Abstract
A framework based on physical optics for simulating the effect of imperfect compound refractive lenses (CRLs) upon an X-ray beam is described, taking into account measured phase errors obtained from at-wavelength metrology. A CRL stack is modelled, with increasing complexity, as a single thin phase element, then as a more realistic compound element including absorption and thickness effects, and finally adding realistic optical imperfections to the CRL. Coherent and partially coherent simulations using Synchrotron Radiation Workshop (SRW) are used to evaluate the different models, the effects of the phase errors and to check the validity of the design equations and suitability ofthe figures of merit.
Highlights
The use of refractive optics for the focusing of X-rays dates back to the mid-1990s (Tomie, 1994; Snigirev et al, 1996) which is relatively recent when compared with the use of diffractive and reflective optics
The recent development and establishment of fourth-generation synchrotron light sources – as upgrades of existing machines or the construction of new facilities – and the emergence of the X-ray free-electron lasers (XFELs) poses a new challenge for X-ray optics: wavefront preservation, as at modern sources the X-ray beam quality at the sample is primarily limited by the optical quality (Schroer & Falkenberg, 2014; Yabashi et al, 2014)
It is important to have simulation tools to allow for the accurate implementation of synchrotron or XFEL light sources, allowing the compound refractive lenses (CRLs) to be included in a complete beamline configuration in combination with other optical elements
Summary
The use of refractive optics for the focusing of X-rays dates back to the mid-1990s (Tomie, 1994; Snigirev et al, 1996) which is relatively recent when compared with the use of diffractive (early 1930s) and reflective optics (late 1940s). The basic implementation of X-ray lenses is already available on the two most widespread beamline simulation tools: SHADOW (Sanchez del Rio et al, 2011) and SRW (Chubar & Elleaume, 1998) Both implementations, based on different schemes, i.e. ray tracing (Alianelli et al, 2007) and wave optics (Baltser et al, 2011), respectively, are based on an ideal model combining refraction and absorption for the stacked lenses. It is important to have simulation tools to allow for the accurate implementation of synchrotron or XFEL light sources, allowing the compound refractive lenses (CRLs) to be included in a complete beamline configuration in combination with other optical elements. This is possible with both SHADOW and SRW. With the X-ray beam moving along the positive z-direction in Fig. 1, the refracting power of the vacuum/lens interface is given by
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