## 1 Introduction  
The protection of natural stones used in historical architecture is generally carried out through the application of suitable water-repellent coatings, which prevent the capillary absorption of condensed water and dissolved atmospheric pollutants into the porous stone network, thereby limiting the associated deterioration phenomena [1]. Since the effectiveness of these coatings mostly relies on their ability to modify the interaction of the treated surface with water, understanding the extent of surface modification, both in terms of effective surface coverage and change of chemical properties, is a key issue for the prediction of protective efficacy [2]. The effects of a hydrophobic coating on the surface properties can be studied at the macroscopic level by evaluating the behaviour of the treated stone with respect to established physical parameters, among which capillary water absorption and surface wettability have the highest relevance. Complementary to this, electron and atomic force microscopy give an insight into treatment-induced changes of the stone surface morphology at the micro- and nano-scale [3; 4], while SEM-EDX (Scanning Electron Microscopy with Energy-dispersive X-ray probe) and FTIR spectroscopies may allow one to detect the presence and the surface distribution of a coating material through the observation of atomic [5] and molecular spectra [6], respectively. However, linking information at the microscale, e.g., from observation of stone surface morphology, to macroscopic effects in terms of physical behaviour can be especially arduous. In the first place, natural stones are heterogeneous systems with high complexity and variety in terms of microstructure and mineralogical composition. Secondly, the wide range of coating materials that may be used in stone protection show markedly different properties, as well. Thus, the main factors responsible for the overall behaviour of the system towards water may be very difficult to identify, all of which makes a prediction of the effectiveness of a coating material an arduous or impossible task [7]. Besides that, for porous solids such as natural stones, the very concept of \"surface\" defies a clear-cut definition; in fact, the effective surface area interacting with external agents and/or with a protective coating material upon its application includes both the macroscopic outer surface and the outermost part of the pore network, insofar as the pore walls may also be involved in such interaction. Thus, upon application of a water repellent treatment, its contribution to the modification of surface topography and properties depends on the product penetration, reactivity and distribution. Unfortunately, surface analysis of stones, e.g., by electron microscopy techniques to explore the outer surface or even polished cross-sectional ones, does not allow a 3D description of the stone surface morphology and of the pore network topography sufficiently complete and representative of the inner microstructure [8]. In particular, only limited information about the actual amount and distribution of the treating material can be attained in this way. This is a significant limitation, since the interaction of the stone with condensed water is determined not only by the outermost surface, but also by the pore walls and shape near the very surface. As further shortcomings, the spectroscopic detection of silicon-based products, which are currently the class of materials most widely employed for natural stone treatment [9], is generally difficult on stones containing quartz or clay minerals, while the detection of the presence and homogenous distribution of a coating layer based on morphology can be critical on any stone if the applied product generates nanometric layers resulting in barely visible modifications of the stone surface [10].