Ultrafast X-ray Sonography

• Ultrafast X-ray sonography is a pump–probe method that combines ultrafast diffraction with propagating strain pulses to reveal hidden, transient internal structures.
• It enables depth-sensitive imaging by decoding phase-specific Bragg shifts, allowing precise, layer-by-layer analysis of phase transitions in complex materials.
• The technique unifies approaches like picosecond ultrasonics and XFEL microscopy, offering actionable insights into transient strain dynamics and non-equilibrium states.

Ultrafast X-ray sonography denotes a class of pump–probe X-ray methods that infer transient internal structure from how an ultrafast X-ray probe interacts with a nonstationary material system. In its narrowest and most explicit current usage, it combines ultrafast hard-X-ray diffraction with a propagating strain pulse that acts as a universal and non-invasive probe, so that phase-specific diffraction shifts encode the spatial heterogeneity of a phase transition (Mattern et al., 22 Jul 2025). In adjacent literature, closely related approaches include picosecond ultrasonics with X-rays, ultrafast dynamical diffraction, XFEL bright-/dark-field microscopy, shock radiography, coherence-based fluctuation sensing, and ultrafast scattering from electronic wave packets (Mattern et al., 2023). The term therefore spans a rigorously defined strain-sonography method and a broader family of X-ray techniques that are sonography-like in the sense that they reveal hidden internal dynamics rather than only static structure.

1. Terminology, scope, and research lineage

The most explicit formulation of the field appears in the FeRh study, where ultrafast X-ray sonography is presented as an approach that combines ultrafast hard-X-ray diffraction with a propagating strain pulse as a universal and non-invasive probe, thereby resolving the phase-specific strain response and capturing spatio-temporal phase heterogeneity in detail (Mattern et al., 22 Jul 2025). A closely related review uses the term picosecond ultrasonics with X-rays and describes it as a method that extracts the transient strain response of laser-excited nanoscopic structures from Bragg-peak shifts, providing direct, layer-specific, and quantitative information on the picosecond strain response for structures down to few-nm thickness (Mattern et al., 2023). Other papers explicitly place themselves near, but not exactly within, conventional sonography: XFEL bright-/dark-field microscopy is described as “not pure absorption sonography” but as a multimodal hybrid for crystalline bulk dynamics; ultrafast X-ray speckle visibility is described as sonography-like in a broader structural-sensing sense; and several electronic-scattering papers discuss ultrafast X-ray sonography of electrons rather than acoustic waves (Dresselhaus-Marais et al., 2022).

This heterogeneous usage suggests two operative meanings. The narrow meaning refers to strain-pulse-based depth encoding in diffraction experiments. The broader meaning covers ultrafast X-ray methods that sense buried transient structure, internal wave propagation, or evolving electronic configurations in a way analogous to sonography, even when the contrast mechanism is diffraction, speckle, resonant scattering, or radiography rather than echo timing. The literature from 2014 to 2025 traces this expansion from quantum-electrodynamical theories of ultrafast scattering from electronic wave packets (Dixit et al., 2014), through shock radiography and nonlinear X-ray imaging (Wood et al., 2018), to explicit sonography formulations for phase-transition heterogeneity (Mattern et al., 22 Jul 2025).

A compact classification of representative modalities is useful before turning to their shared physics.

Modality	Principal observable	Representative paper
Strain-pulse sonography	Phase-specific strain response	(Mattern et al., 22 Jul 2025)
Picosecond ultrasonics with X-rays	Bragg-peak shifts from transient strain	(Mattern et al., 2023)
Ultrafast dynamical diffraction	Echo distribution across the Borrmann fan	(Rodríguez-Fernández et al., 13 Mar 2025)
XFEL bright-/dark-field microscopy	Transmission contrast plus Bragg-selected strain/orientation contrast	(Dresselhaus-Marais et al., 2022)
Shock radiography	Transmission image of moving compression structure	(Wood et al., 2018)
Coherent fluctuation sensing	Speckle visibility	(Hua et al., 2024)

These modalities are not interchangeable. Some are projection measurements, some are reciprocal-space measurements, and some are explicitly depth encoded. Their commonality lies in using ultrafast X-rays to recover transient internal structure that is otherwise hidden by depth averaging or by the inadequacy of surface-sensitive probes.

2. Measurement physics and observables

In the strain-based implementations, the central observable is the transient Bragg-peak shift of a selected crystalline phase. For picosecond ultrasonics with X-rays, the out-of-plane strain is extracted as

$$\eta(t)=\frac{d_3(t)-d_3(t<0)}{d_3(t<0)}=\frac{q_z(t<0)-q_z(t)}{q_z(t)},$$

with $q_z=2\pi n/d_3$ for the relevant reciprocal-lattice component (Mattern et al., 2023). In the FeRh sonography formulation, the same quantity is approximated from the transient shift of the phase-specific $(002)$ Bragg position as

$$\eta(t)\simeq \frac{q_{z,0}^{002}-q_z^{002}(t)}{q_{z,0}^{002}}.$$

Because a propagating bipolar strain pulse traverses different depths at different times, the delay between characteristic extrema in a phase-specific strain trace maps to the thickness occupied by that phase: $$d_\text{phase}=\frac{\Delta t_\text{phase} v_s}{2}.$$ The key decomposition is

$$V_\text{phase}(t)=D_\text{phase}(t)\,A_\text{phase}(t),$$

where $V_\text{phase}$ is the phase volume fraction, $D_\text{phase}$ the relative thickness fraction, and $A_\text{phase}$ the in-plane area coverage (Mattern et al., 22 Jul 2025).

The physical source of the strain signal is laser-induced stress. In the X-ray picosecond-ultrasonics review, the elastic response is modeled with the elastic wave equation, while the driving stress is written with Grüneisen parameters so that laser-induced stress is proportional to energy-density changes in microscopic subsystems such as electrons, phonons, and spins (Mattern et al., 2023). In the 1D thin-film limit, this makes the strain response a direct proxy for local energy density and, with appropriate modeling, for subsystem-specific heating. This is why these measurements do not merely detect acoustic arrival times; they also encode nonequilibrium thermodynamics.

A different measurement physics governs ultrafast scattering from electronic wave packets. There, the central theoretical result is that the differential scattering probability is generally controlled by a time- and space-dependent density–density correlation function, not by the instantaneous electronic density (Dixit et al., 2014). A closely related non-resonant theory shows that time-resolved X-ray scattering with no energy resolution measures the equal-time pair-correlation function, while high-energy-resolution detection measures a generalized dynamic structure factor (Dixit et al., 2014). In that branch of the field, “sonography” refers not to acoustic strain but to ultrafast imaging or sensing of non-equilibrium electronic motion.

This difference in observables is decisive. In strain sonography the dominant measurement is usually a phase-specific average lattice strain. In ultrafast electronic scattering it is a correlation function. In speckle visibility experiments it is the persistence of a coherent scattering fingerprint. The shared framework is ultrafast X-ray interrogation of a nonstationary target, but the quantity actually measured depends on geometry, bandwidth, detector window, and whether the signal is transmission, Bragg diffraction, diffuse coherent scattering, or resonant scattering.

3. Strain-pulse sonography in crystalline solids

The clearest explicit realization of ultrafast X-ray sonography is the FeRh study. In a Pt-capped FeRh film on W/MgO, an 800 nm, 50 fs optical pump both launches coherent strain pulses and drives the antiferromagnetic-to-ferromagnetic magneto-structural transition, while 11.2 keV hard-X-ray pulses record the time-dependent diffraction around the AFM and FM $(002)$ reflections (Mattern et al., 22 Jul 2025). The method exploits the fact that the AFM and FM phases have distinguishable Bragg peaks and different phase-specific strain responses to the same propagating acoustic marker.

The principal result is that the FM phase does not nucleate homogeneously. Instead, the best-fitting scenario is near-surface nucleation as narrow columnar domains that later form a continuous transformed layer at sufficient fluence; the inferred domain diameter is approximately $q_z=2\pi n/d_3$0, with an uncertainty of $q_z=2\pi n/d_3$1 from the peak-broadening analysis (Mattern et al., 22 Jul 2025). The study explicitly compares five nucleation scenarios and uses the full $q_z=2\pi n/d_3$2 sonogram rather than only fitted peak parameters. This makes the method sensitive not only to phase fraction but to whether coexistence is purely lateral, purely out-of-plane, or mixed. A low-fluence regime is distinguished by incomplete final lateral FM coverage, whereas moderate and high fluence favor surface-near columnar nucleation that eventually fills the near-surface region laterally.

The 2023 review of picosecond ultrasonics with X-rays generalizes this logic across nanoscale heterostructures (Mattern et al., 2023). In that framework, ultrafast hard-X-ray diffraction tracks acoustic propagation and quasi-static thermoelastic strain layer by layer. The review emphasizes that the method yields direct, layer-specific, and quantitative strain information even in buried and optically opaque structures, and that the strain response can act as an ultrafast proxy for local energy density. The presented use cases include Pt–Cu–Ni and Au–Ni metal heterostructures, granular and continuous FePt nanolayers, negative thermal expansion in Dy, and buried strain sensing in TbFe$q_z=2\pi n/d_3$3/Nb.

Several specific conclusions illustrate the power of the method. In Pt–Cu–Ni and Au–Ni stacks, separate Bragg peaks from different metallic layers reveal ultrafast energy redistribution between layers and show that buried layers can expand or compress depending on whether hot-electron transport is allowed or blocked (Mattern et al., 2023). In FePt, the out-of-plane strain differs qualitatively between continuous films, granular films, and free-standing grains because the Poisson effect depends on nanoscale morphology (Mattern et al., 2023). In Dy, the extracted phononic and magnetic Grüneisen parameters,

$q_z=2\pi n/d_3$4

show that spin disorder drives a strong contractive stress, so the acoustic waveform itself becomes a probe of magnetic energy flow (Mattern et al., 2023).

A related bulk-sensitive extension is ultrafast dynamical diffraction in symmetric Laue geometry (Rodríguez-Fernández et al., 13 Mar 2025). There, multiple-scattering “echoes” across the Borrmann fan encode the transient strain distribution inside a bulk crystal. The paper states that the measured spatial distribution of the echoes at the detector plane corresponds to a snapshot of the crystal lattice depth profile, with detector coordinate mapped to crystal depth by

$q_z=2\pi n/d_3$5

Applied to a $q_z=2\pi n/d_3$6 Si wafer at 9 keV, the method resolves picosecond evolution of strong lattice distortions below the melting threshold and infers an effective excitation depth of $q_z=2\pi n/d_3$7 (Rodríguez-Fernández et al., 13 Mar 2025). Relative to standard Bragg-shift sonography, this approach is more explicitly depth encoded within a single diffraction image.

Time-resolved X-ray diffraction on thin metallic crystals provides an earlier reciprocal-space precursor to these methods. In 150 nm single-crystal Al, subpicosecond 8.04 keV X-ray diffraction detected transient lattice compression within the first few picoseconds after laser irradiation, followed by expansion and coherent oscillations with an experimental period of about $q_z=2\pi n/d_3$8, close to the $q_z=2\pi n/d_3$9 thickness-mode estimate from $(002)$0 (Li et al., 2018). Although not image-forming, this established that ultrafast X-rays can directly sense the generation, propagation, and reflection of acoustic strain in buried crystalline volumes.

4. Radiographic and microscopy realizations

A second major branch of ultrafast X-ray sonography uses direct imaging rather than only reciprocal-space peak shifts. The XFEL bright-/dark-field microscope is an enabling example for crystalline solids (Dresselhaus-Marais et al., 2022). It records, from the same pumped volume and on the same XFEL pulse, both a bright-field transmitted-beam image and a dark-field Bragg-diffracted image. The bright-field arm is described as density mapping and a magnified version of radiography, while the dark-field arm selectively images the part of the crystal satisfying a chosen Bragg condition and is sensitive to the spatial derivatives of elastic displacement fields, i.e. local lattice strain and orientation.

This dual-channel architecture matters because an acoustic pulse is fundamentally a propagating elastic strain field. The paper explicitly states that dark-field X-ray microscopy is sensitive to distortion waves like phonons, shock waves, and heat, and it presents a pump–probe dark-field image of a strain wave traversing a diamond single crystal (Dresselhaus-Marais et al., 2022). The XFEL implementation uses 10.1 keV, 50 fs pulses at LCLS, with simultaneous TXM and DFXM acquisition and an initial spatial resolution of approximately $(002)$1. The bright-field channel provides through-thickness context on transmission and density-related contrast; the dark-field channel provides reciprocal-space selectivity to strain, orientation change, defects, and domains in the bulk crystal. This is sonography-like in the sense of bulk-penetrating, full-field, ultrafast sensitivity to internal elastic disturbances, while remaining distinct from conventional absorption radiography.

Betatron-X-ray radiography provides a more literal transmission-based sonography analog for shock physics (Wood et al., 2018). Using a laser-wakefield source, single-shot hard X-ray radiographs of a laser-driven shock in silicon were obtained with an intrinsic pulse duration below 100 fs and an assumed probe duration of $(002)$2. The measured source characteristics included a critical energy of $(002)$3 over source-characterization shots, a source size estimate of $(002)$4 diameter, and a measured object-plane resolution of $(002)$5 at geometric magnification 30 (Wood et al., 2018). The radiographs resolved the shock front, the compressed region, and the drive surface motion, and yielded a shock velocity of $(002)$6 and a compressed density of $(002)$7, consistent with established silicon Hugoniot data (Wood et al., 2018). Here the sonography analogy is strongest diagnostically: an ultrashort X-ray backlighter images the internal position and structure of a moving compression wave in opaque matter.

Minimal-view 3D imaging offers a different extension of the concept. Computed stereo lensless X-ray imaging reconstructs 3D structure from two simultaneously acquired diffraction views in a single ultrafast acquisition, producing a 20 fs snapshot and an estimated 3D spatial resolution of $(002)$8 in the demonstrated soft-X-ray experiment (Duarte et al., 2019). This is not sonography in the operational ultrasound sense, but it is relevant as a route to single-shot ultrafast volumetric X-ray imaging when conventional tomography is too slow or too dose intensive.

5. Electronic-motion and coherence-sensitive extensions

The term “ultrafast X-ray sonography” also appears in the context of electrons, where the problem is not acoustic propagation but nonstationary quantum charge motion. Two 2014 theoretical papers established the central caution that time-resolved ultrafast X-ray scattering from an electronic wave packet is generally not a direct diffraction image of the instantaneous electron density (Dixit et al., 2014). Because an ultrashort probe must be spectrally broad, inelastic channels within the bandwidth are unavoidable, and the observed pattern encodes spatiotemporal density–density correlations rather than a simple Fourier transform of $(002)$9 (Dixit et al., 2014). This has direct consequences for any attempt to make “movies” of electron motion from delay-dependent scattering patterns.

The fully quantum electrodynamical description of non-resonant ultrafast scattering yields a differential scattering probability governed by a two-time density correlation function,

$$\eta(t)\simeq \frac{q_{z,0}^{002}-q_z^{002}(t)}{q_{z,0}^{002}}.$$0

filtered by pulse duration and detector energy acceptance (Dixit et al., 2014). Without energy resolution, the signal reduces to the Fourier transform of the equal-time pair-correlation function; with high energy resolution, it measures a generalized dynamic structure factor (Dixit et al., 2014). Only in special cases, such as a crystal containing identical in-phase electronic wave packets, does coherent Bragg enhancement restore sensitivity to the instantaneous electron density (Dixit et al., 2014).

Resonant variants strengthen the dynamical content. Ultrafast resonant X-ray scattering was proposed as a way to image instantaneous interatomic electron current, so that a single scattering pattern from a nonstationary electron system encodes current in addition to structural information (Popova-Gorelova et al., 2015). In the illustrated $$\eta(t)\simeq \frac{q_{z,0}^{002}-q_z^{002}(t)}{q_{z,0}^{002}}.$$1 example, a $$\eta(t)\simeq \frac{q_{z,0}^{002}-q_z^{002}(t)}{q_{z,0}^{002}}.$$2 probe near the Br $$\eta(t)\simeq \frac{q_{z,0}^{002}-q_z^{002}(t)}{q_{z,0}^{002}}.$$3 edge around $$\eta(t)\simeq \frac{q_{z,0}^{002}-q_z^{002}(t)}{q_{z,0}^{002}}.$$4 was shown theoretically to recover current direction from the imaginary part of the Fourier-transformed scattering pattern, with an estimated spatial resolution of about $$\eta(t)\simeq \frac{q_{z,0}^{002}-q_z^{002}(t)}{q_{z,0}^{002}}.$$5 (Popova-Gorelova et al., 2015). A different nonlinear route, X-ray sum frequency generation, was proposed to image transition charge densities of optically excited valence electrons rather than the total charge density dominated by core electrons; in simulations on donor/acceptor substituted stilbene, a 2 fs off-resonant X-ray pulse combined with a visible pump yielded delay-dependent real-space images of transition charge densities (Rouxel et al., 2018).

Coherence-based structural sensing further broadens the field. Time-resolved X-ray speckle visibility spectroscopy in photoexcited Fe$$\eta(t)\simeq \frac{q_{z,0}^{002}-q_z^{002}(t)}{q_{z,0}^{002}}.$$6O$$\eta(t)\simeq \frac{q_{z,0}^{002}-q_z^{002}(t)}{q_{z,0}^{002}}.$$7 used two coherent 50 fs XFEL pulses at 7.12 keV, separated by controlled delays of 0.2, 1.0, and 5.0 ps, to measure whether electronic trimeron domains had rearranged between the two probes (Hua et al., 2024). The observed speckle-visibility decay yielded a characteristic fluctuation time

$$\eta(t)\simeq \frac{q_{z,0}^{002}-q_z^{002}(t)}{q_{z,0}^{002}}.$$8

interpreted as stretched, liquid-like fluctuations of the surviving charge-ordered domains (Hua et al., 2024). This is not real-space sonography, but it is a buried, fluctuation-sensitive ultrafast structural sensing modality.

Two recent diffraction-imaging developments address multiplexing and nonlinear enhancement. “Dichography” reconstructs two distinct images from a single detector-integrated diffraction pattern produced by two collinear XFEL pulses of different photon energies and controllable delay (Hecht et al., 27 Aug 2025). Applied to xenon-doped helium droplets, it provided evidence that xenon structures survive up to 750 fs after the first interaction at a spatial resolution of about 20 nm (Hecht et al., 27 Aug 2025). Separately, transient resonances in few-femtosecond single-shot diffraction from Xe nanoparticles were shown to increase image brightness by up to about an order of magnitude over the static neutral-atom expectation under favorable short-pulse resonant conditions, especially at 1500 eV (Kuschel et al., 2022). These results suggest that ultrafast X-ray sonography-like probing of non-equilibrium nanomatter can depend not only on geometry and timing but also on electronically enhanced scattering during the probe itself.

6. Limitations, misconceptions, and outlook

A recurring misconception is that shorter X-ray pulses automatically yield direct snapshots of the instantaneous state. The literature shows that this is only conditionally true. In ultrafast electronic scattering, shorter pulses imply broader bandwidth, which admits inelastic pathways and invalidates the naive instantaneous-density picture unless special coherence conditions are met (Dixit et al., 2014). In strain sonography, shorter pulses improve temporal freezing of the probe, but the interpretation still depends on how the strain pulse samples the structure and on whether the phase-specific diffraction signatures are sufficiently distinct (Mattern et al., 22 Jul 2025).

Another important limitation is morphology. The picosecond-ultrasonics review emphasizes that the nanoscale morphology must be known for accurate interpretation because the Poisson effect can qualitatively alter the out-of-plane strain response (Mattern et al., 2023). Continuous films, granular films, and free-standing grains can exhibit different signs and amplitudes of ultrafast out-of-plane strain under otherwise similar excitation conditions. Likewise, in the FeRh sonography work, the inference of $$\eta(t)\simeq \frac{q_{z,0}^{002}-q_z^{002}(t)}{q_{z,0}^{002}}.$$9 FM columnar domains relies on modeling extra FM peak broadening as a consequence of transient in-plane expansion and Poisson-coupled out-of-plane broadening (Mattern et al., 22 Jul 2025).

Most methods also impose material constraints. Dark-field XFEL microscopy requires crystalline samples aligned to a chosen $$d_\text{phase}=\frac{\Delta t_\text{phase} v_s}{2}.$$0, and dynamical-diffraction sonography requires high-quality single crystals in suitable Laue geometry (Dresselhaus-Marais et al., 2022). Betatron shock radiography requires sufficient X-ray energy and flux for the target thickness and introduces complications from broadband attenuation and phase contrast (Wood et al., 2018). Speckle-visibility methods require enough coherent flux and mutual pulse coherence; the reported Fe$$d_\text{phase}=\frac{\Delta t_\text{phase} v_s}{2}.$$1O$$d_\text{phase}=\frac{\Delta t_\text{phase} v_s}{2}.$$2 experiment could not yet construct a full high-resolution $$d_\text{phase}=\frac{\Delta t_\text{phase} v_s}{2}.$$3 map because of count-rate limitations (Hua et al., 2024). Electronic-motion imaging demands attosecond-to-femtosecond probes, phase control, and careful interpretation of what observable is actually measured (Popova-Gorelova et al., 2015).

The outlook across the field is therefore dual. In the narrow sense, ultrafast X-ray sonography is becoming a practical platform for extracting the spatio-temporal heterogeneity of structural phase transitions and for tracking buried strain pulses in crystalline matter (Mattern et al., 22 Jul 2025). In the broader sense, the associated family of methods is expanding toward multimodal XFEL microscopy, 3D minimal-view imaging, coherence-based fluctuation sensing, two-frame diffraction recovery, and ultrafast probing of electronic charge and current (Dresselhaus-Marais et al., 2022). What unifies these developments is not a single contrast mechanism, but a shared experimental ambition: to turn ultrafast X-ray interactions into depth-sensitive or configuration-sensitive measurements of transient internal structure, rather than mere time traces of spatial averages.