X-ray imaging methods for high-energy density physics applications

X-ray imaging is one of the several classes of diagnostics for high-energy density physics and plasma experiments.^1–8 X rays find particular use in radiography of these experiments because they are able to transmit through highly ionized materials, including plasmas, and allow probing of the internal structure of optically opaque materials. In contrast, visible light is strongly absorbed by ionized materials when the critical density is exceeded. Additionally, in systems such as inertial confinement fusion (IFC) targets, the self-emission tends to be in the x-ray regime. Imaging of the self-emission x rays can provide information about the plasma shape, volume, and temperature. A number of different diagnostic instruments make use of the x-ray self-emission to determine the shape or volume of important experimental parameters. For example, the x-ray emission profile from a hohlraum enables the determination of the uniformity of the x-ray drive for indirect-drive ICF targets. The self-emission from a compressed ICF capsule is used to determine the drive symmetry and to better tune the drive profile for improved performance.^9–12 Related experiments use self-emission from tracer dopants to measure hydrodynamic growth,¹³ understanding a mix of ablator material into the hotspot.¹⁴ 

X rays undergo very little refraction, making them excellent for probing internal structures of materials, particularly during the dynamic phase in High Energy Density (HED) experiments. However, it is possible to create optical elements that operate in the x-ray regime by use of specially designed mirror surfaces, lenses, or diffractive structures. Although this Review will touch on refraction and diffraction in the context of imaging optics, phase-contrast imaging methods used for characterization, in particular, will be described in a separate review article.¹⁵ 

The density and chemical composition give rise to the linear attenuation coefficient in a material at a particular x-ray energy. Attenuation contrast in the samples forms the basis for most radiographic imaging methods where thickness or density changes are typically assumed to account for spatially varying image intensity.

While absorption dominates in many experiments, the real part of the index of refraction, while usually small, can result in refraction or diffraction at interfaces. This enables the production of x-ray optics as will be described in more detail later in the article. Many principles from visible light optics can be carried over to x-ray imaging including the lens equation, optical system aberrations, depth of field, numerical aperture, and point spread function. Many of the tools used to design x-ray optics have analog to visible light, and many commercial packages will work in the geometric optic limits by using the appropriate material index of refraction. That said, there are a number of special computer programs that are common in the field. Some examples are Shadow,²¹ a more recent graphical version called OASYS,²² the multilayer modeling package IMD,²³ and XRT.²⁴ 

The basic components of x-ray imaging are the x-ray source, imaging optic, and detector. An optimization that includes all three of these components is needed to successfully meet HEDP experimental goals. Common considerations include the composition of the experimental package, which helps to determine the range of x-ray energies used, spatial and temporal resolution required, signal-to-noise and image contrast, physical footprint, alignment, and shielding requirements needed to prevent secondary radiation emission from degrading the primary signal. For example, design considerations, particularly field of view and collection efficiency, were considered for the National Ignition Facility (NIF) in a paper by Koch et al.,²⁵ in particular, to evaluate methods to obtain images at higher x-ray energies than achieved in earlier facilities. The effects of the x ray, neutron, and debris environment of the Laser Megajoule (LMJ) on diagnostics were also described²⁶ and place constraints on both optic and detector locations.

There are multiple different x-ray imaging systems that have been used over the years in HEDP, including point projection, pinholes, and x-ray microscopes, to name a few. Figure 1 shows some of the most common x-ray imaging arrangements used in HEDP facilities. Improvements in laser and pulsed-power delivery systems have allowed several new or upgraded HEDP facilities to produce brighter and higher energy x-ray sources.^27–34 

Broadly, we can classify x-ray imaging as either self-emission, where the object under investigation emits x rays, or backlit imaging, where a separate source of x rays is used to illuminate an object. The x-ray source spectrum should be selected to provide sufficient contrast based on the experimental object composition, typically accomplished by selecting different foil materials, while also including the relative emission for the materials in the determination. The foils are used to generate an area source, typically 0.1–1 mm in lateral extent.^35–37 The foils tend to output characteristic lines and a broader continuum. Laser light strikes the foil and the foil explodes. The conversion efficiency from laser light to x rays is the subject of many investigations.^38–46 Making larger backlighters is challenging because a high conversion efficiency from laser to x rays requires a high intensity on the sample. Efforts to improve these designs have had some success.⁴⁷ The foil can also be viewed edge on to provide a line source rather than an area. This improves the spatial resolution in one dimension, as is typically used in hydro-growth radiography experiments.

This Review will review the various x-ray imaging sources and optics in use at ICF and HEDP facilities, each with their own particular advantages over the others. Of the geometries shown in Fig. 1, the most common imaging arrangement for HEDP facilities is pinhole arrays because they offer multiple advantages over other imaging modalities, including cost, ease of alignment, redundancy, nearly achromatic response, compatibility with gated detector geometries, resolution down to ∼10 μm, and can produce data without the need of detailed calibration or post-processing. Many of the x-ray optics described later in this Review improve upon collection efficiency, resolution, and bandwidth selectivity; however, these come with the cost of increased alignment complexity and fewer images per experiment. A summary of the trade-off in collection efficiency, field of view, and resolution for multiple x-ray imagers can be found in Ref. 25. However, pinhole imaging remains the primary choice in many experimental HEDP campaigns.

The description of the imaging geometries is organized into three sections, with specific implements described in corresponding subsections. Section II covers aperture-based imaging, where the image is generated without the use of focusing optics. Section III covers the use of reflective optics, including mirrors and crystals, to form images. Next, transmissive optics are covered in Sec. IV, followed by a summary.

It is impractical to place the object very close to the detector in most HEDP experiments due to the damage the experiment would cause to the detector. Instead, many radiography experiments use a small x-ray source to minimize the impact of penumbral blur on imaging, as shown in Fig. 1(b). Furthermore, the detector can be located a large distance away to maximize the geometric magnification of the object onto the detector, thereby improving the resolution since typical detectors have large pixel sizes or large point spread functions.⁴⁸ These imaging systems are optimized when the penumbral blur is comparable to the effective pixel size. Typically, wires are used as x-ray sources for these point-projection geometries.^49–52 Target build accuracy, which determines the line of sight to the detector, can limit the relative distances between the target and backlighter, and hence, the photon density passing through the object. The wire size and material can further limit the resolution since the wires will tend to expand due to the laser heating, and may result in a time-dependent resolution. Good reviews of point-projection imaging can be found in Refs 35 and 53.

Another approach is to replace the small wire with a pinhole between the area backlighter source and the object to be imaged, as shown in Fig. 1(c). The area backlighter is easier to illuminate with lasers and does not cool as fast as expanding wires, while the pinhole defines the backlighter size.^54,55 Higher conversion efficiency from laser light to x rays enables better signal-to-noise than the wires. However, in these geometries the pinhole should be as close to the backlighter as possible to maximize the source emission. This requirement makes the pinhole susceptible to closure of the pinhole due to x-ray heating of the substrate and expansion into the pinhole.^56,57

Compton radiography is a specific application of point-projection imaging. Time-resolved x-ray radiography of the dense cold fuel and remaining ablator surrounding the hotspot represents an alternate and powerful way to characterize the asymmetries and non-uniformities. Radiographs can be obtained using Compton scattering rather than traditional photo-absorption to cast a shadow of the imploding capsule.^58,59

Indeed, the optical depth of the fuel of an ICF target is dominated by the Compton cross section for photon energies above ∼40 keV and is largely independent of photon energy, up to ∼200 keV. As a result, the opacity is largely insensitive to temperature and density, in contrast to radiographs obtained in the photo-absorption-dominated regime,⁵⁹ so that the areal density of the fuel can be directly and accurately measured using a broadband (e.g., Bremsstrahlung)-emitting source.

The implosion efficiency in Inertial Confinement Fusion (ICF) experiments depends on the symmetry and uniformity of the final compressed state of the hotspot and the surrounding fusing fuel and can be severely degraded by asymmetries in the drive and target, and by hydrodynamic instabilities seeded by capsule imperfections.

Information about the shape of the core near or at final assembly can be obtained by imaging of the x-ray⁶⁰ or primary neutron emission,⁶¹ but the analysis is complicated by the combined effects of the emission gradients and reabsorption in the stagnating fuel surrounding the hotspot. Down-scattered neutron imaging⁶¹ can be used to retrieve the fuel areal density; however, the measurement can be affected by energy-dependent kinematics and by the deconvolution of the primary neutron source (the hotspot) with size comparable to the fuel. Primary and down-scattered neutron imaging are also limited to burn-weighted measurements around the peak emission, and do not provide information about the temporal evolution of the implosion.

Radiography performed in the hard x-ray energy spectral range minimizes refractive blurring due to expected steep density gradients (>10²⁵ electrons/cm³/μm) and allows removal of the self-emission from the stagnating capsule, which is largely limited to below ∼20 keV, by filtering. Thus, radiographic images near peak compression can be recorded, with the energies of the x-ray photons producing the radiograph selected by a combination of a high-pass filter and the response function of a gated hard x-ray detector used to optimize signal-to-background. Finally, since Compton scattering is sensitive to electron density and not to the atomic number, as in the case of the photoelectric effect, Compton-based radiography is ideal for probing the low-Z deuterium–tritium fuel in ICF implosions.

The experimental setup for recording Compton radiographs at the NIF⁶² is shown in Fig. 3(a). The x rays, generated by illuminating the inside of a gold hohlraum⁶³ with 188 NIF laser beams, drive the implosion by the pressure produced from the soft x-ray ablation of a spherical, thin, low-Z capsule, i.e., the ablator, encasing the fuel. To minimize the backgrounds from DT neutrons interacting with the detector, the cryogenic layer and gas fill used a surrogate tritium–hydrogen mix in a ratio of 3:1, with a nominal deuterium fraction of 0.2%, maintaining hydro-equivalence to usual 50/50 DT layers. The $>$ 50 keV point-projection backlighters⁶⁴ are generated by illuminating two Au wires with four 900J/30 ps 1 ω (1.05 μmm) pulses from the ARC laser at the NIF facility,⁶⁵ two on each wire. To intercept more of the 100 μm-level focal spot size ARC beams and still maintain a point source, the Au micro-wires are longer than the laser spot size, tipped 3°–6° to the line of sight to avoid x-ray reabsorption. In addition, the wires are surrounded by V- or U-shaped plastic structures that reduce signal sensitivity to ARC beam transverse misalignment and enhance the laser-wire energy coupling by refraction at the plasma mirror surface generated by the ARC pre-pulse.⁵⁹ 

The backlighter sources are positioned at about 8 mm from the target and angularly spaced to separate by parallax the two radiographs on the passive detector, an MS image plate (IP),⁶⁶ placed at 600 mm from the hohlraum for a magnification of 75×. The IP is filtered with 500 μm Cu and 500 μm Al to remove core self-emission and softer backlighter x rays (⁠$<$40 keV). The backlighter temporal and spatial resolutions are measured using an x-ray streak camera and by radiographs of static tungsten spheres, respectively, and closely match the laser pulse duration and wire diameter.

Figure 3(b) shows two radiographs recorded 10 ps before and 160 ps after bang time, using 25 μm diameter Au backlighters.⁵⁹ In subsequent experiments, we were able to record radiographs at a higher resolution, using 10 μm diameter Au wires, and the signal-to-noise ratio per resolution element is between better than 150.

Having two radiographs on the same shot, independently timed with respect to the peak compression time of the implosion, provides previously unattainable insight into the dynamics of the fuel trajectory and, in particular, its kinetic energy. Since Compton radiography can produce high-resolution images of the fuel near bang time, it provides unique experimental data that complement nuclear measurements. Of particular interest is the measurement of residual kinetic energy and the study of the correlations between Compton radiographs and images produced by the neutron imaging systems (NISs), including the comparison of the areal density asymmetries derived from the radiographs with the measurements of the down-scattered neutron fraction derived from NIS.

Moving beyond projection imaging requires the use of imaging optics. There are a number of different optics to describe, the first being a simple pinhole imager, based on the same principle as pinhole cameras or camera obscura used with visible light. Figure 1(d) illustrates the principle of pinhole imaging, with the pinhole located between the object and detector. The ideal pinhole is small compared to the resolution in the geometric optics limit, so that the pinhole maps each location on the detector to a unique location on the object to create an image. The magnification for a pinhole imager is given by M = q/p. Pinhole imaging is the most commonly used x-ray imaging diagnostics because pinholes are easy to fabricate and align and also easy to replace as needed if damaged. Additionally, pinhole arrays^35,67,68 are usually fabricated to allow multiple images on a single detector. Figure 1(e) shows the geometry of a pinhole array, with each pinhole in the array generating one image. The array needs to be sized to prevent the overlap of the individual images on the detector, consistent with the magnification. A pinhole imager can be used with both self-emission and backlit imaging geometries.

One limit of pinhole imaging is that the resolution and throughput are coupled. As an example, 20 μm diameter pinholes located 100 mm from the object have a solid angle of 3 × 10⁻⁸ sr. Improving the resolution by a factor of 2 requires a reduction in the throughput by a factor of 4. This will lead into a reduction in the signal-to-noise ratio, and possibly limit the minimum exposure time when used with a time-gated detector. Another drawback of pinholes is that the substrate is ideally thin so that misalignment does not result in a loss of effective area. However, thin substrates will transmit higher-energy x rays, which results in a loss of resolution and increased background. Methods to overcome this problem include using conical-shaped apertures in the substrate, or stacking arrays with multiple pinhole sizes to block the higher energies without increasing the obscurations.

There are many examples of pinhole imaging implemented at HEDP facilities, and only a small subset can be described here. Several pinhole imagers are currently in use at the Sandia National Laboratories Z Facility. These include the Time-Integrated Pinhole Camera (TIPC)⁷¹ and the Time-Resolved In-Chamber X-ray Imager (TRICXI).⁷² The TRICXI allows a range of magnifications and pinhole sizes to adjust the field of view and resolution as needed to image dynamics of magnetized liner inertial fusion targets, as well as other experiments. The TIPC and TRICXI pinholes are close to the experiment to obtain a large solid angle, ∼1 × 10⁻⁷ sr and 1 × 10⁻⁸ sr, respectively. A large solid angle is particularly important for time-gated detectors in order to obtain sufficient signal-to-noise levels in short time intervals. A large solid angle results in a spatial resolution of 900 μm for the TIPC and 45 μm for TRICXCI, which are sufficient for their respective experimental goals. Experiments at the Omega Laser Facility include pinhole arrays onto multi-channel plate (MCP) detectors,^53,67 and a pinhole imager onto a single-line-of-sight detector, the SLOS-TRXI.⁶⁸ A pinhole array was used with a 1D streak camera and post-processing of the data to provide 0.01 ns time resolution with 2D images⁷³ of an imploding core and fast-ignition targets. The NIF has developed a dilation x-ray imager, which, when coupled with the pinhole array, allows a time resolution of 0.01–0.03 ns.^74,75 Pinhole imagers are also used to determine the closure of the laser entrance holes.^76–78 

The signal-to-noise for a pinhole imager can be improved by designing the experiment to have symmetry along one direction, allowing a rectangular slit to be used instead of the pinhole. The slit acts as a 1D imager and the signal is averaged along the slit direction to increase the signal. These are particularly useful when coupled with a streak camera, which has temporal resolution in one dimension on the detector and spatial resolution on the other.^35,79

Pinhole imaging is convenient since it provides a direct image of the object and is easy to interpret. However, pinhole imaging is limited in resolution and throughput as just described. One method that improves upon pinhole imaging while retaining much of the fabrication and alignment benefits is penumbral imaging. Figure 1(f) shows the geometry of the penumbral imager. A relatively large aperture, or opaque mask, is used instead of a small pinhole and placed at a distance p from the object. The shadow cast by the aperture onto the detector a distance q from the aperture is not a direct image of the object. Rather, the modulation of intensity that is detected at the edge of the aperture encodes information regarding the spatial distribution of the source. The source emission profile can be reconstructed from the shadow by means of an algorithm.^80–82 The benefit of using a penumbral imager is that the signal level is not as strongly coupled to the aperture size as for the pinhole imager. The downside is that the penumbral aperture needs to be larger than the source, the detector needs to have a large dynamic range to extract the source distribution, and the penumbral edges must be sufficiently opaque to prevent x rays from partially transiting the aperture edge.

Penumbral imaging is used extensively in neutron imaging systems.^84–87 There has been an increasing use of penumbral imaging in the x-ray regime over the last few years,^{10,80,82,83,88,89} as well as the application of proton penumbral imaging^90,91 and knock-on neutron penumbral imaging.⁹² The high signal throughput, and thus, high achievable signal-to-noise ratio and spatial resolution that can be achieved with these imagers have enabled challenging measurements of plasma parameters, such as morphology,^83,92,93 electron temperature,^82,89,94,95 fuel–ablator mix measurements in inertial confinement fusion,⁹⁶ and heat conduction driven by a localized mix of different plasma species.⁹⁵ Penumbral imagers are one class of aperture imaging methods known more broadly as coded aperture imaging.^97–100 These imagers make use of the fact that the x rays generally travel in straight paths from the source, which allows mapping of the spatial information on the detector back to the source shape distribution. Coded apertures include regular or random patterns, and a myriad of reconstruction techniques have been developed over the years.^{81,83–85,101–106} Typically, the patterns are sparse, but redundancy in the array allows better reconstructions than a single aperture by reducing the noise by averaging over the redundant apertures. Critical factors that determine the spatial resolution and signal-to-noise ratio that can be achieved with this technique are the Fresnel diffraction on the aperture edge, the aperture edge quality and how transmissive the edge is for x rays, and the detector resolution and magnification of the imager.⁸³ 

There are a range of x-ray microscopes that have been developed over the years.²⁵ These optical systems include reflective, refractive, and diffractive elements. Rather than pinhole or aperture imaging, which selectively blocks x rays to create images, the microscope optical systems actively re-direct the x rays to create an image, as shown in Fig. 1(g). There have been multiple systems employed in HEDP over the years, several of which will be reviewed here. Many x-ray optics have found widespread use in other fields, such as focus optics at coherent light sources such as synchrotrons or free-electron lasers, and have been adapted to HEDP facilities.

X rays can be reflected from surfaces if they are incident on the surface at less than the critical angle. The x-ray index of refraction is less than 1 in most materials, which results in a range of angles for which total external reflections will occur. The terminology in the literature is that mirrors operating below the critical angle are grazing incidence mirrors. The small index of refraction for even dense materials such as gold and platinum limits these mirrors to very low energies, typically less than ∼3 keV. Figure 5 shows a plot of the reflectivity for several metal surfaces as a function of energy and angle. A benefit of these mirrors is that they do not reflect higher energy and can act to filter out higher x-ray energies, which can be difficult to do with absorption filtering.

The short wavelength for x rays results in stringent requirements for fabrication of the mirror surfaces. Typically, the surfaces need to be polished to have rms surface roughness less than 1 nm, down to 0.3 nm being typical for energies $>$10 keV. Figure errors, which encompass spatial frequencies comparable to the mirror lengths, must also be tightly controlled, with errors on the order of a micrometer over a few mm being typical. As a point of comparison, recent optics have a radius of curvature of 10–1000 m, which means that the mirror surface deviation from a flat surface, or sag, is on the order of a 0.5–20 μm over a length of 10–100 mm.^112,113

One key benefit of mirror-based microscopes is that they are free of chromatic aberrations. This allows them to form good images from polychromatic sources, within the bandwidth limits of their reflectivity. An additional benefit is that some designs will reflect the image off the line-of-sight to the detector, which allows additional shielding to be placed before the detector. However, the complexity in fabrication, most notably, the small grazing angles, results in several constraints that limit the practical application of these optical systems in HEDP applications. One limitation is that the energy range is fixed for a given instrument and cannot be readily adjusted from one experiment to the next, limiting the utility in a facility. The more commonly used x-ray optics will be discussed with their respective trade-offs.

A number of facilities make use of a pinhole imager with a multilayer mirror to select a defined energy bandwidth for each of the images. Similar to the pinhole array imaging described earlier, the key advantage of the multilayer mirror imagers (MMI) is that many images can be acquired per experiment, in this case, with x-ray energy selectivity. Figure 6 shows a sketch of the MMI. Individual pinhole images are reflected from the multilayer mirror onto a detector.

One early implementation at the Omega Laser Facility used a multilayer mirror that operated between 3 and 5 keV, with each image having a bandwidth of ∼0.08 keV.¹¹⁴ Similar instruments include the multilayer mirror (MLM)¹¹⁵ imager at the Sandia Z facility, which operated at 0.28 keV with a 0.01 keV bandwidth, and a system that also operated at 0.53 keV at the Sandia Z-Machine and Saturn.¹¹⁶ A multilayer mirror imager (MMI) was designed by Los Alamos and fielded on the NIF to cover a range of 8–13 keV.¹¹⁷ These instruments can project multiple pinhole images to a time-gated detector allowing simultaneous space, time, and energy-resolved imaging. An important use of these and similar imagers is to probe the time and electron temperature in plasmas^118,119 by fitting the measured output vs energy to a black body spectrum, and to find tracer elements within the larger continuum.¹²⁰ 

The principle drawbacks to MMI instruments are throughput and resolution. The throughput and resolution are coupled, just as with pinhole arrays, and the multilayer coating further limits the throughput. The narrow energy bandwidth of the multilayer restricts the photon flux and reduces the image brightness.¹¹⁴ These instruments can also have a chromatic shift across the image, depending on the imaging geometry, which could impact the data analysis depending on the experimental requirements.¹²¹ Similar versions of the MMI have been proposed, which utilize flat or bent crystals rather than a multilayer to achieve better energy resolution.^122,123

Kirkpatrick-Baez (K-B) imaging optics are commonly used in many areas of x-ray research and in many different capacities.¹²⁴ The optical design use two mirrors in succession, each of which focuses in one direction. The benefit is that polishing is only needed with one curvature on each mirror, greatly simplifying the fabrication process. The primary drawback to K-B mirrors is that the two optical surfaces are located sequentially and, hence, at different distances from the source, as shown in Fig. 7. The two mirrors need to have different focal lengths due to the offset in distance, which results in different magnifications (M_i = q_i/p_i, i = 1, 2) in the horizontal and vertical directions, astigmatism in the optic. This astigmatism is minimized by keeping the separation of the mirrors as small as possible. Additional errors, including coma, are common with K-B optics. The field of view over which good resolution is achieved is limited for the K-B optics. It is possible to design mirror systems that reduce the aberrations with the cost of increased complexity. These include increasing the number of mirrors from two to four^125–127 and using elliptical and hyperbolic surfaces.^128,129

There are several examples of K-B imagers used for HEDP applications.^113,130,131 One particularly good example is a 16-image instrument fielded at the LLE Omega Laser.¹³² The instrument is designed to have four images fall onto each of the four strips of a framing camera, although it can also use a time-integrated image plate. The resolution was measured as 6 μm over a field of view of 400 μm. The mirrors had an Ir coating and were operated below the critical angle, limiting the spectral range to less than ∼7 keV, with filtering used to adjust the spectral response of the channels. The system has been used to image the hotspot dynamics of DT target implosions.¹³³ 

Other examples include an eight-channel instrument for the Shenguang-II facility that operates below 3.5 keV;¹³⁴ a two-channel instrument optimized for simultaneous backlit and self-emission imaging¹³⁵ at the Shenguang-III facility; and a four-channel instrument at the NIF¹³⁶ that operates at ∼10 keV. The typical mirror alignment accuracy needed is ∼100–200 micro-radians, and positional accuracy of 5–10 μm.¹³² Typical solid angles for these microscopes are in the order of 1–3 × 10⁻⁷ sr.

An improvement to the K-B design is to polish the mirrors as a segment of a torus rather than a simple cylinder.^111,112,137 Figure 8 shows an example of a toroidal mirror shape, with the two radii of curvature.

The toroidal shape preserves the imaging resolution over a larger field of view than a typical K-B microscope because the torus can match optical path lengths over a larger surface of the mirror than a cylindrical mirror. Figure 9 shows the geometry for grazing incidence mirrors. The mirror is located at a distance p from the source or object to image, and a distance r_m from the optical axis. When viewed down the optical axis, the ray path length increases from r_m at the center of the mirror to r_m + δl at the edges of a simple cylindrical mirror with one curvature. However, the ray path length is identical over the mirror surface when the mirror is a torus with a minor radius of r_m. Additionally, when the mirrors have a multilayer coating, the angle of incidence is preserved over a larger surface of the mirror and reduces the energy bandwidth of the microscope. An instrument based on this design was fielded at the Laser Integration Line (LIL) at the LMJ facility¹³¹ and demonstrated 5–10 μm resolution over a ±1 mm field of view for the toroidal mirrors, compared to 10–25 μm resolution over the same field of view for cylindrical K-B. Similar instruments, called the High Resolution X-ray Imager (HRXI) and the Extended High Resolution X-ray Imager (EHRXI), were fielded at the Omega Laser Facility^138,139 with 5 μm resolution over a 2 mm field of view. The LMJ facility has also implemented a microscope based on this mirror design.¹⁴⁰ Typical values for the radii of the torus are major radii of 100–1000 s of meters, while the minor radii are 0.02–0.05 m.¹⁴¹ Just like with the K-B optics, the energy response and throughput can vary over the field of view. This requires calibration of the microscopes and post-processing of the data to remove the instrument response. Typical solid angles are in the range of 1–10 × 10⁻⁷ sr.

Wolter microscopes are adapted from a telescope design¹⁴² that minimizes the resolution degradation off-axis.¹⁴³ One key advantage of the Wolter microscope is that it has a full surface of revolution that provides a very large solid angle and, hence, is suitable for imaging a source with low output. As a point of comparison, the solid angle for a Wolter microscope can be ∼1 × 10⁻⁴ sr, compared to 1 × 10⁻⁸ for a typical 10 μm diameter pinhole. The type-I Wolter microscope design has two optical surfaces, a hyperbola and an ellipse, where the hyperbola section faces the object and the ellipse toward the image in a M > 1 geometry, as shown in Fig. 10(a). A typical design will specify the grazing angle to the mirror, magnification, and working distance. Adding in an additional constraint such as either the mirror length or desired solid angle will fully constrain a standard optical prescription. More complex optical prescriptions allow correction of higher-order aberrations and better performance, but come at the cost of reduced reflectivity.¹⁴⁴ The type-I Wolter design is a hollow cylinder and can be nested, as shown in Fig. 10(b), to increase the collection efficiency.

The increased collection efficiency of the Wolter microscope often comes with a short depth of field. This is true for all optical systems: the depth of field is inversely proportional to the numerical aperture. The Wolter microscope collects rays along a hollow cone and, thus, the out-of-focus point spread function is an annulus and the resolution degrades faster than for a full-aperture optic with similar NA.

One major challenge to Wolter fabrication is in polishing the inner surface to meet the tight conditions on roughness and figure. A Wolter microscope was fabricated by diamond-turning the interior surface of an electro-less nickel-coated steel substrate¹⁴³ and fielded on the NOVA laser.^145–147 This optic was later paired with a series of relay mirrors that allowed four images to be acquired onto a time-gated MCP. Additionally, apertures with 5° sectors were used to increase the depth of field of the optic.¹⁴⁸ The optic operated below the critical angle and was limited to 3–5 keV.

There have been a number of advances in fabrication over the last two decades. Several options for x rays less than 1 keV are possible, as the critical angle is relatively large for the lower energies.^149–151 Evaporative coatings can extend the energy range for these optics.

A multilayer coating can extend the x-ray energy range for the Wolter microscope, just as with the K-B or toroidal imagers. Recently, optic production using a replication process that was developed for x-ray telescopes¹⁵² has been adapted to microscope designs.¹⁵³ First, a mandrel is figured and polished. Next, a multilayer can be deposited on the mandrel if desired, and then, a shell is electroplated onto the mandrel or multilayer. The optic is released from the mandrel and mounted. First tests of this process have been demonstrated at the Sandia Z-machine and demonstrate improved signal-to-noise ratios compared to pinhole images in a 1–2 keV spectral bandwidth.^153,154

Crystal-based optics are reflective x-ray optics that take advantage of Bragg reflection from crystal lattice planes. Collimated x rays incident on a flat mirror are reflected only when the wavelength satisfies Bragg’s law, Eq. (8), for the angle of incidence θ relative to the plane of the surface. Figure 11(a) illustrates the geometry of collimated rays incident on a flat mirror surface. Each ray is incident at the same angle on the mirror, so only the wavelengths that meet the Bragg condition are reflected and create a monochromatic beam.

The range of energies reflected in the case of an ideal crystal is determined by the Darwin width of the crystal.¹⁵⁵ The reflectivity of real crystals is typically broadened in angle and energy due to lattice imperfections such as dislocations, mosaicity, or strain. The angular width over which the crystal reflects is measured using monochromatic x rays and rotating the crystal about the Bragg angle. This is termed the rocking curve of the crystal. The range of angles is typically small, tens to hundreds of micro-radians or in the order of 0.1–10 eV in energy.

Crystal-based optics are ideal for producing narrow-band x-ray imagers, which is one of their primary uses in the HEDP community. Additionally, the much shorter lattice plane spacing of the crystal than that of multilayers allows the crystals to reflect x rays at multi-keV energies (relevant to many HEDP experiments) at very high Bragg angles. This allows for optics that operate at near-normal incidence, which minimizes imaging aberrations, provided that a crystal with the appropriate d-spacing to match the desired energy can be obtained. Owing to the reduced aberration, the solid angle of near-normal crystal optics can be significantly larger than that of grazing incidence optics for the same spatial resolution. The monochromatic imaging from crystals is very useful in HEDP experiments because it can reduce the background emission outside the wavelengths of interest. This allows studies of specific atomic transitions for self-emission, and to use backlight imaging (radiography) to probe absorption over narrow energies in the presence of high backgrounds.

Most x-ray sources in HEDP applications are not collimated as shown in Fig. 11(a). Rather, point sources or area sources are more common. Figure 11(b) illustrates the case of a point-source illuminating a flat crystal mirror. Each point on the mirror surface is illuminated at a different angle from the source and corresponds to a different x-ray energy being reflected according to Bragg’s law. This leads to the condition that the spectral content of the image depends on the position of the rays on the surface of the flat mirror in the case of a point source, or broader spectral width in the case of an area source. Flat mirrors have been used with pinhole imagers, such as was used at the OMEGA laser facility^114,123 to image the Ti and Ar emission in the 3–5 keV spectral range. These are similar to the multilayer monochromatic imagers described earlier, but have a narrower energy bandwidth. However, the limited collection efficiency of the pinhole and narrow bandwidth of the crystal result in low brightness images and, hence, poor signal-to-noise ratios.²⁵ This kind of system can be improved by using curved crystal reflectors as described next.

Spherically bent-crystal imagers have been used in multiple HEDP facilities over the last couple of decades due to their ability to collect large solid angles and preserve narrow spectral bandwidths.^156–161 Typically, a flat crystal is bonded to a curved, polished substrate to force the crystal lattice planes to the curved geometry. Figure 12 shows a typical cross section of a bent crystal. The crystal has a radius of curvature R, which for a spherical mirror has a focal length of R/2. The Rowland circle radius is defined as the circle of radius R/2 that passes through the center of curvature of the mirror (point O) and the mirror surface. The Rowland circle has two useful properties. The first is that a point source on the Rowland circle will be reflected to another point on the Rowland circle. The second is that all rays from the point source on the Rowland have the same angle of incidence on the mirror, allowing the entire crystal to satisfy the Bragg condition for a given wavelength simultaneously. A point-source at point O of a spherical mirror shown in Fig. 12 would be reflected back to the same location without distortion, but this configuration does not make a very useful imager as the detector needs to be in the same location as the source. The object point p is usually moved inside the Rowland circle and off normal-incidence to allow a magnified image at point q to be captured using a detector. Many designs have been explored over the years, to best match the x-ray source emission and optimizing spatial resolution.^161–168 The relatively large numerical aperture for the spherical crystal imagers allows microscopes with resolutions down to the 5–10 μm regime.

Emission points located away from O as shown in Fig. 12 are not incident at the same angles in the horizontal and vertical planes for a spherical mirror. Similar to the toroidal mirror description for grazing incidence, toroidally bent crystals or multiple crystal reflectors can correct for these asymmetries to produce images with better spatial and energy resolution images.^169–173 

Transmissive x-ray optics focus by imparting a phase and amplitude change to the incoming wavefront. The two optics to be discussed here are Fresnel zone plates and refractive optics work via diffraction and refraction, respectively. In both cases, the complex index of refraction is used to compute the phase and amplitude shift imparted to the x-ray wave as it propagates through the lens material. Snell’s law of refraction can be used to compute the refraction of rays through the refractive lenses based on the material and geometry. While a geometric argument can be made for the zone plates, they can also be treated via classic diffraction theory.

Both optical systems are subject to chromatic aberrations because of the wavelength dependence of their focusing, which makes them more difficult to use in HEDP experiments that typically have a large out-of-band x-ray background. However, their advantages include reduced astigmatism compared to mirrors, comparable solid angles for collection, and relatively small form factors. Zone plates, in particular, have been applied to multiple HEDP experiments.

Improvements in fabrication methods of small features have enabled the production of high-performance FZPs.^180–182 This resulted in the re-start of FZPs’ usage in HEDP and ICF, first in an x-ray self-emission setup^183,184 and later in a radiography setup^185–188 for energy ranging from 1.8–9 keV. In a self-emission setup, because of the chromatic aberrations, a spectral selection is required, and the wider the band, the worse will be the resolution but increased depth of field, easing the alignment process. A multilayer mirror has been used for this purpose at the LULI200 laser facility,^183,184 reducing the bandwidth to 100 eV and reaching a resolution of 2.7 ± 0.3 μm on shot, with a single channel at 1.85 keV, as shown in Fig. 14 of Ref. ¹⁸³ and two channels at 1.85 and 4.7 keV¹⁸⁴ for buried layer experiments.¹⁸⁹ The latter demonstrated the capability to image different energy bandwidths with high resolution on the same shot using different FZPs and multilayer designs. Following the success of these experiments, the use of FZPs has continued, passing onto x-ray radiography setup. The advantage of using a backlighter is that the spectrum is naturally constrained by the material line emission, providing a bandwidth of few hundreds of eV. They were successfully used to image hydrodynamic instabilities at 9¹⁸⁸ and 4.5 keV,¹⁸⁶ and double-shell capsule implosion experiments^187,190 with measured resolution ranging from 1.5 up to 5 μm.

The FZP-multilayer mirror setup for x-ray self-emission imaging is currently in use at the Apollon laser facility¹⁹¹ and is in study for capsule implosion experiments both at the OMEGA and NIF laser facilities. While using FZPs for radiography has demonstrated high resolution, it faces a challenge for quantitative studies. The high level of background due to the multiple diffraction orders and chromaticity prevents the direct measurement of quantities such as opacity and degrades image signal-to-noise ratio when used with time-gated detectors, which often have a limited dynamic range. This can be mitigated with the use of a central blocker,¹⁸⁷ but this central block needs to be on the order of 1.5× larger than the backlighter source, which further complicates the FZP fabrication. A different option could be the use of the same setup as for the self-emission imaging, i.e., using a multilayer with the FZP, to reduce the energy bandwidth and reduce the amount of background. Overall, FZPs are a promising optic for HEDP and ICF experiments with the potential to produce self-emission and radiography x-ray images with sub-5 μm resolution, enough fluence to allow a gate time lower than 100 ps and for energy up to 30 keV.

Refractive optics, typically made of beryllium or other low-Z materials, are employed extensively at synchrotrons and XFELS. The refractive index change is small in most materials, which leads to low refractive power for a single lens. A typical lens system consists of multiple lens elements stacked together, which increases the refractive power of the entire stack. These optics are not used at laser or pulsed power facilities to date, but the trade-offs will be briefly discussed.

An effective lens needs a small radius of curvature to have significant optical power. Commercial lenses have a parabolic shape with apex radii from 0.05–2 mm. Absorption in the lenses limits the number of lens elements and the effective aperture. Typical values for effective aperture for Be lenses are 0.2–0.3 mm. With typical focal lengths from 100–1000 mm, the solid angle is typically 10× larger than pinhole imagers and comparable to zone plates. Just like zone plates, the refractive lenses are subject to chromatic aberrations and work best with monochromatic sources. The bandwidth limits the resolution of the optic.

Application of refractive lenses has been done at the Matter at Extreme Conditions (MEC)¹⁹² end station at the Linac Coherent Light Source (LCLS) and the HEDP end station at the European XFEL. In these experimental platforms, the lenses are used to re-focus the XFEL beam closer to the sample to produce a small source in a point-projection imaging geometry. Additionally, the lenses can be used to image the object in a traditional microscope. These applications work well since the monochromatic x-ray source is not subject to chromatic aberration and the beam size is comparable to the entrance aperture, making effective use of the collection efficiency. Furthermore, the focal length changes with the number of lenses allowing one to easily adjust the imaging geometry based on experimental needs.

X-ray imaging methods are frequently used in HEDP facilities worldwide, with pinhole imaging being the most commonly used method, and spatial resolution in the ∼10 μm neighborhood typical. Advances in x-ray optics offer improved resolution and throughput, but with the cost of added complexity in terms of alignment and calibration. As neutron yields increase, however, it may become necessary to use x-ray optics to relay the images further from the interaction point to protect electronic detectors from neutron damage. Additionally, as detectors continue to advance and enable shorter exposures and higher x-ray energies, optics with increased collection efficiency compared to pinholes may be required to take advantage of the newer detectors. Similarly, advanced optics may be needed to explore physics at or below the micron level.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. This document may contain research results that are experimental in nature, and neither the United States Government, any agency thereof, Lawrence Livermore National Security, LLC, nor any of their respective employees makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not constitute or imply an endorsement or recommendation by the U.S. Government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily reflect those of the U.S. Government or Lawrence Livermore National Security, LLC, and will not be used for advertising or product endorsement purposes.

The authors have no conflicts to disclose.

B. Kozioziemski: Writing – original draft (lead). B. Bachmann: Writing – original draft (equal). A. Do: Writing – original draft (equal). R. Tommasini: Writing – original draft (equal).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.