PSF-Compensated analytical reconstruction for improved image quality in cone-beam computed laminography

Abstract Non-destructive evaluation of high-aspect-ratio electronic components, such as insulated gate bipolar transistors and printed circuit boards, demands reconstruction methods that combine measurement accuracy with high throughput. Cone-beam rotary computed laminography (CL) is usually implemented by tilting the source–detector assembly or the object within a conventional CT geometry. Though mechanically simple, this tilting breaks circular symmetry, so analytic reconstruction suffers from inter-slice aliasing and structural distortion. The CL-FBP and CL-FDK methods directly adopt the ramp filter and weighting factor used in cone-beam CT, without a detailed justification or derivation for why they remain valid in this geometry. This paper derives a frequency-domain pseudoinverse filter over the measurable frequency support from the point spread function (PSF) of the CL geometry. To avoid the prohibitive cost of direct 3D image-domain filtering, we reformulate the operation in the 2D projection domain and handle the resulting nonlinear coordinate mapping via a principled approximation. The key theoretical result is that, under practical assumptions, this approximated filter collapses analytically to a scaled ramp filter, thereby providing the first theoretical justification for the ramp filter and clarifying precisely when it fails. The improved image quality, however, stems from two further components: the projection weighting and a complementary 2D spectral filter that corrects the residual ap proximation errors. Experiments confirm that the proposed CL-PSF method consistently outperforms other analytic algorithms in correcting structural distortion. The theoretical derivation further motivates three practical strategies for suppressing inter-slice aliasing: restricting the valid reconstruction thickness, restricting the reconstruction volume to a compact region of interest, and adopting a detector with a smaller in-plane size. All three strategies are validated experimentally. The proposed method thus offers a fast and well founded reconstruction approach for quantitative industrial inspection.