Mathematical considerations for evaluating X‐ray beam size in micro‐XRF analysis

Abstract

AbstractMicro X‐ray fluorescence spectrometry (micro‐XRF) is conducted for elemental imaging and analysis of small regions, by focusing on primary X‐rays. An appropriate beam diameter evaluation is essential as is directly related to the spatial resolution of micro‐XRF imaging. The X‐ray beam size was experimentally determined from the XRF intensity with respect to the scanning distance (thin‐wire scanning method) or its differentiated curve (knife‐edge scanning method). However, a beam diameter is not currently evaluated in a mathematically appropriate method and is known to differ significantly from the actual value under certain conditions. A formula to correct this difference has been proposed; however, to the best of our knowledge, no study has discussed the performance of the correction formula and conditions under which they can be applied. By mathematically analyzing the overlapping volume between the X‐ray beam and the scanning material, we succeeded in deriving an appropriate fitting function that replaces the Gaussian function taking into account the effect of absorption. The fitting function is effective for each method. This technique was applied to evaluate the micro X‐ray beam created using polycapillary X‐ray focusing optics. Both thin‐wire and knife‐edge scanning methods were used with wires of different sizes to determine the X‐ray beam size. The beam size obtained by the conventional fitting function can be accurately corrected using the newly derived correction formula. Simulations were performed using the derived fitting function, and the applicability of the correction formulas was demonstrated.