Abstract

A silica plate of plane-parallel faces is inserted into one gap of a double-layer interferometer that transmits white light to a prism spectrograph in order to produce elliptic rings of equal chromatic order (RECO’s). The silica plate is rotated and the expanding RECO’s are counted at their center while this center is coincident with a standard wavelength. An analytic formula that relates the fringe count to the rotated angle enables the refractive index of the rotated plate to be accurately determined for different wavelengths. The results are fitted to a single-term Sellmeier dispersion function to find the peak wavelength of the ultraviolet absorption band and the atomic number density for such a transition. The variation of either the dispersion coefficient or the group-velocity factor with wavelength is determined from either the displacement of the RECO center across the visible spectrum if one of the double-layer interferometer’s mirrors is displaced parallel to itself or from measurements on the RECO diameters.

© 1997 Optical Society of America

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References

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  1. M. A. Khashan, “Multiple-beam interference refractometer and comparator,” Optik 35, 421–430 (1972).
  2. M. A. Khashan, “Channeled spectrum with the double-layer interferometer,” Opt. Commun. 8, 220–221 (1973).
    [CrossRef]
  3. M. A. Khashan, “Measurement of group-velocity dispersion by double-layer interferometer,” Optik 76, 73–77 (1987).
  4. R. B. Sosman, The Properties of Silica (Chemical Catalog, New York, 1927).
  5. W. C. Heraeus, 60 Jahre Quarzglas 25 Jahre Hochvakuumtechnik (GmbH, Hanau, Germany, 1961). A review of this book was published in J. Opt. Soc. Am. 54, 1067–1068 (1964).
  6. S. Yamagata, “Effect of OH-group on distribution of refractive index in silica glass,” J. Ceram. Soc. Jpn. 100, 337–341 (1992).
    [CrossRef]
  7. N. Kitamura, I. Y. Toguchi, S. Funco, H. Yamashita, M. Kinoshita, “Refractive index of densified silica glass,” J. Non-Cryst. Solids 159, 241–245 (1993).
    [CrossRef]
  8. R. Schenker, P. Schermerhorn, W. Q. Oldham, “Deep-ultraviolet damage to fused silica,” J. Vac. Sci. Technol. B 12, 3275–3279 (1994).
    [CrossRef]
  9. L. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965).
    [CrossRef]
  10. K. Siva Rama Krishna, A. Sharma, “Model for analyzing optical properties of silicate glasses,” Appl. Opt. 33, 8030–8035 (1994).
    [CrossRef]
  11. G. Ghosh, “Sellmeier coefficients and chromatic dispersions for some tellurite glasses,” J. Am. Ceram. Soc. 78, 2828–2830 (1995).
    [CrossRef]
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), pp. 364–367.
  13. M. A. Khashan, A. Y. Nassif, “Measurement of birefringence, dispersion and line splitting for biaxial crystals by double-layer interferometer,” J. Mod. Opt. 36, 785–796 (1989).
    [CrossRef]
  14. M. A. Khashan, “Order transformation, a new exact method for the Fabry–Perot spectrometer,” Opt. Acta 26, 873–879 (1979).
    [CrossRef]
  15. L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960), p. 96.
  16. C. Candler, Modern Interferometers (Hilger Watts, Glasgow, 1951), p. 218–227.
  17. W. Burckhardt, “Refractive index and dispersion of glasses with different degrees of linking,” J. Non-Cryst. Solids 50, 173–182 (1982).
    [CrossRef]
  18. H. Hsiu, “Accurate measurement of refractive-indices,” in Engineering & Laboratory Notes, Opt. Photon. News 4(11), S4–S5 (1993).
  19. B. C. Platt, H. W. Icenogle, J. E. Harvey, R. Korniski, W. L. Wolf, “Technique for measuring the refractive index and its change with temperature in the infrared,” J. Opt. Soc. Am. 65, 1264–1266 (1975).
    [CrossRef]
  20. W. L. Wolf, “More on the accurate measurement of refractive indices,” Appl. Opt. 33, 8129–8130 (1994).
    [CrossRef]
  21. M. Medhat, “Measurement of the refraction and dispersion of solids and liquids by the rings of equal chromatic order,” Optik 85, 73–77 (1990).
  22. S. M. Yang, K. H. Chang, T. K. Kung, “Refractive index measurement for irregular-shaped samples,” in International Symposium on Optical Fabrication. Testing and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE720, 419–425 (1992).
  23. S. A. Aleksandrov, I. V. Chernyh, “Interferometer for measurement of absolute refractive index and thickness,” in Interferometry: Applications, G. M. Brown, W. P. Jueptner, R. J. Pryputniewicz, eds., Proc. SPIE1756, 221–226 (1992).
  24. S. F. Nee, H. E. Bennett, “Accurate null polarimetry for measuring the refractive index of transparent materials,” J. Opt. Soc. Am. A 10, 2076–2083 (1993).
    [CrossRef]
  25. S. Nemoto, “Measurement of the refractive index of liquid using laser beam displacement,” Appl. Opt. 31, 6690–6694 (1992).
    [CrossRef] [PubMed]
  26. E. M. Georgieva, “Experimental determination of the refractive index of solids by reflection,” Opt. Appl. 21, 221–224 (1991).
  27. T. Hashimoto, H. Matsuzaki, H. Tsuchida, K. Yamamoto, “High-precision measurement for refractive index distribution and dispersion using an improved scanning total reflection method,” Jpn. J. Appl. Phys. 31, 1602–1605 (1992).
    [CrossRef]
  28. Z. Bor, K. Osvay, B. Racz, G. Szabo, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
    [CrossRef]
  29. M. D. Hopler, J. R. Rogers, “Interferometric measurement of group and phase refractive index,” Appl. Opt. 30, 735–744 (1991).
    [CrossRef] [PubMed]
  30. A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, New York, 1961), p. 142.
  31. A. Sommerfeld, Optics (Academic, London, 1967), p. 105.
  32. M. A. Khashan, “Application of the Fabry–Perot interferometer as a refractometer,” Opt. Acta 26, 881–888 (1979).
    [CrossRef]
  33. M. A. Khashan, “Comparison of group and phase velocities of light using the Michelson Interferometer,” Optik 64, 285–297 (1983).

1995 (1)

G. Ghosh, “Sellmeier coefficients and chromatic dispersions for some tellurite glasses,” J. Am. Ceram. Soc. 78, 2828–2830 (1995).
[CrossRef]

1994 (3)

1993 (3)

N. Kitamura, I. Y. Toguchi, S. Funco, H. Yamashita, M. Kinoshita, “Refractive index of densified silica glass,” J. Non-Cryst. Solids 159, 241–245 (1993).
[CrossRef]

S. F. Nee, H. E. Bennett, “Accurate null polarimetry for measuring the refractive index of transparent materials,” J. Opt. Soc. Am. A 10, 2076–2083 (1993).
[CrossRef]

H. Hsiu, “Accurate measurement of refractive-indices,” in Engineering & Laboratory Notes, Opt. Photon. News 4(11), S4–S5 (1993).

1992 (3)

S. Nemoto, “Measurement of the refractive index of liquid using laser beam displacement,” Appl. Opt. 31, 6690–6694 (1992).
[CrossRef] [PubMed]

S. Yamagata, “Effect of OH-group on distribution of refractive index in silica glass,” J. Ceram. Soc. Jpn. 100, 337–341 (1992).
[CrossRef]

T. Hashimoto, H. Matsuzaki, H. Tsuchida, K. Yamamoto, “High-precision measurement for refractive index distribution and dispersion using an improved scanning total reflection method,” Jpn. J. Appl. Phys. 31, 1602–1605 (1992).
[CrossRef]

1991 (2)

M. D. Hopler, J. R. Rogers, “Interferometric measurement of group and phase refractive index,” Appl. Opt. 30, 735–744 (1991).
[CrossRef] [PubMed]

E. M. Georgieva, “Experimental determination of the refractive index of solids by reflection,” Opt. Appl. 21, 221–224 (1991).

1990 (2)

M. Medhat, “Measurement of the refraction and dispersion of solids and liquids by the rings of equal chromatic order,” Optik 85, 73–77 (1990).

Z. Bor, K. Osvay, B. Racz, G. Szabo, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

1989 (1)

M. A. Khashan, A. Y. Nassif, “Measurement of birefringence, dispersion and line splitting for biaxial crystals by double-layer interferometer,” J. Mod. Opt. 36, 785–796 (1989).
[CrossRef]

1987 (1)

M. A. Khashan, “Measurement of group-velocity dispersion by double-layer interferometer,” Optik 76, 73–77 (1987).

1983 (1)

M. A. Khashan, “Comparison of group and phase velocities of light using the Michelson Interferometer,” Optik 64, 285–297 (1983).

1982 (1)

W. Burckhardt, “Refractive index and dispersion of glasses with different degrees of linking,” J. Non-Cryst. Solids 50, 173–182 (1982).
[CrossRef]

1979 (2)

M. A. Khashan, “Application of the Fabry–Perot interferometer as a refractometer,” Opt. Acta 26, 881–888 (1979).
[CrossRef]

M. A. Khashan, “Order transformation, a new exact method for the Fabry–Perot spectrometer,” Opt. Acta 26, 873–879 (1979).
[CrossRef]

1975 (1)

1973 (1)

M. A. Khashan, “Channeled spectrum with the double-layer interferometer,” Opt. Commun. 8, 220–221 (1973).
[CrossRef]

1972 (1)

M. A. Khashan, “Multiple-beam interference refractometer and comparator,” Optik 35, 421–430 (1972).

1965 (1)

Aleksandrov, S. A.

S. A. Aleksandrov, I. V. Chernyh, “Interferometer for measurement of absolute refractive index and thickness,” in Interferometry: Applications, G. M. Brown, W. P. Jueptner, R. J. Pryputniewicz, eds., Proc. SPIE1756, 221–226 (1992).

Bennett, H. E.

Bor, Z.

Z. Bor, K. Osvay, B. Racz, G. Szabo, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), pp. 364–367.

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960), p. 96.

Burckhardt, W.

W. Burckhardt, “Refractive index and dispersion of glasses with different degrees of linking,” J. Non-Cryst. Solids 50, 173–182 (1982).
[CrossRef]

Candler, C.

C. Candler, Modern Interferometers (Hilger Watts, Glasgow, 1951), p. 218–227.

Chang, K. H.

S. M. Yang, K. H. Chang, T. K. Kung, “Refractive index measurement for irregular-shaped samples,” in International Symposium on Optical Fabrication. Testing and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE720, 419–425 (1992).

Chernyh, I. V.

S. A. Aleksandrov, I. V. Chernyh, “Interferometer for measurement of absolute refractive index and thickness,” in Interferometry: Applications, G. M. Brown, W. P. Jueptner, R. J. Pryputniewicz, eds., Proc. SPIE1756, 221–226 (1992).

Funco, S.

N. Kitamura, I. Y. Toguchi, S. Funco, H. Yamashita, M. Kinoshita, “Refractive index of densified silica glass,” J. Non-Cryst. Solids 159, 241–245 (1993).
[CrossRef]

Georgieva, E. M.

E. M. Georgieva, “Experimental determination of the refractive index of solids by reflection,” Opt. Appl. 21, 221–224 (1991).

Ghosh, G.

G. Ghosh, “Sellmeier coefficients and chromatic dispersions for some tellurite glasses,” J. Am. Ceram. Soc. 78, 2828–2830 (1995).
[CrossRef]

Harvey, J. E.

Hashimoto, T.

T. Hashimoto, H. Matsuzaki, H. Tsuchida, K. Yamamoto, “High-precision measurement for refractive index distribution and dispersion using an improved scanning total reflection method,” Jpn. J. Appl. Phys. 31, 1602–1605 (1992).
[CrossRef]

Heraeus, W. C.

W. C. Heraeus, 60 Jahre Quarzglas 25 Jahre Hochvakuumtechnik (GmbH, Hanau, Germany, 1961). A review of this book was published in J. Opt. Soc. Am. 54, 1067–1068 (1964).

Hopler, M. D.

Hsiu, H.

H. Hsiu, “Accurate measurement of refractive-indices,” in Engineering & Laboratory Notes, Opt. Photon. News 4(11), S4–S5 (1993).

Icenogle, H. W.

Khashan, M. A.

M. A. Khashan, A. Y. Nassif, “Measurement of birefringence, dispersion and line splitting for biaxial crystals by double-layer interferometer,” J. Mod. Opt. 36, 785–796 (1989).
[CrossRef]

M. A. Khashan, “Measurement of group-velocity dispersion by double-layer interferometer,” Optik 76, 73–77 (1987).

M. A. Khashan, “Comparison of group and phase velocities of light using the Michelson Interferometer,” Optik 64, 285–297 (1983).

M. A. Khashan, “Application of the Fabry–Perot interferometer as a refractometer,” Opt. Acta 26, 881–888 (1979).
[CrossRef]

M. A. Khashan, “Order transformation, a new exact method for the Fabry–Perot spectrometer,” Opt. Acta 26, 873–879 (1979).
[CrossRef]

M. A. Khashan, “Channeled spectrum with the double-layer interferometer,” Opt. Commun. 8, 220–221 (1973).
[CrossRef]

M. A. Khashan, “Multiple-beam interference refractometer and comparator,” Optik 35, 421–430 (1972).

Kinoshita, M.

N. Kitamura, I. Y. Toguchi, S. Funco, H. Yamashita, M. Kinoshita, “Refractive index of densified silica glass,” J. Non-Cryst. Solids 159, 241–245 (1993).
[CrossRef]

Kitamura, N.

N. Kitamura, I. Y. Toguchi, S. Funco, H. Yamashita, M. Kinoshita, “Refractive index of densified silica glass,” J. Non-Cryst. Solids 159, 241–245 (1993).
[CrossRef]

Korniski, R.

Kung, T. K.

S. M. Yang, K. H. Chang, T. K. Kung, “Refractive index measurement for irregular-shaped samples,” in International Symposium on Optical Fabrication. Testing and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE720, 419–425 (1992).

Malitson, L. H.

Matsuzaki, H.

T. Hashimoto, H. Matsuzaki, H. Tsuchida, K. Yamamoto, “High-precision measurement for refractive index distribution and dispersion using an improved scanning total reflection method,” Jpn. J. Appl. Phys. 31, 1602–1605 (1992).
[CrossRef]

Medhat, M.

M. Medhat, “Measurement of the refraction and dispersion of solids and liquids by the rings of equal chromatic order,” Optik 85, 73–77 (1990).

Mitchell, A. C. G.

A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, New York, 1961), p. 142.

Nassif, A. Y.

M. A. Khashan, A. Y. Nassif, “Measurement of birefringence, dispersion and line splitting for biaxial crystals by double-layer interferometer,” J. Mod. Opt. 36, 785–796 (1989).
[CrossRef]

Nee, S. F.

Nemoto, S.

Oldham, W. Q.

R. Schenker, P. Schermerhorn, W. Q. Oldham, “Deep-ultraviolet damage to fused silica,” J. Vac. Sci. Technol. B 12, 3275–3279 (1994).
[CrossRef]

Osvay, K.

Z. Bor, K. Osvay, B. Racz, G. Szabo, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Platt, B. C.

Racz, B.

Z. Bor, K. Osvay, B. Racz, G. Szabo, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Rogers, J. R.

Schenker, R.

R. Schenker, P. Schermerhorn, W. Q. Oldham, “Deep-ultraviolet damage to fused silica,” J. Vac. Sci. Technol. B 12, 3275–3279 (1994).
[CrossRef]

Schermerhorn, P.

R. Schenker, P. Schermerhorn, W. Q. Oldham, “Deep-ultraviolet damage to fused silica,” J. Vac. Sci. Technol. B 12, 3275–3279 (1994).
[CrossRef]

Sharma, A.

Siva Rama Krishna, K.

Sommerfeld, A.

A. Sommerfeld, Optics (Academic, London, 1967), p. 105.

Sosman, R. B.

R. B. Sosman, The Properties of Silica (Chemical Catalog, New York, 1927).

Szabo, G.

Z. Bor, K. Osvay, B. Racz, G. Szabo, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Toguchi, I. Y.

N. Kitamura, I. Y. Toguchi, S. Funco, H. Yamashita, M. Kinoshita, “Refractive index of densified silica glass,” J. Non-Cryst. Solids 159, 241–245 (1993).
[CrossRef]

Tsuchida, H.

T. Hashimoto, H. Matsuzaki, H. Tsuchida, K. Yamamoto, “High-precision measurement for refractive index distribution and dispersion using an improved scanning total reflection method,” Jpn. J. Appl. Phys. 31, 1602–1605 (1992).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), pp. 364–367.

Wolf, W. L.

Yamagata, S.

S. Yamagata, “Effect of OH-group on distribution of refractive index in silica glass,” J. Ceram. Soc. Jpn. 100, 337–341 (1992).
[CrossRef]

Yamamoto, K.

T. Hashimoto, H. Matsuzaki, H. Tsuchida, K. Yamamoto, “High-precision measurement for refractive index distribution and dispersion using an improved scanning total reflection method,” Jpn. J. Appl. Phys. 31, 1602–1605 (1992).
[CrossRef]

Yamashita, H.

N. Kitamura, I. Y. Toguchi, S. Funco, H. Yamashita, M. Kinoshita, “Refractive index of densified silica glass,” J. Non-Cryst. Solids 159, 241–245 (1993).
[CrossRef]

Yang, S. M.

S. M. Yang, K. H. Chang, T. K. Kung, “Refractive index measurement for irregular-shaped samples,” in International Symposium on Optical Fabrication. Testing and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE720, 419–425 (1992).

Zemansky, M. W.

A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, New York, 1961), p. 142.

Appl. Opt. (4)

Engineering & Laboratory Notes, Opt. Photon. News (1)

H. Hsiu, “Accurate measurement of refractive-indices,” in Engineering & Laboratory Notes, Opt. Photon. News 4(11), S4–S5 (1993).

J. Am. Ceram. Soc. (1)

G. Ghosh, “Sellmeier coefficients and chromatic dispersions for some tellurite glasses,” J. Am. Ceram. Soc. 78, 2828–2830 (1995).
[CrossRef]

J. Ceram. Soc. Jpn. (1)

S. Yamagata, “Effect of OH-group on distribution of refractive index in silica glass,” J. Ceram. Soc. Jpn. 100, 337–341 (1992).
[CrossRef]

J. Mod. Opt. (1)

M. A. Khashan, A. Y. Nassif, “Measurement of birefringence, dispersion and line splitting for biaxial crystals by double-layer interferometer,” J. Mod. Opt. 36, 785–796 (1989).
[CrossRef]

J. Non-Cryst. Solids (2)

N. Kitamura, I. Y. Toguchi, S. Funco, H. Yamashita, M. Kinoshita, “Refractive index of densified silica glass,” J. Non-Cryst. Solids 159, 241–245 (1993).
[CrossRef]

W. Burckhardt, “Refractive index and dispersion of glasses with different degrees of linking,” J. Non-Cryst. Solids 50, 173–182 (1982).
[CrossRef]

J. Opt. Soc. Am. (2)

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

J. Vac. Sci. Technol. B (1)

R. Schenker, P. Schermerhorn, W. Q. Oldham, “Deep-ultraviolet damage to fused silica,” J. Vac. Sci. Technol. B 12, 3275–3279 (1994).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Hashimoto, H. Matsuzaki, H. Tsuchida, K. Yamamoto, “High-precision measurement for refractive index distribution and dispersion using an improved scanning total reflection method,” Jpn. J. Appl. Phys. 31, 1602–1605 (1992).
[CrossRef]

Opt. Acta (2)

M. A. Khashan, “Application of the Fabry–Perot interferometer as a refractometer,” Opt. Acta 26, 881–888 (1979).
[CrossRef]

M. A. Khashan, “Order transformation, a new exact method for the Fabry–Perot spectrometer,” Opt. Acta 26, 873–879 (1979).
[CrossRef]

Opt. Appl. (1)

E. M. Georgieva, “Experimental determination of the refractive index of solids by reflection,” Opt. Appl. 21, 221–224 (1991).

Opt. Commun. (2)

Z. Bor, K. Osvay, B. Racz, G. Szabo, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

M. A. Khashan, “Channeled spectrum with the double-layer interferometer,” Opt. Commun. 8, 220–221 (1973).
[CrossRef]

Optik (4)

M. A. Khashan, “Measurement of group-velocity dispersion by double-layer interferometer,” Optik 76, 73–77 (1987).

M. A. Khashan, “Multiple-beam interference refractometer and comparator,” Optik 35, 421–430 (1972).

M. A. Khashan, “Comparison of group and phase velocities of light using the Michelson Interferometer,” Optik 64, 285–297 (1983).

M. Medhat, “Measurement of the refraction and dispersion of solids and liquids by the rings of equal chromatic order,” Optik 85, 73–77 (1990).

Other (9)

S. M. Yang, K. H. Chang, T. K. Kung, “Refractive index measurement for irregular-shaped samples,” in International Symposium on Optical Fabrication. Testing and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE720, 419–425 (1992).

S. A. Aleksandrov, I. V. Chernyh, “Interferometer for measurement of absolute refractive index and thickness,” in Interferometry: Applications, G. M. Brown, W. P. Jueptner, R. J. Pryputniewicz, eds., Proc. SPIE1756, 221–226 (1992).

A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, New York, 1961), p. 142.

A. Sommerfeld, Optics (Academic, London, 1967), p. 105.

R. B. Sosman, The Properties of Silica (Chemical Catalog, New York, 1927).

W. C. Heraeus, 60 Jahre Quarzglas 25 Jahre Hochvakuumtechnik (GmbH, Hanau, Germany, 1961). A review of this book was published in J. Opt. Soc. Am. 54, 1067–1068 (1964).

L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960), p. 96.

C. Candler, Modern Interferometers (Hilger Watts, Glasgow, 1951), p. 218–227.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), pp. 364–367.

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Figures (9)

Fig. 1
Fig. 1

DLI with, a, nonidentical layers; b, identical layers. The heavy lines represent three plane-parallel mirrors, M1, M2, and M3. In (a) the glass layer is made wholly from one glass plate with plane-parallel faces at 24.00-mm geometric thickness. In b two plane-parallel plates of 12.00-mm geometric thickness compensate for dispersion effects in both layers.

Fig. 2
Fig. 2

Setup for photographing spectra channeled with a DLI as a refractometer and a thin Fabry–Perot interferometer (FPI) as a wavelength étalon. The DLI contains the rotatable silica plate T in one of its gaps.

Fig. 3
Fig. 3

RECO’s of a DLI with nonidentical layers. The RECO center coincides with the Hg doublet line of wavelength components 577.1 and 579.2 nm.

Fig. 4
Fig. 4

RECO’s with a DLI of identical layers but containing a silica plate of 4.260-mm geometric thickness. The RECO center is moved from the red side to the violet side of the visible spectrum as one of the interferometer mirrors is shifted parallel to itself.

Fig. 5
Fig. 5

Relationship of the squared ring radii (σ - σ c)2 and the interference order m.

Fig. 6
Fig. 6

Plot illustrating the dependence of the dispersion coefficient of the group velocity of light (dnG)/dσ on the wave number σ.

Fig. 7
Fig. 7

Rotation of a plane-parallel plate of thickness l and inclination angle α in one layer of the DLI. The normal to the plate at refraction point R is N, and the common wave front to both refracted and unrefracted rays is W.

Fig. 8
Fig. 8

Straight lines that relate the fringe count Δ m to the rotated angle α. Note that the experimental values are more dense the greater the fringe count. Note also that the slope decreases with the increase of the wavelength λ.

Fig. 9
Fig. 9

Dispersion of n and nG for a silica plate with a thickness of l = 4.260 mm at a temperature of 33°C. The measured values (filled circles) are fitted to the dispersion functions (23) and (25) (continuous curves).

Tables (2)

Tables Icon

Table 1 Dependence of Refractive Indices n and nG and Dispersion Coefficients dn/dλ and dnG/dλ on Wavelength λ as Measured by the DLI

Tables Icon

Table 2 Error Estimation δn of the Refractive Index as Measured by Sample Rotation inside the DLI

Equations (25)

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

σ-σcA2+yB2=m-.
A=1/l dnGdσ1/2,
B=Mncλcnc2G-11/2,
G=1+σdnndσ;
δdnG/dσdnG/dσ=δll2+4δAA21/2.
2n1-cos θ-n01-cos αl=λΔm.
n=2n0-ρn0 sin2α/2-ρ2/22n0 sin2α/2-ρ,
1sin2α/2=CΔm+D,
C=4n-n0n0l/nλ,
D=2n0/n.
δn=nρδρ2+nαδα2+nn0δn021/2,
nρ=nn0-ρn2n0 sin2α2-1,
nα=-n2n0-ρρ2n0 sin2α2 tanα2,
nn0=nn0-ρ1-ρn2n02 sin2α2,
δρρ=δλλ2+δΔmΔm2+δll21/2.
x=nG-1l,
δnG=δxl2+xδll21/2.
n2-1= 2aikλ2λ2-λik2,
aik=r0/2π Nfikλik2,
r0=e2/mc2;
n2-1= aik1+coth ψik,
ψik=lnλλik.
n2=aik1+coth ψik+b,
b=1+2 amn
n2G2=aik1+coth ψikcoth ψik+b.

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