1. A method of investigating a specimen using a tomographic imaging apparatus comprising: a specimen holder, for holding the specimen; a source, for producing a beam of radiation that can be directed at the specimen; a detector, for detecting a flux of radiation transmitted through the specimen from the source; a stage apparatus, for producing relative motion of the source with respect to the specimen, so as to allow the source and detector to image the specimen along a series of different viewing axes; and a processing apparatus, for performing a mathematical reconstruction step whereby output from the detector is compiled into a tomographic image of at least part of the specimen, wherein said reconstruction step is performed in multiple iterations, comprising: using a Back Projection technique to produce an initial tomogram from a set of initial images; subjecting said initial tomogram to a mathematical filtering operation, thereby producing an adjusted tomogram; using a Forward Projection technique on said adjusted tomogram to dissociate it into a set of calculated images; and repeating the back projection, mathematical filtering, and forward projection until said calculated images satisfy an acceptance criterion.