The principle possibility of the detection of the sort of material a surface consists of (in other words, obtaining the spectroscopic, or "Hamaker constant" image of the surface) is proven for the atomic force microscopy method. It is shown that the problem can be reduced to the Fredgolm integral equation of the first kind with a core of the Hilbert-Schmidt type. This problem is demonstrated to have a unique solution, provided the model case of exact measurements and the surface topography is known in advance. It is shown that the latter can be considered as the topography obtained in the contact mode. The possibility of the spectroscopic image recovery for the measurements with errors is discussed. As an example, obtaining the Hamaker constant is demonstrated for an example of the surface consisting of two different materials.