Tilt-Series Neutron Tomography

• Tilt-series neutron tomography is a limited-angle CT technique that reconstructs three-dimensional volumes from incomplete angular data while accommodating constraints like sample geometry.
• It integrates interleaved radiography with tomography to capture both quantitative water dynamics and qualitative structural details in complex environments such as rhizobox root–soil systems.
• Adaptive sampling strategies and reconstruction methods like MBIR and golden-ratio sequences are employed to mitigate missing wedge artifacts and improve imaging fidelity.

Tilt-series neutron tomography is a class of neutron computed tomography in which projections are acquired over a limited angular interval rather than a full $360^\circ$ rotation, and a three-dimensional volume is reconstructed from incomplete angular data. In the rhizobox context, the method is presented as a practical compromise when slab-like sample geometry, the need to preserve an intact plant, and limited neutron penetration through moist soil make conventional full-turn neutron tomography difficult or impossible (Kaestner et al., 15 Sep 2025). The defining technical consequence is a “missing wedge” in Radon space, which introduces bias and reconstruction artifacts but relaxes geometric and mechanical constraints. Within neutron imaging more broadly, tilt-series acquisition is not restricted to attenuation radiographs: it also encompasses adaptive orientation selection for sparse-view neutron CT (Yang et al., 2022), diffraction-based phase sinograms reconstructed into density maps (Heacock et al., 2018), and hyperspectral rotational datasets that are decomposed into isotope-specific sinograms before reconstruction (Balke et al., 2021).

1. Geometric definition and relation to other neutron tomographic modes

Tilt-series neutron tomography differs from conventional neutron CT primarily in angular coverage and acquisition geometry. In a typical full-turn scan, the sample is rotated through all angles while maintaining acceptable neutron transmission; this is feasible for small cylindrical samples, but not for flat rhizoboxes designed to give roots an unconstrained growth direction (Kaestner et al., 15 Sep 2025). In that setting, traditional neutron radiography remains highly effective for time-resolved monitoring of water movement in root–soil systems, but it is intrinsically two-dimensional and cannot localize structures along the beam direction (Kaestner et al., 15 Sep 2025).

Laminography has been used for flat samples because it rotates around a tilted axis, but the rhizobox study identifies several constraints that remain important: the box content must be immobilized to avoid rearrangement, a complete rotation may be impossible if the shoot remains intact, and radiography and tomography often cannot be acquired in the same mounting (Kaestner et al., 15 Sep 2025). The vertical-acquisition-axis tilt series was therefore proposed as especially well suited to rhizoboxes, because it avoids those geometric and mechanical restrictions while still providing 3D information (Kaestner et al., 15 Sep 2025). The method explicitly accepts a limited angular range $\alpha_{\text{scan}}=[-\alpha,\alpha]$ and the associated missing wedge, trading exact Radon-space completeness for flexibility and compatibility with intact plants.

A common misconception is to treat tilt-series neutron tomography as synonymous with a degraded version of conventional radiographic CT. The literature is broader. In "Sub-micrometer resolution neutron tomography" (Heacock et al., 2018), the rotation parameter $\beta$ plays the same role as in a tilt series, but the measured observable is a momentum-space diffraction spectrum from a double crystal diffractometer rather than a position-sensitive attenuation image. In "Hyperspectral Neutron CT with Material Decomposition" (Balke et al., 2021), each angular view is a time-of-flight-resolved hyperspectral projection rather than a single radiograph. Tilt-series geometry is therefore a sampling framework, not a unique contrast mechanism.

2. Acquisition geometries, instrumentation, and scan design

The rhizobox implementation provides a concrete realization of tilt-series neutron tomography under geometric constraints. The rhizoboxes were aluminum to minimize attenuation by the container itself, with outer dimensions $140 \times 140 \times 16\ \text{mm}^3$ and an inner soil slab of $125 \times 125 \times 10\ \text{mm}^3$ (Kaestner et al., 15 Sep 2025). Sample mounting used a base with three in-line pins attached to the turntable and matching holes in the bottom plate, enabling repeatable positioning on the beamline. The root substrate was sand with porosity $42\%$, and the plants were maize grown for six weeks so that the root network filled the rhizobox (Kaestner et al., 15 Sep 2025).

The scans were performed at the ICON neutron imaging beamline at PSI, using the midi setup on experiment position 2. The detector system consisted of an Andor iKon L camera, an Otus 55 mm lens, and a $30\ \mu\text{m}$ GadOx scintillator, yielding a field of view of $150 \times 150\ \text{mm}^2$ and a pixel size of $90.9\ \mu\text{m}$ (Kaestner et al., 15 Sep 2025). The key geometrical feature was the vertical acquisition axis: standard radiographs at $0^\circ$ and tilted projections could be acquired without remounting the sample.

In the demonstrated daytime scan, 320 radiographs were recorded, with every second exposure taken at $\alpha_{\text{scan}}=[-\alpha,\alpha]$0 for radiography and the alternating exposures taken from a golden-ratio tilt sequence spanning $\alpha_{\text{scan}}=[-\alpha,\alpha]$1 (Kaestner et al., 15 Sep 2025). At the end of the time series, a separate full $\alpha_{\text{scan}}=[-\alpha,\alpha]$2 scan was acquired as a reference, after moving the slab farther from the detector to avoid collision (Kaestner et al., 15 Sep 2025). This interleaved protocol is central to the method because it yields a radiographic time series and a tomographic time series simultaneously.

More generally, neutron tilt-series acquisition appears in several instrumental regimes. The adaptive neutron CT study evaluates sparse-view tilt series on simulated phantoms and on a volcanic rock sample on a metal ring measured at the High Flux Isotope Reactor at Oak Ridge National Laboratory, with a reference reconstruction created using MBIR from 1200 projections (Yang et al., 2022). The hyperspectral study acquires 100 views and 2290 TOF bins with $\alpha_{\text{scan}}=[-\alpha,\alpha]$3 bin width at Flight Path 5 of the 20 Hz spallation neutron source at LANSCE, using a neutron-sensitive MCP detector with four Timepix readout chips and a pixel pitch of $\alpha_{\text{scan}}=[-\alpha,\alpha]$4 (Balke et al., 2021). The diffraction-based method uses a double crystal diffractometer, a perfect-silicon analyzer crystal, and a $\alpha_{\text{scan}}=[-\alpha,\alpha]$5He proportional counter, with sample rotation over ranges such as $\alpha_{\text{scan}}=[-\alpha,\alpha]$6 to $\alpha_{\text{scan}}=[-\alpha,\alpha]$7 in 1–1.5 degree steps (Heacock et al., 2018).

3. Limited-angle reconstruction, angular sampling, and adaptive view selection

The reconstruction principle in rhizobox tilt-series imaging is limited-angle or missing-wedge tomography. The choice of tilt range is dictated by a trade-off: larger tilt angles improve angular sampling and reconstruction fidelity, but they reduce neutron transmission and increase blurring due to the larger sample-to-detector distance at oblique incidence (Kaestner et al., 15 Sep 2025). Transmission is modeled using Beer–Lambert attenuation, with the tilted path length given by $\alpha_{\text{scan}}=[-\alpha,\alpha]$8, and the scan range is chosen so that transmission remains above 10%, because lower transmission would lead to unacceptable noise and scattering contributions (Kaestner et al., 15 Sep 2025). For the 10 mm slab with 42% porosity and ICON’s nominal $\alpha_{\text{scan}}=[-\alpha,\alpha]$9 for the 20 mm aperture, both the transmission limit and the penumbra blur constrain the usable range (Kaestner et al., 15 Sep 2025).

To support dynamic imaging, the rhizobox study uses a golden-ratio angular sequence because it minimizes motion artifacts and ensures that any consecutive subset of projections covers the angular range relatively uniformly (Kaestner et al., 15 Sep 2025). The adapted limited-range sequence is

$\beta$0

with

$\beta$1

and the interleaved scan protocol is

$\beta$2

This yields truly interleaved tomography and radiography rather than separate measurement blocks (Kaestner et al., 15 Sep 2025).

Processing in that study was split into radiography and tomography tracks. Both were normalized using scattering correction following the black-body-based methods of Boillat et al. and Carminati et al., and further filtered to suppress outlier spots and ring artifacts (Kaestner et al., 15 Sep 2025). Radiography was analyzed with Python scripts based on NumPy and scikit-image, while tomography was reconstructed with filtered back projection in MuhRec, including support for golden-ratio projection ordering and weighting for missing-wedge data (Kaestner et al., 15 Sep 2025). The result is explicitly a weighted limited-angle FBP solution rather than an exact inversion of fully sampled Radon space.

A different response to sparse-view limitations is the adaptive orientation selection method of "An Edge Alignment-based Orientation Selection Method for Neutron Tomography" (Yang et al., 2022). There, the next view is selected by maximizing

$\beta$3

where $\beta$4 is an edge-alignment term derived from Canny edge detection and the Progressive Probabilistic Hough Transform on the current MBIR reconstruction, and $\beta$5 is an orientation-diversity regularizer (Yang et al., 2022). The method uses svMBIR, and the paper reports faster NRMSE convergence than golden-ratio sampling on both synthetic and experimental data, with the improvement especially visible early in the scan (Yang et al., 2022). This suggests that limited-angle neutron tomography can be improved not only by reconstruction design but also by adaptive acquisition.

4. Measurement models beyond conventional attenuation radiography

Tilt-series neutron tomography includes several distinct forward models. The rhizobox implementation is based on transmitted-beam projections and conventional attenuation physics, with complementary radiography and tomography in the same scan (Kaestner et al., 15 Sep 2025). By contrast, the diffraction-based technique reconstructs phase rather than intensity. In that method, neutron diffraction spectra $\beta$6 are measured as a function of sample rotation, a phase retrieval algorithm recovers the real-space phase profile at each angle, the recovered phases are stacked into a sinogram, and filtered back projection with a Hann filter reconstructs a 2D map of scattering length density $\beta$7 (Heacock et al., 2018). The paper describes this explicitly as a tomographic version of neutron diffraction-based phase retrieval rather than conventional tilt-series neutron tomography based on radiographs.

For the silicon phase-grating samples in that study, the grating period was $\beta$8, with depths $\beta$9, $140 \times 140 \times 16\ \text{mm}^3$0, and $140 \times 140 \times 16\ \text{mm}^3$1, corresponding to phase amplitudes 2.6, 2.2, and 1.4 rad at $140 \times 140 \times 16\ \text{mm}^3$2 Å (Heacock et al., 2018). The reconstructions had a resolution of about 300 nm, which the paper states is more than an order of magnitude smaller than the resolution of radiographic, phase contrast, differential phase contrast, and dark field neutron tomography methods (Heacock et al., 2018). The method assumes a phase-only sample, quasi-periodicity over the beam, and a measurable angular span tied to sample aspect ratio and diffraction visibility.

A third model is hyperspectral tilt-series acquisition. In the ERNI framework, each projection angle yields a TOF-resolved transmission spectrum per pixel, and the rotational series forms a hyperspectral tilt series (Balke et al., 2021). The counts for object and blank scans are modeled with signal and background components, transmission is computed after background subtraction, and attenuation is expressed through Beer’s law in the form $140 \times 140 \times 16\ \text{mm}^3$3 (Balke et al., 2021). The material model $140 \times 140 \times 16\ \text{mm}^3$4 leads to $140 \times 140 \times 16\ \text{mm}^3$5, with $140 \times 140 \times 16\ \text{mm}^3$6, so the measurements are first decomposed into material-decomposed sinograms $140 \times 140 \times 16\ \text{mm}^3$7 via a weighted, nonnegative BPDN-like problem and then reconstructed per material using SVMBIR with a q-GGMRF prior (Balke et al., 2021). Because the experiment had $140 \times 140 \times 16\ \text{mm}^3$8 TOF bins and $140 \times 140 \times 16\ \text{mm}^3$9 materials, the pipeline reduces dimensionality before reconstruction (Balke et al., 2021).

These examples clarify that “tilt-series neutron tomography” refers to rotational sampling under angular or acquisition constraints, while the underlying image quantity may be attenuation, phase, or isotope/material-specific areal density. The shared tomographic structure is the formation of angle-indexed projection data and subsequent inversion under incomplete, noisy, or spectrally structured measurements.

5. Rhizobox root–soil imaging and dynamic water studies

The clearest application domain in the cited literature is root–soil interaction imaging in rhizoboxes. Traditional neutron radiography is well suited to time-resolved monitoring of water movement in root–soil systems, but the rhizobox study shows that a vertical-axis tilt series can add 3D structural information without sacrificing the time-series radiographic capability (Kaestner et al., 15 Sep 2025). The experiments used six-week-old maize plants in sand-filled rhizoboxes, and the main result was that even with the missing wedge, the tilt-series data could recover the overall root network structure in the rhizobox (Kaestner et al., 15 Sep 2025).

The reference full-turn scan of the dry slab reconstructed the entire root architecture. When that complete dataset was downsampled to wedges of $125 \times 125 \times 10\ \text{mm}^3$0, $125 \times 125 \times 10\ \text{mm}^3$1, $125 \times 125 \times 10\ \text{mm}^3$2, and $125 \times 125 \times 10\ \text{mm}^3$3, degradation with narrower angular coverage became obvious, and reconstructed root features became less faithful and more distorted (Kaestner et al., 15 Sep 2025). The authors conclude that the chosen $125 \times 125 \times 10\ \text{mm}^3$4 scan range provides an acceptable balance: the missing wedge is visible, but the root network shape remains well reconstructed (Kaestner et al., 15 Sep 2025).

For the time-series scan, 160 golden-ratio projections were reconstructed into three temporal volumes (Kaestner et al., 15 Sep 2025). Differences between the first and last volume reveal changes in water content, and the reconstruction qualitatively shows where water moved during the daytime period (Kaestner et al., 15 Sep 2025). However, the tomographic water signal is explicitly qualitative rather than quantitative. The missing-wedge volumes exhibit bias and reconstruction artifacts, so they cannot be used for quantitative water-content analysis (Kaestner et al., 15 Sep 2025). The methodological distinction is therefore sharp: radiography is the quantitative tool for water dynamics, while tilt-series tomography is the structural tool for root network topology and qualitative water localization (Kaestner et al., 15 Sep 2025).

This division of labor is important for interpreting the method. Tilt-series tomography in this application is not a replacement for quantitative neutron radiography. Rather, the combined protocol measures two complementary aspects of the rhizosphere simultaneously: radiographs provide robust, quantitative temporal information on moisture dynamics, and tomographic slices provide 3D spatial context for roots and the qualitative location of wet regions (Kaestner et al., 15 Sep 2025). The study identifies root–soil interaction, irrigation responses, drought stress, and rhizosphere transport processes as relevant targets, and states that the approach is a promising route toward improving model accuracy for soil–root interactions (Kaestner et al., 15 Sep 2025).

6. Artifacts, limitations, and methodological frontiers

The principal limitation of tilt-series neutron tomography is incomplete angular coverage. In the rhizobox study, the severe artifacts from the missing wedge include shape distortions and cross-talk along the beam direction; these artifacts are asymmetric and become more pronounced as the scan range narrows (Kaestner et al., 15 Sep 2025). Even in the demonstrated $125 \times 125 \times 10\ \text{mm}^3$5 case, the reconstruction is biased and therefore unsuitable for quantitative estimation of soil water content (Kaestner et al., 15 Sep 2025). The transmission constraint and penumbra blur further restrict how far tilt angles can be increased (Kaestner et al., 15 Sep 2025).

Sparse-view and noisy-data limitations appear in other neutron CT settings as well. The adaptive orientation-selection paper notes that conventional FBP performs poorly with sparse views or noisy data, motivating the use of MBIR and improved sampling strategies (Yang et al., 2022). The hyperspectral ERNI study emphasizes that neutron TOF imaging is extremely noise-limited because of low neutron flux, many energy bins, poor statistics at resonances, and background-dominated regions; it also states that the method is not yet fully quantitative, and that $125 \times 125 \times 10\ \text{mm}^3$6U and $125 \times 125 \times 10\ \text{mm}^3$7Pu deviate substantially from SAMMY-derived areal densities in the reported results (Balke et al., 2021). The diffraction-based method adds a different set of constraints: phase-only assumption, periodicity assumption, coherence-length limit, rotation-range limit, and the difficulty of measuring high diffraction orders (Heacock et al., 2018).

These limitations delimit what tilt-series neutron tomography can presently do and help avoid overinterpretation. It is not inherently equivalent to full-angle neutron CT, and in several implementations it is not fully quantitative for all target variables. At the same time, the cited work identifies clear methodological frontiers. For rhizobox imaging, future work is aimed at longer time series, systematic optimization of image quality, and possibly iterative reconstruction methods to reduce the impact of the missing wedge (Kaestner et al., 15 Sep 2025). For sparse-view nCT, adaptive orientation selection using MBIR reconstructions from already acquired projections offers one route to reducing total scan time while preserving reconstruction quality (Yang et al., 2022). For diffraction-based tomography, the authors consider further optimization of phase recovery and tomographic reconstruction, as well as extensions to 2D phase retrieval and 3D tomography by rotating about more than one axis (Heacock et al., 2018). For hyperspectral CT, the pipeline from TOF-resolved projections to material sinograms and then to MBIR reconstruction establishes a computationally practical, semi-quantitative route to isotope-specific tomograms (Balke et al., 2021).

Taken together, these developments show that tilt-series neutron tomography is less a single algorithm than a family of constrained-angle neutron tomographic methods. Its unifying feature is the reconstruction of 3D structure from rotationally sampled neutron measurements when full-angle acquisition, direct quantitative inversion, or conventional projection imaging alone is inadequate.