Abstract

We show how the complexity of a micropolished optical surface can be investigated in detail by measurement of the distribution of scattered light. We deal with problems of roughness anisotropy and uniformity together with cleaning problems. Experimental results concern numerous black glasses from different polishing shops and allow a determination of the polish inhomogeneity in a same glass set. After that, we present a detailed study of the apparatus function of the scatterometer, and we determine the limits of validity of our optical characterization method.

© 1989 Optical Society of America

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References

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  1. C. Grezes-Besset, C. Amra, B. Cousin, G. Otrio, E. Pelletier, R. Richier, “Etude de la diaphonie d’un systéme de démultiplexage par filtres interférentiels. Conséquences de la diffusion de la lumière par les irrégularités des surfaces optiques,” Conf. présentée à TELEMAT 87, Marseille, 1–5 juin 1987, Ann. Télécommun. FRA43, 105–000 (1988).
  2. P. Roche, C. Amra, E. Pelletier, “Measurement of Scattering Distribution for Characterization of the Roughness of Coated or Uncoated Substrates,” Proc. Soc. Photo-Opt. Instrum. Eng. 652, 256–000 (1986).
  3. J. M. Bennett, “Scattering and Surface Evaluation Techniques for the Optics of the Future,” Opt. News 11, 17 (July1985).
    [Crossref]
  4. P. Roche, E. Pelletier, “Characterizations of Optical Surfaces by Measurement of Scattering Distribution,” Appl. Opt. 23, 3561–3566 (1984).
    [Crossref] [PubMed]
  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. C. Amra, P. Roche, E. Pelletier, “Interface Roughness Cross-Correlation Laws Deduced from Scattering Diagram Measurements on Optical Multilayers: Effect of the Material Grain Size,” J. Opt. Soc. Am. B 4, 1087–1093 (1987).
    [Crossref]
  7. E. Casparis-Hauser, K. H. Guenther, K. Tiefenthaler, “Spectrophotometry and Ellipsometric Study of Leached Layers Formed on Optical Glass by a Diffusion Process,” Proc. Soc. Photo-Opt. Instrum. Eng. 401, 211 (1983).
  8. 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]

1987 (1)

1986 (1)

P. Roche, C. Amra, E. Pelletier, “Measurement of Scattering Distribution for Characterization of the Roughness of Coated or Uncoated Substrates,” Proc. Soc. Photo-Opt. Instrum. Eng. 652, 256–000 (1986).

1985 (1)

J. M. Bennett, “Scattering and Surface Evaluation Techniques for the Optics of the Future,” Opt. News 11, 17 (July1985).
[Crossref]

1984 (1)

1983 (2)

E. Casparis-Hauser, K. H. Guenther, K. Tiefenthaler, “Spectrophotometry and Ellipsometric Study of Leached Layers Formed on Optical Glass by a Diffusion Process,” Proc. Soc. Photo-Opt. Instrum. Eng. 401, 211 (1983).

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]

1981 (1)

Amra, C.

C. Amra, P. Roche, E. Pelletier, “Interface Roughness Cross-Correlation Laws Deduced from Scattering Diagram Measurements on Optical Multilayers: Effect of the Material Grain Size,” J. Opt. Soc. Am. B 4, 1087–1093 (1987).
[Crossref]

P. Roche, C. Amra, E. Pelletier, “Measurement of Scattering Distribution for Characterization of the Roughness of Coated or Uncoated Substrates,” Proc. Soc. Photo-Opt. Instrum. Eng. 652, 256–000 (1986).

C. Grezes-Besset, C. Amra, B. Cousin, G. Otrio, E. Pelletier, R. Richier, “Etude de la diaphonie d’un systéme de démultiplexage par filtres interférentiels. Conséquences de la diffusion de la lumière par les irrégularités des surfaces optiques,” Conf. présentée à TELEMAT 87, Marseille, 1–5 juin 1987, Ann. Télécommun. FRA43, 105–000 (1988).

Bennett, J. M.

Bousquet, P.

Casparis-Hauser, E.

E. Casparis-Hauser, K. H. Guenther, K. Tiefenthaler, “Spectrophotometry and Ellipsometric Study of Leached Layers Formed on Optical Glass by a Diffusion Process,” Proc. Soc. Photo-Opt. Instrum. Eng. 401, 211 (1983).

Cousin, B.

C. Grezes-Besset, C. Amra, B. Cousin, G. Otrio, E. Pelletier, R. Richier, “Etude de la diaphonie d’un systéme de démultiplexage par filtres interférentiels. Conséquences de la diffusion de la lumière par les irrégularités des surfaces optiques,” Conf. présentée à TELEMAT 87, Marseille, 1–5 juin 1987, Ann. Télécommun. FRA43, 105–000 (1988).

Elson, J. M.

Flory, F.

Grezes-Besset, C.

C. Grezes-Besset, C. Amra, B. Cousin, G. Otrio, E. Pelletier, R. Richier, “Etude de la diaphonie d’un systéme de démultiplexage par filtres interférentiels. Conséquences de la diffusion de la lumière par les irrégularités des surfaces optiques,” Conf. présentée à TELEMAT 87, Marseille, 1–5 juin 1987, Ann. Télécommun. FRA43, 105–000 (1988).

Guenther, K. H.

E. Casparis-Hauser, K. H. Guenther, K. Tiefenthaler, “Spectrophotometry and Ellipsometric Study of Leached Layers Formed on Optical Glass by a Diffusion Process,” Proc. Soc. Photo-Opt. Instrum. Eng. 401, 211 (1983).

Otrio, G.

C. Grezes-Besset, C. Amra, B. Cousin, G. Otrio, E. Pelletier, R. Richier, “Etude de la diaphonie d’un systéme de démultiplexage par filtres interférentiels. Conséquences de la diffusion de la lumière par les irrégularités des surfaces optiques,” Conf. présentée à TELEMAT 87, Marseille, 1–5 juin 1987, Ann. Télécommun. FRA43, 105–000 (1988).

Pelletier, E.

C. Amra, P. Roche, E. Pelletier, “Interface Roughness Cross-Correlation Laws Deduced from Scattering Diagram Measurements on Optical Multilayers: Effect of the Material Grain Size,” J. Opt. Soc. Am. B 4, 1087–1093 (1987).
[Crossref]

P. Roche, C. Amra, E. Pelletier, “Measurement of Scattering Distribution for Characterization of the Roughness of Coated or Uncoated Substrates,” Proc. Soc. Photo-Opt. Instrum. Eng. 652, 256–000 (1986).

P. Roche, E. Pelletier, “Characterizations of Optical Surfaces by Measurement of Scattering Distribution,” Appl. Opt. 23, 3561–3566 (1984).
[Crossref] [PubMed]

C. Grezes-Besset, C. Amra, B. Cousin, G. Otrio, E. Pelletier, R. Richier, “Etude de la diaphonie d’un systéme de démultiplexage par filtres interférentiels. Conséquences de la diffusion de la lumière par les irrégularités des surfaces optiques,” Conf. présentée à TELEMAT 87, Marseille, 1–5 juin 1987, Ann. Télécommun. FRA43, 105–000 (1988).

Rahn, J. P.

Richier, R.

C. Grezes-Besset, C. Amra, B. Cousin, G. Otrio, E. Pelletier, R. Richier, “Etude de la diaphonie d’un systéme de démultiplexage par filtres interférentiels. Conséquences de la diffusion de la lumière par les irrégularités des surfaces optiques,” Conf. présentée à TELEMAT 87, Marseille, 1–5 juin 1987, Ann. Télécommun. FRA43, 105–000 (1988).

Roche, P.

Tiefenthaler, K.

E. Casparis-Hauser, K. H. Guenther, K. Tiefenthaler, “Spectrophotometry and Ellipsometric Study of Leached Layers Formed on Optical Glass by a Diffusion Process,” Proc. Soc. Photo-Opt. Instrum. Eng. 401, 211 (1983).

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

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

Opt. News (1)

J. M. Bennett, “Scattering and Surface Evaluation Techniques for the Optics of the Future,” Opt. News 11, 17 (July1985).
[Crossref]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

P. Roche, C. Amra, E. Pelletier, “Measurement of Scattering Distribution for Characterization of the Roughness of Coated or Uncoated Substrates,” Proc. Soc. Photo-Opt. Instrum. Eng. 652, 256–000 (1986).

E. Casparis-Hauser, K. H. Guenther, K. Tiefenthaler, “Spectrophotometry and Ellipsometric Study of Leached Layers Formed on Optical Glass by a Diffusion Process,” Proc. Soc. Photo-Opt. Instrum. Eng. 401, 211 (1983).

Other (1)

C. Grezes-Besset, C. Amra, B. Cousin, G. Otrio, E. Pelletier, R. Richier, “Etude de la diaphonie d’un systéme de démultiplexage par filtres interférentiels. Conséquences de la diffusion de la lumière par les irrégularités des surfaces optiques,” Conf. présentée à TELEMAT 87, Marseille, 1–5 juin 1987, Ann. Télécommun. FRA43, 105–000 (1988).

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Figures (10)

Fig. 1
Fig. 1

Scattering distribution from rough surface: (a) Polar representation in the incident plane (ϕ = 0) of the angular scattering curve of a glass surface calculated with 5-nm roughness. The specular beams are drawn, and Oz is the normal to the surface. The radius of the polar curve is the scattered flux BRDF · cosθ per unit of surface and solid angle normalized to the incident flux. (b) Angles θ and ϕ describing a scattering direction. The surface with normal Oz is illuminated at incidence i (no reflected or transmitted beam is shown here), σ is the spatial frequency of the grating responsible for scattering in direction (θ,ϕ). Thus we can see that the polar representation of (a) concerns the variations of scattered intensity I(θ,ϕ) in the incident plane ϕ = 0.

Fig. 2
Fig. 2

Principles of the apparatus and scattering representations: (a) principle of the apparatus where the incident and reflected beams have been superimposed. In fact, the sample Σ of normal on is illuminated at i = 1.5°. In these conditions, the minimum angle for scattering measurements is θ = 3.3° with respect to on, which is 1.8° with respect to the reflected beam. The receiver records 100 measurement data points I(θ) in the incident plane π. Moreover, the sample can rotate around its normal on so that we can measure for each direction θ the value I(θ,ϕ) for 250 rotations Δϕ of the sample. (b), (c) Polar representations of the function BRDF · cosθ(θ,ϕ). In the case of (b), the polar radius is the BRDF · cosθ value, while in (c) the polar radius is the scattering angle θ. The interest of either curve depends on the dynamic range of scattered flux.

Fig. 3
Fig. 3

Scatterometer response when there is no sample in the measurement room. The angular ranges (0 → 90°) and (90° → 180°), respectively, correspond to scattering by reflection and transmission.

Fig. 4
Fig. 4

Level curves [see Fig. 2(c)] of scattering for two different zones Σ1 and Σ2 of the same sample.

Fig. 5
Fig. 5

Examples for isotropic and nonisotropic surfaces.

Fig. 6
Fig. 6

Plane sections of the angular scattering curve: (a) angular scattering measured for different scattering planes ϕ; (b) mean plane section of the angular scattering curve over 250 measurement planes ϕ.

Fig. 7
Fig. 7

Angular autocorrelation functions F(α) of surface defects of two samples with their anisotropy curves. Curve F(α) with a high decrease (isotropy degree = 0.25) corresponds to the anisotropic surface, while the constant curve (isotropy degree = 1) corresponds to the isotropic surface. Each function F(α) is normalized to its zero value F(0).

Fig. 8
Fig. 8

Mean angular scattering curves of four black glasses from the first set of glasses with their anisotropy curves. Each experimental curve has been superimposed with a theoretical curve calculated with a roughness spectrum that is the Hankel transform of the sum of an exponential and Gaussian function. Agreement between calculated and measured curves is very good here. In the case of sample d, we could use a third analytic function for a better agreement for θ > 65°.

Fig. 9
Fig. 9

Mean plane sections of angular scattering curves of four black glasses from the second set of glasses with their anisotropy curves.

Fig. 10
Fig. 10

Mean plane sections of angular scattering curves of different samples of the third set of glasses. The polish quality is very homogeneous for this glass series.

Tables (5)

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Table I Total Integrated Scattering DE of Six Black Glasses Measured After Two Cleanings with an Interval of One Year Between Them: We Observe no Variation of Scattering (1 ppm = 10−6)

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Table II Partially Integrated Scattering (for Different Angular Ranges) of One Sample G5N After Two Cleanings with an Interval of One Year Between Them: Angular Scattering Remains Practically the Same

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Table III Total Integrated Scattering DE of Five Black Glasses Measured After Two Cleanings with an Interval of One Year Between Them: There is a Slight Increase in Scattering

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Table IV Total Integrated Scattering D E 1 and D E 2 of Six Black Glasses Measured In Two Different Zones Σ1 and Σ2

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Table V Parameters for Gaussian and Exponential Functions that Characterize Defects of Four Samples from the First Set of Glasses (samples a, b, c, and d of Fig. 8)

Equations (12)

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Γ ( τ ) = δ g 2 exp [ ( τ / L g ) 2 ] + δ e 2 exp ( | τ / L e | ) , γ ( σ ) = π δ g 2 L g 2 exp [ ( σ L g / 2 ) 2 ] + 2 π δ e 2 L e 2 ( 1 + σ 2 L e 2 ) 3 / 2 ,
11 ppm D E 18 ppm for set 3 , 12 ppm D E 25 ppm for set 4 .
( δ e ; L e ) = ( 1 nm ; 3000 nm ) ( δ g ; L g ) = ( 0 . 5 nm ; 200 nm ) .
( δ e ; L e ) = ( 1 nm ; 4000 nm ) ( δ g ; L g ) = ( 0 . 7 nm ; 200 nm ) .
h ˆ ( σ ) h ˆ ( σ ) * G ˆ ( σ ) * D ˆ ( σ ) * L ˆ ( σ ) = h ˆ ( σ ) * f ˆ ( σ ) , Gaussian distribution of the incident energy Δ σ = 0 . 002 μ m 1 divergence of incident beam Δ σ = 0 . 009 μ m 1 laser bandpass Δ σ = 10 5 μ m 1
Γ m ( τ ) = Γ ( τ ) · g ( τ ) ,
δ 2 = 2 π k σ γ ( σ ) d σ
Γ m = Γ * ( f g )
f = 2 π k 2 J ( k τ ) k τ , g = 2 π 2 J ( τ ) τ ,
δ = δ e 2 + δ g 2
δ = δ e 2 + δ g 2
δ 2 = 2 π k σ γ ( σ ) d σ

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