Abstract

The scattering cross sections for large finitely conducting spheres with rough surfaces are determined for optical frequencies using the full wave approach. For the roughness scales considered the scattering cross sections differ significantly from those of smooth conducting spheres. Several illustrative examples are presented, and the results are compared to earlier solutions to the problem.

© 1985 Optical Society of America

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References

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  1. D. E. Barrick, Rough Surfaces, in Radar Cross Section Handbook (Plenum, New York, 1970), Chap. 9.
  2. E. Bahar, D. E. Barrick, “Scattering Cross Sections for Composite Surfaces that Cannot be Treated as Perturbed Physical Optics Problems,” Radio Sci., 18, 129 (1983).
    [Crossref]
  3. M. K. Abdelazeez, “Wave Scattering from a Large Sphere with Rough Surface,” IEEE Trans. Antennas Propag. AP-31, 375 (1983).
    [Crossref]
  4. S. O. Rice, “Reflection of Electromagnetic Waves from a Slightly Rough Surface,” Commun. Pure Applied Math. 4, 351 (1951).
    [Crossref]
  5. A. Ishimaru, Wave Propagation and Scattering in Random Media in Multiple Scattering, Turbulence, Rough Surfaces and Remote Sensing,. Vol. 2 (Academic, New York, 1978).
  6. G. S. Brown, “Backscattering from Gaussian-Distributed Perfectly Conducting Rough Surfaces,” IEEE Trans. Antennas Propag. AP-26, 472 (1978).
    [Crossref]
  7. M. L. Burrows, “On the Composite Model for Rough Surface Scattering,” IEEE Trans. Antennas Propag. AP-21, (1967).
  8. G. R. Valenzuela, “Scattering of Electromagnetic Waves from a Tilted Slightly Rough Surface,” Radio Sci., 3, 1051 (1968).
  9. E. Bahar, “Scattering Cross Sections for Composite Random Surfaces—Full Wave Analysis,” Radio Sci. 16, 1327 (1981).
    [Crossref]
  10. E. Bahar, “Scattering Cross Sections for Composite Surfaces with Large Mean Square Slopes—Full Wave Solution,” Int. J. Remote Sensing 3, 327 (1982).
    [Crossref]
  11. M. K. Sancer, “Shadow-Corrected Electromagnetic Scattering from a Randomly Rough Surface,” IEEE Trans. Antennas Propag. AP-17, 577 (1969).
    [Crossref]
  12. B. G. Smith, “Geometrical Shadowing of a Randomly Rough Surface,” IEEE Trans. Antennas Propag. AP-15, 668 (1967).
    [Crossref]
  13. H. Ehrenreich, “The Optical Properties of Metals,” IEEE Spectrum 2, 162 (1965).
    [Crossref]

1983 (2)

E. Bahar, D. E. Barrick, “Scattering Cross Sections for Composite Surfaces that Cannot be Treated as Perturbed Physical Optics Problems,” Radio Sci., 18, 129 (1983).
[Crossref]

M. K. Abdelazeez, “Wave Scattering from a Large Sphere with Rough Surface,” IEEE Trans. Antennas Propag. AP-31, 375 (1983).
[Crossref]

1982 (1)

E. Bahar, “Scattering Cross Sections for Composite Surfaces with Large Mean Square Slopes—Full Wave Solution,” Int. J. Remote Sensing 3, 327 (1982).
[Crossref]

1981 (1)

E. Bahar, “Scattering Cross Sections for Composite Random Surfaces—Full Wave Analysis,” Radio Sci. 16, 1327 (1981).
[Crossref]

1978 (1)

G. S. Brown, “Backscattering from Gaussian-Distributed Perfectly Conducting Rough Surfaces,” IEEE Trans. Antennas Propag. AP-26, 472 (1978).
[Crossref]

1969 (1)

M. K. Sancer, “Shadow-Corrected Electromagnetic Scattering from a Randomly Rough Surface,” IEEE Trans. Antennas Propag. AP-17, 577 (1969).
[Crossref]

1968 (1)

G. R. Valenzuela, “Scattering of Electromagnetic Waves from a Tilted Slightly Rough Surface,” Radio Sci., 3, 1051 (1968).

1967 (2)

B. G. Smith, “Geometrical Shadowing of a Randomly Rough Surface,” IEEE Trans. Antennas Propag. AP-15, 668 (1967).
[Crossref]

M. L. Burrows, “On the Composite Model for Rough Surface Scattering,” IEEE Trans. Antennas Propag. AP-21, (1967).

1965 (1)

H. Ehrenreich, “The Optical Properties of Metals,” IEEE Spectrum 2, 162 (1965).
[Crossref]

1951 (1)

S. O. Rice, “Reflection of Electromagnetic Waves from a Slightly Rough Surface,” Commun. Pure Applied Math. 4, 351 (1951).
[Crossref]

Abdelazeez, M. K.

M. K. Abdelazeez, “Wave Scattering from a Large Sphere with Rough Surface,” IEEE Trans. Antennas Propag. AP-31, 375 (1983).
[Crossref]

Bahar, E.

E. Bahar, D. E. Barrick, “Scattering Cross Sections for Composite Surfaces that Cannot be Treated as Perturbed Physical Optics Problems,” Radio Sci., 18, 129 (1983).
[Crossref]

E. Bahar, “Scattering Cross Sections for Composite Surfaces with Large Mean Square Slopes—Full Wave Solution,” Int. J. Remote Sensing 3, 327 (1982).
[Crossref]

E. Bahar, “Scattering Cross Sections for Composite Random Surfaces—Full Wave Analysis,” Radio Sci. 16, 1327 (1981).
[Crossref]

Barrick, D. E.

E. Bahar, D. E. Barrick, “Scattering Cross Sections for Composite Surfaces that Cannot be Treated as Perturbed Physical Optics Problems,” Radio Sci., 18, 129 (1983).
[Crossref]

D. E. Barrick, Rough Surfaces, in Radar Cross Section Handbook (Plenum, New York, 1970), Chap. 9.

Brown, G. S.

G. S. Brown, “Backscattering from Gaussian-Distributed Perfectly Conducting Rough Surfaces,” IEEE Trans. Antennas Propag. AP-26, 472 (1978).
[Crossref]

Burrows, M. L.

M. L. Burrows, “On the Composite Model for Rough Surface Scattering,” IEEE Trans. Antennas Propag. AP-21, (1967).

Ehrenreich, H.

H. Ehrenreich, “The Optical Properties of Metals,” IEEE Spectrum 2, 162 (1965).
[Crossref]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media in Multiple Scattering, Turbulence, Rough Surfaces and Remote Sensing,. Vol. 2 (Academic, New York, 1978).

Rice, S. O.

S. O. Rice, “Reflection of Electromagnetic Waves from a Slightly Rough Surface,” Commun. Pure Applied Math. 4, 351 (1951).
[Crossref]

Sancer, M. K.

M. K. Sancer, “Shadow-Corrected Electromagnetic Scattering from a Randomly Rough Surface,” IEEE Trans. Antennas Propag. AP-17, 577 (1969).
[Crossref]

Smith, B. G.

B. G. Smith, “Geometrical Shadowing of a Randomly Rough Surface,” IEEE Trans. Antennas Propag. AP-15, 668 (1967).
[Crossref]

Valenzuela, G. R.

G. R. Valenzuela, “Scattering of Electromagnetic Waves from a Tilted Slightly Rough Surface,” Radio Sci., 3, 1051 (1968).

Commun. Pure Applied Math. (1)

S. O. Rice, “Reflection of Electromagnetic Waves from a Slightly Rough Surface,” Commun. Pure Applied Math. 4, 351 (1951).
[Crossref]

IEEE Spectrum (1)

H. Ehrenreich, “The Optical Properties of Metals,” IEEE Spectrum 2, 162 (1965).
[Crossref]

IEEE Trans. Antennas Propag. (5)

M. K. Abdelazeez, “Wave Scattering from a Large Sphere with Rough Surface,” IEEE Trans. Antennas Propag. AP-31, 375 (1983).
[Crossref]

M. K. Sancer, “Shadow-Corrected Electromagnetic Scattering from a Randomly Rough Surface,” IEEE Trans. Antennas Propag. AP-17, 577 (1969).
[Crossref]

B. G. Smith, “Geometrical Shadowing of a Randomly Rough Surface,” IEEE Trans. Antennas Propag. AP-15, 668 (1967).
[Crossref]

G. S. Brown, “Backscattering from Gaussian-Distributed Perfectly Conducting Rough Surfaces,” IEEE Trans. Antennas Propag. AP-26, 472 (1978).
[Crossref]

M. L. Burrows, “On the Composite Model for Rough Surface Scattering,” IEEE Trans. Antennas Propag. AP-21, (1967).

Int. J. Remote Sensing (1)

E. Bahar, “Scattering Cross Sections for Composite Surfaces with Large Mean Square Slopes—Full Wave Solution,” Int. J. Remote Sensing 3, 327 (1982).
[Crossref]

Radio Sci. (3)

G. R. Valenzuela, “Scattering of Electromagnetic Waves from a Tilted Slightly Rough Surface,” Radio Sci., 3, 1051 (1968).

E. Bahar, “Scattering Cross Sections for Composite Random Surfaces—Full Wave Analysis,” Radio Sci. 16, 1327 (1981).
[Crossref]

E. Bahar, D. E. Barrick, “Scattering Cross Sections for Composite Surfaces that Cannot be Treated as Perturbed Physical Optics Problems,” Radio Sci., 18, 129 (1983).
[Crossref]

Other (2)

D. E. Barrick, Rough Surfaces, in Radar Cross Section Handbook (Plenum, New York, 1970), Chap. 9.

A. Ishimaru, Wave Propagation and Scattering in Random Media in Multiple Scattering, Turbulence, Rough Surfaces and Remote Sensing,. Vol. 2 (Academic, New York, 1978).

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Figures (6)

Fig. 1
Fig. 1

Scattering of electromagnetic waves from a rough conducting sphere.

Fig. 2
Fig. 2

Vertically polarized scattering cross section: β = 1.0, ◊, total cross section 〈σvv〉; ○, σ V V = | R V | 2; ×, 〈σVVl = | RVχs | 2; +, 〈σVVs1; △, 〈σVVs2.

Fig. 3
Fig. 3

Horizontally polarized cross section β = 1.0, ◊, total cross section 〈σHH〉; ○, σ H H = | R H | 2; ×, 〈σHHl = | RHχs | 2; +,〈σHHs1; △, 〈σHHs2.

Fig. 4
Fig. 4

Cross-polarized cross section, β = 1.0, +, total cross section 〈σVH〉 = 〈σVH〉; ○, 〈σHVs1; △, 〈σVHs2.

Fig. 5
Fig. 5

Vertically polarized scattering cross section for (a) β = 2.0, (b) β = 1.0, (c) β = 0.5, (d) β= 0.1; △, 〈σVV〉 total cross-section, +, 〈σVVl + 〈σVVs1 (Barrick's solution), ○, 〈σVVl = | RVχs | 2 (Abdelazeez's solution).

Fig. 6
Fig. 6

Cross-polarized cross section for (a) β = 2.0, (b) β = 1.0, (c) β = 0.5, (d) β = 0.1; △, 〈σVHs = 〈σHVs total cross-section, ○, 〈σVHs1 = 〈σHVs1 (Barrick's solution).

Equations (28)

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r s = h 0 â r + h s â r ,
W ( υ x , υ z ) = 1 π 2 h s h s exp ( i υ x x d + i υ z z d ) d x d d z d ,
v = k 0 ( n ̂ f n ̂ i ) ,
n ̂ i = â y 0
n ̂ f = sin θ 0 f â x 0 + cos θ 0 f â y 0 ,
n ̂ = ( n ̂ × â z 0 ) / | n ̂ × â z 0 | , n ̂ 2 = n ̂ = â r , n ̂ 3 = n ̂ 1 × n ̂ .
r d [ ( x x ) 2 + ( z z ) 2 ] 1 / 2 = ( x d 2 + z d 2 ) 1 / 2 π h 0 .
k d < k = ( υ x 2 + υ z 2 ) 1 / 2 < k c ,
σ P Q = σ P Q l + σ P Q s ,
σ P Q l = | χ s ( υ ) | 2 σ P Q ,
χ s ( υ ) = exp ( i υ h s ) ,
| χ s | 2 = exp [ 4 k 0 2 h s 2 cos 2 ( θ 0 f / 2 ) ] = exp ( υ 2 h s 2 ) .
σ P Q = δ P Q | R P | 2 ,
σ P Q s = m = 1 σ P Q s m ,
σ P Q s m = 4 π k 0 2 | D P Q | 2 P 2 ( n ̂ f , n ̂ i | n ̂ ) n ̂ â y exp ( υ y 2 h s 2 ) ( υ y 2 ) 2 m W m ( υ x , υ z ) m ! p ( h x , h z ) d h x d h z .
v = υ x n ̂ 1 + υ y n ̂ 2 + υ z n ̂ 3 .
W m ( υ x , υ z ) 2 2 m = 1 ( 2 π ) 2 h s h s m exp ( i υ x x d + i υ z z d ) d x d d z d = 1 2 2 m W m 1 ( x x , υ z ) W 1 ( υ x υ x , υ z υ z ) d υ x d υ z = 1 2 2 m W m 1 ( υ x , υ z ) W 1 ( υ x , υ z ) .
W ( υ x , υ z ) = W ( k ) = { 2 π B / k 4 k d < k < k c , 0 k > k c and k < k d ,
k 2 = υ x 2 + υ z 2 ( cm ) 2 .
k d = ( 2 π ) / d ,
λ 0 = 0.555 × 10 4 cm ( k 0 = 2 π λ 0 = 1.132 × 10 5 cm 1 ) .
k c = 4.5 × 10 5 cm 1 .
h s 2 = 0 2 π k d k c W ( k ) 4 kdkd ϕ = B 2 ( 1 k d 2 1 k c 2 ) .
B = β k c 2 k d 2 2 k 0 2 ( k c 2 k d 2 ) .
h s 2 = { 0.390 × 10 10 cm 2 , β = 2.0 , 0.195 × 10 10 cm 2 , β = 1.0 , 0.975 × 10 11 cm 2 , β = 0.5 , 0.195 × 10 11 cm 2 , β = 0.1 .
B = { 0.250 × 10 2 , β = 2.0 , 0.125 × 10 2 , β = 1.0 , 0.625 × 10 3 , β = 0.5 , 0.125 × 10 3 , β = 0.1 .
r = 40 i 12.
p ( h x , h z ) d h x d h z p ( γ , δ ) d γ d δ = sin γ cos γ d γ d δ π , 0 < δ < π 2 , 0 < δ < 2 π .

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