Abstract

We have characterized macrorough surfaces by measuring angle-resolved Stokes parameters of scattering. The analysis of the parameters as a function of a virtual scattering angle shows that polarization properties of the scattering in the plane of incidence display a very strong dependence on the surface roughness. The method and results of this analysis have a significant impact on the application of light scattering to the inspection and process-evaluation industry.

© 2010 Optical Society of America

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References

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2009

2002

2000

1999

1996

S. F. Nee, Appl. Opt. 35, 3570 (1996).
[CrossRef]

E. L. Church and J. C. Stover, Proc. SPIE 2862, 54 (1996).
[CrossRef]

1995

1992

1979

D. E. Aspnes, J. B. Theeten, and F. Hottier, Phys. Rev. B 20, 3292 (1979).
[CrossRef]

Amra, C.

Arnaud, L.

Asmail, C. C.

Aspnes, D. E.

D. E. Aspnes, J. B. Theeten, and F. Hottier, Phys. Rev. B 20, 3292 (1979).
[CrossRef]

Aunard, L.

Bickel, W. S.

Chipman, R. A.

J. L. Pezzaniti and R. A. Chipman, Opt. Eng. 34, 1593 (1995).
[CrossRef]

Church, E. L.

E. L. Church and J. C. Stover, Proc. SPIE 2862, 54 (1996).
[CrossRef]

Deumie, C.

Deumié, C.

Georges, G.

Germer, T. A.

Gilbert, O.

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, U.S. National Bureau of Standards monograph, (October 1977).

Hottier, F.

D. E. Aspnes, J. B. Theeten, and F. Hottier, Phys. Rev. B 20, 3292 (1979).
[CrossRef]

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, U.S. National Bureau of Standards monograph, (October 1977).

Hsu, J.

Jin, L.

L. Jin and K. Takizawa, Proc. SPIE 7432, 74320B (2009).
[CrossRef]

Karabacak, T.

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, U.S. National Bureau of Standards monograph, (October 1977).

Lu, T.

Luna, R. E.

Mendex, E. R.

Navarrete, A. G.

Nee, S. F.

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, U.S. National Bureau of Standards monograph, (October 1977).

Pezzaniti, J. L.

J. L. Pezzaniti and R. A. Chipman, Opt. Eng. 34, 1593 (1995).
[CrossRef]

Quayle, B.

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, U.S. National Bureau of Standards monograph, (October 1977).

Sorrentini, J.

Stover, J. C.

E. L. Church and J. C. Stover, Proc. SPIE 2862, 54 (1996).
[CrossRef]

Stowe, M.

Takizawa, K.

L. Jin and K. Takizawa, Proc. SPIE 7432, 74320B (2009).
[CrossRef]

Theeten, J. B.

D. E. Aspnes, J. B. Theeten, and F. Hottier, Phys. Rev. B 20, 3292 (1979).
[CrossRef]

Tompkins, H. G.

H. G. Tompkins, A User's Guide to Ellipsometry (Dover Publications, 1993).

Videen, G.

Wang, G.

Wolfe, W. L.

Zerrad, M.

Zhao, Y.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng.

J. L. Pezzaniti and R. A. Chipman, Opt. Eng. 34, 1593 (1995).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

D. E. Aspnes, J. B. Theeten, and F. Hottier, Phys. Rev. B 20, 3292 (1979).
[CrossRef]

Proc. SPIE

E. L. Church and J. C. Stover, Proc. SPIE 2862, 54 (1996).
[CrossRef]

L. Jin and K. Takizawa, Proc. SPIE 7432, 74320B (2009).
[CrossRef]

Other

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, U.S. National Bureau of Standards monograph, (October 1977).

J.C.Stover, Ed., Proc. SPIE 2541, 2 (1995).

H. G. Tompkins, A User's Guide to Ellipsometry (Dover Publications, 1993).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram showing the in-plane scattering geometry, the various angles used in the analysis, and the measurement geometry.

Fig. 2
Fig. 2

Light scattering from a rough surface of the diffuser. The dashed line represents the average plane. The dotted line in (a) represents the average plane of micro rough surface. (b) Equivalent effective medium on a substrate of the original diffuser material.

Fig. 3
Fig. 3

Normalized Stokes parameter S 1 S 3 (absolute value) and the polarization degree P for three types of diffusers as a function of the virtual scattering angle θ v s at illumination angle of 50°. Circles, diffuser polished by grit size of 240; triangles, diffuser by 600; squares, diffuser by 1500. The dashed line is the Stokes simulated using the facet model for the diffuser ( n = 1.51 ) with no effective medium layer.

Fig. 4
Fig. 4

Normalized Stokes parameters S 1 S 3 and the polarization degree P as a function of the virtual scattering angle θ v s at illumination angles of 30° (solid triangles), 45° (solid squares), 50° (open squares), and 60° (open triangles), respectively.

Equations (8)

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θ i = π θ vs 2 .
S 0 2 S 1 2 + S 2 2 + S 3 2 .
S 0 = S p + I depolarized = R p ( θ vs ) + R s ( θ vs ) + I depolarized ,
S 1 = R p ( θ vs ) R s ( θ vs ) ,
S 2 = 2 R p ( θ vs ) R s ( θ vs ) cos δ ( θ vs ) ,
S 3 = 2 R p ( θ vs ) R s ( θ vs ) sin δ ( θ vs ) ,
P = S p S 0 , ( 0 P 1 ) ,
S p = R s ( θ vs ) + R p ( θ vs ) = S 1 2 + S 2 2 + S 3 2 .

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