Determination of Angle of Refraction in X-Ray Phase-Contrast Imaging Using Geometric Optics

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.