Diffraction Imaging Research Articles

Phase retrieval in incoherent diffractive imaging using higher-order photon correlation functions

To obtain spatial information about an arbitrary atomic distribution in x-ray structure analysis, e.g. in molecules or proteins, the standard method is to measure the intensity in the far field, i.e. the first-order photon correlation function of the coherently scattered x-ray photons (coherent diffractive imaging). Recently, it was suggested to record alternatively the incoherently scattered photons and measure the second-order photon correlation function to reconstruct the geometry of the unknown atomic distribution (incoherent diffractive imaging). Yet, besides various advantages of the latter method, both techniques suffer from the so-called phase retrieval problem. Lately, an ab-initio phase retrieval algorithm to reconstruct the phase of the so-called structure factor of the scattering objects based on the third-order photon correlation function was reported. The algorithm makes use of the closure phase, which contains important, yet incomplete phase information, well-known from triple correlations and their bispectrum in speckle masking and astronomy applications. Here, we provide a detailed analysis of the underlying scheme and quantities in the context of x-ray structure analysis. In particular, we explicitly calculate for the first time the third-order photon correlation function for single photon emitters in a full quantum mechanical treatment and discuss the uniqueness of the closure phase equations constructed from. In this context, we recapitulate the sign problem of the closure phase and how it can be lifted using redundant information. We further show how the algorithm can be improved using even higher-order photon correlation functions produced by single photon emitters, e.g. the fourth-order correlation function, delivering new phase relations appearing in the four-point correlations.

Strain Heterogeneity and Extended Defects in Halide Perovskite Devices.

Strain is an important property in halide perovskite semiconductors used for optoelectronic applications because of its ability to influence device efficiency and stability. However, descriptions of strain in these materials are generally limited to bulk averages of bare films, which miss important property-determining heterogeneities that occur on the nanoscale and at interfaces in multilayer device stacks. Here, we present three-dimensional nanoscale strain mapping using Bragg coherent diffraction imaging of individual grains in Cs0.1FA0.9Pb(I0.95Br0.05)3 and Cs0.15FA0.85SnI3 (FA = formamidinium) halide perovskite absorbers buried in full solar cell devices. We discover large local strains and striking intragrain and grain-to-grain strain heterogeneity, identifying distinct islands of tensile and compressive strain inside grains. Additionally, we directly image dislocations with surprising regularity in Cs0.15FA0.85SnI3 grains and find evidence for dislocation-induced antiphase boundary formation. Our results shine a rare light on the nanoscale strains in these materials in their technologically relevant device setting.

Optical diffractive neural network imaging through double diffusive mediums

The optical diffractive neural network (ODNN) offers the benefits of high-speed parallelism and low energy consumption. This kind of method holds great potential in the task of reconstructing diffusive images. In this work, we capture a double-scattering dataset by designing optical experiments and use it to evaluate the image reconstruction capability of the constructed ODNNs under more complex scattering scenarios. The Pearson Correlation Coefficient, which is used as a quantitative index of the reconstruction performance, shows that the constructed diffractive networks enable to achieve high performance in the direct recovery of double-scattering data, as well as in the recovery task of stitching images based on two different kinds of double-scattering data. Meanwhile, due to the high redundancy of valid information in the speckle patterns of scattering images, even if parts of the information in the speckle patterns are blocked, the constructed diffractive networks can also show high reconstruction performance without retraining. The capability of the proposed ODNN to reconstruct double-scattering images indicates that the optical diffractive network has the potential to bring transformative applications in more complex scattering scenarios.

All-optical complex field imaging using diffractive processors.

Complex field imaging, which captures both the amplitude and phase information of input optical fields or objects, can offer rich structural insights into samples, such as their absorption and refractive index distributions. However, conventional image sensors are intensity-based and inherently lack the capability to directly measure the phase distribution of a field. This limitation can be overcome using interferometric or holographic methods, often supplemented by iterative phase retrieval algorithms, leading to a considerable increase in hardware complexity and computational demand. Here, we present a complex field imager design that enables snapshot imaging of both the amplitude and quantitative phase information of input fields using an intensity-based sensor array without any digital processing. Our design utilizes successive deep learning-optimized diffractive surfaces that are structured to collectively modulate the input complex field, forming two independent imaging channels that perform amplitude-to-amplitude and phase-to-intensity transformations between the input and output planes within a compact optical design, axially spanning ~100 wavelengths. The intensity distributions of the output fields at these two channels on the sensor plane directly correspond to the amplitude and quantitative phase profiles of the input complex field, eliminating the need for any digital image reconstruction algorithms. We experimentally validated the efficacy of our complex field diffractive imager designs through 3D-printed prototypes operating at the terahertz spectrum, with the output amplitude and phase channel images closely aligning with our numerical simulations. We envision that this complex field imager will have various applications in security, biomedical imaging, sensing and material science, among others.

Single-exposure multi-wavelength optical diffraction tomography based on space-angle dual multiplexing holography.

We present a space-angle dual multiplexing holographic recording system for realizing single-exposure multi-wavelength optical diffraction tomographic (ODT) imaging. This system is achieved by combining the principle of single-exposure multi-wavelength holographic imaging technique based on angle-division multiplexing with the principle of single-exposure ODT imaging technique based on microlens array multi-angle illuminations and space-division multiplexing. Compared with the existing multi-wavelength ODT imaging methods, it enables the holographic recording of all the diffraction tomography information of a measured specimen at multiple illumination wavelengths in a single camera exposure without any scan mechanism. Using our proposed data processing method, the multi-wavelength three-dimensional (3D) refractive index tomograms of a specimen can be eventually reconstructed from single recorded multiplexing hologram. Experimental results of a static polystyrene bead and a living C. elegans worm demonstrate the feasibility of this system.

Simulation of gradient period polarization volume gratings for augmented reality displays

Augmented reality (AR) displays are gaining attention as next-generation intelligent display technologies. Diffractive waveguide technologies are progressively becoming the AR display industry's preferred option. Gradient period polarization volume holographic gratings (PVGs), which are considered to have the potential to expand the field of view (FOV) of waveguide display systems due to their wide bandwidth diffraction characteristics, have been proposed as coupling elements for diffraction waveguide systems in recent years. Here, what we believe to be a novel modeling method for gradient period PVGs is proposed by incorporating grating stacking and scattering analysis utilizing rigorous coupled-wave analysis (RCWA) theory. The diffraction efficiency and polarization response were extensively explored using this simulation model. In addition, a dual-layer full-color diffractive waveguide imaging simulation using proposed gradient period PVGs is accomplished in Zemax software using a self-compiled dynamic link library (DLL), achieving a 53° diagonal FOV at a 16:9 aspect ratio. This work furthers the development of PVGs by providing unique ideas for the field of view design of AR display.

Fast X-ray ptychography: towards nanoscale imaging of large volume of brain

X-ray ptychography, a scanning coherent diffraction imaging technique, is one of the most used techniques at synchrotron facilities for high resolution imaging, with applications spanning from life science to nano-electronics. In the recent years there has been a great effort to make the technique faster to enable high throughput nanoscale imaging. Here we apply a fast ptychography scanning method to image in 3D 106μm3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^6\\upmu \\mathrm{{m}}^3$$\\end{document} of brain-like phantom at 3 kHz, in a 7 h acquisition with a resolution of 270 nm. We then present the latest advances in fast ptychography by showing 2D images acquired at 110 kHz by combining the fast-acquisition scheme with a high-acquisition rate prototype detector from DECTRIS Ltd. We finally review the experimental outcome and discuss the prospective use of fast ptychography schemes for the investigation of mm3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{3}$$\\end{document} size samples of brain-like phantom, by extrapolating the current results to the high coherent flux scenario of diffraction limited storage rings.

In-situ monitoring of sintering and analytical modeling of densification and shrinkage in binder jetted 316 L stainless steel

In binder jetting, shrinkage and deformation occur during the sintering step, both of which are affected by the green density of the binder jetted materials. The study innovatively introduces a cost-effective, practical, and in-process monitoring system for visualizing shrinkage and deformation on larger samples than conventionally observed using small-scale specimens in dillatometry equipment. The powder characteristics and binder jet printing process itself influence the initial green density. The comprehensive analysis of powder flowability and packing density, densification behavior, and shrinkage reveals that the consolidated parts using virgin powder (with a green density of 55 %) can achieve a relative density above 99.9 % with an anisotropic shrinkage in the Z > X > Y direction. In contrast, the used or recycled powder exhibits a lower green density of ∼48 %, higher shrinkage rate in all three dimensions, and a decreased degree of anisotropy. Using in-process imaging and experimental data on the grain size attained through optical microscopy and electron backscatered diffraction imaging, the material's shear and bulk viscosities were determined. The formation of delta-ferrite and its impact on densification were discussed in the context of solid-state and supersolidus liquid phase sintering. The model relied on the continuum sintering theory formulated by Skorohod and Olevsky. The strain evolution from the in-situ imaging of sintering process is correlated with porosity based on the used feedstock and applied sintering temperatures. The outcomes of this study offer valuable perspectives on anisotropic sintering mechanisms, bridging the knowledge gap regarding the relationships between structures produced through binder jetting and subsequent sintering of materials.

The energy-resolved neutron imaging instrument at the China spallation neutron source

The energy-resolved neutron imaging instrument (ERNI) is built on the number 13 beamline at the China Spallation Neutron Source (CSNS), which is the first instrument dedicated to pulsed neutron imaging in China. ERNI is designed as a multi-scale, multi-dimensional, multi-modality characterization platform. The analytical techniques will include conventional neutron radiography and tomography, Bragg-edge neutron imaging, neutron grating imaging, neutron resonance imaging, neutron diffraction, and complementary X-ray tomography. The spatial resolution for conventional neutron imaging is about 15 μm; the maximum field of view could achieve 200 mm × 200 mm; the spectral resolution is better than 0.5%. ERNI is expected to serve the growing multidisciplinary imaging user community from materials science, engineering, energy, cultural heritage, biology, geosciences, industry, and so on.

Three-dimensional tomographic reconstruction using Voronoi weighting

Three-dimensional tomographic reconstruction requires careful selection of the illumination angles, often under certain measurement constraints. When the angular distribution must be nonuniform, appropriate selection of the reconstruction weights is necessary. We show that Voronoi weighting can significantly improve the fidelity of optical diffraction tomography.

Unveiling Core-Shell Structure Formation in a Ni3Fe Nanoparticle with In Situ Multi-Bragg Coherent Diffraction Imaging.

Solid-state reactions play a key role in materials science. The evolution of the structure of a single 350 nm Ni3Fe nanoparticle, i.e., its morphology (facets) as well as its deformation field, has been followed by applying multireflection Bragg coherent diffraction imaging. Through this approach, we unveiled a demixing process that occurs at high temperatures (600 °C) under an Ar atmosphere. This process leads to the gradual emergence of a highly strained core-shell structure, distinguished by two distinct lattice parameters with a difference of 0.4%. Concurrently, this transformation causes the facets to vanish, ultimately yielding a rounded core-shell nanoparticle. This final structure comprises a Ni3Fe core surrounded by a 40 nm Ni-rich outer shell due to preferential iron oxidation. Providing in situ 3D imaging of the lattice parameters at the nanometer scale while varying the temperature, this study─with the support of atomistic simulations─not only showcases the power of in situ multireflection BCDI but also provides valuable insights into the mechanisms at work during a solid-state reaction characterized by a core-shell transition.

An efficient method for determining the pozzolanic reaction degrees of low-calcium supplementary cementitious materials in blended cement pastes

The pozzolanic reaction degree of supplementary cementitious materials (SCMs) is a crucial parameter influencing the performance of SCM-blended concrete. Although several methods, such as partial-or-no-known-crystal-structure (PONKCS) analysis with X-ray diffraction (XRD) testing and image analysis, have been developed to estimate the pozzolanic reaction degree of SCMs, they have their own challenges in achieving reliable estimation. Ethylenediaminetetraacetic acid (EDTA) with NaOH is an efficient and reliable agent for selectively dissolving calcium-rich phases (e.g., cement clinkers and hydration products) without dissolving low-calcium SCMs. In this study, the ionic selective dissolution method (ISDM) that combines the use of an EDTA–NaOH dissolving agent and inductively coupled plasma–optical emission spectroscopy is developed to efficiently and reliably determine the pozzolanic reaction degree of low-calcium SCMs. Furthermore, the chemical compositions of aluminium-incorporated calcium–silicate–hydrate gel are determined via the ISDM coupled with the Rietveld analysis of XRD data, according to mass conservation principles.

MolDStruct: Modeling the dynamics and structure of matter exposed to ultrafast x-ray lasers with hybrid collisional-radiative/molecular dynamics.

We describe a method to compute photon-matter interaction and atomic dynamics with x-ray lasers using a hybrid code based on classical molecular dynamics and collisional-radiative calculations. The forces between the atoms are dynamically determined based on changes to their electronic occupations and the formation of a free electron cloud created from the irradiation of photons in the x-ray spectrum. The rapid transition from neutral solid matter to dense plasma phase allows the use of screened potentials, reducing the number of non-bonded interactions. In combination with parallelization through domain decomposition, the hybrid code handles large-scale molecular dynamics and ionization. This method is applicable for large enough samples (solids, liquids, proteins, viruses, atomic clusters, and crystals) that, when exposed to an x-ray laser pulse, turn into a plasma in the first few femtoseconds of the interaction. We present four examples demonstrating the applicability of the method. We investigate the non-thermal heating and scattering of bulk water and damage-induced dynamics of a protein crystal using an x-ray pump-probe scheme. In both cases, we compare to the experimental data. For single particle imaging, we simulate the ultrafast dynamics of a methane cluster exposed to a femtosecond x-ray laser. In the context of coherent diffractive imaging, we study the fragmentation as given by an x-ray pump-probe setup to understand the evolution of radiation damage in the time range of hundreds of femtoseconds.

A step towards 6D WAXD tensor tomography.

X-ray scattering/diffraction tensor tomography techniques are promising methods to acquire the 3D texture information of heterogeneous biological tissues at micrometre resolution. However, the methods suffer from a long overall acquisition time due to multi-dimensional scanning across real and reciprocal space. Here, a new approach is introduced to obtain 3D reciprocal information of each illuminated scanning volume using mathematic modeling, which is equivalent to a physical scanning procedure for collecting the full reciprocal information required for voxel reconstruction. The virtual reciprocal scanning scheme was validated by a simulated 6D wide-angle X-ray diffraction tomography experiment. The theoretical validation of the method represents an important technological advancement for 6D diffraction tensor tomography and a crucial step towards pervasive applications in the characterization of heterogeneous materials.

Computational study of diffraction image formation from XFEL irradiated single ribosome molecule

Single particle imaging at atomic resolution is perhaps one of the most desired goals for ultrafast X-ray science with X-ray free-electron lasers. Such a capability would create great opportunity within the biological sciences, as high-resolution structural information of biosamples that may not crystallize is essential for many research areas therein. In this paper, we report on a comprehensive computational study of diffraction image formation during single particle imaging of a macromolecule, containing over one hundred thousand non-hydrogen atoms. For this study, we use a dedicated simulation framework, SIMEX, available at the European XFEL facility. Our results demonstrate the full feasibility of computational single-particle imaging studies for biological samples of realistic size. This finding is important as it shows that the SIMEX platform can be used for simulations to inform relevant single-particle-imaging experiments and help to establish optimal parameters for these experiments. This will enable more focused and more efficient single-particle-imaging experiments at XFEL facilities, making the best use of the resource-intensive XFEL operation.

Crystal structures of two new high-pressure oxynitrides with composition SnGe4N4O4, from single-crystal electron diffraction.

SnGe4N4O4 was synthesized at high pressure (16 and 20 GPa) and high temperature (1200 and 1500°C) in a large-volume press. Powder X-ray diffraction experiments using synchrotron radiation indicate that the derived samples are mixtures of known and unknown phases. However, the powder X-ray diffraction patterns are not sufficient for structural characterization. Transmission electron microscopy studies reveal crystals of several hundreds of nanometres in size with different chemical composition. Among them, crystals of a previously unknown phase with stoichiometry SnGe4N4O4 were detected and investigated using automated diffraction tomography (ADT), a three-dimensional electron diffraction method. Via ADT, the crystal structure could be determined from single nanocrystals in space group P63mc, exhibiting a nolanite-type structure. This was confirmed by density functional theory calculations and atomic resolution scanning transmission electron microscopy images. In one of the syntheses runs a rhombohedral 6R polytype of SnGe4N4O4 could be found together with the nolanite-type SnGe4N4O4. The structure of this polymorph was solved as well using ADT.

Lens-free reflective topography for high-resolution wafer inspection

The demand for high-resolution and large-area imaging systems for non-destructive wafer inspection has grown owing to the increasing complexity and extremely fine nature of semiconductor processes. Several studies have focused on developing high-resolution imaging systems; however, they were limited by the tradeoff between image resolution and field of view. Hence, computational imaging has arisen as an alternative method to conventional optical imaging, aimed at enhancing the aforementioned parameters. This study proposes a method for improving the resolution and field of view of an image in a lens-less reflection-type system. Our method was verified by computationally restoring the final image from diffraction images measured at various illumination positions using a visible light source. We introduced speckle illumination to expand the numerical aperture of the entire system, simultaneously improving image resolution and field of view. The image reconstruction process was accelerated by employing a convolutional neural network. Using the reconstructed phase images, we implemented high-resolution topography and demonstrated its applicability in wafer surface inspection. Furthermore, we demonstrated an ideal diffraction-limited spatial resolution of 1.7 μm over a field of view of 1.8 × 1.8 mm2 for the topographic imaging of targets with various surface roughness. The proposed approach is suitable for applications that simultaneously require high throughput and resolution, such as wafer-wide integrated metrology, owing to its compact design, cost-effectiveness, and mechanical robustness.

Revealing the inhomogeneous nature of microstructure and texture evolution in the cold-rolled CoCrFeMnNi alloy during static recrystallization

In the present investigation, equiatomic CoCrFeMnNi high entropy alloy (HEA) was subjected to 80% cold rolling (as-rolled) followed by isothermal annealing treatment at 700 °C for different time periods. Microstructural characterization was performed using electron back-scattered diffraction (EBSD) and electron channeling contrast imaging (ECCI) techniques on the as-rolled and annealed samples. The as-rolled microstructure consisted of elongated grains mainly composed of strong α-fiber and weak γ-fiber textures. The as-rolled sample showed the formation of ingrain SBs in the γ-fiber grains, which served as preferential sites for grain nucleation. The annealing treatment of as-rolled samples at 700 °C cause static recovery (SRV) before 5 minutes of heat-treatment, whereas static recrystallization (SRX) was observed after 5 minutes of heat-treatment in the CoCrFeMnNi alloy samples. A faster rate of recrystallization kinetics was observed after 15 minutes of heat-treatment. The annealing treatment reduced the intensity of α-fiber and enhanced the Copper, Cube and P ({011}<122>) texture components. Copper components originated from coarse recrystallized grains, which were the results of localized grain growth phenomena. Unusual behavior of banded featured α-fiber grains was observed during the annealing process. These banded grains in the partially annealed samples consisted of subgrain-boundaries and showed a delayed response to recrystallization as compared to grains with other orientations. Stored energy (SE) and Taylor factor (M) calculations were also used to understand the delayed recrystallization response of the banded featured/retained deformed grains. The microhardness value of the as-rolled sample was approximately 450 Hv, which decreased to around 230 Hv for the fully recrystallized grains.

The evolution of intergranular networks during grain growth and its effect on percolation behavior

Triple junctions (TJs) are line defects in three-dimensional (3D) polycrystalline materials where three grains meet. Transport along the TJs depends on the connectivity between them. Here, we investigate the connectivity of more than 6000 TJs in a 3D microstructure of pure iron (Fe) through the lens of bond percolation. Our efforts are made possible by synchrotron-based x-ray diffraction tomography, which allows us to resolve the TJ network both temporally and spatially, during grain growth. In the framework of standard percolation theory, we determine a percolation threshold of the TJs, above which there exists a continuous pathway of TJs that travels infinitely far. Our experimental results indicate a surprisingly different percolation threshold (by 16%) compared to models and theories. The reason for the discrepancy is that the real TJ network has a topological disorder that is not present in the idealized microstructures considered in prevailing models and theories. Leveraging the wealth of time-resolved data we trace the origin of this disorder by following the topological transitions that accompany grain growth. Overall, the insights obtained in this study can help guide the design of polycrystalline materials via defect engineering.

Imaging and ferroelectric orientation mapping of photostriction in a single Bismuth Ferrite nanocrystal

The exploration of multiferroic materials and their interaction with light at the nanoscale presents a captivating frontier in materials science. Bismuth Ferrite (BiFeO3, BFO), a standout among these materials, exhibits room-temperature ferroelectric and antiferromagnetic behaviour and magnetoelectric coupling. Of particular interest is the phenomenon of photostriction, the light-induced deformation of crystal structures, which enhances the prospect for device functionality based on these materials. Understanding and harnessing multiferroic phenomena holds significant promise in various technological applications, from optoelectronics to energy storage. The orientation of the ferroelectric axis is an important design parameter for devices formed from multiferroic materials. Determining its orientation in the laboratory frame of reference usually requires knowing multiple wavevector transfer (Q-Vector) directions, which can be challenging to establish due to the need for extensive reciprocal-space searches. Our study demonstrates a method to identify the ferroelectric axis orientation using Bragg Coherent X-ray Diffraction Imaging (BCDI) measurements at a single Q-vector direction. This method involves applying photostriction-inducing laser illumination across various laser polarisations. Our findings reveal that photostriction primarily occurs as a surface phenomenon at the nanoscale. Moreover, a photo-induced crystal length change ranging from 30 to 60 nm was observed, consistent with earlier findings on bulk material.