Transport-of-intensity diffraction tomography with nonuniform axial sampling (TIDT-NAS)

Abstract

Transport-of-intensity diffraction tomography (TIDT) extends the transport-of-intensity equation (TIE) from 2D phase retrieval to 3D refractive index (RI) tomography, enabling non-interferometric volumetric imaging under partially coherent illumination. By combining parallel spectral filling with reduced sensitivity to coherence noise and strong optical sectioning capability, TIDT provides high-fidelity RI reconstruction while retaining compatibility with a standard bright-field microscope. However, its volumetric imaging throughput is constrained by the need for densely and uniformly sampled axial intensity stacks, which are required to preserve tomographic resolution but impose substantial data burdens and limit imaging speed. Here, we introduce TIDT-NAS, a nonuniform axial-sampling framework that preserves full tomographic resolution while substantially reducing acquisition requirements. Dense sampling over the specimen-containing axial range captures high-frequency structural details, whereas coarse sampling over the extended defocus range retains low-frequency volumetric information. A physics-guided, alias-aware Fourier fusion integrates these complementary stacks into an alias-free 3D spectrum, enabling accurate volumetric reconstruction using only a minimal fraction of the data required by conventional TIDT. Experiments on live cells show that TIDT-NAS reduces the measurement burden to ∼\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim$$\end{document}30% while maintaining reconstruction fidelity comparable to conventional TIDT, enabling sustained ∼\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim$$\end{document}1-Hz 4D (x-y-z-t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x-y-z-t$$\end{document}) RI imaging over extended periods. These results establish TIDT-NAS as a high-throughput, high-resolution tomographic method that overcomes TIDT’s long-standing acquisition bottleneck and significantly broadens its utility to long-term, dynamic volumetric imaging of thick biological samples.