Abstract

The thickness and the complex refractive index of a moderately thin absorbing film on a transparent substrate of known optical properties can be determined by measuring the values of reflectance of the sample from opposite sides, and the transmittance. The technique and its use in measuring properties of films of RbI in the uv are described. Errors are reduced by averaging the values of thickness obtained at several wavelengths and by iterating the computations.

© 1970 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. O. S. Heavens, in Physics of Thin Films, Vol. 2, G. Hass and R. Thun, Eds. (Academic Press Inc., New York, 1964).
  2. A. Vašíček, Optics of Thin Films (North-Holland Publ. Co., Amsterdam, 1960).
  3. See, e.g., G. Meyer, Z. Physik 168, 169 (1962).
    [Crossref]

1962 (1)

See, e.g., G. Meyer, Z. Physik 168, 169 (1962).
[Crossref]

Heavens, O. S.

O. S. Heavens, in Physics of Thin Films, Vol. 2, G. Hass and R. Thun, Eds. (Academic Press Inc., New York, 1964).

Meyer, G.

See, e.g., G. Meyer, Z. Physik 168, 169 (1962).
[Crossref]

Vašícek, A.

A. Vašíček, Optics of Thin Films (North-Holland Publ. Co., Amsterdam, 1960).

Z. Physik (1)

See, e.g., G. Meyer, Z. Physik 168, 169 (1962).
[Crossref]

Other (2)

O. S. Heavens, in Physics of Thin Films, Vol. 2, G. Hass and R. Thun, Eds. (Academic Press Inc., New York, 1964).

A. Vašíček, Optics of Thin Films (North-Holland Publ. Co., Amsterdam, 1960).

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

Light fluxes reflected and transmitted from a thin film n-ik deposited on a semi-infinite and transparent substrate n0. Both incidence from the vacuum side n1=1 and from the substrate side are considered.

Fig. 2
Fig. 2

Reflection and transmission scheme for a thin film deposited on a finite and transparent substrate.

Fig. 3
Fig. 3

Room-temperature reflectances R1 —— and R2 – – – for a thin film of RbI deposited on a fused-silica substrate. Thickness 420±30 Å.

Fig. 4
Fig. 4

Room-temperature transmittance T1 of a thin film of RbI deposited on a fused-silica substrate. Same film as for Fig. 3.

Fig. 5
Fig. 5

Extinction coefficient k for RbI determined from the data of Figs. 3 and 4 according to the procedures described in this paper.

Fig. 6
Fig. 6

Refractive index n for RbI determined from the data of Figs. 3 and 4 according to the procedures described in this paper.

Equations (9)

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

Δ - Δ 0 = f ( n , k , a ; λ ) ψ - ψ 0 = g ( n , k , a ; λ ) ,
R A = [ A B + F 2 G D - 2 F ( E cos φ - S sin φ ) ] / [ A D + F 2 B G - 2 F ( T cos φ - V sin φ ) ] R S = [ D G + F 2 B A - 2 F ( E cos φ + S sin φ ) ] / [ A D + F 2 B G - 2 F ( T cos φ - V sin φ ) ] T A = [ 16 n 0 ( n 2 + k 2 ) F ] / [ A D + F 2 B G - 2 F ( T cos φ - V sin φ ) ] ,
R 1 = R A + T A 2 R 0 T 0 2 / ( 1 - R 0 R s T 0 2 ) , R 2 = R 0 + ( 1 - R 0 ) 2 T 0 2 R s / ( 1 - T 0 2 R s R 0 ) , T 1 = T A T 0 ( 1 - R 0 ) / ( 1 - T 0 2 R s R 0 ) ,
R 0 = R 0 [ 1 + ( 1 - R 0 ) 2 T 0 2 / ( 1 - R 0 2 T 0 2 ) ] T 0 = T 0 ( 1 - R 0 ) 2 / ( 1 - R 0 2 T 0 2 ) .
Δ R 1 = ( R 1 / n ) Δ n + ( R 1 / k ) Δ k + ( R 1 / a / λ ) Δ a / λ Δ R 2 = ( R 2 / n ) Δ n + ( R 2 / k ) Δ k + ( R 2 / a / λ ) Δ a / λ Δ T 1 = ( T 1 / n ) Δ n + ( T 1 / k ) Δ k + ( T 1 / a / λ ) Δ a / λ .
Δ n = C 11 Δ R 1 + C 12 Δ R 2 + C 13 Δ T 1 Δ k = C 21 Δ R 1 + C 22 Δ R 2 + C 23 Δ T 1 Δ a / λ = C 31 Δ R 1 + C 32 Δ R 2 + C 33 Δ T 1 .
Δ n = ( C 11 2 + C 12 2 + C 13 2 ) 1 2 · Δ Δ k = ( C 21 2 + C 22 2 + C 23 2 ) 1 2 · Δ Δ a = λ ( C 31 2 + C 32 2 + C 33 2 ) 1 2 · Δ ,
n = 1.5 Δ n = 0.15 k = 1 Δ k = 0.05 a = 420 Å Δ a = 50 Å ,
R A = R 1 - R 0 T 1 2 / ( R 0 R 2 - 2 R 0 + 1 ) R s = ( R 2 - R 0 ) / T 0 2 ( R 0 R 2 - 2 R 0 + 1 ) T A = T 1 ( 1 - R 0 ) / T 0 ( R 0 R 2 - 2 R 0 + 1 ) .