Abstract

The seven participating laboratories received films of two different thicknesses of Sc2O3 and Rh. All samples of each material were prepared in a single deposition run. Brief descriptions are given of the various methods used for determination of the optical constants of these coating materials. The measurement data are presented, and the results are compared. The mean of the variances of the Sc2O3 refractive-index determinations in the 0.40–0.75-nm spectral region was 0.03. The corresponding variances for the refractive index and absorption coefficient of Rh were 0.35 and 0.26, respectively.

© 1984 Optical Society of America

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References

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  1. J. M. Bennett, “Optical Evaluation Techniques for Thin Films,” J. Opt. Soc. Am. 73, 1865A (1983).
  2. H. K. Pulker, “Mechanical Characterization of Optical Films,” J. Opt. Soc. Am. 73, 1865A (1983).
  3. D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972), p. 6–28 (refractive index of fused silica); p. 6–120 (equations for calculating n and k from Tf, Rf, and film thickness).
  4. F. Rainer, W. H. Lowdermilk, D. Milam, T. Tuttle Hart, T. L. Lichtenstein, C. K. Carniglia, “Scandium Oxide Coatings for High-Power UV Laser Applications,” Appl. Opt. 21, 3685 (1982).
    [CrossRef] [PubMed]
  5. J. K. Coulter, G. Hass, J. B. Ramsey, “Optical Constants of Rh Films in Visible,” J. Opt. Soc. Am. 63, 1149 (1973).
    [CrossRef]
  6. D. L. Decker, in Laser Induced Damage in Optical Materials: 1975, A. J. Glass, A. H. Guenther, Eds., NBS Spec. Publ. 435 (Apr.1976), pp. 230–235.
  7. H. E. Bennett, J. L. Stanford, “Structure-Related Optical Characteristics of Thin Metallic Films in the Visible and Ultraviolet,” J. Res. Natl. Bur. Stand. Sect. A 80, 643 (1976).
    [CrossRef]
  8. J. M. Bennett, J. H. Dancy, “Stylus Profiling Instrument for Measuring Statistical Properties of Smooth Optical Surfaces,” Appl. Opt. 20, 1785 (1981).
    [CrossRef] [PubMed]
  9. J. M. Bennett, “Measurement of the rms Roughness, Autoco-variance Function, and Other Statistical Properties’ of Optical Surfaces Using a FECO Scanning Interferometer,” Appl. Opt. 15, 2705 (1976).
    [CrossRef] [PubMed]
  10. H. E. Bennett, “Scattering Characteristics of Optical Materials,” Opt. Eng. 17, 480 (1978); P. C. Archibald, H. E. Bennett, “Scattering from Infrared Missile Domes,” Opt. Eng. 17, 647 (1978).
    [CrossRef]
  11. H. E. Bennett, J. M. Bennett, in Physics of Thin Films, Vol. 4, G. Hass, R. E. Thun, Eds. (Academic, New York, 1967), pp. 1–96 (see especially pp. 42–44, “Transmittance of a Thin Film on a Nonabsorbing Substrate”).
  12. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  13. Ref. 12, Secs. 3.7 and 5.4.
  14. I. H. Malitson, “Refractive Index of Fused Silica,” J. Opt. Soc. Am. 55, 1205 (1965).
    [CrossRef]
  15. R. M. A. Azzam, A.-R. M. Zaghloul, N. M. Bashara, “Ellipsometric Function of a Film–Substrate System: Applications to the Design of Refraction-type Optical Devices and to Ellipsometry,” J. Opt. Soc. Am. 65, 252 (1975).
    [CrossRef]
  16. J. P. Borgogno, B. Lazarides, E. Pelletier, “Automatic Determination of the Optical Constants of Inhomogeneous Thin Films,” Appl. Opt. 21, 4020 (1982).
    [CrossRef] [PubMed]
  17. J. P. Borgogno, B. Lazarides, “An Improved Method for the Determination of the Extinction Coefficient of Thin Film Materials,” Thin Solid Films 102, 209 (1983).
    [CrossRef]
  18. E. Pelletier, P. Roche, B. Vidal, “Détermination Automatique des Constantes Optiques et de l’Épaisseur des Couches Minces: Application aux Couches Diélectriques,” Nouv. Rev. Opt. 7, 353 (1976).
    [CrossRef]
  19. J. Strong, Procedures in Experimental Physics (Prentice-Hall, Englewood Cliffs, N.J., 1963), p. 376.
  20. A. Savitsky, M. J. E. Golay, “Smoothing and Differentiation of Data by Simplified Least Squares Procedures,” Anal. Chem. 36, 1627 (1964).
    [CrossRef]
  21. A. S. Valeev, “Determination of the Optical Constants of Weakly Absorbing Thin Films,” Opt. Spectrosc. USSR 15, 269 (1963).
  22. A. S. Valeev, “Constants of Thin Weakly Absorbing Lasers,” Opt. Spectrosc. USSR 18, 498 (1965).
  23. J. E. Nestell, R. W. Christy, “Derivation of Optical Constants of Metals from Thin-Film Measurements at Oblique Incidence,” Appl. Opt. 11, 643 (1972).
    [CrossRef] [PubMed]
  24. C. K. Carniglia, B. Vidal, “Optical Constants of Oxidized Thin Metal Films,” J. Opt. Soc. Am. 71, 1554 (1981).
  25. W. E. Case, “Algebraic Method for Extracting Thin-Film Optical Parameters from Spectrophotometer Measurements,” Appl. Opt. 22, 1832 (1983); Also, W. E. Case, M. K. Purvis, “Method for Synthesis of Optical Thin-Film Coatings on Small Computers,” J. Opt. Soc. Am. 73, 1879A (1983).
    [CrossRef] [PubMed]
  26. S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Clarendon, Oxford, 1983).
  27. J. A. Dobrowolski, F. C. Ho, A. Waldorf, “Determination of Optical Constants of Thin Film Coating Materials Based on Inverse Synthesis,” Appl. Opt. 22, 3191 (1983).
    [CrossRef] [PubMed]
  28. J. M. Bennett, M. J. Booty, “Computational Method for Determining n and k for a Thin Film from the Measured Reflectance, Transmittance, and Film Thickness,” Appl. Opt. 5, 41 (1966).
    [CrossRef] [PubMed]
  29. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1983), p. 55.
  30. J. C. Manifacier, J. Gasiot, J. D. Fillard, “A Simple Method for the Determination of the Optical Constants n1k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002 (1976).
    [CrossRef]

1983 (5)

J. P. Borgogno, B. Lazarides, “An Improved Method for the Determination of the Extinction Coefficient of Thin Film Materials,” Thin Solid Films 102, 209 (1983).
[CrossRef]

J. M. Bennett, “Optical Evaluation Techniques for Thin Films,” J. Opt. Soc. Am. 73, 1865A (1983).

H. K. Pulker, “Mechanical Characterization of Optical Films,” J. Opt. Soc. Am. 73, 1865A (1983).

W. E. Case, “Algebraic Method for Extracting Thin-Film Optical Parameters from Spectrophotometer Measurements,” Appl. Opt. 22, 1832 (1983); Also, W. E. Case, M. K. Purvis, “Method for Synthesis of Optical Thin-Film Coatings on Small Computers,” J. Opt. Soc. Am. 73, 1879A (1983).
[CrossRef] [PubMed]

J. A. Dobrowolski, F. C. Ho, A. Waldorf, “Determination of Optical Constants of Thin Film Coating Materials Based on Inverse Synthesis,” Appl. Opt. 22, 3191 (1983).
[CrossRef] [PubMed]

1982 (2)

1981 (2)

C. K. Carniglia, B. Vidal, “Optical Constants of Oxidized Thin Metal Films,” J. Opt. Soc. Am. 71, 1554 (1981).

J. M. Bennett, J. H. Dancy, “Stylus Profiling Instrument for Measuring Statistical Properties of Smooth Optical Surfaces,” Appl. Opt. 20, 1785 (1981).
[CrossRef] [PubMed]

1978 (1)

H. E. Bennett, “Scattering Characteristics of Optical Materials,” Opt. Eng. 17, 480 (1978); P. C. Archibald, H. E. Bennett, “Scattering from Infrared Missile Domes,” Opt. Eng. 17, 647 (1978).
[CrossRef]

1976 (4)

H. E. Bennett, J. L. Stanford, “Structure-Related Optical Characteristics of Thin Metallic Films in the Visible and Ultraviolet,” J. Res. Natl. Bur. Stand. Sect. A 80, 643 (1976).
[CrossRef]

E. Pelletier, P. Roche, B. Vidal, “Détermination Automatique des Constantes Optiques et de l’Épaisseur des Couches Minces: Application aux Couches Diélectriques,” Nouv. Rev. Opt. 7, 353 (1976).
[CrossRef]

J. C. Manifacier, J. Gasiot, J. D. Fillard, “A Simple Method for the Determination of the Optical Constants n1k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002 (1976).
[CrossRef]

J. M. Bennett, “Measurement of the rms Roughness, Autoco-variance Function, and Other Statistical Properties’ of Optical Surfaces Using a FECO Scanning Interferometer,” Appl. Opt. 15, 2705 (1976).
[CrossRef] [PubMed]

1975 (1)

1973 (1)

1972 (1)

1966 (1)

1965 (2)

I. H. Malitson, “Refractive Index of Fused Silica,” J. Opt. Soc. Am. 55, 1205 (1965).
[CrossRef]

A. S. Valeev, “Constants of Thin Weakly Absorbing Lasers,” Opt. Spectrosc. USSR 18, 498 (1965).

1964 (1)

A. Savitsky, M. J. E. Golay, “Smoothing and Differentiation of Data by Simplified Least Squares Procedures,” Anal. Chem. 36, 1627 (1964).
[CrossRef]

1963 (1)

A. S. Valeev, “Determination of the Optical Constants of Weakly Absorbing Thin Films,” Opt. Spectrosc. USSR 15, 269 (1963).

Azzam, R. M. A.

Bashara, N. M.

Bennett, H. E.

H. E. Bennett, “Scattering Characteristics of Optical Materials,” Opt. Eng. 17, 480 (1978); P. C. Archibald, H. E. Bennett, “Scattering from Infrared Missile Domes,” Opt. Eng. 17, 647 (1978).
[CrossRef]

H. E. Bennett, J. L. Stanford, “Structure-Related Optical Characteristics of Thin Metallic Films in the Visible and Ultraviolet,” J. Res. Natl. Bur. Stand. Sect. A 80, 643 (1976).
[CrossRef]

H. E. Bennett, J. M. Bennett, in Physics of Thin Films, Vol. 4, G. Hass, R. E. Thun, Eds. (Academic, New York, 1967), pp. 1–96 (see especially pp. 42–44, “Transmittance of a Thin Film on a Nonabsorbing Substrate”).

Bennett, J. M.

Booty, M. J.

Borgogno, J. P.

J. P. Borgogno, B. Lazarides, “An Improved Method for the Determination of the Extinction Coefficient of Thin Film Materials,” Thin Solid Films 102, 209 (1983).
[CrossRef]

J. P. Borgogno, B. Lazarides, E. Pelletier, “Automatic Determination of the Optical Constants of Inhomogeneous Thin Films,” Appl. Opt. 21, 4020 (1982).
[CrossRef] [PubMed]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1983), p. 55.

Carniglia, C. K.

Case, W. E.

Christy, R. W.

Coulter, J. K.

Dancy, J. H.

Decker, D. L.

D. L. Decker, in Laser Induced Damage in Optical Materials: 1975, A. J. Glass, A. H. Guenther, Eds., NBS Spec. Publ. 435 (Apr.1976), pp. 230–235.

Dobrowolski, J. A.

Fillard, J. D.

J. C. Manifacier, J. Gasiot, J. D. Fillard, “A Simple Method for the Determination of the Optical Constants n1k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002 (1976).
[CrossRef]

Gasiot, J.

J. C. Manifacier, J. Gasiot, J. D. Fillard, “A Simple Method for the Determination of the Optical Constants n1k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002 (1976).
[CrossRef]

Golay, M. J. E.

A. Savitsky, M. J. E. Golay, “Smoothing and Differentiation of Data by Simplified Least Squares Procedures,” Anal. Chem. 36, 1627 (1964).
[CrossRef]

Hass, G.

Ho, F. C.

Lazarides, B.

J. P. Borgogno, B. Lazarides, “An Improved Method for the Determination of the Extinction Coefficient of Thin Film Materials,” Thin Solid Films 102, 209 (1983).
[CrossRef]

J. P. Borgogno, B. Lazarides, E. Pelletier, “Automatic Determination of the Optical Constants of Inhomogeneous Thin Films,” Appl. Opt. 21, 4020 (1982).
[CrossRef] [PubMed]

Lichtenstein, T. L.

Lowdermilk, W. H.

Malitson, I. H.

Manifacier, J. C.

J. C. Manifacier, J. Gasiot, J. D. Fillard, “A Simple Method for the Determination of the Optical Constants n1k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002 (1976).
[CrossRef]

Milam, D.

Nestell, J. E.

Pelletier, E.

J. P. Borgogno, B. Lazarides, E. Pelletier, “Automatic Determination of the Optical Constants of Inhomogeneous Thin Films,” Appl. Opt. 21, 4020 (1982).
[CrossRef] [PubMed]

E. Pelletier, P. Roche, B. Vidal, “Détermination Automatique des Constantes Optiques et de l’Épaisseur des Couches Minces: Application aux Couches Diélectriques,” Nouv. Rev. Opt. 7, 353 (1976).
[CrossRef]

Pulker, H. K.

H. K. Pulker, “Mechanical Characterization of Optical Films,” J. Opt. Soc. Am. 73, 1865A (1983).

Rainer, F.

Ramsey, J. B.

Roche, P.

E. Pelletier, P. Roche, B. Vidal, “Détermination Automatique des Constantes Optiques et de l’Épaisseur des Couches Minces: Application aux Couches Diélectriques,” Nouv. Rev. Opt. 7, 353 (1976).
[CrossRef]

Savitsky, A.

A. Savitsky, M. J. E. Golay, “Smoothing and Differentiation of Data by Simplified Least Squares Procedures,” Anal. Chem. 36, 1627 (1964).
[CrossRef]

Stanford, J. L.

H. E. Bennett, J. L. Stanford, “Structure-Related Optical Characteristics of Thin Metallic Films in the Visible and Ultraviolet,” J. Res. Natl. Bur. Stand. Sect. A 80, 643 (1976).
[CrossRef]

Strong, J.

J. Strong, Procedures in Experimental Physics (Prentice-Hall, Englewood Cliffs, N.J., 1963), p. 376.

Tolansky, S.

S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Clarendon, Oxford, 1983).

Tuttle Hart, T.

Valeev, A. S.

A. S. Valeev, “Constants of Thin Weakly Absorbing Lasers,” Opt. Spectrosc. USSR 18, 498 (1965).

A. S. Valeev, “Determination of the Optical Constants of Weakly Absorbing Thin Films,” Opt. Spectrosc. USSR 15, 269 (1963).

Vidal, B.

C. K. Carniglia, B. Vidal, “Optical Constants of Oxidized Thin Metal Films,” J. Opt. Soc. Am. 71, 1554 (1981).

E. Pelletier, P. Roche, B. Vidal, “Détermination Automatique des Constantes Optiques et de l’Épaisseur des Couches Minces: Application aux Couches Diélectriques,” Nouv. Rev. Opt. 7, 353 (1976).
[CrossRef]

Waldorf, A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1983), p. 55.

Zaghloul, A.-R. M.

Anal. Chem. (1)

A. Savitsky, M. J. E. Golay, “Smoothing and Differentiation of Data by Simplified Least Squares Procedures,” Anal. Chem. 36, 1627 (1964).
[CrossRef]

Appl. Opt. (8)

J. M. Bennett, M. J. Booty, “Computational Method for Determining n and k for a Thin Film from the Measured Reflectance, Transmittance, and Film Thickness,” Appl. Opt. 5, 41 (1966).
[CrossRef] [PubMed]

J. E. Nestell, R. W. Christy, “Derivation of Optical Constants of Metals from Thin-Film Measurements at Oblique Incidence,” Appl. Opt. 11, 643 (1972).
[CrossRef] [PubMed]

J. M. Bennett, “Measurement of the rms Roughness, Autoco-variance Function, and Other Statistical Properties’ of Optical Surfaces Using a FECO Scanning Interferometer,” Appl. Opt. 15, 2705 (1976).
[CrossRef] [PubMed]

J. M. Bennett, J. H. Dancy, “Stylus Profiling Instrument for Measuring Statistical Properties of Smooth Optical Surfaces,” Appl. Opt. 20, 1785 (1981).
[CrossRef] [PubMed]

F. Rainer, W. H. Lowdermilk, D. Milam, T. Tuttle Hart, T. L. Lichtenstein, C. K. Carniglia, “Scandium Oxide Coatings for High-Power UV Laser Applications,” Appl. Opt. 21, 3685 (1982).
[CrossRef] [PubMed]

J. P. Borgogno, B. Lazarides, E. Pelletier, “Automatic Determination of the Optical Constants of Inhomogeneous Thin Films,” Appl. Opt. 21, 4020 (1982).
[CrossRef] [PubMed]

W. E. Case, “Algebraic Method for Extracting Thin-Film Optical Parameters from Spectrophotometer Measurements,” Appl. Opt. 22, 1832 (1983); Also, W. E. Case, M. K. Purvis, “Method for Synthesis of Optical Thin-Film Coatings on Small Computers,” J. Opt. Soc. Am. 73, 1879A (1983).
[CrossRef] [PubMed]

J. A. Dobrowolski, F. C. Ho, A. Waldorf, “Determination of Optical Constants of Thin Film Coating Materials Based on Inverse Synthesis,” Appl. Opt. 22, 3191 (1983).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (6)

I. H. Malitson, “Refractive Index of Fused Silica,” J. Opt. Soc. Am. 55, 1205 (1965).
[CrossRef]

J. K. Coulter, G. Hass, J. B. Ramsey, “Optical Constants of Rh Films in Visible,” J. Opt. Soc. Am. 63, 1149 (1973).
[CrossRef]

R. M. A. Azzam, A.-R. M. Zaghloul, N. M. Bashara, “Ellipsometric Function of a Film–Substrate System: Applications to the Design of Refraction-type Optical Devices and to Ellipsometry,” J. Opt. Soc. Am. 65, 252 (1975).
[CrossRef]

J. M. Bennett, “Optical Evaluation Techniques for Thin Films,” J. Opt. Soc. Am. 73, 1865A (1983).

H. K. Pulker, “Mechanical Characterization of Optical Films,” J. Opt. Soc. Am. 73, 1865A (1983).

C. K. Carniglia, B. Vidal, “Optical Constants of Oxidized Thin Metal Films,” J. Opt. Soc. Am. 71, 1554 (1981).

J. Phys. E (1)

J. C. Manifacier, J. Gasiot, J. D. Fillard, “A Simple Method for the Determination of the Optical Constants n1k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002 (1976).
[CrossRef]

J. Res. Natl. Bur. Stand. Sect. A (1)

H. E. Bennett, J. L. Stanford, “Structure-Related Optical Characteristics of Thin Metallic Films in the Visible and Ultraviolet,” J. Res. Natl. Bur. Stand. Sect. A 80, 643 (1976).
[CrossRef]

Nouv. Rev. Opt. (1)

E. Pelletier, P. Roche, B. Vidal, “Détermination Automatique des Constantes Optiques et de l’Épaisseur des Couches Minces: Application aux Couches Diélectriques,” Nouv. Rev. Opt. 7, 353 (1976).
[CrossRef]

Opt. Eng. (1)

H. E. Bennett, “Scattering Characteristics of Optical Materials,” Opt. Eng. 17, 480 (1978); P. C. Archibald, H. E. Bennett, “Scattering from Infrared Missile Domes,” Opt. Eng. 17, 647 (1978).
[CrossRef]

Opt. Spectrosc. USSR (2)

A. S. Valeev, “Determination of the Optical Constants of Weakly Absorbing Thin Films,” Opt. Spectrosc. USSR 15, 269 (1963).

A. S. Valeev, “Constants of Thin Weakly Absorbing Lasers,” Opt. Spectrosc. USSR 18, 498 (1965).

Thin Solid Films (1)

J. P. Borgogno, B. Lazarides, “An Improved Method for the Determination of the Extinction Coefficient of Thin Film Materials,” Thin Solid Films 102, 209 (1983).
[CrossRef]

Other (8)

D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972), p. 6–28 (refractive index of fused silica); p. 6–120 (equations for calculating n and k from Tf, Rf, and film thickness).

H. E. Bennett, J. M. Bennett, in Physics of Thin Films, Vol. 4, G. Hass, R. E. Thun, Eds. (Academic, New York, 1967), pp. 1–96 (see especially pp. 42–44, “Transmittance of a Thin Film on a Nonabsorbing Substrate”).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Ref. 12, Secs. 3.7 and 5.4.

D. L. Decker, in Laser Induced Damage in Optical Materials: 1975, A. J. Glass, A. H. Guenther, Eds., NBS Spec. Publ. 435 (Apr.1976), pp. 230–235.

J. Strong, Procedures in Experimental Physics (Prentice-Hall, Englewood Cliffs, N.J., 1963), p. 376.

S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Clarendon, Oxford, 1983).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1983), p. 55.

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Figures (17)

Fig. 1
Fig. 1

Reflection ellipsometry method. Changes in the ellipsometric parameter from its value at the center as a function of position on the thick Sc2O3 film (λ = 632.8 nm, ϕ = 60°).

Fig. 2
Fig. 2

Reflection ellipsometry method. Changes in the ellipsometric parameter Δ from its value at the center as a function of position on the thick Sc2O3 film (λ = 632.8 nm, ϕ = 60°).

Fig. 3
Fig. 3

Reflection ellipsometry method. Changes in film thickness t from its center value as a function of position in the thick Sc2O3 film. Obtained from Figs. 1 and 2, assuming a uniform refractive index of 1.81 (λ = 632.8 nm, ϕ = 60°).

Fig. 4
Fig. 4

Wideband spectrophotometric method. Refractive indices n, n1, and ni as a function of wavelength for the 447.8-nm thick Sc2O3 film. Error bars for n assume that the errors in reflectance and transmittance are 0.003.

Fig. 5
Fig. 5

Wideband spectrophotometric method. Refractive indices n, n1, and ni as a function of wavelength for the 217.6-nm thick Sc2O3 film.

Fig. 6
Fig. 6

Modified Valeev turning point method. Measured Tobs and Rf for the thinner Sc2O3 film (solid curves) and the theoretical Rs,c of fused silica (dashed curve). Interpolated minimum values of Tobs are indicated by plusses. Order numbers m are given by the corresponding maxima of T.

Fig. 7
Fig. 7

Modified Valeev turning point method. Measured index and inhomogeneity of the Sc2O3 films. Stars indicate average index values. Bars indicate range of index.

Fig. 8
Fig. 8

Nestell and Christy method. Measured n and k for the Rh films. Crosses represent Hass’s data.16

Fig. 9
Fig. 9

Algebraic inversion method. Comparison of transmittance T between the Sc2O3 samples and the uncoated substrate. Note the intersections near the 420- and 560-nm wavelength.

Fig. 10
Fig. 10

Algebraic inversion method. Example of data reduction. Two index solutions exist at the measured film thickness. However, the solution between n = 1.8 and 1.9 is believed to be the correct choice.

Fig. 11
Fig. 11

Algebraic inversion method. Example of error analysis (NWC = Naval Weapons Center, China Lake, Calif.).

Fig. 12
Fig. 12

Algebraic inversion method. Solution traces for the thick Rh film at 500-nm wavelength. Corresponding parts of the n and k curves are labeled 1, 2, and 3.

Fig. 13
Fig. 13

Inverse synthesis method. Spectrophotometric measurements used in determination of the optical constants of the Sc2O3 films.

Fig. 14
Fig. 14

Inverse synthesis method. Average refractive index of the Sc2O3 films.

Fig. 15
Fig. 15

Inverse synthesis method. Spectrophotometric measurements used in determination of the Rh films.

Fig. 16
Fig. 16

Inverse synthesis method. Average optical constants of the Rh films.

Fig. 17
Fig. 17

Bennett and Booty method. Optical constants of Rh. The broken curve represents the results based on the thickness supplied by the Michelson Laboratory (Sec. III.A).

Tables (18)

Tables Icon

Table I Terminology Used in This Paper

Tables Icon

Table II R, T and t Method: Measurements of Optical Constants Using an Argon-ion Laser

Tables Icon

Table III R, T and t Method: Measurements of Optical Constants Using Spectrophotometer-type Instruments

Tables Icon

Table IV R, T and t Method: Measurements on the 14.2-nm Thick Rh Film Using the Argon Laser; λ = 488.0 nm

Tables Icon

Table V Reflection Ellipsometry Method: Ellipsometric Angles ψ and Δ (in degrees) of the Thin and Thick Sc2O3 and Rh Films and the Resulting Optical Constants

Tables Icon

Table VI Reflection Ellipsometry Method: Thicknesses of Rh Thin Films Independently Determined at Each Wavelength

Tables Icon

Table VII Wideband Spectrophotometric Method: Measured Spectral Reflectance and Transmittance of the Sc2O3 Films

Tables Icon

Table VIII Wideband Spectrophotometric Method: Positions of Reflectance Extrema of Sc2O3 Films

Tables Icon

Table IX Modified Valeev Turning Point Method: Data and Results for Sc2O3 Films

Tables Icon

Table X Nestell and Christy Method: Data and Results for Rh Films

Tables Icon

Table XI Algebraic Inversion Method: Spectrophotometric Data and Refractive-Index Solutions for Sc2O3 Films

Tables Icon

Table XII Algebraic Inversion Method: Spectrophotometric Data and Optical Constants for Rh Films

Tables Icon

Table XIII Algebraic Inversion Method: Refractive Index of SiO2

Tables Icon

Table XIV Bennett and Booty Method: Data for Thin Rh Film

Tables Icon

Table XV Bennett and Booty Method: Effect of Perturbations on Optical Constants Determination

Tables Icon

Table XVI Envelope Method: Data and Results for Sc2O3 Films

Tables Icon

Table XVII Summary of the Results for Sc2O3 Films

Tables Icon

Table XVIII Summary of the Results for Rh Films

Equations (33)

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n s 2 - 1 = 0.69617 λ 2 λ 2 - 0.0046792 + 0.40704 λ 2 λ 2 - 0.013512 + 0.89748 λ 2 λ 2 - 97.93 ,
Sc 2 O 3 ( thick ) 452.5 ± 1.4 nm , Rh ( thick ) 27.1 ± 1.4 nm , ( thin ) 224.5 ± 0.7 nm , ( thin ) 14.2 ± 1.7 nm .
T f = T ( 1 - R f R s ) / T s ,
T f = T obs ( 1 - R s + R s A f ) / [ 1 + R s ( 1 - T obs ) ] ,
R f = R - T f 2 R f R ( 1 - T f 2 )
n = A + B λ 2 + C λ 4 .
T obs = T / T w .
R f = R obs R s , c / R s ,
m λ / 2 = n t ,
k = n A / 2 π m ,
A = 1 - R min - T f .
T f T max ( 1 - R s , c R min ) / ( 1 + R s , c ) .
Δ n n ( R s , c - R min ) / ( 4.4 R s , c ) .
n i = n + Δ n / 2
n 1 = n - Δ n / 2.
( m - 1 ) λ 2 n t < m λ 2 ,             m = 1 , 2 , ,
( n t ) Δ t ~ 3 ( n T ) Δ T .
( n t ) Δ t ~ ½ ( n T ) Δ T .
n 2 = A + k 2 + B λ 2 ( 1 + C 2 λ 2 ) + i = 1 2 [ B i λ 2 ( λ 2 - C i 2 ) ( λ 2 - C i 2 ) 2 + D i 2 λ 2 ] k = 1 2 n { B C λ 3 ( 1 + C 2 λ 2 ) + i = 1 2 [ B i D i λ 3 ( λ 2 - C i 2 ) 2 + D i 2 λ 2 ] } ,
[ ( n i / n 1 ) 1 / 2 cos δ i ( sin δ ) / ( n 1 n i ) 1 / 2 i ( n 1 n i ) 1 / 2 sin δ ( n 1 / n i ) 1 / 2 cos δ ] ,
δ = 2 π ( n - i k ) t / λ = α + i β ,
n = ( 1 / d ) 0 t n ( z ) d z = 0.5 ( n 1 + n 1 ) .
x = n o n s / ( n 1 n i ) 1 / 2 + ( n 1 n i ) 1 / 2 , y = n o n s / ( n 1 n i ) 1 / 2 - ( n 1 n i ) 1 / 2 , p = n o ( n i / n 1 ) 1 / 2 + n s ( n 1 / n i ) 1 / 2 , q = n o ( n i / n 1 ) 1 / 2 - n x ( n 1 / n i ) 1 / 2 ,
( x + β p ) 2 = 4 n o n s / T min , ( p + β x ) 2 = 4 n o n s / T max , ( y + β q ) 2 = 4 n o n s ( R max / T min ) , ( a + β y ) 2 = 4 n o n s ( R min / T max ) .
x = 2 ( n o n s / T min ) 1 / 2 - β p , p = 2 ( n o n s / T max ) 1 / 2 - β x , y = - 2 ( n o n s R max / T min ) 1 / 2 - β q , q = - 2 ( n o n s R min / T max ) 1 / 2 - β y , β = 0.5 C [ ( 1 - T min - R max ) / T min ] + [ ( 1 - T max - R min ) / T max ] [ ( n s / n i + n i / n s ) + β ] ,
n 1 = n o [ ( x - y ) ( p - q ) ( x + y ) ( p + q ) ] 1 / 2 , n i = n s [ ( x - y ) ( p + q ) ( x + y ) ( p - q ) ] 1 / 2 .
2 π [ ( n 1 + n i ) / 2 ] ( t / λ ) = m π / 2.
k = δ λ / ( 2 π t ) .
T = T s T f ( 1 - R s R f )             R = R f - R s ( R f 2 - T f 2 ) ( 1 - R s R f ) ,
T f = T ( 1 - R s R f ) T s             R f = R ( 1 - R s R f ) + R s ( R f 2 - T f 2 ) ,
T f = T s             R f = R s = 1 - T s ,
T s = 2 T / ( 1 + T )             R s = ( 1 - T ) / ( 1 + T ) .
n s = ( 1 + R s 1 / 2 ) ( 1 - R s 1 / 2 ) .

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