Methods for discriminating among x-ray beams of distinct energy content. A first volume of scintillation medium converts energy of incident penetrating radiation into scintillation light which is extracted from a scintillation light extraction region by a plurality of optical waveguides that convert the scintillation light to light of a longer wavelength. An x-ray beam initially incident upon the first volume of scintillation medium and traversing the first volume is then incident on a second volume of scintillation medium. The first and second scintillation media may be separated by an absorber or one or more further volumes of scintillation medium, and may also have differential spectral sensitivities. Scintillation light from the first and second scintillation volumes is detected in respective detectors and processed to yield a measure of respective low energy and high-energy components of the incident x-ray beam.