Fangke Zong

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.

Streak cameras, known for their ultra-high spatiotemporal resolution, rely heavily on the spatial resolution capabilities of their core component, the streak tube, to ensure engineering stability. However, factors such as assembly inaccuracies and external magnetic fields, including geomagnetic interference, often cause deformation and shifts in the imaging plane. To enhance equipment stability and accelerate engineering advancements, a dual approach involving hardware improvements and computational imaging-based software corrections is essential. Future image reconstruction efforts in software require robust benchmarks; however, existing benchmarks are predominantly validated under idealized conditions, neglecting real-world interference factors. This study, grounded in electron optical imaging principles, experimentally confirms that the Lagrange–Helmholtz relationship remains valid within streak tube systems under geomagnetic field influences. These findings affirm that the imaging plane retains spatial resolution consistency despite such environmental disturbances. Consequently, the need for specific image orientations during reconstruction can be eliminated, enabling the development of more robust and efficient image reconstruction algorithms.

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.

For an electron-optical imaging system with wide beam focusing, the calculation of the field curvature can be performed only theoretically and requires the specific analytical expressions of the axial potential distribution in the streak tube and its corresponding derivatives, making the calculation cumbersome. Even when the electron trajectory is tracked using the numerical calculation method, the calculated results cannot be verified experimentally. A method for measuring the field curvature of the streak tube based on the spherical fluorescent screen is proposed for the first time, to the best of our knowledge. This method can directly measure the field curvature from the experimental image without requiring information on the internal structure of the streak tube, which is extremely useful for the design of the subsequent image reconstruction algorithm.

A Monte Carlo model is developed and implemented to calculate the characteristics of x-ray induced secondary electron (SE) emission from a CsI photocathode used in an x-ray streak camera. Time distributions of emitted SEs are investigated with an incident x-ray energy range from 1 to 30 keV and a CsI thickness range from 100 to 1000 nm. Simulation results indicate that SE time distribution curves have little dependence on the incident x-ray energy and CsI thickness. The calculated time dispersion within the CsI photocathode is about 70 fs, which should be the temporal resolution limit of x-ray streak cameras that use CsI as the photocathode material.