In an effort to improve sub-molecular imaging precision, a general distributed-based modeling approach for the atomic force microscope system is proposed which allows for the design of a stabilizing controller/estimation scheme that stabilizes the micro-cantilever based system while asymptotically identifying the atomic interaction force, that is, the estimated interaction force asymptotically approaches the actual interaction force; hence the estimated interaction force can be utilized to generate high precision atomic-resolution images. Differing from current practices of simple lumped model sets of ordinary differential equations, the proposed approach attacks the more difficult distributed parameter model.