Abstract

In this paper we propose group refractive index measurement with a spectral interferometric set-up using a broadband supercontinuum generated in an air-silica Microstructured Optical Fibre (MOF) pumped with a picosecond pulsed microchip laser. This source authorizes high fringes visibility for dispersion measurements by Spectroscopic Analysis of White Light Interferograms (SAWLI). Phase calculation is assumed by a wavelet transform procedure combined with a curve fit of the recorded channelled spectrum intensity. This approach provides high resolution and absolute group refractive index measurements along one line of the sample by recording a single 2D spectral interferogram without mechanical scanning.

© 2006 Optical Society of America

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References

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  1. D. Reolon, M. Jacquot, I. Verrier, G. Brun and C. Veillas, "Broadband supercontinuum interferometer for high-resolution profilometry," Opt. Express 14, 128 (2006).
    [CrossRef] [PubMed]
  2. P. Hlubina, "White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica," Opt. Commun. 193, 1 (2001).
    [CrossRef]
  3. Y. Wang, Y. Zhao, J. S. Nelson, and Z. Chen, "Ultrahigh-resolution optical coherence tomography by broadband continuum generation from a photonic crystal fiber," Opt. Lett. 28, 182 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [PubMed]
  6. J. Calatroni, C. Sáinz and A. L. Guerrero, "Multi-channelled white-light interferometry for real-time dispersion measurements," Opt. Commun. 157, 202 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2006 (3)

2005 (3)

2004 (1)

2003 (3)

2002 (1)

2001 (1)

P. Hlubina, "White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica," Opt. Commun. 193, 1 (2001).
[CrossRef]

1998 (1)

J. Calatroni, C. Sáinz and A. L. Guerrero, "Multi-channelled white-light interferometry for real-time dispersion measurements," Opt. Commun. 157, 202 (1998).
[CrossRef]

Auguste, J. L.

Blondy, J. M.

Brun, G.

Calatroni, J.

J. Calatroni, C. Sáinz and R. Escalona, "The stationary phase in spectrally resolved white-light interferometry as a refractometry tool," J. Opt. A: Pure Appl. Opt. 5, 207 (2003).
[CrossRef]

J. Calatroni, C. Sáinz and A. L. Guerrero, "Multi-channelled white-light interferometry for real-time dispersion measurements," Opt. Commun. 157, 202 (1998).
[CrossRef]

Chai, L.

Champert, P.

Chen, Z.

Couderc, V.

Debnath, S. K.

Deng, Y.

Eggleton, B.

Escalona, R.

J. Calatroni, C. Sáinz and R. Escalona, "The stationary phase in spectrally resolved white-light interferometry as a refractometry tool," J. Opt. A: Pure Appl. Opt. 5, 207 (2003).
[CrossRef]

Février, S.

Froehly, C.

Fu, Y.

Grossard, L.

Guerrero, A. L.

J. Calatroni, C. Sáinz and A. L. Guerrero, "Multi-channelled white-light interferometry for real-time dispersion measurements," Opt. Commun. 157, 202 (1998).
[CrossRef]

Hirai, A.

Hlubina, P.

P. Hlubina, T. Martynkien and W. Urbañczyk, "Dispersion of group and phase modal birefringence in elliptical-core fiber measured by white-light spectral interferometry," Opt. Express 11, 2793 (2003).
[PubMed]

P. Hlubina, "White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica," Opt. Commun. 193, 1 (2001).
[CrossRef]

Huss, G.

Jacquot, M.

Jui, C.

Knox, W. H.

Kothiyal, M. P.

Labonté, L.

Leproux, P.

Lesvigne, C.

Liu, X.

Martynkien, T.

Matsumoto, H.

Miao, H.

Morita, R.

Nelson, J. S.

Nérin, P.

Pioger, P. H.

Quan, C.

Reolon, D.

Roy, P.

Sáinz, C.

J. Calatroni, C. Sáinz and R. Escalona, "The stationary phase in spectrally resolved white-light interferometry as a refractometry tool," J. Opt. A: Pure Appl. Opt. 5, 207 (2003).
[CrossRef]

J. Calatroni, C. Sáinz and A. L. Guerrero, "Multi-channelled white-light interferometry for real-time dispersion measurements," Opt. Commun. 157, 202 (1998).
[CrossRef]

Tombelaine, V.

Urbañczyk, W.

Veillas, C.

Verrier, I.

Viswanathan, N. K.

Wang, C.

Wang, Y.

Windeler, R. S.

Wu, Z.

Xu, C.

Yamane, K.

Yamashita, M.

Yan, M. F.

Ye, Q.

Zhang, Z.

Zhao, Y.

Appl. Opt. (3)

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

J. Calatroni, C. Sáinz and R. Escalona, "The stationary phase in spectrally resolved white-light interferometry as a refractometry tool," J. Opt. A: Pure Appl. Opt. 5, 207 (2003).
[CrossRef]

Opt. Commun. (2)

P. Hlubina, "White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica," Opt. Commun. 193, 1 (2001).
[CrossRef]

J. Calatroni, C. Sáinz and A. L. Guerrero, "Multi-channelled white-light interferometry for real-time dispersion measurements," Opt. Commun. 157, 202 (1998).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

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Figures (5)

Fig. 1.
Fig. 1.

Experimental set-up: white light spectral supercontinuum interferometer: with L1 (f1=60mm), L2 (f2=200mm), L3 (f3=400mm), L4 (f4=65mm), and L5 (f5=50mm).

Fig. 2.
Fig. 2.

Recorded channelled spectrum with a BK7 plate sample of 2.39 mm thickness.

Fig. 3.
Fig. 3.

Ridge extraction applied on one line of the analysed interferogram from the intensity wavelet transform (a) and from the phase wavelet transform (b).

Fig. 4.
Fig. 4.

Experimental BK7 group refractive index profile along the 18mm line (a) and its variation for y=9mm position in dashed line compared with the theoretical law deduced from Sellmeier equation in solid line (b); (δ=-1220µm, e=2390µm, A=2.2308×103, B=-1.3689×104, C=3.1672×104, D=-3.1736×104, and E=1.1961×104).

Fig. 5.
Fig. 5.

Group refractive index laws of the BK7 glass plate measured for three mirror positions δ 1=-1210µm (+), δ 2=-1220µm (•), and δ 3=-1230µm (-).

Equations (4)

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I ( y , σ ) = I 0 ( y , σ ) · ( 1 + V ( y , σ ) · cos ( Δ Φ 12 ( y , σ ) ) ) ,
Δ Φ 12 ( y , σ ) = 4 π σ ( δ + ( n ( y , σ ) 1 ) · e ( y ) ) ,
{ W ( a , b ) = + f ( v ) · ψ a , b * ( v ) · d v with : ψ a , b ( v ) = 1 a exp { ( v b ) 2 2 a 2 } · exp { 2 i π v 0 ( v b ) a }
n g ( σ ) = n ( σ ) + σ · n ( σ ) σ = 1 4 π e · Δ Φ exp ( σ ) σ ( δ e e )

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