Abstract

A technique for the measurement of the group refractive index wavelength dependence of optical materials using a low-coherence tandem interferometer and a spectrometer is proposed. Four channeled spectra resulting from interferences of light beams from different pairs of optical paths are used for the calculation of optical path differences. The group refractive index wavelength dependence is calculated from these optical path differences generated from the sample under measurement. No a priori information of the geometric thickness of a sample is required. The wavelength dependence of the group refractive index of the samples BK7 parallel plate of 5.200 and 10.025  mm from 675 to 850  nm is experimentally measured with an accuracy of the order of 105 and a repeatability of the order of 109.

© 2006 Optical Society of America

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References

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2004 (4)

T. Imran, K.-H. Hong, T. J. Yu, and C. H. Nam, "Measurement of the group-delay dispersion of femtosecond optics using white-light interferometry," Rev. Sci. Instrum. 75, 2266-2270 (2004).
[CrossRef]

Y. L. Kim, J. T. Walsh, Jr., T. K. Goldstick, and M. R. Glucksberg, "Variation of corneal refractive index with hydration," Phys. Med. Biol. 49, 859-868 (2004).
[CrossRef] [PubMed]

R. C. Lin, M. A. Shure, A. M. Rollins, J. A. Izatt, and D. Huang, "Group index of the human cornea at 1.3-μm wavelength obtained in vitro by optical coherence domain reflectometry," Opt. Lett. 29, 83-85 (2004).
[CrossRef] [PubMed]

R. D. Peters, A. Hirai, M. Jeganathan, and O. P. Lay, "Near-IR demonstration of adaptive nuller based on deformable mirror," in New Frontiers in Stellar Interferometry, W. A. Traub, ed., Proc. SPIE 5491, 1630-1638 (2004).
[CrossRef]

2003 (2)

2002 (1)

I. Mandelbaum and M. Achtenhagen, "Novel technique for group velocity dispersion measurements in optical fibers," IEEE Photon. Technol. Lett. 14, 349-351 (2002).
[CrossRef]

2001 (1)

M. Yoshida, K. Nakamura, and H. Ito, "A new method for measurement of group velocity dispersion of optical fibers by using a frequency-shifted feedback fiber laser," IEEE Photon. Technol. Lett. 13, 227-229 (2001).
[CrossRef]

2000 (2)

D. F. Murphy and D. A. Flavin, "Dispersion-insensitive measurement of thickness and group refractive index by low-coherence interferometry," Appl. Opt. 39, 4607-4615 (2000).
[CrossRef]

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, 45-51 (2000).
[CrossRef]

1998 (1)

1996 (2)

1991 (1)

1990 (1)

1982 (1)

Achtenhagen, M.

I. Mandelbaum and M. Achtenhagen, "Novel technique for group velocity dispersion measurements in optical fibers," IEEE Photon. Technol. Lett. 14, 349-351 (2002).
[CrossRef]

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, 45-51 (2000).
[CrossRef]

Ciddor, P. E.

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, 45-51 (2000).
[CrossRef]

Diddams, S. A.

Equal, R.

Flavin, D. A.

Fukano, T.

Glucksberg, M. R.

Y. L. Kim, J. T. Walsh, Jr., T. K. Goldstick, and M. R. Glucksberg, "Variation of corneal refractive index with hydration," Phys. Med. Biol. 49, 859-868 (2004).
[CrossRef] [PubMed]

Goldstick, T. K.

Y. L. Kim, J. T. Walsh, Jr., T. K. Goldstick, and M. R. Glucksberg, "Variation of corneal refractive index with hydration," Phys. Med. Biol. 49, 859-868 (2004).
[CrossRef] [PubMed]

Haruna, M.

Hashimoto, M.

Hirai, A.

R. D. Peters, A. Hirai, M. Jeganathan, and O. P. Lay, "Near-IR demonstration of adaptive nuller based on deformable mirror," in New Frontiers in Stellar Interferometry, W. A. Traub, ed., Proc. SPIE 5491, 1630-1638 (2004).
[CrossRef]

A. Hirai and H. Matsumoto, "Low-coherence tandem interferometer for measurement of group refractive index without knowledge of the thickness of the test sample," Opt. Lett. 28, 2112-2114 (2003).
[CrossRef] [PubMed]

Hollberg, L.

Hong, K.-H.

T. Imran, K.-H. Hong, T. J. Yu, and C. H. Nam, "Measurement of the group-delay dispersion of femtosecond optics using white-light interferometry," Rev. Sci. Instrum. 75, 2266-2270 (2004).
[CrossRef]

Hopler, M. D.

Huang, D.

Imran, T.

T. Imran, K.-H. Hong, T. J. Yu, and C. H. Nam, "Measurement of the group-delay dispersion of femtosecond optics using white-light interferometry," Rev. Sci. Instrum. 75, 2266-2270 (2004).
[CrossRef]

Ina, H.

Ito, H.

M. Yoshida, K. Nakamura, and H. Ito, "A new method for measurement of group velocity dispersion of optical fibers by using a frequency-shifted feedback fiber laser," IEEE Photon. Technol. Lett. 13, 227-229 (2001).
[CrossRef]

Izatt, J. A.

Jeganathan, M.

R. D. Peters, A. Hirai, M. Jeganathan, and O. P. Lay, "Near-IR demonstration of adaptive nuller based on deformable mirror," in New Frontiers in Stellar Interferometry, W. A. Traub, ed., Proc. SPIE 5491, 1630-1638 (2004).
[CrossRef]

Kim, Y. L.

Y. L. Kim, J. T. Walsh, Jr., T. K. Goldstick, and M. R. Glucksberg, "Variation of corneal refractive index with hydration," Phys. Med. Biol. 49, 859-868 (2004).
[CrossRef] [PubMed]

Kobayashi, S.

Lay, O. P.

R. D. Peters, A. Hirai, M. Jeganathan, and O. P. Lay, "Near-IR demonstration of adaptive nuller based on deformable mirror," in New Frontiers in Stellar Interferometry, W. A. Traub, ed., Proc. SPIE 5491, 1630-1638 (2004).
[CrossRef]

Lin, R. C.

Mandelbaum, I.

I. Mandelbaum and M. Achtenhagen, "Novel technique for group velocity dispersion measurements in optical fibers," IEEE Photon. Technol. Lett. 14, 349-351 (2002).
[CrossRef]

Maruyama, H.

Matsumoto, H.

Mitsuyama, T.

Mogi, K.

Murphy, D. F.

Naganuma, K.

Nakamura, K.

M. Yoshida, K. Nakamura, and H. Ito, "A new method for measurement of group velocity dispersion of optical fibers by using a frequency-shifted feedback fiber laser," IEEE Photon. Technol. Lett. 13, 227-229 (2001).
[CrossRef]

Nam, C. H.

T. Imran, K.-H. Hong, T. J. Yu, and C. H. Nam, "Measurement of the group-delay dispersion of femtosecond optics using white-light interferometry," Rev. Sci. Instrum. 75, 2266-2270 (2004).
[CrossRef]

Ohmi, M.

Peters, R. D.

R. D. Peters, A. Hirai, M. Jeganathan, and O. P. Lay, "Near-IR demonstration of adaptive nuller based on deformable mirror," in New Frontiers in Stellar Interferometry, W. A. Traub, ed., Proc. SPIE 5491, 1630-1638 (2004).
[CrossRef]

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, 45-51 (2000).
[CrossRef]

Rogers, J. R.

Rollins, A. M.

Shure, M. A.

Tajiri, H.

Takeda, M.

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, 45-51 (2000).
[CrossRef]

Thomann, I.

Walsh, J. T.

Y. L. Kim, J. T. Walsh, Jr., T. K. Goldstick, and M. R. Glucksberg, "Variation of corneal refractive index with hydration," Phys. Med. Biol. 49, 859-868 (2004).
[CrossRef] [PubMed]

Yamada, H.

Yamaguchi, I.

Yoshida, M.

M. Yoshida, K. Nakamura, and H. Ito, "A new method for measurement of group velocity dispersion of optical fibers by using a frequency-shifted feedback fiber laser," IEEE Photon. Technol. Lett. 13, 227-229 (2001).
[CrossRef]

Yu, T. J.

T. Imran, K.-H. Hong, T. J. Yu, and C. H. Nam, "Measurement of the group-delay dispersion of femtosecond optics using white-light interferometry," Rev. Sci. Instrum. 75, 2266-2270 (2004).
[CrossRef]

Appl. Opt. (4)

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, 45-51 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

M. Yoshida, K. Nakamura, and H. Ito, "A new method for measurement of group velocity dispersion of optical fibers by using a frequency-shifted feedback fiber laser," IEEE Photon. Technol. Lett. 13, 227-229 (2001).
[CrossRef]

I. Mandelbaum and M. Achtenhagen, "Novel technique for group velocity dispersion measurements in optical fibers," IEEE Photon. Technol. Lett. 14, 349-351 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (5)

Phys. Med. Biol. (1)

Y. L. Kim, J. T. Walsh, Jr., T. K. Goldstick, and M. R. Glucksberg, "Variation of corneal refractive index with hydration," Phys. Med. Biol. 49, 859-868 (2004).
[CrossRef] [PubMed]

Proc. SPIE (1)

R. D. Peters, A. Hirai, M. Jeganathan, and O. P. Lay, "Near-IR demonstration of adaptive nuller based on deformable mirror," in New Frontiers in Stellar Interferometry, W. A. Traub, ed., Proc. SPIE 5491, 1630-1638 (2004).
[CrossRef]

Rev. Sci. Instrum. (1)

T. Imran, K.-H. Hong, T. J. Yu, and C. H. Nam, "Measurement of the group-delay dispersion of femtosecond optics using white-light interferometry," Rev. Sci. Instrum. 75, 2266-2270 (2004).
[CrossRef]

Other (1)

Ohara, Inc., Optical Glass Data, S-BSL7, http://www.ohara-inc.co.jpen/product/optical/list/dl/esbsl07.pdf.

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Figures (6)

Fig. 1
Fig. 1

Optical setup of the proposed technique. Sample S; shutters S1 and S2; spectrometer SP. See the text for the explanation of (a)–(d).

Fig. 2
Fig. 2

Examples of channeled spectra of a 5.200 mm thick sample with (a) SLD1 and (b) SLD2.

Fig. 3
Fig. 3

Optical path differences calculated from mirror displacements and the total OPD of the tandem interferometer calculated from the channeled spectra.

Fig. 4
Fig. 4

Experimental results. (a) Comparison of the group refractive index wavelength dependence experimentally measured and calculated from Sellmeier's formula, and (b) standard deviation of the results of six measurements of a 5.200 mm thick sample. (c) Comparison of the group refractive index wavelength dependence experimentally measured and calculated from Sellmeier's formula, and (d) standard deviation of the results of six measurements of a 10.025 mm thick sample.

Fig. 5
Fig. 5

Error of n gS caused by sample tilt. (a) Error of n gS as the function of the wavelength and tilt angle. (b) Dependency of error of n gS at 830 nm on the tilt angle.

Fig. 6
Fig. 6

Error of n gS caused by the sample wedge. (a) Error of n gS as the function of the wavelength and wedge angle. (b) Dependency of the error of n gS at 830 nm on the wedge angle.

Tables (3)

Tables Icon

Table 1 Uncertainty Budget of ngS

Tables Icon

Table 2 Uncertainty Budget of d4

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Table 3 Uncertainty Budget of d3

Equations (14)

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

D 1 ( λ ) = 2 n g a ( λ ) | d 1 | ,
D 2 ( λ ) = | 2 n g a ( λ ) d 2 2 n g a ( λ ) Δ | ,
D 3 ( λ ) = 2 n g a ( λ ) d 3 2 { n g a ( λ ) Δ + [ n g S ( λ ) n g a ( λ ) ] L S } .
D 4 ( λ ) = 2 n g a ( λ ) d 4 2 n g S ( λ ) L S .
d 1 ( λ ) = 2 n g a ( λ ) d 1 D 1 ( λ ) = 0 ,
d 2 ( λ ) = 2 n g a ( λ ) d 2 D 2 ( λ ) = 2 n g a ( λ ) Δ ,
d 3 ( λ ) = 2 n g a ( λ ) d 3 D 3 ( λ ) = 2 { n g a ( λ ) Δ + [ n g S ( λ ) n g a ( λ ) ] L S } ,
d 4 ( λ ) = 2 n g a ( λ ) d 4 D 4 ( λ ) = 2 n g S ( λ ) L S ,
n g S = n g a ( d 4 - d 1 ) / ( d 4 - d 1 - d 3 + d 2 )
L S = ( d 4 - d 1 - d 3 + d 2 ) / n g a .
   d n p S / d T absolute = d n p S / d T relative + n p S ( d n p a / d T ) .
d 4 = d 4 - d 1 = 2 L S ( n g S n g a sin θ r sin θ i ) / cos θ r ,
d 3 = d 3 - d 2 = 2 L S ( n g S / cos θ r n g a / cos θ i ) ,
Z tan ( 2 α n p S / n p a ) < ε r

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