X-ray Ptychography is a high-resolution coherent diffraction imaging method, which has been widely used in the third generation of synchrotron radiation sources. In this method, diffraction images are collected with a series of probe incident positions on an extended sample with partial overlapping between neighbored exposure areas. Accurate location information of the probe is very crucial to obtain high-resolution reconstruction images in experiment. However, the motor movement errors are usually unavoidable, which are caused by thermal drift or mechanical inaccuracy. We proposed an effective method to correct the scanning position errors, which combined the Fresnel CDI algorithm and the image registration method. The feasibility and robustness of the algorithm have been verified by both simulation and xray experiments.
The mutual optical intensity (MOI) package is developed to simulate the mutual optical intensity propagation through beamline and is available online at www.moixray.cn. In this paper we describe the basic principles of the MOI package. The propagation of the mutual optical intensity is numerically carried out by dividing the wave plane into many small elements to meet the requirements of the Fraunhofer or the Fresnel approximations. From the mutual optical intensity, the intensity, the phase distribution and the coherence between any two points in a wave plane can be extracted. The in-plane wave vector distribution in the wave plane of partially coherent beam can be obtained by considering the phase distribution inside each element. The consideration of the in-plane wave vector provides both higher accuracy and higher efficiency, which is very important to the future development of the 2D MOI code. We demonstrate applications of the MOI package on propagation simulations of partially coherent beams in different optical setup, including the propagation through an elliptically cylinder mirror and a parabolically cylinder mirror. The dependence of the in-plane wavevector on the beam coherence is analyzed. Clear shifts are seen in the in-plane wavevector profile and disappear with decreasing coherence. The knowledge of the in-plane wave vector gives detailed analysis of the beam wavefront. The calculation efficiency depends on the number of elements. The calculation speed for the mutual optical intensity propagation with 1000 elements through one optics is about 2.5 seconds.
A wavefront propagation analysis of a soft X-ray beamline using the HYBRID method is reported. All elements of the beamline: the energy dependence of the insertion device emission, the beamline mirrors and their measured figure errors, the variable-line-spacing grating and its measured figure error, and several exit slit settings, are included in the simulations. The analysis of the propagated undulator radiation through the beamline at two slightly different deflection parameter values demonstrates that, within the beamline angular acceptance and when the monochromator is tuned to the same energy, the flux is higher when the undulator is tuned to slightly higher energy than that of the monochromator. The energy resolution determined from the FWHM of the energy bandwidth transmitted through the exit slit is narrower when the undulator is tuned to higher energy than the monochromator. This is not the case when the resolution is based on the standard deviation of the transmitted energy band. The diffraction effects due to the exit slit size and their consequence on the spot size at the sample position are investigated for a few photon energies.
We continue to develop MOI method to analyze the mutual optical intensity (MOI) propagation through non-ideal optics. Local stationary phase approximation is implemented to calculate the MOI propagating through a non-ideal mirror. The phase generated by the path length from the incident to exit plane is the key to solve the MOI propagation through the mirror. The effect of figure error can be expressed as phase shift. There are two methods to deal with the figure error, the analytical method and numerical one. The two methods are compared at different spatial frequency range of the figure error. An APS beamline is analyzed with the developed MOI model, in which a partially coherent beam with 10keV energy is focused to ~20nm by a non-ideal elliptical mirror. The MOI at the focal plane is acquired after propagation through the non-ideal mirror. The intensity profile, the wavefront and the global coherence degree can be get from the MOI. The results indicate that the figure error with low spatial frequency generates oscillations, redistributes coherence property and damages the wavefront on the image plane. However, the figure error does not change the global coherence degree. Comparison with other codes such as Hybrid and SRW was performed. The results show that MOI model and SRW have similar intensity profiles. The apparent oscillations from MOI model and SRW indicate high coherence. Limitation on the beam size by the BDA and mirror will increase the coherence, which can be quantitatively analyzed by global coherence degree from MOI.
The mutual optical intensity (MOI) is a four-dimensional coherence function and contains the full coherence information of the beam. The propagation of mutual optical intensity through a soft x-ray beamline is analyzed with a new developed model named MOI. The MOI model is based on statistical optics. The wavefront is separated into many elements and every element is assumed to has full coherence and constant complex amplitude, which is reasonable if the dimension of element is much smaller than the coherent length and beam spot size. The propagation of MOI for every element can be analytically solved with Fraunhofer or Fresnel approximations. The total MOI propagation through free space can be obtained by summing the contribution of all elements. Local stationary phase approximation is implemented to simulate MOI propagating through ideal mirrors and gratings. The MOI model provides not only intensity profile, but also wavefront and coherence information of the beam. These advantages make MOI model a useful tool for beamline design and optimization. The nano-ARPES beamline at SSRF is analyzed using the MOI model. A zone plate is used to focus the beam. The intensity profile and local coherence degree at the zone plate are acquired. The horizontal coherence is much worse than the vertical one. By cutting the horizontal beam with the exit slit the horizontal coherence can be improved but at the flux loss. The quantitative analysis on the coherence improvement and flux loss at different exit slit size are obtained with the MOI model.
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