Coherent Diffraction Microscopy Research Articles

Asynchronous domain dynamics and equilibration in layered oxide battery cathode

To improve lithium-ion battery technology, it is essential to probe and comprehend the microscopic dynamic processes that occur in a real-world composite electrode under operating conditions. The primary and secondary particles are the structural building blocks of battery cathode electrodes. Their dynamic inconsistency has profound but not well-understood impacts. In this research, we combine operando coherent multi-crystal diffraction and optical microscopy to examine the chemical dynamics in local domains of layered oxide cathode. Our results not only pinpoint the asynchronicity of the lithium (de)intercalation at the sub-particle level, but also reveal sophisticated diffusion kinetics and reaction patterns, involving various localized processes, e.g., chemical onset, reaction front propagation, domains equilibration, particle deformation and motion. These observations shed new lights onto the activation and degradation mechanisms of state-of-the-art battery cathode materials.

Ensemble Diffraction Microscopy: An Imaging Technique That Allows High-Resolution Diffraction Imaging Using Both Totally and Partially Coherent Sources

Coherent diffraction microscopy (CDM) is a potential approach to image micromaterials at atomic resolution without crystals. Due to the lack of high-angle scattering, the achieved resolution is limited to several nanometers. Small-angle scattering allows researchers to reveal high-resolution 3D structures of specimens by fitting 1D diffraction signals. However, prerequisite 3D models and non-unique solutions restrict the potential to image general specimens. Under the assumption of an ensemble containing large amounts of identical specimens with the same orientation, the intensity distribution of the diffraction pattern of the whole ensemble is approximated to the form factor of a single specimen multiplied by the number of identical specimens. Since the diffraction intensities are contributed from the whole ensemble, the signal can be significantly extended to high-frequency regions. The feasibility of ensemble diffraction microscopy (EDM) was demonstrated by a designed sample using both totally and partially coherent X-ray sources at Taiwan Photon Source (TPS). The reconstructed images show excellent consistency with the image of a scanning electron microscope. This work represents a new protocol for directly characterizing the structures of nanomaterials, or potentially biomacromolecules, from accumulated X-ray scattering data.

Special Issue on Trends in Sub-Microsecond X-ray Science with Coherent Beams

Large increases in synchrotron brightness have brought notable breakthroughs in measurement techniques that exploit transverse coherence, such as X-ray photon correlation spectroscopy (XPCS), coherent diffraction imaging (CDI), diffraction microscopy, and ptychography [...]

Algorithm for characterizing the subcellular structures of nanometer-sized biological specimens in a solution using x-ray free-electron lasers

Coherent diffraction imaging using third generation synchrotron sources and x-ray free-electron lasers has been demonstrated to be an excellent tool for revealing the inner structures of a single particle. The primary challenge in imaging pure, tiny, and isolated biological specimens is obtaining a reliable reconstruction from diffraction data that have a poor signal-to-noise ratio. Thus, we developed a robust method that yields the internal density distribution of liposome vesicles immersed in a solution. By combining the guided hybrid input-output method and a new order parameter defined by the consistency of the reconstruction, we, without prior knowledge, retrieved both pure and drug-containing liposome vesicles from individual diffraction patterns. This result is currently the smallest noncrystalline biological specimen resolved by single-shot coherent diffraction microscopy.

Quantitative Imaging of Single Unstained Magnetotactic Bacteria by Coherent X-ray Diffraction Microscopy.

Novel coherent diffraction microscopy provides a powerful lensless imaging method to obtain a better understanding of the microorganism at the nanoscale. Here we demonstrated quantitative imaging of intact unstained magnetotactic bacteria using coherent X-ray diffraction microscopy combined with an iterative phase retrieval algorithm. Although the signal-to-noise ratio of the X-ray diffraction pattern from single magnetotactic bacterium is weak due to low-scattering ability of biomaterials, an 18.6 nm half-period resolution of reconstructed image was achieved by using a hybrid input-output phase retrieval algorithm. On the basis of the quantitative reconstructed images, the morphology and some intracellular structures, such as nucleoid, polyβ-hydroxybutyrate granules, and magnetosomes, were identified, which were also confirmed by scanning electron microscopy and energy dispersive spectroscopy. With the benefit from the quantifiability of coherent diffraction imaging, for the first time to our knowledge, an average density of magnetotactic bacteria was calculated to be ∼1.19 g/cm(3). This technique has a wide range of applications, especially in quantitative imaging of low-scattering biomaterials and multicomponent materials at nanoscale resolution. Combined with the cryogenic technique or X-ray free electron lasers, the method could image cells in a hydrated condition, which helps to maintain their natural structure.

High-resolution chemical imaging of gold nanoparticles using hard x-ray ptychography

We combine resonant scattering with (ptychographic) scanning coherent diffraction microscopy to determine the chemical state of gold nanoparticles with high spatial resolution. Ptychographic images of the sample are recorded for a series of energies around the gold L3 absorption edge. From these data, chemical information in the form of absorption and resonant scattering spectra is reconstructed at each location in the sample. For gold nanoparticles of about 100 nm diameter, a spatial resolution of about 20–30 nm is obtained. In the future, this microscopy approach will open the way to operando studies of heterogeneous catalysts on the nanometer scale.

Coherent x-ray zoom condenser lens for diffractive and scanning microscopy

We propose a coherent x-ray zoom condenser lens composed of two-stage deformable Kirkpatrick-Baez mirrors. The lens delivers coherent x-rays with a controllable beam size, from one micrometer to a few tens of nanometers, at a fixed focal position. The lens is suitable for diffractive and scanning microscopy. We also propose non-scanning coherent diffraction microscopy for extended objects by using an apodized focused beam produced by the lens with a spatial filter. The proposed apodized-illumination method will be useful in highly efficient imaging with ultimate storage ring sources, and will also open the way to single-shot coherent diffraction microscopy of extended objects with x-ray free-electron lasers.

High numerical aperture reflection mode coherent diffraction microscopy using off-axis apertured illumination

We extend coherent diffraction imaging (CDI) to a high numerical aperture reflection mode geometry for the first time. We derive a coordinate transform that allows us to rewrite the recorded far-field scatter pattern from a tilted object as a uniformly spaced Fourier transform. Using this approach, FFTs in standard iterative phase retrieval algorithms can be used to significantly speed up the image reconstruction times. Moreover, we avoid the isolated sample requirement by imaging a pinhole onto the specimen, in a technique termed apertured illumination CDI. By combining the new coordinate transformation with apertured illumination CDI, we demonstrate rapid high numerical aperture imaging of samples illuminated by visible laser light. Finally, we demonstrate future promise for this technique by using high harmonic beams for high numerical aperture reflection mode imaging.

Hard x-ray scanning microscopy with coherent radiation: Beyond the resolution of conventional x-ray microscopes

We demonstrate x-ray scanning coherent diffraction microscopy (ptychography) with 10 nm spatial resolution, clearly exceeding the resolution limits of conventional hard x-ray microscopy. The spatial resolution in a ptychogram is shown to depend on the shape (structure factor) of a feature and can vary for different features in the object. In addition, the resolution and contrast are shown to increase with increasing coherent fluence. For an optimal ptychographic x-ray microscope, this implies a source with highest possible brilliance and an x-ray optic with a large numerical aperture to generate the optimal probe beam.

Coherent X-Ray Diffraction Imaging

For centuries, lens-based microscopy, such as optical, phase-contrast, fluorescence, confocal, and electron microscopy, has played an important role in the evolution of modern science and technology. In 1999, a novel form of microscopy, i.e., coherent diffraction imaging (also termed coherent diffraction microscopy or lensless imaging), was developed and transformed our conventional view of microscopy, in which the diffraction pattern of a noncrystalline specimen or a nanocrystal was first measured and then directly phased to obtain a high-resolution image. The well-known phase problem was solved by combining the oversampling method with iterative algorithms. In this paper, we will briefly discuss the principle of coherent diffraction imaging, present various implementation schemes of this imaging modality, and illustrate its broad applications in materials science, nanoscience, and biology. As coherent X-ray sources such as high harmonic generation and X-ray free-electron lasers are presently under rapid development worldwide, coherent diffraction imaging can potentially be applied to perform high-resolution imaging of materials/nanoscience and biological specimens at the femtosecond time scale.

Full optical characterization of coherent x-ray nanobeams by ptychographic imaging

Scanning coherent diffraction microscopy (ptychography) is an emerging hard x-ray microscopy technique that yields spatial resolutions well below the lateral size of the probing nanobeam. Besides a high resolution image of the object, the complex wave field of the probe can be reconstructed at the position of the object. By verifying the consistency of several independent wave field measurements along the optical axis, we address the question of how well the reconstruction represents the nanobeam. With a single ptychogram the wave field can be properly determined over a large range along the optical axis, also at positions inaccessible otherwise.

Three-dimensional image reconstruction of radiation-sensitive samples with x-ray diffraction microscopy

Coherent diffraction microscopy determines the three-dimensional (3D) structure of a noncrystalline sample by acquiring a set of diffraction patterns at multiple sample orientations. In order to achieve a high spatial resolution, it usually requires a large number of diffraction patterns with small increments of tilt angles. However, this is not easily attainable for biological or other radiation-sensitive samples due to the radiation damage issue. With the constraint that only a limited number of diffraction patterns is available, a new method is proposed to optimize the effect of these data for three-dimensional image reconstruction. The method combines the concepts of selecting angles with a constant slope increment, the pseudopolar Fourier transform, and the guided hybrid input-output method for direct 3D phase retrieval. Based on simulated and experimental data, it is shown that the proposed method has a better accuracy than some existing three-dimensional image reconstruction techniques. The method is also examined for its stability and consistency by reducing data points used for image reconstruction. The relationship between the number of diffraction patterns used and the accuracy of the reconstructed images is also studied.

Coherent diffraction microscopy at SPring-8: instrumentation, data acquisition and data analysis.

Since the first demonstration of coherent diffraction microscopy in 1999, this lensless imaging technique has been experimentally refined by continued developments. Here, instrumentation and experimental procedures for measuring oversampled diffraction patterns from non-crystalline specimens using an undulator beamline (BL29XUL) at SPring-8 are presented. In addition, detailed post-experimental data analysis is provided that yields high-quality image reconstructions. As the acquisition of high-quality diffraction patterns is at least as important as the phase-retrieval procedure to guarantee successful image reconstructions, this work will be of interest for those who want to apply this imaging technique to materials science and biological samples.

Low-dose x-ray phase-contrast and absorption CT using equally sloped tomography

Tomographic reconstruction from undersampled and noisy projections is often desirable in transmission CT modalities for purposes of low-dose tomography and fast acquisition imaging. However under such conditions, due to the violation of the Nyquist sampling criteria and the presence of noise, reconstructions with acceptable accuracy may not be possible. Recent experiments in transmission electron tomography and coherent diffraction microscopy have shown that the technique of equally sloped tomography (EST), an exact tomographic method utilizing an oversampling iterative Fourier-based reconstruction, provides more accurate image reconstructions when the number of projections is significantly undersampled relative to filtered back projection and algebraic iterative methods. Here we extend this technique by developing new reconstruction algorithms which allow for the incorporation of advanced mathematical regularization constraints, such as the nonlocal means total variational model, in a manner that is consistent with experimental projections. We then evaluate the resulting image quality of the developed algorithm through simulations and experiments at the European Synchrotron Radiation Facility on image quality phantoms using the x-ray absorption and phase contrast CT modalities. Both our simulation and experimental results have indicated that the method can reduce the number of projections by 60–75% in parallel beam modalities, while achieving comparable or better image quality than the conventional reconstructions. As large-scale and compact synchrotron radiation facilities are currently under rapid development worldwide, the implementation of low-dose x-ray absorption and phase-contrast CT can find broad applications in biology and medicine using these advanced x-ray sources.

Three-Dimensional Electron Density Mapping of Shape-Controlled Nanoparticle by Focused Hard X-ray Diffraction Microscopy

Coherent diffraction microscopy using highly focused hard X-ray beams allows us to three-dimensionally observe thick objects with a high spatial resolution, also providing us with unique structural information, i.e., electron density distribution, not obtained by X-ray tomography with lenses, atom probe microscopy, or electron tomography. We measured high-contrast coherent X-ray diffraction patterns of a shape-controlled Au/Ag nanoparticle and successfully reconstructed a projection and a three-dimensional image of the nanoparticle with a single pixel (or a voxel) size of 4.2 nm in each dimension. The small pits on the surface and a hollow interior were clearly visible. The Au-rich regions were identified based on the electron density distribution, which provided insight into the formation of Au/Ag nanoboxes.

Hard x-ray nanobeam characterization by coherent diffraction microscopy

We have carried out a ptychographic scanning coherent diffraction imaging experiment on a test object in order to characterize the hard x-ray nanobeam in a scanning x-ray microscope. In addition to a high resolution image of the test object, a detailed quantitative picture of the complex wave field in the nanofocus is obtained with high spatial resolution and dynamic range. Both are the result of high statistics due to the large number of diffraction patterns. The method yields a complete description of the focus, is robust against inaccuracies in sample positioning, and requires no particular shape or prior knowledge of the test object.

Development and Optimization of Regularized Tomographic Reconstruction Algorithms Utilizing Equally-Sloped Tomography

We develop two new algorithms for tomographic reconstruction which incorporate the technique of equally-sloped tomography (EST) and allow for the optimized and flexible implementation of regularization schemes, such as total variation constraints, and the incorporation of arbitrary physical constraints. The founding structure of the developed algorithms is EST, a technique of tomographic acquisition and reconstruction first proposed by Miao in 2005 for performing tomographic image reconstructions from a limited number of noisy projections in an accurate manner by avoiding direct interpolations. EST has recently been successfully applied to coherent diffraction microscopy, electron microscopy, and computed tomography for image enhancement and radiation dose reduction. However, the bottleneck of EST lies in its slow speed due to its higher computation requirements. In this paper, we formulate the EST approach as a constrained problem and subsequently transform it into a series of linear problems, which can be accurately solved by the operator splitting method. Based on these mathematical formulations, we develop two iterative algorithms for tomographic image reconstructions through EST, which incorporate Bregman and continuative regularization. Our numerical experiment results indicate that the new tomographic image reconstruction algorithms not only significantly reduce the computational time, but also improve the image quality. We anticipate that EST coupled with the novel iterative algorithms will find broad applications in X-ray tomography, electron microscopy, coherent diffraction microscopy, and other tomography fields.

Feasibility study of high-resolution coherent diffraction microscopy using synchrotron x rays focused by Kirkpatrick–Baez mirrors

High-flux coherent x rays are necessary for the improvement of the spatial resolution in coherent x-ray diffraction microscopy (CXDM). In this study, high-resolution CXDM using Kirkpatrick–Baez (KB) mirrors is proposed, and the mirrors are designed for experiments of the transmission scheme at SPring-8. Both the photon density and spatial coherence of synchrotron x rays focused by the KB mirrors are investigated by wave optical simulation. The KB mirrors can produce nearly diffraction-limited two-dimensional focusing x rays of ∼1μm in size at 8keV. When the sample size is less than ∼1μm, the sample can be illuminated with full coherent x rays by adjusting the cross-slit size set between the source and the mirrors. From the estimated photon density at the sample position, the feasibility of CXDM with a sub-1-nm spatial resolution is suggested. The present ultraprecise figuring process enables us to fabricate mirrors for carrying out high-resolution CXDM experiments.

Tomographic image alignment in three-dimensional coherent diffraction microscopy

We report the development of a tomographic image alignment method, based on the moment of charge density, for three-dimensional (3D) coherent diffraction microscopy. By using a 3D model system, we demonstrate that the moment of charge density improves the alignment accuracy over the conventional cross-correlation method. Better results are also obtained when we apply this method to the alignment of 27 experimental projections from a ${\text{GaN-Ga}}_{2}{\text{O}}_{3}$ quantum dot nanoparticle.

Coherent diffraction microscopy: present and future

Coherent diffraction microscopy: present and future