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Forward and backward scattering provide complementary volumetric and interfacial information, yet conventional three-dimensional (3D) imaging typically accesses only one. We present a substrate-enhanced diffraction tomography approach that simultaneously recovers both channels under multi-angle epi-illumination. This geometry captures one forward- and two backward-scattering bands in axially symmetric Fourier regions, where their complementary coverage enables phase–absorption separation in a non-Hermitian spectrum. Explicit 3D transfer functions are derived for both channels, and an axial Kramers–Kronig relation is established to incorporate substrate-induced boundary conditions in a unified framework. Our results establish a label-free, high-resolution 3D imaging modality that surpasses the limits of existing methods. 

We introduce a reflection-mode diffraction tomography technique that enables the simultaneous recovery of forward- and backward-scattering information for high-resolution 3D refractive index reconstruction. Our technique works by imaging a sample on a highly reflective substrate and employing a multiple-scattering model and a reconstruction algorithm. It combines the modified Born series as the forward model, Bloch and perfect electric conductor boundary conditions to handle oblique incidence and substrate reflections, and the adjoint method for efficient gradient computation in solving the inverse-scattering problem. We validate the technique through simulations and experiments, achieving accurate reconstructions in samples with high refractive index contrasts and complex geometries. Forward scattering captures smooth axial features, while backward scattering reveals complementary interfacial details. Experimental results on dual-layer resolution targets, 3D randomly distributed beads, phase structures obscured by highly scattering fibers, fixed breast cancer cells, and fixedC. elegansdemonstrate its robustness and versatility. This technique holds promise for applications in semiconductor metrology and biomedical imaging. 

We propose a novel algorithm based on the split-step non-paraxial model for different intensity diffraction tomography setups to recover the 3D refractive index distribution of multiple-scattering biological samples. 

Recovering 3D phase features of complex biological samples traditionally sacrifices computational efficiency and processing time for physical model accuracy and reconstruction quality. Here, we overcome this challenge using an approximant-guided deep learning framework in a high-speed intensity diffraction tomography system. Applying a physics model simulator-based learning strategy trained entirely on natural image datasets, we show our network can robustly reconstruct complex 3D biological samples. To achieve highly efficient training and prediction, we implement a lightweight 2D network structure that utilizes a multi-channel input for encoding the axial information. We demonstrate this framework on experimental measurements of weakly scattering epithelial buccal cells and strongly scattering C. elegans worms. We benchmark the network’s performance against a state-of-the-art multiple-scattering model-based iterative reconstruction algorithm. We highlight the network’s robustness by reconstructing dynamic samples from a living worm video. We further emphasize the network’s generalization capabilities by recovering algae samples imaged from different experimental setups. To assess the prediction quality, we develop a quantitative evaluation metric to show that our predictions are consistent with both multiple-scattering physics and experimental measurements. 

Abstract Deep learning has been broadly applied to imaging in scattering applications. A common framework is to train a descattering network for image recovery by removing scattering artifacts. To achieve the best results on a broad spectrum of scattering conditions, individual “expert” networks need to be trained for each condition. However, the expert’s performance sharply degrades when the testing condition differs from the training. An alternative brute-force approach is to train a “generalist” network using data from diverse scattering conditions. It generally requires a larger network to encapsulate the diversity in the data and a sufficiently large training set to avoid overfitting. Here, we propose an adaptive learning framework, termed dynamic synthesis network (DSN), which dynamically adjusts the model weights and adapts to different scattering conditions. The adaptability is achieved by a novel “mixture of experts” architecture that enables dynamically synthesizing a network by blending multiple experts using a gating network. We demonstrate the DSN in holographic 3D particle imaging for a variety of scattering conditions. We show in simulation that our DSN provides generalization across a continuum of scattering conditions. In addition, we show that by training the DSN entirely on simulated data, the network can generalize to experiments and achieve robust 3D descattering. We expect the same concept can find many other applications, such as denoising and imaging in scattering media. Broadly, our dynamic synthesis framework opens up a new paradigm for designing highly adaptive deep learning and computational imaging techniques. 

We propose a novel intensity diffraction tomography (IDT) reconstruction algorithm based on the split-step non-paraxial (SSNP) model for recovering the 3D refractive index (RI) distribution of multiple-scattering biological samples. High-quality IDT reconstruction requires high-angle illumination to encode both low- and high- spatial frequency information of the 3D biological sample. We show that our SSNP model can more accurately compute multiple scattering from high-angle illumination compared to paraxial approximation-based multiple-scattering models. We apply this SSNP model to both sequential and multiplexed IDT techniques. We develop a unified reconstruction algorithm for both IDT modalities that is highly computationally efficient and is implemented by a modular automatic differentiation framework. We demonstrate the capability of our reconstruction algorithm on both weakly scattering buccal epithelial cells and strongly scattering live C. elegans worms and live C. elegans embryos. 

We demonstrate an adaptive learning framework, termed dynamic synthesis network (DSN), which dynamically synthesizes model weights and adapts to different scattering conditions. The efficiency of DSN is demonstrated in holographic 3D particle descattering.