Abstract

Like- and cross-polarized scattering cross sections are determined at optical frequencies for conducting cylinders with rough surfaces. Both normal and oblique incidence with respect to the cylinder axis are considered. The full wave approach is used to account for both the specular point scattering and the diffuse scattering. For the roughness scales considered, the scattering cross sections differ significantly from those derived for smooth or slightly rough conducting cylinders. Several illustrative examples are presented and the albedos for smooth and rough cylinders are compared.

© 1986 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. 8.
  2. G. S. Brown, “Backscattering from Gaussian-Distributed Perfectly Conducting Rough Surfaces,” IEEE Trans. Antennas Propag. AP-26, 472 (1978).
    [Crossref]
  3. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).
  4. E. Bahar, “Full Wave Solutions for the Depolarization of the Scattered Radiation Fields by Rough Surfaces of Arbitrary Slope,” IEEE Trans. Antennas Propag. AP-29, 443 (1981).
    [Crossref]
  5. E. Bahar, “Depolarization of the Scattered Radiation Fields by Conducting Objects of Irregular Shape Above Rough Land and Sea: Full Wave Solutions,” Radio Sci. 17, 1055 (1982).
    [Crossref]
  6. P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
  7. E. Bahar, “Depolarization of Electromagnetic Waves Excited by Distributions of Electric and Magnetic Sources in Inhomogeneous Multilayered Structures of Arbitrarily Varying Thickness. Generalized Field Transforms,” J. Math. Phys. 14, 1502 (1973).
    [Crossref]
  8. E. Bahar, “Depolarization of Electromagnetic Waves Excited by Distributions of Electric and Magnetic Sources in Inhomogeneous Multilayered Structures of Arbitrarily Varying Thickness. Full Wave Solutions,” J. Math. Phys. 14, 1510 (1973).
    [Crossref]
  9. E. Bahar, 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-27, 214 (1979).
    [Crossref]
  10. S. O. Rice, “Reflection of Electromagnetic Waves from a Slightly Rough Surface,” Commun. Pure Appl. Math. 4, 351 (1951).
    [Crossref]
  11. E. Bahar, “Scattering Cross Sections for Composite Random Surfaces—Full Wave Analysis,” Radio Sci. 16, 1327 (1981).
    [Crossref]
  12. 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]
  13. H. Ehrenreich, “The Optical Properties of Metals,” IEEE Spectrum 2, (3) 162 (1965).
    [Crossref]

1983 (1)

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]

1982 (1)

E. Bahar, “Depolarization of the Scattered Radiation Fields by Conducting Objects of Irregular Shape Above Rough Land and Sea: Full Wave Solutions,” Radio Sci. 17, 1055 (1982).
[Crossref]

1981 (2)

E. Bahar, “Full Wave Solutions for the Depolarization of the Scattered Radiation Fields by Rough Surfaces of Arbitrary Slope,” IEEE Trans. Antennas Propag. AP-29, 443 (1981).
[Crossref]

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

1979 (1)

E. Bahar, 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-27, 214 (1979).
[Crossref]

1978 (1)

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

1973 (2)

E. Bahar, “Depolarization of Electromagnetic Waves Excited by Distributions of Electric and Magnetic Sources in Inhomogeneous Multilayered Structures of Arbitrarily Varying Thickness. Generalized Field Transforms,” J. Math. Phys. 14, 1502 (1973).
[Crossref]

E. Bahar, “Depolarization of Electromagnetic Waves Excited by Distributions of Electric and Magnetic Sources in Inhomogeneous Multilayered Structures of Arbitrarily Varying Thickness. Full Wave Solutions,” J. Math. Phys. 14, 1510 (1973).
[Crossref]

1965 (1)

H. Ehrenreich, “The Optical Properties of Metals,” IEEE Spectrum 2, (3) 162 (1965).
[Crossref]

1951 (1)

S. O. Rice, “Reflection of Electromagnetic Waves from a Slightly Rough Surface,” Commun. Pure Appl. Math. 4, 351 (1951).
[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, “Depolarization of the Scattered Radiation Fields by Conducting Objects of Irregular Shape Above Rough Land and Sea: Full Wave Solutions,” Radio Sci. 17, 1055 (1982).
[Crossref]

E. Bahar, “Full Wave Solutions for the Depolarization of the Scattered Radiation Fields by Rough Surfaces of Arbitrary Slope,” IEEE Trans. Antennas Propag. AP-29, 443 (1981).
[Crossref]

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

E. Bahar, 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-27, 214 (1979).
[Crossref]

E. Bahar, “Depolarization of Electromagnetic Waves Excited by Distributions of Electric and Magnetic Sources in Inhomogeneous Multilayered Structures of Arbitrarily Varying Thickness. Generalized Field Transforms,” J. Math. Phys. 14, 1502 (1973).
[Crossref]

E. Bahar, “Depolarization of Electromagnetic Waves Excited by Distributions of Electric and Magnetic Sources in Inhomogeneous Multilayered Structures of Arbitrarily Varying Thickness. Full Wave Solutions,” J. Math. Phys. 14, 1510 (1973).
[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. 8.

Beckmann, P.

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

Brown, G. S.

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

Ehrenreich, H.

H. Ehrenreich, “The Optical Properties of Metals,” IEEE Spectrum 2, (3) 162 (1965).
[Crossref]

Feshbach, H.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Morse, P. M.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Rajan, G. G.

E. Bahar, 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-27, 214 (1979).
[Crossref]

Rice, S. O.

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

Spizzichino, A.

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

Commun. Pure Appl. Math. (1)

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

IEEE Spectrum (1)

H. Ehrenreich, “The Optical Properties of Metals,” IEEE Spectrum 2, (3) 162 (1965).
[Crossref]

IEEE Trans. Antennas Propag. (3)

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

E. Bahar, “Full Wave Solutions for the Depolarization of the Scattered Radiation Fields by Rough Surfaces of Arbitrary Slope,” IEEE Trans. Antennas Propag. AP-29, 443 (1981).
[Crossref]

E. Bahar, 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-27, 214 (1979).
[Crossref]

J. Math. Phys. (2)

E. Bahar, “Depolarization of Electromagnetic Waves Excited by Distributions of Electric and Magnetic Sources in Inhomogeneous Multilayered Structures of Arbitrarily Varying Thickness. Generalized Field Transforms,” J. Math. Phys. 14, 1502 (1973).
[Crossref]

E. Bahar, “Depolarization of Electromagnetic Waves Excited by Distributions of Electric and Magnetic Sources in Inhomogeneous Multilayered Structures of Arbitrarily Varying Thickness. Full Wave Solutions,” J. Math. Phys. 14, 1510 (1973).
[Crossref]

Radio Sci. (3)

E. Bahar, “Depolarization of the Scattered Radiation Fields by Conducting Objects of Irregular Shape Above Rough Land and Sea: Full Wave Solutions,” Radio Sci. 17, 1055 (1982).
[Crossref]

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 (3)

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

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

D. E. Barrick, “Rough Surfaces,” in Radar Cross Section Handbook (Plenum, New York, 1970), Chap. 8.

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Figures (12)

Fig. 1
Fig. 1

Incident and scattered waves in the x-y plane.

Fig. 2
Fig. 2

Plane wave incident in the y-z plane.

Fig.3
Fig.3

σVV〉,Eq.(24),case 1, θ 0 i = 0 °, total solid line,|χ|2 σ VV (X), 〈σVVs1(□), 〈σVVs2(▵).

Fig. 4
Fig. 4

σHH〉, Eq. (24), case 1, θ 0 i = 0 °, total solid line, |χ|2 σ HH (X), 〈σHHs1 (□), 〈σHHs2 (▵).

Fig. 5
Fig. 5

σVV〉, Eq. (24), case 2, θ 0 i = 0 °, total solid line, |χ|2 σ VV (X), 〈σVVs1(□), 〈σVVs2(▵).

Fig. 6
Fig. 6

σHH〉, Eq. (24), case 2, θ 0 i = 0 °, total solid line, |χ|2 σ HH (X), 〈σHHs1 (□), 〈σHHs2 (▵).

Fig. 7
Fig. 7

σVV〉, Eq. (24), case 2, θ 0 i = 30 °, smooth cylinder (+), rough cylinder (□).

Fig. 8
Fig. 8

σHH〉, Eq. (24), case 2, θ 0 i = 30 °, smooth cylinder (+), rough cylinder (□).

Fig. 9
Fig. 9

σHV〉 = 〈σVH〉, Eq. (24), case 2, θ 0 i = 30 °, smooth cylinder (+), rough cylinder (□).

Fig. 10
Fig. 10

σVV〉, Eq. (24), case 2, θ 0 i = 30 °, scatter plane, smooth cylinder (+), rough cylinder (□).

Fig. 11
Fig. 11

σHH〉, Eq. (24), case 2, θ 0 i = 30 °, scatter plane, smooth cylinder (+), rough cylinder (□).

Fig. 12
Fig. 12

σHV〉 = 〈σVH〉, Eq. (24), case 2, θ 0 i = 30 °, scatter plane, smooth cylinder (+), rough cylinder (□).

Tables (2)

Tables Icon

Table II θ 0 i = 30 °

Equations (34)

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( G Vf G Hf ) = G 0 ( D VV D VH D HV D HH ) ( G Vi G Hi ) exp [ i υ ̅ r ̅ s ] dS
D = C 0 i n T f FT i U ( n ̅ i n ̅ ) U ( n ̅ f n ̅ ) ,
G 0 = i k 0 exp ( i k 0 r ) / 2 π r .
υ ̅ = k 0 ( n ̅ f n ̅ i ) = υ x ā x + υ y ā y + υ z ā z ,
C 0 i n = n ̅ i n ̅ ,
dS = dxdz / ( n ̅ ā y ) .
exp ( i υ z z ) dz = 2 π δ ( υ z ) .
G f = G 0 i DG i exp [ i υ ̅ ( x ā x + y ā y ) ] dx / ( n ̅ ā y ) ,
G 0 i = ( k 0 2 π ρ cos θ 0 i ) 1 / 2 exp ( i π / 4 ) exp [ i k 0 ( ρ cos θ 0 i + z sin θ 0 i ) ] ,
n ̅ i = cos θ 0 i ā y + sin θ 0 i ā z .
n ̅ f = sin θ 0 f cos ϕ f ā x + cos θ 0 f ā y + sin θ 0 f sin ϕ f ā z
sin θ 0 f sin ϕ f = sin θ 0 i .
n ̅ f = cos θ 0 i ( sin ϕ ā x + cos ϕ ā y ) + sin θ 0 i ā z ,
n ̅ s = υ ̅ / υ = sin ( ϕ / 2 ) ā x + cos ( ϕ / 2 ) ā y = ā r = sin θ 0 f cos ϕ f ā x + ( cos θ 0 f + cos θ 0 i ) ā y [ 2 cos θ 0 i ( cos θ 0 i + cos θ 0 f ) ] 1 / 2 .
σ PQ = | G Pf | 2 | G Qi | 2 2 π ρ π a = k 0 π a cos θ 0 i D PQ D PQ * exp [ i υ x ( x x ) + i υ y ( y y ) ] ( n ̅ ā y ) ( n ̅ ā y ) × χ 2 dxd x ,
r ̅ s = ( a + h s ) ā r = ( a + h s ) ( x ā x + y ā y ) a ,
χ = exp ( i υ n h s ) ,
υ ̅ = 2 k 0 cos θ 0 i cos ( ϕ / 2 ) n ̅ s , υ n = υ ̅ n ̅ ,
χ 2 = exp [ i υ n ( h s h s ) ] .
| χ | 2 = exp [ υ n 2 h s 2 ] ,
χ 2 = | χ | 2 exp ( υ n 2 h s h s ) .
| χ | 2 | χ | 2 = exp [ υ 2 h s 2 ] = exp [ β cos 2 ( ϕ / 2 ) cos 2 θ 0 i ] .
W ( k ) 4 = 1 2 π h s h s exp ( i k τ ) d τ .
σ PQ = | χ | 2 σ PQ + σ PQ s .
σ PQ = k 0 π a cos θ 0 i a a D PQ ( n ̅ ā y ) | exp ( i υ x x + i υ y y ) dx | 2 = cos ( ϕ / 2 ) cos 2 θ 0 i | D PQ n ̅ ā y | n ̅ = n ̅ s 2 .
σ PQ = cos ( ϕ / 2 ) | R P | 2 δ PQ ,
σ PQ s = k 0 π a cos θ 0 i A i | D PQ | 2 exp ( i υ T τ ) ( χ 2 | χ | 2 ) d τ dx n ̅ ā y ,
σ PQ s = m = 1 σ PQ sm = 2 k 0 cos θ 0 i | D PQ | 2 Q ( υ n , υ T ) d γ ,
Q ( υ n , υ T ) = 1 2 π ( χ 2 | χ | 2 ) exp ( i υ T τ ) d τ = | χ ( υ n ) | 2 m ( υ n 2 ) 2 m W m ( υ T ) m ! ,
W m = 2 2 m 2 π h s h s m exp ( i υ T τ ) d τ = W m 1 W W m 1 ( υ T k ) W ( k ) dk .
σ PQ s = k 0 2 cos θ 0 i | D PQ | 2 υ n 2 W ( υ T ) d γ .
W ( k ) = { 2 B π k 4 , k d < | k | < k c , 0 , elsewhere , k d = π / a and k c = 4.5 × 10 5 cm 1
W ( k ) = { 2 B ( k k d ) 4 π [ ( k k d ) 2 + κ 2 ] 4 , k d < | k | < k c , 0 , elsewhere , k d = 2 / a , k c = 4 k 0 , and κ = 0.3 k d
h s 2 = W ( k ) 4 d k = β / 4 k 0 2 .

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