A tomographic energy dispersive diffraction imaging apparatus comprises a radiation source for directing incident radiation (1, 3) at a sample (4) mounted on a support, and detection means (9, 10) mounted for detecting radiation transmitted through the sample (4) at a given angle to the direction of incidence of the radiation. The detection means comprises an array of energy dispersive detectors (9) and an array of collimators (10), such that each energy dispersive detector (9) has a respective collimator (10) associated therewith. Each collimator of the collimator array may comprise a plurality of collimator plates with apertures formed therein which are spaced apart along a direction of the transmitted radiation.