, D. Y. Kim, “Measurement method for profiling the residual stress and the strain-optic coefficient of an optical fiber,” Appl. Opt. 41, 21–26 (2002).
[CrossRef] [PubMed]

B. H. Kim, Y. Park, T.-J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, W.-T. Han, “Residual stress relaxation in core of optical fibers by CO2 laser irradiation,” Opt. Lett. 26, 1657–1659 (2001).
[CrossRef]

B. H. Kim, Y. Park, D. Y. Kim, U. C. Paek, W.-T. Han, “Effect of OH impurity on residual stress development in optical fiber,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 173–174, paper WA3.

Handerek, V. A.

Hermann, W.

Kanellopoulos, S. E.

Kim, B. H.

B. H. Kim, Y. Park, T.-J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, W.-T. Han, “Residual stress relaxation in core of optical fibers by CO2 laser irradiation,” Opt. Lett. 26, 1657–1659 (2001).
[CrossRef]

B. H. Kim, Y. Park, D. Y. Kim, U. C. Paek, W.-T. Han, “Effect of OH impurity on residual stress development in optical fiber,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 173–174, paper WA3.

Kim, D. Y.

Kim, Y. H.

Koga, H.

Kropp, J.-R.

Th. Rose, D. Spriegel, J.-R. Kropp, “Fast photoelastic stress determination application to monomode fibers and splices,” Meas. Sci. Technol. 4, 431–434 (1993).
[CrossRef]

Kurkjian, C. R.

U. C. Paek, C. R. Kurkjian, “Calculation of cooling rate and induced stresses in drawing of optical fibers,” J. Am. Ceram. Soc. 58, 330–334 (1975).
[CrossRef]

Lee, B. H.

Lee, Y.-K.

T. Volotinen, M. Zimnol, M. Tomozawa, Y.-K. Lee, K. Raine, “Effect of mechanical striping and arc-fusion on the strength and aging of a spliced recoated optical fiber,” in Reliability of Photonics Materials and Structures, E. Suhir, M. Fukuda, C. R. Kurkjian, eds., Mater. Res. Soc. Symp. Proc.531, 163–168 (1998).
[CrossRef]

Limberger, H. G.

Mitsunaga, Y.

Niay, P.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329–1342 (1997).
[CrossRef]

Paek, U. C.

Y. Park, U. C. Paek, D. Y. Kim, “Complete determination of the stress tensor of a polarization-maintaining fiber by photoelastic tomography,” Opt. Lett. 27, 1217–1219 (2002).
[CrossRef]

Y. Park, T.-J. Ahn, Y. H. Kim, W.-T. Han, U. C. Paek, D. Y. Kim, “Measurement method for profiling the residual stress and the strain-optic coefficient of an optical fiber,” Appl. Opt. 41, 21–26 (2002).
[CrossRef] [PubMed]

B. H. Kim, Y. Park, T.-J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, W.-T. Han, “Residual stress relaxation in core of optical fibers by CO2 laser irradiation,” Opt. Lett. 26, 1657–1659 (2001).
[CrossRef]

U. C. Paek, C. R. Kurkjian, “Calculation of cooling rate and induced stresses in drawing of optical fibers,” J. Am. Ceram. Soc. 58, 330–334 (1975).
[CrossRef]

B. H. Kim, Y. Park, D. Y. Kim, U. C. Paek, W.-T. Han, “Effect of OH impurity on residual stress development in optical fiber,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 173–174, paper WA3.

Park, Y.

Poignant, H.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329–1342 (1997).
[CrossRef]

Poumellec, B.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329–1342 (1997).
[CrossRef]

Raine, K.

T. Volotinen, M. Zimnol, M. Tomozawa, Y.-K. Lee, K. Raine, “Effect of mechanical striping and arc-fusion on the strength and aging of a spliced recoated optical fiber,” in Reliability of Photonics Materials and Structures, E. Suhir, M. Fukuda, C. R. Kurkjian, eds., Mater. Res. Soc. Symp. Proc.531, 163–168 (1998).
[CrossRef]

Raine, K. W.

Rose, Th.

Th. Rose, D. Spriegel, J.-R. Kropp, “Fast photoelastic stress determination application to monomode fibers and splices,” Meas. Sci. Technol. 4, 431–434 (1993).
[CrossRef]

Salathé, R. P.

Spriegel, D.

Th. Rose, D. Spriegel, J.-R. Kropp, “Fast photoelastic stress determination application to monomode fibers and splices,” Meas. Sci. Technol. 4, 431–434 (1993).
[CrossRef]

Stirling, J. F.

J. F. Stirling, “Frozen strains in glass fibers,” J. Soc. Glass Technol. 39, 134T–144T (1955).

Taunay, T.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329–1342 (1997).
[CrossRef]

Timoshenko, S. P.

S. P. Timoshenko, J. N. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1970), pp. 65–68.

Tomozawa, M.

T. Volotinen, M. Zimnol, M. Tomozawa, Y.-K. Lee, K. Raine, “Effect of mechanical striping and arc-fusion on the strength and aging of a spliced recoated optical fiber,” in Reliability of Photonics Materials and Structures, E. Suhir, M. Fukuda, C. R. Kurkjian, eds., Mater. Res. Soc. Symp. Proc.531, 163–168 (1998).
[CrossRef]

Volotinen, T.

T. Volotinen, M. Zimnol, M. Tomozawa, Y.-K. Lee, K. Raine, “Effect of mechanical striping and arc-fusion on the strength and aging of a spliced recoated optical fiber,” in Reliability of Photonics Materials and Structures, E. Suhir, M. Fukuda, C. R. Kurkjian, eds., Mater. Res. Soc. Symp. Proc.531, 163–168 (1998).
[CrossRef]

Wehr, H.

Whitbread, T.

P. L. Chu, T. Whitbread, “Stress transformation due to fusion splicing in optical fiber,” Electron. Lett. 20, 599–600 (1984).
[CrossRef]

P. L. Chu, T. Whitbread, “Measurement of stresses in optical fibers and preforms,” Appl. Opt. 21, 4241–4245 (1982).
[CrossRef] [PubMed]

Wiechert, D. U.

Xie, W. X.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329–1342 (1997).
[CrossRef]

Zimnol, M.

T. Volotinen, M. Zimnol, M. Tomozawa, Y.-K. Lee, K. Raine, “Effect of mechanical striping and arc-fusion on the strength and aging of a spliced recoated optical fiber,” in Reliability of Photonics Materials and Structures, E. Suhir, M. Fukuda, C. R. Kurkjian, eds., Mater. Res. Soc. Symp. Proc.531, 163–168 (1998).
[CrossRef]

Appl. Opt.

Electron. Lett.

P. L. Chu, T. Whitbread, “Stress transformation due to fusion splicing in optical fiber,” Electron. Lett. 20, 599–600 (1984).
[CrossRef]

J. Am. Ceram. Soc.

M. Goldstein, T. H. Davies, “Glass fibers with oriented chain molecules,” J. Am. Ceram. Soc. 38, 223–226 (1955).
[CrossRef]

U. C. Paek, C. R. Kurkjian, “Calculation of cooling rate and induced stresses in drawing of optical fibers,” J. Am. Ceram. Soc. 58, 330–334 (1975).
[CrossRef]

J. Lightwave Technol.

M. Douay, W. X. Xie, T. Taunay, P. Bernage, P. Niay, P. Cordier, B. Poumellec, L. Dong, J. F. Bayon, H. Poignant, E. Delevaque, “Densification involved in the UV-based photosensitivity of silica glasses and optical fibers,” J. Lightwave Technol. 15, 1329–1342 (1997).
[CrossRef]

J. Opt. Soc. Am. A

J. Soc. Glass Technol.

J. F. Stirling, “Frozen strains in glass fibers,” J. Soc. Glass Technol. 39, 134T–144T (1955).

Meas. Sci. Technol.

Th. Rose, D. Spriegel, J.-R. Kropp, “Fast photoelastic stress determination application to monomode fibers and splices,” Meas. Sci. Technol. 4, 431–434 (1993).
[CrossRef]

Opt. Lett.

Other

T. Volotinen, M. Zimnol, M. Tomozawa, Y.-K. Lee, K. Raine, “Effect of mechanical striping and arc-fusion on the strength and aging of a spliced recoated optical fiber,” in Reliability of Photonics Materials and Structures, E. Suhir, M. Fukuda, C. R. Kurkjian, eds., Mater. Res. Soc. Symp. Proc.531, 163–168 (1998).
[CrossRef]

B. H. Kim, Y. Park, D. Y. Kim, U. C. Paek, W.-T. Han, “Effect of OH impurity on residual stress development in optical fiber,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 173–174, paper WA3.

D. Marcuse, ed., Principles of Optical Fiber Measurements (Academic, London, 1981).

R. Ditteon, ed., Modern Geometrical Optics (Wiley, New York, 1998).

S. P. Timoshenko, J. N. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1970), pp. 65–68.

S. Rabinovich, ed., Measurement Errors: Theory and Practice (AIP Press, New York, 1995).

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Figures (14)

Fig. 1
Fig. 1

Schematic of a polariscopic phase-retardation measurement setup.

Fig. 2
Fig. 2

(a) Ideal case of ray paths without deflection. (b) Real case of ray paths with deflection. (c) Schematic of our proposed system for reducing deflection.

Fig. 3
Fig. 3

(a) Ray in an optical fiber. (b) Complete ray tracing for our measurement system including the optical fiber and a triplet microscope objective lens.

Fig. 4
Fig. 4

Intensity distributions of light on three different planes: at s = 32.024, s = 32.064 (image plane), and s = 32.104 mm.

Fig. 5
Fig. 5

Captured transverse fiber images at three different fiber locations when a CCD used for taking the image of the fiber was fixed (a) +16 μm off the original object position, (b) at the original object position, and (c) -16 μm off the original object position.

Fig. 6
Fig. 6

Line-scan intensity profiles of the captured images: at positions marked relative to the object position.

Fig. 7
Fig. 7

Power spectra in the high-spatial-frequency range for the line-scanned intensity profiles shown in Fig. 6 at positions shown relative to the object position.

Fig. 8
Fig. 8

Variation of the summed power spectrum as a function of displacement of the object fiber position.

Fig. 9
Fig. 9

Calculated temperature distribution with respect to the radius of the hollow fiber.

Fig. 10
Fig. 10

Experimental and calculated thermally induced axial stress profiles of the hollow fiber.

Fig. 11
Fig. 11

Measured axial stress profiles of hollow silica fibers into which index-matching liquids with three values of Δn have been inserted.

Fig. 12
Fig. 12

Reproducibility test with ten repeated measurements of a conventional SM fiber (Corning SMF-28). We show the mean axial stress profile (solid curve) and its SD (error bars) at each radial point.

Fig. 13
Fig. 13

Absolute error test for multiple measurements of a conventional single-mode fiber (Samsung) whose incremental fiber elongation of 0.00651% corresponds to a 4.71-MPa step size in tension.

Fig. 14
Fig. 14

Linear response (filled rectangles) of the measured average axial stress versus the incremental elongation length of a fiber and it linear fit.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

It, sp=i I0 exp-t-Tisp2Δt2,
σzr=αE1-v2r22-r12r1r2 Trrdr-Tr,
TrT0-Tir=a1+brc,
SDr=i=1nσzir-σ¯zr2n-11/2,
σz=0a σzrrdr0a rdr,
R=σz|σz|=0a σzrrdr0a |σzr| rdr.

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