Modelling tomographic cone-beam projection data from a polyhedral phantom

Analytical phantoms are used to generate projection data for testing reconstruction accuracy in computed axial tomography. A circular source locus (equivalent to rotating specimen with a fixed source) provides insufficient data for 'exact' reconstruction in cone-beam transmission tomography, thus phantom data are useful for studying the consequent errors and also for investigating alternative scanning loci and reconstruction techniques. We present an algorithm that can compute phantom cone-beam projection data from a phantom comprising geometrically defined polyhedra. Each polyhedron is defined as a set of polygons enclosing a volume of fixed linear attenuation coefficient. The algorithm works by projecting each polygon in turn onto the modelled detector array, which accumulates the product of source to polygon intersection distance (for the rays intersecting each detector element), linear attenuation coefficient and sign of projected polygon area (indicating whether rays enter or exit the polyhedron at this face). The phantom data are rotated according to the projection angle, whilst the source location and detector plane remain fixed. Polyhedra can be of simple geometric form, or complex surfaces derived from 3D images of real specimens. This algorithm is illustrated using a phantom comprising 989 238 polygons, representing an iso-surface generated from a microtomographic reconstruction of a piece of walrus tusk.