Abstract

A new nondestructive method for determination of the outer diameter of optical fibers is described. The principle of this technique is based on observing interference maxima in the scattered light from a fiber that is side illuminated by a laser beam at oblique incidence. This technique is easy to implement and can be applied to a fiber with an inhomogeneous and large core.

© 1994 Optical Society of America

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References

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  1. M. Young, P. Hale, S. Mechels, “Optical fiber geometry: accurate measurement of cladding diameter,” J. Res. Natl. Inst. Stand. Technol. 98, 203–216 (1993).
    [CrossRef]
  2. J. G. Baines, A. G. Hallam, K. W. Raine, N. P. Turner, “Fiber diameter measurements and their calibration,” J. Lightwave Technol. 8, 1259–1268 (1990).
    [CrossRef]
  3. J. Baines, K. Raine, “Review of recent developments in fiber geometry measurements,” in Technical Digest, Symposium on Optical Fiber Measurements, Natl. Inst. Stand. Technol. Spec. Publ.839, 45–50 (1992).
  4. W. Farone, M. Kerker, “Light scattering from long submicron cylinder at normal incidence,” J. Opt. Soc. Am. 56, 481–487 (1966).
    [CrossRef]
  5. J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, “Determination of optical-fiber diameter from resonances in the elastic scattering spectrum,” Opt. Lett. 6, 272–274 (1981).
    [CrossRef] [PubMed]
  6. A. Ashkin, J. M. Dziedzic, R. H. Stolen, “Outer diameter measurement of low birefringence optical fibers by a new resonant backscatter technique,” Appl. Opt. 20, 2299–2303 (1981).
    [CrossRef] [PubMed]
  7. M. B. van der Mark, L. Bosselaar, “Noncontact calibration of optical fiber cladding diameter using exact scattering theory,” J. Lightwave Technol. 12, 1–5 (1994).
    [CrossRef]
  8. D. Marcuse, Principles of Optical Fiber Measurements (Academic, New York, 1981).
  9. L. S. Watkins, “Scattering from side-illuminated clad glass fibers for determination of fiber parameters,” J. Opt. Soc. Am. 64, 767–772 (1974).
    [CrossRef]
  10. W. Farone, C. Querfeld, “Electromagnetic scattering from radially inhomogeneous infinite cylinders at oblique incidence,” J. Opt. Soc. Am. 56, 476–480 (1966).
    [CrossRef]
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 8, pp. 445–449.

1994 (1)

M. B. van der Mark, L. Bosselaar, “Noncontact calibration of optical fiber cladding diameter using exact scattering theory,” J. Lightwave Technol. 12, 1–5 (1994).
[CrossRef]

1993 (1)

M. Young, P. Hale, S. Mechels, “Optical fiber geometry: accurate measurement of cladding diameter,” J. Res. Natl. Inst. Stand. Technol. 98, 203–216 (1993).
[CrossRef]

1990 (1)

J. G. Baines, A. G. Hallam, K. W. Raine, N. P. Turner, “Fiber diameter measurements and their calibration,” J. Lightwave Technol. 8, 1259–1268 (1990).
[CrossRef]

1981 (2)

1974 (1)

1966 (2)

Ashkin, A.

Baines, J.

J. Baines, K. Raine, “Review of recent developments in fiber geometry measurements,” in Technical Digest, Symposium on Optical Fiber Measurements, Natl. Inst. Stand. Technol. Spec. Publ.839, 45–50 (1992).

Baines, J. G.

J. G. Baines, A. G. Hallam, K. W. Raine, N. P. Turner, “Fiber diameter measurements and their calibration,” J. Lightwave Technol. 8, 1259–1268 (1990).
[CrossRef]

Barber, P. W.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 8, pp. 445–449.

Bosselaar, L.

M. B. van der Mark, L. Bosselaar, “Noncontact calibration of optical fiber cladding diameter using exact scattering theory,” J. Lightwave Technol. 12, 1–5 (1994).
[CrossRef]

Chang, R. K.

Dziedzic, J. M.

Farone, W.

Hale, P.

M. Young, P. Hale, S. Mechels, “Optical fiber geometry: accurate measurement of cladding diameter,” J. Res. Natl. Inst. Stand. Technol. 98, 203–216 (1993).
[CrossRef]

Hallam, A. G.

J. G. Baines, A. G. Hallam, K. W. Raine, N. P. Turner, “Fiber diameter measurements and their calibration,” J. Lightwave Technol. 8, 1259–1268 (1990).
[CrossRef]

Kerker, M.

Marcuse, D.

D. Marcuse, Principles of Optical Fiber Measurements (Academic, New York, 1981).

Mechels, S.

M. Young, P. Hale, S. Mechels, “Optical fiber geometry: accurate measurement of cladding diameter,” J. Res. Natl. Inst. Stand. Technol. 98, 203–216 (1993).
[CrossRef]

Messinger, B. J.

Owen, J. F.

Querfeld, C.

Raine, K.

J. Baines, K. Raine, “Review of recent developments in fiber geometry measurements,” in Technical Digest, Symposium on Optical Fiber Measurements, Natl. Inst. Stand. Technol. Spec. Publ.839, 45–50 (1992).

Raine, K. W.

J. G. Baines, A. G. Hallam, K. W. Raine, N. P. Turner, “Fiber diameter measurements and their calibration,” J. Lightwave Technol. 8, 1259–1268 (1990).
[CrossRef]

Stolen, R. H.

Turner, N. P.

J. G. Baines, A. G. Hallam, K. W. Raine, N. P. Turner, “Fiber diameter measurements and their calibration,” J. Lightwave Technol. 8, 1259–1268 (1990).
[CrossRef]

van der Mark, M. B.

M. B. van der Mark, L. Bosselaar, “Noncontact calibration of optical fiber cladding diameter using exact scattering theory,” J. Lightwave Technol. 12, 1–5 (1994).
[CrossRef]

Watkins, L. S.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 8, pp. 445–449.

Young, M.

M. Young, P. Hale, S. Mechels, “Optical fiber geometry: accurate measurement of cladding diameter,” J. Res. Natl. Inst. Stand. Technol. 98, 203–216 (1993).
[CrossRef]

Appl. Opt. (1)

J. Lightwave Technol. (2)

M. B. van der Mark, L. Bosselaar, “Noncontact calibration of optical fiber cladding diameter using exact scattering theory,” J. Lightwave Technol. 12, 1–5 (1994).
[CrossRef]

J. G. Baines, A. G. Hallam, K. W. Raine, N. P. Turner, “Fiber diameter measurements and their calibration,” J. Lightwave Technol. 8, 1259–1268 (1990).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Res. Natl. Inst. Stand. Technol. (1)

M. Young, P. Hale, S. Mechels, “Optical fiber geometry: accurate measurement of cladding diameter,” J. Res. Natl. Inst. Stand. Technol. 98, 203–216 (1993).
[CrossRef]

Opt. Lett. (1)

Other (3)

J. Baines, K. Raine, “Review of recent developments in fiber geometry measurements,” in Technical Digest, Symposium on Optical Fiber Measurements, Natl. Inst. Stand. Technol. Spec. Publ.839, 45–50 (1992).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 8, pp. 445–449.

D. Marcuse, Principles of Optical Fiber Measurements (Academic, New York, 1981).

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Figures (7)

Fig. 1
Fig. 1

Scattering cone of a tilted fiber. γ0 is the angle between the direction of the incident beam and the fiber axis (oz).

Fig. 2
Fig. 2

Geometry of the optical path in a cylindrical medium.

Fig. 3
Fig. 3

Superior view of the optical path.

Fig. 4
Fig. 4

Fiber cross section. The dashed curve denotes the projections of the optical path on a plane perpendicular to the z axis.

Fig. 5
Fig. 5

Projections of rays trajectories on a plane perpendicular to the z axis.

Fig. 6
Fig. 6

Pattern of scattered light in the interval 0 ≤ θ ≤ π obtained for γ0 = 9.5°. The point of maximal intensity corresponds to θ = 0.

Fig. 7
Fig. 7

Continuous curve shows the calculated values of d as a function of refractive index n for γ0 = 9.5° and N = 47.6. The dashed curve shows the calculated values of d as a function of refractive index n in forward scattering (γ0 = 90°) for N = 47.6 (θ1 ≅ 28.8°, θ2 = 10°).

Equations (24)

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n ( d r / d s ) = ( n 2 - α 2 - c 2 / r 2 ) 1 / 2 ,
n r ( d ϕ / d s ) = c / r ,
n ( d z / d s ) = α ,
α = n cos γ = cos γ 0
c = n r cos δ = ( d / 2 ) cos δ 0 ,
sin γ = ( 1 - cos 2 γ ) 1 / 2 = [ 1 - ( cos γ 0 / n 2 ] 1 / 2 ,
K = ( 2 π / λ ) ( n 2 - cos 2 γ 0 ) 1 / 2 .
A P ¯ = d cos α 2 ,
Ψ 1 = K A P ¯ = ( 2 π d / λ ) ( n 2 - cos 2 γ 0 ) 1 / 2 cos α 2 .
θ = 2 ( α 1 - α 2 ) .
cos δ = sin γ sin α 2 ,
cos δ 0 = sin     γ 0 sin     α 1 ;
sin γ 0 sin α 1 = n sin γ sin α 2 .
sin γ 0 sin α 1 = ( n 2 - cos 2 γ 0 ) 1 / 2 sin α 2 .
D Q ¯ + Q E ¯ = d [ 1 - sin ( α 1 - α 2 ) ] = d [ 1 - sin ( θ / 2 ) ] ,
Ψ 2 = 2 π ( D Q ¯ + Q E ¯ ) ( λ / sin γ 0 ) = ( 2 π d / λ ) sin γ 0 [ 1 - sin ( θ / 2 ) ] .
Ψ 1 = Ψ 1 + 2 π ( A A ¯ + P P ¯ ) ( λ / sin γ 0 ) = ( 2 π d / λ ) [ ( n 2 - cos 2 γ 0 ) 1 / 2 cos α 2 + sin γ 0 ( 1 - cos α 1 ) ] .
cos α 2 = - sin γ 0 cos ( θ / 2 ) + ( n 2 - cos 2 γ 0 ) 1 / 2 [ n 2 - cos ( 2 γ 0 ) - 2 sin γ 0 ( n 2 - cos 2 γ 0 ) 1 / 2 cos ( θ / 2 ) ] 1 / 2 ,
cos α 1 = - sin γ 0 + ( n 2 - cos 2 γ 0 ) 1 / 2 cos ( θ / 2 ) [ n 2 - cos ( 2 γ 0 ) - 2 sin γ 0 ( n 2 - cos 2 γ 0 ) 1 / 2 cos ( θ / 2 ) ] 1 / 2 .
Δ Ψ ( θ ) = Ψ 1 ( θ ) - Ψ 2 ( θ ) = ( 2 π d / λ ) { [ n 2 - cos ( 2 γ 0 ) - 2 sin γ 0 ( n 2 - cos 2 γ 0 ) 1 / 2 cos ( θ / 2 ) ] 1 / 2 + sin γ 0 sin ( θ / 2 ) } .
N = ( p 1 - p 2 ) = [ Δ Ψ ( θ 1 ) - Δ Ψ ( θ 2 ) ] / 2 π .
d = N λ / [ F ( θ 1 ) - F ( θ 2 ) ] ,
F ( θ ) = [ n 2 - cos ( 2 γ 0 ) - 2 sin γ 0 ( n 2 - cos 2 γ 0 ) 1 / 2 × cos ( θ / 2 ) ] 1 / 2 + sin γ 0 sin ( θ / 2 ) .
d N λ / { 2 1 / 2 γ 0 [ sin ( θ 1 / 2 - π / 4 ) - sin ( θ 2 / 2 - π / 4 ) ] } .

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