Partially coherent X-ray wavefront propagation simulations including grazing-incidence focusing optics

Abstract

X-ray beamlines in modern synchrotron radiation sources make extensive use of grazing-incidence reflective optics, in particular Kirkpatrick-Baez elliptical mirror systems. These systems can focus the incoming X-rays down to nanometer-scale spot sizes while maintaining relatively large acceptance apertures and high flux in the focused radiation spots. In low-emittance storage rings and in free-electron lasers such systems are used with partially or even nearly fully coherent X-ray beams and often target diffraction-limited resolution. Therefore, their accurate simulation and modeling has to be performed within the framework of wave optics. Here the implementation and benchmarking of a wave-optics method for the simulation of grazing-incidence mirrors based on the local stationary-phase approximation or, in other words, the local propagation of the radiation electric field along geometrical rays, is described. The proposed method is CPU-efficient and fully compatible with the numerical methods of Fourier optics. It has been implemented in the Synchrotron Radiation Workshop (SRW) computer code and extensively tested against the geometrical ray-tracing code SHADOW. The test simulations have been performed for cases without and with diffraction at mirror apertures, including cases where the grazing-incidence mirrors can be hardly approximated by ideal lenses. Good agreement between the SRW and SHADOW simulation results is observed in the cases without diffraction. The differences between the simulation results obtained by the two codes in diffraction-dominated cases for illumination with fully or partially coherent radiation are analyzed and interpreted. The application of the new method for the simulation of wavefront propagation through a high-resolution X-ray microspectroscopy beamline at the National Synchrotron Light Source II (Brookhaven National Laboratory, USA) is demonstrated.

Recent updates in the “Synchrotron Radiation Workshop” code, on-going developments, simulation activities, and plans for the future

“…39 The obtained agreements and differences in the simulation results at the different conditions were analyzed and explained; this allows for the recently-implemented method to be safely used in various simulations for soft and hard X-ray beamlines.…”

Simulations of x-ray optics for ESRF-upgrade programme

“…The limitation of one method is usually overcome with the partial introduction of the other method. For example, SRW recently included local ray tracing for simulating grazing-incidence focusing optics [23]. For coherence calculations, a new method combining geometric ray tracing and wavefront propagation has been recently proposed [24].…”

A hybrid method for X-ray optics simulation: combining geometric ray-tracing and wavefront propagation

“…Until recently, optical elements were modeled in SRW assuming the thin-lens approximation. Elliptical cylinders, used in most beamlines in a Kirkpatrick-Baez (KB) configuration (Kirkpatrick & Baez, 1948), have been recently included in the code (Canestrari et al, 2014). The implementation of additional optical surfaces in SRW, including gratings and crystals, is in progress.…”

“…SRW then propagates the radiation from individual micro-electrons through the optical system and sums up intensities from all micro-electrons at a plane perpendicular to the optical axis. SRW is wave-optics-based and recently included local ray-tracing for simulating grazingincidence focusing optics (Canestrari et al, 2014). The method is straightforward and accurate; however, the multi-electron procedure required by simulating partially coherent sources is computationally expensive since it requires several hours to run in a multi-core environment.…”

“…Based on equation (1), these state-of-the-art mirrors should be treated using the waveoptics approach even for low spatial frequencies. Among the available wave-optics codes, mirror figure errors can be simulated on programs based on the stationary phase approximation up to a certain frequency (Bahrdt, 1997;Bahrdt et al, 2011), over a broad spatial frequency range (Reininger et al, 2001) used to simulate figure errors in ideal optics (De Andrade et al, 2011) and could also potentially cover the simulation of figure errors in its recent extension that includes grazingincidence mirrors (Canestrari et al, 2014).…”