A ray-trace analysis of X-ray multilayer Laue lenses for nanometer focusing

TL;DR

This paper uses ray-tracing to analyze and optimize X-ray multilayer Laue lenses for nanometer focusing, addressing design, aberrations, and manufacturing tolerances to improve high-resolution X-ray imaging.

Contribution

It introduces a ray-tracing analysis method for thick diffractive lenses, providing design optimization, aberration expressions, and tolerancing strategies for nanometer-scale X-ray focusing.

Findings

Aplanatic zone-plate designs can correct aberrations over large fields.

Performance is limited by Bragg diffraction acceptance angles.

Aberrations impact lenses with longer focal lengths.

Abstract

Thick diffractive optical elements offer a promising way to achieve focusing or imaging at a resolution approaching 1 nm for X-ray wavelengths shorter than about 0.1 nm. Efficient focusing requires that these are fabricated with structures that vary in period and orientation so that rays obey Bragg's law over the entire lens aperture and give rise to constructive interference at the focus. Here the analysis method of ray-tracing of thick diffractive optical elements is applied to such lenses to optimise their designs and to investigate their operating and manufacturing tolerances. Expressions are provided of the fourth-order series expansions of the wavefront aberrations and transmissions of both axi-symmetric lenses and pairs of crossed lenses that each focuses in only one dimension like a cylindrical lens. We find that aplanatic zone-plate designs, whereby aberrations are corrected over a large field of view, can be achieved by axi-symmetric lenses but not the crossed lenses. We investigate the performance of 1 nm-resolution lenses with focal lengths of about 1 mm and show their fields of view are mainly limited by the acceptance angle of Bragg diffraction, and that aberrations can limit the performance of lenses with longer focal lengths. We apply the ray-tracing formalism for a tolerancing analysis of imperfect lenses and examine some strategies for the correction of their aberrations.