In the sense of metrology, sample stage actuators (piezos) of scanning probe microscopes are far from being perfect. Therefore raw surface profile data may contain trending components owing to the non-linearity of the actuators. Consequently, raw data should be subjected to a detrending algorithm. According to current standards, this procedure is limited to the removal of piston, slope and curvature. It is a well known effect for experimenters that undesired artifacts may arise, which negatively influence the precision of scanning probe measurements. However, by using the covariance matrix of the surface a method for the multivariate estimation of the systematic error can be derived. It leads to the concept of the principal surface for the removal of instrument errors.