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.
The mutual optical intensity (MOI) model is extended to include the propagation of partially coherent radiation through non-ideal mirrors. The propagation of the MOI from the incident to the exit plane of the mirror is realised by local ray tracing. The effects of figure errors can be expressed as phase shifts obtained by either the phase projection approach or the direct path length method. Using the MOI model, the effects of figure errors are studied for diffraction-limited cases using elliptical cylinder mirrors. Figure errors with low spatial frequencies can vary the intensity distribution, redistribute the local coherence function and distort the wavefront, but have no effect on the global degree of coherence. The MOI model is benchmarked against HYBRID and the multi-electron Synchrotron Radiation Workshop (SRW) code. The results show that the MOI model gives accurate results under different coherence conditions of the beam. Other than intensity profiles, the MOI model can also provide the wavefront and the local coherence function at any location along the beamline. The capability of tuning the trade-off between accuracy and efficiency makes the MOI model an ideal tool for beamline design and optimization.
The BL02B bending-magnet beamline at the Shanghai Synchrotron Radiation Facility (SSRF) has been constructed and is now operational for ambientpressure photoelectron spectroscopy (APPES) and photon-in/photon-out spectroscopy (PIPOS) experimental use. Optical optimization was implemented for realization of high performance, e.g. photon flux, energy-resolving power and focus spot size. X-ray photoelectron spectroscopy experiments show that the energy range extends from 40 to 2000 eV. Argon, nitrogen and neon gas core-shell excitation spectra indicate energy-resolving powers of over 1.4 Â 10 4 @ 244 eV, 1.0 Â 10 4 @ 401 eV and 7.0 Â 10 3 @ 867 eV, respectively. The measured photon flux is 1.3 Â 10 11 photons s À1 @ E/ÁE = 3700 at 244 eV at the expected sample position, for the SSRF electron energy of 3.5 GeV and electron current of 240 mA. The spot sizes are 177 mm 23 mm and 150 mm 46 mm at the APPES and PIPOS samples, respectively.
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