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Grating-based X-ray phase-contrast imaging and tomography, applicable with traditional polychromatic X-ray tubes, have shown great potential for future applications of imaging with multimodal information indicating materials and microstructures simultaneously. The parameters and performance of the grating system could be simulated by a wave-optical simulation framework and proved feasible for the design and optimization of both coherent and incoherent gratings systems. However, the simulation involves real-space point-wise calculation of the Fourier transformation, and the direct expression of the relationship of the parameters was absent. In this work, we analyzed the Fourier domain characteristics of the simulated system and the presented visibility of the system of different energies in an analytical form. The derived direct expression which omitted the simulation process was validated with results of both simulation and real experiments and may help future designs, optimizations and studies of the energy-resolved characteristics of the system.

Visibility of Polychromatic Grating-Based X-Ray Imaging Systems Based on Wave-Optical Theories and Frequency Domain Analysis