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DOE OSTI · 3024490

Framework for X-ray mirror surface shape fitting

Huang, Lei [Brookhaven National Laboratory (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II)] (ORCID:0000000256455173)·Xu, Ruochen [Brookhaven National Laboratory (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II); Ward Melville High School, East Setauket, NY (United States)] (ORCID:0009000555645687)·Wang, Tianyi [Brookhaven National Laboratory (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II)] (ORCID:0000000168808194)·Yamada, Jumpei [Osaka Univ., Suita (Japan)] (ORCID:0000000254764327)·Dvorak, Joseph [Brookhaven National Laboratory (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II)] (ORCID:0000000338445462)·Austin, Corey [Brookhaven National Laboratory (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II)] (ORCID:0000000154889480)·Eeckhout, Albert Van [ALBA Synchrotron Light Source, Cerdanyola del Valles (Spain)]·Roman, Josep Nicolàs [ALBA Synchrotron Light Source, Cerdanyola del Valles (Spain)]·Goldberg, Kenneth [Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). Advanced Light Source (ALS)] (ORCID:0000000199845780)·Idir, Mourad [Brookhaven National Laboratory (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II)] (ORCID:0000000333017274)
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Abstract

For accurate characterization of grazing-incidence X-ray mirrors, we present a comprehensive framework to fit measured surface shapes (either slope or height) of X-ray mirrors used in synchrotron radiation and free-electron laser facilities. We summarize the closed-form expressions of some typical surface shapes of X-ray mirrors including elliptic cylinders, hyperbolic cylinders, ellipsoids, hyperboloids, and diaboloids. This framework is composed of four layers: definition of standard shapes with closed-form expressions, generation of theoretical surface with pose parameters (six degrees of freedom defining an object's position and orientation relative to a coordinate system), parameter optimization with the ability to select which parameters are fit and which are held constant, and the development of user-friendly fitting function wrappers for particular fitting tasks. A few practical fitting examples are demonstrated to verify the effectiveness of the proposed fitting framework. We discuss the physical meanings of the fitting parameters, and provide several examples using the elliptic cylinder and ellipsoid shapes to highlight some features of the framework. Moreover, we provide the presented framework as open-source codes (MATLAB and Python codes available at https://github.com/nsls2omf/xmf) to the community to encourage academic collaboration and further improvements.

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36 MATERIALS SCIENCEX-ray mirrorleast-squares optimizationmirror characterizationsurface shape fitting

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Huang, Lei [Brookhaven National Laboratory (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II)] (ORCID:0000000256455173), Xu, Ruochen [Brookhaven National Laboratory (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II); Ward Melville High School, East Setauket, NY (United States)] (ORCID:0009000555645687), Wang, Tianyi [Brookhaven National Laboratory (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II)] (ORCID:0000000168808194), Yamada, Jumpei [Osaka Univ., Suita (Japan)] (ORCID:0000000254764327), Dvorak, Joseph [Brookhaven National Laboratory (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II)] (ORCID:0000000338445462), Austin, Corey [Brookhaven National Laboratory (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II)] (ORCID:0000000154889480), Eeckhout, Albert Van [ALBA Synchrotron Light Source, Cerdanyola del Valles (Spain)], Roman, Josep Nicolàs [ALBA Synchrotron Light Source, Cerdanyola del Valles (Spain)], Goldberg, Kenneth [Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). Advanced Light Source (ALS)] (ORCID:0000000199845780), Idir, Mourad [Brookhaven National Laboratory (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II)] (ORCID:0000000333017274). 2026-01-22. Framework for X-ray mirror surface shape fitting. https://doi.org/10.1107/s1600577525011282

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