Simulation of partially coherent image formation in x-ray microscopy

We present the theory and implementation of a numerical model capable of simulating two-dimensional images for an x-ray microscope using partially coherent illumination considerations. Partially coherent illumination is found in all x-ray microscopes and particularly in the latest generation of our in-house compact soft x-ray microscope. This is due to an introduced mismatch in numerical aperture of the condenser and objective zone plate, and will yield diffraction-like artifacts in phase-shifting objects. The numerical model approximates the condenser zone plate as a secondary incoherent source represented by individually coherent but mutually incoherent source emitters, each giving rise to a separate image. A final image is obtained by adding up the image intensities of the individual contributions. The simulation has been a useful tool for investigating the influence of coherence on images in both the mirror and zone plate condenser arrangement of the in-house compact soft x-ray microscope. The latest development included in the program is the effect of astigmatism and partial coherence, where the calculated results show good qualitative agreement with respect to the microscope images.