Abstract: Computed tomography (CT) technology has transformed non-destructive testing and medical diagnostics by enabling three-dimensional reconstructions and quantitative information analyses. Circular-orbit cone-beam CT systems dominate current applications due to their ability to provide detailed imaging. However, these systems require either object rotation or gantry movement, which imposes significant limitations for non-rotatable or oversized specimens. Linear trajectory CT (L-CT) systems address these constraints by scanning objects along a linear path, making them particularly valuable for specialized industrial and security applications. Despite their advantages, precise geometric calibration in L-CT systems is essential for high-fidelity image reconstruction. Minor miscalibrations propagate through the reconstruction pipeline, generating severe artifacts that degrade diagnostic and analytical utility. Unlike circular CT systems with mature calibration protocols, L-CT systems confront distinct challenges arising from non-circular scanning trajectories and pronounced magnification variations across projection views. Geometric calibration methods specifically designed for L-CT systems were investigated in this research. Three primary geometric error sources were identified: in-plane detector offset, in-plane detector rotation, and out-of-plane detector position errors. Mathematical derivations reveal how these errors propagate through the reconstruction process, producing characteristic artifacts and distortions in the final images. To mitigate these effects, a dedicated calibration phantom was engineered, comprising metallic spheres embedded in a low-density polyethylene matrix. This design explicitly accommodates L-CT’s unique imaging properties that notably magnification variability across projection views. When scanned along a linear trajectory, the phantom produces distinct projection signatures. These features enable geometric parameter extraction via quantitative pattern analysis. Crucially, mathematical relationships were established between projection characteristics, such as centroid coordinates and feature deformation metrics, and the underlying geometric error parameters. A key theoretical contribution of this work is the extension of the sum of projections (SOP) property, originally developed for circular CT systems, to linear trajectory configurations. The linear trajectory SOP (LSOP) property is shown to exhibit symmetry under ideal geometric conditions, and deviations from this symmetry are quantified to verify calibration accuracy. Simulation experiments with predefined error parameters, such as detector offsets of 3 mm and 15 mm and a rotation error of 0.5°, result in calibrated values of 2.89 mm, 14.04 mm, and 0.4943°, respectively, showing agreement with input values. Experimental validation using an actual L-CT system further confirms the method’s effectiveness by comparing results to conventional circular trajectory calibration methods, demonstrating a strong correlation. The findings validate the proposed calibration method as a robust solution for identifying and quantifying geometric errors in L-CT systems. By addressing challenges such as magnification variability across projection views, this method improves reconstruction quality and expands CT’s utility in applications where circular scanning is impractical. Future work will focus on refining projection models, optimizing parameter estimation, and extending LSOP theory for more complex system configurations.