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.