X-ray Multi-Projection Imaging (XMPI)

• XMPI is a multi-angle X-ray imaging technique that splits a single beam into several beamlets to acquire sparse projections, ideal for fast and non-repeatable dynamics.
• It utilizes advanced optical architectures, such as in-line and in-parallel geometries, to preserve image quality while bypassing the need for sample rotation.
• Robust reconstruction methods, including regularized inversion and physics-informed deep learning, are essential to overcome the challenges of sparse angular sampling and noise.

X-ray Multi-Projection Imaging (XMPI) denotes X-ray methodologies that obtain multiple projections of the same subject from different view angles with far fewer acquisitions than conventional computed tomography. In much of the recent synchrotron and XFEL literature, XMPI refers specifically to rotation-free, simultaneous multi-view acquisition in which a single incident beam is split into several beamlets that intersect at the sample and are recorded on synchronized detectors; related formulations include stereo or trinocular X-ray geometry for sparse 3D feature localization from two or three projections, and “virtual XMPI” in which additional projections are synthesized from limited input views (Villanueva-Perez et al., 2018, Shang et al., 2023, Liu et al., 16 Apr 2025).

1. Conceptual scope and historical emergence

XMPI emerged from the need to recover volumetric or quasi-volumetric information in regimes where conventional X-ray tomography is too slow, mechanically intrusive, or fundamentally incompatible with the experiment. The original hard-X-ray formulation proposed simultaneous acquisition of several projections without rotating the sample at significant tomographic angles, explicitly targeting single-shot operation at high-brilliance sources and fast dynamical processes that cannot tolerate multi-exposure acquisition (Villanueva-Perez et al., 2018). Subsequent optical and beamline developments generalized this idea into practical synchrotron and XFEL instrumentation, including schemes compatible with large samples and complex sample environments (Bellucci et al., 2024).

The central distinction from conventional tomography is operational rather than purely geometric. Standard CT reconstructs volumetric attenuation from hundreds to thousands of projections acquired over a broad angular range, whereas XMPI typically acquires only two to three simultaneous projections and therefore trades dense angular sampling for temporal fidelity, mechanical simplicity at the sample, and compatibility with non-repeatable dynamics. This trade is decisive in problems such as binary droplet collisions, fiber failure, molten-metal foaming, additive-manufacturing melt pools, and multiphase flow in opaque media, where high-speed rotation would either perturb the physics or fail to provide the required temporal resolution (Villanueva-Perez et al., 2023, Asimakopoulou et al., 2023).

A broader usage has also developed in medical and image-synthesis contexts. There, XMPI is defined as the practice of acquiring or synthesizing multiple X-ray projections of the same subject from different view angles for multi-view radiography, stereoscopic and volumetric visualization, and improved CT/tomosynthesis workflows or interventional guidance. This broader definition preserves the multi-view objective while relaxing the requirement that every view be physically acquired (Liu et al., 16 Apr 2025).

2. Optical architectures and acquisition geometry

Physical XMPI is based on beam splitting by high-perfection single crystals, typically diamond, silicon, or germanium, operated in Bragg or Laue geometry. In the simplest description, each splitter diffracts a fraction of the incident beam into a beamlet deflected by $2\theta_B$, where $\theta_B$ satisfies Bragg’s law,

$n\lambda = 2 d \sin \theta_B.$

The sample is positioned at the common intersection point of the beamlets, and each beamlet is recorded by its own detector arm (Villanueva-Perez et al., 2018, Bellucci et al., 2024).

Two acquisition geometries have been developed in detail. In the In-Line geometry, multiple splitters are placed sequentially in the direct beam, each sending one beamlet toward the sample. For a required horizontal offset $D$ between sample and direct beam, the longitudinal splitter position is

$P = \frac{D}{\tan(2\theta_B)}.$

In the In-Parallel geometry, a single multi-wave Laue splitter generates several beamlets distributed around the direct beam, and recombiner crystals redirect them toward a common point. The angular separation between opposing views is controlled by

$\theta_V = 4(\theta_{Br} - \theta_{Bs}).$

These schemes were designed explicitly to preserve large working distances and compatibility with complex environments while maintaining simultaneous multi-view acquisition (Bellucci et al., 2024).

Optical design is governed by a familiar set of trade-offs: transmission of the direct beam, integrated diffracted intensity, Darwin width, thermal robustness, and geometric footprint. Diamond is favored for XFEL splitters because of low absorption and exceptional thermal conductivity, whereas silicon and germanium are attractive for recombiners because of larger acceptances and easier alignment. Bragg geometry generally favors higher image sharpness, whereas symmetric Laue geometry can relax active-area constraints but may introduce blur through the Borrmann triangle effect (Bellucci et al., 2024, Rogalinski et al., 29 Aug 2025).

Practical systems illustrate these choices clearly. At the European XFEL, MHz-XMPI used synthetic diamond crystals C(111) and C(220) in symmetric Laue geometry at 10 keV; C(111) deflected the beam by $35.0^\circ$ and C(220) by $58.8^\circ$ relative to the direct beam, giving a relative angular separation $\Delta \theta \approx 23.8^\circ$ between the two multi-projection beamlets (Villanueva-Perez et al., 2023). At the ForMAX beamline, perfect Si and Ge crystals produced three simultaneous projections with total angular coverage of $48^\circ$ and viewpoints of $\theta_B$0, $\theta_B$1, and $\theta_B$2 relative to the primary beam axis; one splitter used symmetric Laue geometry to relax active-area size constraints, while the others used Bragg geometry to preserve image sharpness (Rogalinski et al., 29 Aug 2025).

3. Imaging physics and the sparse-view inverse problem

Despite the unusual acquisition geometry, XMPI is governed by the standard X-ray transmission model. For view $\theta_B$3, detector coordinates $\theta_B$4, and attenuation field $\theta_B$5, the measured intensity obeys Beer–Lambert attenuation,

$\theta_B$6

and the logarithmic projection is

$\theta_B$7

In discrete form, the multi-view forward model is written as

$\theta_B$8

where $\theta_B$9 is the discretized attenuation volume, $n\lambda = 2 d \sin \theta_B.$0 stacks the per-view projection operators, and $n\lambda = 2 d \sin \theta_B.$1 models measurement noise (Rogalinski et al., 29 Aug 2025, Rosén et al., 2024).

The reconstruction difficulty is a direct consequence of extreme angular sparsity. The ForMAX three-view layout spans only $n\lambda = 2 d \sin \theta_B.$2, and the literature explicitly notes that such sampling violates Crowther’s criterion,

$n\lambda = 2 d \sin \theta_B.$3

so that, for $n\lambda = 2 d \sin \theta_B.$4 horizontal pixels, conventional tomography would require about $n\lambda = 2 d \sin \theta_B.$5 projections rather than the two or three available in XMPI. Standard filtered backprojection is therefore inadequate, and stable inversion requires regularization, learned priors, or task-specific simplifications (Rogalinski et al., 29 Aug 2025).

Representative static and dynamic optimization formulations follow the usual limited-angle pattern. A static reconstruction can be posed as

$n\lambda = 2 d \sin \theta_B.$6

whereas time-resolved reconstruction couples frames by temporal smoothness,

$n\lambda = 2 d \sin \theta_B.$7

These formulations underlie iterative ART/SART, MBIR, compressed sensing with sparsity or TV priors, and physics-informed deep learning (Rogalinski et al., 29 Aug 2025).

Recent XMPI reconstruction frameworks embed the projection physics directly in trainable models. ONIX and 4D-ONIX use differentiable projection operators and neural implicit representations to reconstruct 3D movies from ultra-sparse views; 4D-ONIX models the sample as a continuous $n\lambda = 2 d \sin \theta_B.$8, uses a ResNet34 encoder, an MLP with ResBlocks as IoR generator, and a PatchGAN discriminator, and optimizes self-consistency with the measured projections before adversarial refinement (Zhang et al., 2024). X-Hexplane and its adaptations factorize the 4D field into feature planes and optimize against measured projections at all times and angles without ground-truth volumes; this approach underlies both porous-network XMPI at 50 Hz and rotation-XMPI of alumina melt pools at 25 kHz (Wegele et al., 13 Mar 2026, Witte et al., 15 Mar 2026).

A key rate argument appears in rotation-enabled XMPI. If $n\lambda = 2 d \sin \theta_B.$9 is the camera frame rate, $D$0 the number of simultaneous projections per time step, and $D$1 the number of angles required per volume, then

$D$2

In rotation-XMPI, each volume is reconstructed from exactly the $D$3 simultaneous angles collected at that time step, so $D$4 and temporal resolution becomes detector-limited rather than rotation-limited (Witte et al., 15 Mar 2026).

4. Epipolar triangulation and sparse feature localization

A distinct XMPI regime replaces dense volumetric reconstruction with direct localization of sparse structures. In stereo X-ray tomography, each calibrated cone-beam view is represented by a projection matrix

$D$5

with homogeneous object point $D$6 and detector coordinate $D$7. Once the same point is identified in two views, its 3D position is specified by projective geometry; candidate correspondences are restricted by the epipolar constraint

$D$8

Triangulation can then be performed by solving $D$9 with SVD, or by closest-point estimation between backprojected rays (Shang et al., 2023).

The difficulty is not the geometry but the image formation. Transmission images are line integrals of overlapping attenuation, so classical reflective-image feature detectors such as SIFT, SURF, FAST, and Harris are unreliable. The reported solution uses a 2D U-Net to segment point-like and line-like features in each projection and, optionally, a 3D U-Net to fuse filtered backprojections of those feature masks into a localized volumetric feature map. Sparse feature sets are advantageous because they reduce combinatorial ambiguity; a third view is especially useful when two-view matching is confounded by ray superposition or by multiple features on the same epipolar plane (Shang et al., 2023).

The feature-localization results quantify the feasibility of this regime. On a synthetic dataset of 100 3D volumes with random shapes plus sparse point and line features and two orthogonal projections, feature detection reached ROC AUC $P = \frac{D}{\tan(2\theta_B)}.$0, TPR $P = \frac{D}{\tan(2\theta_B)}.$1, and FPR $P = \frac{D}{\tan(2\theta_B)}.$2. On a real carbon fiber tape consolidation dataset acquired in a Nikon XTH225 system, using 60 stereo pairs with faint $P = \frac{D}{\tan(2\theta_B)}.$3 copper wires and detectors binned to $P = \frac{D}{\tan(2\theta_B)}.$4, detection on blocks yielded TPR $P = \frac{D}{\tan(2\theta_B)}.$5 and PPV $P = \frac{D}{\tan(2\theta_B)}.$6; stronger attenuation improved performance to near-perfect AUC, whereas halved attenuation yielded AUC $P = \frac{D}{\tan(2\theta_B)}.$7. For 3D localization on synthetic data, learned fusion with a 3D U-Net achieved average absolute 3D localization error below 1.5 voxels and remained robust to single-view occlusion, whereas purely epipolar geometric triangulation failed in occlusion cases even when it had similar accuracy for features visible in both views (Shang et al., 2023).

This feature-centric interpretation is important because it clarifies a frequent misconception: stereo XMPI does not recover full volumetric attenuation without strong priors. Its native target is the rapid localization of salient points, endpoints, and thin line-like structures when calibrated geometry and sparse correspondences are available (Shang et al., 2023).

5. Experimental platforms and reported operating regimes

XMPI has progressed from proof-of-principle single-shot imaging to sustained high-speed operation on multiple large-scale X-ray facilities. The reported platforms span XFEL pulse-train experiments, diffraction-limited synchrotron beamlines, flow-focused stereography, and slow-rotation hybrid systems (Villanueva-Perez et al., 2023, Asimakopoulou et al., 2023, Rogalinski et al., 29 Aug 2025, Rosén et al., 2024, Witte et al., 15 Mar 2026).

Platform	Multi-view configuration	Reported operating point
European XFEL MHz-XMPI	2 split beamlets from C(111) and C(220), $P = \frac{D}{\tan(2\theta_B)}.$8	$P = \frac{D}{\tan(2\theta_B)}.$9 MHz, $\theta_V = 4(\theta_{Br} - \theta_{Bs}).$0 ns, $\theta_V = 4(\theta_{Br} - \theta_{Bs}).$1 volumes/train, $\theta_V = 4(\theta_{Br} - \theta_{Bs}).$2s per 3D frame
ESRF ID19	3-arm XMPI in static tests; 2 views in dynamic aluminum experiment	up to $\theta_V = 4(\theta_{Br} - \theta_{Bs}).$3 fps static; $\theta_V = 4(\theta_{Br} - \theta_{Bs}).$4 fps dynamic; $\theta_V = 4(\theta_{Br} - \theta_{Bs}).$5m resolution per projection
ForMAX XMPI	3 beamlets, $\theta_V = 4(\theta_{Br} - \theta_{Bs}).$6 total coverage at $\theta_V = 4(\theta_{Br} - \theta_{Bs}).$7, $\theta_V = 4(\theta_{Br} - \theta_{Bs}).$8, $\theta_V = 4(\theta_{Br} - \theta_{Bs}).$9	at least $35.0^\circ$0 kHz with $35.0^\circ$1m pixels; $35.0^\circ$2 Hz with $35.0^\circ$3m pixels
ForMAX multiphase-flow stereography	2 synchronized views separated by $35.0^\circ$4	$35.0^\circ$5 Hz, $35.0^\circ$6m effective pixel size, $35.0^\circ$7 frames per detector
MAX IV rotation-XMPI	3 simultaneous angles at $35.0^\circ$8, $35.0^\circ$9, and $58.8^\circ$0	$58.8^\circ$1 kHz, $58.8^\circ$2s temporal spacing, $58.8^\circ$3 reconstructed volumes per second

At the European XFEL, MHz-XMPI exploited the 10 keV SASE pulse structure with intra-train repetition rate $58.8^\circ$4 MHz, recorded 127 frames per train, and reconstructed 3D movies of binary droplet collisions at 0.89 $58.8^\circ$5s temporal resolution. The same line of work reports that EuXFEL can operate up to 4.514 MHz intra-train, and that the demonstrated XMPI rate is at least three orders of magnitude faster than state-of-the-art time-resolved tomography (Villanueva-Perez et al., 2023, Zhang et al., 2024).

At ESRF ID19, a pink-beam implementation with Si-111, Si-220, and Ge-400 splitters achieved simultaneous triple-view acquisition up to 3000 fps and captured 3D dynamics in melted aluminum at 1000 fps with $58.8^\circ$6m resolution per projection, using the full 12-bit dynamic range of Photron Nova S16 cameras. The dynamic experiment revealed millisecond-scale bubble coalescence and a previously unreported spike-formation phenomenon in aluminum foams (Asimakopoulou et al., 2023).

At ForMAX, the three-view beam-splitting endstation used narrow-band 16.5 keV illumination and indirect detectors tailored either to temporal resolution or spatial resolution. The reported demonstrations established at least 12.5 kHz with $58.8^\circ$7m pixel sizes for fibers under mechanical load and 40 Hz with $58.8^\circ$8m pixel sizes for particle suspension in multi-phase flow, explicitly using the detector’s full dynamical range in each regime (Rogalinski et al., 29 Aug 2025). A related two-view ForMAX implementation for multiphase flow used two identical indirect X-ray microscopes with Andor Zyla 5.5 cameras, achieved 40 Hz and $58.8^\circ$9m effective pixel size, triangulated $\Delta \theta \approx 23.8^\circ$0–$\Delta \theta \approx 23.8^\circ$1m tracer particles in glycerol and human blood, and recovered a Poiseuille-consistent flow profile together with Segré–Silberberg inertial focusing at peak concentration $\Delta \theta \approx 23.8^\circ$2 and a particle-free layer of about $\Delta \theta \approx 23.8^\circ$3 mm (Rosén et al., 2024).

Hybridization with slow rotation has produced a further operating regime rather than a return to conventional tomography. In operando alumina laser remelting at MAX IV, rotation-XMPI combined three simultaneous beamlets with 25 Hz continuous rotation and 25 kHz detectors. Reconstructions covered a $\Delta \theta \approx 23.8^\circ$4 voxel domain over 700 time steps with $\Delta \theta \approx 23.8^\circ$5m isotropic voxels, required under one hour on a single NVIDIA GeForce RTX 4070 Ti, and resolved melt-pool morphology and keyhole dynamics at 40 $\Delta \theta \approx 23.8^\circ$6s steps. The reported effective rate was 25,000 reconstructed volumes per second, corresponding to a 500-fold enhancement relative to the 50 volumes per second imposed by 25 Hz rotation over $\Delta \theta \approx 23.8^\circ$7, and a 250-fold increase compared to prior state-of-the-art operando LPBF tomography (Witte et al., 15 Mar 2026).

Quantitative algorithmic benchmarks accompany these hardware demonstrations. For 4D-ONIX on simulated binary droplet collisions with two projections per timestamp, reproducible-process training over 16 experiments gave MSE $\Delta \theta \approx 23.8^\circ$8, DSSIM $\Delta \theta \approx 23.8^\circ$9, FSC half-bit spatial resolution $48^\circ$0 voxels, and FRC half-bit 2D resolution $48^\circ$1 pixels on trained views and $48^\circ$2 pixels on unseen views. Under quasi-reproducible variation, the corresponding values degraded to MSE $48^\circ$3, DSSIM $48^\circ$4, FSC $48^\circ$5 voxels, and FRC $48^\circ$6 pixels on trained views and $48^\circ$7 pixels on unseen views (Zhang et al., 2024).

6. Applications, virtual XMPI, and open technical issues

The application space of XMPI is broad but internally coherent: it is strongest where rapid, non-repeatable, mechanically sensitive, or optically opaque processes demand simultaneous multi-angle observation. Reported use cases include crack-tip tracking and growth monitoring, fiber and wire endpoint localization, fiducial tracking for motion compensation, particle tracking in opaque media, dense multiphase suspensions, blood-flow studies, pore-scale Haines jumps in porous networks, and melt-pool or keyhole dynamics in additive manufacturing (Shang et al., 2023, Rosén et al., 2024, Wegele et al., 13 Mar 2026, Witte et al., 15 Mar 2026).

In multiphase-flow and porous-media studies, XMPI has enabled direct 4D observation of phenomena that conventional high-speed tomography cannot capture without perturbing the system. In a homogeneous spherical-pore network imaged at ForMAX with two simultaneous beamlets, 1.3 $48^\circ$8m effective pixel size, and 50 Hz temporal resolution, XMPI visualized non-repeatable imbibition events and resolved step-wise Haines jumps. The measured dynamics showed capillary dominance, with a representative fast event exhibiting capillary pressure decrease from about 295 Pa to about 129 Pa while viscous losses rose only to about 1.6 Pa; comparison with Shan–Chen multiphase Lattice Boltzmann simulations revealed systematic differences in filling order and a roughly tenfold timescale mismatch, attributed to boundary conditions, wall roughness simplification, and absent dynamic contact-line physics (Wegele et al., 13 Mar 2026).

A separate extension of the XMPI idea replaces physical beamlets with synthesized views. The DL-GIPS framework defines “virtual XMPI” by taking a single acquired projection $48^\circ$9, disentangling geometry and texture through separate encoders,

$\theta_B$00

mapping geometry features through back-projection, optional 3D refinement, and forward projection,

$\theta_B$01

and synthesizing source and target projections with a generator $\theta_B$02. On LIDC-IDRI-derived DRRs, one-to-one AP$\theta_B$03LT synthesis improved over a UNet baseline with MAE 0.052 vs 0.078, RMSE 0.272 vs 0.362, SSIM 0.862 vs 0.851, and PSNR 19.46 vs 16.43; LT$\theta_B$04AP yielded MAE 0.051 vs 0.073, RMSE 0.256 vs 0.341, SSIM 0.893 vs 0.871, and PSNR 20.17 vs 18.58. Multi-to-multi synthesis of $\theta_B$05 and $\theta_B$06 views from AP and LT inputs reported SSIM 0.814 vs 0.793, PSNR 23.53 vs 21.46, and RMSE 0.116 vs 0.132 relative to UNet, at an inference time of around 0.56 s per sample versus 0.04 s for the baseline (Liu et al., 16 Apr 2025).

These advances also define the main technical limitations. First, sparse angular coverage remains fundamental: two views suffice for 3D triangulation of sparse tracers or features, but not for artifact-free reconstruction of arbitrary dense attenuation fields. Three views over $\theta_B$07 still require strong priors or regularization, and stereo XMPI explicitly targets point and line localization rather than full volumetric attenuation recovery (Shang et al., 2023, Rogalinski et al., 29 Aug 2025). Second, optics and detector hardware remain demanding: crystal perfection, clamping, thermal management, beamlet overlap, detector alignment, and synchronization directly determine usable image quality. Laue geometry can introduce blur via the Borrmann triangle, amplitude splitting reduces field of view, and dividing flux among beamlets lowers per-view photon statistics even when simultaneous acquisition improves temporal fidelity (Bellucci et al., 2024, Rogalinski et al., 29 Aug 2025, Villanueva-Perez et al., 2023). Third, learned methods bring model dependence: 4D-ONIX requires sufficient diversity across experiments to generalize, and DL-GIPS was trained on DRRs from CT rather than on real radiographs, so domain gaps due to scatter, beam hardening, detector noise, and patient positioning remain open (Zhang et al., 2024, Liu et al., 16 Apr 2025).

The near-term development agenda is explicit in the literature. Proposed directions include more beamlets and wider angular coverage; improved crystal fabrication, clamping, and strain-relief designs; thermalization and cooling; direct-conversion detectors and faster cameras; phase-retrieval integration where appropriate; uncertainty quantification; hybrid XMPI-tomography with slow rotation when dynamics permit; and continued development of physics-informed reconstruction frameworks such as ONIX, 4D-ONIX, and X-Hexplane (Rogalinski et al., 29 Aug 2025, Zhang et al., 2024, Witte et al., 15 Mar 2026). A permanent XMPI endstation at ForMAX has been proposed as the operational basis for these extensions (Rogalinski et al., 29 Aug 2025).

In aggregate, XMPI is best understood not as a replacement for full-angle tomography, but as a family of sparse-view, geometry-aware X-ray strategies optimized for simultaneity. Its defining contribution is to exchange angular completeness for temporal access, enabling 3D or 4D inference in experimental regimes where rotation-based acquisition is too slow, too perturbative, or simply impossible (Villanueva-Perez et al., 2018, Bellucci et al., 2024).