Abstract

An apparatus to record scattered light in whole space over a large range of visible and infrared wavelengths (0.45–10.6 μm) is described. Parasitic light, calibration, and dynamic range are discussed to point out performances and limits of the experimental setup. Angular measurements at several wavelengths give access to bidimensional roughness spectra of polished samples in different frequency bandwidths. The results show overlap of the spectra at the intersection of the bandwidths, which provides an extended view of surface microroughness. In the midinfrared, measurements are more difficult, and specific problems such as thermal emission are analyzed.

© 1993 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. J. M. Elson, J. M. Bennett, “Relation between the angular dependence of scattering and the statistical properties of optical surfaces,” J. Opt. Soc. Am. 69, 31–47 (1979).
    [Crossref]
  3. P. Roche, E. Pelletier, “Characterization of optical surfaces by measurement of scattering distribution,” Appl. Opt. 23, 3561–3566 (1984).
    [Crossref] [PubMed]
  4. J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
    [Crossref]
  5. P. Bousquet, F. Flory, P. Roche, “Scattering from multilayer thin films: theory and experiment,” J. Opt. Soc. Am. 71, 1115–1123 (1981).
    [Crossref]
  6. E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” in Pattern Recognition Studies, D. L. Kelly, ed., Proc. Soc. Photo-Opt. Instrum. Eng.18, 125–136 (1979).
  7. P. Croce, “Sur l'effet des couches très minces et des rugosités dur la reflection, la transmission et la diffusion de la lumière par un dioptre,” J. Opt. (Paris) 8, 127–139 (1977).
    [Crossref]
  8. P. Croce, L. Prod'homme, “Ecarts observés dans l'interprétation des indicatrices de diffusion optique par des théories vectorielles simples,” J. Opt. (Paris) 16, 143–151 (1985).
    [Crossref]
  9. J. M. Elson, J. P. Rahn, J. M. Bennett, “Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation-length, and roughness cross-correlation properties,” Appl. Opt. 22, 3207–3219 (1983).
    [Crossref] [PubMed]
  10. E. L. Church, “Comments on the correlation length,” in Surface Characterization and Testing, K. Creath, ed., Proc. Soc. Photo-Opt. Instrum. Eng.680, 102–111 (1986).
  11. R. D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R. McNeil, J. M. Bennett, L. Mattsson, “Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques,” Appl. Opt. 31, 1426–1435 (1992).
    [Crossref] [PubMed]
  12. Z. Lu, J.-F. Tang, “Characterization of thin film surfaces over an extended spatial wavelength range,” Appl. Opt. 28, 2765–2768 (1989).
    [Crossref] [PubMed]
  13. D. W. Ricks, “Relationship between near-angle scatter and surface characteristics,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 1009–1018 (1988).
  14. C. Amra, C. Grèzes-Besset, P. Roche, E. Pelletier, “Description of a scattering apparatus: Application to the problems of characterization of opaque surfaces,” Appl. Opt. 28, 2723–2730 (1989).
    [Crossref] [PubMed]
  15. This work was first presented at the Joint Session on Scattering of the First Topical Meeting on Surface Roughness and Scattering and the Fifth Topical Meeting on Optical Interference Coating of the Optical Society of America that was held in Tucson, Arizona, June 1992.
  16. C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: recent advances for a better investigation of experiment,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 82–97 (1988).
  17. C. Amra, “Introduction à l'étude de la diffusion de la lumière par les rugosités des surfaces optiques,” in Ecole d'Eté Systèmes Optiques, Vol. 1 of Les Editions de Physique, 1992.
  18. C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
    [Crossref] [PubMed]
  19. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1991).
  20. C. Amra, “From light scattering to the microstructure of thin-film multilayers,” Appl. Opt. 32, 5481–5491 (1993).
    [Crossref] [PubMed]
  21. E. L. Dereniak, L. G. Brod, J. E. Hubbs, “Bidirectional transmittance distribution function measurements on ZnSe,” Appl. Opt. 21, 4421–4425 (1982).
    [Crossref] [PubMed]
  22. J. E. Hubbs, L. D. Brooks, M. J. Nofziger, F. O. Bartell, W. L. Wolfe, “Bidirectional reflectance distribution function of the Infrared Astronomical Satellite solar-shield material,” Appl. Opt. 21, 3323–3328 (1982).
    [Crossref] [PubMed]
  23. F. O. Bartell, J. E. Hubbs, M. J. Nofziger, W. L. Wolfe, “Measurements of Martin Black at ∼10 μm,” Appl. Opt. 21, 3178–3180 (1982).
    [Crossref] [PubMed]

1993 (1)

1992 (3)

1989 (2)

1985 (1)

P. Croce, L. Prod'homme, “Ecarts observés dans l'interprétation des indicatrices de diffusion optique par des théories vectorielles simples,” J. Opt. (Paris) 16, 143–151 (1985).
[Crossref]

1984 (2)

P. Roche, E. Pelletier, “Characterization of optical surfaces by measurement of scattering distribution,” Appl. Opt. 23, 3561–3566 (1984).
[Crossref] [PubMed]

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[Crossref]

1983 (1)

1982 (3)

1981 (1)

1979 (1)

1977 (1)

P. Croce, “Sur l'effet des couches très minces et des rugosités dur la reflection, la transmission et la diffusion de la lumière par un dioptre,” J. Opt. (Paris) 8, 127–139 (1977).
[Crossref]

Al-Jumaily, G. A.

Amra, C.

C. Amra, “From light scattering to the microstructure of thin-film multilayers,” Appl. Opt. 32, 5481–5491 (1993).
[Crossref] [PubMed]

C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
[Crossref] [PubMed]

C. Amra, “Introduction à l'étude de la diffusion de la lumière par les rugosités des surfaces optiques,” in Ecole d'Eté Systèmes Optiques, Vol. 1 of Les Editions de Physique, 1992.

C. Amra, C. Grèzes-Besset, P. Roche, E. Pelletier, “Description of a scattering apparatus: Application to the problems of characterization of opaque surfaces,” Appl. Opt. 28, 2723–2730 (1989).
[Crossref] [PubMed]

C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: recent advances for a better investigation of experiment,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 82–97 (1988).

Apfel, J. H.

Bartell, F. O.

Bennett, J. M.

Bousquet, P.

P. Bousquet, F. Flory, P. Roche, “Scattering from multilayer thin films: theory and experiment,” J. Opt. Soc. Am. 71, 1115–1123 (1981).
[Crossref]

C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: recent advances for a better investigation of experiment,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 82–97 (1988).

Brod, L. G.

Brooks, L. D.

Church, E. L.

E. L. Church, “Comments on the correlation length,” in Surface Characterization and Testing, K. Creath, ed., Proc. Soc. Photo-Opt. Instrum. Eng.680, 102–111 (1986).

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” in Pattern Recognition Studies, D. L. Kelly, ed., Proc. Soc. Photo-Opt. Instrum. Eng.18, 125–136 (1979).

Croce, P.

P. Croce, L. Prod'homme, “Ecarts observés dans l'interprétation des indicatrices de diffusion optique par des théories vectorielles simples,” J. Opt. (Paris) 16, 143–151 (1985).
[Crossref]

P. Croce, “Sur l'effet des couches très minces et des rugosités dur la reflection, la transmission et la diffusion de la lumière par un dioptre,” J. Opt. (Paris) 8, 127–139 (1977).
[Crossref]

Dereniak, E. L.

Elson, J. M.

Flory, F.

Grèzes-Besset, C.

Hubbs, J. E.

Jacobson, R. D.

Jenkinson, H. A.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” in Pattern Recognition Studies, D. L. Kelly, ed., Proc. Soc. Photo-Opt. Instrum. Eng.18, 125–136 (1979).

Lu, Z.

Mattsson, L.

McNeil, J. R.

Nofziger, M. J.

Pelletier, E.

Prod'homme, L.

P. Croce, L. Prod'homme, “Ecarts observés dans l'interprétation des indicatrices de diffusion optique par des théories vectorielles simples,” J. Opt. (Paris) 16, 143–151 (1985).
[Crossref]

Rahn, J. P.

Ricks, D. W.

D. W. Ricks, “Relationship between near-angle scatter and surface characteristics,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 1009–1018 (1988).

Roche, P.

Tang, J.-F.

Wilson, S. R.

Wolfe, W. L.

Zavada, J. M.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” in Pattern Recognition Studies, D. L. Kelly, ed., Proc. Soc. Photo-Opt. Instrum. Eng.18, 125–136 (1979).

Appl. Opt. (10)

P. Roche, E. Pelletier, “Characterization of optical surfaces by measurement of scattering distribution,” Appl. Opt. 23, 3561–3566 (1984).
[Crossref] [PubMed]

J. M. Elson, J. P. Rahn, J. M. Bennett, “Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation-length, and roughness cross-correlation properties,” Appl. Opt. 22, 3207–3219 (1983).
[Crossref] [PubMed]

R. D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R. McNeil, J. M. Bennett, L. Mattsson, “Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques,” Appl. Opt. 31, 1426–1435 (1992).
[Crossref] [PubMed]

Z. Lu, J.-F. Tang, “Characterization of thin film surfaces over an extended spatial wavelength range,” Appl. Opt. 28, 2765–2768 (1989).
[Crossref] [PubMed]

C. Amra, C. Grèzes-Besset, P. Roche, E. Pelletier, “Description of a scattering apparatus: Application to the problems of characterization of opaque surfaces,” Appl. Opt. 28, 2723–2730 (1989).
[Crossref] [PubMed]

C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
[Crossref] [PubMed]

C. Amra, “From light scattering to the microstructure of thin-film multilayers,” Appl. Opt. 32, 5481–5491 (1993).
[Crossref] [PubMed]

E. L. Dereniak, L. G. Brod, J. E. Hubbs, “Bidirectional transmittance distribution function measurements on ZnSe,” Appl. Opt. 21, 4421–4425 (1982).
[Crossref] [PubMed]

J. E. Hubbs, L. D. Brooks, M. J. Nofziger, F. O. Bartell, W. L. Wolfe, “Bidirectional reflectance distribution function of the Infrared Astronomical Satellite solar-shield material,” Appl. Opt. 21, 3323–3328 (1982).
[Crossref] [PubMed]

F. O. Bartell, J. E. Hubbs, M. J. Nofziger, W. L. Wolfe, “Measurements of Martin Black at ∼10 μm,” Appl. Opt. 21, 3178–3180 (1982).
[Crossref] [PubMed]

Ecole d'Eté Systèmes Optiques (1)

C. Amra, “Introduction à l'étude de la diffusion de la lumière par les rugosités des surfaces optiques,” in Ecole d'Eté Systèmes Optiques, Vol. 1 of Les Editions de Physique, 1992.

J. Opt. (Paris) (2)

P. Croce, “Sur l'effet des couches très minces et des rugosités dur la reflection, la transmission et la diffusion de la lumière par un dioptre,” J. Opt. (Paris) 8, 127–139 (1977).
[Crossref]

P. Croce, L. Prod'homme, “Ecarts observés dans l'interprétation des indicatrices de diffusion optique par des théories vectorielles simples,” J. Opt. (Paris) 16, 143–151 (1985).
[Crossref]

J. Opt. Soc. Am. (2)

Phys. Rev. B (1)

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[Crossref]

Other (7)

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

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” in Pattern Recognition Studies, D. L. Kelly, ed., Proc. Soc. Photo-Opt. Instrum. Eng.18, 125–136 (1979).

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1991).

This work was first presented at the Joint Session on Scattering of the First Topical Meeting on Surface Roughness and Scattering and the Fifth Topical Meeting on Optical Interference Coating of the Optical Society of America that was held in Tucson, Arizona, June 1992.

C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: recent advances for a better investigation of experiment,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 82–97 (1988).

D. W. Ricks, “Relationship between near-angle scatter and surface characteristics,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 1009–1018 (1988).

E. L. Church, “Comments on the correlation length,” in Surface Characterization and Testing, K. Creath, ed., Proc. Soc. Photo-Opt. Instrum. Eng.680, 102–111 (1986).

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Figures (32)

Fig. 1
Fig. 1

Definition of scattering angles θ, ϕ. z = 0 is the mean plane of the rough surface. θ is from the sample normal, and ϕ is the polar angle. k is the wave vector scattered in direction θ, ϕ, and its tangential component is σ = 2πν, where ν is the spatial frequency.

Fig. 2
Fig. 2

Schematic view of the roughness spectrum γ(σ) in different frequency bandwidths. Far-infrared roughness is close to visible flatness. Light scattering does not give access to spatial frequencies that are characteristic of electron microscopy, x rays, or nanoprobe instruments. Extrapolation of spectra outside the measurable bandwidth cannot be justified a priori.

Fig. 3
Fig. 3

Schematic view of the angle-resolved multiwavelength scattermeter (see text).

Fig. 4
Fig. 4

Schematic view of different axes for sample mounting (see text).

Fig. 5
Fig. 5

Detectivity and dynamic range of the scattermeter at wavelengths (a) λ = 515 nm, (b) λ = 600 ran, (c) λ = 1.064 μm, (d) λ = 3.39 μm, (e) λ = 10.6 μm. Curves 1 were measured in the absence of a sample (see text), and curves 2 were measured for a spectral étalon of diffuse reflectance close to unity. The angular ranges 0°–90° and 90°–180° correspond to measurements made by reflection and by transmission, respectively. All curves are calibrated.

Fig. 6
Fig. 6

Angular scattering from a rough and nonisotropic Cu sample measured at wavelength λ = 515 nm. In (A), curve m designates the mean section of angular scattering over polar angle α, while curves min and max are for extrema values (see text), in particular, polar planes. (B) represents level maps of scattering, which are given by x = θ cos α and y = θ sin α at a given scattering level. The angular origin of level maps depends on the angular starting position of the sample.

Fig. 7
Fig. 7

Same as Fig. 6, except that λ = 633 nm.

Fig. 8
Fig. 8

Same as Fig. 6, except that λ = 1.06 μm.

Fig. 9
Fig. 9

Same as Fig. 6, except that λ = 3.39 μm.

Fig. 10
Fig. 10

Same as Fig. 6, except that λ = 10.6 μm.

Fig. 11
Fig. 11

Roughness spectra measured for the Cu sample in the measurable bandwidths given by each wavelength (515 and 633 nm, and 1.064, 3.39, and 10.6 μm). Nonoverlapping is due to high slope scratches and local defects (see text).

Fig. 12
Fig. 12

Mean sections of angular scattering measured for a black glass at visible wavelengths (580, 596, 600, 604, 620 and 633 nm). The curves are plotted versus σ = (2π/λ) sin θ, with a linear horizontal scale. The measurable bandwidths are almost identical because of the narrow spectral range.

Fig. 13
Fig. 13

Mean roughness spectra calculated from the measurements of Fig. 12. The curves overlap in the common bandwidth.

Fig. 14
Fig. 14

Isotropy degree curves measured in the bandwidths for the black glass sample of Figs. 12 and 13.

Fig. 15
Fig. 15

Mean sections of angular scattering measured for a black glass at different visible wavelengths (458, 515, 600, and 633 nm). The curves are plotted versus σ = (2π/λ) sin θ, with a linear horizontal scale. The measurable bandwidths are no longer identical.

Fig. 16
Fig. 16

Mean roughness spectra calculated from the measurements of Fig. 15. The curves overlap at the intersection of bandwidths.

Fig. 17
Fig. 17

Isotropy degree curves measured in the bandwidths for the black glass sample of Figs. 15 and 16.

Fig. 18
Fig. 18

Mean sections of angular scattering measured for an Al surface at visible (λ = 633-nm) and near-infrared (λ = 1.064-μm) wavelengths. The curves are plotted versus σ = (2π/λ)sin θ, with a linear horizontal scale. The measurable bandwidths are significantly different.

Fig. 19
Fig. 19

Mean roughness spectra calculated from the measurements of Fig. 18. The curves overlap at the intersection of the bandwidths.

Fig. 20
Fig. 20

Isotropy degree curves measured in the bandwidths for the Al sample of Figs. 18 and 19.

Fig. 21
Fig. 21

Angular correlations FN(θ, α) measured at λ = 633 nm for directions θ = 5°, 15°, 30°, 45°, 60° and 75°. The sample is that of Figs. 1820.

Fig. 22
Fig. 22

Mean sections of angular scattering measured for the Al surface at visible (λ = 633-nm) and midinfrared (λ = 3.39-μm) wavelengths. The curves are plotted versus σ = (2π/λ)sin θ, with a logarithmic horizontal scale. The measurable bandwidths are now disconnected.

Fig. 23
Fig. 23

Mean roughness spectra calculated from the measurements of Fig. 22. The curves appear to show good continuation.

Fig. 24
Fig. 24

Schematic view of the procedure for the measurement of laser-induced thermal emission. The incident beam is visible (458 nm < λ < 514 nm) with 5-W of power modulated at frequency Ω. The angular data are recorded in the midinfrared (λ ≈ 10.6 μm).

Fig. 25
Fig. 25

Angular emissivity or thermal radiation measured at λ = 10.6 μm with modulation frequency (A) Ω = 300 Hz, (B) Ω = 3 kHz. The curve (threshold) is obtained in the absence of the incident beam. No calibration is used here.

Fig. 26
Fig. 26

Mean sections of angular scattering measured for black glass at visible (λ = 0.63-μm) and midinfrared (λ = 10.6-μm) wavelengths. The curves are plotted versus σ = (2π/λ)sin θ, with a logarithmic horizontal scale. The measurable bandwidths are disconnected.

Fig. 27
Fig. 27

Mean roughness spectra calculated from the measurements of Fig. 26. Linear extrapolation does not permit accurate overlapping to be reached (see text).

Fig. 28
Fig. 28

Isotropy degree curves measured in the bandwidths for the sample of Figs. 26 and 27.

Fig. 29
Fig. 29

Angular correlations FN(θ, α) measured at λ = 10.6 μm for directions θ = 10°, 12°, 16°, 18°, 22° and 30°. The sample is that of Figs. 2628.

Fig. 30
Fig. 30

Mean sections of angular scattering measured for another black glass at near-infrared (λ = 1.064-μm) and midinfrared (λ = 10.6-μm) wavelengths. The curves are plotted versus σ = (2π/λ)sin θ with a logarithmic horizontal scale.

Fig. 31
Fig. 31

Mean roughness spectra calculated from the measurements of Fig. 30. Linear extrapolation shows accurate overlapping (see text).

Fig. 32
Fig. 32

Isotropy degree curves measured in the bandwidths for the sample of Figs. 30 and 31.

Tables (2)

Tables Icon

Table 1 Total Scattering D and Roughness δ Measured for a Cu Sample at Different Wavelengths λ from the Visible to the Midinfrareda

Tables Icon

Table 2 Total Scattering D and Roughness δ Measured for Black Glass at Different Visible Wavelengths λa

Equations (16)

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γ ( θ , ϕ ) = I ( θ , ϕ ) / C ( θ , ϕ ) ,
δ 2 = ( 2 π / λ ) 2 θ = 0 π / 2 ϕ = 0 2 π γ ( θ , ϕ ) sin θ cos θ d θ d ϕ ,
ν = sin θ λ ( cos ϕ , sin ϕ ) ,
B ( λ , θ min , θ max ) = ( 1 / λ ) ( sin θ min , sin θ max ) ,
δ 2 = B γ ( σ ) d σ ,
I ( θ , ϕ , α = 0 ) = I ( θ , ϕ = 0 , α = ϕ ) .
I ( θ , α ) = C υ ( θ , α ) / υ ref ( θ , α ) .
C = R d / θ , α η L ( θ , α ) sin θ d θ d α ,
I L ( θ , α ) = d L cos θ ,
Ī ( θ ) = ( 1 2 π ) α = 0 2 π I ( θ , α ) d α .
I ( α ) = θ = 0 π / 2 I ( θ , α ) sin θ d θ .
x = θ cos α , y = θ sin α ,
F N ( θ , α ) = F ( θ , α ) / F ( θ , 0 ) ,
F ( θ , α ) = ϕ = 0 2 π I ( θ , ϕ ) I ( θ , ϕ + α ) d ϕ .
d ( θ ) = min α [ F N ( θ , α ) ] 1 .
n Al = 1.39 + j 7.65 at λ = 633 nm , n Al = 1.21 + j 10.6 at λ = 1.06 μ m .

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