Abstract: This invention relates to multi-purpose probe-based apparatus, and to methods for providing images of surface topography, and detection and quantitative mapping of local mechanical and electromagnetic properties in non-resonant oscillatory mode. These methods may include filtering of incoming probe signals. These incoming probe signals provide time deflection curves, parts of which are used for the control of scanning and collection of data that reflects sample adhesion, stiffness, elastic modulus and viscoelastic response, electric and magnetic interactions. These methods permit adaptive choice of an AFM's deflection set-point, which allows imaging at the contact repulsive force for precise surface profilometry, as non-resonant oscillation brings tip and sample into intermittent contact. These methods permit choosing a desired deformation model that allows an extraction of quantitative mechanical properties including viscoelastic response from deflection curves.