Graphite surfaces exposed to the deuterium plasma in the TEXTOR tokamak were characterized in detail by means of scanning probe microscopy, ion beam analysis and colorimetry methods. The aim is to study the composition and structure of thin layer deposits formed on surfaces subjected to the tokamak plasma. The surface roughness was measured and parametrized in terms of fractal dimension and scaling constant. Several different methods for the fractal analysis of plasma-exposed surfaces have been critically evaluated. The main emphasis of this paper is on the correlation between surface roughness (fractal parameters), the amount of deposited atoms and the layer thickness.