The accurate calculation of the angle of refraction of X-rays passing through an object is essential in X-ray phase-contrast imaging. While the wave optics-based method is commonly employed to calculate the angle of refraction, it presents several limitations. First, in cases where the object induces significant phase variations, the angle of refraction becomes divergent. Second, the method fails to adequately account for point-source illumination conditions, particularly the influence of the finite X-ray source size on the angle of refraction. In this study, we demonstrate that a geometric optics-based method can effectively simulate propagation-based X-ray phase-contrast imaging with a low-brilliance X-ray source and compute the angle of refraction more accurately than the wave optics-based method. Our studies reveal that the geometric optics-based method can robustly determine the angle of refraction, even under conditions of substantial phase variations within the object. Furthermore, we show that reducing both the X-ray source size and the detector pixel size increases the angle of refraction in both simulations and experiments. Additionally, our results highlight that the angle of refraction is not invariant. Instead, it increases with the system’s total length and as the object moves closer to the light source. For systems with a Fresnel number of N ≥ 1, our method exhibits full compatibility with wave optics methods and can be extended to grating-based X-ray interferometry. The approach offers a robust alternative for calculating the angle of refraction under diverse imaging conditions.

Calculating the angle of refraction when X-rays pass through an object is a fundamental concern in X-ray phase-contrast imaging. When using wave optics to calculate the angle of refraction, several challenges arise. First, when the phase of the object changes significantly, the angle of refraction is divergent. Second, the method is unable to address the case of point-source illumination, specifically regarding the influence of the X-ray source's focal spot size on the angle of refraction. Here, a geometric optics based method is established to simulate the propagation-based X-ray phase-contrast imaging (pbXPCI) and calculate the angle of refraction. The results indicate that the angle of refraction can be effectively determined by geometric optics even when the phase of the object changes significantly, and reducing the focal spot size of the X-ray source and the pixel size of the detector will result in a larger angle of refraction. The results also indicate that the angle of refraction would vary with the object’s position and the system’s length, rather than remaining constant regardless of its location.