Off-axis representation of hyperbolic mirror shapes for X-ray beamlines

Goldberg, Kenneth A.; Sanchez del Rio, Manuel

doi:10.1107/s1600577523001492

Off-axis representation of hyperbolic mirror shapes for X-ray beamlines

Journal Article · Fri Mar 10 00:00:00 EST 2023 · Journal of Synchrotron Radiation (Online)

DOI:https://doi.org/10.1107/s1600577523001492· OSTI ID:2234134

^[1]; ^[2]

Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). Advanced Light Source (ALS)
European Synchrotron Radiation Facility (ESRF), Grenoble (France)

Mirror-centered, closed-form expressions for hyperbolic surfaces used in X-ray beamlines have been derived. Hyperbolic mirrors create a virtual focus or source point and can be used to lengthen or shorten the effective focal distance of a compound optical system. The derivations here express off-axis segments of a hyperbolic surface in terms of the real and virtual focal distances and the incident glancing angle at the center of the mirror. Conventional mathematical expressions of hyperbolic shapes describe the surfaces in Cartesian or polar coordinates centered on an axis of symmetry, necessitating cumbersome rotation and translation to mirror-centered coordinates. The representation presented here, with zero slope and the origin at the central point, is most convenient for modeling, metrology, aberration correction, and general surface analysis of off-axis configurations. The direct derivation avoids the need for nested coordinate transforms. A series expansion provides a helpful approximation; the coefficients of the implicit equation are also provided.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

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

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 2234134

Journal Information:: Journal of Synchrotron Radiation (Online), Journal Name: Journal of Synchrotron Radiation (Online) Journal Issue: 3 Vol. 30; ISSN 1600-5775

Publisher:: International Union of CrystallographyCopyright Statement

Country of Publication:: United States

Language:: English

References (20)

Spiegelsysteme streifenden Einfalls als abbildende Optiken für Röntgenstrahlen Wolter, Hans Annalen der Physik, Vol. 445, Issue 1-2 https://doi.org/10.1002/andp.19524450108	journal	January 1952
Verallgemeinerte Schwarzschildsche Spiegelsysteme streifender Reflexion als Optiken für Röntgenstrahlen Wolter, Hans Annalen der Physik, Vol. 445, Issue 4-5 https://doi.org/10.1002/andp.19524450410	journal	January 1952
On a New Kind of Rays Rontgen, W. C. Nature, Vol. 53, Issue 1369, p. 274-276 https://doi.org/10.1038/053274b0	journal	January 1896
Mirror profile optimization for nano-focusing KB mirror Zhang, Lin; Baker, Robert; Barrett, Ray AIP Conference Proceedings https://doi.org/10.1063/1.3463335	conference	January 2010
Ex situ metrology and data analysis for optimization of beamline performance of aspherical pre-shaped x-ray mirrors at the advanced light source Yashchuk, Valeriy V.; Lacey, Ian; Gevorkyan, Gevork S. Review of Scientific Instruments, Vol. 90, Issue 2 https://doi.org/10.1063/1.5057441	journal	February 2019
Solar X-Ray Image Obtained Using Grazing-Incidence Optics. Giacconi, R.; Reidy, W. P.; Zehnpfennig, T. The Astrophysical Journal, Vol. 142 https://doi.org/10.1086/148404	journal	October 1965
An Overview of the Performance and Scientific Results from the Chandra X‐Ray Observatory Weisskopf, M. C.; Brinkman, B.; Canizares, C. Publications of the Astronomical Society of the Pacific, Vol. 114, Issue 791 https://doi.org/10.1086/338108	journal	January 2002
Analytic descriptions of parabolic X-ray mirrors Goldberg, Kenneth A. Journal of Synchrotron Radiation, Vol. 29, Issue 4 https://doi.org/10.1107/S1600577522004593	journal	May 2022
Derivation of closed-form ellipsoidal X-ray mirror shapes from Fermat's principle Goldberg, Kenneth A. Journal of Synchrotron Radiation, Vol. 29, Issue 4 https://doi.org/10.1107/S1600577522005793	journal	June 2022
Theory and practice of elliptically bent x-ray mirrors Howells, Malcolm R. Optical Engineering, Vol. 39, Issue 10 https://doi.org/10.1117/1.1289879	journal	October 2000
Development of achromatic full-field hard x-ray microscopy with two monolithic imaging mirrors Matsuyama, S.; Kino, H.; Yasuda, S. SPIE Proceedings https://doi.org/10.1117/12.2188583	conference	September 2015
New schemes in the adjustment of bendable elliptical mirrors using a long trace profiler Rah, Seung Y.; Locklin, Scott C.; Irick, Steven C. SPIE Proceedings https://doi.org/10.1117/12.295552	conference	November 1997
An alternative optical design for x-ray telescopes Zocchi, Fabio E.; Vernani, Dervis SPIE Proceedings https://doi.org/10.1117/12.736413	conference	September 2007
Development of a one-dimensional Wolter mirror for achromatic full-field x-ray microscopy Matsuyama, S.; Kidani, N.; Mimura, H. SPIE Proceedings https://doi.org/10.1117/12.892987	conference	September 2011
Properties And Performance Of Grazing Incidence Reflectors Aspnes, D. E.; Kelso, S. M. SPIE Proceedings https://doi.org/10.1117/12.932985	conference	May 1982
Kirkpatrick–Baez and Wolter X-Ray Focusing Optics (Review) Lider, V. V. Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques, Vol. 13, Issue 4 https://doi.org/10.1134/S102745101904027X	journal	July 2019
Optical Design of a Glancing Incidence X-ray Telescope Mangus, J. D.; Underwood, J. H. Applied Optics, Vol. 8, Issue 1 https://doi.org/10.1364/AO.8.000095	journal	January 1969
Formation of Optical Images by X-Rays Kirkpatrick, Paul; Baez, A. V. Journal of the Optical Society of America, Vol. 38, Issue 9 https://doi.org/10.1364/JOSA.38.000766	journal	January 1948
Development of an advanced Kirkpatrick–Baez microscope Kodama, R.; Katori, Y.; Iwai, T. Optics Letters, Vol. 21, Issue 17 https://doi.org/10.1364/OL.21.001321	journal	January 1996
WHO? DISCOVERED CODDINGTON'S Equations? Kingslake, Rudolf Optics and Photonics News, Vol. 5, Issue 8 https://doi.org/10.1364/OPN.5.8.000020	journal	January 1994

Similar Records

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

Journal Article · Mon Oct 28 20:00:00 EDT 2024 · Journal of Synchrotron Radiation (Online) · OSTI ID:2533557

Analytic descriptions of parabolic X-ray mirrors

Journal Article · Tue May 24 20:00:00 EDT 2022 · Journal of Synchrotron Radiation (Online) · OSTI ID:1893887

Derivation of closed-form ellipsoidal X-ray mirror shapes from Fermat's principle

Journal Article · Sun Jun 19 20:00:00 EDT 2022 · Journal of Synchrotron Radiation (Online) · OSTI ID:1894090

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Wolter
X-ray
beamline
hyperbolic
mirror

Off-axis representation of hyperbolic mirror shapes for X-ray beamlines

Citation Formats

References (20)

Similar Records

Related Subjects