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The roughness spectrum $g(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ (or spectral density function) for surfaces of silver, copper, gold, and magnesium deposits is deduced from surface profiles determined by using microdensitometer analysis of micrographs of shadowed-surface carbon replicas. A process based on computation of autocovariance function via the fast-Fourier-transform algorithm is used. It is shown that the $g(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ function is not a perfect Gaussian function as is usually assumed. An analytical model is given that provides a rather suitable fit to the computed $g(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ functions. Results are compared with those obtained from optical experiments (mainly the attenuated-total-reflection method). Discrepancies between the values of $\ensuremath{\delta}$ (rms roughness) and $\ensuremath{\sigma}$ (autocorrelation length) determined by the use of our procedure and corresponding values deduced from optical experiments are elucidated.

Autocovariance functions (ACF's) for rough surfaces of copper, silver, and gold deposits are deduced from surface profiles determined by the use of microdensitometer analysis of surface-shadowed carbon replicas. It is shown that the initial portions of the ACF's have a Gaussian form. The root-mean-square (rms) surface roughness $\ensuremath{\delta}$ and the autocorrelation length $\ensuremath{\sigma}$ are deduced for each surface. Values of $\ensuremath{\sigma}$ agree with corresponding values deduced from the ACF's of the surface slopes. Results of this study are compared with those previously obtained for rough magnesium deposits. We conclude that the Gaussian model is suitable to represent in general the ACF's of rough metallic surfaces. Lastly, it is shown that $\ensuremath{\sigma}$ increases with $\ensuremath{\delta}$, and within the accuracy range of their measurements there is a linear relation between $\ensuremath{\delta}$ and $\ensuremath{\sigma}$.