A commonly used estimator for the microtopography of an optical surface is its rms-roughness. Raw surface profile data may contain trending components. Therefore they should be subjected to a detrending procedure before estimating the rms value. This procedure is limited in most cases to the removal of piston, slope, and curvature. Consequently, undesired artifacts may arise, which negatively influence the precision of rms-roughness estimation. In scanning surface metrology, the eigenvalues and eigenvectors of the covariance matrix of the surface can be used for a robust and precise multivariate estimation of rms-roughness.