Manufacturability-based optical design optimization for advanced Kirkpatrick-Baez X-ray focusing mirrors

Area of Science:

• Optics
• Materials Science
• X-ray Physics

Background:

• Advanced Kirkpatrick-Baez (AKB) mirror setups are crucial for stable X-ray nano-focusing.
• Fabricating these mirrors presents challenges due to stringent slope requirements.
• Existing methods may not fully address geometric and practical fabrication constraints.

Purpose of the Study:

• To develop an optimized AKB mirror design approach.
• To mitigate fabrication difficulties by minimizing mirror slope ranges.
• To achieve desired focusing performance while satisfying multiple constraints.

Main Methods:

• Implemented an optimization approach considering geometry constraints (beam acceptance, numerical aperture, mirror gaps, working distance).
• Incorporated practical fabrication constraints (mirror length, curvature uncertainty).
• Utilized progressive objective optimization for an automated, guess-free process.

Main Results:

• Successfully minimized total slope ranges of four curved mirrors.
• Achieved expected nano-focusing performance for X-ray beamlines.
• Validated the optimized design through ray tracing and wavefront propagation simulations.
• Demonstrated high tolerance to beam incident angle variations.

Conclusions:

• The proposed optimization approach effectively addresses AKB mirror fabrication challenges.
• It enables the development of Wolter-I or Wolter-III type AKB designs satisfying multiple constraints.
• The method provides insights into necessary trade-offs when constraints conflict.
• Optimized designs exhibit robustness and high tolerance for X-ray applications.