Progress in Three-Dimensional Coherent X-Ray Diffraction Imaging
S. Marchesini, H. N. Chapman, A. Barty, A. Noy, S. P. Hau-Riege, J. M. Kinney, C. Cui, M. R. Howells, R. Rosen, J. C. H. Spence, U. Weierstall, D. Shapiro, T. B… 展开作者
S. Marchesini, H. N. Chapman, A. Barty, A. Noy, S. P. Hau-Riege, J. M. Kinney, C. Cui, M. R. Howells, R. Rosen, J. C. H. Spence, U. Weierstall, D. Shapiro, T. Beetz, C. Jacobsen, E. Lima, A. M. Minor, H. He
The Fourier inversion of phased coherent diffraction patterns offers images without the resolution and depth-of-focus limitations of lens-based tomographic systems. We report on our recent experimental images inverted using recent developments in phase retrieval algorithms, and summarize efforts that led to these accomplishments. These include ab-initio reconstruction of a two-dimensional test pattern, infinite depth of focus image of a thick object, and its high-resolution (~10 nm resolution) three-dimensional image. Developments on the structural imaging of low density aerogel samples are discussed.
Coherent diffraction imaging is a high-resolution imaging technique whose potential can be greatly enhanced by applying the extrapolation method presented here. We demonstrate enhancement in resolution of a non-periodical object reconstructed from an experimental X-ray diffraction record which contains about 10% missing information, including the pixels in the center of the diffraction pattern. A diffraction pattern is extrapolated beyond the detector area and as a result, the object is reconstructed at an enhanced resolution and better agreement with experimental amplitudes is achieved. The o…
We report on the experimental findings of a thin-slit grid diffraction of a coherent light beam with sinusoidal amplitude. We create the sinusoidal amplitude by placing a thin-slit grid at the center of the dark fringes of an interference pattern resulting from laser light passing through a dual pinhole. The experimental results show good agreement with diffraction calculations of a thin-slit grid placed at the center of the dark fringes produced by two coherent beams that intersect at small angle. The results are applied to wire-grid diffraction in the Afshar experiment.
We propose and experimentally demonstrate temporally low-coherent optical diffraction tomography (ODT) based on angle-scanning Mach-Zehnder interferometry. Using a digital micromirror device based on diffractive tilting, we successfully maintain full-field interference of incoherent light during every scan sequence. The ODT reconstruction principles for temporally incoherent illuminations are thoroughly reviewed and developed. Several limitations of incoherent illumination are also discussed, such as the nondispersive assumption, optical sectioning capacity, and illumination angle limitation. …
We present a fiber-diffraction interferometer using a coherent fiber optic taper for optical testing in an uncontrolled environment. We use a coherent fiber optic taper and a single-mode fiber having thermally-expanded core. Part of the measurement wave coming from a test target is condensed through a fiber optic taper and spatially filtered from a single-mode fiber to be reference wave. Vibration of the cavity between the target and the interferometer probe is common to both reference and measurement waves, thus the interference fringe is stabilized in an optical way. Generation of the refere…
Conventional microscopic records represent intensity distributions whereby local sample information is mapped onto local information at the detector. In coherent microscopy, the superposition principle of waves holds; field amplitudes are added, not intensities. This non-local representation is spread out in space and interference information combined with wave continuity allows extrapolation beyond the actual detected data. Established resolution criteria are thus circumvented and hidden object details can retrospectively be recovered from just a fraction of an interference pattern.
The evolution from 3rd to 4th generation synchrotron radiation (SR) sources significantly enhanced their coherence, making coherent scattering techniques such as coherent X-ray diffraction imaging (CXDI) and X-ray photon correlation spectroscopy (XPCS) more accessible. We take advantage of a coherent modes decomposition and propagation model to carry out coherence analysis and simulations of CXDI experiments for the coherent Hard X-ray Coherent Scattering (HXCS) beamline at High Energy Photon Source.
Modern imaging techniques at the molecular scale rely on utilizing novel coherent light sources like X-ray free electron lasers for the ultimate goal of visualizing such objects as individual biomolecules rather than crystals. Here, unlike in the case of crystals where structures can be solved by model building and phase refinement, the phase distribution of the wave scattered by an individual molecule must directly be recovered. There are two well-known solutions to the phase problem: holography and coherent diffraction imaging (CDI). Both techniques have their pros and cons. In holography, t…
Quantum interference is shown to deliver a means of regulating the diffraction pattern of a thermal atomic beam interacting with two standing wave electric fields. Parameters have been identified to enhance the diffraction probability of one momentum component over the others, with specific application to Rb atoms.
Free space delay lines provide pulses of variable time spacing for optical experiments such as pump-probe spectroscopy and coherent quantum control, including spin and photon echo techniques. However, in the terahertz (THz) region of the spectrum, beam divergence due to diffraction limits the useful length of traditional free space delay lines. We present a novel double-folded variable delay line for light in the frequency range 0.24-1.2 THz, which incorporates a symmetric arrangement of lenses whose spacing can be adjusted to compensate for diffraction at each delay. Scalable for use in other…
Coherent diffraction imaging (CDI) for visualizing objects at atomic resolution has been realized as a promising tool for imaging single molecules. Drawbacks of CDI are associated with the difficulty of the numerical phase retrieval from experimental diffraction patterns; a fact which stimulated search for better numerical methods and alternative experimental techniques. Common phase retrieval methods are based on iterative procedures which propagate the complex-valued wave between object and detector plane. Constraints in both, the object and the detector plane are applied. While the constrai…
Laser-induced transient opacity in helium nanodroplets probed by single-shot coherent diffraction
ETH Zurich（苏黎世联邦理工学院）；University of Rostock（罗斯托克大学）；Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy（马克斯·玻恩非线性光学和超快光谱研究所）；Technical University of Berlin（柏林工业大学）
We present a novel adaptive machine-learning based approach for reconstructing three-dimensional (3D) crystals from coherent diffraction imaging (CDI). We represent the crystals using spherical harmonics (SH) and generate corresponding synthetic diffraction patterns. We utilize 3D convolutional neural networks (CNN) to learn a mapping between 3D diffraction volumes and the SH which describe the boundary of the physical volumes from which they were generated. We use the 3D CNN-predicted SH coefficients as the initial guesses which are then fine tuned using adaptive model independent feedback fo…
We demonstrate that the resolution of three-dimensional (3D) real-space images obtained from Bragg x-ray coherent diffraction measurements is direction dependent. We propose and demonstrate the effectiveness of a metric to determine the spatial resolution of images that accounts for the direc- tional dependence. The measured direction dependent resolution of ~ 4-9nm is about 2 times higher than the best previously obtained 3D measurements. Finally, we quantify the relationship between the resolution of recovered real-space images and dosage, and discuss its implications in the light of next ge…
Unveiling Nano-scale Crystal Deformation using Coherent X-ray Dynamical Diffraction
Shanghai Advanced Research Institute, Chinese Academy of Sciences（上海高等研究院，中国科学院）；Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory（布鲁克海文国家实验室凝聚态物理与材料科学部）；Department of Physics, University of Science and Technology of China（中国科学技术大学物理学院）；Computational Science Initiative, Brookhaven National Laboratory（布鲁克海文国家实验室计算科学倡议）；Advanced Photon Source, Argonne National Laboratory（阿贡国家实验室先进光子源）；London Centre for Nanotechnology, University College London（伦敦纳米技术中心，伦敦大学学院）
The inversion of a diffraction pattern offers aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems, the only limitation being radiation damage. We review our experimental results, discuss the fundamental limits of this technique and future plans.
Coherent Diffraction Imaging (CDI), a technique where an object is reconstructed from a single (2D or 3D) diffraction pattern, recovers the lost diffraction phases without a priori knowledge of the extent (support) of the object, which prevents an unambiguous metric evaluation of solutions. We propose to use a 'free' log-likelihood indicator, where a small percentage of points are masked from the reconstruction algorithms, as an unbiased metric to evaluate the validity of proposed solutions, independent of the sample studied. We also show how a set of solutions can be analysed through an eigen…
In coherent diffractive imaging (CDI) the resolution of the reconstructed object is limited by the numerical aperture of the experimental setup. We present here a theoretical and numerical study for achieving super-resolution by post-extrapolation of coherent diffraction images, such as diffraction patterns or holograms. We demonstrate that a diffraction pattern can unambiguously be extrapolated from only a fraction of the entire pattern and that the ratio of the extrapolated signal to the originally available signal is linearly proportional to the oversampling ratio. While there could be in p…
In coherent X-ray diffraction microscopy the diffraction pattern generated by a sample illuminated with coherent x-rays is recorded, and a computer algorithm recovers the unmeasured phases to synthesize an image. By avoiding the use of a lens the resolution is limited, in principle, only by the largest scattering angles recorded. However, the imaging task is shifted from the experiment to the computer, and the algorithm's ability to recover meaningful images in the presence of noise and limited prior knowledge may produce aberrations in the reconstructed image. We analyze the low order aberrat…
Coherent X-ray beams with energies $\geq 50$ keV can potentially enable three-dimensional imaging of atomic lattice distortion fields within individual crystallites in bulk polycrystalline materials through Bragg coherent diffraction imaging (BCDI). However, the undersampling of the diffraction signal due to Fourier space compression at high X-ray energies renders conventional phase retrieval algorithms unsuitable for three-dimensional reconstruction. To address this problem we utilize a phase retrieval method with a Fourier constraint specifically tailored for undersampled diffraction data me…
Optical diffraction tomography is an indispensable tool for studying objects in three-dimensions due to its ability to accurately reconstruct scattering objects. Until now this technique has been limited to coherent light because spatial phase information is required to solve the inverse scattering problem. We introduce a method that extends optical diffraction tomography to imaging spatially incoherent contrast mechanisms such as fluorescent emission. Our strategy mimics the coherent scattering process with two spatially coherent illumination beams. The interferometric illumination pattern en…
We generalize the notion of the Franhoufer diffraction from a single slit and a circular aperture to the case of partially temporal coherent and quasimonochromatic light. The problem is studied analytically and the effect of coherence length on the diffraction pattern is investigated. In this case the far-field distribution of the irradiance depends on the newly introduced parameter(decoherence parameter) which governs the deviation of the diffraction pattern from the usual one. The corrections due to temporal decoherency on the irradiance distribution in the far field is obtained. Numerical s…
Recent advances in the field of attosecond science hold the promise of tracking electronic processes at the shortest space and time scales. Imaging methods that combine attosecond temporal with nanometer spatial resolution are currently out of reach. Coherent diffractive imaging is based on the diffraction by a sample of a quasi-monochromatic illumination with a coherence time that exceeds the duration of an attosecond pulse. Due to the extremely broad nature of attosecond spectra, novel imaging techniques are required. Here, we present an approach that enables coherent diffractive imaging wit…
The history of computing started with analog computers consisting of physical devices performing specialized functions such as predicting the trajectory of cannon balls. In modern times, this idea has been extended, for example, to ultrafast nonlinear optics serving as a surrogate analog computer to probe the behavior of complex phenomena such as rogue waves. Here we discuss a new paradigm where physical phenomena coded as an algorithm perform computational imaging tasks. Specifically, diffraction followed by coherent detection, not in its analog realization but when coded as an algorithm, bec…
Dynamical diffraction effects in single crystals produce highly monochromatic parallel X-ray beams with a mutual separation of a few micrometer and a time-delay of a few fs -the so-called echoes. This ultrafast diffraction effect is used at X-ray Free Electron Lasers in self-seeding schemes to improve beam monochromaticity. Here, we present a coherent X-ray imaging measurement of echoes from Si crystals and demonstrate that a small surface strain can be used to tune their temporal delay. These results represent a first step towards the ambitious goal of strain-tailoring new X-ray optics.
We present a deep neural network to reduce coherent noise in three-dimensional quantitative phase imaging. Inspired by the cycle generative adversarial network, the denoising network was trained to learn a transform between two image domains: clean and noisy refractive index tomograms. The unique feature of this network, distinct from previous machine learning approaches employed in the optical imaging problem, is that it uses unpaired images. The learned network quantitatively demonstrated its performance and generalization capability through denoising experiments of various samples. We concl…
A structural understanding of whole cells in three dimensions at high spatial resolution remains a significant challenge and, in the case of X-rays, has been limited by radiation damage. By alleviating this limitation, cryogenic coherent diffraction imaging (cryo-CDI) could bridge the important resolution gap between optical and electron microscopy in bio-imaging. Here, we report for the first time 3D cryo-CDI of a whole, frozen-hydrated cell - in this case a Neospora caninum tachyzoite - using 8 keV X-rays. Our 3D reconstruction reveals the surface and internal morphology of the cell, includi…
We propose a method to generate isolated relativistic terahertz (THz) pulses using a high-power laser irradiating a mirco-plasma-waveguide (MPW). When the laser pulse enters the MPW, high-charge electron bunches are produced and accelerated to ~ 100 MeV by the transverse magnetic modes. A substantial part of the electron energy is transferred to THz emission through coherent diffraction radiation as the electron bunches exit the MPW. We demonstrate this process with three-dimensional particle-in-cell simulations. The frequency of the radiation is determined by the incident laser duration, and …
Coherent diffraction imaging (CDI) is a promising imaging technique revealing most of the information from diffraction measurements. An ideal CDI should reconstruct complex-valued object from a single-shot far-field diffraction without any priori information about the target. To realize the ideal CDI, we propose a class of parameter-robust illumination pattern. A direct phase optimizing algorithm is also raised here to improve the performance of phase retrieval in strong noise. Experimental result demonstrates the efficiency of our scheme in practical noisy measurement for complex-valued targe…
Rice University（莱斯大学）；Northwestern University（西北大学）；California Institute of Technology（加州理工学院）
In this work, we propose using camera arrays coupled with coherent illumination as an effective method of improving spatial resolution in long distance images by a factor of ten and beyond. Recent advances in ptychography have demonstrated that one can image beyond the diffraction limit of the objective lens in a microscope. We demonstrate a similar imaging system to image beyond the diffraction limit in long range imaging. We emulate a camera array with a single camera attached to an X-Y translation stage. We show that an appropriate phase retrieval based reconstruction algorithm can be used …
When a coherent quasi-monochromatic light is reflected from a step, a diffraction pattern is formed that can be described by Fresnel-Kirchhoff integral and visibility of the fringes depends on the height of the step. In this paper, it is shown that the Fresnel diffraction from a step can be described by an interference-like formula. A relationship is derived between the visibility of the diffraction pattern from 1D step and the step height. Finally, a novel method is presented for 1D surface testing. The theoretical and experimental results are presented.
Ultra-low density polymers, metals, and ceramic nanofoams are valued for their high strength-to-weight ratio, high surface area and insulating properties ascribed to their structural geometry. We obtain the labrynthine internal structure of a tantalum oxide nanofoam by X-ray diffractive imaging. Finite element analysis from the structure reveals mechanical properties consistent with bulk samples and with a diffusion limited cluster aggregation model, while excess mass on the nodes discounts the dangling fragments hypothesis of percolation theory.
Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）
A new reference design is introduced for holographic coherent diffraction imaging. This consists in two references - "block" and "pinhole" shaped regions - placed adjacent to the imaging specimen. An efficient recovery algorithm is provided for the resulting holographic phase retrieval problem, which is based on solving a structured, overdetermined linear system. Analysis of the expected recovery error on noisy data, which is contaminated by Poisson shot noise, shows that this simple modification synergizes the individual references and hence leads to uniformly superior performance over single…
Coherent diffractive imaging (CDI) provides new opportunities for high resolution X-ray imaging with simultaneous amplitude and phase contrast. Extensions to CDI broaden the scope of the technique for use in a wide variety of experimental geometries and physical systems. Here, we experimentally demonstrate a new extension to CDI that encodes additional information through the use of a series of randomly coded masks. The information gained from the few additional diffraction measurements removes the need for typical object-domain constraints; the algorithm uses prior information about the masks…
Complex-field imaging is indispensable for numerous applications at wavelengths from X-ray to THz, with amplitude describing transmittance (or reflectivity) and phase revealing intrinsic structure of the target object. Coherent diffraction imaging (CDI) employs iterative phase retrieval algorithms to process diffraction measurements and is the predominant non-interferometric method to image complex fields. However, the working spectrum of CDI is quite narrow, because the diffraction measurements on which it relies require dense array detection with ultra-high dynamic range. Here we report a si…
Coherent diffraction imaging (CDI) allows the retrieval of the structure of an isolated object, such as a macromolecule, from its diffraction pattern. CDI requires the fulfilment of two conditions: the imaging radiation must be coherent and the object must be isolated. We discuss that it is possible to directly retrieve the molecular structure from its diffraction pattern which was acquired neither with coherent radiation nor from an individual molecule, provided the molecule exhibits periodicity in one direction, as in the case of fiber diffraction. We demonstrate that by applying iterative p…
We demonstrate a three-dimensional (3D) optical diffraction tomographic technique with optimal frequency combination (OFC-ODT) for the 3D quantitative phase imaging of unlabeled specimens. Three sets of through-focus intensity images are captured under an annular aperture and two circular apertures with different coherence parameters. The 3D phase optical transfer functions (POTF) corresponding to different illumination apertures are combined to obtain an optimally synthesized frequency response, achieving high-quality, low-noise 3D reconstructions with imaging resolution up to the incoherent …
Single particle diffraction imaging experiments at free-electron lasers (FEL) have a great potential for structure determination of reproducible biological specimens that can not be crystallized. One of the challenges in processing the data from such an experiment is to determine correct orientation of each diffraction pattern from samples randomly injected in the FEL beam. We propose an algorithm (see also O. Yefanov et al., Photon Science - HASYLAB Annual Report 2010) that can solve this problem and can be applied to samples from tens of nanometers to microns in size, measured with sub-nanom…
We reconstructed the 3D Fourier intensity distribution of mono-disperse prolate nano-particles using single-shot 2D coherent diffraction patterns collected at DESY's FLASH facility when a bright, coherent, ultrafast X-ray pulse intercepted individual particles of random, unmeasured orientations. This first experimental demonstration of cryptotomography extended the Expansion-Maximization-Compression (EMC) framework to accommodate unmeasured fluctuations in photon fluence and loss of data due to saturation or background scatter. This work is an important step towards realizing single-shot diffr…
The current state of the art in structural biology is led by NMR, X-ray crystallography and TEM investigations. These powerful tools however all rely on averaging over a large ensemble of molecules. Here, we present an alternative concept aiming at structural analysis at the single molecule level. We show that by combining electron holography and coherent diffraction imaging estimations concerning the phase of the scattered wave become needless as the phase information is extracted from the data directly and unambiguously. Performed with low-energy electrons the resolution of this lens-less mi…
Lensless imaging is a popular research field for the advantages of small size, wide field-of-view and low aberration in recent years. However, some traditional lensless imaging methods suffer from slow convergence, mechanical errors and conjugate solution interference, which limit its further application and development. In this work, we proposed a lensless imaging method based on spatial light modulator (SLM) with unknown modulation curve. In our imaging system, we use SLM to modulate the wavefront of object, and introduce the ptychographic scanning algorithm that is able to recover the compl…
Coherent diffractive imaging is a technique that recovers the sample image by numerically inverting its diffraction pattern. We propose a generalization of this method for the inversion of multi-wavelength data. Using this approach, we show that separate reconstructions for each wavelength can be recovered from a single polychromatic diffraction pattern. Limitations on the number of wavelengths is provided by adapting the constraint ratio to the polychromatic situation. The method's performance is demonstrated as a function of the source spectrum, the degree of complexity within the exit wave …
