Reflection-Mode Multi-Slice Fourier Ptychographic Tomography

Diffraction tomography (DT) has been widely explored in transmission-mode configurations, enabling high-resolution, label-free 3D imaging. However, industrial metrology applications, such as semiconductor inspection, typically involve opaque or highly reflective substrates (e.g., silicon or metal), necessitating a reflection-mode imaging configuration. In this work, we introduce reflection-mode Multi-Slice Fourier Ptychographic Tomography (rMS-FPT) that achieves high-resolution, volumetric imaging of multi-layered, strongly scattering samples on reflective substrates. We develop a reflection-mode multi-slice beam propagation method (rMSBP) to model multiple scattering and substrate interactions, enabling precise 3D reconstruction. By incorporating darkfield measurements, rMS-FPT enhances resolution beyond the traditional brightfield limit and provides sub-micrometer lateral resolution while achieving optical sectioning. We validate rMS-FPT through numerical simulations on a four-layer resolution target and experimental demonstrations using a reflection-mode LED array microscope. Experiments on a two-layer resolution target and a multi-layer scattering sample confirm the method's effectiveness. Our optimized implementation enables rapid imaging, covering a 1.2mm × 1.2mm area in 1.6 seconds, reconstructing over 109voxels within a 0.4mm3volume. This work represents a significant step in extending DT to reflection-mode configurations, providing a robust and scalable solution for 3D metrology and industrial inspection.