  Roughness determines many functional properties of surfaces, such as
adhesion, friction, and (thermal and electrical) contact conductance. Recent
analytical models and simulations enable quantitative prediction of these
properties from knowledge of the power spectral density (PSD) of the surface
topography. The utility of the PSD is that it contains statistical information
that is unbiased by the particular scan size and pixel resolution chosen by the
researcher. In this article, we first review the mathematical definition of the
PSD, including the one- and two-dimensional cases, and common variations of
each. We then discuss strategies for reconstructing an accurate PSD of a
surface using topography measurements at different size scales. Finally, we
discuss detecting and mitigating artifacts at the smallest scales, and
computing upper/lower bounds on functional properties obtained from models. We
accompany our discussion with virtual measurements on computer-generated
surfaces. This discussion summarizes how to analyze topography measurements to
reconstruct a reliable PSD. Analytical models demonstrate the potential for
tuning functional properties by rationally tailoring surface topography -
however, this potential can only be achieved through the accurate, quantitative
reconstruction of the power spectral density of real-world surfaces.
