Abstract

The surface roughness of polished glass substrates and optical thin-film coatings is studied with atomic force microscopy and x-ray scattering. It is demonstrated that both methods permit the determination of power spectral density functions in a wide range of spatial frequencies. The results are in good quantitative agreement.

© 1999 Optical Society of America

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References

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  1. J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington D.C., 1989).
  2. K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 3820–3836 (1984).
    [CrossRef] [PubMed]
  3. J. M. Bennett, J. Jahannir, J. C. Podlency, T. L. Balter, D. T. Hobbs, “Scanning force microscope as a tool for studying optical surfaces,” Appl. Opt. 43, 213–230 (1995).
    [CrossRef]
  4. C. Ruppe, A. Duparré, “Roughness analysis of optical films and substrates by atomic force microscopy,” Thin Solid Films 288, 8–13 (1996).
    [CrossRef]
  5. S. K. Sinha, “X-ray diffuse scattering as a probe for thin film and interface structure,” J. Phys. (Paris) III 4, 1543–1557 (1994).
  6. I. V. Kozhevnikov, V. E. Asadchikov, B. M. Alaudinov, A. Yu. Karabekov, A. V. Vinogradov, “X-ray investigations of supersmooth surfaces,” in X-Ray Optics and Surface Science, A. V. Vinogradov, ed., Proc. SPIE2453, 141–153 (1995).
    [CrossRef]
  7. C. Deumie, R. Richier, P. Dumas, C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35, 5583–5594 (1996).
    [CrossRef] [PubMed]
  8. A. Duparré, S. Jakobs, “Combination of surface characterization techniques for investigating optical thin-film components,” Appl. Opt. 35, 5052–5058 (1996).
    [CrossRef] [PubMed]
  9. W. M. Bruno, J. A. Roth, P. E. Burke, W. B. Hewitt, R. E. Holmbeck, D. G. Neal, “Prediction of the bidirectional reflectance-distribution function from atomic force and scanning tunneling microscope measurements of interfacial roughness,” Appl. Opt. 34, 1229–1238 (1996).
    [CrossRef]
  10. E. J. Bawolek, J. B. Mohr, E. D. Hirleman, A. Majmudar, “Light scatter from polysilicon and aluminum surfaces and comparison with surface roughness statistics by atomic force microscopy,” Appl. Opt. 32, 3377–3400 (1993).
    [CrossRef] [PubMed]
  11. I. V. Kozhevnikov, A. V. Vinogradov, “Reflection and scattering of x-rays from rough surfaces,” X-Ray Optics, Tr. Fiz. Inst. Akad. Nauk. SSSR196, 18–46 (1989) (in Russian); J. Russian Laser Research, 16, 229–258 (1995).
  12. V. E. Asadchikov, A. Yu. Karabekov, V. V. Klechkovskaya, I. V. Kozhevnikov, V. E. Levashov, S. I. Sagitov, “Experimental x-ray study of the correlation of the surface profiles of a film and a substrate,” Crystallogr. Rep. 43, 110–120 (1998).
  13. S. Jakobs, A. Duparré, H. Truckenbrodt, “Interfacial roughness and related scatter in ultraviolet optical coatings: a systematic experimental approach,” Appl. Opt. 37, 1180–1193 (1998).
    [CrossRef]
  14. H. Truckenbrodt, A. Duparré, U. Schuhmann, “Roughness and defect characterization of optical surfaces by light scattering measurements,” Specification and Measurement of Optical Systems, L. R. Baker, ed., Proc. SPIE1781, 139–151 (1992).
    [CrossRef]
  15. A. Duparré, S. Kassam, “Relation between light scattering and the microstructure of optical thin films,” Appl. Opt. 32, 5475–5480 (1993).
    [CrossRef] [PubMed]
  16. A. Duparré, “Light scattering of thin dielectric films,” in Thin Films for Optical Coatings, Vol. 1 of Handbook of Optical Properties Series, R. E. Hummel, K. H. Günther, eds. (CRC Press, Boca Raton, Fla., 1995), pp. 273–304.
  17. A. V. Andreev, “Theory of x-ray scattering by rough surfaces without distorted wave approximation,” Phys. Lett. A 219, 349–354 (1996).
    [CrossRef]
  18. J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Institute of Physics, Bristol, UK, 1992), pp. 10–12.

1998 (2)

V. E. Asadchikov, A. Yu. Karabekov, V. V. Klechkovskaya, I. V. Kozhevnikov, V. E. Levashov, S. I. Sagitov, “Experimental x-ray study of the correlation of the surface profiles of a film and a substrate,” Crystallogr. Rep. 43, 110–120 (1998).

S. Jakobs, A. Duparré, H. Truckenbrodt, “Interfacial roughness and related scatter in ultraviolet optical coatings: a systematic experimental approach,” Appl. Opt. 37, 1180–1193 (1998).
[CrossRef]

1996 (5)

1995 (1)

J. M. Bennett, J. Jahannir, J. C. Podlency, T. L. Balter, D. T. Hobbs, “Scanning force microscope as a tool for studying optical surfaces,” Appl. Opt. 43, 213–230 (1995).
[CrossRef]

1994 (1)

S. K. Sinha, “X-ray diffuse scattering as a probe for thin film and interface structure,” J. Phys. (Paris) III 4, 1543–1557 (1994).

1993 (2)

1984 (1)

Alaudinov, B. M.

I. V. Kozhevnikov, V. E. Asadchikov, B. M. Alaudinov, A. Yu. Karabekov, A. V. Vinogradov, “X-ray investigations of supersmooth surfaces,” in X-Ray Optics and Surface Science, A. V. Vinogradov, ed., Proc. SPIE2453, 141–153 (1995).
[CrossRef]

Amra, C.

Andreev, A. V.

A. V. Andreev, “Theory of x-ray scattering by rough surfaces without distorted wave approximation,” Phys. Lett. A 219, 349–354 (1996).
[CrossRef]

Asadchikov, V. E.

V. E. Asadchikov, A. Yu. Karabekov, V. V. Klechkovskaya, I. V. Kozhevnikov, V. E. Levashov, S. I. Sagitov, “Experimental x-ray study of the correlation of the surface profiles of a film and a substrate,” Crystallogr. Rep. 43, 110–120 (1998).

I. V. Kozhevnikov, V. E. Asadchikov, B. M. Alaudinov, A. Yu. Karabekov, A. V. Vinogradov, “X-ray investigations of supersmooth surfaces,” in X-Ray Optics and Surface Science, A. V. Vinogradov, ed., Proc. SPIE2453, 141–153 (1995).
[CrossRef]

Balter, T. L.

J. M. Bennett, J. Jahannir, J. C. Podlency, T. L. Balter, D. T. Hobbs, “Scanning force microscope as a tool for studying optical surfaces,” Appl. Opt. 43, 213–230 (1995).
[CrossRef]

Bawolek, E. J.

Bennett, J. M.

J. M. Bennett, J. Jahannir, J. C. Podlency, T. L. Balter, D. T. Hobbs, “Scanning force microscope as a tool for studying optical surfaces,” Appl. Opt. 43, 213–230 (1995).
[CrossRef]

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 3820–3836 (1984).
[CrossRef] [PubMed]

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington D.C., 1989).

Bruno, W. M.

Burke, P. E.

Deumie, C.

Dumas, P.

Duparré, A.

S. Jakobs, A. Duparré, H. Truckenbrodt, “Interfacial roughness and related scatter in ultraviolet optical coatings: a systematic experimental approach,” Appl. Opt. 37, 1180–1193 (1998).
[CrossRef]

C. Ruppe, A. Duparré, “Roughness analysis of optical films and substrates by atomic force microscopy,” Thin Solid Films 288, 8–13 (1996).
[CrossRef]

A. Duparré, S. Jakobs, “Combination of surface characterization techniques for investigating optical thin-film components,” Appl. Opt. 35, 5052–5058 (1996).
[CrossRef] [PubMed]

A. Duparré, S. Kassam, “Relation between light scattering and the microstructure of optical thin films,” Appl. Opt. 32, 5475–5480 (1993).
[CrossRef] [PubMed]

A. Duparré, “Light scattering of thin dielectric films,” in Thin Films for Optical Coatings, Vol. 1 of Handbook of Optical Properties Series, R. E. Hummel, K. H. Günther, eds. (CRC Press, Boca Raton, Fla., 1995), pp. 273–304.

H. Truckenbrodt, A. Duparré, U. Schuhmann, “Roughness and defect characterization of optical surfaces by light scattering measurements,” Specification and Measurement of Optical Systems, L. R. Baker, ed., Proc. SPIE1781, 139–151 (1992).
[CrossRef]

Guenther, K. H.

Hewitt, W. B.

Hirleman, E. D.

Hobbs, D. T.

J. M. Bennett, J. Jahannir, J. C. Podlency, T. L. Balter, D. T. Hobbs, “Scanning force microscope as a tool for studying optical surfaces,” Appl. Opt. 43, 213–230 (1995).
[CrossRef]

Holmbeck, R. E.

Jahannir, J.

J. M. Bennett, J. Jahannir, J. C. Podlency, T. L. Balter, D. T. Hobbs, “Scanning force microscope as a tool for studying optical surfaces,” Appl. Opt. 43, 213–230 (1995).
[CrossRef]

Jakobs, S.

Karabekov, A. Yu.

V. E. Asadchikov, A. Yu. Karabekov, V. V. Klechkovskaya, I. V. Kozhevnikov, V. E. Levashov, S. I. Sagitov, “Experimental x-ray study of the correlation of the surface profiles of a film and a substrate,” Crystallogr. Rep. 43, 110–120 (1998).

I. V. Kozhevnikov, V. E. Asadchikov, B. M. Alaudinov, A. Yu. Karabekov, A. V. Vinogradov, “X-ray investigations of supersmooth surfaces,” in X-Ray Optics and Surface Science, A. V. Vinogradov, ed., Proc. SPIE2453, 141–153 (1995).
[CrossRef]

Kassam, S.

Klechkovskaya, V. V.

V. E. Asadchikov, A. Yu. Karabekov, V. V. Klechkovskaya, I. V. Kozhevnikov, V. E. Levashov, S. I. Sagitov, “Experimental x-ray study of the correlation of the surface profiles of a film and a substrate,” Crystallogr. Rep. 43, 110–120 (1998).

Kozhevnikov, I. V.

V. E. Asadchikov, A. Yu. Karabekov, V. V. Klechkovskaya, I. V. Kozhevnikov, V. E. Levashov, S. I. Sagitov, “Experimental x-ray study of the correlation of the surface profiles of a film and a substrate,” Crystallogr. Rep. 43, 110–120 (1998).

I. V. Kozhevnikov, V. E. Asadchikov, B. M. Alaudinov, A. Yu. Karabekov, A. V. Vinogradov, “X-ray investigations of supersmooth surfaces,” in X-Ray Optics and Surface Science, A. V. Vinogradov, ed., Proc. SPIE2453, 141–153 (1995).
[CrossRef]

I. V. Kozhevnikov, A. V. Vinogradov, “Reflection and scattering of x-rays from rough surfaces,” X-Ray Optics, Tr. Fiz. Inst. Akad. Nauk. SSSR196, 18–46 (1989) (in Russian); J. Russian Laser Research, 16, 229–258 (1995).

Levashov, V. E.

V. E. Asadchikov, A. Yu. Karabekov, V. V. Klechkovskaya, I. V. Kozhevnikov, V. E. Levashov, S. I. Sagitov, “Experimental x-ray study of the correlation of the surface profiles of a film and a substrate,” Crystallogr. Rep. 43, 110–120 (1998).

Majmudar, A.

Mattsson, L.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington D.C., 1989).

Mohr, J. B.

Neal, D. G.

Ogilvy, J. A.

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Institute of Physics, Bristol, UK, 1992), pp. 10–12.

Podlency, J. C.

J. M. Bennett, J. Jahannir, J. C. Podlency, T. L. Balter, D. T. Hobbs, “Scanning force microscope as a tool for studying optical surfaces,” Appl. Opt. 43, 213–230 (1995).
[CrossRef]

Richier, R.

Roth, J. A.

Ruppe, C.

C. Ruppe, A. Duparré, “Roughness analysis of optical films and substrates by atomic force microscopy,” Thin Solid Films 288, 8–13 (1996).
[CrossRef]

Sagitov, S. I.

V. E. Asadchikov, A. Yu. Karabekov, V. V. Klechkovskaya, I. V. Kozhevnikov, V. E. Levashov, S. I. Sagitov, “Experimental x-ray study of the correlation of the surface profiles of a film and a substrate,” Crystallogr. Rep. 43, 110–120 (1998).

Schuhmann, U.

H. Truckenbrodt, A. Duparré, U. Schuhmann, “Roughness and defect characterization of optical surfaces by light scattering measurements,” Specification and Measurement of Optical Systems, L. R. Baker, ed., Proc. SPIE1781, 139–151 (1992).
[CrossRef]

Sinha, S. K.

S. K. Sinha, “X-ray diffuse scattering as a probe for thin film and interface structure,” J. Phys. (Paris) III 4, 1543–1557 (1994).

Truckenbrodt, H.

S. Jakobs, A. Duparré, H. Truckenbrodt, “Interfacial roughness and related scatter in ultraviolet optical coatings: a systematic experimental approach,” Appl. Opt. 37, 1180–1193 (1998).
[CrossRef]

H. Truckenbrodt, A. Duparré, U. Schuhmann, “Roughness and defect characterization of optical surfaces by light scattering measurements,” Specification and Measurement of Optical Systems, L. R. Baker, ed., Proc. SPIE1781, 139–151 (1992).
[CrossRef]

Vinogradov, A. V.

I. V. Kozhevnikov, V. E. Asadchikov, B. M. Alaudinov, A. Yu. Karabekov, A. V. Vinogradov, “X-ray investigations of supersmooth surfaces,” in X-Ray Optics and Surface Science, A. V. Vinogradov, ed., Proc. SPIE2453, 141–153 (1995).
[CrossRef]

I. V. Kozhevnikov, A. V. Vinogradov, “Reflection and scattering of x-rays from rough surfaces,” X-Ray Optics, Tr. Fiz. Inst. Akad. Nauk. SSSR196, 18–46 (1989) (in Russian); J. Russian Laser Research, 16, 229–258 (1995).

Wierer, P. G.

Appl. Opt. (8)

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 3820–3836 (1984).
[CrossRef] [PubMed]

J. M. Bennett, J. Jahannir, J. C. Podlency, T. L. Balter, D. T. Hobbs, “Scanning force microscope as a tool for studying optical surfaces,” Appl. Opt. 43, 213–230 (1995).
[CrossRef]

C. Deumie, R. Richier, P. Dumas, C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35, 5583–5594 (1996).
[CrossRef] [PubMed]

A. Duparré, S. Jakobs, “Combination of surface characterization techniques for investigating optical thin-film components,” Appl. Opt. 35, 5052–5058 (1996).
[CrossRef] [PubMed]

W. M. Bruno, J. A. Roth, P. E. Burke, W. B. Hewitt, R. E. Holmbeck, D. G. Neal, “Prediction of the bidirectional reflectance-distribution function from atomic force and scanning tunneling microscope measurements of interfacial roughness,” Appl. Opt. 34, 1229–1238 (1996).
[CrossRef]

E. J. Bawolek, J. B. Mohr, E. D. Hirleman, A. Majmudar, “Light scatter from polysilicon and aluminum surfaces and comparison with surface roughness statistics by atomic force microscopy,” Appl. Opt. 32, 3377–3400 (1993).
[CrossRef] [PubMed]

S. Jakobs, A. Duparré, H. Truckenbrodt, “Interfacial roughness and related scatter in ultraviolet optical coatings: a systematic experimental approach,” Appl. Opt. 37, 1180–1193 (1998).
[CrossRef]

A. Duparré, S. Kassam, “Relation between light scattering and the microstructure of optical thin films,” Appl. Opt. 32, 5475–5480 (1993).
[CrossRef] [PubMed]

Crystallogr. Rep. (1)

V. E. Asadchikov, A. Yu. Karabekov, V. V. Klechkovskaya, I. V. Kozhevnikov, V. E. Levashov, S. I. Sagitov, “Experimental x-ray study of the correlation of the surface profiles of a film and a substrate,” Crystallogr. Rep. 43, 110–120 (1998).

J. Phys. (Paris) III (1)

S. K. Sinha, “X-ray diffuse scattering as a probe for thin film and interface structure,” J. Phys. (Paris) III 4, 1543–1557 (1994).

Phys. Lett. A (1)

A. V. Andreev, “Theory of x-ray scattering by rough surfaces without distorted wave approximation,” Phys. Lett. A 219, 349–354 (1996).
[CrossRef]

Thin Solid Films (1)

C. Ruppe, A. Duparré, “Roughness analysis of optical films and substrates by atomic force microscopy,” Thin Solid Films 288, 8–13 (1996).
[CrossRef]

Other (6)

I. V. Kozhevnikov, V. E. Asadchikov, B. M. Alaudinov, A. Yu. Karabekov, A. V. Vinogradov, “X-ray investigations of supersmooth surfaces,” in X-Ray Optics and Surface Science, A. V. Vinogradov, ed., Proc. SPIE2453, 141–153 (1995).
[CrossRef]

I. V. Kozhevnikov, A. V. Vinogradov, “Reflection and scattering of x-rays from rough surfaces,” X-Ray Optics, Tr. Fiz. Inst. Akad. Nauk. SSSR196, 18–46 (1989) (in Russian); J. Russian Laser Research, 16, 229–258 (1995).

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Institute of Physics, Bristol, UK, 1992), pp. 10–12.

A. Duparré, “Light scattering of thin dielectric films,” in Thin Films for Optical Coatings, Vol. 1 of Handbook of Optical Properties Series, R. E. Hummel, K. H. Günther, eds. (CRC Press, Boca Raton, Fla., 1995), pp. 273–304.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington D.C., 1989).

H. Truckenbrodt, A. Duparré, U. Schuhmann, “Roughness and defect characterization of optical surfaces by light scattering measurements,” Specification and Measurement of Optical Systems, L. R. Baker, ed., Proc. SPIE1781, 139–151 (1992).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

AFM image of SQ1 surface. Scan size 10 µm × 10 µm.

Fig. 2
Fig. 2

Schematic picture of the XRS measurement setup: 1, x-ray tube; 2, collimation system; 3, crystal monochromator; 4, studied sample; 5–7, adjustment block; 8, rotation block; 9, goniometer axis; 10, detector slit; 11, x-ray detector.

Fig. 3
Fig. 3

1D-PSD function of a polished glass surface obtained directly from the measured XRS diagrams. Measurements were performed at three different grazing angles of the probe beam: θ0 = 350, 450, and 600 arc sec.

Fig. 4
Fig. 4

2D-PSD function of the SQ1 surface determined with AFM and XRS.

Fig. 5
Fig. 5

Same as in Fig. 4, but for BK7 sample.

Fig. 6
Fig. 6

Same as in Fig. 4, but for Al2O3 sample.

Fig. 7
Fig. 7

Same as in Fig. 4, but for MgF2 sample.

Fig. 8
Fig. 8

Roughness height distributions p(h) for the BK7 and the MgF2 samples as well as for a polished glass surface (GS) and a fluoride mirror (ML) of 1.5 µm total thickness. The distributions were derived from AFM images with 10 µm × 10 µm scan sizes. The effective rms roughness was σeff was 22 and 31 Å for the GS sample and the ML sample, respectively. Solid curve corresponds to the normal law of height distribution.

Tables (1)

Tables Icon

Table 1 Effective rms Roughness Found from AFM and XRS Measurementsa

Equations (11)

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

Cρ=zρ+ρzρ;  ρx, y,
PSD2Df= exp2πifρCρd2ρ.
Φθ, φ=1WincdWscatdΩ=Aθ0, θ, φ, λ, εPSD2Df,
Πθ= Φθ, φdφ=1WincdWscatdθ=Bθ0, θ, λ, εPSD1Dν,
ν=1λ |cos θ0-cos θ|.
PSD1Dν=2π  Cρcos2πνρdρ.
PSD2Df=-12πfddνPSD1Dνdνν2-f21/2, PSD1Dν=4 fPSD2Dffdff2-ν21/2.
σeff2=2π fminfmaxPSD2Dffdf.
PSD2Dfx, fy=1L2m=1Nn=1N zmn×exp2πiΔLfxm+fymΔL22,
PSD2Df=12π02πPSD2Df, αdα.
kσ sin θ0  1;  kσ sin θ  1; kσ|ε-cos θ01/2|  1;  kσ|ε-cos2 θ1/2|  1,

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