Operando Synchrotron Nano-holo-Tomography

• Operando synchrotron X-ray nano-holo-tomography is a phase-contrast imaging method that combines coherent X-ray illumination with multi-distance holographic acquisition for 3D mapping.
• It reconstructs quantitative refractive index and electron density maps at the nanoscale using advanced phase retrieval and tomographic inversion techniques.
• The technique enables non-destructive, operando 4D imaging of complex materials, linking nanostructural evolution to functional performance in devices like battery electrodes.

Searching arXiv for papers on synchrotron X-ray holo-tomography, operando holotomography, and reconstruction methods. Operando synchrotron X-ray nano-holo-tomography is a propagation-based, phase-contrast tomographic imaging methodology that combines coherent hard X-ray illumination, multi-distance holographic projection acquisition, and tomographic reconstruction to recover three-dimensional maps of refractive-index decrement and, in suitable regimes, electron density at nanoscale resolution during or near device-relevant conditions. In the literature considered here, the method is established through non-destructive synchrotron X-ray holographic tomography of buried three-dimensional silicon photonic crystals (Grishina et al., 2018), extended algorithmically by software and inverse methods for holographic and tomographic X-ray imaging (Lucht et al., 13 Jun 2025, Nikitin et al., 2024), and demonstrated in fully operando 4D form for a silicon-graphite battery anode, where repeated multi-distance scans are coupled with Digital Volume Correlation and transport analysis to connect evolving nanostructure to chemomechanical function (Vanpeene et al., 8 Aug 2025).

1. Definition and methodological scope

Synchrotron X-ray holographic tomography, also referred to as nano-holo-tomography, is described as propagation-based (inline) phase-contrast imaging with multi-distance phase retrieval and tomographic rotation to reconstruct a 3D map of the refractive index decrement $\delta$ and, via $\delta$, the electron density (Grishina et al., 2018). The acquisition uses a focused, coherent hard X-ray beam to illuminate the sample with a spherical wave; radiographs are recorded at multiple propagation conditions while rotating the sample, after which phase retrieval is performed projection-wise and the recovered phase projections are reconstructed tomographically (Grishina et al., 2018).

The relevant imaging physics is expressed through the complex refractive index

$n(x,y,z) = 1 - \delta(x,y,z) + i \beta(x,y,z),$

with absorption coefficient

$\mu = \frac{4\pi \beta}{\lambda},$

exit-wave amplitude

$$A(x,y) = \exp\!\left[-\frac{2\pi}{\lambda}\int \beta(x,y,z)\,dz\right],$$

and projected phase

$$\phi(x,y) = -\frac{2\pi}{\lambda}\int \delta(x,y,z)\,dz = -k\int \delta(x,y,z)\,dz,$$

where $k=2\pi/\lambda$ (Grishina et al., 2018). As a general phase-contrast framework, the Transport-of-Intensity Equation is

$$\frac{\partial I}{\partial z} = -k \nabla \cdot (I \nabla \phi),$$

although the cited silicon photonic-crystal study employed a Paganin-type single-material phase-retrieval approach extended to multiple propagation distances rather than directly solving the TIE (Grishina et al., 2018).

In the operando context, the method becomes 4D when successive 3D reconstructions are acquired during a realistic process sequence. In the silicon-graphite anode study, operando synchrotron X-ray nano-holo-tomography is defined as a 4D $(3\mathrm{D}+\mathrm{time})$ methodology using propagation-based phase contrast in the near-field Fresnel regime to recover quantitative phase images of a low-$Z$, multiphase battery electrode during its formation cycle, then reconstruct them tomographically at nanoscale resolution with minutes temporal sampling (Vanpeene et al., 8 Aug 2025). This establishes the distinction between non-destructive in situ tomography, in which no irreversible preparation is required, and true operando imaging, in which the sample is imaged under an active thermal, electrochemical, fluidic, optical, or electrical stimulus (Grishina et al., 2018, Vanpeene et al., 8 Aug 2025).

2. Imaging geometry, beamline configurations, and acquisition protocols

The method has been implemented at high-coherence synchrotron nanoprobe beamlines using focused hard X-ray illumination and geometric magnification. In the ESRF ID16A-NI study on silicon photonic crystals, the source was the synchrotron ID16A-NI nano-imaging beamline, operated at photon energy $\delta$0 keV with wavelength $\delta$1 Å, using multilayer-coated Kirkpatrick–Baez mirrors to produce a diffraction-limited focused spot of $\delta$2 nm$\delta$3 (Grishina et al., 2018). The sample was placed a short distance $\delta$4 downstream of the focus and the detector at distance $\delta$5 downstream of the sample, with spherical-wave illumination and Fresnel scaling relations

$\delta$6

Four different sample-to-focus distances were used, with 1500 radiographs acquired at each distance while rotating the sample from $\delta$7 to $\delta$8; exposure time was $\delta$9 s per projection, for a total of 6000 projections (Grishina et al., 2018).

A later nano-holotomography reconstruction study at ESRF ID16A used the Projection X-ray Microscope with KB mirrors at $n(x,y,z) = 1 - \delta(x,y,z) + i \beta(x,y,z),$0 keV and four sample planes with $n(x,y,z) = 1 - \delta(x,y,z) + i \beta(x,y,z),$1, $n(x,y,z) = 1 - \delta(x,y,z) + i \beta(x,y,z),$2, $n(x,y,z) = 1 - \delta(x,y,z) + i \beta(x,y,z),$3, and $n(x,y,z) = 1 - \delta(x,y,z) + i \beta(x,y,z),$4 mm, total focus-to-detector distance $n(x,y,z) = 1 - \delta(x,y,z) + i \beta(x,y,z),$5 m, geometrical magnifications approximately $n(x,y,z) = 1 - \delta(x,y,z) + i \beta(x,y,z),$6, $n(x,y,z) = 1 - \delta(x,y,z) + i \beta(x,y,z),$7, $n(x,y,z) = 1 - \delta(x,y,z) + i \beta(x,y,z),$8, and $n(x,y,z) = 1 - \delta(x,y,z) + i \beta(x,y,z),$9, and $\mu = \frac{4\pi \beta}{\lambda},$0 angles over $\mu = \frac{4\pi \beta}{\lambda},$1 at $\mu = \frac{4\pi \beta}{\lambda},$2 s exposure per projection (Nikitin et al., 2024). The detector had $\mu = \frac{4\pi \beta}{\lambda},$3 pixels with $\mu = \frac{4\pi \beta}{\lambda},$4m pitch, objective magnification $\mu = \frac{4\pi \beta}{\lambda},$5, and an effective pixel of approximately $\mu = \frac{4\pi \beta}{\lambda},$6 nm; data were typically binned $\mu = \frac{4\pi \beta}{\lambda},$7 for processing (Nikitin et al., 2024).

The 2025 battery study demonstrates explicitly operando acquisition. It used the ESRF ID16B hard X-ray nanoprobe at $\mu = \frac{4\pi \beta}{\lambda},$8 keV with photon flux approximately $\mu = \frac{4\pi \beta}{\lambda},$9 ph s$$A(x,y) = \exp\!\left[-\frac{2\pi}{\lambda}\int \beta(x,y,z)\,dz\right],$$0 and a focused nanobeam of about $$A(x,y) = \exp\!\left[-\frac{2\pi}{\lambda}\int \beta(x,y,z)\,dz\right],$$1 nm (horizontal) by $$A(x,y) = \exp\!\left[-\frac{2\pi}{\lambda}\int \beta(x,y,z)\,dz\right],$$2 nm (vertical) in cone-beam geometry (Vanpeene et al., 8 Aug 2025). For each projection angle, images were recorded at four sample-detector distances. The operando geometry placed the sample approximately $$A(x,y) = \exp\!\left[-\frac{2\pi}{\lambda}\int \beta(x,y,z)\,dz\right],$$3 mm from the focal spot and approximately $$A(x,y) = \exp\!\left[-\frac{2\pi}{\lambda}\int \beta(x,y,z)\,dz\right],$$4 mm from the detector, giving voxel size $$A(x,y) = \exp\!\left[-\frac{2\pi}{\lambda}\int \beta(x,y,z)\,dz\right],$$5 nm, field of view approximately $$A(x,y) = \exp\!\left[-\frac{2\pi}{\lambda}\int \beta(x,y,z)\,dz\right],$$6m$$A(x,y) = \exp\!\left[-\frac{2\pi}{\lambda}\int \beta(x,y,z)\,dz\right],$$7, and reconstructed volume approximately $$A(x,y) = \exp\!\left[-\frac{2\pi}{\lambda}\int \beta(x,y,z)\,dz\right],$$8m$$A(x,y) = \exp\!\left[-\frac{2\pi}{\lambda}\int \beta(x,y,z)\,dz\right],$$9 (Vanpeene et al., 8 Aug 2025). Each scan used $$\phi(x,y) = -\frac{2\pi}{\lambda}\int \delta(x,y,z)\,dz = -k\int \delta(x,y,z)\,dz,$$0 projections over $$\phi(x,y) = -\frac{2\pi}{\lambda}\int \delta(x,y,z)\,dz = -k\int \delta(x,y,z)\,dz,$$1 with exposure time $$\phi(x,y) = -\frac{2\pi}{\lambda}\int \delta(x,y,z)\,dz = -k\int \delta(x,y,z)\,dz,$$2 ms per projection, plus $$\phi(x,y) = -\frac{2\pi}{\lambda}\int \delta(x,y,z)\,dz = -k\int \delta(x,y,z)\,dz,$$3 flats and $$\phi(x,y) = -\frac{2\pi}{\lambda}\int \delta(x,y,z)\,dz = -k\int \delta(x,y,z)\,dz,$$4 darks per distance, for a total operando scan time of approximately $$\phi(x,y) = -\frac{2\pi}{\lambda}\int \delta(x,y,z)\,dz = -k\int \delta(x,y,z)\,dz,$$5 minutes per four-distance dataset (Vanpeene et al., 8 Aug 2025).

These configurations illustrate the defining acquisition pattern of nano-holo-tomography: coherent nanofocused or quasi-point-source illumination, geometric magnification, multi-distance Fresnel imaging, and dense angular sampling. A plausible implication is that the principal design variable is not a single propagation distance but a coupled geometry that must simultaneously satisfy phase-contrast transfer, magnification, field-of-view coverage, and mechanical stability constraints.

3. Phase retrieval, probe treatment, and tomographic inversion

The standard reconstruction pipeline in the photonic-crystal study consists of scaling radiographs to a common magnification, registering them across distances and angles, performing initial phase retrieval using the Paganin et al. single-material method assuming a homogeneous $$\phi(x,y) = -\frac{2\pi}{\lambda}\int \delta(x,y,z)\,dz = -k\int \delta(x,y,z)\,dz,$$6 ratio, refining the phase map with 15 iterations of non-linear least-squares optimization, and reconstructing $$\phi(x,y) = -\frac{2\pi}{\lambda}\int \delta(x,y,z)\,dz = -k\int \delta(x,y,z)\,dz,$$7 by filtered backprojection in ESRF PyHST2 (Grishina et al., 2018). For silicon at $$\phi(x,y) = -\frac{2\pi}{\lambda}\int \delta(x,y,z)\,dz = -k\int \delta(x,y,z)\,dz,$$8 keV, the single-material ratio used was $$\phi(x,y) = -\frac{2\pi}{\lambda}\int \delta(x,y,z)\,dz = -k\int \delta(x,y,z)\,dz,$$9 (Grishina et al., 2018). Electron density was then obtained through

$k=2\pi/\lambda$0

equivalently,

$k=2\pi/\lambda$1

(Grishina et al., 2018).

The 2025 battery work follows the same broad logic but in a multiphase porous composite. After multi-distance stack alignment and flat-field/dark-field correction, a Paganin-like phase-retrieval filter with $k=2\pi/\lambda$2 was applied to the four-distance stack for each angle, followed by FBP in PyHST2, ring artifact correction, and conversion to 16-bit (Vanpeene et al., 8 Aug 2025). The study states explicitly that the constant $k=2\pi/\lambda$3 assumption is a source of systematic bias in multiphase objects (Vanpeene et al., 8 Aug 2025). This is a central methodological caveat: the phase retrieval is quantitative within the adopted prior, but compositional heterogeneity violates the single-material model.

A major algorithmic development addresses probe-related artifacts in coherent nano-holotomography. The conventional flat-field step divides each sample projection by a reference image taken without the sample, but when the illumination is coherent this approach overlooks the phase component of the probe, and focusing optics can introduce high-frequency probe structure (Nikitin et al., 2024). The cited work formulates a conic-beam holotomography forward model in which the complex probe and the angular sequence of sample transmissions are jointly retrieved from multi-distance data (Nikitin et al., 2024). The preferred objective is the amplitude-space least-squares functional

$k=2\pi/\lambda$4

with Wirtinger-calculus gradients and nonlinear conjugate gradients using the Dai–Yuan update (Nikitin et al., 2024). Experimentally, this scheme resolved twice thinner layers in a 3D ALD standard sample measured using nano-holotomography (Nikitin et al., 2024). In the reported ALD case, layers as thin as approximately $k=2\pi/\lambda$5 nm were resolved, versus approximately $k=2\pi/\lambda$6 nm with conventional TXM full-field imaging, and synthetic-data SSIM improved from $k=2\pi/\lambda$7 to $k=2\pi/\lambda$8 in the noise-free case and from $k=2\pi/\lambda$9 to $$\frac{\partial I}{\partial z} = -k \nabla \cdot (I \nabla \phi),$$0 with Poisson noise (Nikitin et al., 2024).

The software dimension is represented by HoToPy, a Python toolbox for holographic and tomographic X-ray imaging (Lucht et al., 13 Jun 2025). It supports both a direct contrast regime and a holographic regime, with explicit implementations of CTF, ICT, nonlinear Tikhonov, TikhonovTV, AP, Paganin, Generalized Paganin, Bronnikov-aided correction, and Modified Bronnikov (Lucht et al., 13 Jun 2025). HoToPy is implemented in PyTorch for GPU acceleration and automatic differentiation, uses ASTRA for high-performance tomographic primitives, and provides modules for phase retrieval, preprocessing, alignment, ring removal, and trajectory modeling (Lucht et al., 13 Jun 2025). The toolbox therefore systematizes the algorithmic ecosystem around nano-holo-tomography rather than defining a new imaging physics.

4. Operando implementation: environmental integration, stability, and throughput

The 2018 photonic-crystal demonstration is explicitly non-destructive and in situ in the sense that the samples were mounted “as is” without cutting, thinning, or heavy-element doping, but no operando stimuli were applied during X-ray imaging (Grishina et al., 2018). The same source states that to make the technique operando one would integrate sample environments such as heating, biasing stages, microfluidic cells, or optical excitation compatible with near-focus geometry and rotational tomography (Grishina et al., 2018). It also notes that current acquisition of four distances with 1500 projections and $$\frac{\partial I}{\partial z} = -k \nabla \cdot (I \nabla \phi),$$1 s exposures implies tens of minutes per tomogram, so time-resolved operando imaging would require reducing projections or distances, faster detectors, continuous rotation, and potentially compressive or iterative reconstruction strategies (Grishina et al., 2018).

The battery study realizes this transition in practice. It used a miniaturized operando half-cell with approximately $$\frac{\partial I}{\partial z} = -k \nabla \cdot (I \nabla \phi),$$2 mm diameter housing and $$\frac{\partial I}{\partial z} = -k \nabla \cdot (I \nabla \phi),$$3 mm sample, PFA body, stainless-steel connectors, constant compression of approximately $$\frac{\partial I}{\partial z} = -k \nabla \cdot (I \nabla \phi),$$4 kPa, shortened upper connector to minimize wobble during rotation, and UV glue sealing (Vanpeene et al., 8 Aug 2025). Electrochemistry was run galvanostatically at C/6 between $$\frac{\partial I}{\partial z} = -k \nabla \cdot (I \nabla \phi),$$5 mV and $$\frac{\partial I}{\partial z} = -k \nabla \cdot (I \nabla \phi),$$6 V vs Li$$\frac{\partial I}{\partial z} = -k \nabla \cdot (I \nabla \phi),$$7/Li, with a potentiostatic hold at $$\frac{\partial I}{\partial z} = -k \nabla \cdot (I \nabla \phi),$$8 mV and tomography performed at open circuit during scans; OCV drift was approximately $$\frac{\partial I}{\partial z} = -k \nabla \cdot (I \nabla \phi),$$9 mV over $(3\mathrm{D}+\mathrm{time})$0 min (Vanpeene et al., 8 Aug 2025). Imaging during OCV, small rotating mass, rigid compression, short exposures, and dose control were all part of the stability strategy (Vanpeene et al., 8 Aug 2025).

Dose and damage considerations become much more stringent in operando settings than in the silicon-photonics case. The battery study reports cumulative dose approximately $(3\mathrm{D}+\mathrm{time})$1 MGy in electrolyte and approximately $(3\mathrm{D}+\mathrm{time})$2 MGy in active material over the entire experiment, below a previously established threshold of approximately $(3\mathrm{D}+\mathrm{time})$3 MGy for observable beam-induced artifacts (Vanpeene et al., 8 Aug 2025). This contrasts with the photonic-crystal paper, which did not report dose and notes only contextual values for other material classes (Grishina et al., 2018). A plausible implication is that operando nano-holo-tomography is constrained not only by temporal resolution and mechanical stability but also by dose budgeting across an entire time series.

Algorithmic support for operando deployment is supplied by HoToPy, which provides center-of-rotation estimation, tilt estimation, registration-based reprojection alignment, bandpass filtering, directional Fourier filters, wavelet ring removal, and per-projection geometry modeling in ASTRA (Lucht et al., 13 Jun 2025). These capabilities are explicitly described as relevant for operando conditions with mechanical or thermal drifts (Lucht et al., 13 Jun 2025). The simultaneous-probe-retrieval framework is similarly positioned as operando-relevant because it reduces reliance on frequent empty-beam measurements, allows chunked processing with periodic probe re-estimation, and is compatible with streaming reconstruction workflows, although time-resolved 4D reconstruction is not claimed in HoToPy itself (Nikitin et al., 2024, Lucht et al., 13 Jun 2025).

5. Quantitative performance and representative case studies

Representative implementations

Study	Imaging context	Key reported performance
(Grishina et al., 2018)	Buried 3D silicon photonic band-gap crystals	Real-space 3D density distributions with 20 nanometer resolution
(Nikitin et al., 2024)	ALD standard in nano-holotomography with simultaneous probe retrieval	Resolved layers as thin as ~40 nm; SSIM 0.81 vs 0.49 noise-free
(Vanpeene et al., 8 Aug 2025)	4D operando silicon-graphite anode	Voxel size 50 nm; effective spatial resolution typically ~150–200 nm; ~9 min per scan

In the silicon photonic-crystal study, the central scientific result is the structural discrimination of samples that appear similar in scanning electron microscopy but differ radically in photonic function (Grishina et al., 2018). The “Good” crystal showed the designed 3D inverse woodpile periodicity, with $(3\mathrm{D}+\mathrm{time})$4-directed pores of depth $(3\mathrm{D}+\mathrm{time})$5 nm and radius $(3\mathrm{D}+\mathrm{time})$6 nm, aspect ratio $(3\mathrm{D}+\mathrm{time})$7, and $(3\mathrm{D}+\mathrm{time})$8-directed pores of maximum depth $(3\mathrm{D}+\mathrm{time})$9 nm and aspect ratio $Z$0; tomography also revealed a slight $Z$1 shear between pore arrays, within a typical range $Z$2–$Z$3, and optical reflectivity showed a broad band gap consistent with theory and tomography-derived geometry with $Z$4 (Grishina et al., 2018). The “Bad” crystal lacked a band gap because tomography revealed a buried stiction-induced internal void formed during drying after colloidal quantum dot infiltration. The “Ugly” crystal had very shallow pores of about $Z$5 nm owing to erroneous etching parameters and therefore lacked the required 3D periodic depth (Grishina et al., 2018). The significance is methodological as much as substantive: surface-sensitive SEM could not distinguish these buried failure modes, whereas non-destructive 3D electron-density mapping could (Grishina et al., 2018).

The simultaneous-probe-retrieval study provides a different performance benchmark. For an ALD standard sample, the method improved reconstruction fidelity by accounting for the complex probe rather than assuming flat-field division was sufficient (Nikitin et al., 2024). The reported reconstruction of the full ALD volume, including phase retrieval and tomography, took approximately four hours on two nodes with $Z$6A100 GPUs each, while tomography of the full volume completed in approximately $Z$7 minutes for $Z$8 conjugate-gradient iterations (Nikitin et al., 2024). The result that “3D reconstruction resolving twice thinner layers” was achieved is concretized experimentally by clean separation of approximately $Z$9 nm ZnO/Al$\delta$00O$\delta$01 layers that were not reliably separated by conventional holotomography (Nikitin et al., 2024).

The HoToPy paper reports computational benchmarks rather than new physical application claims. For phase retrieval on a single angle with two distances at $\delta$02 pixels, timings range from approximately $\delta$03 ms for unconstrained CTF on an A6000 Ada to approximately $\delta$04 ms for Tikhonov with non-positivity and disk-shaped support; for the full catalytic-particle dataset, timings range from approximately $\delta$05 s to approximately $\delta$06 min depending on algorithm and constraints (Lucht et al., 13 Jun 2025). Tomographic reprojection alignment with $\delta$07 iterations, $\delta$08 binning, and bandpass filtering took approximately $\delta$09 min on a 24-core CPU plus A6000 Ada GPU, and FDK reconstruction of the full volume took approximately $\delta$10 min (Lucht et al., 13 Jun 2025). These figures indicate that advanced holographic phase retrieval and alignment are already computationally practical at synchrotron scale, though not yet necessarily real-time.

6. Multiphysics analysis and scientific reach in true operando studies

The 2025 silicon-graphite anode study extends nano-holo-tomography from structural diagnosis to multiscale process science (Vanpeene et al., 8 Aug 2025). Quantitative phase maps reconstructed at successive time points were combined with Digital Volume Correlation to extract displacement and strain fields and with diffusion/tortuosity analysis to relate evolving pore topology to ionic transport (Vanpeene et al., 8 Aug 2025). For DVC, local affine transforms were computed over cubic correlation windows at a pyramidal sequence of $\delta$11m$\delta$12 with $\delta$13 overlap, and strain invariants were derived through the deformation gradient $\delta$14 and its polar decomposition:

$\delta$15

$\delta$16

For reference, the small-strain tensor is

$\delta$17

(Vanpeene et al., 8 Aug 2025).

The electrode was observed to have initial macro-porosity of approximately $\delta$18 vol%, partitioned into approximately $\delta$19 inner-particle and approximately $\delta$20 interparticle porosity (Vanpeene et al., 8 Aug 2025). During lithiation, a two-step sequence occurred: above about $\delta$21–$\delta$22 mV vs Li$\delta$23/Li, graphite and porosity increased together, whereas below about $\delta$24 mV, in the silicon activity regime, macro-porosity dropped abruptly, with relative decreases of $\delta$25 to $\delta$26, inner-particle porosity decreasing by about $\delta$27 and interparticle porosity by about $\delta$28 (Vanpeene et al., 8 Aug 2025). During delithiation, interparticle porosity recovered while inner-particle porosity increased beyond the fresh state by $\delta$29 relative, with local pore size in graphite increasing from approximately $\delta$30 nm to approximately $\delta$31 nm (Vanpeene et al., 8 Aug 2025). Electrode thickness changed from about $\delta$32m in the fresh state to about $\delta$33m at end of lithiation and about $\delta$34m at end of cycle (Vanpeene et al., 8 Aug 2025).

At the mechanics level, mean orthogonal strain components during lithiation were reported as $\delta$35, $\delta$36, and $\delta$37, with deviatoric strain showing staircase increases aligned with voltage plateaus near $\delta$38, $\delta$39, and $\delta$40 mV vs Li$\delta$41/Li and about $\delta$42 irreversibility by end of formation (Vanpeene et al., 8 Aug 2025). Hot spots of volumetric and shear strain localized near large CBD-Si clusters and at graphite-graphite interfaces, and local maximum tensile strain approached approximately $\delta$43, which the study links to risk of binder failure (Vanpeene et al., 8 Aug 2025).

Transport analysis was performed by solving steady-state Laplace’s equation across the segmented pore network,

$\delta$44

with Dirichlet conditions at current collector and separator and no-flux lateral boundaries, relating effective diffusivity to porosity and tortuosity by

$\delta$45

Geodesic tortuosity was estimated from

$\delta$46

and “fast geometric paths” were defined by $\delta$47 across the electrode thickness (Vanpeene et al., 8 Aug 2025). In-plane tortuosity remained $\delta$48, through-plane tortuosity was about $\delta$49–$\delta$50 during cycling and stabilized near approximately $\delta$51 at the end, while the number of persistent fast paths increased from $\delta$52 initially to $\delta$53 at the end (Vanpeene et al., 8 Aug 2025). These paths correlated with local flux maxima and were identified as “highways” for ionic transport (Vanpeene et al., 8 Aug 2025).

A scale-bridging analysis grouped 14 local parameters into morphology, diffusion, geometry/position, and mechanics, then correlated them with particle activity and irreversibility using Pearson correlation and an “impact factor” (Vanpeene et al., 8 Aug 2025). The study reports that up to approximately $\delta$54 of the particle-level deviation from ensemble behavior can be rationalized by these local parameters, compared with approximately $\delta$55 if only macro-scale descriptors such as porosity, tortuosity, and thickness are used (Vanpeene et al., 8 Aug 2025). Activity drivers were ranked, with distance to fast path, particle/electrolyte surface fraction, and inner porosity positive, while average local geometric tortuosity and depth position were negative; irreversibility drivers included number of neighbors, maximum volumetric strain at lithiation, irreversible deviatoric strain, and proximity to CBD-Si cluster (Vanpeene et al., 8 Aug 2025). This demonstrates that operando nano-holo-tomography can move beyond morphology tracking into multiscale structure-function inference.

7. Relation to complementary methods, misconceptions, and current limitations

The method differs fundamentally from absorption CT because weakly absorbing materials such as silicon at hard X-ray energies yield poor attenuation contrast, whereas holographic tomography derives contrast from phase shifts and is therefore sensitive to electron-density variations in weakly absorbing matter (Grishina et al., 2018). It also differs from ptychographic X-ray computed tomography, which uses scanning coherent diffraction imaging with overlapping probe positions and iterative far-field phase retrieval; PXCT can achieve very high resolution but often requires smaller samples or destructive thinning and heavier computation (Grishina et al., 2018). SEM reveals surfaces only, FIB-SEM serial slicing is destructive and volume-limited, TEM tomography requires sub-micrometre lamellae, and SAXS or coherent scattering provide reciprocal-space information rather than local real-space 3D maps (Grishina et al., 2018). The battery study adds that ptychography and scanning nano-XCT can reach higher spatial resolution but are slower and can be less compatible with minutes-scale operando full-electrode imaging, whereas STXM and BCDI offer single-particle chemical or strain sensitivity but limited representativeness (Vanpeene et al., 8 Aug 2025).

A common misconception is that nano-holo-tomography is inherently quantitative simply because it reconstructs phase. The cited literature qualifies this strongly. Quantitativeness depends on the validity of assumptions such as homogeneous $\delta$56 in Paganin-type retrieval (Grishina et al., 2018, Vanpeene et al., 8 Aug 2025), adequacy of probe treatment under coherent illumination (Nikitin et al., 2024), and stability of geometry, magnification, and alignment (Lucht et al., 13 Jun 2025). Another misconception is that flat-field correction is sufficient preprocessing in coherent cone-beam holography. The simultaneous-probe-retrieval study shows explicitly that this is not the case because $\delta$57; ignoring probe phase injects line artifacts that later amplify in CT (Nikitin et al., 2024).

Several limitations remain explicit in the record. The photonic-crystal paper does not report exact $\delta$58 and $\delta$59 values, detector native pixel size, field of view, dose, or the method used to estimate resolution (Grishina et al., 2018). The battery study states that the effective spatial resolution is typically about $\delta$60–$\delta$61 nm despite $\delta$62 nm voxels, sufficient for graphite microporosity and large CBD-Si clusters but not for individual approximately $\delta$63 nm silicon nanoparticles (Vanpeene et al., 8 Aug 2025). It further notes that only about $\delta$64 vol% of CBD-Si clusters are visible versus about $\delta$65 vol% expected, implying that approximately $\delta$66 of Si is mixed at sub-resolution (Vanpeene et al., 8 Aug 2025). The simultaneous-probe-retrieval framework assumes a stationary probe within an angular chunk, so stronger time-varying probe behavior would require more frequent probe updates (Nikitin et al., 2024). HoToPy does not claim real-time streaming, dedicated sparse-view recovery, explicit detector PSF modeling, or automated dose optimization (Lucht et al., 13 Jun 2025).

Taken together, these studies define operando synchrotron X-ray nano-holo-tomography as a method family rather than a single fixed protocol. Its core is propagation-based multi-distance phase-contrast tomography under coherent synchrotron illumination; its present frontier lies in robust inverse methods, stability-aware acquisition, and coupling to downstream analyses such as DVC, segmentation, and transport modeling. The available evidence shows that the method can non-destructively image buried nanostructures in millimetre-scale supports (Grishina et al., 2018), can be substantially improved by explicit treatment of the complex probe (Nikitin et al., 2024), is now supported by modular GPU-enabled reconstruction software (Lucht et al., 13 Jun 2025), and has matured into a genuinely operando 4D platform capable of revealing multiscale chemomechanical dynamics in realistic electrochemical materials (Vanpeene et al., 8 Aug 2025).