Abstract: A fan-shaped beam or a fan array of individual beamlets of penetrating radiation, such as X-ray or .gamma.-ray radiation, is directed through a planar slice of the body to be analyzed to a position sensitive detector. The fan beam and the detector are caused to move in a rectilinear or nearly rectilinear fashion so that the individual beamlets or rays of penetrating radiation scan across the body and each detector records a parallel ray shadowgraph at a different angle of rotation (scan angle) with respect to the body and covering a range of scan angles less than 180.degree. and typically approximately 90.degree.. The recorded shadowgraphic data is then reconstructed into a 3-D tomograph of the body using a method of successive approximations. The resultant scanner may be used to analyze planes of the body parallel to the major axis thereof such as saggital or coronal as well as transaxial planes.