We analyse the mechanisms of contrast formation in non-contact atomic force microscopy (NC-AFM) on insulators and use comparisons of theoretical models with experiment to establish tip and surface properties. The results for the CaF2 (1 1 1) surface provide information about the character of the tip-surface interaction, tip sharpness and electrostatic potential. and the distance range of imaging. We analyse whether knowledge of the electrostatic potential at the imaging distance is enough to interpret the image and show that account of the surface deformation is crucial for quantitative understanding of the image contrast. Then we turn to a more complex CaCO3 (1 0 1 4) surface, which has a complex anion. We demonstrate that with an ionic tip the atomic structure of the CO32- group cannot be resolved, and we also study the dependence of imaging on the tip orientation. Again, the surface deformation induced by the tip during scanning plays a crucial role in image contrast. We argue that if the relation between the tip structures, potential and observed image could be uniquely established for some systems. these systems could serve as a reference for tip characterisation in further studies. (C) 2002 Elsevier Science B.V All rights reserved.