  When measuring the roughness of rough surfaces, the limited sizes of scanned
areas lead to its systematic underestimation. Levelling by polynomials and
other filtering used in real-world processing of atomic force microscopy data
increases this bias considerably. Here a framework is developed providing
explicit expressions for the bias of squared mean square roughness in the case
of levelling by fitting a model background function using linear least squares.
The framework is then applied to polynomial levelling, for both one-dimensional
and two-dimensional data processing, and basic models of surface
autocorrelation function, Gaussian and exponential. Several other common
scenarios are covered as well, including median levelling, intermediate
Gaussian--exponential autocorrelation model and frequency space filtering.
Application of the results to other quantities, such as Rq, Sq, Ra and~Sa is
discussed. The results are summarized in overview plots covering a range of
autocorrelation functions and polynomial degrees, which allow graphical
estimation of the bias.
