  We analyze the surface morphology of metals after plastic deformation over a
range of scales from 10 nm to 2 mm, using a combination of atomic force
microscopy and scanning white-light interferometry. We demonstrate that an
initially smooth surface during deformation develops self-affine roughness over
almost four orders of magnitude in scale. The Hurst exponent $H$ of
one-dimensional surface profiles is initially found to decrease with increasing
strain and then stabilizes at $H \approx 0.75$. By analyzing their statistical
properties we show that the one-dimensional surface profiles can be
mathematically modelled as graphs of a fractional Brownian motion. Our findings
can be understood in terms of a fractal distribution of plastic strain within
the deformed samples.
