Abstract

For the first time to our knowledge, digital holography is used to determine the distribution of parabolic or nonparabolic refractive index fields in graded index optical fibers. The fiber is embedded in an index matching fluid whose refractive index can be varied to a matching and mismatching index with respect to that of the cladding. In experiments for both cases high precision phase-shifting digital holographic interferometry is applied with numerical evaluation employing the multilayer model for recognition of the refraction. Due to the higher redundancy in the multiple phase-shifted holograms better accuracy can be obtained compared to classical two-beam interferometry. Therefore the holographic method is recommended as a nondestructive and noncontacting method for characterizing graded index optical fibers.

© 2009 Optical Society of America

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2008 (1)

T. Z. N. Sokkar, M. A. El-Morsy, and H. H. Wahba, “Automatic fringe analysis of the induced anisotropy of bent optical fibres,” Opt. Commun. 281, 1915-1923 (2008).
[CrossRef]

2007 (1)

A. A. Hamza, A. E. Belal, T. Z. N. Sokkar, H. M. El-Dessouky, and M. A. Agour, “Interferometric studies on the infiuence of temperature on the optical and dispersion parameters of GRIN optical fiber,” Opt. Lasers Eng. 45, 145-152(2007).
[CrossRef]

2006 (2)

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Pelli, G. Righini, and S. Sebastiani, “Digital-holography refractive-index-profile measurement of phase gratings,” Appl. Phys. Lett. 88, 111-114 (2006).

M. M. Hossain, D. S. Mehta, and C. Shakher, “Refractive index determination: an application of lensless Fourier digital holography,” Opt. Eng. 45, 106203 (2006).
[CrossRef]

2005 (2)

2004 (1)

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, and H. H. Wahba, “Coreindex determination of a thick fiber using lens-fiber interference (LFI) technique,” Opt. Lasers Eng. 42, 121-130 (2004).
[CrossRef]

2002 (4)

M. A. El-Morsy, T. Yatagai, A. A. Hamza, M. A. Mabrouk, and T. Z. N. Sokkar, “Multiple-beam Fizeau fringe-pattern analysis using Fourier transform method for accurate measurement of fiber refractive index profile of polymer fiber,” J. Appl. Polym. Sci. 85, 475-484 (2002).
[CrossRef]

M. A. El-Morsy, T. Yatagai, A. A. Hamza, M. A. Mabrouk, and T. Z. N. Sokkar, “Automatic refractive index profiling of fibers by phase analysis method using Fourier transform,” Opt. Lasers Eng. 38, 509-525 (2002).
[CrossRef]

T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, and C. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. 41, 27-37 (2002).
[CrossRef] [PubMed]

R. B. Owen and A. A. Zozulya, “Comparative study with double-exposure digital holographic interferometry and a Shack-Hartmann sensor to characterize transparent material,” Appl. Opt. 41, 5891-5895 (2002).
[CrossRef] [PubMed]

2001 (1)

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, and M. A. Shams-Eldin, “Determination of GRIN optical fiber parameters from transverse interferograms considering the refraction of the incident ray by the fiber,” Opt. Commun. 200, 131-138 (2001).
[CrossRef]

1999 (4)

T. Z. N. Sokkar, M. A. Mabrouk, and H. F. El-Bawab, “Refractive index profile of GRIN optical fiber considering the area under the interference fringe shift: II. The mismatching case,” J. Opt. A: Pure Appl. Opt. 1, 64-72(1999).
[CrossRef]

V. Kebbel, M. Adams, H.-J. Hartmann, and W. Jüptner, “Digital holography as a versatile optical diagnostic method for microgravity experiments,” Meas. Sci. Technol. 10, 893-899 (1999).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994-7001 (1999).
[CrossRef]

F. Dubois, L. Joannes, O. Dupont, J. L. Dewandel, and J. C. Legros, “An integrated optical set-up for fluid-physics experiments under microgravity conditions,” Meas. Sci. Technol. 10, 934-945 (1999).
[CrossRef]

1997 (1)

M. A. Mabrouk and H. F. El-Bawab, “Refractive index profile of GRIN optical fiber considering the area under the interference fringe shift: I. The matching case,” Pure Appl. Opt. 6, 247-256 (1997).
[CrossRef]

1995 (1)

A. A. Hamza, T. Z. N. Sokkar, A. M. Ghander, M. A. Mabrouk, and W. A. Ramadan, “On the determination of the refractive index of a fiber. II. Graded index fiber,” Pure Appl. Opt. 4, 161-177 (1995).
[CrossRef]

1994 (2)

A. A. Hamza, A. M. Ghander, T. Z. N. Sokkar, M. A. Mabrouk, and W. A. Ramadan, “On the determination of the refractive index of a fiber: I. Skin-core fiber,” Pure Appl. Opt. 3, 943-961 (1994).
[CrossRef]

U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011-2015 (1994).
[CrossRef]

1985 (1)

1981 (1)

1977 (1)

1975 (1)

M. E. Marhic, P. S. Ho and M. Epstein, “Nondestructive refractive-index profile measurements of clad optical fibers,” Appl. Phys. Lett. 26, 574-575 (1975).
[CrossRef]

1973 (1)

1965 (2)

R. L. Powell and K. A. Stetson, “Interferometric vibration analysis by wavefront reconstruction,” J. Opt. Soc. Am. 55, 1593-1608 (1965).
[CrossRef]

D. Gabor, G. W. Stroke, D. Brumm, A. Funkhouser, and A. Labeyrie, “Reconstruction of phase objects by holography,” Nature 208, 1159-1162 (1965).
[CrossRef]

1954 (1)

R. C. Faust, “The determination of the refractive indices of inhomogeneous solids by interference microscopy,” Proc. Phys. Soc., London, Sect. B 67, 138-148 (1954).
[CrossRef]

1952 (1)

R. C. Faust, “An interferometric method of studying local variations in the refractive indices of a solid,” Proc. Phys. Soc., London, Sect. B 65, 48-62 (1952).
[CrossRef]

1949 (1)

D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. R. Soc. London, Ser. A 197, 454-487 (1949).
[CrossRef]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Adams, M.

V. Kebbel, M. Adams, H.-J. Hartmann, and W. Jüptner, “Digital holography as a versatile optical diagnostic method for microgravity experiments,” Meas. Sci. Technol. 10, 893-899 (1999).
[CrossRef]

Agour, M. A.

A. A. Hamza, A. E. Belal, T. Z. N. Sokkar, H. M. El-Dessouky, and M. A. Agour, “Interferometric studies on the infiuence of temperature on the optical and dispersion parameters of GRIN optical fiber,” Opt. Lasers Eng. 45, 145-152(2007).
[CrossRef]

Agrawal, G. E.

G. E. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, 2002).
[CrossRef]

Angelis, M. de

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Pelli, G. Righini, and S. Sebastiani, “Digital-holography refractive-index-profile measurement of phase gratings,” Appl. Phys. Lett. 88, 111-114 (2006).

Barakat, N.

Beghuin, D.

Belal, A. E.

A. A. Hamza, A. E. Belal, T. Z. N. Sokkar, H. M. El-Dessouky, and M. A. Agour, “Interferometric studies on the infiuence of temperature on the optical and dispersion parameters of GRIN optical fiber,” Opt. Lasers Eng. 45, 145-152(2007).
[CrossRef]

Brumm, D.

D. Gabor, G. W. Stroke, D. Brumm, A. Funkhouser, and A. Labeyrie, “Reconstruction of phase objects by holography,” Nature 208, 1159-1162 (1965).
[CrossRef]

Cha, S. S.

Colomb, T.

Cuche, E.

Dahlgren, P.

Depeursinge, C.

Dewandel, J. L.

F. Dubois, L. Joannes, O. Dupont, J. L. Dewandel, and J. C. Legros, “An integrated optical set-up for fluid-physics experiments under microgravity conditions,” Meas. Sci. Technol. 10, 934-945 (1999).
[CrossRef]

Dubois, F.

F. Dubois, L. Joannes, O. Dupont, J. L. Dewandel, and J. C. Legros, “An integrated optical set-up for fluid-physics experiments under microgravity conditions,” Meas. Sci. Technol. 10, 934-945 (1999).
[CrossRef]

Dupont, O.

F. Dubois, L. Joannes, O. Dupont, J. L. Dewandel, and J. C. Legros, “An integrated optical set-up for fluid-physics experiments under microgravity conditions,” Meas. Sci. Technol. 10, 934-945 (1999).
[CrossRef]

Dürr, F.

El-Bawab, H. F.

T. Z. N. Sokkar, M. A. Mabrouk, and H. F. El-Bawab, “Refractive index profile of GRIN optical fiber considering the area under the interference fringe shift: II. The mismatching case,” J. Opt. A: Pure Appl. Opt. 1, 64-72(1999).
[CrossRef]

M. A. Mabrouk and H. F. El-Bawab, “Refractive index profile of GRIN optical fiber considering the area under the interference fringe shift: I. The matching case,” Pure Appl. Opt. 6, 247-256 (1997).
[CrossRef]

El-Dessouky, H. M.

A. A. Hamza, A. E. Belal, T. Z. N. Sokkar, H. M. El-Dessouky, and M. A. Agour, “Interferometric studies on the infiuence of temperature on the optical and dispersion parameters of GRIN optical fiber,” Opt. Lasers Eng. 45, 145-152(2007).
[CrossRef]

El-Morsy, M. A.

T. Z. N. Sokkar, M. A. El-Morsy, and H. H. Wahba, “Automatic fringe analysis of the induced anisotropy of bent optical fibres,” Opt. Commun. 281, 1915-1923 (2008).
[CrossRef]

M. A. El-Morsy, T. Yatagai, A. A. Hamza, M. A. Mabrouk, and T. Z. N. Sokkar, “Multiple-beam Fizeau fringe-pattern analysis using Fourier transform method for accurate measurement of fiber refractive index profile of polymer fiber,” J. Appl. Polym. Sci. 85, 475-484 (2002).
[CrossRef]

M. A. El-Morsy, T. Yatagai, A. A. Hamza, M. A. Mabrouk, and T. Z. N. Sokkar, “Automatic refractive index profiling of fibers by phase analysis method using Fourier transform,” Opt. Lasers Eng. 38, 509-525 (2002).
[CrossRef]

Emery, Y.

Epstein, M.

M. E. Marhic, P. S. Ho and M. Epstein, “Nondestructive refractive-index profile measurements of clad optical fibers,” Appl. Phys. Lett. 26, 574-575 (1975).
[CrossRef]

Faust, R. C.

R. C. Faust, “The determination of the refractive indices of inhomogeneous solids by interference microscopy,” Proc. Phys. Soc., London, Sect. B 67, 138-148 (1954).
[CrossRef]

R. C. Faust, “An interferometric method of studying local variations in the refractive indices of a solid,” Proc. Phys. Soc., London, Sect. B 65, 48-62 (1952).
[CrossRef]

Ferraro, P.

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Pelli, G. Righini, and S. Sebastiani, “Digital-holography refractive-index-profile measurement of phase gratings,” Appl. Phys. Lett. 88, 111-114 (2006).

Finizio, A.

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Pelli, G. Righini, and S. Sebastiani, “Digital-holography refractive-index-profile measurement of phase gratings,” Appl. Phys. Lett. 88, 111-114 (2006).

Funkhouser, A.

D. Gabor, G. W. Stroke, D. Brumm, A. Funkhouser, and A. Labeyrie, “Reconstruction of phase objects by holography,” Nature 208, 1159-1162 (1965).
[CrossRef]

Gabor, D.

D. Gabor, G. W. Stroke, D. Brumm, A. Funkhouser, and A. Labeyrie, “Reconstruction of phase objects by holography,” Nature 208, 1159-1162 (1965).
[CrossRef]

D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. R. Soc. London, Ser. A 197, 454-487 (1949).
[CrossRef]

D. Gabor, “A new microscopic principle,” Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Gardner, W. B.

Ghander, A. M.

A. A. Hamza, T. Z. N. Sokkar, A. M. Ghander, M. A. Mabrouk, and W. A. Ramadan, “On the determination of the refractive index of a fiber. II. Graded index fiber,” Pure Appl. Opt. 4, 161-177 (1995).
[CrossRef]

A. A. Hamza, A. M. Ghander, T. Z. N. Sokkar, M. A. Mabrouk, and W. A. Ramadan, “On the determination of the refractive index of a fiber: I. Skin-core fiber,” Pure Appl. Opt. 3, 943-961 (1994).
[CrossRef]

Goneid, A. S.

Hamza, A. A.

A. A. Hamza, A. E. Belal, T. Z. N. Sokkar, H. M. El-Dessouky, and M. A. Agour, “Interferometric studies on the infiuence of temperature on the optical and dispersion parameters of GRIN optical fiber,” Opt. Lasers Eng. 45, 145-152(2007).
[CrossRef]

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, and H. H. Wahba, “Coreindex determination of a thick fiber using lens-fiber interference (LFI) technique,” Opt. Lasers Eng. 42, 121-130 (2004).
[CrossRef]

M. A. El-Morsy, T. Yatagai, A. A. Hamza, M. A. Mabrouk, and T. Z. N. Sokkar, “Automatic refractive index profiling of fibers by phase analysis method using Fourier transform,” Opt. Lasers Eng. 38, 509-525 (2002).
[CrossRef]

M. A. El-Morsy, T. Yatagai, A. A. Hamza, M. A. Mabrouk, and T. Z. N. Sokkar, “Multiple-beam Fizeau fringe-pattern analysis using Fourier transform method for accurate measurement of fiber refractive index profile of polymer fiber,” J. Appl. Polym. Sci. 85, 475-484 (2002).
[CrossRef]

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, and M. A. Shams-Eldin, “Determination of GRIN optical fiber parameters from transverse interferograms considering the refraction of the incident ray by the fiber,” Opt. Commun. 200, 131-138 (2001).
[CrossRef]

A. A. Hamza, T. Z. N. Sokkar, A. M. Ghander, M. A. Mabrouk, and W. A. Ramadan, “On the determination of the refractive index of a fiber. II. Graded index fiber,” Pure Appl. Opt. 4, 161-177 (1995).
[CrossRef]

A. A. Hamza, A. M. Ghander, T. Z. N. Sokkar, M. A. Mabrouk, and W. A. Ramadan, “On the determination of the refractive index of a fiber: I. Skin-core fiber,” Pure Appl. Opt. 3, 943-961 (1994).
[CrossRef]

N. Barakat, A. A. Hamza, and A. S. Goneid, “Multiple-beam interference fringes applied to GRIN optical waveguides to determine fiber characteristics,” Appl. Opt. 24, 4383-4386(1985).
[CrossRef] [PubMed]

N. Barakat and A. A. Hamza, Interferometry of Fibrous Materials (Hilger, 1990).

Hartmann, H.-J.

V. Kebbel, M. Adams, H.-J. Hartmann, and W. Jüptner, “Digital holography as a versatile optical diagnostic method for microgravity experiments,” Meas. Sci. Technol. 10, 893-899 (1999).
[CrossRef]

Ho, P. S.

M. E. Marhic, P. S. Ho and M. Epstein, “Nondestructive refractive-index profile measurements of clad optical fibers,” Appl. Phys. Lett. 26, 574-575 (1975).
[CrossRef]

Hossain, M. M.

M. M. Hossain, D. S. Mehta, and C. Shakher, “Refractive index determination: an application of lensless Fourier digital holography,” Opt. Eng. 45, 106203 (2006).
[CrossRef]

Joannes, L.

F. Dubois, L. Joannes, O. Dupont, J. L. Dewandel, and J. C. Legros, “An integrated optical set-up for fluid-physics experiments under microgravity conditions,” Meas. Sci. Technol. 10, 934-945 (1999).
[CrossRef]

Jüptner, W.

V. Kebbel, M. Adams, H.-J. Hartmann, and W. Jüptner, “Digital holography as a versatile optical diagnostic method for microgravity experiments,” Meas. Sci. Technol. 10, 893-899 (1999).
[CrossRef]

Kebbel, V.

V. Kebbel, M. Adams, H.-J. Hartmann, and W. Jüptner, “Digital holography as a versatile optical diagnostic method for microgravity experiments,” Meas. Sci. Technol. 10, 893-899 (1999).
[CrossRef]

Kreis, T.

T. Kreis, “Digital holography for metrologic applications,” in Interferometry in Speckle Light, P. Jacquot and J. -M. Fournier, eds. (Springer-Verlag, 2000), pp. 205-212.
[CrossRef]

T. Kreis, Holographic Interferometry: Principles and Methods (Akademie-Verlag, 1996).

Kreis, Th.

Th. Kreis, Handbook of Holographic Interferometry, Optical and Digital Methods (Wiley-VCH, 2005).

Labeyrie, A.

D. Gabor, G. W. Stroke, D. Brumm, A. Funkhouser, and A. Labeyrie, “Reconstruction of phase objects by holography,” Nature 208, 1159-1162 (1965).
[CrossRef]

Legros, J. C.

F. Dubois, L. Joannes, O. Dupont, J. L. Dewandel, and J. C. Legros, “An integrated optical set-up for fluid-physics experiments under microgravity conditions,” Meas. Sci. Technol. 10, 934-945 (1999).
[CrossRef]

Limberger, H. G.

Mabrouk, M. A.

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, and H. H. Wahba, “Coreindex determination of a thick fiber using lens-fiber interference (LFI) technique,” Opt. Lasers Eng. 42, 121-130 (2004).
[CrossRef]

M. A. El-Morsy, T. Yatagai, A. A. Hamza, M. A. Mabrouk, and T. Z. N. Sokkar, “Multiple-beam Fizeau fringe-pattern analysis using Fourier transform method for accurate measurement of fiber refractive index profile of polymer fiber,” J. Appl. Polym. Sci. 85, 475-484 (2002).
[CrossRef]

M. A. El-Morsy, T. Yatagai, A. A. Hamza, M. A. Mabrouk, and T. Z. N. Sokkar, “Automatic refractive index profiling of fibers by phase analysis method using Fourier transform,” Opt. Lasers Eng. 38, 509-525 (2002).
[CrossRef]

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, and M. A. Shams-Eldin, “Determination of GRIN optical fiber parameters from transverse interferograms considering the refraction of the incident ray by the fiber,” Opt. Commun. 200, 131-138 (2001).
[CrossRef]

T. Z. N. Sokkar, M. A. Mabrouk, and H. F. El-Bawab, “Refractive index profile of GRIN optical fiber considering the area under the interference fringe shift: II. The mismatching case,” J. Opt. A: Pure Appl. Opt. 1, 64-72(1999).
[CrossRef]

M. A. Mabrouk and H. F. El-Bawab, “Refractive index profile of GRIN optical fiber considering the area under the interference fringe shift: I. The matching case,” Pure Appl. Opt. 6, 247-256 (1997).
[CrossRef]

A. A. Hamza, T. Z. N. Sokkar, A. M. Ghander, M. A. Mabrouk, and W. A. Ramadan, “On the determination of the refractive index of a fiber. II. Graded index fiber,” Pure Appl. Opt. 4, 161-177 (1995).
[CrossRef]

A. A. Hamza, A. M. Ghander, T. Z. N. Sokkar, M. A. Mabrouk, and W. A. Ramadan, “On the determination of the refractive index of a fiber: I. Skin-core fiber,” Pure Appl. Opt. 3, 943-961 (1994).
[CrossRef]

Magistretti, P.

Marhic, M. E.

M. E. Marhic, P. S. Ho and M. Epstein, “Nondestructive refractive-index profile measurements of clad optical fibers,” Appl. Phys. Lett. 26, 574-575 (1975).
[CrossRef]

Marquet, P.

Mehta, D. S.

M. M. Hossain, D. S. Mehta, and C. Shakher, “Refractive index determination: an application of lensless Fourier digital holography,” Opt. Eng. 45, 106203 (2006).
[CrossRef]

Nicola, S. De

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Pelli, G. Righini, and S. Sebastiani, “Digital-holography refractive-index-profile measurement of phase gratings,” Appl. Phys. Lett. 88, 111-114 (2006).

Owen, R. B.

Pelli, S.

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Pelli, G. Righini, and S. Sebastiani, “Digital-holography refractive-index-profile measurement of phase gratings,” Appl. Phys. Lett. 88, 111-114 (2006).

Pierattini, G.

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Pelli, G. Righini, and S. Sebastiani, “Digital-holography refractive-index-profile measurement of phase gratings,” Appl. Phys. Lett. 88, 111-114 (2006).

Powell, R. L.

Ramadan, W. A.

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, and H. H. Wahba, “Coreindex determination of a thick fiber using lens-fiber interference (LFI) technique,” Opt. Lasers Eng. 42, 121-130 (2004).
[CrossRef]

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, and M. A. Shams-Eldin, “Determination of GRIN optical fiber parameters from transverse interferograms considering the refraction of the incident ray by the fiber,” Opt. Commun. 200, 131-138 (2001).
[CrossRef]

A. A. Hamza, T. Z. N. Sokkar, A. M. Ghander, M. A. Mabrouk, and W. A. Ramadan, “On the determination of the refractive index of a fiber. II. Graded index fiber,” Pure Appl. Opt. 4, 161-177 (1995).
[CrossRef]

A. A. Hamza, A. M. Ghander, T. Z. N. Sokkar, M. A. Mabrouk, and W. A. Ramadan, “On the determination of the refractive index of a fiber: I. Skin-core fiber,” Pure Appl. Opt. 3, 943-961 (1994).
[CrossRef]

Rappaz, B.

Righini, G.

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Pelli, G. Righini, and S. Sebastiani, “Digital-holography refractive-index-profile measurement of phase gratings,” Appl. Phys. Lett. 88, 111-114 (2006).

Ruffin, P. B.

S. Yin, P. B. Ruffin, and F. T. S. Yu, eds., Fiber Optic Sensors, 2nd ed. (CRC, 2008).

Salath, R. P.

Saunder, M. J.

Schnars, U.

Sebastiani, S.

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Pelli, G. Righini, and S. Sebastiani, “Digital-holography refractive-index-profile measurement of phase gratings,” Appl. Phys. Lett. 88, 111-114 (2006).

Shakher, C.

M. M. Hossain, D. S. Mehta, and C. Shakher, “Refractive index determination: an application of lensless Fourier digital holography,” Opt. Eng. 45, 106203 (2006).
[CrossRef]

Shams-Eldin, M. A.

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, and M. A. Shams-Eldin, “Determination of GRIN optical fiber parameters from transverse interferograms considering the refraction of the incident ray by the fiber,” Opt. Commun. 200, 131-138 (2001).
[CrossRef]

Sokkar, T. Z. N.

T. Z. N. Sokkar, M. A. El-Morsy, and H. H. Wahba, “Automatic fringe analysis of the induced anisotropy of bent optical fibres,” Opt. Commun. 281, 1915-1923 (2008).
[CrossRef]

A. A. Hamza, A. E. Belal, T. Z. N. Sokkar, H. M. El-Dessouky, and M. A. Agour, “Interferometric studies on the infiuence of temperature on the optical and dispersion parameters of GRIN optical fiber,” Opt. Lasers Eng. 45, 145-152(2007).
[CrossRef]

M. A. El-Morsy, T. Yatagai, A. A. Hamza, M. A. Mabrouk, and T. Z. N. Sokkar, “Multiple-beam Fizeau fringe-pattern analysis using Fourier transform method for accurate measurement of fiber refractive index profile of polymer fiber,” J. Appl. Polym. Sci. 85, 475-484 (2002).
[CrossRef]

M. A. El-Morsy, T. Yatagai, A. A. Hamza, M. A. Mabrouk, and T. Z. N. Sokkar, “Automatic refractive index profiling of fibers by phase analysis method using Fourier transform,” Opt. Lasers Eng. 38, 509-525 (2002).
[CrossRef]

T. Z. N. Sokkar, M. A. Mabrouk, and H. F. El-Bawab, “Refractive index profile of GRIN optical fiber considering the area under the interference fringe shift: II. The mismatching case,” J. Opt. A: Pure Appl. Opt. 1, 64-72(1999).
[CrossRef]

A. A. Hamza, T. Z. N. Sokkar, A. M. Ghander, M. A. Mabrouk, and W. A. Ramadan, “On the determination of the refractive index of a fiber. II. Graded index fiber,” Pure Appl. Opt. 4, 161-177 (1995).
[CrossRef]

A. A. Hamza, A. M. Ghander, T. Z. N. Sokkar, M. A. Mabrouk, and W. A. Ramadan, “On the determination of the refractive index of a fiber: I. Skin-core fiber,” Pure Appl. Opt. 3, 943-961 (1994).
[CrossRef]

Stetson, K. A.

Stroke, G. W.

D. Gabor, G. W. Stroke, D. Brumm, A. Funkhouser, and A. Labeyrie, “Reconstruction of phase objects by holography,” Nature 208, 1159-1162 (1965).
[CrossRef]

Sweeney, D. W.

Vest, C. M.

Wahba, H. H.

T. Z. N. Sokkar, M. A. El-Morsy, and H. H. Wahba, “Automatic fringe analysis of the induced anisotropy of bent optical fibres,” Opt. Commun. 281, 1915-1923 (2008).
[CrossRef]

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, and H. H. Wahba, “Coreindex determination of a thick fiber using lens-fiber interference (LFI) technique,” Opt. Lasers Eng. 42, 121-130 (2004).
[CrossRef]

Yatagai, T.

M. A. El-Morsy, T. Yatagai, A. A. Hamza, M. A. Mabrouk, and T. Z. N. Sokkar, “Multiple-beam Fizeau fringe-pattern analysis using Fourier transform method for accurate measurement of fiber refractive index profile of polymer fiber,” J. Appl. Polym. Sci. 85, 475-484 (2002).
[CrossRef]

M. A. El-Morsy, T. Yatagai, A. A. Hamza, M. A. Mabrouk, and T. Z. N. Sokkar, “Automatic refractive index profiling of fibers by phase analysis method using Fourier transform,” Opt. Lasers Eng. 38, 509-525 (2002).
[CrossRef]

Yin, S.

S. Yin, P. B. Ruffin, and F. T. S. Yu, eds., Fiber Optic Sensors, 2nd ed. (CRC, 2008).

Yu, F. T. S.

S. Yin, P. B. Ruffin, and F. T. S. Yu, eds., Fiber Optic Sensors, 2nd ed. (CRC, 2008).

Zozulya, A. A.

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Appl. Phys. Lett. (2)

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Pelli, G. Righini, and S. Sebastiani, “Digital-holography refractive-index-profile measurement of phase gratings,” Appl. Phys. Lett. 88, 111-114 (2006).

M. E. Marhic, P. S. Ho and M. Epstein, “Nondestructive refractive-index profile measurements of clad optical fibers,” Appl. Phys. Lett. 26, 574-575 (1975).
[CrossRef]

J. Appl. Polym. Sci. (1)

M. A. El-Morsy, T. Yatagai, A. A. Hamza, M. A. Mabrouk, and T. Z. N. Sokkar, “Multiple-beam Fizeau fringe-pattern analysis using Fourier transform method for accurate measurement of fiber refractive index profile of polymer fiber,” J. Appl. Polym. Sci. 85, 475-484 (2002).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

T. Z. N. Sokkar, M. A. Mabrouk, and H. F. El-Bawab, “Refractive index profile of GRIN optical fiber considering the area under the interference fringe shift: II. The mismatching case,” J. Opt. A: Pure Appl. Opt. 1, 64-72(1999).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (2)

V. Kebbel, M. Adams, H.-J. Hartmann, and W. Jüptner, “Digital holography as a versatile optical diagnostic method for microgravity experiments,” Meas. Sci. Technol. 10, 893-899 (1999).
[CrossRef]

F. Dubois, L. Joannes, O. Dupont, J. L. Dewandel, and J. C. Legros, “An integrated optical set-up for fluid-physics experiments under microgravity conditions,” Meas. Sci. Technol. 10, 934-945 (1999).
[CrossRef]

Nature (2)

D. Gabor, G. W. Stroke, D. Brumm, A. Funkhouser, and A. Labeyrie, “Reconstruction of phase objects by holography,” Nature 208, 1159-1162 (1965).
[CrossRef]

D. Gabor, “A new microscopic principle,” Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Opt. Commun. (2)

T. Z. N. Sokkar, M. A. El-Morsy, and H. H. Wahba, “Automatic fringe analysis of the induced anisotropy of bent optical fibres,” Opt. Commun. 281, 1915-1923 (2008).
[CrossRef]

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, and M. A. Shams-Eldin, “Determination of GRIN optical fiber parameters from transverse interferograms considering the refraction of the incident ray by the fiber,” Opt. Commun. 200, 131-138 (2001).
[CrossRef]

Opt. Eng. (1)

M. M. Hossain, D. S. Mehta, and C. Shakher, “Refractive index determination: an application of lensless Fourier digital holography,” Opt. Eng. 45, 106203 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (3)

A. A. Hamza, M. A. Mabrouk, W. A. Ramadan, and H. H. Wahba, “Coreindex determination of a thick fiber using lens-fiber interference (LFI) technique,” Opt. Lasers Eng. 42, 121-130 (2004).
[CrossRef]

M. A. El-Morsy, T. Yatagai, A. A. Hamza, M. A. Mabrouk, and T. Z. N. Sokkar, “Automatic refractive index profiling of fibers by phase analysis method using Fourier transform,” Opt. Lasers Eng. 38, 509-525 (2002).
[CrossRef]

A. A. Hamza, A. E. Belal, T. Z. N. Sokkar, H. M. El-Dessouky, and M. A. Agour, “Interferometric studies on the infiuence of temperature on the optical and dispersion parameters of GRIN optical fiber,” Opt. Lasers Eng. 45, 145-152(2007).
[CrossRef]

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D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. R. Soc. London, Ser. A 197, 454-487 (1949).
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Pure Appl. Opt. (3)

A. A. Hamza, A. M. Ghander, T. Z. N. Sokkar, M. A. Mabrouk, and W. A. Ramadan, “On the determination of the refractive index of a fiber: I. Skin-core fiber,” Pure Appl. Opt. 3, 943-961 (1994).
[CrossRef]

A. A. Hamza, T. Z. N. Sokkar, A. M. Ghander, M. A. Mabrouk, and W. A. Ramadan, “On the determination of the refractive index of a fiber. II. Graded index fiber,” Pure Appl. Opt. 4, 161-177 (1995).
[CrossRef]

M. A. Mabrouk and H. F. El-Bawab, “Refractive index profile of GRIN optical fiber considering the area under the interference fringe shift: I. The matching case,” Pure Appl. Opt. 6, 247-256 (1997).
[CrossRef]

Other (6)

N. Barakat and A. A. Hamza, Interferometry of Fibrous Materials (Hilger, 1990).

G. E. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, 2002).
[CrossRef]

S. Yin, P. B. Ruffin, and F. T. S. Yu, eds., Fiber Optic Sensors, 2nd ed. (CRC, 2008).

T. Kreis, Holographic Interferometry: Principles and Methods (Akademie-Verlag, 1996).

T. Kreis, “Digital holography for metrologic applications,” in Interferometry in Speckle Light, P. Jacquot and J. -M. Fournier, eds. (Springer-Verlag, 2000), pp. 205-212.
[CrossRef]

Th. Kreis, Handbook of Holographic Interferometry, Optical and Digital Methods (Wiley-VCH, 2005).

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Figures (18)

Fig. 1
Fig. 1

Refractive index distribution in (a) step-index fibers and (b) graded index fibers.

Fig. 2
Fig. 2

Geometry of digital Fresnel holography.

Fig. 3
Fig. 3

Arrangement for digital holography interferometry.

Fig. 4
Fig. 4

Phase-shifted digital holograms of the graded index optical fiber immersed in liquid of refractive index n L = 1.46 , with additional phase (a) 0; (b)  π / 2 ; (c) π; (d)  3 π / 2 ; and (e)  2 π .

Fig. 5
Fig. 5

Reconstructed interference phase modulo 2 π from the phase-shifted digital holograms of Fig. 4.

Fig. 6
Fig. 6

Unwrapped interference phase distribution with normalized background.

Fig. 7
Fig. 7

Mean interference phase difference across the graded index optical fiber core relative to the cladding/liquid refractive index.

Fig. 8
Fig. 8

Mean fringe shift across the graded index optical fiber core.

Fig. 9
Fig. 9

(a) Two-beam interferogram; (b) contour lines; and (c) interferogram with overlaid contour lines of graded index optical fiber immersed in liquid of refractive index n L = 1.46 .

Fig. 10
Fig. 10

Refractive index profiles measured across the graded index optical fiber core with digital holographic interferometry and two-beam interferometry.

Fig. 11
Fig. 11

Phase-shifted digital holograms of graded index optical fiber immersed in liquid of refractive index n L = 1.4565 , with additional phase (a) 0; (b)  π / 2 ; (c) π; (d)  3 π / 2 ; and (e)  2 π .

Fig. 12
Fig. 12

Reconstructed interference phase modulo 2 π from the phase-shifted holograms of Fig. 11.

Fig. 13
Fig. 13

Unwrapped interference phase distribution with normalized background.

Fig. 14
Fig. 14

Mean interference phase difference across the optical fiber core and cladding in the mismatching case.

Fig. 15
Fig. 15

Mean fringe shift across the optical fiber regions.

Fig. 16
Fig. 16

(a) Two-beam interferogram; (b) contour lines; and (c) interferogram with overlaid contour lines of graded index optical fiber immersed in liquid of refractive index n L = 1.4565 .

Fig. 17
Fig. 17

Refractive index profiles measured across the graded index optical fiber regions (core and cladding) with digital holographic interferometry and two-beam interference in the mismatching case.

Fig. 18
Fig. 18

Refractive index profiles across the graded index optical fiber core with digital holographic interferometry and two-beam interferometry in the (a) matching and (b) mismatching case after fitting α.

Tables (1)

Tables Icon

Table 1 Statistical Summary of Characterization of Graded Index Optical Fiber in Matching and Mismatching Cases with Digital Holography and Two-Beam Interferometry

Equations (13)

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

n ( r ) = n c Δ n ( r R ) α , 0 r R .
N . A . = n c 2 n cl 2 .
b ( x , y ) = 1 i λ h ( ξ , η ) r * ( ξ , η ) exp { i k ρ } ρ d ξ d η
b ( n Δ x , m Δ y ) = A Σ j = 0 N 1 Σ l = 0 M 1 h ( j Δ ξ , l Δ η ) r * ( j Δ ξ , l Δ η ) exp { i π d λ ( j 2 Δ ξ 2 + l 2 Δ η 2 ) } exp { 2 i π ( j n N + lm M ) } .
Δ x = d λ N Δ ξ , Δ y = d λ M Δ η .
b = A F 1 { { h · r * } · F { g } } ,
Δ x = Δ ξ , Δ y = Δ η .
I n = a ( x , y ) + b ( x , y ) cos ( ϕ ( x , y ) + ϕ R n ) , n = 1 , , 5 ,
Re [ H ( x , y ) ] = 4 I 1 ( x , y ) I 2 ( x , y ) 6 I 3 ( x , y ) I 4 ( x , y ) + 4 I 5 ( x , y ) ,
Im [ H ( x , y ) ] = 7 [ I 4 ( x , y ) I 2 ( x , y ) ] .
λ Z Q h = Σ j = 1 Q 1 2 n j [ ( R ( j 1 ) a ) 2 d Q 2 n L 2 / n j 2 ( R j a ) 2 d Q 2 n L 2 / n j 2 ] + 2 n Q [ ( R ( Q 1 ) a ) 2 d Q 2 n L 2 / n Q 2 ] n L [ R 2 d Q 2 + R 2 x Q 2 ] ,
d Q = n Q [ R ( Q 0.5 ) a ] n L .
OPD = λ Z Q h = λ 2 π Δ ϕ Q .

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