Abstract

Previous analytical efforts are extended and combined to describe the intensity of laser radiation scattered bidirectionally from rough-surface materials. Two scales of roughness are employed to effectively model rough-surface scattering phenomena. Laser scattering distributions are computed and compared with experimental data. The internal consistency and frequency dependence of model parameters, derived from data comparisons, are examined. Model parameter analyses and data comparisons support the validity of the scattering model.

© 1979 Optical Society of America

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  1. J. Renau, P. K. Cheo, and H. G. Cooper, "Depolarization of linearlypolarized em waves backscattered from rough metals and inhornogeneousdielectrics," J. Opt. Soc. Am. 57, 459-466 (1967).
  2. P. K. Cheo and J. Renau, "Wavelength dependence of total and depolarized back-scattered laser light from rough metallic surfaces," J. Opt. Soc. Am. 59, 821–826 (1969).
  3. W. G. Egan, J. Grusauskas, and H. B. Hallock, "optical depolarization properties of surfaces illuminated by coherent light," Appl. Opt. 7, 1529–1534 (1968).
  4. A. S. Toporets, "Specular reflection from a rough surface," Opt. Spectrosk. (USSR) 16, 54–58 (1964).
  5. J. Renau and J. A. Collinson, "Measurement of electromagnetic backscattering from known, rough surfaces," Bell Syst. Tech. J. 44, 2203–2226 (1965).
  6. J. C. Leader and W. A. J. Dalton, "Bidirectional scattering of electromagnetic waves from the volume of dielectric materials," J. Appl. Phys. 43, 3080–3088 (1972).
  7. G. J. Wilhelmi, J. W. Rouse, and A. J. Blanchard, "Depolarization of light backscattered from rough dielectrics," J. Opt. Soc. Am. 65, 1036–1042 (1975).
  8. R. A. Sprague, "Surface roughness measurements using whitelight speckle," Appl. Opt. 11, 2811–2816 (1972).
  9. H. Fujii, T. Asakura, and Y. Shindo, "Measurements of surface roughness properties by means of laser speckle techniques," Opt. Commun. 16, 68–72 (1976).
  10. F. E. Nicodemus, "Directional reflectance and emissivity of an opaque surface," Appl. Opt. 4, 767–773 (1965).
  11. G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook (Plenum, New York, 1970), p. 9.
  12. J. C. Leader, "An analysis of the spatial coherence of laser light scattered from a surface with two scales of roughness," J. Opt. Soc. Am. 66, 536–546 (1976).
  13. J. C. Leader, "Incoherent backscatter from rough surfaces: the two-scale model re-examined," Rad. Science 13,441–457 (1978).
  14. J. C. Leader, "Hemispherical scattering of electromagnetic waves from rough surfaces," J. Opt. Soc. Am. 62, 1356 (1972).
  15. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).
  16. B. G. Smith, "Geometrical shadowing of a random rough surface," IEEE Trans. Ant. Propag. AP-15, 668–671 (1967).
  17. B. G. Smith, "Lunar surface roughness: shadowing and thermal emission," J. Geophys. Res. 72, 4059–4067 (1967).
  18. M. I. Sancer, "Shadow-corrected electromagnetic scattering from a randomly rough surface," IEEE Trans. Ant. Propag. AP-17, 577–585 (1969).
  19. P. Beckmann, "Shadowing of random rough surfaces," IEEE Trans. Ant. Propag. AP-13, 384–388 (1965).
  20. R. A. Brockelman and T. Hagfors, "Note on the effect of shadowing on the backscattering of waves from a random rough surface," IEEE Trans. Ant. Propag. AP-14, 621–628 (1966).
  21. G. J. Wilhelmi, J. C. Leader, and W. A. J. Dalton, "Cross-polarized target signature measurements," Appl. Opt. 15, 1837–1841 (1976).
  22. J. C. Leader, D. P. Owsley, and C. R. Fulkerson, "Active Multispectral Data Analysis," RADC Final Report No. RADC-TR-74-190, Aug. 1974.
  23. J. C. Leader, "Polarization dependence in em scattering from Rayleigh scatterers embedded in a dielectric slab. I. Theory," J. Appl. Phys. 46, 4371–4385 (1975).
  24. J. C. Leader and W. A. J. Dalton, "Polarization dependence in em scattering from Rayleigh scatterers embedded in a dielectric slab. II. Experiment," J. Appl. Phys. 46, 4386–4391 (1975).
  25. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  26. G. E. Hunt, "A review of computational techniques for analysing the transfer of radiation through a model cloudy atmosphere," J. Quant. Spectrosc. Radiat. Transfer 11, 655–690 (1971).
  27. J. E. Hansen, "Multiple scattering of polarized light in planetary atmospheres," J. Atmos. Sciences 28, 1400–1426 (1971).
  28. J. P. Theriault and W. S. Otaguro, "Monostatic BDR Measurement," McDonnell Douglas Astronautics Corp. Report MDC G6128, Sept. 1976.
  29. Abromowitz and Segun, Handbook of Mathematical Functions (Dover, New York, 1965).
  30. J. Ohtsubo and T. Asakura, "Statistical properties of laser speckle produced in the diffraction field," Appl. Opt. 16, 1742–1753 (1977).
  31. Reference 26 investigated speckle statistics for laser transmission through a diffuser. The axial direction for the transmission case is equivalent to the specular angle in reflection.
  32. e.g., see Fig. 6 of Ref. 26.
  33. D. L. Fried, "Statistics of the laser radar cross section of a randomly rough target," J. Opt. Soc. Am. 66, 1150–1160 (1976).
  34. J. C. Leader, "Spatial coherence measurements of Rayleigh-scattered light," J. Opt. Soc. Am. 65, 740–741 (1975).
  35. J. C. Leader and J. M. Putnam, "Rough Surface Scattering Code (ROSSCO) User's Manual," McDonnell Douglas Corp. Report MDC Q0619, Vols. I and II, 22 May 1977.
  36. J. C. Leader, "Laser Signature Analyses," McDonnell Douglas Corp. Report MDC Q0611, 22 October 1976.
  37. J. C. Leader, "Spectral and angular dependence of specular scattering from rough surfaces," 1971 URSI Meeting, Washington, D.C., McDonnell Aircraft Paper No. MCAIR 71-013.
  38. J. R. Maxwell and S. Weiner, "Polarized Radiance. Vol. III: Wavelength Dependence of Polarized Bidirectional Radiance," Environmental Research Institute of Michigan, BRL-CR-156, May 1974. Distributed by National Technical Information Service, AD-782 179.

1978 (1)

J. C. Leader, "Incoherent backscatter from rough surfaces: the two-scale model re-examined," Rad. Science 13,441–457 (1978).

1977 (1)

1976 (4)

1975 (4)

J. C. Leader, "Polarization dependence in em scattering from Rayleigh scatterers embedded in a dielectric slab. I. Theory," J. Appl. Phys. 46, 4371–4385 (1975).

J. C. Leader and W. A. J. Dalton, "Polarization dependence in em scattering from Rayleigh scatterers embedded in a dielectric slab. II. Experiment," J. Appl. Phys. 46, 4386–4391 (1975).

J. C. Leader, "Spatial coherence measurements of Rayleigh-scattered light," J. Opt. Soc. Am. 65, 740–741 (1975).

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

1972 (3)

R. A. Sprague, "Surface roughness measurements using whitelight speckle," Appl. Opt. 11, 2811–2816 (1972).

J. C. Leader and W. A. J. Dalton, "Bidirectional scattering of electromagnetic waves from the volume of dielectric materials," J. Appl. Phys. 43, 3080–3088 (1972).

J. C. Leader, "Hemispherical scattering of electromagnetic waves from rough surfaces," J. Opt. Soc. Am. 62, 1356 (1972).

1971 (2)

G. E. Hunt, "A review of computational techniques for analysing the transfer of radiation through a model cloudy atmosphere," J. Quant. Spectrosc. Radiat. Transfer 11, 655–690 (1971).

J. E. Hansen, "Multiple scattering of polarized light in planetary atmospheres," J. Atmos. Sciences 28, 1400–1426 (1971).

1969 (2)

M. I. Sancer, "Shadow-corrected electromagnetic scattering from a randomly rough surface," IEEE Trans. Ant. Propag. AP-17, 577–585 (1969).

P. K. Cheo and J. Renau, "Wavelength dependence of total and depolarized back-scattered laser light from rough metallic surfaces," J. Opt. Soc. Am. 59, 821–826 (1969).

1968 (1)

1967 (3)

J. Renau, P. K. Cheo, and H. G. Cooper, "Depolarization of linearlypolarized em waves backscattered from rough metals and inhornogeneousdielectrics," J. Opt. Soc. Am. 57, 459-466 (1967).

B. G. Smith, "Geometrical shadowing of a random rough surface," IEEE Trans. Ant. Propag. AP-15, 668–671 (1967).

B. G. Smith, "Lunar surface roughness: shadowing and thermal emission," J. Geophys. Res. 72, 4059–4067 (1967).

1966 (1)

R. A. Brockelman and T. Hagfors, "Note on the effect of shadowing on the backscattering of waves from a random rough surface," IEEE Trans. Ant. Propag. AP-14, 621–628 (1966).

1965 (3)

F. E. Nicodemus, "Directional reflectance and emissivity of an opaque surface," Appl. Opt. 4, 767–773 (1965).

P. Beckmann, "Shadowing of random rough surfaces," IEEE Trans. Ant. Propag. AP-13, 384–388 (1965).

J. Renau and J. A. Collinson, "Measurement of electromagnetic backscattering from known, rough surfaces," Bell Syst. Tech. J. 44, 2203–2226 (1965).

1964 (1)

A. S. Toporets, "Specular reflection from a rough surface," Opt. Spectrosk. (USSR) 16, 54–58 (1964).

Asakura, T.

J. Ohtsubo and T. Asakura, "Statistical properties of laser speckle produced in the diffraction field," Appl. Opt. 16, 1742–1753 (1977).

H. Fujii, T. Asakura, and Y. Shindo, "Measurements of surface roughness properties by means of laser speckle techniques," Opt. Commun. 16, 68–72 (1976).

Barrick, D. E.

G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook (Plenum, New York, 1970), p. 9.

Beckmann, P.

P. Beckmann, "Shadowing of random rough surfaces," IEEE Trans. Ant. Propag. AP-13, 384–388 (1965).

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).

Blanchard, A. J.

Brockelman, R. A.

R. A. Brockelman and T. Hagfors, "Note on the effect of shadowing on the backscattering of waves from a random rough surface," IEEE Trans. Ant. Propag. AP-14, 621–628 (1966).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

Cheo, P. K.

Collinson, J. A.

J. Renau and J. A. Collinson, "Measurement of electromagnetic backscattering from known, rough surfaces," Bell Syst. Tech. J. 44, 2203–2226 (1965).

Cooper, H. G.

Dalton, W. A. J.

G. J. Wilhelmi, J. C. Leader, and W. A. J. Dalton, "Cross-polarized target signature measurements," Appl. Opt. 15, 1837–1841 (1976).

J. C. Leader and W. A. J. Dalton, "Polarization dependence in em scattering from Rayleigh scatterers embedded in a dielectric slab. II. Experiment," J. Appl. Phys. 46, 4386–4391 (1975).

J. C. Leader and W. A. J. Dalton, "Bidirectional scattering of electromagnetic waves from the volume of dielectric materials," J. Appl. Phys. 43, 3080–3088 (1972).

Egan, W. G.

Fried, D. L.

Fujii, H.

H. Fujii, T. Asakura, and Y. Shindo, "Measurements of surface roughness properties by means of laser speckle techniques," Opt. Commun. 16, 68–72 (1976).

Fulkerson, C. R.

J. C. Leader, D. P. Owsley, and C. R. Fulkerson, "Active Multispectral Data Analysis," RADC Final Report No. RADC-TR-74-190, Aug. 1974.

Grusauskas, J.

Hagfors, T.

R. A. Brockelman and T. Hagfors, "Note on the effect of shadowing on the backscattering of waves from a random rough surface," IEEE Trans. Ant. Propag. AP-14, 621–628 (1966).

Hallock, H. B.

Hansen, J. E.

J. E. Hansen, "Multiple scattering of polarized light in planetary atmospheres," J. Atmos. Sciences 28, 1400–1426 (1971).

Hunt, G. E.

G. E. Hunt, "A review of computational techniques for analysing the transfer of radiation through a model cloudy atmosphere," J. Quant. Spectrosc. Radiat. Transfer 11, 655–690 (1971).

Krichbaum, C. K.

G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook (Plenum, New York, 1970), p. 9.

Leader, J. C.

J. C. Leader, "Incoherent backscatter from rough surfaces: the two-scale model re-examined," Rad. Science 13,441–457 (1978).

G. J. Wilhelmi, J. C. Leader, and W. A. J. Dalton, "Cross-polarized target signature measurements," Appl. Opt. 15, 1837–1841 (1976).

J. C. Leader, "An analysis of the spatial coherence of laser light scattered from a surface with two scales of roughness," J. Opt. Soc. Am. 66, 536–546 (1976).

J. C. Leader, "Spatial coherence measurements of Rayleigh-scattered light," J. Opt. Soc. Am. 65, 740–741 (1975).

J. C. Leader, "Polarization dependence in em scattering from Rayleigh scatterers embedded in a dielectric slab. I. Theory," J. Appl. Phys. 46, 4371–4385 (1975).

J. C. Leader and W. A. J. Dalton, "Polarization dependence in em scattering from Rayleigh scatterers embedded in a dielectric slab. II. Experiment," J. Appl. Phys. 46, 4386–4391 (1975).

J. C. Leader and W. A. J. Dalton, "Bidirectional scattering of electromagnetic waves from the volume of dielectric materials," J. Appl. Phys. 43, 3080–3088 (1972).

J. C. Leader, "Hemispherical scattering of electromagnetic waves from rough surfaces," J. Opt. Soc. Am. 62, 1356 (1972).

J. C. Leader and J. M. Putnam, "Rough Surface Scattering Code (ROSSCO) User's Manual," McDonnell Douglas Corp. Report MDC Q0619, Vols. I and II, 22 May 1977.

J. C. Leader, "Spectral and angular dependence of specular scattering from rough surfaces," 1971 URSI Meeting, Washington, D.C., McDonnell Aircraft Paper No. MCAIR 71-013.

J. C. Leader, D. P. Owsley, and C. R. Fulkerson, "Active Multispectral Data Analysis," RADC Final Report No. RADC-TR-74-190, Aug. 1974.

J. C. Leader, "Laser Signature Analyses," McDonnell Douglas Corp. Report MDC Q0611, 22 October 1976.

Maxwell, J. R.

J. R. Maxwell and S. Weiner, "Polarized Radiance. Vol. III: Wavelength Dependence of Polarized Bidirectional Radiance," Environmental Research Institute of Michigan, BRL-CR-156, May 1974. Distributed by National Technical Information Service, AD-782 179.

Nicodemus, F. E.

Ohtsubo, J.

Otaguro, W. S.

J. P. Theriault and W. S. Otaguro, "Monostatic BDR Measurement," McDonnell Douglas Astronautics Corp. Report MDC G6128, Sept. 1976.

Owsley, D. P.

J. C. Leader, D. P. Owsley, and C. R. Fulkerson, "Active Multispectral Data Analysis," RADC Final Report No. RADC-TR-74-190, Aug. 1974.

Putnam, J. M.

J. C. Leader and J. M. Putnam, "Rough Surface Scattering Code (ROSSCO) User's Manual," McDonnell Douglas Corp. Report MDC Q0619, Vols. I and II, 22 May 1977.

Renau, J.

Rouse, J. W.

Ruck, G. T.

G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook (Plenum, New York, 1970), p. 9.

Sancer, M. I.

M. I. Sancer, "Shadow-corrected electromagnetic scattering from a randomly rough surface," IEEE Trans. Ant. Propag. AP-17, 577–585 (1969).

Shindo, Y.

H. Fujii, T. Asakura, and Y. Shindo, "Measurements of surface roughness properties by means of laser speckle techniques," Opt. Commun. 16, 68–72 (1976).

Smith, B. G.

B. G. Smith, "Lunar surface roughness: shadowing and thermal emission," J. Geophys. Res. 72, 4059–4067 (1967).

B. G. Smith, "Geometrical shadowing of a random rough surface," IEEE Trans. Ant. Propag. AP-15, 668–671 (1967).

Spizzichino, A.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).

Sprague, R. A.

Stuart, W. D.

G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook (Plenum, New York, 1970), p. 9.

Theriault, J. P.

J. P. Theriault and W. S. Otaguro, "Monostatic BDR Measurement," McDonnell Douglas Astronautics Corp. Report MDC G6128, Sept. 1976.

Toporets, A. S.

A. S. Toporets, "Specular reflection from a rough surface," Opt. Spectrosk. (USSR) 16, 54–58 (1964).

Weiner, S.

J. R. Maxwell and S. Weiner, "Polarized Radiance. Vol. III: Wavelength Dependence of Polarized Bidirectional Radiance," Environmental Research Institute of Michigan, BRL-CR-156, May 1974. Distributed by National Technical Information Service, AD-782 179.

Wilhelmi, G. J.

Appl. Opt. (5)

Bell Syst. Tech. J. (1)

J. Renau and J. A. Collinson, "Measurement of electromagnetic backscattering from known, rough surfaces," Bell Syst. Tech. J. 44, 2203–2226 (1965).

IEEE Trans. Ant. Propag. (4)

B. G. Smith, "Geometrical shadowing of a random rough surface," IEEE Trans. Ant. Propag. AP-15, 668–671 (1967).

M. I. Sancer, "Shadow-corrected electromagnetic scattering from a randomly rough surface," IEEE Trans. Ant. Propag. AP-17, 577–585 (1969).

P. Beckmann, "Shadowing of random rough surfaces," IEEE Trans. Ant. Propag. AP-13, 384–388 (1965).

R. A. Brockelman and T. Hagfors, "Note on the effect of shadowing on the backscattering of waves from a random rough surface," IEEE Trans. Ant. Propag. AP-14, 621–628 (1966).

J. Appl. Phys. (3)

J. C. Leader, "Polarization dependence in em scattering from Rayleigh scatterers embedded in a dielectric slab. I. Theory," J. Appl. Phys. 46, 4371–4385 (1975).

J. C. Leader and W. A. J. Dalton, "Polarization dependence in em scattering from Rayleigh scatterers embedded in a dielectric slab. II. Experiment," J. Appl. Phys. 46, 4386–4391 (1975).

J. C. Leader and W. A. J. Dalton, "Bidirectional scattering of electromagnetic waves from the volume of dielectric materials," J. Appl. Phys. 43, 3080–3088 (1972).

J. Atmos. Sciences (1)

J. E. Hansen, "Multiple scattering of polarized light in planetary atmospheres," J. Atmos. Sciences 28, 1400–1426 (1971).

J. Geophys. Res. (1)

B. G. Smith, "Lunar surface roughness: shadowing and thermal emission," J. Geophys. Res. 72, 4059–4067 (1967).

J. Opt. Soc. Am. (7)

J. Quant. Spectrosc. Radiat. Transfer (1)

G. E. Hunt, "A review of computational techniques for analysing the transfer of radiation through a model cloudy atmosphere," J. Quant. Spectrosc. Radiat. Transfer 11, 655–690 (1971).

Opt. Commun. (1)

H. Fujii, T. Asakura, and Y. Shindo, "Measurements of surface roughness properties by means of laser speckle techniques," Opt. Commun. 16, 68–72 (1976).

Opt. Spectrosk. (1)

A. S. Toporets, "Specular reflection from a rough surface," Opt. Spectrosk. (USSR) 16, 54–58 (1964).

Rad. Science (1)

J. C. Leader, "Incoherent backscatter from rough surfaces: the two-scale model re-examined," Rad. Science 13,441–457 (1978).

Other (12)

G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook (Plenum, New York, 1970), p. 9.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).

Reference 26 investigated speckle statistics for laser transmission through a diffuser. The axial direction for the transmission case is equivalent to the specular angle in reflection.

e.g., see Fig. 6 of Ref. 26.

J. C. Leader and J. M. Putnam, "Rough Surface Scattering Code (ROSSCO) User's Manual," McDonnell Douglas Corp. Report MDC Q0619, Vols. I and II, 22 May 1977.

J. C. Leader, "Laser Signature Analyses," McDonnell Douglas Corp. Report MDC Q0611, 22 October 1976.

J. C. Leader, "Spectral and angular dependence of specular scattering from rough surfaces," 1971 URSI Meeting, Washington, D.C., McDonnell Aircraft Paper No. MCAIR 71-013.

J. R. Maxwell and S. Weiner, "Polarized Radiance. Vol. III: Wavelength Dependence of Polarized Bidirectional Radiance," Environmental Research Institute of Michigan, BRL-CR-156, May 1974. Distributed by National Technical Information Service, AD-782 179.

J. P. Theriault and W. S. Otaguro, "Monostatic BDR Measurement," McDonnell Douglas Astronautics Corp. Report MDC G6128, Sept. 1976.

Abromowitz and Segun, Handbook of Mathematical Functions (Dover, New York, 1965).

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

J. C. Leader, D. P. Owsley, and C. R. Fulkerson, "Active Multispectral Data Analysis," RADC Final Report No. RADC-TR-74-190, Aug. 1974.

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