Measurement uncertainty propagation in the case of filtering in roughness measurement

In roughness measurement a standardized Gaussian filter according to ISO 11562 is used to separate roughness from waviness. If the uncertainty of the measured profile is known, the uncertainty of the roughness profile as well as the waviness profile can be obtained by calculating the propagation of the measurement uncertainty in case of the filtering process. It turns out that, even in the case of uncorrelated measured data, the filtered data are always correlated. This correlation must be taken into account when calculating roughness or waviness parameters.