Mirror-centered representation of a focusing hyperbolic mirror for X-ray beamlines

Torras, Jean-Pierre

doi:10.1107/s1600577524009603

Mirror-centered representation of a focusing hyperbolic mirror for X-ray beamlines

Journal Article · Tue Oct 29 00:00:00 EDT 2024 · Journal of Synchrotron Radiation (Online)

DOI:https://doi.org/10.1107/s1600577524009603· OSTI ID:2533557

Torras, Jean-Pierre ^[1]

SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Conic sections are commonly used in reflective X-ray optics. Hyperbolic mirrors can focus a converging light source and are frequently paired with elliptical or parabolic mirrors in Wolter type configurations. This paper derives the closed-form expression for a mirror-centered hyperbolic shape, with zero-slope at the origin. Combined with the slope and curvature, such an expression facilitates metrology, manufacturing and mirror-bending calculations. Previous works consider ellipses, parabolas, magnifying hyperbolas or employ lengthy approximations. Here, the exact shape function is given in terms of the mirror incidence angle and the source and image distances.

View Accepted Manuscript (DOE)

Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 2533557

Journal Information:: Journal of Synchrotron Radiation (Online), Journal Name: Journal of Synchrotron Radiation (Online) Journal Issue: 6 Vol. 31; ISSN 1600-5775

Publisher:: International Union of CrystallographyCopyright Statement

Country of Publication:: United States

Language:: English

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Related Subjects

47 OTHER INSTRUMENTATION
Wolter type configurations
X-ray optics
focusing optics
hyperbolic mirrors
mirror bending
mirror-centered hyperbolic shape

Mirror-centered representation of a focusing hyperbolic mirror for X-ray beamlines

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References (16)

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