A method of investigating a specimen using X-ray tomography, comprising (a) mounting the specimen to a specimen holder, (b) irradiating the specimen with a beam of X-rays along a first line of sight through the specimen, and (c) detecting a flux of X-rays transmitted through the specimen and forming a first image. Then (d) repeating the steps (b) and (c) for a series of different lines of sight through the specimen, thereby producing a corresponding series of images. The method further comprises (e) performing a mathematical reconstruction on said series of images, so as produce a tomogram of at least part of the specimen, wherein the specimen is disposed within a substantially cylindrical metallic shell with an associated cylindrical axis, the beam of X-rays is produced by directing a beam of charged particles onto a zone of said metallic shell, so as to produce a confined X-ray source at said zone, and the series of different lines of sight is achieved by rotating said shell about said cylindrical axis, thereby causing relative motion of said zone relative to the specimen.