Abstract

The scattering and depolarization of electromagnetic waves from perfectly conductive slightly rough random surfaces is studied using the small perturbation method through the Ewald—Oseen extinction theorem. This permits predictions in those cases in which the physical optics, or the Kirchhoff approximation, fails, namely, at grazing incidence and when the wavelength of the incident radiation is comparable with the correlation length of the random heights. In this way it is seen, for example, that, as with the Rayleigh—Fano method, the depolarization of the fields is obtained from the second order of the expansion and exists even in the backscattering and specular directions. Also, unlike the predictions of the Kirchhoff approximation, this depolarization depends on the surface shape. However, this approach yields in the specular direction the same result as the Kirchhoff approximation for those cases in which the latter is known to be valid, i.e., for large correlation lengths and non-grazing-incidence directions and establishes precise conditions under which the Kirchhoff approximation is retrieved in the backscattering direction.

© 1982 Optical Society of America

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  2. E. Bahar and G. G. Rajan, "Depolarization and scattering of electromagnetic waves by irregular boundaries for arbitrary incident and scatter angles: full-wave solutions," IEEE Trans. Antennas Propag. AP-26, 214–225 (1979).
  3. E. Bahar and G. G. Rajan, "Rough surface scattering of horizontally polarized waves and polarization dependence of back-scatter cross section: full wave solutions," Radio Sci. 14, 341–35 (1979).
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  6. P. Beckmann, The Depolarization of Electromagnetic Waves (Golem, Boulder, Colo., 1968).
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  8. J. C. Leader and W. A. J. Dalton, "Bidirectional scattering of electromagnetic waves from the volume of dielectric materials," J. Appl. Phys. 43, 3080–3090 (1972).
  9. F. G. Bass and I. M. Fucks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford, 1979).
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  16. G. R. Valenzuela, "Depolarization of EM waves by slightly rough surfaces," IEEE Trans. Antennas Propag. AP-15, 552–557 (1967).
  17. J. M. Elson, "Light scattering from semi-infinite media for non-normal incidence," Phys. Rev. B 12, 2541–2542 (1975).
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  19. J. M. Elson and J. M. Bennett, "Vector scattering theory," Opt. Eng. 18, 116–124 (1979).
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  21. D. E. Barrick, "Rough surface scattering based on the specular point theory," IEEE Trans. Antennas Propag. AP-16, 449–454 (1968).
  22. G. R. Jiracek, "Numerical comparison of a modified Rayleigh approach with other rough surface EM scattering solutions," IEEE Trans. Antennas Propag. AP-21, 393–396 (1973).
  23. F. Toigo, A. Marvin, V. Celli, and N. R. Hill, "Optical properties of rough surfaces: general theory and the small roughness limit," Phys. Rev. 15, 5618–5626 (1977).
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  31. P. C. Waterman, "Symmetry, unitarity and geometry in electromagnetic scattering," Phys. Rev. D 3, 825–839 (1972).
  32. R. H. T. Bates, "Null field approach to scalar diffraction," Phil. Trans. R. Soc. London Ser. A 287, 45 (1977).
  33. R. H. T. Bates, "Analytic constraints on electromagnetic fields computations," IEEE Trans. Microwave Theory Tech. MTT-23, 605 (1975).
  34. E. Lalor and E. Wolf, "Exact solution of the equations of molecular optics for refraction and reflection of an electromagnetic wave on a semi-infinite dielectric," J. Opt. Soc. Am. 62, 1165–1174 (1972).
  35. G. S. Agarwal, "Scattering from rough surfaces," Opt. Commun. 14, 161–165 (1975).
  36. G. S. Agarwal, "Interaction of electromagnetic waves at rough dielectric surfaces," Phys. Rev. B 15, 2371–2383 (1977).
  37. W. C. Meecham, "Fourier transform method for the treatment of the problem of reflection of radiation from irregular surfaces," J. Acoust. Soc. Am. 28, 370–377 (1956); C. Lopez, F. J. Yndurain, and N. García, "Iterative series for calculating the scattering of waves from a hard corrugated surface," Phys. Rev. B 18, 970–972 (1978).
  38. N. García, V. Celli, and M. Nieto-Vesperinas, "Exact multiple scattering of waves from random rough surfaces," Opt. Commun. 31, 279–281 (1979).
  39. M. Nieto-Vesperinas and N. García, "Exact multiple scattering of waves from random rough surfaces: speckle contrast," Opt. Commun. 32, 217–219 (1980); "Non-circular Gaussian speckle contrast in the exact theory of multiple scattering of waves from random rough surfaces," Opt. Commun. 35, 25–30 (1980).
  40. M. Nieto-Vesperinas and N. García, "A detailed study of the scattering of scalar waves from random rough surfaces," Opt. Acta 28, 1651–1672 (1981).
  41. J. Shen and A. Maradudin, "Multiple scattering of waves from random rough surfaces," Phys. Rev. B 22, 4234–4240 (1980).
  42. P. Beckmann, "Scattering by non-Gaussian surfaces," IEEE Trans. Antennas Propag. AP-21, 169–175 (1973).
  43. R. I. Masel, R. P. Merrill, and W. H. Miller, "Quantum scattering from a sinusoidal hard wall: atomic diffraction from solid surfaces," Phys. Rev. B 12, 5545–5551 (1975).
  44. N. García and N. Cabrera, "New method for solving the scattering of waves from a periodic hard surface: solutions and numerical comparisons with the various formalisms," Phys. Rev. B 18, 576–589 (1978).
  45. E. Wolf, "Three-dimensional structure determination of semitransparent objects from holographic data," Opt. Commun. 1, 153 (1969).
  46. K. Miyamoto and E. Wolf, "Generalization of the Maggi—Rabinowicz theory of the boundary diffraction wave. Part I," J. Opt. Soc. Am. 52, 615–625 (1962).
  47. R. H. Richtie, "Surface plasmons in solids," Surf. Sci. 34, 1–19 (1973).
  48. 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).
  49. K. Gasvik, "A theory of polarization-dependent off-specular peaks of light scattered from rough surfaces," Opt. Acta 27, 965–980 (1980).
  50. J. M. Bennett, "Measurement of the rms roughness, autocovariance function and other statistical properties of optical surfaces using a FECO scanning interferometer," Appl. Opt. 15, 2705–2721 (1976).
  51. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals Series and Products (Academic, New York, 1965).
  52. K. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
  53. E. Jakeman and P. N. Pusey, "Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen," J. Phys. A 8, 369–410 (1975).
  54. A. Zardecki, "Statistical features of phase screens from scattering Vol. 9 in data," in Inverse Source Problems in Optics, H. P. Baltes, ed., Vol. 9 in Topics in Current Physics (Springer-Verlag, Berlin, 1978), pp. 155–189.

1981 (1)

M. Nieto-Vesperinas and N. García, "A detailed study of the scattering of scalar waves from random rough surfaces," Opt. Acta 28, 1651–1672 (1981).

1980 (3)

J. Shen and A. Maradudin, "Multiple scattering of waves from random rough surfaces," Phys. Rev. B 22, 4234–4240 (1980).

M. Nieto-Vesperinas and N. García, "Exact multiple scattering of waves from random rough surfaces: speckle contrast," Opt. Commun. 32, 217–219 (1980); "Non-circular Gaussian speckle contrast in the exact theory of multiple scattering of waves from random rough surfaces," Opt. Commun. 35, 25–30 (1980).

K. Gasvik, "A theory of polarization-dependent off-specular peaks of light scattered from rough surfaces," Opt. Acta 27, 965–980 (1980).

1979 (4)

N. García, V. Celli, and M. Nieto-Vesperinas, "Exact multiple scattering of waves from random rough surfaces," Opt. Commun. 31, 279–281 (1979).

E. Bahar and G. G. Rajan, "Depolarization and scattering of electromagnetic waves by irregular boundaries for arbitrary incident and scatter angles: full-wave solutions," IEEE Trans. Antennas Propag. AP-26, 214–225 (1979).

E. Bahar and G. G. Rajan, "Rough surface scattering of horizontally polarized waves and polarization dependence of back-scatter cross section: full wave solutions," Radio Sci. 14, 341–35 (1979).

J. M. Elson and J. M. Bennett, "Vector scattering theory," Opt. Eng. 18, 116–124 (1979).

1978 (2)

E. Bahar, "Full wave and physical optics solutions for scattered radiation fields by rough surfaces. Energy and reciprocity relationships," IEEE Trans. Antennas Propag. AP-26, 603–614 (1978).

N. García and N. Cabrera, "New method for solving the scattering of waves from a periodic hard surface: solutions and numerical comparisons with the various formalisms," Phys. Rev. B 18, 576–589 (1978).

1977 (3)

G. S. Agarwal, "Interaction of electromagnetic waves at rough dielectric surfaces," Phys. Rev. B 15, 2371–2383 (1977).

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, "Optical properties of rough surfaces: general theory and the small roughness limit," Phys. Rev. 15, 5618–5626 (1977).

R. H. T. Bates, "Null field approach to scalar diffraction," Phil. Trans. R. Soc. London Ser. A 287, 45 (1977).

1976 (1)

1975 (6)

E. Jakeman and P. N. Pusey, "Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen," J. Phys. A 8, 369–410 (1975).

R. I. Masel, R. P. Merrill, and W. H. Miller, "Quantum scattering from a sinusoidal hard wall: atomic diffraction from solid surfaces," Phys. Rev. B 12, 5545–5551 (1975).

R. H. T. Bates, "Analytic constraints on electromagnetic fields computations," IEEE Trans. Microwave Theory Tech. MTT-23, 605 (1975).

J. M. Elson, "Light scattering from semi-infinite media for non-normal incidence," Phys. Rev. B 12, 2541–2542 (1975).

V. Celli, A. Marvin, and F. Toigo, "Light scattering from rough surfaces," Phys. Rev. B 11, 1779–1786 (1975).

G. S. Agarwal, "Scattering from rough surfaces," Opt. Commun. 14, 161–165 (1975).

1973 (3)

G. R. Jiracek, "Numerical comparison of a modified Rayleigh approach with other rough surface EM scattering solutions," IEEE Trans. Antennas Propag. AP-21, 393–396 (1973).

P. Beckmann, "Scattering by non-Gaussian surfaces," IEEE Trans. Antennas Propag. AP-21, 169–175 (1973).

R. H. Richtie, "Surface plasmons in solids," Surf. Sci. 34, 1–19 (1973).

1972 (5)

E. Lalor and E. Wolf, "Exact solution of the equations of molecular optics for refraction and reflection of an electromagnetic wave on a semi-infinite dielectric," J. Opt. Soc. Am. 62, 1165–1174 (1972).

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

D. N. Pattanayak and E. Wolf, "General form and a new interpretation of the Ewald—Oseen extinction theorem," Opt. Commun. 6, 217–220 (1972).

P. C. Waterman, "Symmetry, unitarity and geometry in electromagnetic scattering," Phys. Rev. D 3, 825–839 (1972).

G. R. Valenzuela, J. W. Wright, and J. C. Leader, "Comments on 'The relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory,'" IEEE Trans. Antennas Propag. AP-20, 536–539 (1972).

1971 (2)

J. C. Leader, "The relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory," IEEE Trans. Antennas Propag. AP-19, 786–788 (1971)

J. C. Leader, "Bidirectional scattering of electromagnetic waves from rough surfaces," J. Appl. Phys. 42, 4808–4816 (1971).

1970 (1)

J. J. Sein, "A note on the Ewald—Oseen extinction theorem," Opt. Commun. 2, 170–172 (1970).

1969 (1)

E. Wolf, "Three-dimensional structure determination of semitransparent objects from holographic data," Opt. Commun. 1, 153 (1969).

1968 (2)

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

D. E. Barrick, "Rough surface scattering based on the specular point theory," IEEE Trans. Antennas Propag. AP-16, 449–454 (1968).

1967 (1)

G. R. Valenzuela, "Depolarization of EM waves by slightly rough surfaces," IEEE Trans. Antennas Propag. AP-15, 552–557 (1967).

1966 (2)

1964 (1)

T. Hagfors, "Backscattering from an undulating surface with applications to radar return from the moon," J. Geophys. Res. 69, 3779–3784 (1964); "A study of the depolarization of lunar radar echos," Radio Sci. 2, 445–465 (1967).

1962 (1)

1959 (1)

W. H. Peake, "Theory of radar return from terrain," IRE Natl. Conv. Rec. 7, 27–41 (1959).

1956 (1)

W. C. Meecham, "Fourier transform method for the treatment of the problem of reflection of radiation from irregular surfaces," J. Acoust. Soc. Am. 28, 370–377 (1956); C. Lopez, F. J. Yndurain, and N. García, "Iterative series for calculating the scattering of waves from a hard corrugated surface," Phys. Rev. B 18, 970–972 (1978).

1951 (1)

S. O. Rice, "Reflection of electromagnetic waves from slightly rough surfaces," Commun. Pure Appl. Math. 4, 351–378 (1951).

1941 (1)

Abramowitz, K.

K. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

Agarwal, G. S.

G. S. Agarwal, "Interaction of electromagnetic waves at rough dielectric surfaces," Phys. Rev. B 15, 2371–2383 (1977).

G. S. Agarwal, "Scattering from rough surfaces," Opt. Commun. 14, 161–165 (1975).

Bahar, E.

E. Bahar and G. G. Rajan, "Rough surface scattering of horizontally polarized waves and polarization dependence of back-scatter cross section: full wave solutions," Radio Sci. 14, 341–35 (1979).

E. Bahar and G. G. Rajan, "Depolarization and scattering of electromagnetic waves by irregular boundaries for arbitrary incident and scatter angles: full-wave solutions," IEEE Trans. Antennas Propag. AP-26, 214–225 (1979).

E. Bahar, "Full wave and physical optics solutions for scattered radiation fields by rough surfaces. Energy and reciprocity relationships," IEEE Trans. Antennas Propag. AP-26, 603–614 (1978).

Barrick, D. D.

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

Barrick, D. E.

D. E. Barrick, "Rough surface scattering based on the specular point theory," IEEE Trans. Antennas Propag. AP-16, 449–454 (1968).

Bass, F. G.

F. G. Bass and I. M. Fucks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford, 1979).

Bates, R. H. T.

R. H. T. Bates, "Null field approach to scalar diffraction," Phil. Trans. R. Soc. London Ser. A 287, 45 (1977).

R. H. T. Bates, "Analytic constraints on electromagnetic fields computations," IEEE Trans. Microwave Theory Tech. MTT-23, 605 (1975).

Beckmann, P.

P. Beckmann, "Scattering by non-Gaussian surfaces," IEEE Trans. Antennas Propag. AP-21, 169–175 (1973).

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

Bennett, J. M.

Birkebak, R. C.

Boerner, W. M.

W. M. Boerner, "Polarization utilization in electromagnetic inverse scattering," in Inverse Scattering Problems in Optics, H. P. Baltes, ed, Vol. 20 in Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 237–303.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), Sec. 2.4.

Cabrera, N.

N. García and N. Cabrera, "New method for solving the scattering of waves from a periodic hard surface: solutions and numerical comparisons with the various formalisms," Phys. Rev. B 18, 576–589 (1978).

Celli, V.

N. García, V. Celli, and M. Nieto-Vesperinas, "Exact multiple scattering of waves from random rough surfaces," Opt. Commun. 31, 279–281 (1979).

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, "Optical properties of rough surfaces: general theory and the small roughness limit," Phys. Rev. 15, 5618–5626 (1977).

V. Celli, A. Marvin, and F. Toigo, "Light scattering from rough surfaces," Phys. Rev. B 11, 1779–1786 (1975).

Dalton, W. A. J.

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

Elson, J. M.

J. M. Elson and J. M. Bennett, "Vector scattering theory," Opt. Eng. 18, 116–124 (1979).

J. M. Elson, "Light scattering from semi-infinite media for non-normal incidence," Phys. Rev. B 12, 2541–2542 (1975).

Fano, U.

Fucks, I. M.

F. G. Bass and I. M. Fucks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford, 1979).

Fung, A. K.

A. K. Fung, "Scattering and depolarization of EM waves from a rough surface," Proc. IEEE 54, 395–396 (1966); "Vector scattering applied to Moon and Venus radar return," Proc. IEEE 54, 996–998 (1966).

García, N.

M. Nieto-Vesperinas and N. García, "A detailed study of the scattering of scalar waves from random rough surfaces," Opt. Acta 28, 1651–1672 (1981).

M. Nieto-Vesperinas and N. García, "Exact multiple scattering of waves from random rough surfaces: speckle contrast," Opt. Commun. 32, 217–219 (1980); "Non-circular Gaussian speckle contrast in the exact theory of multiple scattering of waves from random rough surfaces," Opt. Commun. 35, 25–30 (1980).

N. García, V. Celli, and M. Nieto-Vesperinas, "Exact multiple scattering of waves from random rough surfaces," Opt. Commun. 31, 279–281 (1979).

N. García and N. Cabrera, "New method for solving the scattering of waves from a periodic hard surface: solutions and numerical comparisons with the various formalisms," Phys. Rev. B 18, 576–589 (1978).

Gasvik, K.

K. Gasvik, "A theory of polarization-dependent off-specular peaks of light scattered from rough surfaces," Opt. Acta 27, 965–980 (1980).

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals Series and Products (Academic, New York, 1965).

Hagfors, T.

T. Hagfors, "Backscattering from an undulating surface with applications to radar return from the moon," J. Geophys. Res. 69, 3779–3784 (1964); "A study of the depolarization of lunar radar echos," Radio Sci. 2, 445–465 (1967).

Hill, N. R.

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, "Optical properties of rough surfaces: general theory and the small roughness limit," Phys. Rev. 15, 5618–5626 (1977).

Jakeman, E.

E. Jakeman and P. N. Pusey, "Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen," J. Phys. A 8, 369–410 (1975).

Jiracek, G. R.

G. R. Jiracek, "Numerical comparison of a modified Rayleigh approach with other rough surface EM scattering solutions," IEEE Trans. Antennas Propag. AP-21, 393–396 (1973).

Kodis, R. D.

R. D. Kodis, "A note on the theory of scattering from an irregular surface," IEEE Trans. Antennas Propag. AP-14, 77–82 (1966).

Lalor, E.

Leader, J. C.

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

G. R. Valenzuela, J. W. Wright, and J. C. Leader, "Comments on 'The relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory,'" IEEE Trans. Antennas Propag. AP-20, 536–539 (1972).

J. C. Leader, "The relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory," IEEE Trans. Antennas Propag. AP-19, 786–788 (1971)

J. C. Leader, "Bidirectional scattering of electromagnetic waves from rough surfaces," J. Appl. Phys. 42, 4808–4816 (1971).

Maradudin, A.

J. Shen and A. Maradudin, "Multiple scattering of waves from random rough surfaces," Phys. Rev. B 22, 4234–4240 (1980).

Marvin, A.

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, "Optical properties of rough surfaces: general theory and the small roughness limit," Phys. Rev. 15, 5618–5626 (1977).

V. Celli, A. Marvin, and F. Toigo, "Light scattering from rough surfaces," Phys. Rev. B 11, 1779–1786 (1975).

Masel, R. I.

R. I. Masel, R. P. Merrill, and W. H. Miller, "Quantum scattering from a sinusoidal hard wall: atomic diffraction from solid surfaces," Phys. Rev. B 12, 5545–5551 (1975).

Meecham, W. C.

W. C. Meecham, "Fourier transform method for the treatment of the problem of reflection of radiation from irregular surfaces," J. Acoust. Soc. Am. 28, 370–377 (1956); C. Lopez, F. J. Yndurain, and N. García, "Iterative series for calculating the scattering of waves from a hard corrugated surface," Phys. Rev. B 18, 970–972 (1978).

Merrill, R. P.

R. I. Masel, R. P. Merrill, and W. H. Miller, "Quantum scattering from a sinusoidal hard wall: atomic diffraction from solid surfaces," Phys. Rev. B 12, 5545–5551 (1975).

Miller, W. H.

R. I. Masel, R. P. Merrill, and W. H. Miller, "Quantum scattering from a sinusoidal hard wall: atomic diffraction from solid surfaces," Phys. Rev. B 12, 5545–5551 (1975).

Miyamoto, K.

Nieto-Vesperinas, M.

M. Nieto-Vesperinas and N. García, "A detailed study of the scattering of scalar waves from random rough surfaces," Opt. Acta 28, 1651–1672 (1981).

M. Nieto-Vesperinas and N. García, "Exact multiple scattering of waves from random rough surfaces: speckle contrast," Opt. Commun. 32, 217–219 (1980); "Non-circular Gaussian speckle contrast in the exact theory of multiple scattering of waves from random rough surfaces," Opt. Commun. 35, 25–30 (1980).

N. García, V. Celli, and M. Nieto-Vesperinas, "Exact multiple scattering of waves from random rough surfaces," Opt. Commun. 31, 279–281 (1979).

Pattanayak, D. N.

D. N. Pattanayak and E. Wolf, "General form and a new interpretation of the Ewald—Oseen extinction theorem," Opt. Commun. 6, 217–220 (1972).

Peake, W. H.

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

W. H. Peake, "Theory of radar return from terrain," IRE Natl. Conv. Rec. 7, 27–41 (1959).

Pusey, P. N.

E. Jakeman and P. N. Pusey, "Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen," J. Phys. A 8, 369–410 (1975).

Rajan, G. G.

E. Bahar and G. G. Rajan, "Rough surface scattering of horizontally polarized waves and polarization dependence of back-scatter cross section: full wave solutions," Radio Sci. 14, 341–35 (1979).

E. Bahar and G. G. Rajan, "Depolarization and scattering of electromagnetic waves by irregular boundaries for arbitrary incident and scatter angles: full-wave solutions," IEEE Trans. Antennas Propag. AP-26, 214–225 (1979).

Rayleigh, Lord

Lord Rayleigh, Theory of Sound (Dover, New York, 1945), Vol. 2.

Rice, S. O.

S. O. Rice, "Reflection of electromagnetic waves from slightly rough surfaces," Commun. Pure Appl. Math. 4, 351–378 (1951).

Richtie, R. H.

R. H. Richtie, "Surface plasmons in solids," Surf. Sci. 34, 1–19 (1973).

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals Series and Products (Academic, New York, 1965).

Sein, J. J.

J. J. Sein, "A note on the Ewald—Oseen extinction theorem," Opt. Commun. 2, 170–172 (1970).

Shen, J.

J. Shen and A. Maradudin, "Multiple scattering of waves from random rough surfaces," Phys. Rev. B 22, 4234–4240 (1980).

Sparrow, E. M.

Stegun, I.

K. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

Toigo, F.

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, "Optical properties of rough surfaces: general theory and the small roughness limit," Phys. Rev. 15, 5618–5626 (1977).

V. Celli, A. Marvin, and F. Toigo, "Light scattering from rough surfaces," Phys. Rev. B 11, 1779–1786 (1975).

Torrance, K. E.

Valenzuela, G. R.

G. R. Valenzuela, J. W. Wright, and J. C. Leader, "Comments on 'The relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory,'" IEEE Trans. Antennas Propag. AP-20, 536–539 (1972).

G. R. Valenzuela, "Depolarization of EM waves by slightly rough surfaces," IEEE Trans. Antennas Propag. AP-15, 552–557 (1967).

Waterman, P. C.

P. C. Waterman, "Symmetry, unitarity and geometry in electromagnetic scattering," Phys. Rev. D 3, 825–839 (1972).

P. C. Waterman, "Matrix formulation of electromagnetic scattering," Proc. IEEE 53, 805–812 (1965).

Wolf, E.

E. Lalor and E. Wolf, "Exact solution of the equations of molecular optics for refraction and reflection of an electromagnetic wave on a semi-infinite dielectric," J. Opt. Soc. Am. 62, 1165–1174 (1972).

D. N. Pattanayak and E. Wolf, "General form and a new interpretation of the Ewald—Oseen extinction theorem," Opt. Commun. 6, 217–220 (1972).

E. Wolf, "Three-dimensional structure determination of semitransparent objects from holographic data," Opt. Commun. 1, 153 (1969).

K. Miyamoto and E. Wolf, "Generalization of the Maggi—Rabinowicz theory of the boundary diffraction wave. Part I," J. Opt. Soc. Am. 52, 615–625 (1962).

E. Wolf, "A generalized extinction theorem and its role in scattering theory," in Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1973), pp. 339–357.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), Sec. 2.4.

Wright, J. W.

G. R. Valenzuela, J. W. Wright, and J. C. Leader, "Comments on 'The relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory,'" IEEE Trans. Antennas Propag. AP-20, 536–539 (1972).

Zardecki, A.

A. Zardecki, "Statistical features of phase screens from scattering Vol. 9 in data," in Inverse Source Problems in Optics, H. P. Baltes, ed., Vol. 9 in Topics in Current Physics (Springer-Verlag, Berlin, 1978), pp. 155–189.

Appl. Opt. (1)

Commun. Pure Appl. Math. (1)

S. O. Rice, "Reflection of electromagnetic waves from slightly rough surfaces," Commun. Pure Appl. Math. 4, 351–378 (1951).

IEEE Trans. Antennas Propag. (9)

E. Bahar, "Full wave and physical optics solutions for scattered radiation fields by rough surfaces. Energy and reciprocity relationships," IEEE Trans. Antennas Propag. AP-26, 603–614 (1978).

E. Bahar and G. G. Rajan, "Depolarization and scattering of electromagnetic waves by irregular boundaries for arbitrary incident and scatter angles: full-wave solutions," IEEE Trans. Antennas Propag. AP-26, 214–225 (1979).

G. R. Valenzuela, "Depolarization of EM waves by slightly rough surfaces," IEEE Trans. Antennas Propag. AP-15, 552–557 (1967).

R. D. Kodis, "A note on the theory of scattering from an irregular surface," IEEE Trans. Antennas Propag. AP-14, 77–82 (1966).

D. E. Barrick, "Rough surface scattering based on the specular point theory," IEEE Trans. Antennas Propag. AP-16, 449–454 (1968).

G. R. Jiracek, "Numerical comparison of a modified Rayleigh approach with other rough surface EM scattering solutions," IEEE Trans. Antennas Propag. AP-21, 393–396 (1973).

J. C. Leader, "The relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory," IEEE Trans. Antennas Propag. AP-19, 786–788 (1971)

G. R. Valenzuela, J. W. Wright, and J. C. Leader, "Comments on 'The relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory,'" IEEE Trans. Antennas Propag. AP-20, 536–539 (1972).

P. Beckmann, "Scattering by non-Gaussian surfaces," IEEE Trans. Antennas Propag. AP-21, 169–175 (1973).

IEEE Trans. Microwave Theory Tech. (1)

R. H. T. Bates, "Analytic constraints on electromagnetic fields computations," IEEE Trans. Microwave Theory Tech. MTT-23, 605 (1975).

IRE Natl. Conv. Rec. (1)

W. H. Peake, "Theory of radar return from terrain," IRE Natl. Conv. Rec. 7, 27–41 (1959).

J. Acoust. Soc. Am. (1)

W. C. Meecham, "Fourier transform method for the treatment of the problem of reflection of radiation from irregular surfaces," J. Acoust. Soc. Am. 28, 370–377 (1956); C. Lopez, F. J. Yndurain, and N. García, "Iterative series for calculating the scattering of waves from a hard corrugated surface," Phys. Rev. B 18, 970–972 (1978).

J. Appl. Phys. (2)

J. C. Leader, "Bidirectional scattering of electromagnetic waves from rough surfaces," J. Appl. Phys. 42, 4808–4816 (1971).

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

J. Geophys. Res. (1)

T. Hagfors, "Backscattering from an undulating surface with applications to radar return from the moon," J. Geophys. Res. 69, 3779–3784 (1964); "A study of the depolarization of lunar radar echos," Radio Sci. 2, 445–465 (1967).

J. Opt. Soc. Am. (4)

J. Phys. A (1)

E. Jakeman and P. N. Pusey, "Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen," J. Phys. A 8, 369–410 (1975).

Opt. Acta (2)

M. Nieto-Vesperinas and N. García, "A detailed study of the scattering of scalar waves from random rough surfaces," Opt. Acta 28, 1651–1672 (1981).

K. Gasvik, "A theory of polarization-dependent off-specular peaks of light scattered from rough surfaces," Opt. Acta 27, 965–980 (1980).

Opt. Commun. (6)

E. Wolf, "Three-dimensional structure determination of semitransparent objects from holographic data," Opt. Commun. 1, 153 (1969).

N. García, V. Celli, and M. Nieto-Vesperinas, "Exact multiple scattering of waves from random rough surfaces," Opt. Commun. 31, 279–281 (1979).

M. Nieto-Vesperinas and N. García, "Exact multiple scattering of waves from random rough surfaces: speckle contrast," Opt. Commun. 32, 217–219 (1980); "Non-circular Gaussian speckle contrast in the exact theory of multiple scattering of waves from random rough surfaces," Opt. Commun. 35, 25–30 (1980).

G. S. Agarwal, "Scattering from rough surfaces," Opt. Commun. 14, 161–165 (1975).

J. J. Sein, "A note on the Ewald—Oseen extinction theorem," Opt. Commun. 2, 170–172 (1970).

D. N. Pattanayak and E. Wolf, "General form and a new interpretation of the Ewald—Oseen extinction theorem," Opt. Commun. 6, 217–220 (1972).

Opt. Eng. (1)

J. M. Elson and J. M. Bennett, "Vector scattering theory," Opt. Eng. 18, 116–124 (1979).

Phil. Trans. R. Soc. London Ser. A (1)

R. H. T. Bates, "Null field approach to scalar diffraction," Phil. Trans. R. Soc. London Ser. A 287, 45 (1977).

Phys. Rev. (1)

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, "Optical properties of rough surfaces: general theory and the small roughness limit," Phys. Rev. 15, 5618–5626 (1977).

Phys. Rev. B (6)

J. M. Elson, "Light scattering from semi-infinite media for non-normal incidence," Phys. Rev. B 12, 2541–2542 (1975).

V. Celli, A. Marvin, and F. Toigo, "Light scattering from rough surfaces," Phys. Rev. B 11, 1779–1786 (1975).

G. S. Agarwal, "Interaction of electromagnetic waves at rough dielectric surfaces," Phys. Rev. B 15, 2371–2383 (1977).

J. Shen and A. Maradudin, "Multiple scattering of waves from random rough surfaces," Phys. Rev. B 22, 4234–4240 (1980).

R. I. Masel, R. P. Merrill, and W. H. Miller, "Quantum scattering from a sinusoidal hard wall: atomic diffraction from solid surfaces," Phys. Rev. B 12, 5545–5551 (1975).

N. García and N. Cabrera, "New method for solving the scattering of waves from a periodic hard surface: solutions and numerical comparisons with the various formalisms," Phys. Rev. B 18, 576–589 (1978).

Phys. Rev. D (1)

P. C. Waterman, "Symmetry, unitarity and geometry in electromagnetic scattering," Phys. Rev. D 3, 825–839 (1972).

Radio Sci. (2)

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

E. Bahar and G. G. Rajan, "Rough surface scattering of horizontally polarized waves and polarization dependence of back-scatter cross section: full wave solutions," Radio Sci. 14, 341–35 (1979).

Surf. Sci. (1)

R. H. Richtie, "Surface plasmons in solids," Surf. Sci. 34, 1–19 (1973).

Other (11)

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals Series and Products (Academic, New York, 1965).

K. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

A. Zardecki, "Statistical features of phase screens from scattering Vol. 9 in data," in Inverse Source Problems in Optics, H. P. Baltes, ed., Vol. 9 in Topics in Current Physics (Springer-Verlag, Berlin, 1978), pp. 155–189.

A. K. Fung, "Scattering and depolarization of EM waves from a rough surface," Proc. IEEE 54, 395–396 (1966); "Vector scattering applied to Moon and Venus radar return," Proc. IEEE 54, 996–998 (1966).

F. G. Bass and I. M. Fucks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford, 1979).

W. M. Boerner, "Polarization utilization in electromagnetic inverse scattering," in Inverse Scattering Problems in Optics, H. P. Baltes, ed, Vol. 20 in Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 237–303.

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

Lord Rayleigh, Theory of Sound (Dover, New York, 1945), Vol. 2.

E. Wolf, "A generalized extinction theorem and its role in scattering theory," in Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1973), pp. 339–357.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), Sec. 2.4.

P. C. Waterman, "Matrix formulation of electromagnetic scattering," Proc. IEEE 53, 805–812 (1965).

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