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.
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