High-resolution ab initio three-dimensional X-ray diffraction microscopy
H. N. Chapman, A. Barty, S. Marchesini, A. Noy, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, D. Shapiro
Coherent X-ray diffraction microscopy is a method of imaging non-periodic isolated objects at resolutions only limited, in principle, by the largest scattering angles recorded. We demonstrate X-ray diffraction imaging with high resolution in all three dimensions, as determined by a quantitative analysis of the reconstructed volume images. These images are retrieved from the 3D diffraction data using no a priori knowledge about the shape or composition of the object, which has never before been demonstrated on a non-periodic object. We also construct 2D images of thick objects with infinite depth of focus (without loss of transverse spatial resolution). These methods can be used to image biological and materials science samples at high resolution using X-ray undulator radiation, and establishes the techniques to be used in atomic-resolution ultrafast imaging at X-ray free-electron laser sources.
We describe a diffraction microscopy technique based on refractive optics to study structural variations in crystals. The X-ray beam diffracted by a crystal was magnified by beryllium parabolic refractive lenses on a 2D X-ray camera. The microscopy setup was integrated into the 6-circle Huber diffractometer at the ESRF beamline ID06. Our setup allowed us to visualize structural imperfections with a resolution of approximately 1 micrometer. The configuration, however, can easily be adapted for sub-micrometer resolution.
We present an analytical description and an experimental realization of interscale mixing microscopy, a diffraction-based imaging technique that is capable of detecting wavelength/10 objects in far-field measurements with both coherent and incoherent broadband light. This method aims at recovering the spatial spectrum of light diffracted by a subwavelength object based on far-field measurements of the interference created by the object and a finite diffraction grating. A single measurement, analyzing the multiple diffraction orders, is often sufficient to determine the parameters of the object…
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.
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…
We present a theoretical investigation of coherent anti-Stokes Raman scattering (CARS) that is modulated by periodically depleting the ground state population through Rabi oscillations driven by an additional control laser. We find that such a process generates optical sidebands in the CARS spectrum and that the frequency of the sidebands depends on the intensity of the control laser light field. We show that analyzing the sideband frequency upon scanning the beams across the sample allows one to spatially resolve emitter positions where a spatial resolution of 65 nm, which is well below the d…
Lensfree on-chip microscopy is an emerging imaging technique that can be used to visualize and study biological specimens without the need for imaging lens systems. Important issues that can limit the performance of lensfree on-chip microscopy include interferometric aberrations, acquisition noise, and image reconstruction artifacts. In this study, we introduce a Bayesian-based method for performing aberration correction and numerical diffraction that accounts for all three of these issues to improve the effective numerical aperture (NA) and signal-to-noise ratio (SNR) of the reconstructed mic…
I explain what is, what is not, and what is only sort of superresolution microscopy. I discuss optical resolution, first in terms of diffraction theory, then in terms of linear systems theory, and finally in terms of techniques that use prior information, nonlinearity, and other tricks to improve performance. The discussion reveals two classes of superresolution: Pseudo superresolution techniques improve images up to the diffraction limit but not much beyond. True superresolution techniques allow substantial, useful improvements beyond the diffraction limit. The two classes are distinguished b…
We report a novel extension to structured illumination (SI) microscopy that utilizes the Talbot self-imaging effect to generate a SI pattern on a sample with field-of-view (FOV) and resolution unconstrained by the numerical aperture (NA) of the microscope objective. This enables high-resolution SI pattern generation (up to the free-space propagation limit) across large FOVs, which in turn allows SI microscopy to be efficiently adapted for high-throughput imaging. We demonstrated this concept using a simple prototype microscope to image a large FOV (450 x 350 um) with a diffraction-limited fluo…
Light diffraction through a subwavelength aperture located at the apex of a metallic screen with conical geometry is investigated theoretically. A method based on a multipole field expansion is developed to solve Maxwell's equations analytically using boundary conditions adapted both for the conical geometry and for the finite conductivity of a real metal. The topological properties of the diffracted field are discussed in detail and compared to those of the field diffracted through a small aperture in a flat screen, i. e. the Bethe problem. The model is applied to coated, conically tapered op…
Single-emitter microscopy has emerged as a promising method of imaging nanostructures with nanoscale resolution. This technique uses the centroid position of an emitters far-field radiation pattern to infer its position to a precision that is far below the diffraction limit. However, nanostructures composed of high-dielectric materials such as noble metals can distort the far-field radiation pattern. Nanoparticles also exhibit a more complex range of distortions, because in addition to introducing a high dielectric surface, they also act as efficient scatterers. Thus, the distortion effects of…
We report a computational 3D microscopy technique, termed Fourier ptychographic diffraction tomography (FPDT), that iteratively stitches together numerous variably illuminated, low-resolution images acquired with a low-numerical aperture (NA) objective in 3D Fourier space to create a wide field-of-view (FOV), high-resolution, depth-resolved complex refractive index (RI) image across large volumes. Unlike conventional optical diffraction tomography (ODT) approaches that rely on controlled bright-field illumination, holographic phase measurement, and high-NA objective detection, FPDT employs tom…
Light-field microscopy represents a promising solution for microscopic volumetric imaging, thanks to its capability to encode information on multiple planes in a single acquisition. This is achieved through its peculiar simultaneous capture of information on light spatial distribution and propagation direction. However, state-of-the-art light-field microscopes suffer from a detrimental loss of spatial resolution compared to standard microscopes. We propose and experimentally demonstrate a light-field microscopy architecture based on light intensity correlation, in which resolution is limited o…
A four-wave-mixing, frequency-comb-based, hyperspectral imaging technique that is spectrally precise, potentially rapid, and can in principle be applied to any material, is demonstrated in a near-diffraction-limited microscopy application.
The optical diffraction limit, formulated by Abbe 140 years ago, imposes a bound on imaging resolution in classical optics. Over the last twenty years, many theoretical schemes have been presented for overcoming the diffraction barrier in optical imaging using quantum properties of light. An experimental realization of sub-diffraction limited quantum imaging has, however, remained elusive. Here, we demonstrate a quantum imaging method taking advantage of non-classical light naturally produced in fluorescence microscopy due to photon antibunching, a fundamentally quantum phenomenon prohibiting …
Speckle patterns have been widely used in imaging techniques such as ghost imaging, dynamic speckle illumination microscopy, structured illumination microscopy, and photoacoustic fluctuation imaging. Recent advances in the ability to control the statistical properties of speckles has enabled the customization of speckle patterns for specific imaging applications. In this work, we design and create special speckle patterns for parallelized nonlinear pattern-illumination microscopy based on fluorescence photoswitching. We present a proof-of-principle experimental demonstration where we obtain a …
Super-resolved far-field microscopy has emerged as a powerful tool for investigating the structure of objects with resolution well below the diffraction limit of light. Nearly all super-resolution imaging techniques reported to date rely on real energy states of probe molecules to circumvent the diffraction limit, preventing super-resolved imaging of contrast mechanisms that occur via virtual energy states such as harmonic generation (HG). Here we report a super-resolution technique based on SPatIal Frequency modulated Imaging (SPIFI) that permits super-resolved nonlinear microscopy with any c…
This paper proposes a non-computational method of counteracting the effect of image degradation introduced by the diffraction phenomenon in lensless microscopy. All the optical images (whether focused by lenses or not) are diffraction patterns, which preserve the visual information upto a certain extent determined by the size of the point spread functions, like airy disks in some cases. A highly diverging beam can be exploited to reduce the spatial extent of these point spread functions relatively in the transformed projective space, which can help us in the spatial unmixing of the visual info…
Efficient imaging of biomolecules, 2D materials and electromagnetic fields depends on retrieval of the phase of transmitted electrons. We demonstrate a method to measure phase in a scanning transmission electron microscope using a nanofabricated diffraction grating to produce multiple probe beams. The measured phase is more interpretable than phase-contrast scanning transmission electron microscopy techniques without an off-axis reference wave, and the resolution could surpass that of off-axis electron holography. We apply the technique to image nanoparticles, carbon sub- strates and electric …
In this theoretical study, the author firstly discusses the wave interference of Bragg diffraction inside 3D crystal, followed by quantum mechanical interpretation on the diffraction process, and proves that the interference fringe between Bragg diffraction and the incident beam is identical to the lattice plane. By introducing the beam expander concept, we may explain the image projection mechanism of Bragg diffractions propagating through TEM: Transmission Electron Microscope. In practice, we will take projection images at zone axes, because of its symmetric high-density diffractions associa…
Imaging artefacts in scattering-type scanning near field optical microscopy arising from optical diffraction effects and contrast-active sub-surface features
Acoustic-resolution optoacoustic microscopy (AR-OAM) retrieves anatomical and functional contrast from living tissues at depths not reachable with optical microscopy. The imaging performance of AR-OAM has been advanced with image reconstruction algorithms providing high lateral resolution ultimately limited by acoustic diffraction. In this work, we suggest a new model-based framework efficiently exploiting scanning symmetries for high-resolution reconstruction of AR-OAM images. The model accurately accounts for the spatial impulse response and large detection bandwidth of a spherical polyvinyl…
With recent developments in microscopy, such as stimulated emission depletion (STED) microscopy, far-field imaging at resolutions better than the diffraction limit is now a commercially available technique. Here, we show that, in the special case of a diffusive regime, the noise-limited resolution of STED imaging is independent of the saturation intensity of the fluorescent label. Thermal motion limits the signal integration time, which, for a given excited-state lifetime, limits the total number of photons available for detection.
In recent years several far-field microscopy techniques have been developed which manage to overcome the diffraction limit of resolution. A unifying classification scheme for them is clearly desirable. We argue that existing schemes based on the information capacity of the optical system can not easily be extended to cover e.g., STED microscopy or techniques based on single molecule imaging. We suggest a classification based on a reconstruction of the Abbe limit.
Structured illumination microscopy (SIM) provides images of fluorescent objects at an enhanced resolution greater than that of conventional epifluorescence wide-field microscopy. Initially demonstrated in 1999 to enhance the lateral resolution two-fold, it has since been extended to enhance axial resolution two-fold (2008), applied to live-cell imaging (2009) and combined with myriad other techniques, including interferometric detection (2008), confocal microscopy (2010) and light sheet illumination (2012). Despite these impressive developments, SIM remains, perhaps, the most poorly understood…
Super-resolution fluorescence microscopy is an important tool in biomedical research for its ability to discern features smaller than the diffraction limit. However, due to its difficult implementation and high cost, the universal application of super-resolution microscopy is not feasible. In this paper, we propose and demonstrate a new kind of super-resolution fluorescence microscopy that can be easily implemented and requires neither additional hardware nor complex post-processing. The microscopy is based on the principle of stepwise optical saturation (SOS), where $M$ steps of raw fluoresce…
We propose a real-time digital holographic microscopy, that enables simultaneous multiple reconstructed images with arbitrary resolution, depth and positions, using Shifted-Fresnel diffraction instead of Fresnel diffraction. In this system, we used four graphics processing units (GPU) for multiple reconstructions in real-time. We show the demonstration of four reconstruction images from a hologram with arbitrary depths, positions, and resolutions.
Modern optical microscopy methods have been advanced to provide super resolution at high imaging speed, but not chirality discriminative. We recently proposed chiral structured-illumination microscopy (SIM) method to image chiral fluorescent domains at sub-wavelength resolution. Chiral SIM is suitable for imaging chiral domains at sub-wavelength resolution but loses the high spatial frequency of the achiral ones. In order to obtain the full picture of all fluorescent domains at sub-wavelength resolution, we propose an advanced version of chiral SIM, termed double SIM, which enables simultaneou…
The emergence of far-field super-resolution microscopy has rejuvenated the possibility for nanoscale imaging. Approaches to far-field super-resolution that utilize point scanning often depends on spatially reducing the size of the focused spot. However, the focused spot always achieves high resolution at the expense of extremely low light efficiency for the probing mainlobe and high-intensity sidelobes, which limits the applications in nanoscale imaging and might cause misinterpretation of samples. Here we report a sharp probing spot with the diffraction efficiency of 3.76% at the resolution o…
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 …
Any object on earth has two fundamental properties: it is finite, and it is made of atoms. Structural information about an object can be obtained from diffraction amplitude measurements that account for either one of these traits. Nyquist-sampling of the Fourier amplitudes is sufficient to image single particles of finite size at any resolution. Atomic resolution data is routinely used to image molecules replicated in a crystal structure. Here we report an algorithm that requires neither information, but uses the fact that an image of a natural object is compressible. Intended applications inc…
In chiral sum frequency generation (C-SFG), the chiral nature of $χ^{(2)}$ requires the three involved electric fields to be pairwise non-parallel, leading to the traditional non-collinear configuration which is a hindrance for achieving diffraction limited resolution while utilizing it as a label-free imaging contrast mechanism . Here we propose a collinear C-SFG (CC-SFG) microscopy modality by using longitudinal z-polarized vectorial field. Label-free chiral imaging with enhanced spatial resolution (~1.4 times improvement in one lateral and the longitudinal directions over the traditional no…
Breaking the diffraction limit in microscopy by utilizing quantum properties of light has been the goal of intense research in the recent years. We propose a quantum superresolution technique based on non-classical emission statistics of fluorescent markers, routinely used as contrast labels for bio-imaging. The technique can be readily implemented using standard fluorescence microscopy equipment.
We performed extreme ultraviolet spectroscopy using an 80 lines/mm TEM mesh as dispersive element. We present the usefulness of this instrument for dispersing a high harmonic spectrum from the 13th to the 29th harmonic of a Ti:Sapph laser, corresponding to a wavelength range from 60 to 27 nm. The resolution of the instrument is limited by the image size of the high harmonic generation region on the detector. The best resolution in first order diffraction is under 2 nm over the entire spectral range.
We introduce the concept of saturated absorption competition (SAC) microscopy as a means of providing sub-diffraction spatial resolution in fluorescence imaging. Unlike the post-competition process between stimulated and spontaneous emission that is used in stimulated emission depletion (STED) microscopy, SAC microscopy breaks the diffraction limit by emphasizing a pre-competition process that occurs in the fluorescence absorption stage in a manner that shares similarities with ground-state depletion (GSD) microscopy. Moreover, unlike both STED and GSD microscopy, SAC microscopy offers a reduc…
X-ray diffraction microscopy (XDM) is a new form of x-ray imaging that is being practiced at several third-generation synchrotron-radiation x-ray facilities. Although only five years have elapsed since the technique was first introduced, it has made rapid progress in demonstrating high-resolution threedimensional imaging and promises few-nm resolution with much larger samples than can be imaged in the transmission electron microscope. Both life- and materials-science applications of XDM are intended, and it is expected that the principal limitation to resolution will be radiation damage for li…
In traditional optical imaging systems, the spatial resolution is limited by the physics of diffraction, which acts as a low-pass filter. The information on sub-wavelength features is carried by evanescent waves, never reaching the camera, thereby posing a hard limit on resolution: the so-called diffraction limit. Modern microscopic methods enable super-resolution, by employing florescence techniques. State-of-the-art localization based fluorescence subwavelength imaging techniques such as PALM and STORM achieve sub-diffraction spatial resolution of several tens of nano-meters. However, they r…
Deep Learning Enables Large Depth-of-Field Images for Sub-Diffraction-Limit Scanning Superlens Microscopy
City University of Hong Kong（香港城市大学）；State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences（中国科学院沈阳自动化研究所机器人学国家重点实验室）；Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences（中国科学院机器人与智能制造创新研究院）；The University of Hong Kong（香港大学）；City University of Hong Kong Shenzhen Research Institute (CityUSRI)（香港城市大学深圳研究院）
Super-resolution imaging techniques enable nanoscale microscopy in fields such as physics, biology, and chemistry. However, many super-resolution techniques require specialized optical components, such as a helical-phase mask. We present a novel technique, Super-resolution Airy disk Microscopy (SAM) that can be used in a standard confocal microscope without any specialized optics. We demonstrate this technique, in combination with ground state depletion, to image and control nitrogen-vacancy (NV) centers in bulk diamond below the diffraction limit. A greater than 14-fold improvement in resolut…
Nonlinear structured illumination microscopy (nSIM) is an effective approach for super-resolution wide-field fluorescence microscopy with a theoretically unlimited resolution. In nSIM, carefully designed, highly-contrasted illumination patterns are combined with the saturation of an optical transition to enable sub-diffraction imaging. While the technique proved useful for two-dimensional imaging, extending it to three-dimensions (3D) is challenging due to the fading/fatigue of organic fluorophores under intense cycling conditions. Here, we present a compressed sensing approach that allows for…
One of the main characteristics of optical imaging systems is the spatial resolution, which is restricted by the diffraction limit to approximately half the wavelength of the incident light. Along with the recently developed classical super-resolution techniques, which aim at breaking the diffraction limit in classical systems, there is a class of quantum super-resolution techniques which leverage the non-classical nature of the optical signals radiated by quantum emitters, the so-called antibunching super-resolution microscopy. This approach can ensure a factor of $\sqrt{n}$ improvement in th…
Sample-induced image-degradation remains an intricate wave-optical problem in light-sheet microscopy. Here we present biobeam, an open-source software package that enables to simulate operational light-sheet microscopes by combining data from 10^5 - 10^6 multiplexed and GPU-accelerated point-spread-function calculations. The wave-optical nature of these simulations leads to the faithful reproduction of spatially varying aberrations, diffraction artifacts, geometric image distortions, adaptive optics, and emergent wave optical phenomena, and renders image-formation in light-sheet microscopy com…
This work introduces a novel reinterpretation of structured illumination (SI) microscopy for coherent imaging that allows three-dimensional imaging of complex refractive index (RI). To do so, we show that coherent SI is mathematically equivalent to a superposition of angled illuminations. It follows that raw acquisitions for standard SI-enhanced quantitative-phase images can be processed into complex electric-field maps describing sample diffraction under angled illuminations. Standard diffraction tomography (DT) computation can then be used to reconstruct the sample 3D RI distribution at sub-…
Two-photon photopolymerization (TPP) has recently become a popular method for the fabrication of three-dimensional (3D) micro- and nanostructures. The reproduction fidelity of the designed micro- and nanostructures is influenced by experimental writing conditions, including laser power, exposure time, etc. To determine the appropriate writing parameters, characterization of morphological features and surface roughness during the experiment is needed. Traditional characterization methods for TPP, e.g., scanning electron microscopy and atomic force microscopy, have limited speed and cannot study…
