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J Synchrotron Radiat. 2014 Sep;21(Pt 5):1110-21. doi: 10.1107/S1600577514013058. Epub 2014 Aug 6.

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

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Photon Sciences Directorate, Brookhaven National Laboratory, Upton, NY 11973, USA.
Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA.


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.


Fourier optics; benchmarking; geometrical ray-tracing; grazing-incidence mirror; wave optics; wavefront propagation


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