Abstract

We present a new technique for determining the refractive index profiles of axially symmetric optical fibers based on imaging phase gradients introduced into a transmitted optical field by a fiber sample. An image of the phase gradients within the field is obtained using a new non-interferometric technique based on bright field microscopy. This provides sufficient information to reconstruct the refractive index profile using the inverse Abel transform. The technique is robust, rapid and possesses high spatial resolution and we demonstrate its application to the reconstruction of the refractive index profiles of a single-mode and a multimode optical fiber.

© 2005 Optical Society of America

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References

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App. Opt.

E. Brinkmeyer, �??Refractive index profile determination from the diffraction pattern,�?? App. Opt. 16, 2802- 2803 (1977).
[CrossRef]

Appl. Opt.

Comp. Phys. Commun.

C. Fleurier and J. Chapelle, �??Inversion of Abel�??s integral equation-application to plasma spectroscopy,�?? Comp. Phys. Commun. 7, 200-206 (1974).
[CrossRef]

L. S. Fan and W. Squire, �??Inversion of Abel�??s integral equation by a direct method,�?? Comp. Phys. Commun. 10, 98-103 (1975).
[CrossRef]

J. Appl. Phys.

D. J. Butler, K. A. Nugent and A. Roberts, �??Characterisation of optical fibres using near-field scanning optical microscopy,�?? J. Appl. Phys. 75, 2753-2756 (1994).
[CrossRef]

J. Comp. Phys.

H. Brunner, �??The numerical solution of a class of Abel integral equations by piecewise polynomials,�?? J. Comp. Phys., 12, 412-416 (1973)
[CrossRef]

J. Microsc.

E.D. Barone-Nugent, A. Barty and K.A. Nugent, �??Quantitative phase-amplitude micrscopy I: optical microscopy,�?? J. Microsc. 206, 194-203 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

Meas. Sci Technol.

Y. Park, N. H. Seong, Y. Youk and D.Y Kim, �??Simple scanning fibre-optic confocal microscopy for the refractive index profile measurement of an optical fibre,�?? Meas. Sci Technol. 13, 695-699 (2002).
[CrossRef]

Opt. and Quant. Electron.

K. I. White, �??Practical application of refracted near-field technique for the measurement of optical fibre refractive index profile,�?? Opt. and Quant. Electron. 11, 185-196 (1979).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

D. Paganin and K. A. Nugent, �??Non-interferometric phase imaging with partially coherent light,�?? Phys. Rev. Lett. 80, 2586-2589 (1998).
[CrossRef]

Proc. SPIE

G. Makosch and B. Solf, �??Surface profiling by electro-optical phase measurement�??, in High Resolution Soft X-Ray Optics, E. Spiller, ed., Proc. SPIE 316, 43-53 (1981)

SIAM J. Numer. Anal.

G. N. Minerbo and M. E. Levy, �??Inversion of Abel integral equation by means of orthogonal polynomials,�?? SIAM J. Numer. Anal.,6, 598-616 (1969).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram showing coordinate system used in this paper. (a) End view of fiber, (b) transverse view.

Fig. 2.
Fig. 2.

(a) Transverse phase gradient of OFTC GF1 optical fiber. (b) Refractive index image of GF1 fiber reconstructed from Fig. 2(a). Image size is 152 µm×103 µm.

Fig. 3.
Fig. 3.

(a) Transverse phase gradient of Corning 62.5/125 multimode fiber. (b) Refractive index image of corning 62.5/125 multimode fiber reconstructed from Fig. 3(a). Image size is 304 µm×207 µm.

Fig. 4.
Fig. 4.

(a) Refractive index profiles of OFTC GF1 fiber. The solid curve represents the refractive index profile obtained from the bright field intensity images using the transverse phase gradient technique. The dashed curve is the refractive index profile obtained from the commercial profiling (Photon Kinetics S14 profiler) method. (b) Refractive index profiles of Corning 62.5/125 multimode fiber. The solid curve is the refractive index profile obtained from the transverse phase gradient technique. The dashed curve is the calculated parabolic index profile using the specifications obtained from the manufacturer.

Equations (5)

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( I ( x , y , z ) ϕ ( x , y , z ) ) = k I ( x , y , z ) z ,
ϕ = i k I ( x , y ) [ F 1 ( k x k r 2 F ( I ( x , y ) z ) ) x ̂ + F 1 ( k y k r 2 F ( I ( x , y ) z ) ) y ̂ ]
Δ n ( r , y ) = λ 2 π 2 r R ϕ ( x , y ) x ( R 2 x 2 ) 1 2 d x
ϕ ( x , y ) = a 0 ( y ) + m = 1 a m ( y ) cos ( m π x R )
ϕ ( x , y ) x = π R m = 1 m a m ( y ) sin ( m π x R )

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