1. A Compton tomography system for three-dimensional object characterization, comprising: an x-ray source to emit an x-ray beam; a collimator disposed to collimate the x-ray beam into a sheet-like x-ray beam for irradiating a predetermined two-dimensional subset of the object; an x-ray optical element comprising an aperture, having a first surface and a second surface, disposed to receive x-rays produced by Compton scattering of at least a portion of the sheet-like x-ray beam from an object, the aperture having a depth-dependent profile wherein an outer diameter of the aperture at the first surface and the second surface is larger than an inner diameter at a center of the aperture; an x-ray camera disposed to image x-ray photons transmitted by the x-ray optical element and to acquire the resulting images; a scanning arrangement to enable the irradiation and imaging a plurality of two-dimensional subsets of the object; and an image processor for combining the Compton-scattered images corresponding to the plurality of two-dimensional subsets of the object into a three-dimensional representation of the object.