Abstract

In this paper we apply spectrally resolved white light interferometry to measure refractive and group index over a wide spectral band from 400 to 1000 nm. The output of a Michelson interferometer is spectrally decomposed by a homemade prism spectrometer with a high resolution camera. The group index is determined directly from the phase extracted from the spectral interferogram while the refractive index is estimated once its value at a given wavelength is known

© 2016 Optical Society of America

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References

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  1. L. M. Smith and C. C. Dobson, “Absolute displacement measurements using modulation of the spectrum of white light in a Michelson interferometer,” Appl. Opt. 28(16), 3339–3342 (1989).
    [Crossref] [PubMed]
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    [Crossref]
  3. C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
    [Crossref]
  4. P. Hlubina, D. Ciprian, and L. Knyblová, “Direct measurement of dispersion of the group refractive indices of quartz crystal by white-light spectral interferometry,” Opt. Commun. 269(1), 8–13 (2007).
    [Crossref]
  5. J. Calatroni, A. L. Guerrero, C. Sáinz, and R. Escalona, “Spectrally-resolved white-light interferometry as a profilometry tool,” Opt. Laser Technol. 28(7), 485–489 (1996).
    [Crossref]
  6. S. K. Debnath, M. P. Kothiyal, J. Schmit, and P. Hariharan, “Spectrally resolved phase-shifting interferometry of transparent thin films: sensitivity of thickness measurements,” Appl. Opt. 45(34), 8636–8640 (2006).
    [Crossref] [PubMed]
  7. H.-T. Shang, “Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres,” Electron. Lett. 17(17), 603–605 (1981).
    [Crossref]
  8. J. Y. Lee and D. Y. Kim, “Versatile chromatic dispersion measurement of a single mode fiber using spectral white light interferometry,” Opt. Express 14(24), 11608–11615 (2006).
    [Crossref] [PubMed]
  9. R. C. Youngquist, S. M. Simmons, and A. M. Belanger, “Spectrometer wavelength calibration using spectrally resolved white-light interferometry,” Opt. Lett. 35(13), 2257–2259 (2010).
    [Crossref] [PubMed]
  10. R. de la Fuente, “White light spectral interferometry as a spectrometer calibration tool,” Appl. Spectrosc. 68(5), 525–530 (2014).
    [Crossref] [PubMed]
  11. J. Tapia-Mercado, A. V. Khomenko, and A. Garcia-Weidner, “Precision and sensitivity optimization for white-light interferometric fiber-optic sensors,” J. Lightwave Technol. 19(1), 70–74 (2001).
    [Crossref]
  12. S. P. Ng, C. M. L. Wu, S. Y. Wu, and H. P. Ho, “White-light spectral interferometry for surface plasmon resonance sensing applications,” Opt. Express 19(5), 4521–4527 (2011).
    [Crossref] [PubMed]
  13. P. Hlubina, “White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193(1-6), 1–7 (2001).
    [Crossref]
  14. H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70(1), 45–51 (2000).
    [Crossref]
  15. D. Reolon, M. Jacquot, I. Verrier, G. Brun, and C. Veillas, “High resolution group refractive index measurement by broadband supercontinuum interferometry and wavelet-transform analysis,” Opt. Express 14(26), 12744–12750 (2006).
    [Crossref] [PubMed]
  16. Kramida, A., Ralchenko, Yu., Reader, J. and NIST ASD Team (2015). NIST Atomic Spectra Database (version 5.3), [Online]. Available: http://physics.nist.gov/asd (accesed Apr. 27 2016). National Institute of Standards and Technology, Gaithersburg, MD.
  17. C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
    [Crossref]
  18. D. X. Hammer, A. J. Welch, G. D. Noojin, R. J. Thomas, D. J. Stolarski, and B. A. Rockwell, “Spectrally resolved white-light interferometry for measurement of ocular dispersion,” J. Opt. Soc. Am. A 16(9), 2092–2102 (1999).
    [Crossref] [PubMed]
  19. M. N. Polyanskiy, “Refractive index database,” http://refractiveindex.info (accessed Apr. 26 2016)

2014 (1)

2011 (1)

2010 (1)

2007 (1)

P. Hlubina, D. Ciprian, and L. Knyblová, “Direct measurement of dispersion of the group refractive indices of quartz crystal by white-light spectral interferometry,” Opt. Commun. 269(1), 8–13 (2007).
[Crossref]

2006 (3)

2002 (1)

P. Hlubina, “Dispersive white-light spectral interferometry to measure distances and displacements,” Opt. Commun. 21(1-3), 65–70 (2002).
[Crossref]

2001 (2)

P. Hlubina, “White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193(1-6), 1–7 (2001).
[Crossref]

J. Tapia-Mercado, A. V. Khomenko, and A. Garcia-Weidner, “Precision and sensitivity optimization for white-light interferometric fiber-optic sensors,” J. Lightwave Technol. 19(1), 70–74 (2001).
[Crossref]

2000 (1)

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70(1), 45–51 (2000).
[Crossref]

1999 (1)

1996 (1)

J. Calatroni, A. L. Guerrero, C. Sáinz, and R. Escalona, “Spectrally-resolved white-light interferometry as a profilometry tool,” Opt. Laser Technol. 28(7), 485–489 (1996).
[Crossref]

1994 (2)

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

1989 (1)

1981 (1)

H.-T. Shang, “Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres,” Electron. Lett. 17(17), 603–605 (1981).
[Crossref]

Belanger, A. M.

Boucher, D.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70(1), 45–51 (2000).
[Crossref]

Brun, G.

Calatroni, J.

J. Calatroni, A. L. Guerrero, C. Sáinz, and R. Escalona, “Spectrally-resolved white-light interferometry as a profilometry tool,” Opt. Laser Technol. 28(7), 485–489 (1996).
[Crossref]

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

Ciprian, D.

P. Hlubina, D. Ciprian, and L. Knyblová, “Direct measurement of dispersion of the group refractive indices of quartz crystal by white-light spectral interferometry,” Opt. Commun. 269(1), 8–13 (2007).
[Crossref]

de la Fuente, R.

Debnath, S. K.

Delbarre, H.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70(1), 45–51 (2000).
[Crossref]

Dobson, C. C.

Escalona, R.

J. Calatroni, A. L. Guerrero, C. Sáinz, and R. Escalona, “Spectrally-resolved white-light interferometry as a profilometry tool,” Opt. Laser Technol. 28(7), 485–489 (1996).
[Crossref]

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

Garcia-Weidner, A.

Guerrero, A. L.

J. Calatroni, A. L. Guerrero, C. Sáinz, and R. Escalona, “Spectrally-resolved white-light interferometry as a profilometry tool,” Opt. Laser Technol. 28(7), 485–489 (1996).
[Crossref]

Hammer, D. X.

Hariharan, P.

Hlubina, P.

P. Hlubina, D. Ciprian, and L. Knyblová, “Direct measurement of dispersion of the group refractive indices of quartz crystal by white-light spectral interferometry,” Opt. Commun. 269(1), 8–13 (2007).
[Crossref]

P. Hlubina, “Dispersive white-light spectral interferometry to measure distances and displacements,” Opt. Commun. 21(1-3), 65–70 (2002).
[Crossref]

P. Hlubina, “White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193(1-6), 1–7 (2001).
[Crossref]

Ho, H. P.

Jacquot, M.

Jourdain, P.

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

Khomenko, A. V.

Kim, D. Y.

Knyblová, L.

P. Hlubina, D. Ciprian, and L. Knyblová, “Direct measurement of dispersion of the group refractive indices of quartz crystal by white-light spectral interferometry,” Opt. Commun. 269(1), 8–13 (2007).
[Crossref]

Kothiyal, M. P.

Lee, J. Y.

Ng, S. P.

Noojin, G. D.

Przygodzki, C.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70(1), 45–51 (2000).
[Crossref]

Reolon, D.

Rockwell, B. A.

Sáinz, C.

J. Calatroni, A. L. Guerrero, C. Sáinz, and R. Escalona, “Spectrally-resolved white-light interferometry as a profilometry tool,” Opt. Laser Technol. 28(7), 485–489 (1996).
[Crossref]

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

Schmit, J.

Shang, H.-T.

H.-T. Shang, “Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres,” Electron. Lett. 17(17), 603–605 (1981).
[Crossref]

Simmons, S. M.

Smith, L. M.

Stolarski, D. J.

Tapia-Mercado, J.

Tassou, M.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70(1), 45–51 (2000).
[Crossref]

Thomas, R. J.

Veillas, C.

Verrier, I.

Welch, A. J.

Wu, C. M. L.

Wu, S. Y.

Youngquist, R. C.

Appl. Opt. (2)

Appl. Phys. B (1)

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70(1), 45–51 (2000).
[Crossref]

Appl. Spectrosc. (1)

Electron. Lett. (1)

H.-T. Shang, “Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres,” Electron. Lett. 17(17), 603–605 (1981).
[Crossref]

J. Lightwave Technol. (1)

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

Opt. Commun. (5)

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

P. Hlubina, “White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193(1-6), 1–7 (2001).
[Crossref]

P. Hlubina, “Dispersive white-light spectral interferometry to measure distances and displacements,” Opt. Commun. 21(1-3), 65–70 (2002).
[Crossref]

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

P. Hlubina, D. Ciprian, and L. Knyblová, “Direct measurement of dispersion of the group refractive indices of quartz crystal by white-light spectral interferometry,” Opt. Commun. 269(1), 8–13 (2007).
[Crossref]

Opt. Express (3)

Opt. Laser Technol. (1)

J. Calatroni, A. L. Guerrero, C. Sáinz, and R. Escalona, “Spectrally-resolved white-light interferometry as a profilometry tool,” Opt. Laser Technol. 28(7), 485–489 (1996).
[Crossref]

Opt. Lett. (1)

Other (2)

M. N. Polyanskiy, “Refractive index database,” http://refractiveindex.info (accessed Apr. 26 2016)

Kramida, A., Ralchenko, Yu., Reader, J. and NIST ASD Team (2015). NIST Atomic Spectra Database (version 5.3), [Online]. Available: http://physics.nist.gov/asd (accesed Apr. 27 2016). National Institute of Standards and Technology, Gaithersburg, MD.

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Figures (7)

Fig. 1
Fig. 1 Simulation of ideal interferograms, with constant background irradiance and visibility of one, for a typical grating spectrometer (a) and for our home-made prism spectrometer (b) when we insert in one of the arms of the interferometer a silica plate 1 mm thick. In the former case we used the calibration of a commercial portable spectrometer and in the second case we used the calibration discussed in section 2.

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Fig. 2
Fig. 2 Experimental setup; WLS white light source; L1 - L4 lenses; M1 fixed mirror; M2 moving mirror; BS beam splitter; S sample; P prism

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Fig. 3
Fig. 3 Calibration of the spectrometer. (a) Image of the lines of Hg-Ar lamp, showing (red dots) the lines used for calibration; (b) Fit of wavenumber (left) and wavelength (right) versus pixel number; (c) bandpass of each pixel.

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Fig. 4
Fig. 4 Typical spectral interferogram obtained with a BK7 plate 2 mm thick. (a) Total signal for a path difference l = 0.55 mm; (b) the background signal; (c) the visibility function.

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Fig. 5
Fig. 5 Calibration of the mirror displacement: measured displacement versus the scale on the manual micrometer.

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Fig. 6
Fig. 6 Group index retrieved directly from phase derivative for a fused silica sample 1mm thick (continuous line), a BK7 sample 2 mm thick (dashed line) and D293T glass sample 210 μm thick (dashed-dotted line) .

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Fig. 7
Fig. 7 Retrieved refractive index curve versus wavelength for the same samples as Fig. 6.

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Equations (7)

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I( σ )= I 0 ( σ )[ 1+V( σ )cosφ( σ ) ]
φ( σ )=4πσ[ d( n− n air )− n air l ]
cosφ( σ )=2 I( σ )− I 0 ( σ ) I up ( σ )− I lo ( σ )
n g = d dσ ( nσ )= 1 4πd d φ u dσ −( 1+ l d ) d dσ ( n air σ )
n( σ )= A+ B 1−C σ 2
n( σ 0 )− n 0 = D σ 0
n( σ )= A+ B 1−C σ 2 − D σ

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