A method for obtaining a concentrated, monochromatic x-ray beam from a standard x-ray tube or other source of polychromatic emission. X-rays from the anode of the x-ray tube fluoresce an adjoining, independent target that produces a monochromatic spectrum, a portion of which is focused by the x-ray optical system. This two-stage method gives the system considerably versatility without undue loss in signal. The two-stage concentrator makes practical the use of focusing optics in hand-held and portable instruments.