In this study, a geometric model of Wolter-I X-ray focusing mirror was established by a research team led by Prof. Dr.  SHENG Lizhi from Xi'an Institute of Optics and Precision Mechanics (XIOPM) of the Chinese Academy of Sciences (CAS), and a set of equations were derived for determining the parameters of glass substrate focusing mirror.

In order to study the focal spot diffusion at the theoretical focal point under the condition of point light source. A formula for calculating the focal spot size of the single-layer focusing mirror at the theoretical focal length under point-source incident light was derived through theoretical analysis. A set of Wolter-I X-ray focusing mirror were fabricated through a slumping process using Schott D263？T glass, which is designed based on the derived equations.

Ray tracing software was used to simulate the size variations of focal spot under parallel incident light and point-source incident light. A test system was constructed, and experiments were conducted to verify the validity of the calculation formula and the results of the simulation analysis.

The test results showed that the theoretical results are in good agreement with the experimental results.

 Focal spot diffusion diagram. (Image by XIOPM)

(Original research article "OPTIK - INTERNATIONAL JOURNAL FOR LIGHT AND ELECTRON OPTICS (2020)  https://doi.org/10.1016/j.ijleo.2019.163446"）