Framework for X-ray mirror surface shape fitting

Area of Science:

• Optics
• Materials Science
• Instrumentation

Background:

• Accurate characterization of X-ray optics is essential for advanced research facilities.
• Grazing-incidence mirrors are critical components in synchrotron radiation and free-electron laser (FEL) applications.
• Existing methods for surface shape analysis can be complex and time-consuming.

Purpose of the Study:

• To develop a comprehensive and user-friendly framework for fitting measured surface shapes of X-ray mirrors.
• To provide accurate characterization of grazing-incidence X-ray mirrors used in demanding scientific environments.
• To facilitate community collaboration and further development through open-source code.

Main Methods:

• Summarizing closed-form expressions for typical X-ray mirror shapes (cylinders, ellipsoids, etc.).
• Generating theoretical surfaces incorporating pose parameters (position and orientation).
• Implementing parameter optimization with selectable fixed or fitted parameters and user-friendly wrappers.

Main Results:

• Demonstrated the effectiveness of the fitting framework through practical examples.
• Provided clear explanations of fitting parameter physical meanings.
• Highlighted framework features using elliptic cylinder and ellipsoid shape examples.

Conclusions:

• The developed framework offers an effective solution for accurate X-ray mirror surface characterization.
• Open-source availability (MATLAB and Python) promotes wider adoption and collaborative improvements.
• This tool enhances the performance and reliability of X-ray optics in cutting-edge research facilities.