Aberration-free aspherical lens shape for shortening the focal distance of an already convergent beam
Open Access
- 6 October 2017
- journal article
- research article
- Published by International Union of Crystallography (IUCr) in Journal of Synchrotron Radiation
- Vol. 24 (6), 1120-1136
- https://doi.org/10.1107/s1600577517011808
Abstract
The shapes of single lens surfaces capable of focusing divergent and collimated beams without aberration have already been calculated. However, nanofocusing compound refractive lenses (CRLs) require many consecutive lens surfaces. Here a theoretical example of an X-ray nanofocusing CRL with 48 consecutive surfaces is studied. The surfaces on the downstream end of this CRL accept X-rays that are already converging toward a focus, and refract them toward a new focal point that is closer to the surface. This case, so far missing from the literature, is treated here. The ideal surface for aberration-free focusing of a convergent incident beam is found by analytical computation and by ray tracing to be one sheet of a Cartesian oval. An `X-ray approximation' of the Cartesian oval is worked out for the case of small change in index of refraction across the lens surface. The paraxial approximation of this surface is described. These results will assist the development of large-aperture CRLs for nanofocusing.Keywords
This publication has 16 references indexed in Scilit:
- Effective aperture of X-ray compound refractive lensesJournal of Synchrotron Radiation, 2017
- Development of Hard X-ray Focusing Optics at Diamond Light SourceSynchrotron Radiation News, 2016
- Aberration-free short focal length x-ray lensesOptics Letters, 2015
- Nanofocusing optics for synchrotron radiation made from polycrystalline diamond.Optics Express, 2014
- High efficiency nano-focusing kinoform optics for synchrotron radiation.Optics Express, 2011
- Using Compound Kinoform Hard-X-Ray Lenses to Exceed the Critical Angle LimitPhysical Review Letters, 2007
- Single-element elliptical hard x-ray micro-optics.Optics Express, 2003
- X-ray refractive planar lens with minimized absorptionApplied Physics Letters, 2000
- Imaging by parabolic refractive lenses in the hard X-ray rangeJournal of Synchrotron Radiation, 1999
- Transmission and gain of singly and doubly focusing refractive x-ray lensesJournal of Applied Physics, 1998