In X-ray optical systems, conventional camera-based direct imaging cannot achieve positioning accuracy below the size of a single pixel. Therefore, developing enhanced spot localization methods for X-rays is crucial for obtaining higher accuracy position information. This paper presents a novel X-ray spot localization method utilizing a dual-grating approach through diffraction grating positioning calibration. The method detects the diffraction pattern of the beam passing through the dual gratings on the detector simultaneously, integrates and compares scattered photons in different regions through regional division, enabling convenient and rapid determination of the X-ray spot position on a two-dimensional plane. This approach facilitates single calibration spot positioning in X-ray optical systems.

The schematic of the dual-grating positioning system is presented in Fig. 1(a). X-rays emitted from a miniature X-ray source irradiate the dual-grating structure, where gratings G₁ and G₂ partially overlap to modulate the X-ray beam and induce diffraction. As illustrated in Fig. 1(c), the X-ray spot incident on the dual gratings is divided into three distinct regions including areas where the spot passes through either the transverse or longitudinal gratings alone, as well as the overlapping region where it traverses both gratings simultaneously. The diffracted X-rays from the dual-grating structure are detected by a single-photon-sensitive detector, with the resultant diffraction pattern displayed in Fig. 1(b). By correlating the segmented regions of the X-ray spot in Fig. 1(c) with the corresponding zones in the diffraction pattern shown in Fig. 1(b), the light intensities of these specific regions are extracted. The movement of the spot signifies a change in the area, which covers through different structural parts of the dual gratings, leading to variations in the integrated intensity of different regions. Consequently, the position of the X-ray spot’s center is calculated by integrating the diffraction intensities across the defined regions on the detector.

Simulations indicate that positioning errors follow a normal distribution. Results demonstrate that with photon counts exceeding 10⁵, the positioning accuracy reaches below 2 μm, while photon counts above 10⁶ achieve sub-micrometer precision. Additionally, multi-point sampling (e.g., two sampling points) further enhances accuracy to approximately 1 μm. The study also reveals that higher grating throughput in specific quadrants improves measurement accuracy. When the number of sampling points exceeds four positions, the 3σ accuracy tends to be saturated, which can reach up to 0.5 μm.

This paper presents a novel X-ray spot positioning method based on dual-grating technology. The theoretical framework demonstrates how positioning is achieved by correlating regional light intensities with the spot’s center position, with simulation results validating the method’s feasibility. The calculations indicate that the proposed scheme enables simultaneous acquisition of positional coordinates in two directions from a single exposure. Under conditions of 10? scattered photons, the method achieves micron-level positioning accuracy. Simulations demonstrate that increased photon counts enhance positioning accuracy in single exposures. The research examines positioning accuracy relative to spot location and grating structure, revealing that greater spot-grating structure overlap yields higher positioning accuracy. Furthermore, enhanced positioning accuracy is achievable through multiple samplings of diffraction data at different positions. This positioning method presents significant potential for applications in X-ray optical systems requiring precise spot positioning.