Abstract

In internal reflection spectroscopy effective thickness is defined as the thickness of material required to give a spectrum of the same contrast in a transmission measurement as that obtained via internal reflection. Simple expressions for effective thickness are given for bulk materials and for thin films which are useful as guide lines in determining the optimum conditions required to record internal reflection spectra. Depending on angle of incidence and index of refraction, the effective thickness for bulk materials may be much greater or much less than the wavelength of light. Similarly for thin films the effective thickness may be much greater or much less than the actual thickness.

© 1966 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. J. Harrick, J. Opt. Soc. Am. 55, 851 (1965).
    [CrossRef]
  2. A discussion concerning the theory for anisotropic films has been given by P. A. Flournoy, W. J. Schaffers, Spectrochim. Acta 22, 5 (1966).
    [CrossRef]
  3. A displacement of the internal reflection spectra of thin films relative to transmission spectra of a fraction of a wavenumber towards shorter wavelengths was detected in some measurements. This has also been observed by R. W. Hannah (see Ref. 5).
  4. T. S. Hermann, Appl. Spectry. 19, 10 (1965).
    [CrossRef]
  5. R. W. Hannah, Perkin–Elmer Corporation, Norwalk, Conn. (paper presented at Pittsburgh Conference on Analytic Chemistry and Applied Spectroscopy, 25 February 1966).

1966 (1)

A discussion concerning the theory for anisotropic films has been given by P. A. Flournoy, W. J. Schaffers, Spectrochim. Acta 22, 5 (1966).
[CrossRef]

1965 (2)

T. S. Hermann, Appl. Spectry. 19, 10 (1965).
[CrossRef]

N. J. Harrick, J. Opt. Soc. Am. 55, 851 (1965).
[CrossRef]

Flournoy, P. A.

A discussion concerning the theory for anisotropic films has been given by P. A. Flournoy, W. J. Schaffers, Spectrochim. Acta 22, 5 (1966).
[CrossRef]

Hannah, R. W.

R. W. Hannah, Perkin–Elmer Corporation, Norwalk, Conn. (paper presented at Pittsburgh Conference on Analytic Chemistry and Applied Spectroscopy, 25 February 1966).

Harrick, N. J.

Hermann, T. S.

T. S. Hermann, Appl. Spectry. 19, 10 (1965).
[CrossRef]

Schaffers, W. J.

A discussion concerning the theory for anisotropic films has been given by P. A. Flournoy, W. J. Schaffers, Spectrochim. Acta 22, 5 (1966).
[CrossRef]

Appl. Spectry. (1)

T. S. Hermann, Appl. Spectry. 19, 10 (1965).
[CrossRef]

J. Opt. Soc. Am. (1)

Spectrochim. Acta (1)

A discussion concerning the theory for anisotropic films has been given by P. A. Flournoy, W. J. Schaffers, Spectrochim. Acta 22, 5 (1966).
[CrossRef]

Other (2)

A displacement of the internal reflection spectra of thin films relative to transmission spectra of a fraction of a wavenumber towards shorter wavelengths was detected in some measurements. This has also been observed by R. W. Hannah (see Ref. 5).

R. W. Hannah, Perkin–Elmer Corporation, Norwalk, Conn. (paper presented at Pittsburgh Conference on Analytic Chemistry and Applied Spectroscopy, 25 February 1966).

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 (9)

Fig. 1
Fig. 1

Relative penetration depth and effective thickness vs angle of incidence for an interface whose refractive index ratio is n21 = 0.423.

Fig. 2
Fig. 2

Relative effective thickness of bulk materials for polarization vs angle of incidence for a number of interfaces.

Fig. 3
Fig. 3

Relative effective thickness of bulk materials for || polarization vs angle of incidence for a number of interfaces.

Fig. 4
Fig. 4

Curves showing range of validity of approximate effective thickness formulas for bulk materials. n1 = 4. n21 = 0.333. θc = 19.5°. λ1 = 0.1μ.

Fig. 5
Fig. 5

Relative effective thickness for a thin film of refractive index n2 = 1.6 on plates of various refractive indices. Here θc, is the critical angle of the crystal air interface and not that of the crystal film interface.

Fig. 6
Fig. 6

Relative effective thickness for a thin film of refractive index n2 = 4 on plates of various refractive indices. Here θc is the critical angle of the crystal air interface and not that of the crystal film interface.

Fig. 7
Fig. 7

Multiple internal reflection spectrum at various angles of incidence of a thin film of polystyrene on a silicon internal reflection plate for unpolarized light.

Fig. 8
Fig. 8

Comparison of transmission spectrum and internal reflection spectrum of the band at 3.4 μ of a thin polystyrene film. — Transmission spectrum. - - - Internal reflection spectrum.

Fig. 9
Fig. 9

Spectra of the C–H band at 3.4 μ of a thin polystyrene film on a Si plate and on an Al2O3 plate ⊥ and || polarization. The O–H band at 3.0 μ is caused by adsorbed water on the surfaces of the plates.

Equations (6)

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

d e λ 1 = n 21 cos θ π ( 1 - n 21 2 ) ( sin 2 θ - n 21 2 ) 1 / 2
d e | | λ 1 = n 21 cos θ ( 2 sin 2 θ - n 21 2 ) π ( 1 - n 21 2 ) [ ( 1 + n 21 2 ) sin 2 θ - n 21 2 ] ( sin 2 θ - n 21 2 ) 1 / 2 .
d e = [ 4 n 21 d cos θ / ( 1 - n 31 2 ) ]
d e | | = 4 n 21 d cos θ [ ( 1 + n 32 4 ) sin 2 θ - n 31 2 ] ( 1 - n 31 2 ) [ ( 1 + n 31 2 ) sin 2 θ - n 31 2 ] .
E | | = 2 cos θ / ( 1 - n 31 2 ) 1 / 2
E = 2 cos θ [ ( 1 + n 32 4 ) sin 2 θ - n 31 2 ] 1 / 2 ( 1 - n 31 2 ) 1 / 2 [ ( 1 + n 31 2 ) sin 2 θ - n 31 2 ] 1 / 2 .

Metrics