Abstract

The determination of optical parameters of thin films from experimental data is a typical task in the field of optical-coating technology. The optical characterization of a single layer deposited on a substrate with known optical parameters is widely used for this purpose. Results of optical characterization are dependent on not only the choice of the thin-film model but also on the quality of experimental data. The theoretical results presented highlight the effect of systematic errors in measurement data on the determination of thin-film parameters. Application of these theoretical results is illustrated by the analysis of experimental data for magnesium fluoride thin films.

© 2002 Optical Society of America

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References

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    [CrossRef]

2000 (1)

E. Quesnel, L. Dumas, D. Jacob, F. Peiró, “Optical and microstructural properties of MgF2 UV coatings grown by ion beam sputtering process,” J. Vac. Sci. Technol. A 18, 2869–2876 (2000).
[CrossRef]

1997 (1)

1984 (2)

1983 (1)

1982 (1)

1981 (1)

1961 (1)

G. Koppelmann, K. Krebs, “Die Optischen Eigenschaften Dielektrischer Schichten mit Kleinen Homogenitatsstorungen,” Z. Phys. 164, 539–556 (1961).

1941 (1)

H. Schröder, “Bemerkung zur Theorie des Lichtdurchgangs durch inhomogene durchsichtige Schichten,” Ann. Phys. 39, 55–58 (1941).
[CrossRef]

Albrand, G.

Arndt, D. P.

Azzam, R. M. A.

Bennett, J. M.

Borgogno, J. P.

Bousquet, P.

Carniglia, C. K.

Case, W. E.

Dobrowolski, J. A.

Dumas, L.

E. Quesnel, L. Dumas, D. Jacob, F. Peiró, “Optical and microstructural properties of MgF2 UV coatings grown by ion beam sputtering process,” J. Vac. Sci. Technol. A 18, 2869–2876 (2000).
[CrossRef]

Flory, F.

Gibson, U. J.

Ho, F. C.

Hodgkin, V. A.

Jacob, D.

E. Quesnel, L. Dumas, D. Jacob, F. Peiró, “Optical and microstructural properties of MgF2 UV coatings grown by ion beam sputtering process,” J. Vac. Sci. Technol. A 18, 2869–2876 (2000).
[CrossRef]

Klapp, W. P.

Koppelmann, G.

G. Koppelmann, K. Krebs, “Die Optischen Eigenschaften Dielektrischer Schichten mit Kleinen Homogenitatsstorungen,” Z. Phys. 164, 539–556 (1961).

Krebs, K.

G. Koppelmann, K. Krebs, “Die Optischen Eigenschaften Dielektrischer Schichten mit Kleinen Homogenitatsstorungen,” Z. Phys. 164, 539–556 (1961).

Lazarides, B.

Macleod, H. A.

Peiró, F.

E. Quesnel, L. Dumas, D. Jacob, F. Peiró, “Optical and microstructural properties of MgF2 UV coatings grown by ion beam sputtering process,” J. Vac. Sci. Technol. A 18, 2869–2876 (2000).
[CrossRef]

Pelletier, E.

Purvis, M. K.

Quesnel, E.

E. Quesnel, L. Dumas, D. Jacob, F. Peiró, “Optical and microstructural properties of MgF2 UV coatings grown by ion beam sputtering process,” J. Vac. Sci. Technol. A 18, 2869–2876 (2000).
[CrossRef]

Quinn, D. M.

Roche, P.

Schmitt, B.

Schröder, H.

H. Schröder, “Bemerkung zur Theorie des Lichtdurchgangs durch inhomogene durchsichtige Schichten,” Ann. Phys. 39, 55–58 (1941).
[CrossRef]

Strome, D. H.

Sullivan, B. T.

Swenson, R.

Temple, P. A.

Thonn, T. F.

Tikhonravov, A. V.

Trubetskov, M. K.

Tuttle Hart, T.

Waldorf, A.

Ann. Phys. (1)

H. Schröder, “Bemerkung zur Theorie des Lichtdurchgangs durch inhomogene durchsichtige Schichten,” Ann. Phys. 39, 55–58 (1941).
[CrossRef]

Appl. Opt. (6)

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

E. Quesnel, L. Dumas, D. Jacob, F. Peiró, “Optical and microstructural properties of MgF2 UV coatings grown by ion beam sputtering process,” J. Vac. Sci. Technol. A 18, 2869–2876 (2000).
[CrossRef]

Z. Phys. (1)

G. Koppelmann, K. Krebs, “Die Optischen Eigenschaften Dielektrischer Schichten mit Kleinen Homogenitatsstorungen,” Z. Phys. 164, 539–556 (1961).

Other (1)

A. V. Tikhonravov, M. K. Trubetskov, OptiChar Software, http://www.optilayer.com , Version 3.58, 2001.

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Figures (5)

Fig. 1
Fig. 1

Refractive index of the model film (solid curve), the restored refractive indices corresponding to the simulated reflectance data with systematic errors (dashed curve), with random 0.1% errors (dotted-dashed curve), and with 0.5% errors (dotted curve).

Fig. 2
Fig. 2

Exact reflectance of the model thin film (solid curve), simulated reflectance with systematic errors (dashed curve), and simulated reflectance data with 0.5% random errors (crosses).

Fig. 3
Fig. 3

Achieved fitting of the measured reflectance by the theoretical reflectance: MgF2 Sample 2.

Fig. 4
Fig. 4

Refractive indices of three MgF2 films on CaF2 substrates, Commissariat à l’Energie Atomique samples: solid curve, sample 1; dashed curve, sample 2; dotted curve, sample 3.

Fig. 5
Fig. 5

Measured reflectance data of three MgF2 films on CaF2 substrates, Commissariat à l’Energie Atomique samples: solid curve, sample 1; dashed curve, sample 2; dotted curve, sample 3.

Tables (3)

Tables Icon

Table 1 Comparison of the Results of the Analysis of Simulated Reflectance Data with the Actual Parameters of the Model Thin Film

Tables Icon

Table 2 Effect of Systematic Errors in Reflectance (Transmittance) Data on the Determined Values of the Refractive Index and Degree of Inhomogeneity of the Film

Tables Icon

Table 3 Results of the Analysis of Reflectance Data for Three MgF2 Films Deposited on CaF2 Substrates

Equations (6)

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

nλ=n+Aλ0λ2+Bλ0λ4,
δ=n0-nin,
δ=na+ns34nansns-na δRmin.
Rmaxhom=Rmaxinh=n2-nansn2+nans2.
δ=na+ns34nansns-na δRmax.
Rminhom=Rmininh=n2-nansn2+nans2.

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