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The mutual optical intensity (MOI) model is a partially coherent radiation propagation tool that can sequentially simulate beamline optics and provide beam intensity, local degree of coherence and phase distribution at any location along a beamline. This paper extends the MOI model to non-ideal two-dimensional (2D) optical systems, such as ellipsoidal and toroidal mirrors with 2D figure errors. Simulation results show that one can tune the trade-off between calculation efficiency and accuracy by varying the number of wavefront elements. The focal spot size of an ellipsoidal mirror calculated with 100 × 100 elements gives less than 0.4% deviation from that with 250 × 250 elements, and the computation speed is nearly two orders of magnitude faster. Effects of figure errors on 2D focusing are also demonstrated for a non-ideal ellipsoidal mirror and by comparing the toroidal and ellipsoidal mirrors. Finally, the MOI model is benchmarked against the multi-electron Synchrotron Radiation Workshop (SRW) code showing the model's high accuracy.

Combining wave optics propagation and geometric ray tracing, the mutual optical intensity (MOI) model is extended to quantitatively simulate the propagation of partially coherent light through a kinoform lens at high speed. The MOI model can provide both a high accuracy and a high efficiency simulation. The intensity and coherence degree distributions at the focal plane are calculated using the MOI model. It is beneficial to improve the focusing capability of the kinoform lens by reducing the coherence or increasing the number of lens steps. In addition, increasing the number of steps is also beneficial to increase the photon flux and reduce the depth of focus.