Influence of random zone positioning errors on the resolving power of Fresnel zone plates

Fresnel zone plates produced by electron beam lithography and planar etching techniques provide a resolving power of about 10 nm. An alternative zone plate fabrication approach is based on alternately coating a micro-wire with two different materials. With this process, very thin zone layers with very high aspect ratios can be deposited. However, depending on the fabrication method, random zone positioning errors may introduce strong aberrations. We simulate the effect of positioning errors using different random fluctuations and study their influence on zone plate resolution. We find that random errors significantly decrease the contrast transfer of X-ray microscopes. Additionally, we derive an upper bound for the mean acceptable variance of the deposition rate.