Lensless X-Ray Holotomography Goes Gigavoxel Scale While Taming Multiple Scattering

X-ray imaging has long promised a tantalizing goal: the ability to peer inside intact, three-dimensional objects at nanometre resolution without slicing, staining, or otherwise destroying them. A newly reported advance in lensless holotomography moves that promise substantially closer to routine reality. Described in Light: Science & Applications, the work demonstrates a computational and experimental framework capable of reconstructing tomographic volumes at the gigavoxel scale — volumes containing billions of resolvable image elements — while explicitly accounting for one of the most stubborn artifacts in high-resolution X-ray phase imaging: multiple scattering, the phenomenon in which waves deflected by one part of a sample go on to interact with other parts before reaching the detector.

Holotomography, in its standard form, is a phase-contrast technique. Rather than relying on the absorption of X-rays, which becomes vanishingly small for light elements at the energies needed for nanoscale work, it measures the phase shifts that a wavefront accumulates as it passes through material of varying electron density. By illuminating the sample from many angles and recording holographic interference patterns, an algorithm can recover the refractive-index distribution throughout the object, producing quantitative three-dimensional maps in which contrast reflects electron density rather than mere attenuation. Because it avoids the resolving-power limits of physical X-ray optics, lensless holotomography uses computed diffractive imaging: a coherent, focused beam illuminates the specimen, and the fine structure of the outgoing wave is inferred entirely from measured diffraction and hologram data.

The fundamental obstacle to scaling this approach is computational as much as it is experimental. In the weak-object approximation that underlies most conventional reconstructions, the sample is treated as a thin, gently refracting phase screen: the wave is assumed to pass straight through, accumulating phase but never changing direction more than trivially. This approximation simplifies the mathematics dramatically, allowing fast Fourier-based solvers to run on the angle-by-angle projections independently. It works admirably for isolated cells and thin sections. But as reconstructed field of view and resolution grow together — the two axes along which gigavoxel datasets are defined — the assumption breaks down. Thick or densely structured specimens scatter light more than once, and those higher-order scattering events inject systematic errors that standard algorithms either ignore or mistake for genuine structure, producing artifacts that can be mistaken for biological features.

The new framework confronts this limitation head-on by embedding a multiple-scattering-aware forward model directly into the tomographic reconstruction. Instead of treating each projection as a simple line integral through the refractive-index distribution, the method models wave propagation through the sample using a multi-slice formulation. In this picture, the three-dimensional specimen is conceptually divided into a stack of thin slices along the beam direction. The wave is propagated through one slice, picks up the local phase, then is free-space propagated to the next slice, where it interacts again. Repeated through the full stack, this scheme naturally generates the beam-broadening, inter-slice coupling, and dynamical diffraction effects that single-pass approximations miss. Crucially, the inverse problem — recovering the slice-by-slice refractive index from the measured holograms — is solved iteratively, with the forward model refined at each step until the simulated exit wave agrees with the data.

What makes the achievement notable is not merely the physical fidelity of the model but the sheer scale at which it can be executed. Multi-slice wave propagation, when performed naively, is orders of magnitude more expensive than projection-based tomography, and iterative inversion multiplies that cost. The researchers coupled their scattering-aware solver to a computational architecture that distributes the work across many processing units, exploiting the fact that the propagation between slices is dominated by fast Fourier transforms — operations that parallelize efficiently and that modern graphics processors execute at extraordinary throughput. Combined with strategies for managing the gigantic datasets involved, in which each individual projection can occupy many gigabytes and the final reconstructed volume approaches a billion or more voxels, the pipeline brings what was previously a computationally prohibitive calculation within practical reach.

The payoff is quantitative imaging that remains accurate where conventional methods visibly falter. In single-scattering-based reconstructions of thick, strongly structured specimens, multiple scattering manifests as shadowing, ring-like artifacts, spatially varying resolution loss, and systematic underestimation of electron density in dense regions. These are not cosmetic defects. Quantitative electron density is precisely the measurable that makes holotomography scientifically valuable: it underpins the identification of organelles in cells, the characterization of material phases and porosity in functional materials, and the comparison of healthy and diseased tissue. By modeling the full wave-optical interaction, the new approach recovers electron densities that remain consistent across regions of very different thickness and composition, restoring confidence in the numbers rather than only the pictures.

The gigavoxel scale matters for a practical reason that is easy to overlook in discussions of resolution. Field of view and resolution trade against each other for a fixed detector and beam geometry: to image a large object at high resolution, one must either stitch together many partially overlapping exposures or record enormous detector frames, and in both cases the data volume grows with the cube of the linear resolution improvement. Doubling resolution in all three dimensions yields an eightfold increase in voxels. Datasets at the gigavoxel scale therefore represent the threshold at which whole, intact specimens — an entire cell in three dimensions at nanometre detail, or a sizable volume of battery electrode or bone — can be captured in a single self-consistent reconstruction rather than assembled from fragments, with all the seams and inconsistencies that assembly entails.

Lenslessness is central to reaching this scale. Refractive and diffractive X-ray lenses suffer from limited aperture, efficiency losses, and aberrations, and their use constrains both the achievable field of view and the fidelity of the recovered wavefront. Computed diffractive imaging replaces the lens’s fixed transfer function with an algorithmic reconstruction, letting the detector — which can be made large, efficient, and linear — define the numerical aperture. The cost is computational burden, which is exactly where the new work’s contribution lies: it shows that the computational overhead of a wave-optically accurate model can be absorbed at the very scales where lensless imaging offers its greatest advantages.

The implications extend across the communities that depend on synchrotron and X-ray free-electron laser facilities. For structural biologists, accurate gigavoxel-scale holotomography opens the prospect of imaging whole cryo-preserved cells and small organisms quantitatively, complementing electron tomography’s exquisite resolution with the penetration depth that only X-rays provide. For materials scientists, the technique promises non-destructive, quantitative three-dimensional characterization of energy-storage materials, catalysts, and structural alloys at length scales bridging the gap between electron microscopy and conventional computed tomography. And for the photon-source community, the demonstration establishes that the next generation of brighter, more coherent sources can be exploited fully only if reconstruction algorithms evolve in step — a message that resonates as diffraction-limited storage rings and free-electron lasers come online worldwide.

Challenges remain before such reconstructions become routine. Scattering-aware solvers demand accurate knowledge of experimental parameters — propagation distances, beam profiles, and detector geometry — because errors in these inputs propagate through the multi-slice model in ways that simple approximations tolerate more gracefully. Convergence of the iterative inversion must be monitored carefully for thick, strongly scattering samples, and the data and memory footprints will continue to strain storage and workflow infrastructure at user facilities. Yet the direction is unmistakable. As computational power grows and wave-optical forward models mature, the dividing line between what can be measured and what must be assumed continues to shift toward measurement. Gigavoxel-scale, multiple-scattering-aware lensless holotomography marks a concrete step across that line, bringing quantitative, non-destructive, nanometre-resolution three-dimensional imaging of whole intact specimens closer to everyday practice.

Subject of Research: Gigavoxel-scale multiple-scattering-aware lensless X-ray holotomography

Article Title: Gigavoxel-scale multiple-scattering-aware lensless holotomography

Article References: Rogalski, M., Winnik, J., Dudek, J., Arcab, P., Wdowiak, E., Matryba, P., Stefaniuk, M., Zdańkowski, P., & Trusiak, M. (2026). Gigavoxel-scale multiple-scattering-aware lensless holotomography. Light: Science & Applications, 15(1), Article 381. https://doi.org/10.1038/s41377-026-02416-0

Image Credits: AI Generated

DOI: 10.1038/s41377-026-02416-0

Keywords: holotomography, X-ray phase contrast, lensless imaging, multiple scattering, multi-slice method, computed tomography, synchrotron imaging, electron density, gigavoxel reconstruction, computational imaging, X-ray optics, nanoscale imaging