Open AccessAn analytical approach to estimating aberrations in curved multilayer optics for hard x-rays: 1. Derivation of caustic shapes
Author(s) -
Jean-Pierre Guigay,
Ch. Morawe,
Vito Mocella,
C. Ferrero
Publication year - 2008
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.16.012050
Subject(s) - caustic (mathematics) , optics , ray tracing (physics) , geometrical optics , refractive index , physics , parametric statistics , refraction , physical optics , photon , x ray optics , mathematical analysis , mathematics , statistics , x ray , mathematical physics
An analytical approach has been developed to derive aberration effects in parabolic and elliptic multilayer optics with weak interaction between photons and matter. The method is based on geometrical ray tracing including refraction effects up to the first order of the refractive index decrement delta. In the parabolic case, the derivation leads to simple parametric equations for the caustic shape. In the elliptic case, the analytical results more involved, but can be well approximated by the parabolic solution. Both geometries are compared with regard to the fundamental impact on their focusing properties.