A 3-D Fourier-Domain Interpretation of Synchronous Linear Computed Laminography and Its Tangent-Aligned Filtering Rule

Computed Laminography (CL) is attractive for inspecting laterally extended objects such as printed circuit boards, where conventional circular CT is difficult to apply due to limited object accessibility and geometric constraints. However, in synchronous linear CL (SLCL), the filtered-backprojection (FBP) mechanism is less intuitive than in circular CT, and the correct filtering direction becomes ambiguous when different trajectory segments translate along different in-plane directions. In this paper, a compact 3-D Fourier-domain interpretation of SLCL is presented, which shows that the required ramp filtering variable is determined by the translation direction of each straight-line trajectory segment. Specifically, under the detector parameterzation adopted in this work, trajectories translating in the x- and y-directions require row-wise and column-wise filtering, respectively; for mixed multi-line trajectories, the filtering direction should therefore be selected segment-wise. Numerical experiments on a 3-D PCB phantom illustrate that the proposed segment-wise filtering strategy improves reconstruction quality compared with globally fixed filtering directions in the tested mixed-line setting. The proposed interpretation provides a concise rule for implementing FBP in SLCL and offers a basis for future trajectory design.