Abstract

A globally flat, locally rough, reflecting surface scatters incident radiation in all angular directions. This scattered radiation is depolarized, that is, it is transformed into a different state of polarization from that of the incident radiation. The expected state of polarization of the scattered radiation (described by a Stokes vector where each element is an ensemble average), is different for different materials and for different angles of incidence and detection (where the scattered radiation is measured). The surface properties are described by a Mueller matrix, so that the Stokes vector of thescattered radiation can be obtained by multiplying the Stokes vector of the incident radiation to the matrix. Many elements in the matrix are always zero, or only sometimes zero, depending on the material and the angle of incidence and detection. An experiment that measures how the nonzero elements change with angles of incidence and scatter for two rough surfaces whose surface profiles have the same statistics is described; however, one is a conductor and the other is a nonconductor. The actual results for the experimental geometry in which the angle, where the scattered radiation is detected, is equal and opposite to the angle of incidence (called specular scatter) are included. In this geometry the angular behavior of the various nonzero matrix elements show marked differences for the two surfaces. The authors postulate that the differences are primarily dependent on the material properties, rather than surface roughness, and that the differences are sufficiently gross to enable them to distinguish a conducting from a nonconducting rough surface. This postulate is reinforced by plotting, for comparison purposes, the theoretical Mueller matrix for a flat dielectric mirror (calculated from the Fresnel reflection coefficients) and the same for a flat metallic mirror. Comparing the polarized state of radiation reflected from a flat surface with the polarized state of radiation scattered from a rough surface shows that the state is largely independent of the roughness and dependent on the conducting properties of the surface.

© 1979 Optical Society of America

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  1. A. K. Fung, "On depolarization of electromagnetic waves backscattered from a rough surface," Planet. Space Sci. 14, 563–568 (1966).
  2. A. K. Fung, "Character of wave depolarization by a perfectly conducting rough surface and its application to earth and moon experiments," Planet. Space Sci. 15, 1337–1347 (1967).
  3. J. Renau, P. K. Cheo, and G. H. Cooper, "Depolarization of linearly polarized EM waves backscattered from rough metals and inhomogeneous dielectrics," J. Opt. Soc. Am. 57, 459–466 (1967).
  4. T. Hagfors, "A study of the depolarization of lunar radar echoes," Radio Sci. 2, 445–465 (1967).
  5. P. K. Cheo and J. Renau, "Wavelength dependence of total and depolarized backscattered laser light from rough metallic surfaces," J. Opt. Soc. Am. 59, 821–826 (1969).
  6. G. J. Wilhelmi, J. W. Rouse, Jr., and A. J. Blanchard, "Depolarization of light backscattered from rough dielectrics," J. Opt. Soc. Am. 65, 1036–1042 (1975).
  7. G. J. Wilhelmi, J. C. Leader, and W. A. J. Dalton, "Cross-polarized target signature measurements," Appl. Opt. 15, 1837–1941 (1976).
  8. J. C. Leader, "Incoherent backscatter from rough surfaces: the two-scale model reexamined," Radio Sci. 13, 441–457 (1978).
  9. K. M. Mitzner, "Change in polarization on reflection from a tilted plane," Radio Sci. 1, 27–29 (1966).
  10. P. Beckman, The Depolarization of Electromagnetic Waves (Golem, Boulder, 1968).
  11. D. E. Barrick and W. H. Peake, "A review of scattering from the surfaces with different roughness scales," Radio Sci. 3, 865–868 (1968).
  12. D. E. Barrick, "Unacceptable height correlation coefficients and the quasi-specular component in rough surface scattering," Radio Sci. 5, 647–653 (1970).
  13. C. L. Rudder and R. L. Carpenter, "Polarization effects of scattered coherent light on imagery," Appl. Opt. 8, 419–421 (1969).
  14. K. E. Torrance, E. M. Sparrow, and R. C. Birkebak, "Polarization, directional distribution and off-specular peak phenomena in light reflected from roughened surfaces," J. Opt. Soc. Am. 56, 916–925 (1966).
  15. D. W. Berreman, "Reflectance and ellipsometry when submicroscopic particles bestrew a surface," J. Opt. Soc. Am. 60, 499–505 (1970).
  16. T. Smith, "Effect of surface roughness on ellipsometry of aluminum," Surf. Sci. 56, 252–271 (1976).
  17. N. George, A. Jain, and R. D. S. Melville, Jr., "Speckle, diffusers and depolarization," Appl. Phys. 6, 65–70 (1975).
  18. K. Brudzewski, "Effect of surface roughness on change of the polarization state of light reflected from silicon and germanium," Appl. Opt. 15, 115–119 (1976).
  19. M. J. Walker, "Matrix calculus and the stokes parameters of polarized radiation," Am. J. Phys. 22, 170–174 (1954).
  20. F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1976).
  21. H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  22. W. G. Egan, J. Grusauskas, and H. B. Hallock, "Optical depolarization properties of surfaces illuminated by coherent light," Appl. Opt. 7, 1529–1534 (1968).
  23. D. C. Carmer and M. E. Bair, "Some polarization characteristics of magnesium oxide and other diffuse reflectors," Appl. Opt. 8, 1597–1605 (1969).
  24. A. C. Holland and G. Gagne, "The scattering of polarized light by polydisperse systems of irregular particles," Appl. Opt. 9, 1113–1121 (1970).
  25. J. C. Leader and W. A. Dalton, "Bidirectional scattering of electromagnetic waves from the volume of dielectric materials," J. Appl. Phys. 43, 3080–3090 (1972).
  26. P. S. Hauge, "Mueller matrix ellipsometry with imperfect compensators," J. Opt. Soc. Am. 68, 1518–1528 (1978).

1978 (2)

J. C. Leader, "Incoherent backscatter from rough surfaces: the two-scale model reexamined," Radio Sci. 13, 441–457 (1978).

P. S. Hauge, "Mueller matrix ellipsometry with imperfect compensators," J. Opt. Soc. Am. 68, 1518–1528 (1978).

1976 (3)

1975 (2)

N. George, A. Jain, and R. D. S. Melville, Jr., "Speckle, diffusers and depolarization," Appl. Phys. 6, 65–70 (1975).

G. J. Wilhelmi, J. W. Rouse, Jr., and A. J. Blanchard, "Depolarization of light backscattered from rough dielectrics," J. Opt. Soc. Am. 65, 1036–1042 (1975).

1972 (1)

J. C. Leader and W. A. Dalton, "Bidirectional scattering of electromagnetic waves from the volume of dielectric materials," J. Appl. Phys. 43, 3080–3090 (1972).

1970 (3)

1969 (3)

1968 (2)

W. G. Egan, J. Grusauskas, and H. B. Hallock, "Optical depolarization properties of surfaces illuminated by coherent light," Appl. Opt. 7, 1529–1534 (1968).

D. E. Barrick and W. H. Peake, "A review of scattering from the surfaces with different roughness scales," Radio Sci. 3, 865–868 (1968).

1967 (3)

A. K. Fung, "Character of wave depolarization by a perfectly conducting rough surface and its application to earth and moon experiments," Planet. Space Sci. 15, 1337–1347 (1967).

J. Renau, P. K. Cheo, and G. H. Cooper, "Depolarization of linearly polarized EM waves backscattered from rough metals and inhomogeneous dielectrics," J. Opt. Soc. Am. 57, 459–466 (1967).

T. Hagfors, "A study of the depolarization of lunar radar echoes," Radio Sci. 2, 445–465 (1967).

1966 (3)

A. K. Fung, "On depolarization of electromagnetic waves backscattered from a rough surface," Planet. Space Sci. 14, 563–568 (1966).

K. M. Mitzner, "Change in polarization on reflection from a tilted plane," Radio Sci. 1, 27–29 (1966).

K. E. Torrance, E. M. Sparrow, and R. C. Birkebak, "Polarization, directional distribution and off-specular peak phenomena in light reflected from roughened surfaces," J. Opt. Soc. Am. 56, 916–925 (1966).

1954 (1)

M. J. Walker, "Matrix calculus and the stokes parameters of polarized radiation," Am. J. Phys. 22, 170–174 (1954).

Bair, M. E.

Barrick, D. E.

D. E. Barrick, "Unacceptable height correlation coefficients and the quasi-specular component in rough surface scattering," Radio Sci. 5, 647–653 (1970).

D. E. Barrick and W. H. Peake, "A review of scattering from the surfaces with different roughness scales," Radio Sci. 3, 865–868 (1968).

Beckman, P.

P. Beckman, The Depolarization of Electromagnetic Waves (Golem, Boulder, 1968).

Berreman, D. W.

Birkebak, R. C.

Blanchard, A. J.

Brudzewski, K.

Carmer, D. C.

Carpenter, R. L.

Cheo, P. K.

Cooper, G. H.

Dalton, W. A.

J. C. Leader and W. A. Dalton, "Bidirectional scattering of electromagnetic waves from the volume of dielectric materials," J. Appl. Phys. 43, 3080–3090 (1972).

Dalton, W. A. J.

Egan, W. G.

Fung, A. K.

A. K. Fung, "Character of wave depolarization by a perfectly conducting rough surface and its application to earth and moon experiments," Planet. Space Sci. 15, 1337–1347 (1967).

A. K. Fung, "On depolarization of electromagnetic waves backscattered from a rough surface," Planet. Space Sci. 14, 563–568 (1966).

Gagne, G.

George, N.

N. George, A. Jain, and R. D. S. Melville, Jr., "Speckle, diffusers and depolarization," Appl. Phys. 6, 65–70 (1975).

Grusauskas, J.

Hagfors, T.

T. Hagfors, "A study of the depolarization of lunar radar echoes," Radio Sci. 2, 445–465 (1967).

Hallock, H. B.

Hauge, P. S.

P. S. Hauge, "Mueller matrix ellipsometry with imperfect compensators," J. Opt. Soc. Am. 68, 1518–1528 (1978).

Holland, A. C.

Jain, A.

N. George, A. Jain, and R. D. S. Melville, Jr., "Speckle, diffusers and depolarization," Appl. Phys. 6, 65–70 (1975).

Jenkins, F. A.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1976).

Leader, J. C.

J. C. Leader, "Incoherent backscatter from rough surfaces: the two-scale model reexamined," Radio Sci. 13, 441–457 (1978).

G. J. Wilhelmi, J. C. Leader, and W. A. J. Dalton, "Cross-polarized target signature measurements," Appl. Opt. 15, 1837–1941 (1976).

J. C. Leader and W. A. Dalton, "Bidirectional scattering of electromagnetic waves from the volume of dielectric materials," J. Appl. Phys. 43, 3080–3090 (1972).

Melville, Jr., R. D. S.

N. George, A. Jain, and R. D. S. Melville, Jr., "Speckle, diffusers and depolarization," Appl. Phys. 6, 65–70 (1975).

Mitzner, K. M.

K. M. Mitzner, "Change in polarization on reflection from a tilted plane," Radio Sci. 1, 27–29 (1966).

Peake, W. H.

D. E. Barrick and W. H. Peake, "A review of scattering from the surfaces with different roughness scales," Radio Sci. 3, 865–868 (1968).

Renau, J.

Rouse, Jr., J. W.

Rudder, C. L.

Smith, T.

T. Smith, "Effect of surface roughness on ellipsometry of aluminum," Surf. Sci. 56, 252–271 (1976).

Sparrow, E. M.

Torrance, K. E.

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Walker, M. J.

M. J. Walker, "Matrix calculus and the stokes parameters of polarized radiation," Am. J. Phys. 22, 170–174 (1954).

White, H. E.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1976).

Wilhelmi, G. J.

Am. J. Phys. (1)

M. J. Walker, "Matrix calculus and the stokes parameters of polarized radiation," Am. J. Phys. 22, 170–174 (1954).

Appl. Opt. (6)

Appl. Phys. (1)

N. George, A. Jain, and R. D. S. Melville, Jr., "Speckle, diffusers and depolarization," Appl. Phys. 6, 65–70 (1975).

J. Appl. Phys. (1)

J. C. Leader and W. A. Dalton, "Bidirectional scattering of electromagnetic waves from the volume of dielectric materials," J. Appl. Phys. 43, 3080–3090 (1972).

J. Opt. Soc. Am. (6)

Planet. Space Sci. (2)

A. K. Fung, "On depolarization of electromagnetic waves backscattered from a rough surface," Planet. Space Sci. 14, 563–568 (1966).

A. K. Fung, "Character of wave depolarization by a perfectly conducting rough surface and its application to earth and moon experiments," Planet. Space Sci. 15, 1337–1347 (1967).

Radio Sci. (5)

T. Hagfors, "A study of the depolarization of lunar radar echoes," Radio Sci. 2, 445–465 (1967).

J. C. Leader, "Incoherent backscatter from rough surfaces: the two-scale model reexamined," Radio Sci. 13, 441–457 (1978).

K. M. Mitzner, "Change in polarization on reflection from a tilted plane," Radio Sci. 1, 27–29 (1966).

D. E. Barrick and W. H. Peake, "A review of scattering from the surfaces with different roughness scales," Radio Sci. 3, 865–868 (1968).

D. E. Barrick, "Unacceptable height correlation coefficients and the quasi-specular component in rough surface scattering," Radio Sci. 5, 647–653 (1970).

Surf. Sci. (1)

T. Smith, "Effect of surface roughness on ellipsometry of aluminum," Surf. Sci. 56, 252–271 (1976).

Other (3)

P. Beckman, The Depolarization of Electromagnetic Waves (Golem, Boulder, 1968).

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1976).

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

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