Abstract

An ellipsometric technique based on angle-resolved light scattering is addressed to open applications in the field of imaging in random media. The first experimental demonstration is given to prove the selective extinction of different scattering sources such as surface roughness and bulk heterogeneity in optical components and liquids. The results are compared with theory.

© 2007 Optical Society of America

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References

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  1. J. M. Elson, J. P. Rahn, and 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. 22,3207-19 (1983).
    [CrossRef] [PubMed]
  2. S. Kassam, A. Duparre, K. Hehl, P. Bussemer, and J. Neubert, "Light scattering from the volume of optical thin films: theory and experiment," Appl. Opt. 31,1304-13 (1992).
    [CrossRef] [PubMed]
  3. C. Amra, "From light scattering to the microstructure of thin-film multilayers," Appl. Opt. 32,5481-91 (1993).
    [CrossRef] [PubMed]
  4. C. Amra, J. H. Apfel, and E. Pelletier, "Role of interface correlation in light scattering by a multilayer," Appl. Opt. 31,3134-51 (1992).
    [CrossRef] [PubMed]
  5. C. Amra, C. Grezes-Besset, and L. Bruel, "Comparison of surface and bulk scattering in optical multilayers," Appl. Opt. 32,5492-503 (1993).
    [CrossRef] [PubMed]
  6. T. A. Germer and C. C. Asmail, "Polarization of light scattered by microrough surfaces and subsurface defects," J. Opt. Soc. Am. A 16,1326-32 (1999).
    [CrossRef]
  7. S. Maure, G. Albrand, and C. Amra, "Low-level scattering and localized defects," Appl. Opt. 35,5573-82 (1996).
    [CrossRef] [PubMed]
  8. C. Amra, G. Albrand, and P. Roche, "Theory and application of antiscattering single layers: antiscattering antireflection coatings," Appl. Opt. 25,2695-702 (1986).
    [CrossRef] [PubMed]
  9. J. H. Apfel, "Optical coating design with reduced electric field intensity," Appl. Opt. 16,1880-5 (1977).
    [CrossRef] [PubMed]
  10. T. A. Germer and C. C. Asmail, "Goniometric optical scatter instrument for out-of-plane ellipsometry measurements," Rev. Sci. Instrum. 70,3688-95 (1999).
    [CrossRef]
  11. C. Deumie, H. Giovannini, and C. Amra, "Ellipsometry of light scattering from multilayer coatings," Appl. Opt. 35,5600-8 (1996).
    [CrossRef] [PubMed]
  12. O. Gilbert, C. Deumie, and C. Amra, "Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks," Opt. Exp. 13,2403-2418 (2005).
    [CrossRef]
  13. C. Deumié, O. Gilbert, G. Georges, L. Arnaud, and C. Amra, "Ellipsometry of reflected and scattered fields for the analysis of substrates optical quality," Appl. Opt. 45,1640-1649 (2005).
    [CrossRef]
  14. C. Amra, C. Deumié, and O. Gilbert, "Elimination of polarized light scattered by surface roughness or bulk heterogeneity," Opt. Express. 13,10854-10864 (2005).
    [CrossRef] [PubMed]
  15. C. Amra and C. Deumié, "Z-probing of optical multilayers: theory," Opt. Lett. 31,2704-2706 (2006).
    [CrossRef] [PubMed]
  16. C. Amra, "First-order vector theory of bulk scattering in optical multilayers," J. Opt. Soc. Am. A 10,365-374 (1993).
    [CrossRef]
  17. C. Amra, "Light scattering from multilayer optics. I. Tools of investigation," J. Opt. Soc. Am. A 11,197-210 (1994).
    [CrossRef]
  18. I. Grillo, "Small-angle neutron scattering study of a world-wide known emulsion: Le Pastis," Colloids and surfaces A 225,153-160 (2003).
    [CrossRef]

2006

2005

O. Gilbert, C. Deumie, and C. Amra, "Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks," Opt. Exp. 13,2403-2418 (2005).
[CrossRef]

C. Amra, C. Deumié, and O. Gilbert, "Elimination of polarized light scattered by surface roughness or bulk heterogeneity," Opt. Express. 13,10854-10864 (2005).
[CrossRef] [PubMed]

C. Deumié, O. Gilbert, G. Georges, L. Arnaud, and C. Amra, "Ellipsometry of reflected and scattered fields for the analysis of substrates optical quality," Appl. Opt. 45,1640-1649 (2005).
[CrossRef]

2003

I. Grillo, "Small-angle neutron scattering study of a world-wide known emulsion: Le Pastis," Colloids and surfaces A 225,153-160 (2003).
[CrossRef]

1999

T. A. Germer and C. C. Asmail, "Polarization of light scattered by microrough surfaces and subsurface defects," J. Opt. Soc. Am. A 16,1326-32 (1999).
[CrossRef]

T. A. Germer and C. C. Asmail, "Goniometric optical scatter instrument for out-of-plane ellipsometry measurements," Rev. Sci. Instrum. 70,3688-95 (1999).
[CrossRef]

1996

1994

1993

1992

1986

1983

1977

Albrand, G.

Amra, C.

C. Amra and C. Deumié, "Z-probing of optical multilayers: theory," Opt. Lett. 31,2704-2706 (2006).
[CrossRef] [PubMed]

C. Deumié, O. Gilbert, G. Georges, L. Arnaud, and C. Amra, "Ellipsometry of reflected and scattered fields for the analysis of substrates optical quality," Appl. Opt. 45,1640-1649 (2005).
[CrossRef]

C. Amra, C. Deumié, and O. Gilbert, "Elimination of polarized light scattered by surface roughness or bulk heterogeneity," Opt. Express. 13,10854-10864 (2005).
[CrossRef] [PubMed]

O. Gilbert, C. Deumie, and C. Amra, "Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks," Opt. Exp. 13,2403-2418 (2005).
[CrossRef]

S. Maure, G. Albrand, and C. Amra, "Low-level scattering and localized defects," Appl. Opt. 35,5573-82 (1996).
[CrossRef] [PubMed]

C. Deumie, H. Giovannini, and C. Amra, "Ellipsometry of light scattering from multilayer coatings," Appl. Opt. 35,5600-8 (1996).
[CrossRef] [PubMed]

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

C. Amra, C. Grezes-Besset, and L. Bruel, "Comparison of surface and bulk scattering in optical multilayers," Appl. Opt. 32,5492-503 (1993).
[CrossRef] [PubMed]

C. Amra, "From light scattering to the microstructure of thin-film multilayers," Appl. Opt. 32,5481-91 (1993).
[CrossRef] [PubMed]

C. Amra, "First-order vector theory of bulk scattering in optical multilayers," J. Opt. Soc. Am. A 10,365-374 (1993).
[CrossRef]

C. Amra, J. H. Apfel, and E. Pelletier, "Role of interface correlation in light scattering by a multilayer," Appl. Opt. 31,3134-51 (1992).
[CrossRef] [PubMed]

C. Amra, G. Albrand, and P. Roche, "Theory and application of antiscattering single layers: antiscattering antireflection coatings," Appl. Opt. 25,2695-702 (1986).
[CrossRef] [PubMed]

Apfel, J. H.

Arnaud, L.

Asmail, C. C.

T. A. Germer and C. C. Asmail, "Polarization of light scattered by microrough surfaces and subsurface defects," J. Opt. Soc. Am. A 16,1326-32 (1999).
[CrossRef]

T. A. Germer and C. C. Asmail, "Goniometric optical scatter instrument for out-of-plane ellipsometry measurements," Rev. Sci. Instrum. 70,3688-95 (1999).
[CrossRef]

Bennett, J. M.

Bruel, L.

Bussemer, P.

Deumie, C.

O. Gilbert, C. Deumie, and C. Amra, "Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks," Opt. Exp. 13,2403-2418 (2005).
[CrossRef]

C. Deumie, H. Giovannini, and C. Amra, "Ellipsometry of light scattering from multilayer coatings," Appl. Opt. 35,5600-8 (1996).
[CrossRef] [PubMed]

Deumié, C.

Duparre, A.

Elson, J. M.

Georges, G.

Germer, T. A.

T. A. Germer and C. C. Asmail, "Polarization of light scattered by microrough surfaces and subsurface defects," J. Opt. Soc. Am. A 16,1326-32 (1999).
[CrossRef]

T. A. Germer and C. C. Asmail, "Goniometric optical scatter instrument for out-of-plane ellipsometry measurements," Rev. Sci. Instrum. 70,3688-95 (1999).
[CrossRef]

Gilbert, O.

C. Deumié, O. Gilbert, G. Georges, L. Arnaud, and C. Amra, "Ellipsometry of reflected and scattered fields for the analysis of substrates optical quality," Appl. Opt. 45,1640-1649 (2005).
[CrossRef]

C. Amra, C. Deumié, and O. Gilbert, "Elimination of polarized light scattered by surface roughness or bulk heterogeneity," Opt. Express. 13,10854-10864 (2005).
[CrossRef] [PubMed]

O. Gilbert, C. Deumie, and C. Amra, "Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks," Opt. Exp. 13,2403-2418 (2005).
[CrossRef]

Giovannini, H.

Grezes-Besset, C.

Grillo, I.

I. Grillo, "Small-angle neutron scattering study of a world-wide known emulsion: Le Pastis," Colloids and surfaces A 225,153-160 (2003).
[CrossRef]

Hehl, K.

Kassam, S.

Maure, S.

Neubert, J.

Pelletier, E.

Rahn, J. P.

Roche, P.

Appl. Opt.

J. H. Apfel, "Optical coating design with reduced electric field intensity," Appl. Opt. 16,1880-5 (1977).
[CrossRef] [PubMed]

J. M. Elson, J. P. Rahn, and 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. 22,3207-19 (1983).
[CrossRef] [PubMed]

C. Amra, G. Albrand, and P. Roche, "Theory and application of antiscattering single layers: antiscattering antireflection coatings," Appl. Opt. 25,2695-702 (1986).
[CrossRef] [PubMed]

C. Amra, J. H. Apfel, and E. Pelletier, "Role of interface correlation in light scattering by a multilayer," Appl. Opt. 31,3134-51 (1992).
[CrossRef] [PubMed]

C. Amra, "From light scattering to the microstructure of thin-film multilayers," Appl. Opt. 32,5481-91 (1993).
[CrossRef] [PubMed]

C. Deumie, H. Giovannini, and C. Amra, "Ellipsometry of light scattering from multilayer coatings," Appl. Opt. 35,5600-8 (1996).
[CrossRef] [PubMed]

S. Kassam, A. Duparre, K. Hehl, P. Bussemer, and J. Neubert, "Light scattering from the volume of optical thin films: theory and experiment," Appl. Opt. 31,1304-13 (1992).
[CrossRef] [PubMed]

C. Amra, C. Grezes-Besset, and L. Bruel, "Comparison of surface and bulk scattering in optical multilayers," Appl. Opt. 32,5492-503 (1993).
[CrossRef] [PubMed]

S. Maure, G. Albrand, and C. Amra, "Low-level scattering and localized defects," Appl. Opt. 35,5573-82 (1996).
[CrossRef] [PubMed]

C. Deumié, O. Gilbert, G. Georges, L. Arnaud, and C. Amra, "Ellipsometry of reflected and scattered fields for the analysis of substrates optical quality," Appl. Opt. 45,1640-1649 (2005).
[CrossRef]

Colloids and surfaces A

I. Grillo, "Small-angle neutron scattering study of a world-wide known emulsion: Le Pastis," Colloids and surfaces A 225,153-160 (2003).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Exp.

O. Gilbert, C. Deumie, and C. Amra, "Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks," Opt. Exp. 13,2403-2418 (2005).
[CrossRef]

Opt. Express.

C. Amra, C. Deumié, and O. Gilbert, "Elimination of polarized light scattered by surface roughness or bulk heterogeneity," Opt. Express. 13,10854-10864 (2005).
[CrossRef] [PubMed]

Opt. Lett.

Rev. Sci. Instrum.

T. A. Germer and C. C. Asmail, "Goniometric optical scatter instrument for out-of-plane ellipsometry measurements," Rev. Sci. Instrum. 70,3688-95 (1999).
[CrossRef]

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Figures (11)

Fig. 1.
Fig. 1.

Light scattering is recorded at each direction θ through a rotating analyzer and a tunable retardation plate

Fig. 2.
Fig. 2.

Depending on the analyzer and the retardation plate that are matched for selective extinction conditions, different combinations can be observed, such as the total field diffracted or scattered from the two objects (a), the field diffracted from one or the other object (b–c), or the interaction between objects (d)

Fig. 3.
Fig. 3.

Analyzer position for normal (i=0°) and oblique (i=50°) illumination - Extinction conditions at wavelength 633 nm - The surface and bulk curves are identical for normal illumination

Fig. 4.
Fig. 4.

Tunable phase term for normal (i=0°) and oblique (i=50°) illumination - Extinction conditions at wavelength 633 nm - All curves are identical except for the surface curve at oblique illumination

Fig. 5.
Fig. 5.

Maximum (left photo) and minimum (right photo) scattering levels recorded from the rough surface illuminated at normal incidence (i=0°) and observed at a 30° scattering angle. The average gray level was N=66 for the left photo, while it was close to the noise (N=2) in the right photo

Fig. 6.
Fig. 6.

Maximum (left photo) and minimum (right photo) scattering levels recorded from the rough surface illuminated at oblique incidence (56°) and observed at a 65° scattering angle. The average gray level was N=254 (overloaded) for the left photo, while it was close to the noise (N=2) in the right photo

Fig. 7.
Fig. 7.

Maximum (left photo) and minimum (right photo) scattering levels from the liquid illuminated at normal incidence and observed at a 30° scattering angle. The average gray level was overloaded (N=254) for the left photo while it was equal to N=52 in the right photo (out of the region containing bubbles that gave N=200).

Fig. 8.
Fig. 8.

Maximum (left photo) and minimum (right photo) scattering levels from the liquid illuminated at oblique incidence (56°) and observed at a 30° scattering angle. The average gray level was overloaded (N=254) for the left photo while it was equal to N=37 in the right photo (out of the region containing bubbles that gave N=184).

Fig. 9.
Fig. 9.

Maximum (left photo) and minimum (right photo) scattering from the two surfaces of a Zerodur sample illuminated at 56° incidence and observed at a 65° scattering angle. The bulk scattering remains practically unchanged (see text for the gray levels).

Fig. 10.
Fig. 10.

Photos recorded for maximum and minimum scattering at normal incidence and 30° scattering angle from a turbid liquid inside a flask with letters applied to the back surface

Fig. 11.
Fig. 11.

Maximum (left photo) and minimum (right photo) scattering levels recorded at 30 degrees for a normally incident beam focused on the boundary between the multilayer coating (central region) and the bare glass substrate

Tables (2)

Tables Icon

Table 1. Comparison of theory and experiment: extinction parameters (see text)

Tables Icon

Table 2. Comparison of theory and experiment: extinction parameters (see text)

Equations (17)

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E = E 1 + E 2 + E 12
f ( E , θ ) = E s ( θ ) + α ( θ ) E p ( θ )
α ( θ ) = tan [ ψ ( θ ) ] exp ( j ( Δ η + Δ η * ( θ ) ) )
f ( E , θ ) = 0 α ( θ ) = α A ( θ ) = E s ( θ ) E p ( θ )
tan [ ψ ( θ ) ] = E s ( θ ) E p ( θ )
Δ η * ( θ ) = π [ Δ δ ( θ ) + Δ η ]
Δ δ ( θ ) = δ p ( θ ) δ s ( θ )
f ( E ) = f ( E 1 + E 2 + E 12 ) = f ( E 1 ) + f ( E 2 ) + f ( E 12 )
f ( E i ) = E is ( θ ) + α ( θ ) E ip ( θ ) with i = 1 or 2
f ( E 12 ) = E 12 s ( θ ) + α ( θ ) E 12 p ( θ )
f ( E i ) = 0 α iA ( θ ) = E is ( θ ) E ip ( θ )
f ( E 12 ) = 0 α 12 A ( θ ) = E 12 s ( θ ) E 12 p ( θ )
f ( E = i = 1 N E i = E 1 N ) = i = 1 N f ( E i ) + f ( E 1 N )
sin θ b = n 2 ( n 2 sin 2 i ) n 2 + ( n 4 1 ) sin 2 i
f ( E ) = f ( E 1 + E 2 + E 12 ) = f ( E 1 ) + f ( E 12 )
f ( E ) = f ( E 1 + E 2 + E 12 ) = f ( E 2 ) + f ( E 12 )
f ( E ) = f ( E i ) f ( E j + E 12 ) = 0

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