Abstract

The wavelength dependence of both the total back-scatter cross section σT and the depolarized back-scatter cross section σD for rough metallic surfaces of known statistical characteristics has been determined experimentally by comparing data at 0.63-, 3.39- and 10.6 μ wavelengths. The rms height from the mean, h, and the mean scale size l of the two surfaces used in the experiment are: h≈1 μ, l≈10 μ; h≈7 μ, l≈50 μ. At or near normal incidence, results show that the total cross section per beam area σT/A0 is independent of wavelength λ, provided that h/λ is greater than approximately 14. When h/λ14, σT/A0 increases rapidly with decreasing h/λ. Previous microwave data suggest that the metallic surface reflects nearly as a perfectly smooth surface without significant scattering losses when h/λ≲1/40. At or near normal incidence the ratio of σD to σT varies as (h/l)4λ/4πδ for all values of h/λ studied, where δ is the skin depth of the metallic surface. For incident angles ψ in the range from 20° to 80° and h/λ>14, both σT/A0 and σD/A0 vary as λn where n increases with increasing ψ. n has a value of 0.40 (±0.2) at 4ψ=20° and 0.8 (±0.2) at 80°.

© 1969 Optical Society of America

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References

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  1. H. Davies and G. G. MacFarlane, Proc. Phys. Soc. (London) 58, 717 (1946).
    [CrossRef]
  2. C. R. Grant and B. S. Yaplee, Proc. IRE 45, 976 (1957).
    [CrossRef]
  3. J. C. Wiltse, S. P. Schlesinger, and C. M. Johnson, Proc. IRE 45, 220 (1957).
    [CrossRef]
  4. J. V. Evans and G. H. Pettengill, J. Geophys. Res. 68, 423 (1963).
    [CrossRef]
  5. M. W. Long, IEEE Trans. Ant. Prop. AP-13, 749 (1965).
    [CrossRef]
  6. M. I. Skolnik, Introduction to Radar Systems (McGraw–Hill Book Co., New York, 1962), p. 531.
  7. J. Renau and J. A. Collinson, Bell System Tech. J. 44, 2203 (1965).
    [CrossRef]
  8. J. Renau, P. K. Cheo, and H. G. Cooper, J. Opt. Soc. Am. 57, 459 (1967).
    [CrossRef] [PubMed]
  9. T. J. Bridges and J. W. Kluver, Appl. Opt. 4, 1121 (1965).
    [CrossRef]
  10. T. J. Bridges, T. Y. Chang, and P. K. Cheo, Appl. Phys. Letters 12, 297 (1968).
    [CrossRef]
  11. For the case of a radar, Pi=PTGTA0/4πR2, where is the PT power at the transmitting antenna, and GT is the gain of the antenna. Moreover, the receiver gain GR and the area of the receiving antenna Arec are related by GR=4πArec/λ2. When these substitutions are made in Eq. (1), we get the usual radar equation, Pr/PT=GTGRλ2σ/(4π)3R4.
  12. T. B. A. Senior, IEEE Trans. Ant. Prop. AP-13, 629 (1965).
    [CrossRef]
  13. J. Ruze, Proc. IEEE 54, 633 (1966).
    [CrossRef]
  14. H. Zucker, Bell System Tech. J. 47, 1637 (1968).
    [CrossRef]
  15. G. P. Harnwell, Principles of Electricity and Electromagnetism (McGraw–Hill Book Co., New York, 1949), 2nd ed. p. 585.

1968 (2)

T. J. Bridges, T. Y. Chang, and P. K. Cheo, Appl. Phys. Letters 12, 297 (1968).
[CrossRef]

H. Zucker, Bell System Tech. J. 47, 1637 (1968).
[CrossRef]

1967 (1)

1966 (1)

J. Ruze, Proc. IEEE 54, 633 (1966).
[CrossRef]

1965 (4)

T. B. A. Senior, IEEE Trans. Ant. Prop. AP-13, 629 (1965).
[CrossRef]

T. J. Bridges and J. W. Kluver, Appl. Opt. 4, 1121 (1965).
[CrossRef]

M. W. Long, IEEE Trans. Ant. Prop. AP-13, 749 (1965).
[CrossRef]

J. Renau and J. A. Collinson, Bell System Tech. J. 44, 2203 (1965).
[CrossRef]

1963 (1)

J. V. Evans and G. H. Pettengill, J. Geophys. Res. 68, 423 (1963).
[CrossRef]

1957 (2)

C. R. Grant and B. S. Yaplee, Proc. IRE 45, 976 (1957).
[CrossRef]

J. C. Wiltse, S. P. Schlesinger, and C. M. Johnson, Proc. IRE 45, 220 (1957).
[CrossRef]

1946 (1)

H. Davies and G. G. MacFarlane, Proc. Phys. Soc. (London) 58, 717 (1946).
[CrossRef]

Bridges, T. J.

T. J. Bridges, T. Y. Chang, and P. K. Cheo, Appl. Phys. Letters 12, 297 (1968).
[CrossRef]

T. J. Bridges and J. W. Kluver, Appl. Opt. 4, 1121 (1965).
[CrossRef]

Chang, T. Y.

T. J. Bridges, T. Y. Chang, and P. K. Cheo, Appl. Phys. Letters 12, 297 (1968).
[CrossRef]

Cheo, P. K.

T. J. Bridges, T. Y. Chang, and P. K. Cheo, Appl. Phys. Letters 12, 297 (1968).
[CrossRef]

J. Renau, P. K. Cheo, and H. G. Cooper, J. Opt. Soc. Am. 57, 459 (1967).
[CrossRef] [PubMed]

Collinson, J. A.

J. Renau and J. A. Collinson, Bell System Tech. J. 44, 2203 (1965).
[CrossRef]

Cooper, H. G.

Davies, H.

H. Davies and G. G. MacFarlane, Proc. Phys. Soc. (London) 58, 717 (1946).
[CrossRef]

Evans, J. V.

J. V. Evans and G. H. Pettengill, J. Geophys. Res. 68, 423 (1963).
[CrossRef]

Grant, C. R.

C. R. Grant and B. S. Yaplee, Proc. IRE 45, 976 (1957).
[CrossRef]

Harnwell, G. P.

G. P. Harnwell, Principles of Electricity and Electromagnetism (McGraw–Hill Book Co., New York, 1949), 2nd ed. p. 585.

Johnson, C. M.

J. C. Wiltse, S. P. Schlesinger, and C. M. Johnson, Proc. IRE 45, 220 (1957).
[CrossRef]

Kluver, J. W.

Long, M. W.

M. W. Long, IEEE Trans. Ant. Prop. AP-13, 749 (1965).
[CrossRef]

MacFarlane, G. G.

H. Davies and G. G. MacFarlane, Proc. Phys. Soc. (London) 58, 717 (1946).
[CrossRef]

Pettengill, G. H.

J. V. Evans and G. H. Pettengill, J. Geophys. Res. 68, 423 (1963).
[CrossRef]

Renau, J.

J. Renau, P. K. Cheo, and H. G. Cooper, J. Opt. Soc. Am. 57, 459 (1967).
[CrossRef] [PubMed]

J. Renau and J. A. Collinson, Bell System Tech. J. 44, 2203 (1965).
[CrossRef]

Ruze, J.

J. Ruze, Proc. IEEE 54, 633 (1966).
[CrossRef]

Schlesinger, S. P.

J. C. Wiltse, S. P. Schlesinger, and C. M. Johnson, Proc. IRE 45, 220 (1957).
[CrossRef]

Senior, T. B. A.

T. B. A. Senior, IEEE Trans. Ant. Prop. AP-13, 629 (1965).
[CrossRef]

Skolnik, M. I.

M. I. Skolnik, Introduction to Radar Systems (McGraw–Hill Book Co., New York, 1962), p. 531.

Wiltse, J. C.

J. C. Wiltse, S. P. Schlesinger, and C. M. Johnson, Proc. IRE 45, 220 (1957).
[CrossRef]

Yaplee, B. S.

C. R. Grant and B. S. Yaplee, Proc. IRE 45, 976 (1957).
[CrossRef]

Zucker, H.

H. Zucker, Bell System Tech. J. 47, 1637 (1968).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Letters (1)

T. J. Bridges, T. Y. Chang, and P. K. Cheo, Appl. Phys. Letters 12, 297 (1968).
[CrossRef]

Bell System Tech. J. (2)

J. Renau and J. A. Collinson, Bell System Tech. J. 44, 2203 (1965).
[CrossRef]

H. Zucker, Bell System Tech. J. 47, 1637 (1968).
[CrossRef]

IEEE Trans. Ant. Prop. (2)

T. B. A. Senior, IEEE Trans. Ant. Prop. AP-13, 629 (1965).
[CrossRef]

M. W. Long, IEEE Trans. Ant. Prop. AP-13, 749 (1965).
[CrossRef]

J. Geophys. Res. (1)

J. V. Evans and G. H. Pettengill, J. Geophys. Res. 68, 423 (1963).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. IEEE (1)

J. Ruze, Proc. IEEE 54, 633 (1966).
[CrossRef]

Proc. IRE (2)

C. R. Grant and B. S. Yaplee, Proc. IRE 45, 976 (1957).
[CrossRef]

J. C. Wiltse, S. P. Schlesinger, and C. M. Johnson, Proc. IRE 45, 220 (1957).
[CrossRef]

Proc. Phys. Soc. (London) (1)

H. Davies and G. G. MacFarlane, Proc. Phys. Soc. (London) 58, 717 (1946).
[CrossRef]

Other (3)

M. I. Skolnik, Introduction to Radar Systems (McGraw–Hill Book Co., New York, 1962), p. 531.

For the case of a radar, Pi=PTGTA0/4πR2, where is the PT power at the transmitting antenna, and GT is the gain of the antenna. Moreover, the receiver gain GR and the area of the receiving antenna Arec are related by GR=4πArec/λ2. When these substitutions are made in Eq. (1), we get the usual radar equation, Pr/PT=GTGRλ2σ/(4π)3R4.

G. P. Harnwell, Principles of Electricity and Electromagnetism (McGraw–Hill Book Co., New York, 1949), 2nd ed. p. 585.

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Figures (6)

Fig. 1
Fig. 1

The total back-scattering cross section per beam area at normal incidence, σT(0)/A0, vs the ratio of the surface rms height to wavelength, h/λ, for two rough metallic surfaces and three different wavelengths; 0.63 μ(□), 3.39 μ (○) and 10.6 μ(△). The dashed curve in the smooth region is calculated from Eq. (3). A0≃0.20 cm2 (surface No. 1: h≃7 μ, l≃50 μ; surface No. 3: h≃1 μ, l≃10 μ).

Fig. 2
Fig. 2

Normalized total back-scattering cross section σT(ψ)/σT(0) vs angle of incidence ψ for three different wavelengths; 0.63 μ(△), 3.39 μ(□) and 10.6 μ(○). (Surface No. 1: h≃7 μ, l≃50 μ; h / λ 1 4.)

Fig. 3
Fig. 3

Exponent n (assuming that σT∝λn) vs angles of incidence ψ; h / λ 1 4.

Fig. 4
Fig. 4

Normalized back-scattering cross section of the depolarized component σD(ψ)/σT(0) vs angle of incidence ψ for three different wavelengths; 0.63 μ(△), 3.39 μ(□), and 10.6 μ(○). (Surface No. 1: h≃7 μ, l≃50 μ; h / λ 1 4.)

Fig. 5
Fig. 5

Ratio of the depolarized to the total back-scattering cross sections σD(ψ)/σT(ψ) vs angle of incidence for three different wavelengths; 0.63 μ (□), 3.39 μ(△) and 10.6 μ(○). (Surface No. 1: h≃7 μ, l≃50 μ; h / λ 1 4.)

Fig. 6
Fig. 6

Depolarized back-scattering cross section normalized to its initial value σD(ψ)/σD(0) vs angle of incidence for three different wavelengths; 0.63 μ(○), 3.39 μ(△) and 10.6 μ(□). (Surface No. 1: h≃7 μ, l≃50 μ; h / λ 1 4.)

Tables (3)

Tables Icon

Table I Wavelength dependence of total back-scattering cross section at normal incidence σT(0)/A0.

Tables Icon

Table II Wavelength dependence of the depolarized to the total back-scattering cross sections at normal incidence [σD(0)/σT(0)]λyλ.

Tables Icon

Table III Comparison of measured σD(0)/σT(0) values with calculated values from Eq. (5).

Equations (8)

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σ ( λ , ψ ) A 0 = 4 π Ω rec P r ( λ , ψ ) P i ,
σ T / A 0 1 / [ 2 ( h / l ) 2 ]             ( h / λ 1 4 ) .
σ T ( 0 ) / A 0 = 4 π A 0 / λ 2 ,
σ D ( 0 ) / σ T ( 0 ) = β ( h / l ) m λ 1 2 .
σ D ( 0 ) / σ T ( 0 ) = ( h / l ) 4 ( λ / 4 π δ ) .
σ D ( 0 ) / A 0 = 1 2 ( h / l ) 2 ( λ / 4 π δ ) .
σ T ( 80 ° ) λ - 0.8 ( ± 0.2 ) .
σ D ( ψ ) λ - n ( ψ ) ,