Talbot-Lau x-ray interferometry for high energy density plasma diagnostic

Invited article: X-ray phase contrast imaging in inertial confinement fusion and high energy density research

X-ray phase contrast imaging (XPCI) provides enhanced image contrast beyond absorption-based x-ray imaging alone due to refraction and diffraction from gradients in the object material density. It is sensitive to small variations in density, such as internal voids, cracks, grains, defects, and material flow, as well as to stronger density variations such as from a shock wave. Beyond its initial use in biology and materials science, XPCI is now routinely used in inertial confinement fusion (ICF) and high energy density (HED) research, first to characterize ICF capsules and targets, and later applied in dynamic experiments, where coherent x-ray sources, ultrafast x-ray pulses, and high temporal and spatial resolution are required. In this Review article, XPCI image formation theory is presented, its diverse use in ICF and HED research is discussed, the unique requirements for ultrafast XPCI imaging are given, as well as current challenges and issues in its use.

Current advances on Talbot-Lau x-ray imaging diagnostics for high energy density experiments (invited)

Talbot-Lau x-ray interferometry is a refraction-based diagnostic that can map electron density gradients through phase-contrast methods. The Talbot-Lau x-ray deflectometry (TXD) diagnostics have been deployed in several high energy density experiments. To improve diagnostic performance, a monochromatic TXD was implemented on the Multi-Tera Watt (MTW) laser using 8 keV multilayer mirrors (Δθ/θ = 4.5%-5.6%). Copper foil and wire targets were irradiated at 10¹⁴-10¹⁵ W/cm². Laser pulse length (∼10 to 80 ps) and backlighter target configurations were explored in the context of Moiré fringe contrast and spatial resolution. Foil and wire targets delivered increased contrast <30%. The best spatial resolution (<6 μm) was measured for foils irradiated 80° from the surface. Further TXD diagnostic capability enhancement was achieved through the development of advanced data postprocessing tools. The Talbot Interferometry Analysis (TIA) code enabled x-ray refraction measurements from the MTW monochromatic TXD. Additionally, phase, attenuation, and dark-field maps of an ablating x-pinch load were retrieved through TXD. The images show a dense wire core of ∼60 μm diameter surrounded by low-density material of ∼40 μm thickness with an outer diameter ratio of ∼2.3. Attenuation at 8 keV was measured at ∼20% for the dense core and ∼10% for the low-density material. Instrumental and experimental limitations for monochromatic TXD diagnostics are presented. Enhanced postprocessing capabilities enabled by TIA are demonstrated in the context of high-intensity laser and pulsed power experimental data analysis. Significant advances in TXD diagnostic capabilities are presented. These results inform future diagnostic technique upgrades that will improve the accuracy of plasma characterization through TXD.

Noise Reduction for Single-Shot Grating-Based Phase-Contrast Imaging at an X-ray Backlighter

X-ray backlighters allow the capture of sharp images of fast dynamic processes due to extremely short exposure times. Moiré imaging enables simultaneously measuring the absorption and differential phase-contrast (DPC) of these processes. Acquiring images with one single shot limits the X-ray photon flux, which can result in noisy images. Increasing the photon statistics by repeating the experiment to gain the same image is not possible if the investigated processes are dynamic and chaotic. Furthermore, to reconstruct the DPC and transmission image, an additional measurement captured in absence of the object is required. For these reference measurements, shot-to-shot fluctuations in X-ray spectra and a source position complicate the averaging of several reference images for noise reduction. Here, two approaches of processing multiple reference images in combination with one single object image are evaluated regarding the image quality. We found that with only five reference images, the contrast-to-noise ratio can be improved by approximately 13% in the DPC image. This promises improvements for short-exposure single-shot acquisitions of rapid processes, such as laser-produced plasma shock-waves in high-energy density experiments at backlighter X-ray sources such as the PHELIX high-power laser facility.

Talbot-Lau x-ray deflectometer: Refraction-based HEDP imaging diagnostic

Talbot-Lau x-ray interferometry has been implemented to map electron density gradients in High Energy Density Physics (HEDP) experiments. X-ray backlighter targets have been evaluated for Talbot-Lau X-ray Deflectometry (TXD). Cu foils, wires, and sphere targets have been irradiated by 10-150 J, 8-30 ps laser pulses, while two pulsed-power generators (∼350 kA, 350 ns and ∼200 kA, 150 ns) have driven Cu wire, hybrid, and laser-cut x-pinches. A plasma ablation front generated by the Omega EP laser was imaged for the first time through TXD for densities >10²³ cm^-3. Backlighter optimization in combination with x-ray CCD, image plates, and x-ray film has been assessed in terms of spatial resolution and interferometer contrast for accurate plasma characterization through TXD in pulsed-power and high-intensity laser environments. The results obtained thus far demonstrate the potential of TXD as a powerful diagnostic for HEDP.

Proof-of-concept Talbot-Lau x-ray interferometry with a high-intensity, high-repetition-rate, laser-driven K-alpha source

Talbot-Lau x-ray interferometry is a grating-based phase-contrast technique, which enables measurement of refractive index changes in matter with micrometric spatial resolution. The technique has been established using a variety of hard x-ray sources, including synchrotron, free-electron lasers, and x-ray tubes, and could be used in the optical range for low-density plasmas. The tremendous development of table-top high-power lasers makes the use of high-intensity, laser-driven K-alpha sources appealing for Talbot-Lau interferometer applications in both high-energy-density plasma experiments and biological imaging. To this end, we present the first, to the best of our knowledge, feasibility study of Talbot-Lau phase-contrast imaging using a high-repetition-rate laser of moderate energy (100 mJ at a repetition rate of 10 Hz) to irradiate a copper backlighter foil. The results from up to 900 laser pulses were integrated to form interferometric images. A constant fringe contrast of 20% is demonstrated over 100 accumulations, while the signal-to-noise ratio continued to increase with the number of shots. Phase retrieval is demonstrated without prior ex-situ phase stepping. Instead, correlation matrices are used to compensate for the displacement between reference acquisition and the probing of a PMMA target rod. The steps for improved measurements with more energetic laser systems are discussed. The final results are in good agreement with the theoretically predicted outcomes, demonstrating the applicability of this diagnostic to a range of laser facilities for use across several disciplines.

Implementation of a Talbot-Lau x-ray deflectometer diagnostic platform for the OMEGA EP laser

A Talbot-Lau X-ray Deflectometer (TXD) was implemented in the OMEGA EP laser facility to characterize the evolution of an irradiated foil ablation front by mapping electron densities >10²² cm^-3 by means of Moiré deflectometry. The experiment used a short-pulse laser (30-100 J, 10 ps) and a foil copper target as an x-ray backlighter source. In the first experimental tests performed to benchmark the diagnostic platform, grating survival was demonstrated and x-ray backlighter laser parameters that deliver Moiré images were described. The necessary modifications to accurately probe the ablation front through TXD using the EP-TXD diagnostic platform are discussed.

X-ray backlighter requirements for refraction-based electron density diagnostics through Talbot-Lau deflectometry

Talbot-Lau x-ray interferometers can map electron density gradients in High Energy Density (HED) samples. In the deflectometer configuration, it can provide refraction, attenuation, elemental composition, and scatter information from a single image. X-ray backlighters in Talbot-Lau deflectometry must meet specific requirements regarding source size and x-ray spectra, amongst others, to accurately diagnose a wide range of HED experiments. 8 keV sources produced in the high-power laser and pulsed power environment were evaluated as x-ray backlighters for Talbot-Lau x-ray deflectometry. In high-power laser experiments, K-shell emission was produced by irradiating copper targets (500 × 500 × 12.5 μm³ foils, 20 μm diameter wire, and >10 μm diameter spheres) with 30 J, 8-30 ps laser pulses and a 25 μm copper wire with a 60 J, 10 ps laser pulse. In the pulsed power environment, single (2 × 40 μm) and double (4 × 25 μm) copper x-pinches were driven at ∼1 kA/ns. Moiré fringe formation was demonstrated for all x-ray sources explored, and detector performance was evaluated for x-ray films, x-ray CCDs, and imaging plates in context of spatial resolution, x-ray emission, and fringe contrast.

Talbot-Lau x-ray deflectometry phase-retrieval methods for electron density diagnostics in high-energy density experiments

Talbot-Lau x-ray interferometry uses incoherent x-ray sources to measure refraction index changes in matter. These measurements can provide accurate electron density mapping through phase retrieval. An adaptation of the interferometer has been developed in order to meet the specific requirements of high-energy density experiments. This adaptation is known as a moiré deflectometer, which allows for single-shot capabilities in the form of interferometric fringe patterns. The moiré x-ray deflectometry technique requires a set of object and reference images in order to provide electron density maps, which can be costly in the high-energy density environment. In particular, synthetic reference phase images obtained ex situ through a phase-scan procedure, can provide a feasible solution. To test this procedure, an object phase map was retrieved from a single-shot moiré image obtained from a plasma-produced x-ray source. A reference phase map was then obtained from phase-stepping measurements using a continuous x-ray tube source in a small laboratory setting. The two phase maps were used to retrieve an electron density map. A comparison of the moiré and phase-stepping phase-retrieval methods was performed to evaluate single-exposure plasma electron density mapping for high-energy density and other transient plasma experiments. It was found that a combination of phase-retrieval methods can deliver accurate refraction angle mapping. Once x-ray backlighter quality is optimized, the ex situ method is expected to deliver electron density mapping with improved resolution. The steps necessary for improved diagnostic performance are discussed.

Talbot-Lau x-ray deflectometer electron density diagnostic for laser and pulsed power high energy density plasma experiments (invited)

Talbot-Lau X-ray deflectometry (TXD) has been developed as an electron density diagnostic for High Energy Density (HED) plasmas. The technique can deliver x-ray refraction, attenuation, elemental composition, and scatter information from a single Moiré image. An 8 keV Talbot-Lau interferometer was deployed using laser and x-pinch backlighters. Grating survival and electron density mapping were demonstrated for 25-29 J, 8-30 ps laser pulses using copper foil targets. Moiré pattern formation and grating survival were also observed using a copper x-pinch driven at 400 kA, ∼1 kA/ns. These results demonstrate the potential of TXD as an electron density diagnostic for HED plasmas.

X-ray Moiré deflectometry using synthetic reference images

Moiré fringe deflectometry with grating interferometers is a technique that enables refraction-based x-ray imaging using a single exposure of an object. To obtain the refraction image, the method requires a reference fringe pattern (without the object). Our study shows that, in order to avoid artifacts, the reference pattern must be exactly matched in phase with the object fringe pattern. In experiments, however, it is difficult to produce a perfectly matched reference pattern due to unavoidable interferometer drifts. We present a simple method to obtain matched reference patterns using a phase-scan procedure to generate synthetic Moiré images. The method will enable deflectometric diagnostics of transient phenomena such as laser-produced plasmas and could improve the sensitivity and accuracy of medical phase-contrast imaging.

Single-shot Z(eff) dense plasma diagnostic through simultaneous refraction and attenuation measurements with a Talbot-Lau x-ray moiré deflectometer

The Talbot-Lau x-ray moiré deflectometer is a powerful plasma diagnostic capable of delivering simultaneous refraction and attenuation information through the accurate detection of x-ray phase shift and intensity. The diagnostic can provide the index of refraction n=1-δ+iβ of an object (dense plasma, for example) placed in the x-ray beam by independently measuring both δ and β, which are directly related to the electron density n(e) and the attenuation coefficient μ, respectively. Since δ and β depend on the effective atomic number Z(eff), a map can be obtained from the ratio between phase and absorption images acquired in a single shot. The Talbot-Lau x-ray moiré deflectometer and its corresponding data acquisition and processing are briefly described to illustrate how the above is achieved; Z(eff) values of test objects within the 4-12 range were obtained experimentally through simultaneous refraction and attenuation measurements. We show that Z(eff) mapping of objects does not require previous knowledge of sample length or shape. The determination of Z(eff) from refraction and attenuation measurements with moiré deflectometry could be of high interest to various domains of high energy density research, such as shocked materials and inertial confinement fusion experiments, as well as material science and nondestructive testing.

Moiré deflectometry using the Talbot-Lau interferometer as refraction diagnostic for high energy density plasmas at energies below 10 keV

The highly localized density gradients expected in High Energy Density (HED) plasma experiments can be characterized by x-ray phase-contrast imaging in addition to conventional attenuation radiography. Moiré deflectometry using the Talbot-Lau grating interferometer setup is an attractive HED diagnostic due to its high sensitivity to refraction induced phase shifts. We report on the adaptation of such a system for operation in the sub-10 keV range by using a combination of free standing and ultrathin Talbot gratings. This new x-ray energy explored matches well the current x-ray backlighters used for HED experiments, while also enhancing phase effects at lower electron densities. We studied the performance of the high magnification, low energy Talbot-Lau interferometer, for single image phase retrieval using Moiré fringe deflectometry. Our laboratory and simulation studies indicate that such a device is able to retrieve object electron densities from phase shift measurements. Using laboratory x-ray sources from 7 to 15 μm size we obtained accurate simultaneous measurements of refraction and attenuation for both sharp and mild electron density gradients.

Refraction-enhanced backlit imaging of axially symmetric inertial confinement fusion plasmas

X-ray backlit radiographs of dense plasma shells can be significantly altered by refraction of x rays that would otherwise travel straight-ray paths, and this effect can be a powerful tool for diagnosing the spatial structure of the plasma being radiographed. We explore the conditions under which refraction effects may be observed, and we use analytical and numerical approaches to quantify these effects for one-dimensional radial opacity and density profiles characteristic of inertial-confinement fusion (ICF) implosions. We also show how analytical and numerical approaches allow approximate radial plasma opacity and density profiles to be inferred from point-projection refraction-enhanced radiography data. This imaging technique can provide unique data on electron density profiles in ICF plasmas that cannot be obtained using other techniques, and the uniform illumination provided by point-like x-ray backlighters eliminates a significant source of uncertainty in inferences of plasma opacity profiles from area-backlit pinhole imaging data when the backlight spatial profile cannot be independently characterized. The technique is particularly suited to in-flight radiography of imploding low-opacity shells surrounding hydrogen ice, because refraction is sensitive to the electron density of the hydrogen plasma even when it is invisible to absorption radiography. It may also provide an alternative approach to timing shockwaves created by the implosion drive, that are currently invisible to absorption radiography.

Glancing angle Talbot-Lau grating interferometers for phase contrast imaging at high x-ray energy

A Talbot-Lau interferometer is demonstrated using micro-periodic gratings inclined at a glancing angle along the light propagation direction. Due to the increase in the effective thickness of the absorption gratings, the device enables differential phase contrast imaging at high x-ray energy, with improved fringe visibility (contrast). For instance, at 28° glancing angle, we obtain up to ∼35% overall interferometer contrast with a spectrum having ∼43 keV mean energy, suitable for medical applications. In addition, glancing angle interferometers could provide high contrast at energies above 100 keV, enabling industrial and security applications of phase contrast imaging.