A sample (106) is irradiated with electromagnetic radiation such as X-Rays and diffraction data is sampled at inner and outer caustic rims formed at a sensor surface (108) and defined by a continuum of Debye cones (130, 132) formed by diffraction of the incident radiation. Intensities of the inner and outer rims while translating and rotating the sample are converted using a tomographic technique into X-ray diffraction images and material discrimination is also possible.