## Introduction

X-ray microtomography (microCT) (Feldkamp *et al*., 1984, 1989; Sasov, 1987) has become an important method for the inspection of small objects, thus having a wide spectrum of applications, e.g. in the field of orthopaedics (Rüegsegger *et al*., 1996; Müller & Rüegsegger, 1997), dentistry (Hubscher *et al*., 2002) and biomaterial research (Lin *et al*., 2003). It permits the three-dimensional (3D), non-destructive investigation of the sample with a spatial resolution of up to a few micrometres, without special preparation of the specimen.

Appropriate 3D indices for the quantitative characterization of the examined structure were introduced, such as the model-independent thickness (Tb.Th*) and the structure model index (SMI). The Tb.Th* calculates the thickness in three dimensions, independent of an assumed structure type (Hildebrand & Rüegsegger, 1997a). This method evaluates a volume-based local thickness by fitting maximal spheres to every point contained in the 3D structure. The arithmetic mean value of the local thicknesses (i.e. of the diameters of the maximal spheres), taken over all points of the structure, gives the mean thickness of the structure. The SMI is a topological index that gives an estimate of the characteristic form in terms of plates and rods composing the 3D structure (Hildebrand & Rüegsegger, 1997b). It is calculated using a differential analysis of the triangulated surface of the structure under examination. The SMI assumes integer values of 0, 3 and 4 for ideal plates, rods and spheres, respectively. For a structure containing both plates and rods the SMI value lies between 0 and 3. (Please see the Appendix for the formal description of Tb.Th* and SMI.)

Since their introduction, these 3D parameters have rapidly gained importance for the study of *a priori* unknown or changing structures, as occurs for trabecular bone (Hildebrand *et al*., 1999; Ding & Hvid, 2000; Mittra *et al*., 2005). To determine the accuracy of these 3D parameters, a 3D object of *a priori* well-known material, shape and linear dimensions has to be investigated, i.e. a 3D calibration phantom is needed. The phantom should contain a number of physical elements of known geometries and thicknesses, to allow a number of measurements within a single microCT scan.

To our knowledge, such phantoms are not commonly available. Anthropomorphic phantoms for medical computed tomography are not useful for microCT because of their large size, being bigger than the maximum size allowed for typical microCT scanners or having inserts not designed for accuracy measurements of thin structures in the micrometer range (Kalender, 1992; Royle & Speller, 1992; Rüegsegger & Kalender, 1993). Phantoms dedicated to microCT applications are currently available but their use principally concerns the calibration of density values or general quality assurance (QRM GmbH, 2005). Because of the growing importance of the 3D microCT examination technique in the investigation of trabecular bone samples (Ding & Hvid, 2000; Mittra *et al*., 2005), we decided to design and construct a dedicated 3D microCT calibration sample using available aluminium objects. The sample contained geometrical elements, such as spheres, rods, plates and meshes, embedded in polymethylmethacrylate (PMMA), with tolerances (5–15%) and thicknesses (20–1000 µm) declared by the manufacturer.

This study describes how to construct a calibration phantom for microCT using aluminium objects and reports an application example, together with measurements of Tb.Th* and SMI using a microCT scanner.