Effect of tilt on circular zone plate performance

Abstract

Fresnel zone plates are frequently used as focusing and imaging optics in x-ray microscopy, as they provide the ease of use of normal incidence optics. We consider here the effects of tilt misalignment on their optical performance, both in the thin optics limit and in the case of zone plates that are sufficiently thick that volume diffraction effects come into play. Using multislice propagation, we show that simple analytical models describe the tilt sensitivity of thin zone plates and the thickness at which volume diffraction must be considered, and examine numerically the performance of example zone plates for soft x-ray focusing at 0.5 keV, and hard x-ray focusing at 10 keV.

Supplementary document for Tunable hard x-ray nanofocusing with Fresnel zone plates fabricated using deep etching - 4491630.pdf

“…where r N is the radius, f the focal length of a zone plate and θ is the tilt angle. In separate work [7] we have shown that the former term is wavelength dependent, but that the latter term is not, and that the latter term dominates the tilt limit for hard x-ray zone plates. Applying the Rayleigh quarter wave criterion for maximum optical path length errors, it is shown in Eq.…”

“…Applying the Rayleigh quarter wave criterion for maximum optical path length errors, it is shown in Eq. 15 of [7] that this gives an astigmatism tilt limit θ a of…”

Recent developments in X-ray lens modelling with SRW

“…i The interest in tilted optical elements and compensation is an active field, as evidenced by the literature on that subject -cf. [ [23][24][25] ].…”

Extreme ultraviolet broadband imaging spectrometer using dispersion-matched zone plates

“…This novel device employs a transmission grating in series with a set of one-dimensional zone plates that are individually matched, or tapered, to a particular wavelength according to the grating dispersion. We note that the concept of Fresnel zone tapering was introduced previously, but for optimizing single-and not for multi-wavelength operation [16][17][18]. Our imaging spectrometer is designed for one-dimensional imaging of plasma light sources in the extreme, vacuum, and deep ultraviolet regimes.…”