Size of X-Ray beams successfully evaluated with mathematics

A research group at Osaka Metropolitan University has derived a new evaluation method for the measuring the size X-ray microbeams (diameter) through mathematical analysis. The group then verified the validity of the mathematically derived evaluation method by measuring the diameter of X-ray microbeams using metal wires of various diameters with an X-ray fluorescence analysis system for small areas and found that it was possible to calculate the beam diameter more accurately than the previous conventional evaluation method.

X-ray beam diameter can be calculated more accurately with the new evaluation method than with conventional methods used previously. The new method shows the same X-ray beam diameter, which remained consistent during this test, when using different wires with variable thickness.

X-ray fluorescence analysis allows elemental analysis in a variety of environments without destroying the sample. The smaller diameter of the X-ray microbeam, the more accurate the elemental distribution can be. Because X-ray beams are not visible, an accurate method is needed to determine beam diameter.

A research group led by Professor Kouichi Tsuji and Specially Appointed Assistant Professor Tsugufumi Matsuyama of the Graduate School of Engineering, and Professor Hideyuki Ishi of the Graduate School of Science, at Osaka Metropolitan University, has developed a new method to evaluate the diameter of X-ray microbeams based on mathematical analysis. While validating the new method, it was found that it can be used to calculate beam diameters more accurately than the previously used conventional methods.

Currently, no uniform evaluation method for X-ray beam diameter has been established. Since this evaluation method was derived using mathematical analysis, it is expected to be widely adopted as an international standard. Potential applications of X-ray fluorescence analysis include materials development, environmental analysis, forensic science, biological sample analysis, and analysis of archaeological and culturally significant objects.

Professor Tsuji concluded, “We hope that this evaluation method will be widely used, and that the establishment of this method of evaluating spatial resolution in X-ray fluorescence will contribute to the development of a wide range of fields, including material development and bio-imaging.”

The research results were published in X-Ray Spectrometry on January 9, 2023.


About OMU 

Osaka Metropolitan University is a new public university established by a merger between Osaka City University and Osaka Prefecture University in April 2022. For more science news, see, and follow @OsakaMetUniv_en, or search #OMUScience. 

Published: 08 Feb 2023

Contact details:

Rina Matsuki

3-3-138 Sugimoto, Sumiyoshi-ku,
Osaka 558-8585 JAPAN

Content type: 

Title: Mathematical considerations for evaluating X-ray beam size in micro-XRF analysis
Author: Masanori Nakae, Tsugufumi Matsuyama, Hideyuki Ishi, Kouichi Tsuji

Funding information:

JSPS KAKENHI, Grant/Award Numbers: 21K14655, 22H02108; Osaka Central Advanced Mathematical Institute (MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics), Grant/Award Number: JPMXP0619217849; Osaka City Innovation Project 2022