1. Introduction

Characterization and imaging of an inertial confinement fusion (ICF) target is important to control the quality of target manufacturing and for real time of imaging the target evolution during its filling process. ICF targets are manufactured to contain a deuterium-tritium fuel mixture inside mm-scale spherical capsules. Typically the capsule shell is made of beryllium or plastic (CH) with various dopants [1,2]. Several techniques have been used for ICF target dimensional measurements and multilayer architecture characterization such as optical measurements and X-ray radiography [3,4]. X-ray Phase Contrast Imaging (XPCI) has recently attracted interest as it can be operated on opaque and low Z targets with multilayer structure. Several simulation studies and successful experimental ICF target XPCI characterizations have already been achieved using X-ray micro-focus tubes or synchrotron facilities [5–8].

The first XPCI studies were realized in 1995 with a synchrotron X-ray facility and with X-ray tube radiation [9,10]. This technique requires an X-ray source with a very small effective focal spot size, a high-resolution X-ray detector and an appropriate location of the sample and the detector in the beam path. If the detector is placed in the proximity of the sample, a conventional absorption image is obtained. However, if the X-ray source is sufficiently small (i.e. it is spatially coherent) and the detector is placed far beyond the sample, near-field Fresnel diffraction patterns can be obtained. The images formed in these conditions contain information on both the real (X-ray phase-shift) and the imaginary (X-ray absorption) components of the X-ray refractive index in the object. Therefore, in the case where differences in X-ray absorption between materials are too small to create sufficient image contrast in conventional X-ray radiography, the X-ray phase-shift might provide sufficient image contrast for material differentiation. Many groups have carried out phase contrast imaging with different types of X-ray sources and different geometries [11]. The X-ray tube technology is mature, accessible, and low cost. Yet it has several limitations in terms of spatial resolution, brightness, contrast, and spectrum control. For example, metal jet X-ray sources have high enough X-ray flux to realize fast micro-computed tomography ($\mu$-CT) but are limited in the choice of energy and optimal resolution [12,13]. Concerning large-scale facilities, we already mentioned XPCI demonstration with synchrotron facilities. Novel approaches have also been demonstrated with laser-Compton scattering based X-ray sources [14–16]. An X-ray free-electron laser (XFEL) can also be used for XPCI studies with high repetition rate and flux. An end-station dedicated to XPCI using LCLS XFEL has been recently implemented [17]. Water filled capillaries, MHz X-ray microscopy and phase retrieval has also been demonstrated at the European XFEL [18]. In these cases, the sources have high brilliance and coherence but experiments rely on large infrastructures that limit their accessibility and day-to-day use for many users.

Laser-based X-ray sources could offer the potential of performing XPCI with small source size and high throughput. Our group demonstrated the potential of laser-based X-ray sources based on K$\alpha$ radiation [19–21]. Recently, it has been demonstrated that laser-based synchrotron X-ray sources [22] were opening new horizons in X-ray imaging with the demonstration of single shot XPCI with high contrast [23,24]. Using this last process, high intensity lasers can produce femtosecond broadband X-ray pulses extending up to multi-10 keV energy range. This "Betatron" radiation is generated when an intense femtosecond laser pulse is focused onto a gas jet target. This laser pulse produces an under-dense plasma and laser wakefield acceleration (LWFA) of electrons to high energies over mm range distances. These trapped electrons incur Betatron oscillations across the propagation axis and emit X-ray photons in the wiggler regime [25]. The integrated radiation spectrum is similar to that produced by wigglers at synchrotrons, and is characterized by its critical energy $E_c$. These synchrotron X-ray beams are broadband, collimated within ten’s of mrad, and with femtosecond duration. The micrometer range source size provides radiation with high spatial coherence and permits XPCI. The X-ray beam characteristics are described in several publications [26,27]. One advantage of laser-based synchrotron radiation is to allow short acquisition time with the potential to achieve tomographic imaging to reveal 3D-dimensional detailed structure, for example during the filling process of ICF targets. Ultrashort pulse duration enables real-time examination of the ICF laser driver interaction with the target especially during the acceleration phase of the imploding shell where deleterious hydrodynamical instabilities can take place. This explains recent interest in developing such techniques while PW range short pulse laser have been coupled with large ICF facilities worldwide: PETAL at the LMJ facility [28,29] and ARC at NIF facility [30]. Moreover the X-ray beam can be very accurately timed versus the driver laser pulse during the shell travel and its short duration can freeze the time blurring induced by the fast velocity of the target shell during implosion ($\sim 10^7$ cm/s).

Many approaches have been presented for the optimization of image quality and phase information retrieval in various geometries with micro-focus X-ray sources and synchrotron-facility-based X-ray radiation [31–39]. We have also developed a characterization parameter enabling information extraction on interfaces inside inhomogeneous media and allowing to characterize the imaging set-up on known reference objects like nylon filaments [40].

In this work we demonstrate that a laser-based synchrotron X-ray source can be used to image objects in a single laser shot. We first present images and characterization of simple objects: nylon filaments. Then we present images of spherical capsules similar to ICF targets and show that it is feasible to study the capsule structure. In our case, the resulting resolution is limited by the set-up geometry and the detector to $4.3$ $\mu$m in the object plane. We experimentally retrieve the phase information by a relatively simple method relying on the object of interest imaging at two distances. We also introduce an Imaging Characterization Parameter (ICP) to quantify the phase contrast. This adds an interesting tool to characterize the imaging set-up and to help to understand complex object structures. Finally we discuss the applicability of this technique to the study of ICF targets, in particular for pump-probe experiment during the laser-driver interaction.

2. Laser-based synchrotron X-ray beamline at INRS

Using the Advanced Laser Light Source (ALLS) facility at INRS, we developed and operated a laser-based synchrotron X-ray beamline from 2009 to 2014 [23]. We used a high power Ti:sapphire laser system with 80 TW on target, corresponding to 2.5 J in 30 fs at 10 Hz repetition rate. In practice, the repetition rate was limited to 1 Hz by the target system ability to evacuate the gas target from the vacuum vessel. This provided $1.7\times 10^{19}\:\textrm {W cm}^{-2}$ intensity with a 1.5 m off-axis parabola used to focus the laser beam. With a helium gas jet as a target, we generated $2.2 \times 10^8$ photons/0.1% BW/sr/shot at 10 keV. A fit to a synchrotron distribution provided a critical energy $E_c = 12.3$ keV with $2.5$ keV precision. The X-ray beam divergence was $25\times 31$ mrad$^2$. From the synchrotron distribution fit, we obtained a total number of photons over the whole spectrum $N=10^9$. This value was calculated with the experimental measured solid angle. The X-ray spot size diameter D was measured using a knife-edge technique and found to be 1.7 $\mu$m full width half maximum (FWHM). The details of our measurement procedures have already been described in several publications [23,27].

The ALLS high power laser system was upgraded in 2016 and can now deliver as much as 500 TW (9 J, 18 fs, and 2.5 Hz). In practice, the laser-based synchrotron X-ray beam line uses on-target peak power of 160 TW corresponding to 3.2 J, 20 fs, and 2.5 Hz. This corresponds to a laser intensity of $4.6\times 10^{19}\:\textrm {W cm}^{-2}$. We currently use nitrogen as a gas target, which allows us to inject less gas to produce the X-ray radiation and permits us to work at the 2.5 Hz nominal laser repetition rate. Typically, we obtained $2.7 \times 10^9$ photons/0.1% BW/sr/shot at 10 keV. A fit to a synchrotron distribution provides a critical energy $E_c=15.1\:\textrm {keV}$ with $\pm 5\:\textrm {keV}$ precision. The X-ray beam divergence is $58\times 54$ mrad$^2$. The total number of photons over the whole spectrum is $N= 3.3 \times 10^{10}$. More details can be found in Fourmaux et al. [41]. Such improvements in our beamline parameters are not only the result of the increase of the on-target energy and intensity, but are also related to the reduction of the laser beam imperfections. This is shown using 3D PIC calculations that explain our results with 80 TW on target [42]. Control of the phase and intensity distribution along the laser beam propagation axis inside the target has been introduced in the upgraded laser-based synchrotron X-ray beamline. It has been realized with the help of a deformable mirror in order to fully optimize the LWFA parameters and maximize generation of X-ray radiation.

Imaging has been performed in transmission geometry with a divergent beam as can be seen on Fig. 1. The object to be imaged is positioned between the X-ray source and the detection system. $R1$ and $R2$ are respectively the source-to-object and the object-to-detector distances. The magnification $M$ is thus given by $M=(R1+R2)/R1$.

 

Fig. 1. Imaging geometry showing the X-ray source, object and detector positions. The field-of-view at the object position is several cm wide.

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In the near-field Fresnel regime, which is the most appropriate for the present experiments, the phase shift produced by object edges gives rise to a set of fringes. In addition, the intensity changes due to the absorption by the object. For the imaging experiments discussed here, $R1 = 75$ cm and $R2$ has been changed from 98 cm ($M = 2.3$) to 280 cm ($M = 4.7$). With X-rays in the 10 keV range, the imaging geometry provides access to spatial frequencies up to 80 lp/mm and the imaged object has to be larger than 20 $\mu$m to be in the near-Fresnel imaging regime where $R2 < d^2/\lambda$, with $d$ is the size of the structure to be imaged and $\lambda$ the X-ray wavelength.

The detector is an X-ray CCD camera with $1340\times 1300$ imaging pixels of size 20 $\mu$m $\times 20$ $\mu$m, which is used in direct detection mode. This is a deep depletion model PI-LCX:1300 cooled with liquid nitrogen and named LN here. A vacuum transfer tube placed between the object and the camera allows propagation of X-rays without air absorption along the X-ray propagation path. In the present geometry (with magnification less than 10) the projected source size in the detection plane remains always smaller than the pixel size. Thus, the resolution of this detection system, in the detection plane, is expected to be equal to the pixel size (20 $\mu$m). The resolution in the object plane depends on the projected pixel size in this plane and changes with the magnification. The LN camera was calibrated with Cu K$\alpha$ line at 8 keV to establish the count number to photons conversion factor. The background reference noise level of the camera (no incident X-ray signal on the detector) is monitored at the beginning and at the end of each series of images.

3. Calibration with nylon filaments

To avoid uncertainties in alignment and object interpretation, we used a series of nylon filaments placed in air, because they give rise to sharp edges, with diameter ranging from 10 $\mu$m to 330 $\mu$m for the beamline calibration. Nylon’s real part refractive index $\delta$ is very similar to that of biological tissues. This is an ideal object since in a real complex media the various phase objects can be distributed in an anisotropic and inhomogeneous way. Images of the nylon fibers have been obtained in one laser shot. The calibration object image is presented on Fig. 2(a). The corresponding filaments line profiles with diameter 100, 20 and 10 $\mu$m, and 330 $\mu$m are shown on Figs. 2(b) and 2(c), respectively. The edge enhancement is clearly visible for all filaments. The filaments with diameter larger than 20 $\mu$m are imaged in a near-Fresnel regime. The 10 $\mu$m filament is imaged in a Fresnel/Fraunhofer regime.

 

Fig. 2. a) image of the calibration nylon filaments obtained in one shot ($M=4.7$). From left to right filament diameters are 330, 230, 200, 140, 120, 100, 20, and 10 $\mu$m. On the bottom right corner, the white line scale bar is 200 $\mu$m long. b) image line profiles of the 100, 20, and 10 $\mu$m nylon filaments. c) image line profile of the 330 $\mu$m filament.

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The phase information can be retrieved by imaging the object of interest at two distances from the X-ray source as has been shown in an earlier work with a medical phantom and a K$\alpha$ X-ray source [43]. To validate this method, we retrieved the phase information of the object by using two images recorded at two different $R2$ distances (98 and 280 cm). At this point, the image taken with the highest magnification was resized to the lowest magnification and then subtracted. Figure 3(a) shows the phase information line profile for 100, 20, and 10 $\mu$m fibers obtained by subtraction of the two images recorded at different $R2$ distances. We then compared the object reconstruction obtained from ANKA phase retrieval program with the expected projected thickness of the ideal object [44]. ANKA uses a single-distance phase retrieval algorithm described in Paganin et al. [45]. The input parameters used with ANKA are $\delta /\beta =100$, $\delta = 2\times 10^{-5}$. For the calculation we used a 10 keV X-ray energy, which corresponds to the peak energy of the experimental set-up by taking in account the produced synchrotron distribution, the detector efficiency, and the filters positioned along the X-ray propagation path (Be and Al). Figure 3(b) shows for the 330 $\mu$m fiber both the phase information line profile, obtained by subtraction of two images recorded at different $R2$ distances, and the result of the phase retrieval procedure with ANKA. The calculated ideal profile for the object is compared with the object reconstruction obtained using the phase retrieval algorithm. A good agreement is observed between the two curves. Note that the 10 $\mu$m fiber edges are not resolved in this subtraction process because the final resolution in the object plane is given by the lowest magnification, which is 8.7 $\mu$m in the present case.

 

Fig. 3. a) phase information line profile of several filaments obtained by subtraction of two images recorded at different R2 distances. From left to right, the filaments diameter are 100, 20, and 10 $\mu$m. Each filament position is indicated by a thin black vertical line. b) phase information line profile of the 330 $\mu$m filament obtained by subtraction of two images recorded at different $R2$ distances (grey solid line) and object reconstruction from phase retrieval algorithm (light red line). The red line is the calculated ideal profile for the object.

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The contrast, or intensity difference, between maximum and minimum intensities at the edge of an object is usually used to quantify the strength of the phase transition. Intensities around the edge are calculated with some model and compared to data. Simple rules have been derived for the parameters of projection images of a generic phase edge [46]. We are using an Imaging Characterization Parameter (ICP), proposed by our group [47]. The ICP is a signal ($S^\phi _\Gamma$) to noise ($N_\Gamma$) ratio, where $S^\phi _\Gamma$ is the phase contrast signal corresponding to a region $\Gamma$ around the boundary of the feature of interest, and $N_\Gamma$ is the noise corresponding to this same region $\Gamma$. It can be expressed as:

In this formula, $L_T$ is the FWHM of the first Fresnel fringe (in $\mu$m), $I_{max}$ is the maximum intensity of the edge fringe, and $I_0$ is the incident background intensity. $I_0$ is expressed in counts per pixel. We can retrieve the number of photons per pixel by assuming an energy of 10 keV and knowing that the energy to count conversion factor is 9.65 eV/count. This parameter looks promising for mapping and characterizing interfaces inside complex inhomogeneous media. A numerical model of X-ray propagation [19,20] integrating the properties and geometries of the imaging beamline is used to calculate the image in the detector plane and the ICP in our geometry. It shows that the ICP is sensitive to the object shape and the object density gradient, which is expected, as phase contrast imaging in our configuration is sensitive to the object density laplacian. The ICP value is dependent on the experimental parameters: the X-ray source size, the spatial resolution in the detector plane, and the X-ray spectrum measured by the detector.

In a first step, we calculate the ICP with our numerical model for nylon filaments, which are simple objects with known shape, density, and refractive index. We then compare the numerical ICP values with the measured ones in order to validate the X-ray beam line experimental parameters. The results are shown in Fig. 4 for filaments with diameter 140 and 230 $\mu$m (red and black circles markers respectively). The data corresponding to open circle markers were obtained before the laser upgrade with up to 80 TW power whereas the solid circle markers were obtained with up to 160 TW power. The error bars for the measured data are mainly due to the uncertainty in the determination of $L_T$. The continuous lines were calculated with an X-ray source size of 1.7 $\mu$m, a critical energy of 15.1 keV, and 20 $\mu$m spatial resolution in the detector plane. The dotted lines were calculated with the same parameters except the spatial resolution which was 30 $\mu$m.

 

Fig. 4. Measured ICP in the detection plane ($M=4.7$) as a function of $I_o$ the number of photon per pixel. This is shown for cylindrical nylon filaments with diameter 140 and 230 $\mu$m (respectively red and black circles markers). The open circle markers data were obtained before the laser upgrade with up to 80 TW power, whereas the solid circle markers were obtained with up to 160 TW power. The continuous curves were obtained with the numerical model for a 20 $\mu$m spatial resolution with a 1.7 $\mu$m X-ray source size and 15.1 keV critical energy. The dotted curves were obtained with the numerical model for a 30 $\mu$m spatial resolution.

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The ICP is a signal-to-noise ratio, it is expected to be $\propto I_o^{0.5}$ as shown by the calculation. Some deviations from this scaling law could have been seen if too much noise was produced during the laser matter interaction: secondary radiation due to the energetic electrons for example. The measured data for both wires agree well with the calculated ICP. Thus, the experimental parameters used for the calculation are compatible with the observed images. The spatial resolution is indeed limited by the 20 $\mu$m pixel size.

4. Images of spherical capsules

We used the imaging geometry described in the previous paragraphs to image two spherical capsules provided by CEA-DAM (France). Their dimensional parameters are given in Table 1. They are composed of four layers of plastic (CH) which are numbered 1 to 4, from inside to outside. Layer 2 and 3 also contain Ge dopant with respectively 0.44 % at. (atomic percentage), and 0.29 % at. for each of them. These capsules are a few years old and thus the sizes might be slightly different from the initial fabrication values given in Table 1.

Table 1. Characteristics of the spherical capsules imaged with the INRS laser based synchrotron beamline. All the dimensions are in $\mu$m.

View Table

Figures 5 and 6 present the image of capsule 1 recorded with magnification $M=2.3$ and capsule 2 recorded with $M=4.7$, respectively. Each image was obtained with one laser shot. The phase contrast effects are clearly visible in the images of capsules and the supports located on each capsule side. Two layers with different grey level can be easily seen for each capsule directly on their respective images. It corresponds to the two layers (2 and 4) with the largest thickness. In this case, this is mostly due to absorption contrast and the presence of Ge dopant in layer 2.

 

Fig. 5. Image of the capsule 1 recorded with $M=2.3$ ($8.7 \mu$m/pixel in the object plane). The background, obtained in same conditions without the object, has been subtracted. The capsule diameter is 2049.3 $\mu$m.

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Fig. 6. Image of the capsule 2 recorded with $M=4.7$ ($4.26 \mu$m/pixel in the object plane). The capsule diameter is 2031.8 $\mu$m.

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Figure 7 presents, for capsule 1, the normalized line profiles corresponding to the measured signal (black line) and pure phase signal deduced from subtraction of the same capsule images recorded at two different magnifications (grey line) for $R2 =98$ and 280 cm. To guide the eye, the various layers have been identified and represented on Fig. 7. As observed with the nylon fibers, the 10 $\mu$m structures are observed in a Fresnel/Fraunhofer regime and thus the observation of edges through the phase retrieval method for such thin layers is difficult due to the 7.5 $\mu$m resolution in the subtraction process. Part of the phase signal might be due to the two thin layers (1 and 3) but it is difficult to confirm it with the current spatial resolution. Due to the age of the capsule the Ge dopant might have diffused to the neighbouring layers and the interface between each layer might not be sharp.

 

Fig. 7. Line profiles across the edge of the capsule 1. Black: recorded image with phase and absorption information. Gray: pure phase information retrieved with a $7.27 \mu$m resolution.

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In Fig. 8 we plot, for capsule 2, the normalized line profile corresponding to the measured signal (thick black line) and the pure phase signal deduced from subtraction of the capsule images recorded at two different magnifications (grey line). We show the object line profile (light red curve) reconstructed from the recorded image using the ANKA phase retrieval algorithm. The input parameters used with ANKA are $\delta /\beta =100$, $\delta = 2\times 10^{-5}$, and an energy of 10 keV. The calculated expected object profile across one edge assuming only one layer with a 180 $\mu$m thickness for the object (red line) is compared with the object reconstruction obtained from the phase retrieval algorithm. To guide the eye, the two thickest layers are represented on Fig. 8. The expected simplified object is in good agreement with the reconstructed object line profile.

 

Fig. 8. Lineout across the edge of the capsule 2. Light red: reconstructed object using the phase retrieval algorithm. Red: expected object profile assuming only one layer with a 180 $\mu$m thickness. Black: recorded image with phase and absorption information. Grey: pure phase information retrieved from image subtraction with a resulting $7.27 \mu$m resolution.

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To access the fine structure of the object a higher resolution is needed which is accessible by optimizing the imaging geometry and the detection system. The resolution in the object plane is currently limited by the CCD pixel size. It is easy to improve it to 13.5 $\mu$m using available commercial scientific grade CCD in direct detection. In this case, due to the limited space available in the laboratory, $M=4.7$ would give access to 2.9 $\mu$m resolution in the object plane. Another possibility is to improve the spatial resolution and get close to 1 $\mu$m by using a high-resolution phosphor screen coupled to an imaging system but this would decrease the detection efficiency [8]. In this last case the projected source size in the detection plane can be higher than the pixel size. A good compromise would be $M=2$ magnification with an indirect detection high-resolution system giving access to 1.7 $\mu$m resolution in the object plane. Another improvement would be to work in the Fresnel regime for objects with dimension around 10 $\mu$m. This can be achieved by increasing the X-ray photon energy. It can be done either by using higher laser power (currently we limited it to 160 TW) or by using another gas target like helium, because we already demonstrated that the critical energy can be enhanced by using helium rather than nitrogen [41].

Presently, we could determine the spherical capsule ICP introduced in the previous section at the different layers interfaces of the capsule internal structure and compare them with the corresponding ones extracted from the experimental images. There is little interest to do so with the current resolution as the outer edge that corresponds to air/CH interface is already well known. Of greater interest would be to measure it at CH/CHGe or CHGe/CHGe interfaces to study the density variation due to the Ge diffusion but it would require improved spatial resolution to be able to extract more meaningful information.

5. Discussion and conclusions

These results demonstrate that laser based synchrotron X-ray sources allow, by working in the near-field Fresnel regime, direct measurement of interface edge enhancement associated with sub-10 $\mu$m spatial resolution. The X-ray source repetition rate practical limit is the laser repetition rate. To realize a tomographic scan, assuming 2.5 Hz and 360 images reconstruction, it requires 144 s. This fast acquisition time validates that this technique could be used for real time imaging during the ICF capsule filling process that can last around 100 min [8]. The ultrashort X-ray pulse duration also allows pump-probe experiments during the driver laser interaction. As a first step the direct near field Fresnel image can be compared to the expected one by using hydrodynamic simulation of the ICF target evolution. This technique has been used for example in phase contrast study of laser induced shocks by Antonelli et al. using a laser based backlighter [48]. X-ray backlighters resulting from laser solid interaction and producing both characteristic line emission and Bremsstrahlung are an active research field to record radiographs of ICF implosions at stagnation [49]. Due to the production of very hot electrons during the interaction the X-ray source size can be a lot larger than the focal spot. Backlighters usually use target design and imaging geometry, like wire target and grazing incidence imaging, to reduce the projected source size. A bigger X-ray source size reduces the spatial resolution, it can even prevent access to phase contrast measurement as the phase signal is primarily related to the X-ray source size. Backlighters X-ray pulse duration is related to the laser pulse duration used to produce them. It is required to last $\sim$ 10 ps to be able to observe ICF in-flight implosions. In comparison laser based synchrotron X-ray source can reach a pulse duration of a few 10’s of fs. Such an ultimate time resolution is of interest to be able to observe plasma instabilities in the 1 ps time scale or to improve the signal to noise ratio by using gating techniques.

We also show that the phase can be determined with measurement data obtained with laser based synchrotron X-ray source by using two consecutive measurement planes and confirmed it by also using ANKA algorithm with one measurement plane. ANKA algorithm assumes just one single material. Currently all the phase retrieval algorithms require homogeneous objects with at maximum two compounds. Assuming a homogenous target it has been possible to use a phase retrieval algorithm with laser induced shocks on polystyrene targets [50]. However, in the case of ICF driver laser matter interaction, the target's multilayer architecture might be too complex to directly retrieve the phase using only one measurement plane. In this case the two planes measurement can be achieved simultaneously as has been proposed by Wu et al. by using two detectors at the same time, the first detector (a phosphor screen for example) acting as a filter for the second one [51]. With a similar configuration the phase could be retrieved by using a dual energy reconstruction as each detector see a different range of energy due to the beam hardening when going throughout the first detector [52]. More recent work by Zhang et al. has validated the dual detection configuration for XPCI [53].

The results obtained in this study demonstrate the potential of the laser-based synchrotron X-ray source XPCI for determination of internal structure of spherical capsules with complex structures and compositions similar to ICF targets. It is important for quality control of target manufacturing and for real-time imaging the target evolution during its filling process. We also established the potential for real-time ultrafast imaging of the ICF laser driver interaction with the target. This technique allows to extract the phase information with a simple technique based on imaging an object at difference source-to-object locations and to reconstruct the object using a phase reconstruction algorithm. The obtained images could be improved using a detection system with higher spatial resolution, which could be implemented with the current experimental system.