Numerical modeling of optical properties of a system of two zone plates for focusing hard synchrotron radiation

Abstract

Results of numerical experiments on focusing of a monochromatic spherical wave by a system of two linear zone plates are reported. Calculations were performed for a photon energy of 12.3985 keV and zone plates with a radius of the first zone of 5 μm, a number of zones of 628, and an aperture of 250 μm. To calculate the Kirchhoff integrals, the double Fourier transform method was used and the fast Fourier transform procedure on a grid with a number of points 65 536 = 216 was applied. On the basis of the calculation results, a conclusion was drawn that two zone plates operate as one with a doubled phase shift in zones with a material if the longitudinal distance between them is smaller than 1/3 of the focus depth and the transverse displacement is smaller than 1/3 of the outermost zone width (the focus size). If the distance (displacement) exceeds the focus depth (size), the two zone plates operate independently, similar to refracting lenses with a set of different focusing orders, including the zero order. The nature of the moire pattern at a transverse displacement of the zone plates is discussed.