Talbot-Lau X-ray Research Articles

Phase imaging of irradiated foils at the OMEGA EP facility using phase-stepping X-ray Talbot–Lau deflectometry

Abstract Diagnosing the evolution of laser-generated high energy density (HED) systems is fundamental to develop a correct understanding of the behavior of matter under extreme conditions. Talbot–Lau interferometry constitutes a promising tool, since it permits simultaneous single-shot X-ray radiography and phase-contrast imaging of dense plasmas. We present the results of an experiment at OMEGA EP that aims to probe the ablation front of a laser-irradiated foil using a Talbot–Lau X-ray interferometer. A polystyrene (CH) foil was irradiated by a laser of 133 J, 1 ns and probed with 8 keV laser-produced backlighter radiation from Cu foils driven by a short-pulse laser (153 J, 11 ps). The ablation front interferograms were processed in combination with a set of reference images obtained ex situ using phase-stepping. We managed to obtain attenuation and phase-shift images of a laser-irradiated foil for electron densities above ${10}^{22}\;{\mathrm{cm}}^{-3}$ . These results showcase the capabilities of Talbot–Lau X-ray diagnostic methods to diagnose HED laser-generated plasmas through high-resolution imaging.

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 8keV 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 80ps) 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 (<6μm) 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 ∼60μm diameter surrounded by low-density material of ∼40μm thickness with an outer diameter ratio of ∼2.3. Attenuation at 8keV 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.

Moiré artifacts reduction in Talbot-Lau X-ray phase contrast imaging using a three-step iterative approach.

Talbot-Lau X-ray phase contrast imaging is a promising technique in biological imaging since it can provide absorption, differential phase contrast, and dark-field images simultaneously. However, high accuracy motorized translation stages and high stability of the imaging system are needed to avoid moiré artifacts in the reconstructed images. In this work, the effects of the stepping errors and the dose fluctuations on the transmission, differential phase contrast, and dark-field images are theoretically derived and systematically summarized. A novel three-step iterative method is designed for image reconstruction in Talbot-Lau interferometry with phase-stepping errors and dose fluctuations. Phase distributions, phase-stepping errors, and dose fluctuation coefficients are iteratively updated via the least square method until the convergence criteria are met. Moiré artifacts are mostly reduced via the proposed method in both the numerical simulations and experiments. The reconstructed images are highly coincident with the ground truth, which verifies the high accuracy of this method. The proposed algorithm is also compared with other moiré artifacts reduction algorithms, which further demonstrates the high precision of this algorithm. This work is beneficial for reducing the strict requirements for the hardware system in the conventional Talbot-Lau interferometry, such as the high accuracy motorized stages and the X-ray tube with high stability, which is significant for advancing the X-ray phase contrast imaging towards the practical medical applications.

Reweighted L1-norm regularized phase retrieval for x-ray differential phase contrast radiograph.

Talbot-Lau x-ray grating interferometry greatly decreases the requirements on x-ray sources to realize differential phase contrast imaging and has found many applications in industrial and medical imaging. Phase retrieval from the noisy differential signal is crucial for quantitative analysis, comparison, and fusion with other imaging modalities. In this paper, we introduce a reweighted L1-norm based nonlinear regularization method for the phase retrieval problem. Both simulation and experimental results demonstrated that, comparing with the widely used L1-norm based regularization method and Wiener filter method, the proposed method is more effective both in eliminating the strip noises and in preserving the image detail.

Wire, hybrid, and laser-cut X-pinches as Talbot–Lau backlighters for electron density diagnostics

Talbot–Lau x-ray deflectometry (TXD) enables refraction-based imaging for high-energy-density physics experiments, and thus, it has been studied and developed with the goal of diagnosing plasmas relevant to inertial confinement and magnetic liner inertial fusion. X-pinches, known for reliably generating fast (∼1 ns), small (∼1 µm) x-ray sources, were driven on the compact current driver generator for ablation structure and implosion studies (∼200 kA, 150 ns) as a potential backlighter source for TXD. Considering that different X-pinch configurations have characteristic advantages and drawbacks as x-ray generating loads, three distinct copper X-pinch configurations were studied: the wire X-pinch, the hybrid X-pinch, and the laser-cut X-pinch. The Cu K-shell emission from each configuration was characterized and analyzed regarding the specific backlighter requirements for an 8 keV TXD system: spatial and temporal resolution, number of sources, time of emission, spectrum, and reproducibility. Recommendations for future experimental improvements and applications are presented. The electron density of static objects was retrieved from Moiré images obtained through TXD. This allowed to calculate the mass density of static samples within 4% of the expected value for laser-cut X-pinches, which were found to be the optimal X-pinch configuration for TXD due to their high reproducibility, small source size (⩽5 µm), short duration (∼1 ns), and up to 106 W peak power near 8 keV photon energy. Plasma loads were imaged through TXD for the first-time using laser-cut X-pinch backlighting. Experimental images were compared with simulations from the x-ray wave-front propagation code, demonstrating that TXD can be a powerful x-ray refraction-based diagnostic for dense Z-pinch loads. Future plans for Talbot–Lau interferometry diagnostics in the pulsed-power environment are described.

Statistical optics modeling of dark-field scattering in X-ray grating interferometers: Part 2. Simulation

A grating-based Talbot-Lau X-ray interferometer provides three imaging modalities, namely attenuation, differential phase contrast, and dark field. Of these, dark-field imaging is uniquely capable of detecting and characterizing micron-scale fine structure in an object via small-angle scattering that reduces fringe visibility. In Part 1 [Opt. Express 29, 40891 (2021)10.1364/OE.447794], we formulate a statistical optics model that predicts the change in visibility, or dark-field signal, as a function of the statistical properties of the scattering object as well as its location within the interferometer. In Part 2, we demonstrate use of this model by simulating an object comprising a random collection of scattering microspheres placed in an X-ray grating interferometer designed to operate at 28 keV. The statistical optics results are validated by numerical Fourier optics simulations.

Statistical optics modeling of dark-field scattering in X-ray grating interferometers: Part 1. Theory

A grating-based Talbot-Lau X-ray interferometer provides three imaging modalities, namely attenuation, differential phase contrast, and dark field. Of these, dark-field imaging is uniquely capable of detecting and characterizing micron-scale fine structure in an object via small-angle scattering that reduces fringe visibility. Several empirical studies have been published showing the utility of this imaging modality for a wide range of applications. There also exists a more limited set of theoretical papers, based primarily on wave-optics formulations. In this two-part paper we present a comprehensive statistical optics model of the dark-field effect. In Part 1, we develop the theoretical underpinnings of the model with an emphasis on a scattering object comprising a random collection of microspheres, and in Part 2 [Opt. Express 29, 40917 (2021)10.1364/OE.447798], we provide a variety of example simulation results.

Sequential Projected Newton method for regularization of nonlinear least squares problems

We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the constraint is given by a least squares data fidelity term and expresses the discrepancy principle. The objective function is a convex regularization function that incorporates some prior knowledge, such as the total variation regularization function. Using the Jacobian matrix of the nonlinear forward model, we consider a sequence of quadratically constrained optimization problems that can all be solved using the Projected Newton method. We show that the solution of such a quadratically constrained sub-problem results in a descent direction for an exact merit function. This merit function can then be used to describe a formal line-search method. We also formulate a slightly more heuristic approach that simplifies the algorithm and allows for an inexact solution of the sequence of sub-problems. We illustrate the behavior of the algorithm using a number of numerical experiments, with Talbot-Lau x-ray phase contrast imaging as the main application. The numerical experiments confirm that the quadratically constrained sub-problems need not be solved with high accuracy in early iterations to make sufficient progress towards the solution. In addition, we show that the proposed method is able to produce reconstructions of similar quality compared to other state-of-the-art approaches with a significant reduction in computational time.

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 10-150J, 8-30ps laser pulses, while two pulsed-power generators (∼350 kA, 350ns and ∼200 kA, 150ns) 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 >1023cm-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.

Modeling the Moiré fringe visibility of Talbot-Lau X-ray grating interferometry for single-frame multi-contrast imaging.

Moiré fringe method in X-ray grating interferometry is characterized by its advantage to obtain multi-contrast data through single-frame imaging. However, how the visibility of the Moiré fringe is influenced by the system parameters, such as the misalignment angle, still lacks investigation, although it closely relates to the signal-to-noise ratio of the image data. In this paper, a simplified model of the Moiré fringe visibility is presented, which reveals that the Moiré fringe visibility can be expressed as the product of a misalignment-angle-related "sinc" function and a relatively independent factor. The following experimental results further suggest that the crosstalk between the detector pixels in the direction perpendicular to the Moiré fringe orientation is another main cause for the visibility reduction of the Moiré fringes.

Implementation of Talbot–Lau x-ray deflectometry in the pulsed power environment using a copper X-pinch backlighter

A Talbot–Lau x-ray deflectometer can map electron density gradients in high energy density plasmas, as well as provide information about plasma elemental composition through single-image x-ray refraction and attenuation measurements. A new adaptation to a pulsed power environment used backlighting from copper X-pinches, allowing for electron density mapping of a low-Z object. Even though the X-pinch backlighter is not properly optimized for emitting x-rays in terms of source size and photon fluence, Moire fringe patterns with contrast up to 14% and fringe shift due to refraction on a beryllium object are obtained. Due to the proximity of the deflectometer with the X-pinch (∼6 cm), it is shown that a protective filter is required to avoid damage in the closest (i.e., source) grating due to both plasma debris and mechanical shock. Regarding grating survival, these did not show any damage due to the intense magnetic field or heating induced by plasma radiation. Electron density on beryllium was measured with a difference lower than 16%. The areal electron density mapping of the sample was limited by source size characteristics, in similarity to transmission radiography. These results show the potential of plasma electron density as well as material mapping through Talbot–Lau x-ray deflectometry in a pulsed power environment.

X-ray interferometry without analyzer for breast CT application: asimulation study.

.Purpose: We investigate an analyzer-less x-ray interferometer with a spatially modulated phase grating (MPG) that can deliver three modalities (attenuation image, phase image, and scatter images) in breast computed tomography (BCT). The system can provide three x-ray modalities while preserving the dose to the object and can achieve attenuation image sensitivity similar to that of a standard absorption-only BCT. The MPG system works with a source, a source-grating, a single phase grating, and a detector. No analyzer is necessary. Thus, there is an approximately 2x improvement in fluence at the detector for our system compared with the same source–detector distance Talbot–Lau x-ray interferometry (TLXI) because the TLXI has an analyzer after the object, which is not required for the MPG.Approach: We investigate the MPG BCT system in simulations and find a clinically feasible system geometry. First, the mechanism of MPG interferometry is conceptually shown via Sommerfeld–Rayleigh diffraction integral simulations. Next, we investigate source coherence requirements, fringe visibility, and phase sensitivity dependence on different system parameters and find clinically feasible system geometry.Results: The phase sensitivity of MPG interferometry is proportional to object–detector distance and inversely proportional to a period of broad fringes at the detector, which is determined by the grating spatial modulation period. In our simulations, the MPG interferometry can achieve about 27% fringe visibility with clinically realistic BCT geometry of a total source–detector distance of 950 mm and source–object distance of 500 mm.Conclusions: We simulated a promising analyzer-less x-ray interferometer, with a spatially sinusoidal MPG. Our system is expected to deliver the attenuation, phase and scatter image in a single acquisition without dose or fluence detriment, compared with conventional BCT.

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.

Assessment of the additional clinical potential of X-ray dark-field imaging for breast cancer in a preclinical setup.

Background:Mammography can identify calcifications up to 50–100 μm in size as a surrogate parameter for breast cancer or ductal carcinoma in situ (DCIS). Microcalcifications measuring <50 µm are also associated with breast cancer or DCIS and are frequently not detected on mammography, although they can be detected with dark-field imaging. This study examined whether additional breast examination using X-ray dark-field imaging can increase the detection rate of calcifications. Advances in knowledge: (1) evaluation of additional modality of breast imaging; (2) specific evaluation of breast calcifications.Implications for patient care: the addition of X-ray dark-field imaging to conventional mammography could detect additional calcifications.Methods:Talbot–Lau X-ray phase–contrast imaging and X-ray dark-field imaging were used to acquire images of breast specimens. The radiation dosage with the technique is comparable with conventional mammography. Three X-ray gratings with periods of 5–10 µm between the X-ray tube and the flat-panel detector provide three different images in a single sequence: the conventional attenuation image, differential phase image, and dark-field image. The images were read by radiologists. Radiological findings were marked and examined pathologically. The results were described in a descriptive manner.Results:A total of 81 breast specimens were investigated with the two methods; 199 significant structures were processed pathologically, consisting of 123 benign and 76 malignant lesions (DCIS or invasive breast cancer). X-ray dark-field imaging identified 15 additional histologically confirmed carcinoma lesions that were visible but not declared suspicious on digital mammography alone. Another four malignant lesions that were not visible on mammography were exclusively detected with X-ray dark-field imaging.Conclusions:Adding X-ray dark-field imaging to digital mammography increases the detection rate for breast cancer and DCIS associated lesions with micrometer-sized calcifications.The use of X-ray dark-field imaging may be able to provide more accurate and detailed radiological classification of suspicious breast lesions.Adding X-ray dark-field imaging to mammography may be able to increase the detection rate and improve preoperative planning in deciding between mastectomy or breast-conserving therapy, particularly in patients with invasive lobular breast cancer.

Talbot-Lau x-ray phase-contrast setup for fast scanning of large samples

Compared to conventional attenuation x-ray radiographic imaging, the x-ray Talbot-Lau technique provides further information about the scattering and the refractive properties of the object in the beam path. Hence, this additional information should improve the diagnostic process concerning medical applications and non-destructive testing. Nevertheless, until now, due to grating fabrication process, Talbot-Lau imaging suffers from small grating sizes (70 mm diameter). This leads to long acquisition times for imaging large objects. Stitching the gratings is one solution. Another one consists of scanning Talbot-Lau setups. In this publication, we present a compact and very fast scanning setup which enables imaging of large samples. With this setup a maximal scanning velocity of 71.7 mm/s is possible. A resolution of 4.1 lines/mm can be achieved. No complex alignment procedures are necessary while the field of view comprises 17.5 × 150 cm2. An improved reconstruction algorithm concerning the scanning approach, which increases robustness with respect to mechanical instabilities, has been developed and is presented. The resolution of the setup in dependence of the scanning velocity is evaluated. The setup imaging qualities are demonstrated using a human knee ex-vivo as an example for a high absorbing human sample.

System Design and Evaluation of a Compact and High Energy X-ray Talbot-Lau Grating Interferometer for Industrial Applications

X-ray grating interferometry has been an active area of research in recent years. In particular, various studies have been carried out for the practical use of the x-ray grating interferometer in medical and industrial fields. For the commercialization of the system, it needs to be optimized for its application. In this study, we have developed a prototype of the compact high energy x-ray grating interferometer of which the high effective energy and compactness is of our primary feature of design. We have designed the Talbot-Lau x-ray interferometer in a symmetrical geometry with an effective energy of 54.3 keV. The system has a source-to-analyzer grating distance of 788.4 mm, which is compact enough for a commercial product. In a normal operation, it took less than ten seconds to acquire a set of phase stepping images. The acquired images had a maximum visibility of about 15%, which is relatively high compared with the visibilities of the other high-energy grating interferometric systems reported so far.

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.

Single-shot Talbot–Lau x-ray dark-field imaging of a porcine lung applying the moiré imaging approach

Talbot–Lau x-ray imaging provides additionally to the conventional attenuation image, two further images: the differential phase-contrast image which is especially sensitive to differences in refractive properties and the dark-field image which is showing the x-ray scattering properties of the object. Thus, in the dark-field image sub-pixeled object information can be observed. As it has been shown in recent studies, this is of special interest for lung imaging. Changes in the alveoli structure, which are in the size of one detector pixel, can be seen in the dark-field images. A fast acquisition process is crucial to avoid motion artifacts due to heartbeat and breathing of the patient. Using moiré imaging the images can be acquired with a single-shot exposure. Nevertheless, the spatial resolution is reduced compared to the phase-stepping acquisition. We evaluate the results of both imaging techniques towards their feasibility in clinical routine. Furthermore, we analyse the influence of artificial linear object movement on the image quality, in order to simulate the heartbeat of a patient.

Enhanced reconstruction algorithm for moiré artifact suppression in Talbot–Lau x-ray imaging

Talbot–Lau x-ray imaging (TLXI) is an innovative and promising imaging technique providing information about the x-ray attenuation, scattering, and refraction features of objects. However, the method is susceptible to vibrations and system component imprecisions, which are inevitable in clinical and industrial practice. Those influences provoke grating displacements and hence errors in the acquired raw data, which cause moiré artifacts in the reconstructed images. We developed an enhanced reconstruction algorithm capable of compensating these errors by adjusting the grating positions and thus suppressing the occurrence of moiré artifacts. The algorithm has been developed with regard to a future application in medical practice. The capability of the algorithm is demonstrated on a medical data set of a human hand (post-mortem) acquired under clinical conditions using a pre-clinical TXLI prototype. It is shown that the algorithm reliably suppresses moiré artifacts, preserves image contrast, does not blur anatomical structures or prevent quantitative imaging, and is executable on low-dose data sets. In addition, the algorithm runs autonomously without the need of interaction or rework of the final results. In conclusion, the proposed reconstruction algorithm facilitates the use of TLXI in clinical practice and allows the exploitation of the method’s full diagnostic potential in future medical applications.