A geometric calibration method for source-detector trajectories in circular-trajectory computed laminography system

Abstract In circular-trajectory computed laminography (CL) systems, mechanical assembly imperfections and motion control errors lead to deviations between the designed and actual trajectories of both the detector and x-ray source, resulting in severe geometric artifacts in the reconstructed images. This study presents a calibration method for the trajectories of source and detector in circular-trajectory CL systems, using only several steel spheres without specific geometric relationships as the calibration phantom. Based on the theoretical principle that steel spheres project as ellipses in circular-trajectory CL systems, the objective function is established by comparing elliptical parameters between theoretical and actual projections. The optimization process consists of three steps. First, optimizing the source trajectory under elliptical path constraints using particle swarm optimization; Second, employing the quasi-Newton method to alternately optimize the source trajectory between discrete positions and the overall path; and finally, determining the detector trajectory through forward projection using optimized parameters. Experimental validation demonstrates that the proposed method accurately calibrates both source and detector trajectories in the presence of various deviations, producing reconstructed images with clear structural details and no geometric artifacts. The results indicate significant potential for practical engineering applications.