Abstract

A procedure is described to allow selective cancellation of polarized scattering within optical substrates and multilayers. It is shown how bulk scattering (respectively surface) can be directly eliminated while the remaining roughness (respectively bulk) signal is still measurable. The same procedure can be applied to isolate a single interface or bulk within a stack or to detect slight departure from perfect correlation within multilayers. Experiments and a procedure for selective imaging in random media are described.

© 2008 Optical Society of America

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  1. J. H. Apfel, "Optical coating design with reduced electric field intensity," Appl. Opt. 16, 1880-1885 (1977).
    [CrossRef] [PubMed]
  2. C. Amra, "Minimizing scattering in multilayers: technique for searching optimal realization conditions," in Proceedings of Laser Induced Damage in Optical Materials (NIST, 1987), pp. 265-271.
  3. C. Amra, G. Albrand, and P. Roche, "Theory and application of antiscattering single layers: antiscattering antireflection coatings," Appl. Opt. 25, 2695-2702 (1986).
    [CrossRef] [PubMed]
  4. H. Giovannini and C. Amra, "Dielectric thin films for maximized absorption with standard quality black surfaces," Appl. Opt. 37, 103-105 (1998).
    [CrossRef]
  5. 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]
  6. O. Gilbert, C. Deumie, and C. Amra, "Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks," Opt. Express 13, 2403-2418 (2005).
    [CrossRef] [PubMed]
  7. C. Amra, C. Grezes-Besset, and L. Bruel, "Comparison of surface and bulk scattering in optical multilayers," Appl. Opt. 32, 5492-5503 (1993).
    [CrossRef] [PubMed]
  8. S. Maure, G. Albrand, and C. Amra, "Low-level scattering and localized defects," Appl. Opt. 35, 5573-5582 (1996).
    [CrossRef] [PubMed]
  9. C. Deumie, H. Giovannini, and C. Amra, "Ellipsometry of light scattering from multilayer coatings," Appl. Opt. 35, 5600-5608 (1996).
    [CrossRef] [PubMed]
  10. T. A. Germer and C. C. Asmail, "Polarization of light scattered by microrough surfaces and subsurface defects," J. Opt. Soc. Am. A 16, 1326-1332 (1999).
    [CrossRef]
  11. T. A. Germer and C. C. Asmail, "Goniometric optical scatter instrument for out-of-plane ellipsometry measurements," Rev. Sci. Instrum. 70, 3688-3695 (1999).
    [CrossRef]
  12. T. A. Germer, C. C. Asmail, and B. T. Scheer, "Polarization of out-of-plane scattering from microrough silicon," Opt. Lett. 22, 1284-1286 (1997).
    [CrossRef]
  13. T. A. Germer, "Measuring interfacial roughness by polarized optical scattering," in Light Scattering and Nanoscale Surface Roughness, A. A. Maradudin, ed. (Springer, 2007), Chap. 10, pp. 259-284.
    [CrossRef]
  14. T. A. Germer, "Measurement of roughness of two interfaces of a dielectric film by scattering ellipsometry," Phys. Rev. Lett. 85, 349-352 (2000).
    [CrossRef] [PubMed]
  15. G. Georges, C. Deumié, and C. Amra, "Selective probing and imaging in random media based on the elimination of polarized scattering," Opt. Express 15, 9804-9816 (2007).
    [CrossRef] [PubMed]
  16. 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, 3207-3219 (1983).
    [CrossRef] [PubMed]
  17. 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, 1304-1313 (1992).
    [CrossRef] [PubMed]
  18. C. Amra, "First-order vector theory of bulk scattering in optical multilayers," J. Opt. Soc. Am. A 10, 365-374 (1993).
    [CrossRef]
  19. C. Amra and S. Maure, "Electromagnetic power provided by sources within multilayer optics: free space and modal patterns," J. Opt. Soc. Am. A 14, 3102-3113 (1997).
    [CrossRef]
  20. C. Amra and S. Maure, "Mutual coherence and conical pattern of sources optimally excited within multilayer optics," J. Opt. Soc. Am. A 14, 3114-3124 (1997).
    [CrossRef]
  21. C. Deumié, R. Richier, P. Dumas, and C. Amra, "Multiscale roughness in optical multilayers: atomic force microscopy and light scattering," Appl. Opt. 35, 5583-5594 (1996).
    [CrossRef] [PubMed]
  22. L. Arnaud, G. Georges, C. Deumié, and C. Amra, "Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: theoretical analysis," Opt. Commun. doi:10.1016/j.optcom.2007.11.013.
  23. C. Amra, J. H. Apfel, and E. Pelletier, "Role of interface correlation in light scattering by a multilayer," Appl. Opt. 31, 3134-3151 (1992).
    [CrossRef] [PubMed]
  24. C. Amra, D. Torricini, and P. Roche, "Multiwavelength (0.45 μm-10.6 μm) angle-resolved scatterometer or how to extend the optical window," Appl. Opt. 32, 5462-5474 (1993).
    [CrossRef] [PubMed]
  25. C. Amra and C. Deumié, "Z-probing of optical multilayers: theory," Opt. Lett. 31, 2704-2706 (2006).
    [CrossRef] [PubMed]

2007 (2)

T. A. Germer, "Measuring interfacial roughness by polarized optical scattering," in Light Scattering and Nanoscale Surface Roughness, A. A. Maradudin, ed. (Springer, 2007), Chap. 10, pp. 259-284.
[CrossRef]

G. Georges, C. Deumié, and C. Amra, "Selective probing and imaging in random media based on the elimination of polarized scattering," Opt. Express 15, 9804-9816 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (2)

2000 (1)

T. A. Germer, "Measurement of roughness of two interfaces of a dielectric film by scattering ellipsometry," Phys. Rev. Lett. 85, 349-352 (2000).
[CrossRef] [PubMed]

1999 (2)

T. A. Germer and C. C. Asmail, "Polarization of light scattered by microrough surfaces and subsurface defects," J. Opt. Soc. Am. A 16, 1326-1332 (1999).
[CrossRef]

T. A. Germer and C. C. Asmail, "Goniometric optical scatter instrument for out-of-plane ellipsometry measurements," Rev. Sci. Instrum. 70, 3688-3695 (1999).
[CrossRef]

1998 (1)

1997 (3)

T. A. Germer, C. C. Asmail, and B. T. Scheer, "Polarization of out-of-plane scattering from microrough silicon," Opt. Lett. 22, 1284-1286 (1997).
[CrossRef]

C. Amra and S. Maure, "Electromagnetic power provided by sources within multilayer optics: free space and modal patterns," J. Opt. Soc. Am. A 14, 3102-3113 (1997).
[CrossRef]

C. Amra and S. Maure, "Mutual coherence and conical pattern of sources optimally excited within multilayer optics," J. Opt. Soc. Am. A 14, 3114-3124 (1997).
[CrossRef]

1996 (3)

C. Deumié, R. Richier, P. Dumas, and C. Amra, "Multiscale roughness in optical multilayers: atomic force microscopy and light scattering," Appl. Opt. 35, 5583-5594 (1996).
[CrossRef] [PubMed]

S. Maure, G. Albrand, and C. Amra, "Low-level scattering and localized defects," Appl. Opt. 35, 5573-5582 (1996).
[CrossRef] [PubMed]

C. Deumie, H. Giovannini, and C. Amra, "Ellipsometry of light scattering from multilayer coatings," Appl. Opt. 35, 5600-5608 (1996).
[CrossRef] [PubMed]

1993 (3)

C. Amra, C. Grezes-Besset, and L. Bruel, "Comparison of surface and bulk scattering in optical multilayers," Appl. Opt. 32, 5492-5503 (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, D. Torricini, and P. Roche, "Multiwavelength (0.45 μm-10.6 μm) angle-resolved scatterometer or how to extend the optical window," Appl. Opt. 32, 5462-5474 (1993).
[CrossRef] [PubMed]

1992 (2)

C. Amra, J. H. Apfel, and E. Pelletier, "Role of interface correlation in light scattering by a multilayer," Appl. Opt. 31, 3134-3151 (1992).
[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, 1304-1313 (1992).
[CrossRef] [PubMed]

1987 (1)

C. Amra, "Minimizing scattering in multilayers: technique for searching optimal realization conditions," in Proceedings of Laser Induced Damage in Optical Materials (NIST, 1987), pp. 265-271.

1986 (1)

1983 (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, 3207-3219 (1983).
[CrossRef] [PubMed]

1977 (1)

J. H. Apfel, "Optical coating design with reduced electric field intensity," Appl. Opt. 16, 1880-1885 (1977).
[CrossRef] [PubMed]

Albrand, G.

Amra, C.

G. Georges, C. Deumié, and C. Amra, "Selective probing and imaging in random media based on the elimination of polarized scattering," Opt. Express 15, 9804-9816 (2007).
[CrossRef] [PubMed]

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

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

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]

H. Giovannini and C. Amra, "Dielectric thin films for maximized absorption with standard quality black surfaces," Appl. Opt. 37, 103-105 (1998).
[CrossRef]

C. Amra and S. Maure, "Electromagnetic power provided by sources within multilayer optics: free space and modal patterns," J. Opt. Soc. Am. A 14, 3102-3113 (1997).
[CrossRef]

C. Amra and S. Maure, "Mutual coherence and conical pattern of sources optimally excited within multilayer optics," J. Opt. Soc. Am. A 14, 3114-3124 (1997).
[CrossRef]

C. Deumié, R. Richier, P. Dumas, and C. Amra, "Multiscale roughness in optical multilayers: atomic force microscopy and light scattering," Appl. Opt. 35, 5583-5594 (1996).
[CrossRef] [PubMed]

S. Maure, G. Albrand, and C. Amra, "Low-level scattering and localized defects," Appl. Opt. 35, 5573-5582 (1996).
[CrossRef] [PubMed]

C. Deumie, H. Giovannini, and C. Amra, "Ellipsometry of light scattering from multilayer coatings," Appl. Opt. 35, 5600-5608 (1996).
[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, D. Torricini, and P. Roche, "Multiwavelength (0.45 μm-10.6 μm) angle-resolved scatterometer or how to extend the optical window," Appl. Opt. 32, 5462-5474 (1993).
[CrossRef] [PubMed]

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

C. Amra, J. H. Apfel, and E. Pelletier, "Role of interface correlation in light scattering by a multilayer," Appl. Opt. 31, 3134-3151 (1992).
[CrossRef] [PubMed]

C. Amra, "Minimizing scattering in multilayers: technique for searching optimal realization conditions," in Proceedings of Laser Induced Damage in Optical Materials (NIST, 1987), pp. 265-271.

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

L. Arnaud, G. Georges, C. Deumié, and C. Amra, "Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: theoretical analysis," Opt. Commun. doi:10.1016/j.optcom.2007.11.013.

Apfel, J. H.

C. Amra, J. H. Apfel, and E. Pelletier, "Role of interface correlation in light scattering by a multilayer," Appl. Opt. 31, 3134-3151 (1992).
[CrossRef] [PubMed]

J. H. Apfel, "Optical coating design with reduced electric field intensity," Appl. Opt. 16, 1880-1885 (1977).
[CrossRef] [PubMed]

Arnaud, L.

L. Arnaud, G. Georges, C. Deumié, and C. Amra, "Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: theoretical analysis," Opt. Commun. doi:10.1016/j.optcom.2007.11.013.

Asmail, C. C.

T. A. Germer and C. C. Asmail, "Goniometric optical scatter instrument for out-of-plane ellipsometry measurements," Rev. Sci. Instrum. 70, 3688-3695 (1999).
[CrossRef]

T. A. Germer and C. C. Asmail, "Polarization of light scattered by microrough surfaces and subsurface defects," J. Opt. Soc. Am. A 16, 1326-1332 (1999).
[CrossRef]

T. A. Germer, C. C. Asmail, and B. T. Scheer, "Polarization of out-of-plane scattering from microrough silicon," Opt. Lett. 22, 1284-1286 (1997).
[CrossRef]

Bennett, J. M.

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, 3207-3219 (1983).
[CrossRef] [PubMed]

Bruel, L.

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

Bussemer, P.

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, 1304-1313 (1992).
[CrossRef] [PubMed]

Deumie, C.

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

C. Deumie, H. Giovannini, and C. Amra, "Ellipsometry of light scattering from multilayer coatings," Appl. Opt. 35, 5600-5608 (1996).
[CrossRef] [PubMed]

Deumié, C.

G. Georges, C. Deumié, and C. Amra, "Selective probing and imaging in random media based on the elimination of polarized scattering," Opt. Express 15, 9804-9816 (2007).
[CrossRef] [PubMed]

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

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, R. Richier, P. Dumas, and C. Amra, "Multiscale roughness in optical multilayers: atomic force microscopy and light scattering," Appl. Opt. 35, 5583-5594 (1996).
[CrossRef] [PubMed]

L. Arnaud, G. Georges, C. Deumié, and C. Amra, "Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: theoretical analysis," Opt. Commun. doi:10.1016/j.optcom.2007.11.013.

Dumas, P.

C. Deumié, R. Richier, P. Dumas, and C. Amra, "Multiscale roughness in optical multilayers: atomic force microscopy and light scattering," Appl. Opt. 35, 5583-5594 (1996).
[CrossRef] [PubMed]

Duparre, A.

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, 1304-1313 (1992).
[CrossRef] [PubMed]

Elson, J. M.

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, 3207-3219 (1983).
[CrossRef] [PubMed]

Georges, G.

G. Georges, C. Deumié, and C. Amra, "Selective probing and imaging in random media based on the elimination of polarized scattering," Opt. Express 15, 9804-9816 (2007).
[CrossRef] [PubMed]

L. Arnaud, G. Georges, C. Deumié, and C. Amra, "Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: theoretical analysis," Opt. Commun. doi:10.1016/j.optcom.2007.11.013.

Germer, T. A.

T. A. Germer, "Measuring interfacial roughness by polarized optical scattering," in Light Scattering and Nanoscale Surface Roughness, A. A. Maradudin, ed. (Springer, 2007), Chap. 10, pp. 259-284.
[CrossRef]

T. A. Germer, "Measurement of roughness of two interfaces of a dielectric film by scattering ellipsometry," Phys. Rev. Lett. 85, 349-352 (2000).
[CrossRef] [PubMed]

T. A. Germer and C. C. Asmail, "Goniometric optical scatter instrument for out-of-plane ellipsometry measurements," Rev. Sci. Instrum. 70, 3688-3695 (1999).
[CrossRef]

T. A. Germer and C. C. Asmail, "Polarization of light scattered by microrough surfaces and subsurface defects," J. Opt. Soc. Am. A 16, 1326-1332 (1999).
[CrossRef]

T. A. Germer, C. C. Asmail, and B. T. Scheer, "Polarization of out-of-plane scattering from microrough silicon," Opt. Lett. 22, 1284-1286 (1997).
[CrossRef]

Gilbert, O.

Giovannini, H.

H. Giovannini and C. Amra, "Dielectric thin films for maximized absorption with standard quality black surfaces," Appl. Opt. 37, 103-105 (1998).
[CrossRef]

C. Deumie, H. Giovannini, and C. Amra, "Ellipsometry of light scattering from multilayer coatings," Appl. Opt. 35, 5600-5608 (1996).
[CrossRef] [PubMed]

Grezes-Besset, C.

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

Hehl, K.

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, 1304-1313 (1992).
[CrossRef] [PubMed]

Kassam, S.

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, 1304-1313 (1992).
[CrossRef] [PubMed]

Maure, S.

C. Amra and S. Maure, "Electromagnetic power provided by sources within multilayer optics: free space and modal patterns," J. Opt. Soc. Am. A 14, 3102-3113 (1997).
[CrossRef]

C. Amra and S. Maure, "Mutual coherence and conical pattern of sources optimally excited within multilayer optics," J. Opt. Soc. Am. A 14, 3114-3124 (1997).
[CrossRef]

S. Maure, G. Albrand, and C. Amra, "Low-level scattering and localized defects," Appl. Opt. 35, 5573-5582 (1996).
[CrossRef] [PubMed]

Neubert, J.

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, 1304-1313 (1992).
[CrossRef] [PubMed]

Pelletier, E.

C. Amra, J. H. Apfel, and E. Pelletier, "Role of interface correlation in light scattering by a multilayer," Appl. Opt. 31, 3134-3151 (1992).
[CrossRef] [PubMed]

Rahn, J. P.

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, 3207-3219 (1983).
[CrossRef] [PubMed]

Richier, R.

C. Deumié, R. Richier, P. Dumas, and C. Amra, "Multiscale roughness in optical multilayers: atomic force microscopy and light scattering," Appl. Opt. 35, 5583-5594 (1996).
[CrossRef] [PubMed]

Roche, P.

C. Amra, D. Torricini, and P. Roche, "Multiwavelength (0.45 μm-10.6 μm) angle-resolved scatterometer or how to extend the optical window," Appl. Opt. 32, 5462-5474 (1993).
[CrossRef] [PubMed]

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

Scheer, B. T.

Torricini, D.

C. Amra, D. Torricini, and P. Roche, "Multiwavelength (0.45 μm-10.6 μm) angle-resolved scatterometer or how to extend the optical window," Appl. Opt. 32, 5462-5474 (1993).
[CrossRef] [PubMed]

Appl. Opt. (9)

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

S. Maure, G. Albrand, and C. Amra, "Low-level scattering and localized defects," Appl. Opt. 35, 5573-5582 (1996).
[CrossRef] [PubMed]

C. Deumie, H. Giovannini, and C. Amra, "Ellipsometry of light scattering from multilayer coatings," Appl. Opt. 35, 5600-5608 (1996).
[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, 3207-3219 (1983).
[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, 1304-1313 (1992).
[CrossRef] [PubMed]

J. H. Apfel, "Optical coating design with reduced electric field intensity," Appl. Opt. 16, 1880-1885 (1977).
[CrossRef] [PubMed]

C. Deumié, R. Richier, P. Dumas, and C. Amra, "Multiscale roughness in optical multilayers: atomic force microscopy and light scattering," Appl. Opt. 35, 5583-5594 (1996).
[CrossRef] [PubMed]

C. Amra, J. H. Apfel, and E. Pelletier, "Role of interface correlation in light scattering by a multilayer," Appl. Opt. 31, 3134-3151 (1992).
[CrossRef] [PubMed]

C. Amra, D. Torricini, and P. Roche, "Multiwavelength (0.45 μm-10.6 μm) angle-resolved scatterometer or how to extend the optical window," Appl. Opt. 32, 5462-5474 (1993).
[CrossRef] [PubMed]

Appl. Opt. (2)

J. Opt. Soc. Am. A (3)

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

C. Amra and S. Maure, "Electromagnetic power provided by sources within multilayer optics: free space and modal patterns," J. Opt. Soc. Am. A 14, 3102-3113 (1997).
[CrossRef]

T. A. Germer and C. C. Asmail, "Polarization of light scattered by microrough surfaces and subsurface defects," J. Opt. Soc. Am. A 16, 1326-1332 (1999).
[CrossRef]

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

C. Amra and S. Maure, "Mutual coherence and conical pattern of sources optimally excited within multilayer optics," J. Opt. Soc. Am. A 14, 3114-3124 (1997).
[CrossRef]

Opt. Commun. (1)

L. Arnaud, G. Georges, C. Deumié, and C. Amra, "Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: theoretical analysis," Opt. Commun. doi:10.1016/j.optcom.2007.11.013.

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

T. A. Germer, "Measurement of roughness of two interfaces of a dielectric film by scattering ellipsometry," Phys. Rev. Lett. 85, 349-352 (2000).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

T. A. Germer and C. C. Asmail, "Goniometric optical scatter instrument for out-of-plane ellipsometry measurements," Rev. Sci. Instrum. 70, 3688-3695 (1999).
[CrossRef]

Other (2)

T. A. Germer, "Measuring interfacial roughness by polarized optical scattering," in Light Scattering and Nanoscale Surface Roughness, A. A. Maradudin, ed. (Springer, 2007), Chap. 10, pp. 259-284.
[CrossRef]

C. Amra, "Minimizing scattering in multilayers: technique for searching optimal realization conditions," in Proceedings of Laser Induced Damage in Optical Materials (NIST, 1987), pp. 265-271.

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Figures (11)

Fig. 1
Fig. 1

Procedure for scattering cancellation. In (a) the scattering angles are denoted ( θ 0 , ϕ ) , with σ being the tangential wave vector and n being the refractive index of air ( n 0 ) or the substrate ( n s ) . In (b) the wave vector of the scattered wave is denoted k, with A S and A P being the polarization components. Illumination is performed with linear polarization at 45°.

Fig. 2
Fig. 2

(Color online) Poincaré spheres for low-level scattering for (a) surface or bulk and for (b) surface roughness and (c) bulk heterogeneity that scatter the whole incident light (see text). Illumination incidence is normal. Each point plotted on the sphere characterizes the polarization state of the scattered field in the incidence plane at a specific scattering angle in the range (0°, 90°).

Fig. 3
Fig. 3

Surface (bold curve) and bulk (dashed curve) scattering calculated separately for a glass sample ( n s = 1.5 ) at oblique illumination (i = 56°). The curves are quasi-superimposed (see text). The illumination wavelength is 633 n m .

Fig. 4
Fig. 4

Remaining signal when bulk scattering is eliminated (bold curve) and when surface scattering is eliminated (dashed curve). The signals below 10 14 are the numerical noise after cancellation of surface or bulk scattering (see text).

Fig. 5
Fig. 5

Matching values of analyzer angle to eliminate bulk scattering (dashed curve) or surface scattering (bold curve).

Fig. 6
Fig. 6

Matching values of retardation plate to eliminate bulk scattering (dashed line) or surface scattering (bold line).

Fig. 7
Fig. 7

Scattering from the two interfaces (bold curve) of a single thin film illuminated at normal incidence and scattering from the same layer after cancellation of the top interface scattering (dashed curve).

Fig. 8
Fig. 8

Sensitivity of phase term Δ η to cross-correlation coefficients (see text) in a single layer. Curves are calculated for identical roughnesses (bold curve) and in the case where the roughness ratio is 1.01 (dashed curve) between interfaces.

Fig. 9
Fig. 9

(Color online) Schematic view of the scattering apparatus.

Fig. 10
Fig. 10

(Color online) Selective cancellation of the two images of a scattering liquid (see text).

Fig. 11
Fig. 11

Bulk scattering in a lemon gel, before (left) and after (right) f transformation.

Equations (19)

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Δ η = η P η S ,
A S = A S exp ( j η S ) , A P = A P exp ( j η P ) .
f ( A ) = A S cos ψ + A P sin ψ .
tan ψ = A S / A P .
f ( A ) = A S cos ψ + A P sin ψ exp ( j Δ η * ) ,
f ( A ) = cos ψ ( A S + z A P ) ,
z = tan ψ exp ( j Δ η * ) .
z = z 0 ( ψ , Δ η * ) = A S / A P ( θ , ϕ ) f ( z 0 , A ) = 0 ,
tan ψ ( θ , ϕ ) = A S / A P ,
Δ η * ( θ , ϕ ) = π + A r g ( A S / A P ) .
f ( i A i ) = i f ( A i ) ,
z i = A i S / A i P f ( z i , A i ) = 0.
f ( i A i + A * ) = i f ( A i ) + f ( A * ) ,
δ 2 = ( 1 / S ) r h 2 ( r ) d r ,
κ 2 = ( 1 / S ) r [ Δ n ( r ) / n ] 2 d r ,
z i = A i S / A i P f ( A i ) = 0 f ( A ) = i j f ( A j ) .
z i * = j i A j S / j i A j P f ( A ) = f ( A i ) .
γ i j = α i j γ j ,
h i 1 = h i + g i ,

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