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The Laser Interferometer Space Antenna (LISA), requires high precision displacement measurement between widely spaced pairs of freely floating test masses. We describe a proposed design for the optical telescopes that form an essential part of the laser heterodyne interferometry measurement system and discuss how the design and implementation will address the unique challenges of this specialized application.
Heterodyne interferometer laser gauges are used in space-based astronomical interferometers to very accurately measure and compensate for variations in starlight pathlength.
Shock compression plate impact experiments conventionally rely on point-wise velocimetry measurements based on laser-based interferometric techniques. This study presents an experimental methodology to measure the free surface full-field particle velocity in shock compression experiments using high-speed imaging and three-dimensional (3D) digital image correlation (DIC). The experimental setup has a temporal resolution of 100 ns with a spatial resolution varying from 90 to 200 μm/pixel. Experiments were conducted under three different plate impact configurations to measure spatially resolved free surface velocity and validate the experimental technique. First, a normal impact experiment was conducted on polycarbonate to measure the macroscopic full-field normal free surface velocity. Second, an isentropic compression experiment on Y-cut quartz–tungsten carbide assembly is performed to measure the particle velocity for experiments involving ramp compression waves. To explore the capability of the technique in multiaxial loading conditions, a pressure shear plate impact experiment was conducted to measure both the normal and transverse free surface velocities under combined normal and shear loading. The velocities measured in the experiments using digital image correlation are validated against previous data obtained from laser interferometry. Numerical simulations were also performed using established material models to compare and validate the experimental velocity profiles for these different impact configurations. The novel ability of the employed experimental setup to measure full-field free surface velocities with high spatial resolutions in shock compression experiments is demonstrated for the first time in this work.
The study of shock-driven ejecta production has focused on Richtmyer–Meshkov instability (RMI) growth from geometric features of the material surface. Extensive study of this mechanism under both single- and multiple-shock conditions has found that the ejected mass tends to be closely associated with the shocked surface phase, and its temperature is not dramatically greater than the hydrodynamic shock temperature of the bulk. In this work, we propose and demonstrate a new ejecta production mechanism that can occur under multiple-shock conditions based on the collapse of bubbles near the free surface of the material. This mechanism produces ejected mass that is much greater in quantity than observed in the RMI case. The particles are much hotter than predicted by the shock Hugoniot state, and the ejected mass does not appear to be strongly dependent upon initial surface finish. The ejecta source extends into the material with no clear remaining free surface. We name this mechanism Shallow Bubble Collapse (SBC) and discuss the conditions under which it activates. We demonstrate resolved modeling methods that enable the calculation, design, and study of SBC as a mechanism and perform a series of experiments to compare with the models. Under some multiple-shock conditions, SBC ejection produces ten times more ejected mass than RMI growth.
The fracture response of geologic materials is of interest for applications, including geothermal energy harnessing and containment of underground explosions. To better understand the explosively induced fracture response of geomaterials, polymethyl methacrylate (PMMA) was used as a transparent rock surrogate to allow imaging of internal shock propagation and fracture growth processes. Experiments were conducted using high-speed shadowgraphy and photon Doppler velocimetry (PDV), which were compared to numerical simulations. Experiments measured fractures produced in 304.8mm × 304.8mm × 304.8mm PMMA cubes with two simultaneously initiated detonators. The cubes were subjected to varying amounts and directions of externally applied uniaxial stresses, including no stress, 2 MPa stress, and 20 MPa stress. The fracture radius as a function of time was extracted from the high-speed videos. Post-test images of the PMMA cubes aided in the determination of three-dimensional effects not directly imaged by the cameras. The surface velocity history and the shock response captured in PDV and the high-speed videos were compared to the simulated explosive-induced shock response. The simulation results indicate that the shock drives the fracture for the first 20 μs corresponding to a fracture radius of approximately 15 mm in the experiments. The gas-driven fracture extent was estimated analytically using an equilibrium stress distribution calculated after the shock wave propagation through the sample. Reduction in the gas pressure due to the leakage of the explosive products through the crack as a function of time was accounted for. In conclusion, the estimated fracture lengths were in agreement with the experimentally observed fracture lengths.
Here, in this work, expanding cylinder experiments are performed using a gas gun on the aluminum 6061 alloy to understand the dynamic deformation and failure behavior of this material in the presence of surface defects in the form of scratches. The experiments are then modeled with the modified Tepla (for tensile plasticity) model, which is equipped with the damage yield function of Gurson [“Continuum theory of ductile rupture by void nucleation and growth: Part I—Yield criteria and flow rules for porous ductile media,” (1977)] and Tvergaard and Needleman [Acta Metall. 32(1), 157–169 (1984)], over-stress viscosity [F. Addessio and J. Johnson, J. Appl. Phys. 74(3), 1640–1648 (1993)], and the underlying viscoplastic model of Preston et al. [J. Appl. Phys. 93(1), 211–220 (2003)] (Preston–Tonks–Wallace model) for the dense material. The Tepla model parameters were calibrated using the Bayesian approach against experimentally measured free-surface velocity data obtained from plate impact experiments on the aluminum 6061 alloy. The evolution of radial expansion and shapes of the deformed cylinder from the simulations on a pristine cylinder wall and a cylinder wall with a longitudinal surface defect shows excellent agreement with the corresponding experimental results. Finally, the role of surface defect size and cylinder wall geometry on the dynamic strength of the cylinder wall was also investigated through a series of simulations.
Additive manufacturing has the potential to repair damaged parts, but the performance of additive materials under high strain rate loading is still uncertain—especially with the added complexity of an interface with an existing wrought material. In this work, 304L stainless steel samples were intentionally damaged and then repaired with wire-fed laser additive manufacturing. The samples were subjected to shock loading to generate incipient spall. Velocimetry and post-mortem metallography results show that when the additive repair process parameters are optimized to reduce porosity and match the equation of state of the original material, the influence of the repair region on the shock propagation is negligible. In conclusion, the free-surface velocity profile and internal damage morphology of the repaired sample are shown to be practically identical to the pristine material.
Gas gun shock experiments on cyclotrimethylenetrinitramine (RDX)-based explosive compositions that employ embedded gauge particle velocity tracers have noted a significant amount of electrical noise when compared to other explosive formulations. This paper reexamines previously published embedded gauge data on Cyclotols (60–80 wt. % RDX) to quantify the electromagnetic behavior of these materials. The primary observation is a fourfold increase in the electrical noise when Cyclotols are shocked above 4.22 ± 0.08 GPa. Electromagnetic gauge noise is also observed within particle velocity traces in reactive growth and off-Hugoniot shocks, although at higher pressures than the direct shock case, suggesting a temperature- or kinetically dependent transition. In all cases, the electrical noise disappears upon detonation. By comparing with the static high-pressure phase diagram of RDX, we interpret this change in electromagnetic behavior to be a change in the RDX crystal structure to a piezoelectric phase, although it is uncertain whether the γ or ε phase is responsible for the observed behavior.
Sound speed measurements in shock compressed solids have long been valuable for the development of equations of state at extreme conditions, shock-induced phase transformations, and a comprehensive characterization of the thermophysical response of high-pressure standards. We present results from plate impact experiments to 190 GPa to determine the longitudinal sound speed in copper—an important high-pressure standard. Surprisingly, the sound speeds determined using the two most common experimental techniques—the front surface impact (FSI) approach and the release wave overtake (RWO) approach—diverge significantly for stresses greater than ~100 GPa. Further analyses, including numerical simulations, show that the FSI experiments provide the correct sound speeds and that fundamental assumptions underlying the RWO method are likely violated due to the complex release response of shock compressed copper. The sound speeds determined using the FSI approach provide for a more accurate high-pressure description of copper in dynamic compression experiments. The present findings are in contrast to the results for shock compressed silver [Wallace et al., Phys. Rev. B 104, 214106 (2021)], where both methods provided consistent sound speed results. Thus, the findings presented here demonstrate the need to experimentally verify the validity of the RWO method on a case-by-case basis. Finally, we note that even at the high stresses in the present work, the copper unloading response shows a time-dependent, quasielastic response often observed in metals at lower stresses.
Additive manufacturing has the potential to repair high value components, saving significant time and resources; however, the level of reliability and performance of additive repairs is still relatively unknown. In this work, the structure–property and performance of laser wire additive manufacturing repairs in 1100 aluminum are investigated. Two types of intentional damage are inflicted on the samples and subsequently repaired with pulsed laser deposition additive manufacturing. Quasi-static (10 –3 s –1 ) and high strain-rate (10 –3 s –1 ) mechanical testing is carried out with in situ diagnostics and post-mortem imaging. The results show that while the quasi-static strength and ductility of samples with a repaired region are lower than a pristine sample, the dynamic strength under shock loading is comparable. This work highlights both the potential utility of additive manufacturing for repair purposes, the significant risk of compromised performance of additive parts under specific conditions, and the need to test at varying strain rates to fully characterize material performance.
Materials with high-density gradients are desired for controlling loading paths in dynamic compression, important for studying material properties in extreme conditions and inertial confinement fusion. The large density difference between Al and W makes them ideal choices for producing gradient density materials, but their extremely different melting temperatures make them challenging to fabricate simultaneously. We report a method for producing Al–W porosity-free materials with a fourfold increase in density (2.7–11 g/cm 3 ) across the composition range, from Al-rich to W-rich, without intermetallic phase formation. This was achieved by understanding the aluminum-dominated densification behavior and examining the influence of pressure and temperature on the densification of Al–W composites. Dynamic compression experiments conducted with the Al–W gradient density material produced shock ramp compressions as expected based on the designed composition, and the performed hydrodynamics simulations showed excellent agreement with experimental results. The results demonstrate that current activated pressure-assisted densification allows for the easy and rapid fabrication of gradient density materials with significant density gradients and tailored compositions, facilitating precise control of the loading paths. These materials have the potential to create customized pressure drives for advancing the fields of material science in extreme environments and dynamic compression.
We present an extension of the [Takeda et al., J. Opt. Soc. Am. 72, 156 (1982)] phase extraction method to heterodyne photonic Doppler velocimetry applications. The method yields results equivalent to those obtained by the short-time Fourier transform (STFT), while offering potential improvements in time resolution. Unlike STFT, which relies on window functions, such as the Hamming window, that emphasize central data points and diminish the influence of edges, the extended Takeda method utilizes all data uniformly. This uniform treatment allows for the derivation of empirical equations that directly relate velocity error to the actual time resolution rather than to the local analysis duration. The established equation provides a useful metric for both optimizing hardware configuration and guiding data analysis. Simulation and experimental results confirm that, for a given dataset, specifying a target time resolution yields consistent velocity errors for both methods. These findings underscore the Takeda method’s advantages, particularly its potential higher time resolution and reduced computational burden, making it a valuable tool for high-throughput applications such as laser dynamic compression experiments.
Synchrotron x-ray phase-contrast imaging (XPCI) offers time-resolved visualization of dynamic compression phenomena, but its intrinsically small field-of-view (FOV) limits the time that key features remain in frame. A novel approach to enlarge the FOV is achieved by positioning a two-dimensional parabolic compound refractive lens (CRL) upstream of the sample to deliberately defocus the white beam. Ray-tracing simulations and XPCI measurements show that this CRL configuration can expand the beam by ∼50% vertically and ∼15% horizontally based on the full width at half-maximum of the beam. Implementing the CRL, however, attenuates the photon flux and lowers signal-to-noise ratio (SNR). Task-based analysis using a calibration grid (30 μm dots) showed that both setups fail to consistently meet the Rose criterion (SNR ≥ 5) for features of this size in single-bunch imaging. Extrapolating the measured SNR Rose values suggests that the minimum consistently detectable feature lies closer to 30–40 μm for the standard XPCI setup and above 40 μm for CRL-XPCI. Despite this limitation, the CRL configuration nearly doubles the illuminated area, enabling simultaneous tracking of front and rear observations of boron carbide targets subjected to rod and sphere impacts at 1.0–2.6 km/s. Image tracking algorithms and photonic Doppler velocimetry were used to measure penetration and rear-surface velocity histories. Together, these measurements capture crack fronts, penetration, and material breakout, offering new benchmark data for validating high-strain-rate constitutive models of ceramic materials.
In this work, we report on the experimental characterization of the second-order susceptibility in MoSe 2 /WS 2 heterobilayers, including their hidden complex phases. To this end, we developed a heterodyne-detection scheme for second-harmonic generation and applied it to macroscale heterobilayer samples prepared using the gold-tape exfoliation method. The heterodyne scheme enabled us to distinguish the relative orientation of the crystal domains, and furthermore, it allowed us to characterize the complex phases of the susceptibility relative to a reference quartz sample. By comparing the results from the monolayer regions and the heterobilayer region over several hundred microns of the sample area, we determined that the contribution of interlayer effects to second-harmonic generation is within the experimental uncertainty arising from the sample inhomogeneity. The results here provide fundamental quantitative information necessary for the precise design of nanophotonic systems based on stacking engineering.
This study examines the impact of macroscopic surface defects on the dynamic ductile damage behavior of polycrystalline metals using plate-impact experiments. Defects of various shapes (flat, round, and point) were manufactured on the free or impact surfaces of annealed copper specimens. The experiments were diagnosed with photon Doppler velocimetry measurements and soft recovery techniques. The experimental results revealed that defect shape and location significantly affect velocity–time profiles and void distribution. In order to understand the dynamics of shock propagation and corresponding ductile damage evolution within the target specimens, the impact experiments were modeled with a calibrated Tepla model, a dynamic ductile damage model for polycrystalline metals [Nguyen et al., Int. J. Solids Struct. 329, 113833 (2026)]. Overall, our resulting simulated velocity showed good agreement with measured velocity, and our simulated porosity distributions qualitatively matched experimental data. Based on our simulation results, defects on the free surface were found to distort rarefaction waves and therefore the corresponding spall planes. On the other hand, defects on the impact surface generated a delayed shock when the flyer plate and the defected target area were in contact, leading to distortion of the spall plane. The distortion of the spall plane resulted in a non-uniform distribution of voids within the defected specimens. Lastly, we examined the role of local work hardening due to the defect manufacturing process on the velocity and porosity distribution, using Tepla simulations with a simplified representation of local hardening. This investigation highlights the importance of defect geometry, location, and local hardening associated with defect generation in dynamic ductile damage processes.
This paper discusses the progress in the development of optical interferometers for use in distance measurement gauges with systematic errors below 100 picometers.
Digitally enhanced heterodyne interferometry (DI) is a laser metrology technique employing pseudo-random noise (PRN) codes phase-modulated onto an optical carrier. Combined with heterodyne interferometry, the PRN code is used to select individual signals, returning the inherent interferometric sensitivity determined by the optical wavelength. The signal isolation arises from the autocorrelation properties of the PRN code, enabling both rejection of spurious signals (e.g., from scattered light) and multiplexing capability using a single metrology system. The minimum separation of optical components is determined by the wavelength of the PRN code.
The proposed New Millenium Interferometry consists of three spacecraft separated by up to several kilometers. A heterodyne laser metrology system is proposed to measure the relative distances between the spacecraft.