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Objective <p>To develop a Bayesian analysis framework for characterizing structural parameters of depth-graded multilayers, addressing the challenges of high dimensionality and strong degeneracy in the parameter space.</p> Methods <p>The framework employs DarpanX to compute reflectivity curves and MultiNest nested sampler for parameter estimation and uncertainty quantification. Validation was performed against a publicly reported measured reflectivity dataset, with results compared to those from IMD. Numerical simulations were used to optimize measurement configurations, including exposure time and grazing-incidence angle selection. Multi-angle joint fitting was also implemented.</p> Results and Discussion <p>The framework successfully validated against the reference dataset, with results consistent with IMD while providing additional uncertainty estimates. Simulation-based optimization informed measurement configuration selection. Multi-angle joint fitting was demonstrated to effectively reduce parameter uncertainties and mitigate interparameter correlations.</p> Conclusion <p> Depth-graded multilayers are critical for broadband hard X-ray focusing telescopes, but their structural parameter characterization is challenged by high dimensionality and strong degeneracy. This work develops a robust Bayesian analysis framework that addresses these challenges, validated against measured datasets and optimized for practical measurement configurations.</p>

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Bayesian analysis of structure parameters of depth-graded multilayer coatings for X-ray reflectivity

  • 期刊论文

  • 发表日期：

    2026年7月7日

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  • Haoxuan Gao,
  • Liqiang Qi,
  • Yanjun Lu,
  • Zhengwei Li,
  • Tianxiang Chen,
  • Qianqing Yin,
  • Zeying Cai

摘要

Objective

To develop a Bayesian analysis framework for characterizing structural parameters of depth-graded multilayers, addressing the challenges of high dimensionality and strong degeneracy in the parameter space.

Methods

The framework employs DarpanX to compute reflectivity curves and MultiNest nested sampler for parameter estimation and uncertainty quantification. Validation was performed against a publicly reported measured reflectivity dataset, with results compared to those from IMD. Numerical simulations were used to optimize measurement configurations, including exposure time and grazing-incidence angle selection. Multi-angle joint fitting was also implemented.

Results and Discussion

The framework successfully validated against the reference dataset, with results consistent with IMD while providing additional uncertainty estimates. Simulation-based optimization informed measurement configuration selection. Multi-angle joint fitting was demonstrated to effectively reduce parameter uncertainties and mitigate interparameter correlations.

Conclusion

Depth-graded multilayers are critical for broadband hard X-ray focusing telescopes, but their structural parameter characterization is challenged by high dimensionality and strong degeneracy. This work develops a robust Bayesian analysis framework that addresses these challenges, validated against measured datasets and optimized for practical measurement configurations.