In situ coherent diffractive imaging

Nanoscale Three-Dimensional Network Structure of a Mesoporous Particle Unveiled via Adaptive Multidistance Coherent X-ray Tomography

Mesoporous nanoparticles provide rich platforms to devise functional materials by customizing the three-dimensional (3D) structures of nanopores. With the pore network as a key tuning parameter, the noninvasive and quantitative characterization of these 3D structures is crucial for the rational design of functional materials. This has prompted researchers to develop versatile nanoprobes with a high penetration power to inspect various specimens sized a few micrometers at nanoscale 3D resolutions. Here, with adaptive phase retrievals on independent data sets with different sampling frequencies, we introduce multidistance coherent X-ray tomography as a noninvasive and quantitative nanoprobe to realize high-resolution 3D imaging of micrometer-sized specimens. The 3D density distribution of an entire mesoporous silica nanoparticle was obtained at 13 nm 3D resolution for quantitative physical and morphological analyses of its 3D pore structure. The morphological features of the whole 3D pore network and pore connectivity were examined to gain insight into the potential functions of the particles. The proposed multidistance tomographic imaging scheme with quantitative structural analyses is expected to advance studies of functional materials by facilitating their structure-based rational design.

Non-interferometric stand-alone single-shot holographic camera using reciprocal diffractive imaging

An ideal holographic camera measures the amplitude and phase of the light field so that the focus can be numerically adjusted after the acquisition, and depth information about an imaged object can be deduced. The performance of holographic cameras based on reference-assisted holography is significantly limited owing to their vulnerability to vibration and complex optical configurations. Non-interferometric holographic cameras can resolve these issues. However, existing methods require constraints on an object or measurement of multiple-intensity images. In this paper, we present a holographic image sensor that reconstructs the complex amplitude of scattered light from a single-intensity image using reciprocal diffractive imaging. We experimentally demonstrate holographic imaging of three-dimensional diffusive objects and suggest its potential applications by imaging a variety of samples under both static and dynamic conditions.

Optical design of a monolithic compressed folding imaging lens for infrared/laser dual-band

In order to realize the miniaturization of the dual-band system, the monolithic compressed folding imaging lens (CFIL) is designed for infrared/laser dual-band in this paper. The relationship among the back focal length, field of view, pupil diameter, and central obscuration of the CFIL are derived. The design method of the dual-band CFIL is given, and the stray light of the CFIL can be suppressed by the double-layer hood structure. According to the design method of the CFIL, the infrared/laser dual-band can be applied by a monolithic optical element. The design results show that the minimum MTF for all fields of view in the infrared band is greater than 0.125 at 42lp/mm, the spot uniformity in the laser band is greater than 90%, and the total system length is only 0.305 times the focal length. After tolerance analysis, the MTF of CFIL is greater than 0.1, and the spot diagram is less than 880µm. The working temperature of the system is -20∼50°C, and the compensation distance is given. After stray light optimization, The point source transmittance (PST) value in the infrared band is reduced by 2 to 4 orders of magnitude, and the PST value in the laser band is reduced by 1 to 5 orders of magnitude. Compared with the traditional coaxial reflective system, the infrared/laser dual-band CFIL has only one lens, and the optical structure is compact. It provides a new idea for the integration and miniaturization of the multi-band system.

Phase retrieval via nonlocal complex-domain sparsity

Phase retrieval is indispensable for a number of coherent imaging systems. Owing to limited exposure, it is a challenge for traditional phase retrieval algorithms to reconstruct fine details in the presence of noise. In this Letter, we report an iterative framework for noise-robust phase retrieval with high fidelity. In the framework, we investigate nonlocal structural sparsity in the complex domain by low-rank regularization, which effectively suppresses artifacts caused by measurement noise. The joint optimization of sparsity regularization and data fidelity with forward models enables satisfying detail recovery. To further improve computational efficiency, we develop an adaptive iteration strategy that automatically adjusts matching frequency. The effectiveness of the reported technique has been validated for coherent diffraction imaging and Fourier ptychography, with ≈7 dB higher peak SNR (PSNR) on average, compared with conventional alternating projection reconstruction.

Phase retrieval with a dual recursive scheme

Since optical sensors cannot detect the phase information of the light wave, recovering the missing phase from the intensity measurements, called phase retrieval (PR), is a natural and important problem in many imaging applications. In this paper, we propose a learning-based recursive dual alternating direction method of multipliers, called RD-ADMM, for phase retrieval with a dual and recursive scheme. This method tackles the PR problem by solving the primal and dual problems separately. We design a dual structure to take advantage of the information embedded in the dual problem that can help with solving the PR problem, and we show that it is feasible to use the same operator for both the primal and dual problems for regularization. To demonstrate the efficiency of this scheme, we propose a learning-based coded holographic coherent diffractive imaging system to generate the reference pattern automatically according to the intensity information of the latent complex-valued wavefront. Experiments on different kinds of images with a high noise level indicate that our method is effective and robust, and can provide higher-quality results than other commonly-used PR methods for this setup.

Integrative modeling of the cell

A whole-cell model represents certain aspects of the cell structure and/or function. Due to the high complexity of the cell, an integrative modeling approach is often taken to utilize all available information including experimental data, prior knowledge and prior models. In this review, we summarize an emerging workflow of whole-cell modeling into five steps: (i) gather information; (ii) represent the modeled system into modules; (iii) translate input information into scoring function; (iv) sample the whole-cell model; (v) validate and interpret the model. In particular, we propose the integrative modeling of the cell by combining available (whole-cell) models to maximize the accuracy, precision, and completeness. In addition, we list quantitative predictions of various aspects of cell biology from existing whole-cell models. Moreover, we discuss the remaining challenges and future directions, and highlight the opportunity to establish an integrative spatiotemporal multi-scale whole-cell model based on a community approach.

Iterative phase retrieval with a sensor mask

As an important inverse imaging problem in diffraction optics, Fourier phase retrieval aims at estimating the latent image of the target object only from the magnitude of its Fourier measurement. Although in real applications alternating methods are widely-used for Fourier phase retrieval considering the constraints in the object and Fourier domains, they need a lot of initial guesses and iterations to achieve reasonable results. In this paper, we show that a proper sensor mask directly attached to the Fourier magnitude can improve the efficiency of the iterative phase retrieval algorithms, such as alternating direction method of multipliers (ADMM). Furthermore, we refer to the learning-based method to determine the sensor mask according to the Fourier measurement, and unrolled ADMM is used for phase retrieval. Numerical results show that our method outperforms other existing methods for the Fourier phase retrieval problem.

Multi-slice ptychographic imaging with multistage coarse-to-fine reconstruction

The ability to image 3D samples with optical sectioning is essential for the study of tomographic morphology in material and biological sciences. However, it is often hampered by limitations of acquisition speed and equipment complexity when performing 3D volumetric imaging. Here, we propose, to the best of our knowledge, a new method for 3D reconstruction from a minimum of four intensity-only measurements. The complementary structured patterns provided by the digital micromirror device (DMD) irradiate the outermost layer of the sample to generate the corresponding diffraction intensities for recording, which enables rapid scanning of loaded patterns for fast acquisition. Our multistage reconstruction algorithm first extracts the overall coarse-grained information, and then iteratively optimizes the information of different layers to obtain fine features, thereby achieving high-resolution 3D tomography. The high-fidelity reconstruction in experiments on two-slice resolution targets, unstained Polyrhachis vicina Roger and freely moving C. elegans proves the robustness of the method. Compared with traditional 3D reconstruction methods such as interferometry-based methods or Fourier ptychographic tomography (FPT), our method increases the reconstruction speed by at least 10 times and is suitable for label-free dynamic imaging in multiple-scattering samples. Such 3D reconstruction suggests potential applications in a wide range of fields.

Towards kilohertz synchrotron coherent diffractive imaging

This work shows how spatiotemporal redundancy can overcome the twin-image stagnation mode in coherent diffractive imaging, and explores the relationship between detector frame rate and signal-to-noise ratio in the application of imaging nanoscale dynamic behaviour at kHz frame rates.

X-ray coherent diffractive imaging (CDI) techniques have been applied with widespread impact to study nanoscale material properties. New fast framing detectors may reveal dynamics that occur at millisecond timescales. This work demonstrates by simulation that kilohertz synchrotron CDI is possible, by making use of redundant information from static parts of the image field. Reconstruction ambiguities are strongly suppressed by applying a spatio­temporal constraint, obviating the need for slower methods of introducing diversity such as ptychography. The relationship between image fidelity and time resolution is investigated and shows that dynamics an order of magnitude faster can be reconstructed, compared with conventional CDI.

X-ray Spectroptychography

X-ray spectroptychography is an emerging method for the chemical microanalysis of advanced nanomaterials such as catalysts and batteries. This method builds upon established synchrotron X-ray microscopy and spectromicroscopy techniques with added spatial resolution from ptychography, an algorithmic imaging technique. This minireview will introduce the technique of X-ray spectroptychography, where ptychography is performed with variable photon energy, and discuss recent results and prospects for this method.

Methods of Coherent X-Ray Diffraction Imaging

Abstract

Methods of coherent X-ray diffraction imaging of the spatial structure of noncrystalline objects and nanocrystals (nanostructures) are considered. Particular attention is paid to the methods of scanning-based coherent diffraction imaging (ptychography), visualization based on coherent surface scattering with application of correlation spectroscopy approaches, and specific features of visualization using X-ray free-electron laser radiation. The corresponding data in the literature are analyzed to demonstrate the state of the art of the methods of coherent diffraction imaging and fields of their application.

Spatiotemporal coherent modulation imaging for dynamic quantitative phase and amplitude microscopy

The single-shot capability of coherent modulation imaging (CMI) makes it have great potential in the investigation of dynamic processes. Its main disadvantage is the relatively low signal-to-noise ratio (SNR) which affects the spatial resolution and reconstruction accuracy. Here, we propose the improvement of a general spatiotemporal CMI method for imaging of dynamic processes. By making use of the redundant information in time-series reconstructions, the spatiotemporal CMI can achieve robust and fast reconstruction with higher SNR and spatial resolution. The method is validated by numerical simulations and optical experiments. We combine the CMI module with an optical microscope to achieve quantitative phase and amplitude reconstruction of dynamic biological processes. With the reconstructed complex field, we also demonstrate the 3D digital refocusing ability of the CMI microscope. With further development, we expect the spatiotemporal CMI method can be applied to study a range of dynamic phenomena.

Ultrafast high-harmonic nanoscopy of magnetization dynamics

Light-induced magnetization changes, such as all-optical switching, skyrmion nucleation, and intersite spin transfer, unfold on temporal and spatial scales down to femtoseconds and nanometers, respectively. Pump-probe spectroscopy and diffraction studies indicate that spatio-temporal dynamics may drastically affect the non-equilibrium magnetic evolution. Yet, direct real-space magnetic imaging on the relevant timescales has remained challenging. Here, we demonstrate ultrafast high-harmonic nanoscopy employing circularly polarized high-harmonic radiation for real-space imaging of femtosecond magnetization dynamics. We map quenched magnetic domains and localized spin structures in Co/Pd multilayers with a sub-wavelength spatial resolution down to 16 nm, and strobosocopically trace the local magnetization dynamics with 40 fs temporal resolution. Our compact experimental setup demonstrates the highest spatio-temporal resolution of magneto-optical imaging to date. Facilitating ultrafast imaging with high sensitivity to chiral and linear dichroism, we envisage a wide range of applications spanning magnetism, phase transitions, and carrier dynamics.

Quantitative reconstruction of the complex-valued object based on complementary phase modulations

In the coherent diffraction imaging (CDI) techniques, a key point is to reconstruct the complex-valued object from the far-field intensity measurements, i.e., solving the phase retrieval problem. However, due to this ill-posed problem, traditional phase retrieval algorithms often encounter some problems associated with the iteration convergence. In this work, complementary phase modulations (CPM) are introduced to generate different far-field intensity measurements. The namely CPM-based method aims to find out the global optimal solution by imposing multi-dimensional constraints, including the diverse intensity images at the Fourier plane and the CPM at the object plane. It is proved by the numerical simulations and the optical experiments that the convergence speed and the recovery accuracy could be greatly improved. Furthermore, the shifting complementary phase modulations (SCPM)-based method is proposed by introducing more CPMs. The reconstruction performance is further improved even when the phase range is larger, and the support constraints are not required. In addition, the SCPM-based method is more robust to the Poisson noise. With the outstanding reconstruction performance, the CPM-based methods may be helpful to phase imaging in the application of visible-light microscopy and X-ray imaging.

Demonstration of single-frame coherent X-ray diffraction imaging using triangular aperture: Towards dynamic nanoimaging of extended objects

Coherent diffraction imaging (CDI) is a powerful method for visualizing the structure of an object with a high spatial resolution that exceeds the performance limits of the lens. Single-frame CDI in the X-ray region has potential use for probing dynamic phenomena with a high spatiotemporal resolution. Here, we experimentally demonstrate a general method for single-frame X-ray CDI using a triangular aperture and a Fresnel zone plate. Using 5 keV synchrotron radiation X-rays, we reconstructed the object image of the locally illuminated area with a spatial resolution of higher than 50 nm and an exposure time of more than 0.1 s without prior information about the sample. After a 10 s exposure, a resolution of 17 nm was achieved. The present method opens new frontiers in the study of dynamics at the nanoscale by using next-generation synchrotron radiation X-rays/free-electron lasers as light sources.

X-ray-Based Techniques to Study the Nano-Bio Interface

X-ray-based analytics are routinely applied in many fields, including physics, chemistry, materials science, and engineering. The full potential of such techniques in the life sciences and medicine, however, has not yet been fully exploited. We highlight current and upcoming advances in this direction. We describe different X-ray-based methodologies (including those performed at synchrotron light sources and X-ray free-electron lasers) and their potentials for application to investigate the nano-bio interface. The discussion is predominantly guided by asking how such methods could better help to understand and to improve nanoparticle-based drug delivery, though the concepts also apply to nano-bio interactions in general. We discuss current limitations and how they might be overcome, particularly for future use in vivo.

Illuminating the Brain With X-Rays: Contributions and Future Perspectives of High-Resolution Microtomography to Neuroscience

The assessment of three-dimensional (3D) brain cytoarchitecture at a cellular resolution remains a great challenge in the field of neuroscience and constant development of imaging techniques has become crucial, particularly when it comes to offering direct and clear obtention of data from macro to nano scales. Magnetic resonance imaging (MRI) and electron or optical microscopy, although valuable, still face some issues such as the lack of contrast and extensive sample preparation protocols. In this context, x-ray microtomography (μCT) has become a promising non-destructive tool for imaging a broad range of samples, from dense materials to soft biological specimens. It is a new supplemental method to be explored for deciphering the cytoarchitecture and connectivity of the brain. This review aims to bring together published works using x-ray μCT in neurobiology in order to discuss the achievements made so far and the future of this technique for neuroscience.

Dynamic coherent diffractive imaging using unsupervised identification of spatiotemporal constraints

Dynamic coherent diffractive imaging (CDI) reveals the fine details of structural, chemical, and biological processes occurring at the nanoscale but imposes strict constraints on the object distribution and illumination. Ptychographic CDI relaxes these constraints by exploiting redundant information in data obtained from overlapping regions of an object, but its time resolution is inherently limited. We have extended ptychographic redundancy into the spatiotemporal domain in dynamic CDI, automatically identifying redundant information in time-series coherent diffraction data obtained from dynamic systems. Simulated synchrotron experiments show that high spatiotemporal resolution is achieved without a priori knowledge of the object or its dynamics.

Phase retrieval of a Kolmogorov phase screen from very sparse data using four binary masks

We investigate experimentally the phase retrieval of a Kolmogorov phase screen from very sparse data by modulating its amplitude with four binary masks and compare the retrieved phase screen to the ground truth measured with a surface profiler. Previously, we have shown in simulations that this kind of modulation can be successfully used for the phase retrieval of a Kolmogorov phase screen. After subtracting the ground truth from the retrieved phase screen, the root-mean-square error decreased from 0.14 µm to 0.10 µm. We conclude that a Kolmogorov phase screen can be recovered using simple modulation and very sparse data.

Combining Laue diffraction with Bragg coherent diffraction imaging at 34-ID-C

Measurement modalities in Bragg coherent diffraction imaging (BCDI) rely on finding a signal from a single nanoscale crystal object which satisfies the Bragg condition among a large number of arbitrarily oriented nanocrystals. However, even when the signal from a single Bragg reflection with (hkl) Miller indices is found, the crystallographic axes on the retrieved three-dimensional (3D) image of the crystal remain unknown, and thus localizing in reciprocal space other Bragg reflections becomes time-consuming or requires good knowledge of the orientation of the crystal. Here, the commissioning of a movable double-bounce Si (111) monochromator at the 34-ID-C endstation of the Advanced Photon Source is reported, which aims at delivering multi-reflection BCDI as a standard tool in a single beamline instrument. The new instrument enables, through rapid switching from monochromatic to broadband (pink) beam, the use of Laue diffraction to determine crystal orientation. With a proper orientation matrix determined for the lattice, one can measure coherent diffraction patterns near multiple Bragg peaks, thus providing sufficient information to image the full strain tensor in 3D. The design, concept of operation, the developed procedures for indexing Laue patterns, and automated measuring of Bragg coherent diffraction data from multiple reflections of the same nanocrystal are discussed.

Laser-induced metastable mixed phase of AuNi nanoparticles: a coherent X-ray diffraction imaging study

The laser annealing process for AuNi nanoparticles has been visualized using coherent X-ray diffraction imaging (CXDI). AuNi bimetallic alloy nanoparticles, originally phase separated due to the miscibility gap, transform to metastable mixed alloy particles with rounded surface as they are irradiated by laser pulses. A three-dimensional CXDI shows that the internal part of the AuNi particles is in the mixed phase with preferred compositions at ∼29 at% of Au and ∼90 at% of Au.

Direct 2D spatial-coherence determination using the Fourier-analysis method: multi-parameter characterization of the P04 beamline at PETRA III

We present a systematic 2D spatial-coherence analysis of the soft-X-ray beamline P04 at PETRA III for various beamline configurations. The influence of two different beam-defining apertures on the spatial coherence properties of the beam is discussed and optimal conditions for coherence-based experiments are found. A significant degradation of the spatial coherence in the vertical direction has been measured and sources of this degradation are identified and discussed. The Fourier-analysis method, which gives fast and simple access to the 2D spatial coherence function of the X-ray beam, is used for the experiment. Here, we exploit the charge scattering of a disordered nanodot sample allowing the use of arbitrary X-ray photon energies with this method.

Synchrotron Scattering Methods for Nanomaterials and Soft Matter Research

This article aims to provide an overview of broad range of applications of synchrotron scattering methods in the investigation of nanoscale materials. These scattering techniques allow the elucidation of the structure and dynamics of nanomaterials from sub-nm to micron size scales and down to sub-millisecond time ranges both in bulk and at interfaces. A major advantage of scattering methods is that they provide the ensemble averaged information under in situ and operando conditions. As a result, they are complementary to various imaging techniques which reveal more local information. Scattering methods are particularly suitable for probing buried structures that are difficult to image. Although, many qualitative features can be directly extracted from scattering data, derivation of detailed structural and dynamical information requires quantitative modeling. The fourth-generation synchrotron sources open new possibilities for investigating these complex systems by exploiting the enhanced brightness and coherence properties of X-rays.

Semi-implicit relaxed Douglas-Rachford algorithm (sDR) for ptychography

Alternating projection based methods, such as ePIE and rPIE, have been used widely in ptychography. However, they only work well if there are adequate measurements (diffraction patterns); in the case of sparse data (i.e. fewer measurements) alternating projection underperforms and might not even converge. In this paper, we propose semi-implicit relaxed Douglas-Rachford (sDR), an accelerated iterative method, to solve the classical ptychography problem. Using both simulated and experimental data, we show that sDR improves the convergence speed and the reconstruction quality relative to extended ptychographic iterative engine (ePIE) and regularized ptychographic iterative engine (rPIE). Furthermore, in certain cases when sparsity is high, sDR converges while ePIE and rPIE fail or encounter slow convergence. To facilitate others to use the algorithm, we post the Matlab source code of sDR on a public website (www.physics.ucla.edu/research/imaging/sDR/index.html). We anticipate that this algorithm can be generally applied to the ptychographic reconstruction of a wide range of samples in the physical and biological sciences.

Phase retrieval with extended field of view based on continuous phase modulation

In order to address two main obstacles that affect the practical application of coherent modulation imaging (CMI)i.e., the low signal-to-noise ratio (SNR) and limited field of view (FOV), a new algorithm providing extended FOV based on CMI is proposed. A weak scattering modulator was used instead of a binary random phase modulator with strong scattering ability, to improve the final resolution of CMI combined with probe scanning. An unlimited FOV was achieved in a noniterative manner, resulting in a superior SNR compared with ptychography. Compared with the original CMI with a binary random phase modulator, the errors decreased obviously when continuous phase plate was utilized based on simulation and experimental results. Moreover, the random speckles that are associated with coherent diffractive imaging could be effectively eliminated. The proposed algorithm facilitates single-shot or extended FOV phase imaging with a high SNR and high resolution.

Three-dimensional optical trapping and orientation of microparticles for coherent X-ray diffraction imaging

Optical trapping has been implemented in many areas of physics and biology as a noncontact sample manipulation technique to study the structure and dynamics of nano- and mesoscale objects. It provides a unique approach for manipulating microscopic objects without inducing undesired changes in structure. Combining optical trapping with hard X-ray microscopy techniques, such as coherent diffraction imaging and crystallography, provides a nonperturbing environment where electronic and structural dynamics of an individual particle in solution can be followed in situ. It was previously shown that optical trapping allows the manipulation of micrometer-sized objects for X-ray fluorescence imaging. However, questions remain over the ability of optical trapping to position objects for X-ray diffraction measurements, which have stringent requirements for angular stability. Our work demonstrates that dynamic holographic optical tweezers are capable of manipulating single micrometer-scale anisotropic particles in a microfluidic environment with the precision and stability required for X-ray Bragg diffraction experiments-thus functioning as an "optical goniometer." The methodology can be extended to a variety of X-ray experiments and the Bragg coherent diffractive imaging of individual particles in solution, as demonstrated here, will be markedly enhanced with the advent of brighter, coherent X-ray sources.