Modern microscopy techniques are developing towards high-resolution imaging, and tremendous progress has been made in past decades; however, the imaging of individual biological macromolecules at atomic resolution using short-wavelength radiation such as electrons or X-rays has not yet been achieved. The construction of free-electron lasers in many countries around the world arises from the desire to develop new imaging techniques by employing coherent radiation to image individual macromolecules. This work deals with coherent imaging and related phase retrieval techniques, with an emphasis on their application in the imaging of individual biological macromolecules.
We perform quantitative phase imaging using phase retrieval to implement synthetic aperture imaging. Compared to digital holography, the developed technique is simpler, less expensive, and more stable.
Spatio-temporal coherent molding and retrieval of pulsed signals in optical waveguides
Free University of Tbilisi（第比利斯自由大学）；Javakhishvili Tbilisi State University（贾瓦希什维利第比利斯国立大学）；Nagoya Institute of Technology（名古屋工业大学）；University of Duisburg-Essen（杜伊斯堡-埃森大学）；Center for Nanointegration Duisburg-Essen (CENIDE)（杜伊斯堡-埃森纳米集成中心）；The Pennsylvania State University（宾夕法尼亚州立大学）；Martin-Luther-Universität, Halle-Wittenberg（哈雷-维滕贝格马丁路德大学）
Recovering the transmission matrix of a disordered medium is a challenging problem in disordered photonics. Usually, its reconstruction relies on a complex inversion that aims at connecting a fully-controlled input to the deterministic interference of the light field scrambled by the device. At the moment, iterative phase-retrieval protocols provide the fastest reconstructing frameworks, converging in a few tens of iterations. Exploiting the knowledge of speckle correlations, we construct a new phase retrieval algorithm that reduces the computational cost to a single iteration. Besides being f…
In this work, issues in phase retrieval in the coherent diffractive imaging (CDI) technique, from discussion on parameters for setting up a CDI experiment to evaluation of the goodness of the final reconstruction, are discussed. The distribution of objects under study by CDI often cannot be cross-validated by another imaging technique. It is therefore important to make sure that the developed CDI procedure delivers an artifact-free object reconstruction. Critical issues that can lead to artifacts are presented and recipes on how to avoid them are provided.
Phase retrieval and imaging phase measurements are fields of intense research. It has recently been shown that phase retrieval from self-referencing interferograms (SRI) can be reformulated leading to a stable, linear equation provided the amplitude of the field is known from prior measurement steps (HOLOCAM). Consequently, the numerical solution thereof is straightforward. This is a big achievement since convergence is otherwise not always guaranteed. Applications are expected in X-ray microscopy, general phase retrieval, holography, tomography and optical imaging.
A robust light storage and retrieval (LSR) in high dimensions is highly desirable for light and quantum information processing. However, most schemes on LSR realized up to now encounter problems due to not only dissipation, but also dispersion and diffraction, which make LSR with a very low fidelity. Here we propose a scheme to achieve a robust storage and retrieval of weak nonlinear high-dimensional light pulses in a coherent atomic gas via electromagnetically induced transparency. We show that it is available to produce stable (3+1)-dimensional light bullets and vortices, which have very att…
A novel phase retrieval algorithm for broadband hyperspectral phase imaging from noisy intensity observations is proposed. It utilizes advantages of the Fourier Transform spectroscopy in the self-referencing optical setup and provides, additionally beyond spectral intensity distribution, reconstruction of the investigated object's phase. The noise amplification Fellgett's disadvantage is relaxed by the application of sparse wavefront noise filtering embedded in the proposed algorithm. The algorithm reliability is proved by simulation tests and results of physical experiments on transparent obj…
Complementary to conventional and phase X-ray radiography, dark-field imaging has become central in visualizing diffusive scattering signal due to the spatially-unresolved texture within an object. To date most diffusive-dark-field retrieval methods require either the acquisition of multiple images at the cost of higher radiation dose or significant amounts of computational memory and time. In this work, a simple method of X-ray diffusive dark-field retrieval is presented, applicable to any single-mask imaging setup, with only one exposure of the sample. The approach, which is based on a model…
We introduce a generalized version of phase retrieval called multiplexed phase retrieval. We want to recover the phase of amplitude-only measurements from linear combinations of them. This corresponds to the case in which multiple incoherent sources are sampled jointly, and one would like to recover their individual contributions. We show that a recent spectral method developed for phase retrieval can be generalized to this setting, and that its performance follows a phase transition behavior. We apply this new technique to light focusing at depth in a complex medium. Experimentally, although …
While characterization of coherent wavefields is essential to laser, x-ray and electron imaging, sensors measure the squared magnitude of the field, rather than the field itself. Holography or phase retrieval must be used to characterize the field. The need for a reference severely restricts the utility of holography. Phase retrieval, in contrast, is theoretically consistent with sensors that directly measure coherent or partially coherent fields with no prior assumptions. Unfortunately, phase retrieval has not yet been successfully implemented for large-scale fields. Here we show that both ho…
Phase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches involve techniques as varied as generic gradient-descent routines or specialized spectral methods, to name a few. Yet, the phase-recovery problem remains a challenge to this day. Recently, however, advances in machine learning have revitalized the study of phase retrieval in two ways: significant theoretical advances have emerged from the analogy between pha…
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…
We obtain exact polynomial solutions for two-dimensional coherent complex scalar fields propagating through arbitrary aberrated shift-invariant linear imaging systems. These are used to model nodal-line dynamics of coherent fields output by such systems.
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.
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…
Multi-mode Coherent Detection Ghost Imaging Lidar and Vibration-Mode Imaging
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences（中国科学院上海光学精密机械研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院）
A new algorithmic framework is presented for holographic phase retrieval via maximum likelihood optimization, which allows for practical and robust image reconstruction. This framework is especially well-suited for holographic coherent diffraction imaging in the \textit{low-photon regime}, where data is highly corrupted by Poisson shot noise. Thus, this methodology provides a viable solution towards the advent of \textit{low-photon nanoscale imaging}, which is a fundamental challenge facing the current state of imaging technologies. Practical optimization algorithms are derived and implemented…
Optical imaging through scattering media is a commonly confronted with the problem of reconstruction of complex objects and optical memory effect. To solve the problem, here, we propose a novel configuration based on the combination of ptychography and shower-curtain effect, which enables the retrieval of non-sparse samples through scattering media beyond the memory effect. Furthermore, by virtue of the shower-curtain effect, the proposed imaging system is insensitive to dynamic scattering media. Results from the retrieval of hair follicle section demonstrate the effectiveness and feasibility …
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…
Optical imaging plays a critical role in advancing our understanding of three dimensional dynamics of biological systems. Coherent imaging (CI) methods exploit spatial phase information, encoded through propagation of coherent signal light emerging from a specimen, to extract a three-dimensional representation of the object from a single high-speed measurement. Until now, CI methods could not be applied to incoherent light, severely limiting their ability to image the most powerful biological probes available - fluorescent molecules - with sufficient speed and volume to observe important proce…
Attosecond science has been transforming our understanding of electron dynamics in atoms, molecules and solids. However, to date almost all of the attoscience experiments have been based on spectroscopic measurements because attosecond pulses have intrinsically very broad spectra due to the uncertainty principle and are incompatible with conventional imaging systems. Here we report an important advance towards achieving attosecond coherent diffractive imaging. Using simulated attosecond pulses, we simultaneously reconstruct the spectrum, 17 probes and 17 spectral images of extended objects fro…
Here the role and influence of aberrations in optical imaging systems employing partially coherent complex scalar fields is studied. Imaging systems require aberrations to yield contrast in the output image. For linear shift-invariant optical systems, we develop an expression for the output cross-spectral density under the space-frequency formulation of statistically stationary partially coherentfields. We also develop expressions for the output cross{spectral density and associated spectral density for weak-phase, weak-phase-amplitude, and single-material objects in one transverse spatial dim…
University of Manchester（曼彻斯特大学）；Tampere University（坦佩雷大学）；United States CCDC Army Research Laboratory（美国CCDC陆军研究实验室）；University of Illinois Chicago（伊利诺伊大学芝加哥分校）；Noiseless Imaging Ltd.（Noiseless成像有限公司）
Phase retrieval in optical imaging refers to the recovery of a complex signal from phaseless data acquired in the form of its diffraction patterns. These patterns are acquired through a system with a coherent light source that employs a diffractive optical element (DOE) to modulate the scene resulting in coded diffraction patterns at the sensor. Recently, the hybrid approach of model-driven network or deep unfolding has emerged as an effective alternative to conventional model-based and learning-based phase retrieval techniques because it allows for bounding the complexity of algorithms while …
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…
In recent years nanoscale coherent imaging has emerged as an indispensable imaging modality allowing to surpass the resolution limit given by classical imaging optics. At the same time, attosecond science has experienced enormous progress and has revealed the ultrafast dynamics in atoms, molecules, and complex materials. Combining attosecond temporal resolution of pump-probe experiments with nanometer spatial resolution would allow studying ultrafast dynamics on the smallest spatio-temporal scales but has not been demonstrated yet. Unfortunately, the large bandwidth of attosecond pulses usuall…
We demonstrate a high-speed method to image objects through a thin scattering medium and around a corner. The method employs a reference object of known shape to retrieve the speckle-like point spread function of the scatterer. We extract the point spread function of the scatterer from a dynamic scene that includes a static reference object, and use this to image the dynamic objects. Sharp images are reconstructed from the transmission through a diffuser and from reflection off a rough surface. The sharp and clean reconstructed images from single shot data exemplify the robustness of the metho…
We introduce the concept of coherent temporal imaging and its combination with the anamorphic stretch transform. The new system can measure both temporal profile of fast waveforms as well as their spectrum in real time and at high-throughput. We show that the combination of coherent detection and warped time-frequency mapping also performs time-bandwidth compression. By reducing the temporal width without sacrificing spectral resolution, it addresses the Big Data problem in real time instruments. The proposed method is the first application of the recently demonstrated Anamorphic Stretch Trans…
Super-resolution fluorescence microscopy provides unprecedented insight into cellular and subcellular structures. However, going "beyond the diffraction barrier" comes at a price since most far-field super-resolution imaging techniques trade temporal for spatial super-resolution. We propose the combination of a novel label-free white light quantitative phase tomography with fluorescence imaging to provide high-speed imaging and spatial super-resolution. The non-iterative phase reconstruction relies on the acquisition of single images at each z-location and thus enables straightforward 3D phase…
We demonstrate a coherent imaging system based on a terahertz (THz) frequency quantum cascade laser (QCL) phase-locked to a near-infrared fs-laser comb. The phase locking enables coherent electro-optic sampling of the continuous-wave radiation emitted by the QCL through the generation of a heterodyne beat-note signal. We use this beat-note signal to demonstrate raster scan coherent imaging using a QCL emitting at 2.5 THz. At this frequency the detection noise floor of our system is of 3 pW/Hz and the long-term phase stability is <3 degrees/h, limited by the mechanical stability of the apparatu…
Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets are coherently linked to each other - which is a reasonable assumption for our objective of antenna measurements. Two classes of measurement setups are discussed which can provide this kind of extra information: multi-probe systems and holographic measurements with multiple reference signals. We propose several formulations of the corresponding phase retrie…
Coherent Raman microscopy provide label-free imaging by interrogating the intrinsic vibration of biomolecules. Nevertheless, trade-off between high chemical-specificity and high imaging-speed currently exists in transition from spectroscopy to spectroscopic imaging when capturing dynamics in complex living systems. Here, we present a novel concept in dual-comb scheme to substantially beat this trade-off and facilitate high-resolution broadband coherent anti-Stokes Raman spectroscopic imaging based on down-converted, automatically varying delay-time in spectral focusing excitation. A rapid meas…
The application of the non conventional imaging technique LOFI (Laser Optical Feedback Imaging) to coherent microscopy is presented. This simple and efficient technique using frequency-shifted optical feedback needs the sample to be scanned in order to obtain an image. The effects on magnitude and phase signals such as vignetting and field curvature occasioned by the scanning with galvanometric mirrors are discussed. A simple monitoring method based on phase images is proposed to find the optimal position of the scanner. Finally, some experimental results illustrating this technique are presen…
Massachusetts Institute of Technology（麻省理工学院）；Center for Computational Mathematics, Flatiron Institute（弗拉特龙研究所计算数学中心）；Yale University（耶鲁大学）；New York University（纽约大学）
Phase retrieval is the inverse problem of recovering a signal from magnitude-only Fourier measurements, and underlies numerous imaging modalities, such as Coherent Diffraction Imaging (CDI). A variant of this setup, known as holography, includes a reference object that is placed adjacent to the specimen of interest before measurements are collected. The resulting inverse problem, known as holographic phase retrieval, is well-known to have improved problem conditioning relative to the original. This innovation, i.e. Holographic CDI, becomes crucial at the nanoscale, where imaging specimens such…
University of California, Los Angeles（加州大学洛杉矶分校）；California NanoSystems Institute (CNSI)（加州纳米系统研究所）；David Geffen School of Medicine（大卫·格芬医学院）
We present a deep learning framework based on a generative adversarial network (GAN) to perform super-resolution in coherent imaging systems. We demonstrate that this framework can enhance the resolution of both pixel size-limited and diffraction-limited coherent imaging systems. We experimentally validated the capabilities of this deep learning-based coherent imaging approach by super-resolving complex images acquired using a lensfree on-chip holographic microscope, the resolution of which was pixel size-limited. Using the same GAN-based approach, we also improved the resolution of a lens-bas…
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…
The complete characterization of spatial coherence is difficult because the mutual coherence function is a complex-valued function of four independent variables. This difficulty limits the ability of controlling and optimizing spatial coherence in a broad range of key applications. Here we propose a method for measuring the complete mutual coherence function, which does not require any prior knowledge and can be scaled to measure arbitrary coherence properties for any wavelength. Our method can also be used to retrieve objects illuminated by partially coherent beam with unknown coherence prope…
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 novel diffractive imaging method that harnesses a low-resolution real-space image to guide the phase retrieval. A computational algorithm is developed to utilize such prior knowledge as a real-space constraint in the iterative phase retrieval procedure. Numerical simulations and proof-of-concept experiments are carried out, demonstrating our method's capability of reconstructing high-resolution details that are otherwise inaccessible with traditional phasing algorithms. With the present method, we formulate a conceptual design for the coherent imaging experiments at a next-generat…
Information multiplexing is important for biomedical imaging and chemical sensing. In this paper, we report a microscopy imaging technique, termed state-multiplexed Fourier ptychography (FP), for information multiplexing and coherent-state decomposition. Similar to a typical Fourier ptychographic setting, we use an array of light sources to illuminate the sample from different incident angles and acquire corresponding low-resolution images using a monochromatic camera. In the reported technique, however, multiple light sources are lit up simultaneously for information multiplexing, and the acq…
Conventional methods of wavefront reconstruction from the raw data of the Shack-Hartmann sensor use the focal spot shifts and discard the high-frequency information about the wavefront. Phase-retrieval-based methods treat the Hartmann pattern as the diffraction image and use the Rayleigh-Sommerfeld propagation to estimate the wavefront with greater accuracy and resolution. In this Letter, we propose a novel approach to the phase-retrieval-based reconstruction by considering the Hartmann pattern as a point-spread function of a general imaging system with an introduced phase diversity of a speci…
Ghost imaging (GI) lidar, as a novel remote sensing technique,has been receiving increasing interest in recent years. By combining pulse-compression technique and coherent detection with GI, we propose a new lidar system called pulse-compression GI lidar. Our analytical results, which are backed up by numerical simulations, demonstrate that pulse-compression GI lidar can obtain the target's spatial intensity distribution, range and moving velocity. Compared with conventional pulsed GI lidar system, pulse-compression GI lidar, without decreasing the range resolution, is easy to obtain high sing…
Non-line-of-sight (NLOS) imaging relies on collecting light that is rendered incoherent from the multiple scattering events and is then post-processed to provide an estimate of the hidden scene. Here we employ coherent phase control of the outgoing laser beam phase front so as to refocus the beam behind the obscuring obstacle and then use the speckle memory effect to scan the focused spot across the scene. The back-reflected light intensity provides a direct measurement of the scene with a signal-to-noise ratio that is greatly improved when measured using a temporally gated detector. A spatial…
A centred system forms the coherent image of the optical field on a spherical cap, taken as an object, on another spherical cap, whose vertex and curvature center are the respective paraxial images of the vertex and center of the object cap. That ``double-conjugation'' law, usually obtained in the framework of a scalar theory of diffraction, is deduced from concepts of geometrical optics. A magnification law between radii of conjugate spherical-caps extends the notion of longitudinal magnification to finite distances, and generalizes the longitudinal Lagrange-Helmholtz formula. Applying the do…
In the last five decades, iterative phase retrieval methods draw large amount of interest across the research community as a non-interferometric approach to recover quantitative phase distributions from one (or more) intensity measurement. However, in cases where a unique solution does exist, these methods often require oversampling and high computational resources, which limits the use of this approach in important applications. On the other hand, phase contrast methods are based on a single camera exposure but provides only a qualitative description of the phase, thus are not useful for appl…
We demonstrate high resolution extreme ultraviolet (EUV) coherent diffractive imaging in the most general reflection geometry by combining ptychography with tilted plane correction. This method makes it possible to image extended surfaces at any angle of incidence. Refocused light from a tabletop coherent high harmonic light source at 29 nm illuminates a nanopatterned surface at 45 degree angle of incidence. The reconstructed image contains quantitative amplitude and phase (in this case pattern height) information, comparing favorably with both scanning electron microscope and atomic force mic…
