Abstract

A study of cross-polarized and copolarized intensities backscattered from roughened aluminum surfaces is presented for both linear and circular incident polarization states. The angular variation of measured Mueller matrices is shown to contain only diagonal elements, as predicted by the reciprocity theorem. The ratio of cross-depolarized to copolarized scattered intensities is significantly larger for circular than for linear input polarization states. In the linear case the ratio saturates beyond 50°, whereas in the circular case the ratio continues to increase monotonically with angle. A phenomenological model for copolarization and cross-polarization intensities is shown to predict the observed behavior of both linear and circular input polarization states up to incident angles of 70°.

© 1998 Optical Society of America

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References

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  1. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).
  2. E. I. Thorsos, D. R. Jackson, “Studies of scattering theory using numerical methods,” Waves Random Media 3, 5165–5190 (1991).
  3. J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).
  4. K. A. O’Donnell, M. E. Knotts, “Polarization-dependence of scattering from one-dimensional rough surfaces,” J. Opt. Soc. Am. A 8, 1126–1131 (1991).
    [CrossRef]
  5. T. R. Michel, M. E. Knotts, K. A. O’Donnell, “Stokes matrix of a one-dimensional perfectly conducting rough surface,” J. Opt. Soc. Am. A 9, 585–596 (1992).
    [CrossRef]
  6. M. E. Knotts, T. R. Michel, K. A. O’Donnell, “Comparisons of theory and experiment in light scattering from a randomly rough surface,” J. Opt. Soc. Am. A 10, 928–941 (1993).
    [CrossRef]
  7. M. E. Knotts, K. A. O’Donnell, “Measurements of light scattering by a series of conducting surfaces with one-dimensional roughness,” J. Opt. Soc. Am. A 11, 697–709 (1994).
    [CrossRef]
  8. J. Cariou, B. Le. Jeune, J. Lotrian, Y. Guern, “Polarization effects of seawater and underwater targets,” Appl. Opt. 29, 1689–1695 (1990).
    [CrossRef] [PubMed]
  9. K. A. O’Donnell, E. R. Mendez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
    [CrossRef]
  10. E. R. Mendez, K. A. O’Donnell, “Observation of depolarization and backscattering enhancement in light scattering from Gaussian random surfaces,” Opt. Commun. 61, 91–95 (1987).
    [CrossRef]
  11. D. L. Jordan, F. Moreno, “Enhanced backscattering and cross depolarization from multiscale surfaces,” J. Opt. Soc. Am. A 10, 1989–1995 (1993).
    [CrossRef]
  12. D. L. Knepp, H. L. Houpis, “Altair VHF/UHF observations of multipath and backscatter enhancement,” IEEE Trans. Antennas Propag. 39, 528–534 (1991).
    [CrossRef]
  13. P. Phu, A. Ishimaru, Y. Kuga, “Copolarized and cross-polarized enhanced backscattering from two-dimensional very rough surfaces at millimeter wave frequencies,” Radio Sci. 29, 1275–1291 (1994).
    [CrossRef]
  14. A. Ishimaru, “Backscattering enhancement from radar cross-sections to electrons and light localizations to rough surface scattering,” IEEE Antennas Propag. Mag. 33, 7–11 (1991).
    [CrossRef]
  15. E. Jakeman, “Scattering by particles on an interface,” Appl. Phys. 27, 198–210 (1994).
  16. J. E. Geake, M. Geake, B. H. Zellner, “Experiments to test theoretical models of the polarization of light by rough surfaces,” Mon. Notes R. Astron. Soc. 210, 89–112 (1984).
  17. M. W. Long, “On the polarization and the wavelength dependence of sea echo,” IEEE Trans. Antennas Propag. AP-13, 749–754 (1965).
    [CrossRef]
  18. H. Goldstein, “Sea Echo,” in Propagation of Short Radio Waves, D. E. Kerr, ed. (Peregrinus, London, 1987), Chap. 7.
  19. E. Jakeman, “A particle model for scattering by two-scale rough surfaces,” in Progress in Electromagnetics Research Symposium (PIERS) (Kluwer/Academic, Dordrecht, The Netherlands, 1994, CD-ROM).
  20. E. Collett, Polarized Light: Fundamentals and Applications (Dekker, New York, 1993), pp. 103–106.
  21. W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985).
    [CrossRef]
  22. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 132.
  23. D. L. Jordan, G. D. Lewis, E. Jakeman, “Emission polarization of roughened glass and aluminum surfaces,” Appl. Opt. 35, 3583–3589 (1996).
    [CrossRef] [PubMed]
  24. G. D. Lewis, D. L. Jordan, “Backscattering Mueller matrices from bead-blasted aluminum surfaces,” in Polarization: Measurement, Analysis, and Remote Sensing, R. A. Chipman, ed., Proc SPIE3121, 434–443 (1997).
  25. S. R. Cloude, “The physical interpretation of eigenvalue problems in optical scattering polarimetry,” in Polarization: Measurement, Analysis, and Remote Sensing, R. A. Chipman, ed., Proc. SPIE3121, 88–99 (1997).
    [CrossRef]
  26. M. Pitter, E. Jakeman, M. Harris, “Heterodyne detection of enhanced backscatter,” Opt. Lett. 22, 393–395 (1997).
    [CrossRef] [PubMed]
  27. D. L. Jordan, “Experimental measurements of optical backscattering from surfaces of roughness comparable to the wavelength and their application to radar sea scattering,” Waves Random Media 5, 41–54 (1995).
    [CrossRef]
  28. J. Renau, P. K. Cheo, H. G. Cooper, “Depolarization of linearly polarized EM waves backscattered from rough metals and inhomogeneous dielectrics,” J. Opt. Soc. Am. 58, 459–466 (1967).
    [CrossRef]
  29. J. V. Evans, T. Hagfors, “Study of radio echoes from the Moon at 23 centimetres wavelength,” J. Geophys. Res. 71, 4871–4889 (1966).
    [CrossRef]
  30. G. Videen, W. L. Wolfe, W. S. Bickel, “Light scattering Mueller matrix for a surface contaminated by a single particle in the Rayleigh limit,” Opt. Eng. 31, 341–343 (1992).
    [CrossRef]
  31. D. L. Jordan, R. C. Hollins, E. Jakeman, “Experimental measurements of non-Gaussian scattering by a fractal diffuser,” Appl. Phys. B 31, 179–186 (1983).
    [CrossRef]

1997

1996

1995

D. L. Jordan, “Experimental measurements of optical backscattering from surfaces of roughness comparable to the wavelength and their application to radar sea scattering,” Waves Random Media 5, 41–54 (1995).
[CrossRef]

1994

M. E. Knotts, K. A. O’Donnell, “Measurements of light scattering by a series of conducting surfaces with one-dimensional roughness,” J. Opt. Soc. Am. A 11, 697–709 (1994).
[CrossRef]

P. Phu, A. Ishimaru, Y. Kuga, “Copolarized and cross-polarized enhanced backscattering from two-dimensional very rough surfaces at millimeter wave frequencies,” Radio Sci. 29, 1275–1291 (1994).
[CrossRef]

E. Jakeman, “Scattering by particles on an interface,” Appl. Phys. 27, 198–210 (1994).

1993

1992

G. Videen, W. L. Wolfe, W. S. Bickel, “Light scattering Mueller matrix for a surface contaminated by a single particle in the Rayleigh limit,” Opt. Eng. 31, 341–343 (1992).
[CrossRef]

T. R. Michel, M. E. Knotts, K. A. O’Donnell, “Stokes matrix of a one-dimensional perfectly conducting rough surface,” J. Opt. Soc. Am. A 9, 585–596 (1992).
[CrossRef]

1991

K. A. O’Donnell, M. E. Knotts, “Polarization-dependence of scattering from one-dimensional rough surfaces,” J. Opt. Soc. Am. A 8, 1126–1131 (1991).
[CrossRef]

D. L. Knepp, H. L. Houpis, “Altair VHF/UHF observations of multipath and backscatter enhancement,” IEEE Trans. Antennas Propag. 39, 528–534 (1991).
[CrossRef]

A. Ishimaru, “Backscattering enhancement from radar cross-sections to electrons and light localizations to rough surface scattering,” IEEE Antennas Propag. Mag. 33, 7–11 (1991).
[CrossRef]

E. I. Thorsos, D. R. Jackson, “Studies of scattering theory using numerical methods,” Waves Random Media 3, 5165–5190 (1991).

1990

1987

K. A. O’Donnell, E. R. Mendez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
[CrossRef]

E. R. Mendez, K. A. O’Donnell, “Observation of depolarization and backscattering enhancement in light scattering from Gaussian random surfaces,” Opt. Commun. 61, 91–95 (1987).
[CrossRef]

1985

W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

1984

J. E. Geake, M. Geake, B. H. Zellner, “Experiments to test theoretical models of the polarization of light by rough surfaces,” Mon. Notes R. Astron. Soc. 210, 89–112 (1984).

1983

D. L. Jordan, R. C. Hollins, E. Jakeman, “Experimental measurements of non-Gaussian scattering by a fractal diffuser,” Appl. Phys. B 31, 179–186 (1983).
[CrossRef]

1967

J. Renau, P. K. Cheo, H. G. Cooper, “Depolarization of linearly polarized EM waves backscattered from rough metals and inhomogeneous dielectrics,” J. Opt. Soc. Am. 58, 459–466 (1967).
[CrossRef]

1966

J. V. Evans, T. Hagfors, “Study of radio echoes from the Moon at 23 centimetres wavelength,” J. Geophys. Res. 71, 4871–4889 (1966).
[CrossRef]

1965

M. W. Long, “On the polarization and the wavelength dependence of sea echo,” IEEE Trans. Antennas Propag. AP-13, 749–754 (1965).
[CrossRef]

Bailey, W. M.

W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Bennett, J. M.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).

Bickel, W. S.

G. Videen, W. L. Wolfe, W. S. Bickel, “Light scattering Mueller matrix for a surface contaminated by a single particle in the Rayleigh limit,” Opt. Eng. 31, 341–343 (1992).
[CrossRef]

W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 132.

Cariou, J.

Cheo, P. K.

J. Renau, P. K. Cheo, H. G. Cooper, “Depolarization of linearly polarized EM waves backscattered from rough metals and inhomogeneous dielectrics,” J. Opt. Soc. Am. 58, 459–466 (1967).
[CrossRef]

Cloude, S. R.

S. R. Cloude, “The physical interpretation of eigenvalue problems in optical scattering polarimetry,” in Polarization: Measurement, Analysis, and Remote Sensing, R. A. Chipman, ed., Proc. SPIE3121, 88–99 (1997).
[CrossRef]

Collett, E.

E. Collett, Polarized Light: Fundamentals and Applications (Dekker, New York, 1993), pp. 103–106.

Cooper, H. G.

J. Renau, P. K. Cheo, H. G. Cooper, “Depolarization of linearly polarized EM waves backscattered from rough metals and inhomogeneous dielectrics,” J. Opt. Soc. Am. 58, 459–466 (1967).
[CrossRef]

Evans, J. V.

J. V. Evans, T. Hagfors, “Study of radio echoes from the Moon at 23 centimetres wavelength,” J. Geophys. Res. 71, 4871–4889 (1966).
[CrossRef]

Geake, J. E.

J. E. Geake, M. Geake, B. H. Zellner, “Experiments to test theoretical models of the polarization of light by rough surfaces,” Mon. Notes R. Astron. Soc. 210, 89–112 (1984).

Geake, M.

J. E. Geake, M. Geake, B. H. Zellner, “Experiments to test theoretical models of the polarization of light by rough surfaces,” Mon. Notes R. Astron. Soc. 210, 89–112 (1984).

Goldstein, H.

H. Goldstein, “Sea Echo,” in Propagation of Short Radio Waves, D. E. Kerr, ed. (Peregrinus, London, 1987), Chap. 7.

Guern, Y.

Hagfors, T.

J. V. Evans, T. Hagfors, “Study of radio echoes from the Moon at 23 centimetres wavelength,” J. Geophys. Res. 71, 4871–4889 (1966).
[CrossRef]

Harris, M.

Hollins, R. C.

D. L. Jordan, R. C. Hollins, E. Jakeman, “Experimental measurements of non-Gaussian scattering by a fractal diffuser,” Appl. Phys. B 31, 179–186 (1983).
[CrossRef]

Houpis, H. L.

D. L. Knepp, H. L. Houpis, “Altair VHF/UHF observations of multipath and backscatter enhancement,” IEEE Trans. Antennas Propag. 39, 528–534 (1991).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 132.

Ishimaru, A.

P. Phu, A. Ishimaru, Y. Kuga, “Copolarized and cross-polarized enhanced backscattering from two-dimensional very rough surfaces at millimeter wave frequencies,” Radio Sci. 29, 1275–1291 (1994).
[CrossRef]

A. Ishimaru, “Backscattering enhancement from radar cross-sections to electrons and light localizations to rough surface scattering,” IEEE Antennas Propag. Mag. 33, 7–11 (1991).
[CrossRef]

Jackson, D. R.

E. I. Thorsos, D. R. Jackson, “Studies of scattering theory using numerical methods,” Waves Random Media 3, 5165–5190 (1991).

Jakeman, E.

M. Pitter, E. Jakeman, M. Harris, “Heterodyne detection of enhanced backscatter,” Opt. Lett. 22, 393–395 (1997).
[CrossRef] [PubMed]

D. L. Jordan, G. D. Lewis, E. Jakeman, “Emission polarization of roughened glass and aluminum surfaces,” Appl. Opt. 35, 3583–3589 (1996).
[CrossRef] [PubMed]

E. Jakeman, “Scattering by particles on an interface,” Appl. Phys. 27, 198–210 (1994).

D. L. Jordan, R. C. Hollins, E. Jakeman, “Experimental measurements of non-Gaussian scattering by a fractal diffuser,” Appl. Phys. B 31, 179–186 (1983).
[CrossRef]

E. Jakeman, “A particle model for scattering by two-scale rough surfaces,” in Progress in Electromagnetics Research Symposium (PIERS) (Kluwer/Academic, Dordrecht, The Netherlands, 1994, CD-ROM).

Jeune, B. Le.

Jordan, D. L.

D. L. Jordan, G. D. Lewis, E. Jakeman, “Emission polarization of roughened glass and aluminum surfaces,” Appl. Opt. 35, 3583–3589 (1996).
[CrossRef] [PubMed]

D. L. Jordan, “Experimental measurements of optical backscattering from surfaces of roughness comparable to the wavelength and their application to radar sea scattering,” Waves Random Media 5, 41–54 (1995).
[CrossRef]

D. L. Jordan, F. Moreno, “Enhanced backscattering and cross depolarization from multiscale surfaces,” J. Opt. Soc. Am. A 10, 1989–1995 (1993).
[CrossRef]

D. L. Jordan, R. C. Hollins, E. Jakeman, “Experimental measurements of non-Gaussian scattering by a fractal diffuser,” Appl. Phys. B 31, 179–186 (1983).
[CrossRef]

G. D. Lewis, D. L. Jordan, “Backscattering Mueller matrices from bead-blasted aluminum surfaces,” in Polarization: Measurement, Analysis, and Remote Sensing, R. A. Chipman, ed., Proc SPIE3121, 434–443 (1997).

Knepp, D. L.

D. L. Knepp, H. L. Houpis, “Altair VHF/UHF observations of multipath and backscatter enhancement,” IEEE Trans. Antennas Propag. 39, 528–534 (1991).
[CrossRef]

Knotts, M. E.

Kuga, Y.

P. Phu, A. Ishimaru, Y. Kuga, “Copolarized and cross-polarized enhanced backscattering from two-dimensional very rough surfaces at millimeter wave frequencies,” Radio Sci. 29, 1275–1291 (1994).
[CrossRef]

Lewis, G. D.

D. L. Jordan, G. D. Lewis, E. Jakeman, “Emission polarization of roughened glass and aluminum surfaces,” Appl. Opt. 35, 3583–3589 (1996).
[CrossRef] [PubMed]

G. D. Lewis, D. L. Jordan, “Backscattering Mueller matrices from bead-blasted aluminum surfaces,” in Polarization: Measurement, Analysis, and Remote Sensing, R. A. Chipman, ed., Proc SPIE3121, 434–443 (1997).

Long, M. W.

M. W. Long, “On the polarization and the wavelength dependence of sea echo,” IEEE Trans. Antennas Propag. AP-13, 749–754 (1965).
[CrossRef]

Lotrian, J.

Mattsson, L.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).

Mendez, E. R.

E. R. Mendez, K. A. O’Donnell, “Observation of depolarization and backscattering enhancement in light scattering from Gaussian random surfaces,” Opt. Commun. 61, 91–95 (1987).
[CrossRef]

K. A. O’Donnell, E. R. Mendez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
[CrossRef]

Michel, T. R.

Moreno, F.

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).

O’Donnell, K. A.

Phu, P.

P. Phu, A. Ishimaru, Y. Kuga, “Copolarized and cross-polarized enhanced backscattering from two-dimensional very rough surfaces at millimeter wave frequencies,” Radio Sci. 29, 1275–1291 (1994).
[CrossRef]

Pitter, M.

Renau, J.

J. Renau, P. K. Cheo, H. G. Cooper, “Depolarization of linearly polarized EM waves backscattered from rough metals and inhomogeneous dielectrics,” J. Opt. Soc. Am. 58, 459–466 (1967).
[CrossRef]

Thorsos, E. I.

E. I. Thorsos, D. R. Jackson, “Studies of scattering theory using numerical methods,” Waves Random Media 3, 5165–5190 (1991).

Videen, G.

G. Videen, W. L. Wolfe, W. S. Bickel, “Light scattering Mueller matrix for a surface contaminated by a single particle in the Rayleigh limit,” Opt. Eng. 31, 341–343 (1992).
[CrossRef]

Wolfe, W. L.

G. Videen, W. L. Wolfe, W. S. Bickel, “Light scattering Mueller matrix for a surface contaminated by a single particle in the Rayleigh limit,” Opt. Eng. 31, 341–343 (1992).
[CrossRef]

Zellner, B. H.

J. E. Geake, M. Geake, B. H. Zellner, “Experiments to test theoretical models of the polarization of light by rough surfaces,” Mon. Notes R. Astron. Soc. 210, 89–112 (1984).

Am. J. Phys.

W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Appl. Opt.

Appl. Phys.

E. Jakeman, “Scattering by particles on an interface,” Appl. Phys. 27, 198–210 (1994).

Appl. Phys. B

D. L. Jordan, R. C. Hollins, E. Jakeman, “Experimental measurements of non-Gaussian scattering by a fractal diffuser,” Appl. Phys. B 31, 179–186 (1983).
[CrossRef]

IEEE Antennas Propag. Mag.

A. Ishimaru, “Backscattering enhancement from radar cross-sections to electrons and light localizations to rough surface scattering,” IEEE Antennas Propag. Mag. 33, 7–11 (1991).
[CrossRef]

IEEE Trans. Antennas Propag.

M. W. Long, “On the polarization and the wavelength dependence of sea echo,” IEEE Trans. Antennas Propag. AP-13, 749–754 (1965).
[CrossRef]

D. L. Knepp, H. L. Houpis, “Altair VHF/UHF observations of multipath and backscatter enhancement,” IEEE Trans. Antennas Propag. 39, 528–534 (1991).
[CrossRef]

J. Geophys. Res.

J. V. Evans, T. Hagfors, “Study of radio echoes from the Moon at 23 centimetres wavelength,” J. Geophys. Res. 71, 4871–4889 (1966).
[CrossRef]

J. Opt. Soc. Am.

J. Renau, P. K. Cheo, H. G. Cooper, “Depolarization of linearly polarized EM waves backscattered from rough metals and inhomogeneous dielectrics,” J. Opt. Soc. Am. 58, 459–466 (1967).
[CrossRef]

J. Opt. Soc. Am. A

Mon. Notes R. Astron. Soc.

J. E. Geake, M. Geake, B. H. Zellner, “Experiments to test theoretical models of the polarization of light by rough surfaces,” Mon. Notes R. Astron. Soc. 210, 89–112 (1984).

Opt. Commun.

E. R. Mendez, K. A. O’Donnell, “Observation of depolarization and backscattering enhancement in light scattering from Gaussian random surfaces,” Opt. Commun. 61, 91–95 (1987).
[CrossRef]

Opt. Eng.

G. Videen, W. L. Wolfe, W. S. Bickel, “Light scattering Mueller matrix for a surface contaminated by a single particle in the Rayleigh limit,” Opt. Eng. 31, 341–343 (1992).
[CrossRef]

Opt. Lett.

Radio Sci.

P. Phu, A. Ishimaru, Y. Kuga, “Copolarized and cross-polarized enhanced backscattering from two-dimensional very rough surfaces at millimeter wave frequencies,” Radio Sci. 29, 1275–1291 (1994).
[CrossRef]

Waves Random Media

E. I. Thorsos, D. R. Jackson, “Studies of scattering theory using numerical methods,” Waves Random Media 3, 5165–5190 (1991).

D. L. Jordan, “Experimental measurements of optical backscattering from surfaces of roughness comparable to the wavelength and their application to radar sea scattering,” Waves Random Media 5, 41–54 (1995).
[CrossRef]

Other

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 132.

H. Goldstein, “Sea Echo,” in Propagation of Short Radio Waves, D. E. Kerr, ed. (Peregrinus, London, 1987), Chap. 7.

E. Jakeman, “A particle model for scattering by two-scale rough surfaces,” in Progress in Electromagnetics Research Symposium (PIERS) (Kluwer/Academic, Dordrecht, The Netherlands, 1994, CD-ROM).

E. Collett, Polarized Light: Fundamentals and Applications (Dekker, New York, 1993), pp. 103–106.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).

G. D. Lewis, D. L. Jordan, “Backscattering Mueller matrices from bead-blasted aluminum surfaces,” in Polarization: Measurement, Analysis, and Remote Sensing, R. A. Chipman, ed., Proc SPIE3121, 434–443 (1997).

S. R. Cloude, “The physical interpretation of eigenvalue problems in optical scattering polarimetry,” in Polarization: Measurement, Analysis, and Remote Sensing, R. A. Chipman, ed., Proc. SPIE3121, 88–99 (1997).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Experimental arrangement.

Fig. 2
Fig. 2

Scanning-electron micrograph of a bead-blasted aluminum surface. The image was taken at an angle of 50°.

Fig. 3
Fig. 3

Variation of the backscattered intensity and significant Mueller matrix components with target angle (α) for bead-blasted aluminum surfaces of 5 psi (dotted curves), 15 psi (solid curves), and 90 psi (dashed curves).

Fig. 4
Fig. 4

Comparison of cross-polarized and copolarized linear states and cross-polarized and copolarized circular polarization states.

Fig. 5
Fig. 5

Comparison of linear copolar and cross-polar modeled and experimental data for 15-psi blast pressure. Measured data are shown as symbols, where × represents the copolar intensities and + the cross-polar intensities.

Fig. 6
Fig. 6

Comparison of circular copolar and cross-polar modeled and experimental data for 15-psi blast pressure. Measured data are shown as symbols, where + represents the copolar intensities and ○ the cross-polar intensities.

Tables (1)

Tables Icon

Table 1 Surface Statistics (Form Talysurf Profilometer)

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

S = A M S ,
M beadblasted α = m 11 0 0 0 0 m 22 0 0 0 0 - m 22 0 0 0 0 m 11   -   2 m 22 .
I     sec 2   θ a 2 + tan 2 θ v
a HH = α 2 E H 0 r - 1 sin 2   ψ   cos 2   ϕ + 1 , a HV = α 2 E H 0 r - 1 × sin   ψ   cos   ϕ sin   ψ   sin   ϕ   cos   θ s - cos   ψ   sin   θ s , a VV = α 2 E V 0 r - 1 sin   ψ   sin   ϕ   cos   θ s - cos   ψ   sin   θ s × sin   ϕ   sin   ψ   cos   θ i + cos   ψ   sin   θ i + cos θ i + θ s , a VH = α 2 E V 0 r - 1 × sin   ψ   cos   ϕ sin   ψ   sin   ϕ   cos   θ i + cos   ψ   sin   θ i ,
E PQ = a PQ θ i ,   θ s + R P θ i a PQ π - θ i ,   θ s exp if θ i + R Q θ s a PQ θ i ,   π - θ s exp if θ s + R P θ i R Q θ s a PQ π - θ i ,   π - θ s × exp i f θ i + f θ s ,
E HH = α E H 0 r - 1 sin 2   ψ   cos 2   ϕ + 1 × 1 + R H   exp if 2 , E VV = α E V 0 1 - 2 R V exp if cos   2 θ + R V 2 exp 2 if + r - 1 × sin   ψ   sin   ϕ   cos   θ   +   cos   ψ   sin   θ 2 - 2 R V sin 2   ψ   sin 2   ϕ   cos 2   θ   -   cos 2   ψ   sin 2   θ exp if + R V 2 sin   ψ   sin   ϕ   cos   θ   -   cos   ψ   sin   θ 2 × exp 2 if , E HV = α E H 0 r - 1 sin   ψ cos   ϕ 1 + R H   exp if × sin   ψ   sin   ϕ   cos   θ   +   cos   ψ   sin   θ + R V cos   ψ   sin   θ   -   sin   ψ   sin   ϕ   cos   θ ×   exp if ] , E VH = E EV E V 0 / E H 0 .
| E HV | 2 = 4 α | E H 0 | 2 r - 1 2 | 1 + R H exp if | 2 × 1 + | R V | 2 - 2   Re R V   exp if cos   2 θ .
O CO = | E HH + E VV | 2 , O CROSS = | E HH - E VV + 2 iE HV | 2 ,
O CROSS = | α E 0 | 2 r - 1 2 5 + 2 r - 1 3 + 1 × | 2 R H + R V   cos   2 θ + R H 2 - R V 2 exp if | 2 + 4 | α E 0 r - 1 | 2 15 ( 2   Im 2 R V exp if sin 2   2 θ + | 1 + R H   exp if | 2 { 1 + | R V | 2 - 2   Re R V   exp if cos   2 θ } ) .
O CROSS = | 2 α E 0 | 2 1 - cos   2 θ 2 ,

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