128 3 Fatigue Fracture SEM chamber by an angle that depends on the local roughness of the sur- face.The stereopair is processed via a matching algorithm in order to find corresponding points on both images (homologous points)and the relative z-coordinates of these points are calculated.The 3D model of the depicted surface area usually consists of ten to twenty thousand non-equidistant points and so the Delaunay triangulation must be performed [255. Optical chromatography represents another method useful for a 3D recon- stitution of the fracture surface micromorphology.The profilometer Micro- Prof FRT,Fries Research Technology GmbH,makes use of the chromatic aberration of the optical lens.Different light monochromatic components are focused at different heights from a reference plane at the output of the opti- cal fibre.The light intensity exhibits a maximum at the wavelength exactly focused on the surface and the height of the surface irregularities is deduced by using a calibration table.This optical method was usually employed only for verification of selected results obtained by stereophotogrammetry. According to their mathematical basis,recently used topological param- eters can be divided into five main categories.This classification is based on published works 250-253]and,in particular,on the work of Petropou- los et al.[256].First two categories represent vertical (altitudinal)and length roughness parameters which characterize vertical and horizontal distributions of surface points,respectively.The third group involves hybrid parameters si- multaneously describing more than one of the above-mentioned aspects.The fourth and fifth groups respectively consist of spectral and fractal character- istics of the fracture surface. 3.1.1.1 Roughness Parameters In this brief overview only vertical,length,hybrid,spectral and fractal pa- rameters are mentioned in more detail.The description of other parameters can be found elsewhere [214,249-251.For the sake of simplicity,the assump- tion of non-overlapping surface elements is accepted hereafter.This means that each pair of coordinates(ri,yi)that determine the location of a point on the reference plane perpendicular to the macroscopic fracture surface is uniquely related to one altitudinal coordinate zi.Because of a discrete data set of points utilized here to quantify surface topography,only a discrete form of definition of individual parameters is presented.Integral definition of many topological characteristics can be found,e.g.,in [251,252] Vertical Parameters Most important altitudinal parameters are characteristics associated with the probability of realization of the value zi in terms of central moments,defined as128 3 Fatigue Fracture SEM chamber by an angle that depends on the local roughness of the sur￾face. The stereopair is processed via a matching algorithm in order to find corresponding points on both images (homologous points) and the relative z-coordinates of these points are calculated. The 3D model of the depicted surface area usually consists of ten to twenty thousand non-equidistant points and so the Delaunay triangulation must be performed [255]. Optical chromatography represents another method useful for a 3D recon￾stitution of the fracture surface micromorphology. The profilometer Micro￾Prof FRT, Fries Research & Technology GmbH, makes use of the chromatic aberration of the optical lens. Different light monochromatic components are focused at different heights from a reference plane at the output of the opti￾cal fibre. The light intensity exhibits a maximum at the wavelength exactly focused on the surface and the height of the surface irregularities is deduced by using a calibration table. This optical method was usually employed only for verification of selected results obtained by stereophotogrammetry. According to their mathematical basis, recently used topological param￾eters can be divided into five main categories. This classification is based on published works [250–253] and, in particular, on the work of Petropou￾los et al. [256]. First two categories represent vertical (altitudinal) and length roughness parameters which characterize vertical and horizontal distributions of surface points, respectively. The third group involves hybrid parameters si￾multaneously describing more than one of the above-mentioned aspects. The fourth and fifth groups respectively consist of spectral and fractal character￾istics of the fracture surface. 3.1.1.1 Roughness Parameters In this brief overview only vertical, length, hybrid, spectral and fractal pa￾rameters are mentioned in more detail. The description of other parameters can be found elsewhere [214,249–251]. For the sake of simplicity, the assump￾tion of non-overlapping surface elements is accepted hereafter. This means that each pair of coordinates (xi, yi) that determine the location of a point on the reference plane perpendicular to the macroscopic fracture surface is uniquely related to one altitudinal coordinate zi. Because of a discrete data set of points utilized here to quantify surface topography, only a discrete form of definition of individual parameters is presented. Integral definition of many topological characteristics can be found, e.g., in [251, 252]. Vertical Parameters Most important altitudinal parameters are characteristics associated with the probability of realization of the value zi in terms of central moments, defined as