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°.
P. K. CHEO and J. RENAU, "Wavelength Dependence of Total and Depolarized Back-Scattered Laser Light from Rough Metallic Surfaces," J. Opt. Soc. Am. 59, 821-826 (1969)