When used with coherent light, optical imaging systems, even diffraction-limited, are inherently unable to reproduce both the amplitude and the phase of a two-dimensional field distribution because their impulse response function varies slowly from point to point (a property known as non-isoplanatism). For sufficiently small objects, this usually results in a phase distortion and has no impact on the measured intensity. Here, we show that the intensity distribution can also be dramatically distorted when objects of large extension or of special shapes are imaged. We illustrate the problem using two simple examples: the pinhole camera and the aberration-free thin lens. The effects predicted by our theorical analysis are also confirmed by experimental observations.
The existing description of non-coherent wave field propagation in terms of Fourier transformation has made possible to prove non-existence of the self-imaging phenomenon for non-coherent images.
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.
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）
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…
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…
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 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…
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…
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…
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…
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…
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…
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…
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.
We extend image scanning microscopy to second harmonic generation (SHG) by extracting the complex field amplitude of the second-harmonic beam. While the theory behind coherent image scanning microscopy (ISM) is known, an experimental demonstration wasn't yet established. The main reason is that the naive intensity-reassignment procedure cannot be used for coherent scattering as the point spread function is now defined for the field amplitude rather than for the intensity. We use an inline interferometer to demonstrate super-resolved phase-sensitive SHG microscopy by applying the ISM reassignme…
Fluorescent imaging plays a critical role in a myriad of scientific endeavors, particularly in the biological sciences. Three-dimensional imaging of fluorescent intensity often requires serial data acquisition, that is voxel-by-voxel collection of fluorescent light emitted throughout the specimen with a non-imaging single-element detector. While non-imaging fluorescence detection offers some measure of scattering robustness, the rate at which dynamic specimens can be imaged is severely limited. Other fluorescent imaging techniques utilize imaging detection to enhance collection rates. A notabl…
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.
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 di…
We consider the propagation of both fully coherent and partially coherent complex scalar fields, through linear shift-invariant imaging systems. The state of such imaging systems is characterized by a countable infinity of aberration coefficients, the values for which can be viewed as coordinates for an infinity of orthogonal axes that span the "aberration space" into which the output propagates. For fully coherent complex scalar disturbances, we study the propagation of the field through the imaging system, while for partially coherent disturbances it is the two-point correlation functions wh…
Nonlinear optical methods, such as coherent anti-Stokes Raman scattering (CARS) and stimulated Raman scattering (SRS), are able to perform label free imaging, with chemical bonds specificity. Here, we demonstrate that the use of circularly polarized light allows to retrieve not only the chemical nature but also the symmetry of the probed sample, in a single shot measurement. Our symmetry-resolved scheme offers simple access to the local organization of vibrational bonds and as a result provides enhanced image contrast for anisotropic samples as well as an improved chemical selectivity. We quan…
We present the experimental reconstruction of sub-wavelength features from the far-field intensity of sparse optical objects: sparsity-based sub-wavelength imaging combined with phase-retrieval. As examples, we demonstrate the recovery of random and ordered arrangements of 100 nm features with the resolution of 30 nm, with an illuminating wavelength of 532 nm. Our algorithmic technique relies on minimizing the number of degrees of freedom; it works in real-time, requires no scanning, and can be implemented in all existing microscopes - optical and non-optical.
Characterizing buried layers and interfaces is critical for a host of applications in nanoscience and nano-manufacturing. Here we demonstrate non-invasive, non-destructive imaging of buried interfaces using a tabletop, extreme ultraviolet (EUV), coherent diffractive imaging (CDI) nanoscope. Copper nanostructures inlaid in SiO2 are coated with 100 nm of aluminum, which is opaque to visible light and thick enough that neither optical microscopy nor atomic force microscopy can image the buried interfaces. Short wavelength (29 nm) high harmonic light can penetrate the aluminum layer, yielding high…
Micromolar chemical imaging by high-energy low-photodamage Coherent Anti-stokes Raman Scattering (HELP-CARS)
Boston University（波士顿大学）；The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University（佐治亚理工学院和埃默里大学华莱士·H·考尔特生物医学工程系）
Diffraction limit is manifested in the loss of high spatial frequency information that results from decay of evanescent waves. As a result, conventional far-field optics yields no information about an object's subwavelength features. Here we propose a novel approach to recovering evanescent waves in the far field, thereby enabling subwavelength-resolved imaging and spatial spectroscopy. Our approach relies on shifting the frequency and the wave vector of near-field components via scattering on acoustic phonons. This process effectively removes the spatial frequency cut-off for unambiguous far …
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…
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…
Short laser pulses are widely used for controlling molecular rotational degrees of freedom and inducing molecular alignment, orientation, unidirectional rotation and other types of coherent rotational motion. To follow the ultra-fast rotational dynamics in real time, several techniques for producing molecular movies have been proposed based on the Coulomb explosion of rotating molecules, or recovering molecular orientation from the angular distribution of high-harmonics. The present work offers and demonstrates a novel non-destructive optical method for direct visualization and recording of mo…
Lensless imaging methods that account for partial coherence have become very common in the past decade. However, there are no metrics in use for comparing partially coherent light fields, despite the widespread use of such metrics to compare fully coherent objects and wavefields. Here, we show how reformulating the mean squared error and Fourier ring correlation in terms of quantum state fidelity naturally generalizes them to partially coherent wavefields. These results fill an important gap in the lensless imaging literature and will enable quantitative assessments of the reliability and reso…
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…
The critical properties of functional materials and nanoscale devices often originate from the coexistence of different thermodynamic phases and / or oxidization states, but sample makeup is seldom completely known a priori. Coherent diffractive imaging (CDI) provides the spatial resolution needed to observe nanoscale coexistence while returning the full amplitude and phase information of an object, but to date lacks the spectral information necessary for composition identification. Here we demonstrate CDI spectroscopy (CDIS), acquiring images of the prototypical quantum material vanadium oxid…
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…
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…
In this paper we consider narrow band, active array imaging of weak localized scatterers when only the intensities are recorded at an array with N transducers. We consider that the medium is homogeneous and, hence, wave propagation is fully coherent. This work is an extension of our previous paper, where we showed that using linear combinations of intensity-only measurements imaging of localized scatterers can be carried out efficiently using MUSIC or sparsity promoting optimization. Here we show the same strategy can be accomplished with only 3N-2 illuminations, therefore reducing enormously …
We describe a full-field coherent imaging approach suitable for hard X-rays based on a classical (i.e. Galilean) X-ray microscope. The method combines a series of low-resolution images acquired at different transverse lens positions into a single high-resolution image, overcoming the spatial resolution limit set by the numerical aperture of the objective lens. We describe the optical principles of the approach, demonstrate the successful reconstruction of simulated phantom data, and discuss aspects of the reconstruction. We believe this approach offers some potential benefits over conventional…
Coherent diffractive imaging of individual free nanoparticles has opened novel routes for the in-situ analysis of their transient structural, optical, and electronic properties. So far, single-shot single-particle diffraction was assumed to be feasible only at extreme ultraviolet (XUV) and X-ray free-electron lasers, restricting this research field to large-scale facilities. Here we demonstrate single-shot imaging of isolated helium nanodroplets using XUV pulses from a femtosecond-laser driven high harmonic source. We obtain bright wide-angle scattering patterns, that allow us to uniquely iden…
Coherent terahertz field tomographic imaging in warm Rydberg vapors
Faculty of Physics, University of Warsaw（华沙大学物理学院）；Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw（华沙大学新技术中心量子光学技术研究中心）
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…
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 …
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 and demonstrate a new phase retrieval method for imaging through random media. Although methods to recover the Fourier amplitude through random distortions are well established, recovery of the Fourier phase has been a more difficult problem and is still a very active research area. Here, we show that by simply ensemble averaging shift-corrected images, the Fourier phase of an object obscured by random distortions can be accurately retrieved up to the diffraction limit. The method is simple, fast, does not have any optimization parameters, and does not require prior knowledge or ass…
Coherent diffractive imaging (CDI) is widely used to characterize structured samples from measurements of diffracting intensity patterns. We introduce a numerical framework to quantify the precision that can be achieved when estimating any given set of parameters characterizing the sample from measured data. The approach, based on the calculation of the Fisher information matrix, provides a clear benchmark to assess the performance of CDI methods. Moreover, by optimizing the Fisher information metric using deep learning optimization libraries, we demonstrate how to identify the optimal illumin…
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…
Coherent imaging through scatter is a challenging task in computational imaging. Both model-based and data-driven approaches have been explored to solve the inverse scattering problem. In our previous work, we have shown that a deep learning approach can make high-quality and highly generalizable predictions through unseen diffusers. Here, we propose a new deep neural network (DNN) model that is agnostic to a broader class of perturbations including scatterer change, displacements, and system defocus up to 10X depth of field. In addition, we develop a new analysis framework for interpreting th…
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…
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…
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…
