An instrument and method for measuring the elemental composition of a test material. The instrument has a source of penetrating radiation for irradiating an irradiated region of the test material, a detector for detecting fluorescence emission by the test material and for generating a detector signal, and a controller for converting the detector signal into a spectrum characterizing the composition of the test material. A platen of attenuating material extends outward from adjacent to, and surrounding, the irradiated surface of the test material. In certain embodiments, the thickness of the attenuating platen is tapered such as to decrease with increasing radial distance from the central irradiated region of the test material.