Abstract

The tools of investigation presented in part I of this study [ J. Opt. Soc. Am. A 11, 197 ( 1994)] are applied to the analysis of experimental results. First the limits of the scatterometer are analyzed in detail. Problems of calibration, parasitic light, linearity, and repeatability of measurements are discussed. The roughness spectrum is shown to be an intrinsic property of surface defects. It is proved that this spectrum is perfectly reproduced in the whole range of measurable spatial frequencies by a metallic layer. Dielectric materials under study are TiO2, Ta2O5, and SiO2 obtained by ion-assisted deposition, ion plating, and electron beam evaporation. The inverse problem is solved with isotropy degree curves, and the scattering parameters that are low-pass filters and residual spectra are extracted for single layers and multilayers. Replication of defects in the measurable bandwidth is shown to be perfect at all interfaces of a multilayer. In addition, the thin-film materials bring low residual roughnesses. Coatings are also produced at oblique deposition, and light scattering is used to detect the oblique growth of the thin-film layers. The role of local defects is investigated.

© 1994 Optical Society of America

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References

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  1. C. Amra, “Light scattering from multilayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11, 197–210 (1994).
    [CrossRef]
  2. C. Amra, P. Roche, D. Torriccini, “Multi-wavelength (0.45 μm to 10.6 μm) angle-resolved scatterometer or how to extend the optical window,” Appl. Opt. 32, 5462–5474 (1993).
    [CrossRef] [PubMed]
  3. 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]
  4. P. Roche, E. Pelletier, “Characterizations of optical surfaces by measurement of scattering distribution,” Appl. Opt. 23, 3561–3566 (1984).
    [CrossRef] [PubMed]
  5. 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]
  6. L. Mattsson, “Light scattering and characterization of thin films,” in Thin Film Technologies II, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.652, 215–220 (1986).
    [CrossRef]
  7. P. Roche, E. Pelletier, G. Albrand, “Antiscattering transparent monolayers: theory and experiment,”J. Opt. Soc. Am. 1, 1032–1033 (1984).
    [CrossRef]
  8. C. Amra, G. Albrand, P. Roche, “Theory and application of antiscattering single layers: antiscattering antireflection coatings,” Appl. Opt. 25, 2695–2702 (1986).
    [CrossRef] [PubMed]
  9. J. R. McNeil, G. A. Al-Jumaily, J. M. Bennett, “Surface smoothing effects and optical scatter characteristics of coated metal surfaces,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 140–145 (1988).
    [CrossRef]
  10. 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]
  11. A. Fornier, R. Richier, E. Pelletier, “Realization of Fabry–Perot filters for wavelength demultiplexing,” in Thin Film Technologies II, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.652, 27–32 (1986).
    [CrossRef]
  12. C. Grèzes-Besset, R. Richier, E. Pelletier, “Layer uniformity obtained by vacuum evaporation: application to Fabry–Perot filters,” Appl. Opt. 28, 2960–2964 (1989).
    [CrossRef] [PubMed]
  13. J. M. Bennett, E. Pelletier, G. Albrand, J. P. Borgogno, B. Lazaridès, C. K. Carniglia, R. A. Schmell, T. H. Allen, T. Tuttle-Hart, K. H. Guenther, A. Saxer, “Comparison of the properties of titanium doxide films prepared by various techniques,” Appl. Opt. 28, 3303–3317 (1989).
    [CrossRef] [PubMed]
  14. J. P. Borgogno, B. Lazaridès, E. Pelletier, “Automatic determination of the optical constants of inhomogeneous thin films,” Appl. Opt. 21, 4020–4029 (1982).
    [CrossRef] [PubMed]
  15. E. Pelletier, F. Flory, Y. Hu, “Optical characterization of thin films by guided waves,” Appl. Opt. 28, 2918–2924 (1989).
    [CrossRef] [PubMed]
  16. C. Amra, “Minimizing scattering in multilayers: technique for searching optimal realization conditions,” in Laser Induced Damage in Optical Materials, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newnam, M. J. Soileau, eds., Natl. Inst. Stand. Technol. Spec. Publ.756, 265–271 (1987).
  17. J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
    [CrossRef]
  18. A. G. Dirks, H. J. Leamy, “Columnar microstructure in vapor-deposited thin films,” Thin Solid Films 47, 219–223 (1977).
    [CrossRef]
  19. R. B. Sargent, Dar-Yuan Song, H. A. Macleod, “Computer simulation of substrate defect propagation in thin films,” in Modeling of Optical Thin Films, M. R. Jacobson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.821, (1987).
  20. C. Amra, “Scattering characterization of materials in thin film form,” in Laser-Induced Damage in Optical Materials, H. E. Bennett, L. L. Chase, A. H. Guenther, B. E. Newman, M. J. Soileau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1438, 309–323 (1989).
  21. C. Amra, “Calculs et mesures de diffusion appliqués à l’étude de la rugosité dans les traitements optiques multicouches,”J. Opt. (Paris) 21, 83–98 (1990).
    [CrossRef]
  22. C. Amra, “From light scattering to the microstructure of thin film multilayers,” Appl. Opt. 32, 5481–5491 (1993).
    [CrossRef] [PubMed]
  23. C. Amra, L. Bruel, C. Grèzes-Besset, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–5503 (1993).
    [CrossRef] [PubMed]

1994 (1)

1993 (3)

1992 (1)

1990 (1)

C. Amra, “Calculs et mesures de diffusion appliqués à l’étude de la rugosité dans les traitements optiques multicouches,”J. Opt. (Paris) 21, 83–98 (1990).
[CrossRef]

1989 (4)

1986 (1)

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, G. Albrand, “Antiscattering transparent monolayers: theory and experiment,”J. Opt. Soc. Am. 1, 1032–1033 (1984).
[CrossRef]

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

1982 (1)

1977 (1)

A. G. Dirks, H. J. Leamy, “Columnar microstructure in vapor-deposited thin films,” Thin Solid Films 47, 219–223 (1977).
[CrossRef]

1965 (1)

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Albrand, G.

Al-Jumaily, G. A.

J. R. McNeil, G. A. Al-Jumaily, J. M. Bennett, “Surface smoothing effects and optical scatter characteristics of coated metal surfaces,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 140–145 (1988).
[CrossRef]

Allen, T. H.

Amra, C.

C. Amra, “Light scattering from multilayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11, 197–210 (1994).
[CrossRef]

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

C. Amra, L. Bruel, C. Grèzes-Besset, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–5503 (1993).
[CrossRef] [PubMed]

C. Amra, P. Roche, D. Torriccini, “Multi-wavelength (0.45 μm to 10.6 μm) angle-resolved scatterometer or how to extend the optical window,” Appl. Opt. 32, 5462–5474 (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, “Calculs et mesures de diffusion appliqués à l’étude de la rugosité dans les traitements optiques multicouches,”J. Opt. (Paris) 21, 83–98 (1990).
[CrossRef]

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, G. Albrand, P. Roche, “Theory and application of antiscattering single layers: antiscattering antireflection coatings,” Appl. Opt. 25, 2695–2702 (1986).
[CrossRef] [PubMed]

C. Amra, “Scattering characterization of materials in thin film form,” in Laser-Induced Damage in Optical Materials, H. E. Bennett, L. L. Chase, A. H. Guenther, B. E. Newman, M. J. Soileau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1438, 309–323 (1989).

C. Amra, “Minimizing scattering in multilayers: technique for searching optimal realization conditions,” in Laser Induced Damage in Optical Materials, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newnam, M. J. Soileau, eds., Natl. Inst. Stand. Technol. Spec. Publ.756, 265–271 (1987).

Apfel, J. H.

Bennett, J. M.

J. M. Bennett, E. Pelletier, G. Albrand, J. P. Borgogno, B. Lazaridès, C. K. Carniglia, R. A. Schmell, T. H. Allen, T. Tuttle-Hart, K. H. Guenther, A. Saxer, “Comparison of the properties of titanium doxide films prepared by various techniques,” Appl. Opt. 28, 3303–3317 (1989).
[CrossRef] [PubMed]

J. R. McNeil, G. A. Al-Jumaily, J. M. Bennett, “Surface smoothing effects and optical scatter characteristics of coated metal surfaces,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 140–145 (1988).
[CrossRef]

Borgogno, J. P.

Bruel, L.

Carniglia, C. K.

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]

Dirks, A. G.

A. G. Dirks, H. J. Leamy, “Columnar microstructure in vapor-deposited thin films,” Thin Solid Films 47, 219–223 (1977).
[CrossRef]

Flory, F.

Fornier, A.

A. Fornier, R. Richier, E. Pelletier, “Realization of Fabry–Perot filters for wavelength demultiplexing,” in Thin Film Technologies II, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.652, 27–32 (1986).
[CrossRef]

Grèzes-Besset, C.

Guenther, K. H.

Hu, Y.

Lazaridès, B.

Leamy, H. J.

A. G. Dirks, H. J. Leamy, “Columnar microstructure in vapor-deposited thin films,” Thin Solid Films 47, 219–223 (1977).
[CrossRef]

Macleod, H. A.

R. B. Sargent, Dar-Yuan Song, H. A. Macleod, “Computer simulation of substrate defect propagation in thin films,” in Modeling of Optical Thin Films, M. R. Jacobson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.821, (1987).

Mattsson, L.

L. Mattsson, “Light scattering and characterization of thin films,” in Thin Film Technologies II, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.652, 215–220 (1986).
[CrossRef]

McNeil, J. R.

J. R. McNeil, G. A. Al-Jumaily, J. M. Bennett, “Surface smoothing effects and optical scatter characteristics of coated metal surfaces,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 140–145 (1988).
[CrossRef]

Mead, R.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Nelder, J. A.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Pelletier, E.

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, 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]

J. M. Bennett, E. Pelletier, G. Albrand, J. P. Borgogno, B. Lazaridès, C. K. Carniglia, R. A. Schmell, T. H. Allen, T. Tuttle-Hart, K. H. Guenther, A. Saxer, “Comparison of the properties of titanium doxide films prepared by various techniques,” Appl. Opt. 28, 3303–3317 (1989).
[CrossRef] [PubMed]

E. Pelletier, F. Flory, Y. Hu, “Optical characterization of thin films by guided waves,” Appl. Opt. 28, 2918–2924 (1989).
[CrossRef] [PubMed]

C. Grèzes-Besset, R. Richier, E. Pelletier, “Layer uniformity obtained by vacuum evaporation: application to Fabry–Perot filters,” Appl. Opt. 28, 2960–2964 (1989).
[CrossRef] [PubMed]

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

P. Roche, E. Pelletier, G. Albrand, “Antiscattering transparent monolayers: theory and experiment,”J. Opt. Soc. Am. 1, 1032–1033 (1984).
[CrossRef]

J. P. Borgogno, B. Lazaridès, E. Pelletier, “Automatic determination of the optical constants of inhomogeneous thin films,” Appl. Opt. 21, 4020–4029 (1982).
[CrossRef] [PubMed]

A. Fornier, R. Richier, E. Pelletier, “Realization of Fabry–Perot filters for wavelength demultiplexing,” in Thin Film Technologies II, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.652, 27–32 (1986).
[CrossRef]

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]

Richier, R.

C. Grèzes-Besset, R. Richier, E. Pelletier, “Layer uniformity obtained by vacuum evaporation: application to Fabry–Perot filters,” Appl. Opt. 28, 2960–2964 (1989).
[CrossRef] [PubMed]

A. Fornier, R. Richier, E. Pelletier, “Realization of Fabry–Perot filters for wavelength demultiplexing,” in Thin Film Technologies II, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.652, 27–32 (1986).
[CrossRef]

Roche, P.

Sargent, R. B.

R. B. Sargent, Dar-Yuan Song, H. A. Macleod, “Computer simulation of substrate defect propagation in thin films,” in Modeling of Optical Thin Films, M. R. Jacobson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.821, (1987).

Saxer, A.

Schmell, R. A.

Song, Dar-Yuan

R. B. Sargent, Dar-Yuan Song, H. A. Macleod, “Computer simulation of substrate defect propagation in thin films,” in Modeling of Optical Thin Films, M. R. Jacobson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.821, (1987).

Torriccini, D.

Tuttle-Hart, T.

Appl. Opt. (11)

J. P. Borgogno, B. Lazaridès, E. Pelletier, “Automatic determination of the optical constants of inhomogeneous thin films,” Appl. Opt. 21, 4020–4029 (1982).
[CrossRef] [PubMed]

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

C. Amra, G. Albrand, P. Roche, “Theory and application of antiscattering single layers: antiscattering antireflection coatings,” Appl. Opt. 25, 2695–2702 (1986).
[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]

E. Pelletier, F. Flory, Y. Hu, “Optical characterization of thin films by guided waves,” Appl. Opt. 28, 2918–2924 (1989).
[CrossRef] [PubMed]

C. Grèzes-Besset, R. Richier, E. Pelletier, “Layer uniformity obtained by vacuum evaporation: application to Fabry–Perot filters,” Appl. Opt. 28, 2960–2964 (1989).
[CrossRef] [PubMed]

J. M. Bennett, E. Pelletier, G. Albrand, J. P. Borgogno, B. Lazaridès, C. K. Carniglia, R. A. Schmell, T. H. Allen, T. Tuttle-Hart, K. H. Guenther, A. Saxer, “Comparison of the properties of titanium doxide films prepared by various techniques,” Appl. Opt. 28, 3303–3317 (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, P. Roche, D. Torriccini, “Multi-wavelength (0.45 μm to 10.6 μm) angle-resolved scatterometer or how to extend the optical window,” Appl. Opt. 32, 5462–5474 (1993).
[CrossRef] [PubMed]

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

C. Amra, L. Bruel, C. Grèzes-Besset, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–5503 (1993).
[CrossRef] [PubMed]

Comput. J. (1)

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

J. Opt. (Paris) (2)

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]

C. Amra, “Calculs et mesures de diffusion appliqués à l’étude de la rugosité dans les traitements optiques multicouches,”J. Opt. (Paris) 21, 83–98 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

P. Roche, E. Pelletier, G. Albrand, “Antiscattering transparent monolayers: theory and experiment,”J. Opt. Soc. Am. 1, 1032–1033 (1984).
[CrossRef]

J. Opt. Soc. Am. A (1)

Thin Solid Films (1)

A. G. Dirks, H. J. Leamy, “Columnar microstructure in vapor-deposited thin films,” Thin Solid Films 47, 219–223 (1977).
[CrossRef]

Other (6)

R. B. Sargent, Dar-Yuan Song, H. A. Macleod, “Computer simulation of substrate defect propagation in thin films,” in Modeling of Optical Thin Films, M. R. Jacobson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.821, (1987).

C. Amra, “Scattering characterization of materials in thin film form,” in Laser-Induced Damage in Optical Materials, H. E. Bennett, L. L. Chase, A. H. Guenther, B. E. Newman, M. J. Soileau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1438, 309–323 (1989).

C. Amra, “Minimizing scattering in multilayers: technique for searching optimal realization conditions,” in Laser Induced Damage in Optical Materials, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newnam, M. J. Soileau, eds., Natl. Inst. Stand. Technol. Spec. Publ.756, 265–271 (1987).

L. Mattsson, “Light scattering and characterization of thin films,” in Thin Film Technologies II, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.652, 215–220 (1986).
[CrossRef]

J. R. McNeil, G. A. Al-Jumaily, J. M. Bennett, “Surface smoothing effects and optical scatter characteristics of coated metal surfaces,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 140–145 (1988).
[CrossRef]

A. Fornier, R. Richier, E. Pelletier, “Realization of Fabry–Perot filters for wavelength demultiplexing,” in Thin Film Technologies II, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.652, 27–32 (1986).
[CrossRef]

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Figures (24)

Fig. 1
Fig. 1

Basic principles of the scatterometer. The sample of normal n is illuminated at incidence i with a 633-nm He–Ne laser. The specular reflected and transmitted beams are carefully eliminated with light wells. The sample lies in a vertical plane and rotates around its normal (α variations), while the detector moves in a horizontal incidence plane (θ variations).

Fig. 2
Fig. 2

Detection limit of the scattering apparatus. The angular measurements (0 → 90°) and (90 → 180°) correspond to scattering by reflection and transmission, respectively. Curve 1 is measured in the absence of sample. Curves 2 and 3 are the parasitic light expected for a sample of reflectance R = 0.04 (curve 2) and R = 0.99 (curve 3). Curve 4 is the measurement of an étalon in which diffuse reflectance is close to unity. Curve 4 is measured with an incident flux reduced by a factor close to 8.8 × 10−3, so that the photomultiplier is not damaged. All curves are calibrated here.

Fig. 3
Fig. 3

Measurement of calibration constant CL versus scattering angle θL. The relative variation is 9% between 0 and 60°. The mean constant C ¯ (see text) is obtained at direction θ ≈ 57°.

Fig. 4
Fig. 4

Mean sections of angular scattering from the étalon for different polarization states (NN, SS, SP, PS, PP) of the incident and scattered light. No calibration is used here (C = 1), for which reason measurements with unpolarized light are greater by a factor of 4.

Fig. 5
Fig. 5

Measurement of T′(θ) = v′(θ)/v(θ) versus scattering angle θ (see text). The relative variation is 1.6% in the angular range (1 → 83°).

Fig. 6
Fig. 6

Isotropy degree curves measured two times on the same sample.

Fig. 7
Fig. 7

Angular scattering measured for a black glass substrate before (curve 1) and after (curve 2) cleaning, for nonpolarized (NN) illumination. The minimum angle for measurements is θ = 3.3° from the sample normal.

Fig. 8
Fig. 8

Angular scattering measured after first cleaning (curve 1), 5 h after this cleaning (curve 2), and after second cleaning (curve 3). The total scattering losses are D1 = 56 ppm, D2 = 118 ppm, and D3 = 54 ppm.

Fig. 9
Fig. 9

Dissociation of the spectra with the polarization state (S and P) of incident light. This effect is due to the presence of droplets at the surface that give rise to additional scattering that is not intrinsic to roughness.

Fig. 10
Fig. 10

Measurement of (A) the roughness spectrum and (B) the isotropy degree for NN, SN, and PN polarization configurations. The sample is free of droplets or local defects.

Fig. 11
Fig. 11

(A) Measurement of the roughness spectrum for an Al surface for SS (curve 1) and PP (curve 2) polarization. Curves 3 and 4 are additional SS and PP measurements with an incident flux increased by a factor of 100. (B) Angular scattering from an Al surface measured in SS (curve 1), PP (curve 2), SP (curve 3), and PS (curve 4) polarization. The total losses are D m SS = 1.19 × 10 - 3 , D m PP = 1.46 × 10 - 3 , D m SP = 4 × 10 - 5, and D m PS = 3 × 10 - 5. The presence of a small amount of cross-polarized light at low θ is due to the efficiency of the polarizer and analyzer (not to second-order scattering). (C) Angular function FN′(θ, α) obtained at θ = 30° and θ = 80° from SS and PP measurements on the Al surface.

Fig. 12
Fig. 12

(A) Roughness spectra measured before (curve 1) and after (curve 2) deposition of Al onto a glass surface. Curve 3 is the Al spectrum calculated from the glass measurements (with the causal model), with a cutoff frequency σc = 12.6 μm−1 (smoothing effect introduced by Al). (B) Isotropy degree measured before (curve 1) and after (curve 2) deposition of Al.

Fig. 13
Fig. 13

(A) Measurement of angular correlation FN′(α) before and after deposition of a 6L SiO2 layer (IAD process). The two curves are identical. (B) Isotropy degree curves measured before (curve 1) and after (curve 2) coating by a 6L SiO2 layer (IAD process). (C) Calculation (curve 1) and measurement (curve 2) of angular scattering from a 6L SiO2 layer (IAD process). Curve 1 is the causal scattering calculated for perfect replication (σc = ∞). (D) Roughness spectra measured for the glass substrate (curve 1) and after deposition of Al onto the SiO2 layer (curve 2).

Fig. 14
Fig. 14

(A) Measurement of the isotropy degree before (curve 1) and after (curve 2) coating by a 2L layer of SiO2 obtained by ion plating. The design wavelength is λ0 = 633 nm. Curve 3 is calculated for the coating, with a residual spectrum γ L g given in the text. (B) Calculation (curves 1 and 3) and measurement (curve 2) of angular scattering from a 2L layer of SiO2. Curve 1 is calculated for perfect correlation (Ig = 0 and σL = ∞). Curve 3 is calculated with the residual spectrum γ L g given in the text. (C) Calculation and measurement of angular correlation FN′(θ, α) for a 2L SiO2 layer, at different θ angles (10°, 40°, and 70°). Calculation is performed with the residual spectrum γ L g given in the text. C and M indicate calculation and measurement, respectively.

Fig. 15
Fig. 15

(A) Calculation and measurement of the isotropy degree for a 2H layer of TiO2 (IAD process). Curves 1 and 2 are the measurements before and after coating. Curve 3 is calculated with σH = ∞ and a residual spectrum γ H g given in the text. Curve 4 is the measurement after deposition of Al onto the coating. (B) Calculation and measurement of the mean section of angular scattering. Curves 1 and 2 are measurements before and after coating by the 2H TiO2 layer. Curve 1′ is calculated for the layer, with σH = ∞ and γ H g = 0 (perfect correlation). Curve 3 is calculated for the layer with the residual spectrum γ H g given in the text. The total scattering is 53 ppm before coating and 59 ppm after coating. Curve 4 is the measurement after deposition of Al. (C) Calculation and measurement of the roughness spectrum. Curve 1 is the measurement of the substrate before deposition of TiO2. Curve 2 is the measurement of the Al–air interface after deposition of Al onto the TiO2 layer. Curve 3 is the sum γ s + γ H g of the substrate (γs) and the residual ( γ H g) spectrum. Curve 4 is deduced from curve 3 with a smoothing effect that is due to Al, with σc = 10.5 μm−1. (D) Angular functions measured for the substrate (curves S) and after deposition of Al (curves A) onto the TiO2 layer, at different θ angles. (E) Calculation and measurement of the isotropy degree. Curve 1 is measured for the substrate before coating. Curve 2 is calculated for the TiO2 layer, with σc = ∞:, δg = 0.4 nm, and Lg = 100 nm. Curve 3 is calculated when the layer is Al overcoated; it is assumed here that Al has only a replication effect.

Fig. 16
Fig. 16

(A) Calculation and measurement of angular scattering from a Ta2O5 layer (ion plating). Curves 1 and 2 are the measurements before (1) and after (2) coating. Curve 1′ is calculated for perfect correlation (Ig = 0 and σH = ∞). Curve 3 is calculated with a residual spectrum γ H g given in the text. (B) Isotropy degree measured before (curve 1) and after (curve 2) coating by a Ta2O5 layer. Curve 3 is calculated with γ H g given in the text.

Fig. 17
Fig. 17

(A) Calculation and measurement of the isotropy degree for a 2H2L2H stack. Curves 1 and 2 are the measurements before (1) and after (2) coating. Curve 3 is calculated for perfect replication and with a residual spectrum γg given in the text. Curve 4 is the measurement after deposition of Al. (B) Calculation and measurement of angular scattering by a 2H2L2H stack. Curves 1 and 2 are the measurements before (1) and after (2) coating. Curve 1′ is the causal scattering calculated for perfect correlation (Ig = 0 and σc = ∞). Curve 3 is calculated with a residual spectrum γg given in the text. Curve 4 is the measurement after deposition of Al on the stack. (C) Roughness spectrum measured for the glass substrate (curve 1) and after deposition of Al on the 2H2L2H stack (curve 2).

Fig. 18
Fig. 18

(A) Angular scattering from a 19-layer mirror. Curves 1 and 2 are the measurements before (1) and after (2) coating. Curve 3 is the causal scattering calculated for perfect correlation (Ig = 0 and σc = ∞). (B) Optical properties measured for the 19-layer mirror in the spectral range (400 → 1000 nm). The presence of errors in the design is obvious. (C) Isotropy degree measured before (curve 1) and after (curve 2) coating by a 19-layer mirror. (D) Angular functions measured before (curves S) and after (curves M) coating by a 19-layer mirror, at directions θ = 60° and θ = 80°.

Fig. 19
Fig. 19

(A) Measurement of angular scattering before (curve 1) and after (curve 2) coating by a HLHLH(6L)HLHLH stack. Curve 3 is the causal scattering calculated for perfect correlation (Ig = 0 and σc = ∞) and for a design wavelength of 633 nm. Curve 4 is calculated with the same parameters but with a design wavelength of 645.2 nm. (B) Calculation (pluses) and measurement (solid curve) of the optical properties of the Fabry–Perot stack. The theoretical curve is obtained from a simplex method. (C) Calculation (curve 1) and measurement (curve 2) of angular scattering from the Fabry–Perot stack. Calculation is performed for perfect correlation (Ig = 0 and σc = ∞) and with the design issued from the simplex method (see text). SUB is the measurement of the substrate. (D) Isotropy degree measured before (curve 1) and after (curve 2) coating by a Fabry–Perot stack.

Fig. 20
Fig. 20

Influence of oblique deposition (at incidence β) on the mean section of scattering from a TiO2 layer. Curve 1 is calculated for β = 0, and curve 2 for β = 31.8°. Calculation is performed for perfect correlation (σH = ∞ and γ H g = 0).

Fig. 21
Fig. 21

Calculation and measurement of angular scattering from a TiO2 layer produced at oblique incidence β = 31.8°. Curves 1 and 2 are the measurements before (1) and after (2) coating. Curve 3 is calculated with σH = ∞, ψ(σ) = σ · a = (σ/2)e tan β cos ϕ, and a residual spectrum γ H g given in the text.

Fig. 22
Fig. 22

Calculation and measurement of level maps of scattering for a single TiO2 layer produced at normal (β = 0) and oblique (β = 31.8°) incidence. (A) Measurement of substrate, (B) calculation for the layer produced at β = 0, (C) calculation for the layer produced at β = 31.8°, (D) measurement for the layer produced at β = 31.8°, which shows the shift of isotropy. All calculation is performed in the absence of residual roughness ( γ H g = 0), with σH = ∞ and ψ(σ) = (σ/2)e tan β cos ϕ.

Fig. 23
Fig. 23

Angular functions measured at directions θ = 6°, 10°, 30° and 60° (A) before and (B) after coating by a TiO2 layer produced at oblique incidence β = 31.8°. The period is increased from π to 2π after coating.

Fig. 24
Fig. 24

Calculation and measurement of the isotropy degree of a TiO2 layer produced at oblique deposition β = 31.8°. Curves 1 and 2 are the measurements before (1) and after (2) coating. Curves 3–5 are calculation with different residual spectra γ H g: (3) γ H g = 0, (4) δg = 0.5 nm and Lg = 200 nm, (5) δg = 1.5 nm and Lg = 100 nm. All calculation is performed with β = 31.8°, σh = ∞, and ψ(σ) = (σ/2)e tan β cos ϕ.

Equations (57)

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R ( λ , i , β ) ( 0.05 μ m - 1 , 1.54 μ m - 1 ) .
I m ( θ , α ) = i , j C i j ( θ , ϕ = 0 ) γ i j ( θ , α ) .
C i j SS ( θ , ϕ = 0 ) = 2 C i j NS ( θ ) ,             C i j SP P ( θ , ϕ = 0 ) = 0 , I m SS ( θ , α ) = I m SN ( θ , α ) = 2 I NS ( θ , α ) = I SS ( θ , α ) + I PS ( θ , α ) , I SS ( θ , α ) = I m SS ( θ , α ) cos 2 α , I m PS ( θ , α ) = I m PS ( θ , α ) sin 2 α .
I PP ( θ , α ) = I m PP ( θ , α ) cos 2 α ,             I SP ( θ , α ) = I m SP ( θ , α ) sin 2 α ,
D NS = D SS = D PS D SS = 1 2 D m SS ,             D PP = 1 2 D m PP .
I NN = I m NN = 1 2 ( I SS + I SP + I PS + I PP ) = 1 2 ( I m SS + I m PP ) D NN = D m NN = 1 2 ( D m SS + D m PP ) .
I m ( θ , α ) = C d v ( θ , α ) ,
C d = T d / v 0 Δ Ω ,
C L = d L ( θ L ) cos θ L / v L ( θ L ) ,
C ¯ = R d / D m .
Δ C ¯ C ¯ = Δ D m D m = sin 2 θ m 3 × 10 - 3             for θ min = 3.3 ° .
2 C d - C ¯ C d + C ¯ 7 % .
C X N C NN = 1 τ pol N X ,
C N X C NN = 1 τ an X X ,
C X X C NN = 1 τ pol N X τ an X X ,
C X Y C NN = 1 τ pol NS τ an Y Y ,
C X N = R X D m X N ,
C N X = R N X D m N X ,
C X X = R X X D m X X ,
C X Y = R X Y D m X Y ,
R d = R NN = 1 2 ( R S + R P )
R S = R SS + R SP ,             R P = R PS + R PP ,
R NS = 1 2 ( R SS + R PS ) ,             R NP = 1 2 ( R SP + R PP ) .
R P R S = D m PN D m SN · τ pol NS τ pol NP ,
R NN = R S = R P = R d 1 ,
R SS = R SP = R PS = R PP = R NS = R NP = R d / 2 1 / 2.
γ S ( θ , ϕ ) = I m ( θ , ϕ ) / C 00 ( θ , ϕ ) γ ¯ s ( θ ) = I ¯ m ( θ ) / C 00 ( θ ) .
I ¯ = I ¯ c ( γ ¯ s , σ L = ) + I ¯ g ( γ L g ) ,
I [ γ s ( θ , ϕ ) , σ L , γ L g ( θ ) ]
δ r = 0.47 nm .
δ g = 0.4 nm ,             L g = 100 nm .
I s = C s γ s
I = α γ s + C 00 γ g
a = C 00 + C 11 + 2 Re ( α 01 C 01 ) .
x = I g I c = C 00 a · γ g γ s .
C 00 C s = [ ( n 2 - n 0 2 ) / ( n s 2 - n 0 2 ) ] 2 ,
I g I c > γ g γ s             for a 2 H layer , I g I c < γ g γ s             for a 2 L layer ,
I g I c = γ g γ s             for Al .
d ( 2 L ) < d ( Al ) < d ( 2 H ) .
I = I c + I g d = d + B 1 + B ,
B = ξ x ( 2 + x ) ,             x = I g / I ¯ c ,             ξ = ( γ ¯ s ) 2 γ ¯ s 2 .
d s = d s + B d 1 + B d ,
B d = ξ x d ( 2 + x d ) ,             x d = I d / I ¯ s .
d s > d s .
γ s = I s C s = I s + I d C s = γ s + γ d > γ s .
γ Al = a I s + I d a C s I s C s ,
γ Al γ s < γ s ,
d Al d s < d s .
I m = I c + I g + I d = a I s + I g + I d ,             a = I c / I s ,
d = d s + B 1 + B ,             B = ξ x ( 2 + x ) , x = I g + I d I ¯ c = x g + x d = x g + x d a .
I c = a C s γ s = I c + a I d I c .
I ¯ m I ¯ c = 1 + 1 - a a x d 1 + x d + 1 a x g 1 + x d .
( 17 ) I m < I s + I d + I g = I s + I g , ( 18 ) x > x d + x g > x d d > d s , ( 20 ) I ¯ m / I ¯ c > 1.
( 17 ) I m = I s + I g > I s , ( 18 ) x = x d + x g > x d d > d s , ( 20 ) I ¯ m / I ¯ c = 1 + x g 1 + x d > 1.
( 17 ) I m > I s ' + I g > I s , ( 18 ) x < x d + x g d < > d s , ( 20 ) I ¯ m / I ¯ c = 1 + ɛ ,
ψ ( σ ) = ( σ / 2 ) e tan β cos ϕ ,             σ = ( 2 π / λ ) n sin θ ,
δ g = 1.5 nm ,             L g = 100 nm .

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