Angular spectrum simulation of X-ray focusing by Fresnel zone plates

Abstract

A computing simulation routine to model any type of circularly symmetric diffractive X-ray element has been implemented. The wavefield transmitted beyond the diffractive structures is numerically computed by the angular spectrum propagation method to an arbitrary propagation distance. Cylindrical symmetry is exploited to reduce the computation and memory requirements while preserving the accuracy of the numerical calculation through a quasidiscrete Hankel transform algorithm, an approach described by Guizar-Sicairos & Gutierrez-Vega [J. Opt. Soc. Am. A, (2004), 21, 53-58]. In particular, the code has been used to investigate the requirements for the stacking of two highresolution Fresnel zone plates with an outermost zone width of 20 nm.

More are better, but the details matter: combinations of multiple Fresnel zone plates for improved resolution and efficiency in X-ray microscopy

“…While the fixed dr N approach has been studied previously (Vila-Comamala et al, 2013;Gleber et al, 2014), the fixed d and fixed N approaches have not.…”

“…When multiple zone plates are located well within a depth of focus along the wavefield propagation direction, one can treat the net effect as being due to a zone plate with the combined thickness t as has been demonstrated (Shastri et al, 2001;Maser et al, 2002;Snigireva et al, 2007;Kagoshima et al, 2011;Feng et al, 2007;Aristov et al, 2007;Mohacsi et al, 2014Mohacsi et al, , 2017Rehbein et al, 2015). However, this close proximity is often challenging to achieve in practice, leading to an alternative approach of stacking multiple zone plates with separations larger than 2 z provided each individual zone plate is designed to focus to a common location (Vila-Comamala et al, 2013;Gleber et al, 2014). This has been studied within the approximation that each zone plate is optically thin, so that one can apply each zone plate's optical modulation to a wavefield, and then propagate it by a distance of Áz to the plane of the next zone plate to model the net focusing effect.…”

“…(i) While previous calculations (Vila-Comamala et al, 2013) and experiments (Gleber et al, 2014) considered intermediate distance stacking with zone plates with fixed outermost zone width dr N and adjustable diameter d, we consider the three cases of fixed dr N , fixed d and fixed zone number N in x2.…”

Progress of nanopositioning stages development for hard x-ray nanofocusing and coherence preservation optics at the APS

“…In the hard x-ray regime, very high aspect ratios are required for maximum efficiency with focusing spot sizes of few tens of nanometers, which is required for future hard x-ray nanoprobe beamlines planned as part of the APS Upgrade project [4]. To overcome the limitations of today's fabrication techniques for high-efficiency hard x-ray FZPs, and to avoid the challenges of the proximity condition for near-field stacking of identical FZPs, in 2012, Vila-Comamala et al proposed a new idea to stack FZPs in an intermediate-field with larger distances [5].…”

A Next-Generation Hard X-Ray Nanoprobe Beamline for In Situ Studies of Energy Materials and Devices

“…[43] For ease of comparison with reflective nanofocusing optics, the numerical aperture NA is listed, with NA(E) = 0.5 9 D/f(E), where f is the focal length and E the photon energy in the middle of the relevant energy range of operation. The spatial resolution for optics with circular pupil function, such as ZPs, is obtained from d = 0.61 9 k/NA.…”