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/Ao is independent of wavelength λ, provided that h/λ is greater than approximately ¼. When h/λ≤¼, 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>¼, bothσT/A0 and σD/A0 vary as λ-n where n increases with increasing ψ. n has a value of 0.40 (±0.2) at ψ = 20° and 0.8 (±0.2) at 80°.

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  1. H. Davies and G. G. MacFarlane, Proc. Phys. Soc. (London) 58, 717 (1946).
  2. C. R. Grant and B. S. Yaplee, Proc. IRE 45, 976 (1957).
  3. J. C. Wiltse, S. P. Schlesinger, and C. M. Johnson, Proc. IRE 45, 220 (1957).
  4. J. V. Evans and G. H. Pettengill, J. Geophys. Res. 68, 423 (1963).
  5. M. W. Long, IEEE Trans. Ant. Prop. AP-13, 749 (1965).
  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).
  8. J. Renau, P. K. Cheo, and H. G. Cooper, J. Opt. Soc. Am. 57, 459 (1967).
  9. T. J. Bridges and J. W. Kluver, Appl. Opt. 4, 1121 (1965).
  10. T. J. Bridges, T. Y. Chang, and P. K. Cheo, Appl. Phys. Letters 12, 297 (1968).
  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 = 4πArec2. 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).
  13. J. Ruze, Proc. IEEE 54, 633 (1966).
  14. H. Zucker, Bell System Tech. J. 47, 1637 (1968).
  15. G. P. Harnwell, Principles of Electricity and Electromagnetism (McGraw-Hill Book Co., New York, 1949), 2nd ed. p. 585.

Bridges, T. J.

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

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

Chang, T. Y.

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

Cheo, P. K.

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

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

Collinson, J. A.

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

Cooper, H. G.

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

Davies, H.

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

Evans, J. V.

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

Grant, C. R.

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

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).

Kluver, J. W.

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

Long, M. W.

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

MacFarlane, G. G.

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

Pettengill, G. H.

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

Renau, J.

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

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

Ruze, J.

J. Ruze, Proc. IEEE 54, 633 (1966).

Schlesinger, S. P.

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

Senior, T. B. A.

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

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).

Yaplee, B. S.

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

Zucker, H.

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

Other (15)

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

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

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

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

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

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

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

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

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

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

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 = 4πArec2. When these substitutions are made in Eq. (1), we get the usual radar equation, Pr/PT = GTGRλ2σ/ (4π)3R4.

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

J. Ruze, Proc. IEEE 54, 633 (1966).

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

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

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