Grating-based X-ray phase contrast imaging technology is one of the most potential imaging methods in real applications. It can be classified into two categories: interferometry and non-interferometric imaging. The non-interferometric grating-based X-ray phase contrast imaging (NIGPCI) instrument has a great advantage in the forthcoming commercial applications for the flexible system design and the use of large periodic gratings. The performance of the NIGPCI instrument depends on its angular sensitivity to a great extent. Therefore, good angular sensitivity is mandatory in order to obtain high quality phase-contrast images. Several parameters, such as the X-ray spectrum, the inter-grating distances, and the parameters of the three gratings, influence the angular sensitivity of the imaging system. However, the quantitative relationship between the angular sensitivity and grating duty cycle is unclear. Therefore, this paper is devoted to revealing their internal relation by theoretical deduction and emulation of the imaging process with the theories of linear system and Fourier optics. Furthermore, a quantitative analysis method to optimize the duty cycles of gratings is proposed and its applicability to a general NIGPCI system is verified.
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