Reflection-mode Multi-slice Fourier Ptychographic Tomography

TL;DR

The paper tackles the need for high-resolution 3D refractive-index imaging on reflective substrates used in industrial metrology, where traditional transmission-mode diffraction tomography is impractical. It introduces reflection-mode Fourier Ptychographic Tomography (rMS-FPT) by coupling a reflection-mode Multi-Slice Beam Propagation (rMSBP) forward model with brightfield and darkfield angular measurements to account for substrate reflections and multiple scattering. Through simulations and experiments on dual-layer and multi-layer samples, the approach achieves sub-micrometer lateral resolution and 3D optical sectioning over a wide field of view (1.2 mm × 1.2 mm) and substantial depth, reconstructing over $10^9$ voxels in approximately $1.6$ s. The work provides an open-source implementation and holds promise for rapid, wide-field 3D metrology in semiconductor, photonics, and MEMS applications, extending DT capabilities to challenging reflection geometries.

Abstract

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 1.2 mm $\times$ 1.2 mm area in 1.6 seconds, reconstructing over $10^9$ voxels within a 0.4 mm$^3$ volume. 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.

Figures (4)

• Figure 1: Overview of the rMS-FPT System and Imaging Workflow. (a) 3D schematic of the rMS-FPT system. (b) Hardware setup. (c) Flowchart of iterative rMS-FPT reconstruction with rMSBP model. (d) Details of the rMSBP algorithm.
• Figure 2: Performance evaluation of rMSBP on a simulated four-layer resolution test chart. (a) Generation of the 2D intensity stack using rigorous simulation based on the setup in (b). (b) Schematic of the four-layer 3D resolution target. (c) Comparison of reconstruction results at different depths (10;20;30;40). (I) Reconstructed refractive index (RI) using rMSBP. (II) Magnified regions from (I). (III) Reconstructed RI using the single-scattering model. (IV) Reconstructed intensity using LR-DPC refocusing. (V) Ground truth RI. RI colorbars are shown for (I) and (III), intensity colorbar for (IV).
• Figure 3: 3D Reconstruction of a Dual-Layer Resolution Test Chart Using rMS-FPT. (a) Raw intensity measurements of the dual-layer resolution test chart along with the corresponding LED illumination positions. The intensity of DF images is enhanced $50\times$ for better visualization. (b) 3D rendering of the reconstructed RI distribution, where color opacity represents RI values ranging from 1.53 to 1.54. (c) Reconstructed RI at depths of 17;36.5.
• Figure 4: 3D Reconstruction of a Multi-Layer Scattering Sample Using rMS-FPT. (a) Raw intensity measurement of the multi-layer scattering sample with all 25 BF LEDs simultaneously illuminated. (b) 3D rendering of the reconstructed RI distribution, with transparency applied to highlight RI variations from the background. The color mapping is consistent with (c). (c) $x$-$y$ cross sections of the reconstructed RI distribution at depths of 4;100;200.