Coherent x-ray diffraction imaging (CDI) is an important non-destructive imaging technique available at the U.S. Department of Energy’s (DOE’s) Advanced Photon Source (APS). When probing crystalline materials in three dimensions, the technique is called Bragg coherent diffraction imaging (BCDI). Scientists currently use BCDI to reveal nanoscale properties of crystals, including strain and lattice defects. The APS Upgrade (APS-U) will provide highly coherent x-rays at far greater energies than are now available at the APS, allowing BCDI to reveal crystalline imperfections in even greater detail throughout a far larger volume. Unfortunately, current reconstruction algorithms have difficulty coping with the diffraction patterns resulting from substantially higher x-ray energies. Theoretically, these limitations can be overcome by shrinking detector pixel size, enlarging the dimensions of the experiment, or recording many more diffraction patterns. But each of these options entails significant design drawbacks. A research team has now demonstrated a signal processing method that yields high-resolution BCDI images derived from high-energy x-rays using standard experimental parameters. The new processing method was confirmed through simulations and experimentally at the APS. These results promise unprecedented imaging of complex crystalline materials and polycrystalline interfaces, as well as nanocrystals embedded within a bulk matrix, for instance nanocrystals dispersed within catalytic systems. More generally, the new processing method will encourage broader use of flexible CDI experiments at fourth-generation x-ray light sources.

BCDI involves diffracting a coherent beam of monochromatic x-rays off a crystalline lattice. Monochromatic means the x-rays possess a single frequency, while coherent means they share the same relative phase, with their individual peaks and troughs moving in sync. During a typical BCDI experiment, a nanocrystal is incrementally rotated under an x-ray beam. At certain angles, the diffraction patterns are brightest; these patterns are Bragg peaks. X-ray detectors measure the intensities of each peak, which are recorded and later computer-processed. Figure 1a shows the basic experimental concept. Note the central bright spot in yellow and the surrounding interference fringes.

By employing BCDI at x-ray energies around 10 kiloelectron volts (10 keV), scientists have measured properties like lattice defects and strain in nano-sized crystals embedded in a polycrystalline matrix. However, penetration is relatively limited for larger samples (micrometer-range and above).

With the advent of the APS-U, highly-coherent x-rays with energies of 50 keV and above will become available, allowing imaging of previously-inaccessible crystals residing deep within polycrystalline materials. However, higher-energy BCDI is challenging when using standard experimental setups because the fringe pattern associated with each Bragg peak gets compressed on the detector as the x-ray energy increases, which effectively means that data is lost and image resolution suffers.

In order to achieve high-resolution imaging for next-generation BCDI experiments without radically changing experimental equipment, dimensions, or run times, the research team from Argonne and Aix Marseille University (France) developed a computer processing technique based upon a newly-designed algorithm. This algorithm borrows heavily from standard algorithms used for current BCDI experiments, but is modified for the data compression of higher-energy BCDI. This data compression results from a phenomenon called pixel binning.

Just like a digital camera, x-ray detectors have many individual pixels (picture elements). Capturing the broader Bragg peaks of high-energy BCDI using standard detectors results in binning of the diffraction pattern, in which several adjacent pixels are effectively treated as a single, larger pixel. However, this degrades image resolution. Binning, while often useful in scientific imaging and consumer digital cameras, is undesirable here. The new reconstruction technique takes the highly pixelated data (Fig. 1B) and largely reverses the binning effect by reinterpreting the data as a virtual, high-resolution image with smaller pixels.

To confirm the efficacy of the new reconstruction technique, two experimental sessions were run at X-ray Science Division beamline 34-ID-C of the APS, an Office of Science user facility at Argonne National Laboratory. The first session utilized highly coherent, 15-keV x-rays. A second experiment mimicked x-rays three times as energetic (45 keV). Although the APS can currently produce 45-keV x-rays, they are not sufficiently coherent for BCDI experiments. To get around this limitation, the sample/detector distance was reduced by one-third while utilizing the same highly coherent 15-keV x-rays, which effectively emulated the highly coherent 45-keV x-rays that will become available with the APS-U.

Figure 2 compares images of the same gold nanoparticle derived from the two experiments. The two images are quite similar, indicating that the new processing technique can obtain good images from a higher-energy BCDI experiment. Computer simulations corroborated these findings. The researchers note that the methods demonstrated in this study are applicable to other imaging techniques, such as two-dimensional transmission coherent diffraction imaging. ― Philip Koth

See: S. Maddali¹*, M. Allain², W. Cha¹, R. Harder¹, J.-S. Park¹, P. Kenesei¹, J. Almer¹, Y. Nashed¹, and S. O. Hruszkewycz¹, “Phase retrieval for Bragg coherent diffraction imaging at high x-ray energies,” Phys. Rev. A 99, 053838 (2019). DOI: 10.1103/PhysRevA.99.053838

Author affiliations: ¹Argonne National Laboratory, ²Aix Marseille University

Correspondence: * smaddali@anl.gov

Design and simulation of the phase-retrieval framework for high-energy coherent x-ray diffraction was supported by Laboratory Directed Research and Development funding from Argonne National Laboratory, provided by the Director, Office of Science, U.S. Department of Energy (DOE) under Contract No. DE-AC02-06CH11357. Experimental demonstration of the method was supported by the U.S. DOE Office of Science-Basic Energy Sciences, Materials Science and Engineering Division. This research used resources of the Advanced Photon Source, a U.S. DOE Office of Science User Facility operated for the U.S. DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357.

The U.S. Department of Energy’s Advanced Photon Source at Argonne National Laboratory is one of the world’s most productive x-ray light source facilities. Each year, the APS provides high-brightness x-ray beams to a diverse community of more than 5,000 researchers in materials science, chemistry, condensed matter physics, the life and environmental sciences, and applied research. Researchers using the APS produce over 2,000 publications each year detailing impactful discoveries, and solve more vital biological protein structures than users of any other x-ray light source research facility. APS x-rays are ideally suited for explorations of materials and biological structures; elemental distribution; chemical, magnetic, electronic states; and a wide range of technologically important engineering systems from batteries to fuel injector sprays, all of which are the foundations of our nation’s economic, technological, and physical well-being.

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