Introduction and background

X-ray microscopes1 provide a unique combination of high penetration and low multiple scattering in thick specimens, with the potential for nanoscale spatial resolution due to the short wavelength, λ, of the x-rays. While transmission x-ray microscopes capture all of the pixels in parallel so that they can rapidly acquire a projection image,2 they are limited to working in absorption or phase contrast (including with spectroscopic contrast if images at multiple photon energies are acquired), and furthermore, the spatial resolution is limited by optics. Scanning microscopes (Figure 1) use a focused beam to acquire nanotomography data in series from a set of pixel positions and rotation angles, enabling a larger variety of image modalities. X-ray imaging optics often have efficiencies of less than 20%; in transmission x-ray microscopes, this efficiency loss applies to how the signal is collected (leading to a higher radiation dose on the specimen for the same signal level on the detector), while in scanning x-ray microscopes, this efficiency loss leads to longer exposure times, but with no additional dose to the specimen.

While scanning microscopes provide high spatial resolution, nanotomography in scanning microscopes often requires hours for data acquisition, even with today’s brightest synchrotron light sources. This is due to the requirement of a high degree of coherence in the illumination in order to obtain a small focal spot.1,3 Fortunately, the x-ray brightness that is available at various facilities has been increasing at a pace beyond that of Moore’s Law in computing, and a new generation of diffraction-limited synchrotron light sources is emerging.4 X-ray free-electron lasers (XFELs) offer even higher peak and time-averaged brightness in femtosecond pulses, but the focused XFEL beam often causes photoablation5 or even vaporization6 of the specimen.

When using coherent beams in scanning x-ray microscopy, the far-field diffraction pattern encodes information about the complex wavefield exiting the specimen, which in turn, is affected by the complex x-ray refractive index of the specimen’s material.1 When a spatially limited coherent beam is scanned across the specimen while collecting diffraction patterns, a computational approach called ptychography7 allows one to carry out iterative phasing of the resulting set of diffraction patterns to yield the complex exit wave leaving the specimen. It is this approach that allows transmission images with a spatial resolution dictated by the angular extent of recorded and phased diffraction data, rather than the resolution limit imposed by the optics in conventional scanning microscopy. In soft x-ray studies, 5-nm spatial resolution has been obtained when imaging synthetic multilayer cross sections, and series of images recorded across an absorption edge have been used for three-dimensional (3D) chemical mapping in lithium battery particles. 8 Because of the redundancy of information recorded by the finite illumination spots and the pixels in the detector, one can simultaneously recover the complex illumination wave function9 (often called the “probe function”) along with an image of the specimen, and even correct for errors in the probe position.10,11

The scanned probe’s intensity distribution also excites x-ray fluorescence from elements present in the specimen. The scanned probe provides the spatial resolution, while an energy-resolving detector (such as a silicon energy-dispersive detector) enables quantitative detection of elements present. If ptychography and fluorescence are both used together, the ptychographically recovered probe function can be used to deconvolve the x-ray fluorescence images to reach finer spatial resolution,12 though in practice, the gain in spatial resolution is modest as it is limited by the strength of the fluorescence signal.13

Figure 1
figure 1

Schematic of nanotomography in a scanning microscope at a synchrotron light source. A bright x-ray beam is produced using an undulator, and the beam is then spectrally filtered using a monochromator and focused to a small spot using one of several types of optics (a Fresnel zone plate is shown here). Pixelated detectors can be used to record a set of far-field coherent diffraction patterns as the beam is scanned, either in the case of the transmitted beam or in the case of scattering about a Bragg peak from a nanocrystalline domain. A ptychography reconstruction algorithm (involving an iterative approach to phasing the set of coherent diffraction patterns to yield a complex image) then allows one to see detail in the specimen at a resolution limited by the angular extent of the diffraction data, rather than the focal spot size from the objective lens.

Full size image
Figure 2
figure 2

X-ray ptychographic tomography of a region of an integrated circuit.19 (a) Scanning electron microscope showing a 9.8-μm-diameter pillar carved from a standard Intel microprocessor (22-nm node) by using a focused ion beam (FIB) system. A 14.6-nm resolution reconstructed tomogram was obtained from x-ray ptychographic phase-contrast images acquired at 6.2 keV over 1200 projection angles. (b) Electron density threshold corresponding to copper interconnects within the circuit in the pillar on the left.19 The red and blue structures indicate connective wiring. Images courtesy of M. Holler, Paul Scherrer Institute.

Full size image

For nanoscale 3D fluorescence imaging, a series of 2D scanning x-ray fluorescence images with the specimen rotated between images can be obtained and used as a set of projection images for a standard tomographic reconstruction.14 While there are new acquisition methods that are based on using rotation as the “fast” or first sequential scan axis,10,15 these approaches are not yet widely available due to alignment challenges that may be solved by computational methods after data are collected.

X-ray nanotomography capability is available at many synchrotron light sources worldwide (e.g., lightsources.org16), with no-cost access allocated based on peer-reviewed scientific proposals.

Applications to the study of materials

We first consider transmission imaging using ptychography. At x-ray energies below ∼1 keV, absorption and phase-contrast effects are similar in magnitude; as the photon energy is increased, phase contrast increasingly dominates.1 Therefore, at higher x-ray energies, the ptychographic phase-contrast images are usually used as the set of projection images, allowing the recovery of a quantitative 3D measurement of the specimen’s electron density17,18 at a spatial resolution beyond that of the probe-defining optic. This has been used for a wide range of applications, including nanoscale studies of bone17 and, more recently, of integrated circuits19 (Figure 2). Because the x-ray beam from synchrotron light sources is usually strongly linearly polarized, two images at two different orientations of the specimen in the beam can be obtained and magnetic linear dichroism can be used to reconstruct 3D magnetization profiles20 (Figure 3a). Because the field of view in scanning microscopy is determined not by optical magnification, but simply by the scanning region, faster, lower-resolution images over a larger field of view can be obtained and zoomed in with higher photon density in a smaller field of view for maximum detail.22

If a crystalline specimen region is placed in the beam, a pixelated detector can be placed to capture the intensity distribution around a Bragg peak (Figure 1). With nanocrystalline domains, one can “rock” the angle and use coherent diffraction imaging to reconstruct a 3D phase-contrast image along a direction of the nanocrystal’s lattice and interpret this in terms of crystalline strain.23 Scanning microscopes are no longer limited to nanocrystalline domains, therefore, this Bragg ptychography method24 can be used to study local polarization in ferroelectric thin films25 as well as strain in the lattice along extended crystalline domains (Figure 3b).

One of the applications of fluorescence tomography in scanning microscopes is to understand the 3D distribution of metals in biological systems, since metals play important roles in biological function and their disregulation is associated with various diseases. The first nanotomography example studied the role of iron as a population growth limiter in marine protists (a broad group of eukaryotic organisms that are capable of existence as single cells, although many form colonies that exhibit coordinated behavior)14 imaged after chemical fixation and drying, as shown in Figure 4a, while a more recent example studied an algae rapidly frozen from the living state with excellent preservation of diffusible elements26 (Figure 4b). For thicker specimens, self-absorption of the fluorescence signal can affect quantitation, though approaches are being developed27,28 to partially correct this.

Figure 3
figure 3

Vector tomography in scanning microscopes allows one to observe more than just the electron density of the object. (a) The reconstruction of magnetic field lines in a GdCo2 pillar, 5 μm in diameter, as prepared using a focused ion beam.20 The magnetic field vectors were obtained by collecting ptychographic tomography data with the pillar at two different orientations relative to a circularly polarized x-ray beam; region 1 shows an antivortex, and region 2 an anticlockwise vortex, in the specimen’s magnetization. (b) The methodology of Bragg ptychography is shown at the top, where a focused x-ray beam is used as the input vector ki, and one collects diffraction pattern details around the Bragg diffracted peak vector kf, while the beam is translated through the specimen. The bottom image shows the shape as well as the crystalline strain along the [001] lattice direction of a SiGe nanocrystal as imaged using Bragg ptychography.21 Images (a) from C. Donnelly, University of Oxford, and (b) from S. Hruszkewycz, Argonne National Laboratory. Note: SOI, silicon-on-insulator.

Full size image
Figure 4
figure 4

(a) Examples of x-ray fluorescence nanotomography of biological specimens. The composite image (with black background) shows the freshwater diatom Cyclotella meneghiniana imaged after chemical fixation and air-drying, with a 3D resolution of 400 nm.14 Quantitative maps of the concentration of various elements are shown. (b) The composite image (with white background) shows the green algae Chlamydomon reinhardtii prepared in a frozen hydrated state and imaged at liquid nitrogen temperature, where 125-nm transverse and 140-nm longitudinal resolution have been obtained26 (18-nm resolution has been obtained in 2D ptychographic images13). Cryogenic specimen preparation offers superior chemical and structural fldelity, and cryogenic imaging conditions offer superior radiation damage resistance for studies of hydrated organic materials, such as biological cells.

Full size image

Outlook and challenges

As previously noted, one of the challenges of nanotomography in scanning x-ray microscopes today is the relatively long time (hours) it takes to acquire high-resolution 3D images. The achievable resolution is in part limited by photon statistics;29 the cumulative exposure of a voxel from all illumination angles must be increased by about a factor of 16 to decrease the size of the voxel (the spatial resolution) by a factor of 2. However, as noted earlier, the advent of diffraction-limited storage rings4 (offering coherent flux gains of a hundredfold or more) will soon begin to improve the situation.

As the exposure is increased to ever-smaller voxels, there is concern about radiation effects on the specimen. When using a small beam, heating is reduced by having a large thermal reservoir of specimen material surrounding the beam path; therefore, heating is not much of a problem today, though this may change in the coming years as brighter synchrotron light sources enter operation.30 What is more important is the accumulated radiation dose in the specimen. For biological or soft-matter specimens, mass loss and physical shrinkage can be minimized by studying the specimen under cryogenic conditions, and furthermore, rapid freezing provides good structural and chemical preservation.1,31

Other limitations on the speed of scanning can also be removed. Rather than use a stop-settle-measure approach at each pixel position, the specimen can be scanned continuously and the moving beam can be treated as a set of separate coherent illumination modes in ptychographic reconstruction.32 The required partial illumination overlaps needed for ptychography can be obtained using specimen rotation rather than translation.33 Complete coverage of all voxel positions from all angles is not necessary; one can “learn” about characteristic features in a complete scan of a subregion of the specimen from a broader family of representative samples and use this as a model for better estimation of structure in lightly sampled regions.34

Yet another challenge is limitations of linear translation and rotation stages that become more apparent as the target spatial resolution is pushed farther into the nanoscale. With increasing resolution, imperfections in motion control (often called runout errors, or spindle errors) become more noticeable. Sometimes these errors can be characterized prior to experiment and corrected for after acquisition; however, random drifts and errors due to imperfect roundness of bearings and other factors are challenging to correct for. There are a number of metrology systems to precisely measure the sample positioning with respect to the x-ray beam;35,36 however, restrictions due to experimental constraints such as working distance or vacuum conditions can complicate use of these approaches for specific cases. There are, however, computational approaches that can be used to align or calibrate positioning of the data prior to or during image reconstruction.37–39 While some of these are computationally demanding, they are often mandatory for realizing high 3D spatial resolution.

As noted in the beginning of this article, x-rays offer unique opportunities for imaging millimeter-sized specimens with nanometer-scale spatial resolution. However, the depth of focus in imaging is about 5 (transverse resolution)2/λ, which applies both to direct imaging (such as fluorescence) and to changes in the probe function in ptychography. This can be accounted for by including wavefield propagation effects in multislice ptychography,40–42 and applying it to 3D imaging by summation of the separate in-focus depth planes in standard tomography.43 An alternative is to use the multislice method as the forward model in an optimization approach, allowing the specimen to be treated in a more continuous fashion than as a set of discrete depth-separated planes.44 When using these multislice approaches, the number of specimen rotations can be reduced below what would have normally been expected.45

Taken together, the previously described advances are giving new insights into the nanoscale nature of materials in 3D. With the development worldwide of diffraction limited storage rings, the future of nanotomography with scanning microscopes is bright.