## Abstract

The wavelength dependence of both the total back-scatter cross section *σ** _{T}* and the depolarized back-scatter cross section

*σ*

*for rough metallic surfaces of known statistical characteristics has been determined experimentally by comparing data at 0.63-, 3.39- and 10.6*

_{D}*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

*σ*

*/*

_{T}*A*

_{0}is independent of wavelength λ, provided that

*h*/λ is greater than approximately ${\scriptstyle \frac{1}{4}}$. When $h/\mathrm{\lambda}\le {\scriptstyle \frac{1}{4}}$,

*σ*

*/*

_{T}*A*

_{0}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

*σ*

*to*

_{D}*σ*

*varies as (*

_{T}*h*/

*l*)

^{4}λ/4

*πδ*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 $h/\mathrm{\lambda}>{\scriptstyle \frac{1}{4}}$, both

*σ*

*/*

_{T}*A*

_{0}and

*σ*

*/*

_{D}*A*

_{0}vary as λ

^{−}

*where*

^{n}*n*increases with increasing

*ψ. n*has a value of 0.40 (±0.2) at 4

*ψ*=20° and 0.8 (±0.2) at 80°.

© 1969 Optical Society of America

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