In this paper the characterisation of functionally graded materials is elucidated by several different methods. These methods described here are used for the quantitative analysis of materials with a local dependence of microstructure parameters. Using X-ray microscopy (computed tomography) for 31D-measurements and optical microscopy on polished sections for 1D and 2D measurements on the same sample, a ceramic filter consisting of sintered spherical particles, various mathematical evaluation methods are described and compared. (c) 2006 Springer Science + Business Media, Inc.