Abstract

A simple method is proposed for the refractive index measurement of thick solid and liquid layers. In contrast to interferometric methods, no mirrors are used, and the experimental setup is undemanding and simple. The method is based on the variation of transmission caused by optical interference within the layer as a function of incidence angle. A new equation is derived for the positions of the interference extrema versus incidence angle. Scattering at the surfaces and within the sample, as well as weak absorption, do not play important roles. The method is illustrated by the refractive index measurements of sapphire, window glass, and water.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167-180 (2002).
    [CrossRef]
  2. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
  3. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, 1965).
  4. H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics, 2001).
    [CrossRef]
  5. S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63-65 (1997).
    [CrossRef]
  6. R. Ulrich and R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. 12, 2901-2908 (1973).
    [CrossRef] [PubMed]
  7. M. Galli, F. Marabelli, and D. Comoretto, “Interferometric determination of the anisotropic refractive index dispersion of poly-(p-phenylene-vinylene),” Appl. Phys. Lett. 86, 201119(2005).
    [CrossRef]
  8. M. J. Jang and C. F. Lu,“ A measurement system for determining the thickness of an optical wave plate,” Opt. Commun. 253, 2-9 (2005).
    [CrossRef]
  9. S. Y. El-Zaiat, “Group refractive index measurement by fringes of equal chromatic order,” Opt. Laser Technol. 37, 181-186 (2005).
    [CrossRef]
  10. H. Moosmüller and W. P. Arnott, “Folded Jamin interferometer: a stable instrument for refractive-index measurements,” Opt. Lett. 21, 438-440 (1996).
    [CrossRef] [PubMed]
  11. M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507-515 (1997).
    [CrossRef]
  12. D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetry,” Thin Solid Films 455-456, 3-13 (2004).
    [CrossRef]
  13. M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313-314, 323-332(1998).
    [CrossRef]
  14. R. Goldhahn, S. Shokhovets, J. Scheiner, G. Gobsch, T. S. Cheng, C. T. Foxon, U. Kaiser, D. Kipshidze, and W. Richter, “Determination of group III nitride film properties by reflectance and spectroscopic ellipsometry studies,” Phys. Status Solidi A 177, 107-115 (2000).
    [CrossRef]
  15. T. Fukano and I. Yamaguchi, “Separation of measurement of the refractive index and the geometrical thickness by use of a wavelength-scanning interferometer with a confocal microscope,” Appl. Opt. 38, 4065-4073 (1999).
    [CrossRef]
  16. B. Šantić and F. Scholz, “On the evaluation of optical parameters of a thin semiconductor film from transmission spectra, and application to GaN films,” Meas. Sci. Technol. 19, 105303 (2008).
    [CrossRef]
  17. J. C. Manifacier, J. Gasiot, and J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002-1004 (1976).
    [CrossRef]
  18. W. A. Pliskin, “Refractive index dispersion of dielectric films used in the semiconductor industry,” J. Electrochem. Soc. 134, 2819-2826 (1987).
    [CrossRef]
  19. R. Swanepoel, “Determination of the thickness and optical constants of a-Si,” J. Phys. E 16, 1214-1222(1983).
    [CrossRef]
  20. W. A. Pliskin and E. E. Conrad, “Nondestructive determination of thickness and refractive index of transparent films,” IBM J. Res. Dev. 8, 43-51 (1964).
    [CrossRef]
  21. A. J. Warnecke and P. J. LoPresti, “Refractive index dispersion in semiconductor-related thin films,” IBM J. Res. Dev. 17, 256-262 (1973).
    [CrossRef]
  22. B. Šantić, “Simultaneous measurement of the refractive index and thickness of a thin film,” submitted to Thin Solid Films.
  23. K. Ishikawa, H. Yamano, K. Kagawa, K. Asada, K. Iwata, and M. Ueda, “Measurement of thickness of a thin film by means of laser interference at many incident angles,” Opt. Lasers Eng. 41, 19-29 (2004).
    [CrossRef]
  24. C. Jung and B. K. Rhee, “Simultaneous determination of thickness and optical constants of polymer thin film by analyzing transmittance,” Appl. Opt. 41, 3861-3865(2002).
    [CrossRef] [PubMed]
  25. R. Swanepoel, “Determining refractive index and thickness of thin films from wavelength measurements only,” J. Opt. Soc. Am. A 2, 1339-1343 (1985).
    [CrossRef]
  26. A. Lamminpää, S. Nevas, F. Manoocheri, and E. Ikonen, “Characterization of thin films based on reflectance and transmittance measurements at oblique angles of incidence,” Appl. Opt. 45, 1392-1396 (2006).
    [CrossRef] [PubMed]
  27. B. Cox and Y.-M. Wong, “Direct measurement of the thickness and optical properties of zirconia corrosion films,” J. Nucl. Mater. 199, 258-271 (1993).
    [CrossRef]
  28. G. I. Surdutovich, R. Z. Vitlina, and V. Baranauskas, “Simple reflectometric method for measurement of weakly absorbing films,” Thin Solid Films 355-356, 446-450 (1999).
    [CrossRef]
  29. H. El-Kashef, G. E. Hassan, and I. El-Ghazaly, “Mach-Zehnder optical system as a sensitive measuring instrument,” Appl. Opt. 33, 3540-3544 (1994).
    [CrossRef] [PubMed]
  30. M. A. Khashan and A. Y. Nassif, “Accurate measurement of the refractive indices of solids and liquids by the double-layer interferometer,” Appl. Opt. 39, 5991-5997 (2000).
    [CrossRef]
  31. Properties of sapphire, http://www.mellesgriot.com/products/optics/mp_3_5.htm.

2008 (1)

B. Šantić and F. Scholz, “On the evaluation of optical parameters of a thin semiconductor film from transmission spectra, and application to GaN films,” Meas. Sci. Technol. 19, 105303 (2008).
[CrossRef]

2006 (1)

2005 (3)

M. Galli, F. Marabelli, and D. Comoretto, “Interferometric determination of the anisotropic refractive index dispersion of poly-(p-phenylene-vinylene),” Appl. Phys. Lett. 86, 201119(2005).
[CrossRef]

M. J. Jang and C. F. Lu,“ A measurement system for determining the thickness of an optical wave plate,” Opt. Commun. 253, 2-9 (2005).
[CrossRef]

S. Y. El-Zaiat, “Group refractive index measurement by fringes of equal chromatic order,” Opt. Laser Technol. 37, 181-186 (2005).
[CrossRef]

2004 (2)

D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetry,” Thin Solid Films 455-456, 3-13 (2004).
[CrossRef]

K. Ishikawa, H. Yamano, K. Kagawa, K. Asada, K. Iwata, and M. Ueda, “Measurement of thickness of a thin film by means of laser interference at many incident angles,” Opt. Lasers Eng. 41, 19-29 (2004).
[CrossRef]

2002 (2)

2000 (2)

M. A. Khashan and A. Y. Nassif, “Accurate measurement of the refractive indices of solids and liquids by the double-layer interferometer,” Appl. Opt. 39, 5991-5997 (2000).
[CrossRef]

R. Goldhahn, S. Shokhovets, J. Scheiner, G. Gobsch, T. S. Cheng, C. T. Foxon, U. Kaiser, D. Kipshidze, and W. Richter, “Determination of group III nitride film properties by reflectance and spectroscopic ellipsometry studies,” Phys. Status Solidi A 177, 107-115 (2000).
[CrossRef]

1999 (2)

T. Fukano and I. Yamaguchi, “Separation of measurement of the refractive index and the geometrical thickness by use of a wavelength-scanning interferometer with a confocal microscope,” Appl. Opt. 38, 4065-4073 (1999).
[CrossRef]

G. I. Surdutovich, R. Z. Vitlina, and V. Baranauskas, “Simple reflectometric method for measurement of weakly absorbing films,” Thin Solid Films 355-356, 446-450 (1999).
[CrossRef]

1998 (1)

M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313-314, 323-332(1998).
[CrossRef]

1997 (2)

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507-515 (1997).
[CrossRef]

S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63-65 (1997).
[CrossRef]

1996 (1)

1994 (1)

1993 (1)

B. Cox and Y.-M. Wong, “Direct measurement of the thickness and optical properties of zirconia corrosion films,” J. Nucl. Mater. 199, 258-271 (1993).
[CrossRef]

1987 (1)

W. A. Pliskin, “Refractive index dispersion of dielectric films used in the semiconductor industry,” J. Electrochem. Soc. 134, 2819-2826 (1987).
[CrossRef]

1985 (1)

1983 (1)

R. Swanepoel, “Determination of the thickness and optical constants of a-Si,” J. Phys. E 16, 1214-1222(1983).
[CrossRef]

1976 (1)

J. C. Manifacier, J. Gasiot, and J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002-1004 (1976).
[CrossRef]

1973 (2)

A. J. Warnecke and P. J. LoPresti, “Refractive index dispersion in semiconductor-related thin films,” IBM J. Res. Dev. 17, 256-262 (1973).
[CrossRef]

R. Ulrich and R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. 12, 2901-2908 (1973).
[CrossRef] [PubMed]

1964 (1)

W. A. Pliskin and E. E. Conrad, “Nondestructive determination of thickness and refractive index of transparent films,” IBM J. Res. Dev. 8, 43-51 (1964).
[CrossRef]

Arnott, W. P.

Asada, K.

K. Ishikawa, H. Yamano, K. Kagawa, K. Asada, K. Iwata, and M. Ueda, “Measurement of thickness of a thin film by means of laser interference at many incident angles,” Opt. Lasers Eng. 41, 19-29 (2004).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetry,” Thin Solid Films 455-456, 3-13 (2004).
[CrossRef]

Baranauskas, V.

G. I. Surdutovich, R. Z. Vitlina, and V. Baranauskas, “Simple reflectometric method for measurement of weakly absorbing films,” Thin Solid Films 355-356, 446-450 (1999).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Cheng, T. S.

R. Goldhahn, S. Shokhovets, J. Scheiner, G. Gobsch, T. S. Cheng, C. T. Foxon, U. Kaiser, D. Kipshidze, and W. Richter, “Determination of group III nitride film properties by reflectance and spectroscopic ellipsometry studies,” Phys. Status Solidi A 177, 107-115 (2000).
[CrossRef]

Comoretto, D.

M. Galli, F. Marabelli, and D. Comoretto, “Interferometric determination of the anisotropic refractive index dispersion of poly-(p-phenylene-vinylene),” Appl. Phys. Lett. 86, 201119(2005).
[CrossRef]

Conrad, E. E.

W. A. Pliskin and E. E. Conrad, “Nondestructive determination of thickness and refractive index of transparent films,” IBM J. Res. Dev. 8, 43-51 (1964).
[CrossRef]

Cox, B.

B. Cox and Y.-M. Wong, “Direct measurement of the thickness and optical properties of zirconia corrosion films,” J. Nucl. Mater. 199, 258-271 (1993).
[CrossRef]

El-Ghazaly, I.

El-Kashef, H.

El-Zaiat, S. Y.

S. Y. El-Zaiat, “Group refractive index measurement by fringes of equal chromatic order,” Opt. Laser Technol. 37, 181-186 (2005).
[CrossRef]

S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63-65 (1997).
[CrossRef]

Fillard, J. P.

J. C. Manifacier, J. Gasiot, and J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002-1004 (1976).
[CrossRef]

Foxon, C. T.

R. Goldhahn, S. Shokhovets, J. Scheiner, G. Gobsch, T. S. Cheng, C. T. Foxon, U. Kaiser, D. Kipshidze, and W. Richter, “Determination of group III nitride film properties by reflectance and spectroscopic ellipsometry studies,” Phys. Status Solidi A 177, 107-115 (2000).
[CrossRef]

Fukano, T.

Galli, M.

M. Galli, F. Marabelli, and D. Comoretto, “Interferometric determination of the anisotropic refractive index dispersion of poly-(p-phenylene-vinylene),” Appl. Phys. Lett. 86, 201119(2005).
[CrossRef]

Gasiot, J.

J. C. Manifacier, J. Gasiot, and J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002-1004 (1976).
[CrossRef]

Gobsch, G.

R. Goldhahn, S. Shokhovets, J. Scheiner, G. Gobsch, T. S. Cheng, C. T. Foxon, U. Kaiser, D. Kipshidze, and W. Richter, “Determination of group III nitride film properties by reflectance and spectroscopic ellipsometry studies,” Phys. Status Solidi A 177, 107-115 (2000).
[CrossRef]

Goldhahn, R.

R. Goldhahn, S. Shokhovets, J. Scheiner, G. Gobsch, T. S. Cheng, C. T. Foxon, U. Kaiser, D. Kipshidze, and W. Richter, “Determination of group III nitride film properties by reflectance and spectroscopic ellipsometry studies,” Phys. Status Solidi A 177, 107-115 (2000).
[CrossRef]

Haruna, M.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507-515 (1997).
[CrossRef]

Hassan, G. E.

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, 1965).

Ikonen, E.

Ishikawa, K.

K. Ishikawa, H. Yamano, K. Kagawa, K. Asada, K. Iwata, and M. Ueda, “Measurement of thickness of a thin film by means of laser interference at many incident angles,” Opt. Lasers Eng. 41, 19-29 (2004).
[CrossRef]

Iwata, K.

K. Ishikawa, H. Yamano, K. Kagawa, K. Asada, K. Iwata, and M. Ueda, “Measurement of thickness of a thin film by means of laser interference at many incident angles,” Opt. Lasers Eng. 41, 19-29 (2004).
[CrossRef]

Jang, M. J.

M. J. Jang and C. F. Lu,“ A measurement system for determining the thickness of an optical wave plate,” Opt. Commun. 253, 2-9 (2005).
[CrossRef]

Jung, C.

Kagawa, K.

K. Ishikawa, H. Yamano, K. Kagawa, K. Asada, K. Iwata, and M. Ueda, “Measurement of thickness of a thin film by means of laser interference at many incident angles,” Opt. Lasers Eng. 41, 19-29 (2004).
[CrossRef]

Kaiser, U.

R. Goldhahn, S. Shokhovets, J. Scheiner, G. Gobsch, T. S. Cheng, C. T. Foxon, U. Kaiser, D. Kipshidze, and W. Richter, “Determination of group III nitride film properties by reflectance and spectroscopic ellipsometry studies,” Phys. Status Solidi A 177, 107-115 (2000).
[CrossRef]

Khashan, M. A.

Kipshidze, D.

R. Goldhahn, S. Shokhovets, J. Scheiner, G. Gobsch, T. S. Cheng, C. T. Foxon, U. Kaiser, D. Kipshidze, and W. Richter, “Determination of group III nitride film properties by reflectance and spectroscopic ellipsometry studies,” Phys. Status Solidi A 177, 107-115 (2000).
[CrossRef]

Lamminpää, A.

LoPresti, P. J.

A. J. Warnecke and P. J. LoPresti, “Refractive index dispersion in semiconductor-related thin films,” IBM J. Res. Dev. 17, 256-262 (1973).
[CrossRef]

Lu, C. F.

M. J. Jang and C. F. Lu,“ A measurement system for determining the thickness of an optical wave plate,” Opt. Commun. 253, 2-9 (2005).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics, 2001).
[CrossRef]

Manifacier, J. C.

J. C. Manifacier, J. Gasiot, and J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002-1004 (1976).
[CrossRef]

Manoocheri, F.

Marabelli, F.

M. Galli, F. Marabelli, and D. Comoretto, “Interferometric determination of the anisotropic refractive index dispersion of poly-(p-phenylene-vinylene),” Appl. Phys. Lett. 86, 201119(2005).
[CrossRef]

Moosmüller, H.

Nassif, A. Y.

Nevas, S.

Ohmi, M.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507-515 (1997).
[CrossRef]

Pliskin, W. A.

W. A. Pliskin, “Refractive index dispersion of dielectric films used in the semiconductor industry,” J. Electrochem. Soc. 134, 2819-2826 (1987).
[CrossRef]

W. A. Pliskin and E. E. Conrad, “Nondestructive determination of thickness and refractive index of transparent films,” IBM J. Res. Dev. 8, 43-51 (1964).
[CrossRef]

Rhee, B. K.

Richter, W.

R. Goldhahn, S. Shokhovets, J. Scheiner, G. Gobsch, T. S. Cheng, C. T. Foxon, U. Kaiser, D. Kipshidze, and W. Richter, “Determination of group III nitride film properties by reflectance and spectroscopic ellipsometry studies,” Phys. Status Solidi A 177, 107-115 (2000).
[CrossRef]

Šantic, B.

B. Šantić and F. Scholz, “On the evaluation of optical parameters of a thin semiconductor film from transmission spectra, and application to GaN films,” Meas. Sci. Technol. 19, 105303 (2008).
[CrossRef]

B. Šantić, “Simultaneous measurement of the refractive index and thickness of a thin film,” submitted to Thin Solid Films.

Scheiner, J.

R. Goldhahn, S. Shokhovets, J. Scheiner, G. Gobsch, T. S. Cheng, C. T. Foxon, U. Kaiser, D. Kipshidze, and W. Richter, “Determination of group III nitride film properties by reflectance and spectroscopic ellipsometry studies,” Phys. Status Solidi A 177, 107-115 (2000).
[CrossRef]

Scholz, F.

B. Šantić and F. Scholz, “On the evaluation of optical parameters of a thin semiconductor film from transmission spectra, and application to GaN films,” Meas. Sci. Technol. 19, 105303 (2008).
[CrossRef]

Schubert, M.

M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313-314, 323-332(1998).
[CrossRef]

Shiraishi, T.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507-515 (1997).
[CrossRef]

Shokhovets, S.

R. Goldhahn, S. Shokhovets, J. Scheiner, G. Gobsch, T. S. Cheng, C. T. Foxon, U. Kaiser, D. Kipshidze, and W. Richter, “Determination of group III nitride film properties by reflectance and spectroscopic ellipsometry studies,” Phys. Status Solidi A 177, 107-115 (2000).
[CrossRef]

Singh, S.

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167-180 (2002).
[CrossRef]

Surdutovich, G. I.

G. I. Surdutovich, R. Z. Vitlina, and V. Baranauskas, “Simple reflectometric method for measurement of weakly absorbing films,” Thin Solid Films 355-356, 446-450 (1999).
[CrossRef]

Swanepoel, R.

Tajiri, H.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507-515 (1997).
[CrossRef]

Torge, R.

Ueda, M.

K. Ishikawa, H. Yamano, K. Kagawa, K. Asada, K. Iwata, and M. Ueda, “Measurement of thickness of a thin film by means of laser interference at many incident angles,” Opt. Lasers Eng. 41, 19-29 (2004).
[CrossRef]

Ulrich, R.

Vitlina, R. Z.

G. I. Surdutovich, R. Z. Vitlina, and V. Baranauskas, “Simple reflectometric method for measurement of weakly absorbing films,” Thin Solid Films 355-356, 446-450 (1999).
[CrossRef]

Warnecke, A. J.

A. J. Warnecke and P. J. LoPresti, “Refractive index dispersion in semiconductor-related thin films,” IBM J. Res. Dev. 17, 256-262 (1973).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Wong, Y.-M.

B. Cox and Y.-M. Wong, “Direct measurement of the thickness and optical properties of zirconia corrosion films,” J. Nucl. Mater. 199, 258-271 (1993).
[CrossRef]

Yamaguchi, I.

Yamano, H.

K. Ishikawa, H. Yamano, K. Kagawa, K. Asada, K. Iwata, and M. Ueda, “Measurement of thickness of a thin film by means of laser interference at many incident angles,” Opt. Lasers Eng. 41, 19-29 (2004).
[CrossRef]

Appl. Opt. (6)

Appl. Phys. Lett. (1)

M. Galli, F. Marabelli, and D. Comoretto, “Interferometric determination of the anisotropic refractive index dispersion of poly-(p-phenylene-vinylene),” Appl. Phys. Lett. 86, 201119(2005).
[CrossRef]

IBM J. Res. Dev. (2)

W. A. Pliskin and E. E. Conrad, “Nondestructive determination of thickness and refractive index of transparent films,” IBM J. Res. Dev. 8, 43-51 (1964).
[CrossRef]

A. J. Warnecke and P. J. LoPresti, “Refractive index dispersion in semiconductor-related thin films,” IBM J. Res. Dev. 17, 256-262 (1973).
[CrossRef]

J. Electrochem. Soc. (1)

W. A. Pliskin, “Refractive index dispersion of dielectric films used in the semiconductor industry,” J. Electrochem. Soc. 134, 2819-2826 (1987).
[CrossRef]

J. Nucl. Mater. (1)

B. Cox and Y.-M. Wong, “Direct measurement of the thickness and optical properties of zirconia corrosion films,” J. Nucl. Mater. 199, 258-271 (1993).
[CrossRef]

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

J. Phys. E (2)

J. C. Manifacier, J. Gasiot, and J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002-1004 (1976).
[CrossRef]

R. Swanepoel, “Determination of the thickness and optical constants of a-Si,” J. Phys. E 16, 1214-1222(1983).
[CrossRef]

Meas. Sci. Technol. (1)

B. Šantić and F. Scholz, “On the evaluation of optical parameters of a thin semiconductor film from transmission spectra, and application to GaN films,” Meas. Sci. Technol. 19, 105303 (2008).
[CrossRef]

Opt. Commun. (1)

M. J. Jang and C. F. Lu,“ A measurement system for determining the thickness of an optical wave plate,” Opt. Commun. 253, 2-9 (2005).
[CrossRef]

Opt. Laser Technol. (2)

S. Y. El-Zaiat, “Group refractive index measurement by fringes of equal chromatic order,” Opt. Laser Technol. 37, 181-186 (2005).
[CrossRef]

S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63-65 (1997).
[CrossRef]

Opt. Lasers Eng. (1)

K. Ishikawa, H. Yamano, K. Kagawa, K. Asada, K. Iwata, and M. Ueda, “Measurement of thickness of a thin film by means of laser interference at many incident angles,” Opt. Lasers Eng. 41, 19-29 (2004).
[CrossRef]

Opt. Lett. (1)

Opt. Rev. (1)

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507-515 (1997).
[CrossRef]

Phys. Scr. (1)

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167-180 (2002).
[CrossRef]

Phys. Status Solidi A (1)

R. Goldhahn, S. Shokhovets, J. Scheiner, G. Gobsch, T. S. Cheng, C. T. Foxon, U. Kaiser, D. Kipshidze, and W. Richter, “Determination of group III nitride film properties by reflectance and spectroscopic ellipsometry studies,” Phys. Status Solidi A 177, 107-115 (2000).
[CrossRef]

Thin Solid Films (3)

G. I. Surdutovich, R. Z. Vitlina, and V. Baranauskas, “Simple reflectometric method for measurement of weakly absorbing films,” Thin Solid Films 355-356, 446-450 (1999).
[CrossRef]

D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetry,” Thin Solid Films 455-456, 3-13 (2004).
[CrossRef]

M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313-314, 323-332(1998).
[CrossRef]

Other (5)

B. Šantić, “Simultaneous measurement of the refractive index and thickness of a thin film,” submitted to Thin Solid Films.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, 1965).

H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics, 2001).
[CrossRef]

Properties of sapphire, http://www.mellesgriot.com/products/optics/mp_3_5.htm.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Transparent layer of refractive index n and thickness d between two media of refractive indices v and s, respectively.

Fig. 2
Fig. 2

Transmission intensity versus incidence angle for a glass plate ( d = 0.42 mm , n = 1.514 , λ = 632.8 nm ). The bandwidths of the incoming light are Gaussians with half-widths δ λ . Index p is explained in the text.

Fig. 3
Fig. 3

Detector photocurrent versus sin 2 φ v (points). The transmission has qualitatively the same behavior as the photocurrent. The baseline is subtracted to simplify the convergence of fitting. The solid line is the fit with the Eq. (11). Inset: detector photocurrent before baseline subtraction.

Fig. 4
Fig. 4

Smoothed data (open points) and the extrema (black points). The index p is indicated at some extrema. Inset: Y p = sin 2 φ p points versus the order change p. The solid line is the linear fit.

Fig. 5
Fig. 5

Sample is 2.80 mm thick window glass. The points are the photocurrent versus sin 2 φ v , and the solid line is the fit to Eq. (11).

Fig. 6
Fig. 6

ROT data for the air gap and for water in the gap. The data for water are shifted slightly up for clarity. Data for the air gap are smoothed and spline interpolated (line).

Equations (11)

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

T v n s ( λ , φ ) = A t v n 2 t n s 2 ( s / v ) 1 + A 2 r n s 2 r n v 2 2 A r n s r n v cos ( 4 π n d cos φ n / λ ) .
ξ = 4 π d λ n 2 v 2 sin 2 φ v .
4 d λ n 2 v 2 sin 2 φ p = J p .
Y p = sin 2 φ p .
4 d λ n 2 v 2 Y p = J p .
4 d λ n 2 v 2 Y 0 = J .
Y p = Y 0 + λ n 2 v 2 Y 0 2 d v 2 p λ 2 16 d 2 v 2 p 2 .
λ 2 16 d 2 v 2 / λ n 2 v 2 Y 0 2 d v 2 λ 8 d n .
Z = B + C cos ( 4 π d λ 1 n 2 v 2 X ) .
Z = B + C cos ( 4 π d n λ 2 π v 2 d λ n X π v 4 d 2 λ n 3 X 2 π v 6 d 4 λ n 5 X 3 ) .
Z = B + C cos ( D A 1 X A 2 X 2 A 3 X 3 ) .

Metrics