Numerical analysis of partially coherent radiation at soft x-ray beamline

Abstract

A new model for numerical analysis of partially coherent x-ray at synchrotron beamlines is presented. The model is based on statistical optics. Four-dimensional coherence function, Mutual Optical Intensity (MOI), is applied to describe the wavefront of the partially coherent light. The propagation of MOI through optical elements in the beamline is deduced with numerical calculation. The coherence of x-ray through beamlines can be acquired. We applied the model to analyze the coherence in the STXM beamline at SSRF, and got the coherence length of the beam at the endstation. To verify the theoretical results, the diffraction experiment of a single slit was performed and the diffraction pattern was simulated to get the coherence length, (31 ± 3.0) µm × (25 ± 2.1) µm (H × V), which had a good agreement with the theoretical results, (30.7 ± 0.6) µm × (31 ± 5.3) µm (H × V). The model is applicable to analyze the coherence in synchrotron beamlines.

Mutual optical intensity propagation through non-ideal mirrors

“…The MOI propagation through free space was reported in previous work (Meng et al, 2015) and is summarized here. The four-dimensional MOI, J(P 1 , P 2 ), describes the electric field distribution and the correlation between any two points P 1 and P 2 .…”

“…2(b) shows the local degree of coherence between any point and the central point. The two cases have the same oscillation pattern, which originates from the diffraction of the finite lens/mirror aperture (Meng et al, 2015). The difference in the degree of coherence amplitude is an indication that the elliptical cylinder mirror is not an exact ideal lens for nonpoint-to-point focusing cases.…”

“…The propagation of MOI from the Figure 1 Schematic layout of the MOI propagation through a mirror. incident plane J i (P 1 , P 2 ) to the exit plane J e (Q 1 , Q 2 ) is described as follows (Goodman, 2015;Meng et al, 2015),…”

“…The results from the diffraction and geometric effects are integrated together by numerical convolution and ray re-sampling. The mutual optical intensity (MOI) model was recently developed based on statistical optics to simulate partially coherent radiation propagation through X-ray optics (Meng et al, 2015). The model is based on the MOI function that describes both the wavefront and the coherence property of the beam.…”

“…The wavefront is separated into many small elements to perform the numerical calculation of MOI propagation through free space. Combined with the local ray tracing, MOI propagation through ideal mirrors and gratings was realised (Meng et al, 2015). The main aim of the MOI method is to provide the full coherence property of the beam, which can also be realised by the propagation of the cross-spectral density function (Singer & Vartanyants, 2014;Vartanyants & Singer, 2016).…”