Sparsity-based single-shot subwavelength coherent diffractive imaging

Lens-free auto-focusing imaging algorithm for the ultra-broadband light source

Auto-focusing is an essential task for lens-free holographic microscopy, which has developed many methods for high precision or fast refocusing. In this work, we derive the relationship among intensity derivation, the derivative of spectral distribution, as well as the distribution of the object, and propose a new auto-focusing criterion, the Robert critical function with axial difference (RCAD), to enhance the accuracy of distance estimation for lens-free imaging with the ultra-broadband light source. This method consists of three steps: image acquisition and preprocessing, axial-difference calculation, and distance estimation with sharpness analysis. The simulations and experiments demonstrate that the accuracy of this metric on auto-focusing with the ultra-broadband spectrum can effectively assist in determining the off-focus distance. The experiments are conducted in an ultra-broad-spectrum on-chip system, where the samples including the resolution target and the cross-section of the Tilia stem are employed to maximize the applicability of this method. We believe that the RCAD criterion is expected to be a useful auxiliary tool for lens-free on-chip microscopes with ultra-broadband spectrum illumination.

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

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

Phase flow cytometry with coherent modulation imaging

Label-free imaging and identification of fast-moving cells is a very challenging task. A kind of phase flow cytometry using coherent modulation imaging was proposed to realize label-free imaging and identification on fast-moving cells with compact optical alignment and high accuracy. Phase image of cells under inspection could be computed qualitatively from their diffraction patterns at the accuracy of about 0.01 wavelength and the resolution of about 1.23 μm and the view field of 0.126 mm² . Since the imaging system was mainly composed by a piece of random phase plate a detector without using commonly adopted reference beam and corresponding complex optical alignment, this method has much compacter optical structure and much higher tolerance capability to environmental instability in comparison with other kinds of phase flow cytometry. Current experimental results prove it could be an efficient optical tool for label-free tumor cell detection.

Sparse deconvolution improves the resolution of live-cell super-resolution fluorescence microscopy

A main determinant of the spatial resolution of live-cell super-resolution (SR) microscopes is the maximum photon flux that can be collected. To further increase the effective resolution for a given photon flux, we take advantage of a priori knowledge about the sparsity and continuity of biological structures to develop a deconvolution algorithm that increases the resolution of SR microscopes nearly twofold. Our method, sparse structured illumination microscopy (Sparse-SIM), achieves ~60-nm resolution at a frame rate of up to 564 Hz, allowing it to resolve intricate structures, including small vesicular fusion pores, ring-shaped nuclear pores formed by nucleoporins and relative movements of inner and outer mitochondrial membranes in live cells. Sparse deconvolution can also be used to increase the three-dimensional resolution of spinning-disc confocal-based SIM, even at low signal-to-noise ratios, which allows four-color, three-dimensional live-cell SR imaging at ~90-nm resolution. Overall, sparse deconvolution will be useful to increase the spatiotemporal resolution of live-cell fluorescence microscopy.

Invariance Property of the Fisher Information in Scattering Media

Determining the ultimate precision limit for measurements on a subwavelength particle with coherent laser light is a goal with applications in areas as diverse as biophysics and nanotechnology. Here, we demonstrate that surrounding such a particle with a complex scattering environment does, on average, not have any influence on the mean quantum Fisher information associated with measurements on the particle. As a remarkable consequence, the average precision that can be achieved when estimating the particle's properties is the same in the ballistic and in the diffusive scattering regime, independently of the particle's position within its nonabsorbing environment. This invariance law breaks down only in the regime of Anderson localization, due to increased C_{0}-speckle correlations. Finally, we show how these results connect to the mean quantum Fisher information achievable with spatially optimized input fields.

Parameter retrieval of small particles in dark-field Fourier ptychography and a rectangle in real-space ptychography

We present a parameter retrieval method which incorporates prior knowledge about the object into ptychography. The proposed method is applied to two applications: (1) parameter retrieval of small particles from Fourier ptychographic dark field measurements; (2) parameter retrieval of a rectangular structure with real-space ptychography. The influence of Poisson noise is discussed in the second part of the paper. The Cramér Rao Lower Bound in both applications is computed and Monte Carlo analysis is used to verify the calculated lower bound. With the computation results we report the lower bound for various noise levels and analyze the correlation of particles in application 1. For application 2 the correlation of parameters of the rectangular structure is discussed.

cSPARCOM: Multi-detector reconstruction by confocal super-resolution correlation microscopy

Image scanning microscopy (ISM), an upgraded successor of the ubiquitous confocal microscope, facilitates up to two-fold improvement in lateral resolution, and has become an indispensable element in the toolbox of the bio-imaging community. Recently, super-resolution optical fluctuation image scanning microscopy (SOFISM) integrated the analysis of intensity-fluctuations information into the basic ISM architecture, to enhance its resolving power. Both of these techniques typically rely on pixel-reassignment as a fundamental processing step, in which the parallax of different detector elements to the sample is compensated by laterally shifting the point spread function (PSF). Here, we propose an alternative analysis approach, based on the recent high-performing sparsity-based super-resolution correlation microscopy (SPARCOM) method. Through measurements of DNA origami nano-rulers and fixed cells labeled with organic dye, we experimentally show that confocal SPARCOM (cSPARCOM), which circumvents pixel-reassignment altogether, provides enhanced resolution compared to pixel-reassigned based analysis. Thus, cSPARCOM further promotes the effectiveness of ISM, and particularly that of correlation based ISM implementations such as SOFISM, where the PSF deviates significantly from spatial invariance.

Single-pixel ptychography

Ptychography is a predominant non-interferometric technique to image large complex fields but with quite a narrow working spectrum, because diffraction measurements require dense array detection with an ultra-high dynamic range. Here we report a single-pixel ptychography technique that realizes non-interferometric and non-scanning complex-field imaging in a wide waveband, where 2D dense detector arrays are not available. A single-pixel detector is placed in the far field to record the DC-only component of the diffracted wavefront scattered from the target field, which is illuminated by a sequence of binary modulation patterns. This decreases the measurements' dynamic range by several orders of magnitude. We employ an efficient single-pixel phase-retrieval algorithm to jointly recover the field's 2D amplitude and phase maps from the 1D intensity-only measurement sequence. No a priori object information is needed in the recovery process. We validate the technique's quantitative phase imaging nature using both calibrated phase objects and biological samples and demonstrate its wide working spectrum with both 488-nm visible light and 980-nm near-infrared light.

Ultimate resolution limits of speckle-based compressive imaging

Compressive imaging using sparsity constraints is a very promising field of microscopy that provides a dramatic enhancement of the spatial resolution beyond the Abbe diffraction limit. Moreover, it simultaneously overcomes the Nyquist limit by reconstructing an N-pixel image from less than N single-point measurements. Here we present fundamental resolution limits of noiseless compressive imaging via sparsity constraints, speckle illumination and single-pixel detection. We addressed the experimental setup that uses randomly generated speckle patterns (in a scattering media or a multimode fiber). The optimal number of measurements, the ultimate spatial resolution limit and the surprisingly important role of discretization are demonstrated by the theoretical analysis and numerical simulations. We show that, in contrast to conventional microscopy, oversampling may decrease the resolution and reconstruction quality of compressive imaging.

Optimizing illumination for precise multi-parameter estimations in coherent diffractive imaging

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 illumination scheme that minimizes the estimation error under specified experimental constraints. This work paves the way for an efficient characterization of structured samples at the sub-wavelength scale.

Far-field signature of sub-wavelength microscopic objects

Information about microscopic objects with features smaller than the diffraction limit is almost entirely lost in a far-field diffraction image but could be partly recovered with data completition techniques. Any such approach critically depends on the level of noise. This new path to superresolution has been recently investigated with use of compressed sensing and machine learning. We demonstrate a two-stage technique based on deconvolution and genetic optimization which enables the recovery of objects with features of 1/10 of the wavelength. We indicate that l1-norm based optimization in the Fourier domain unrelated to sparsity is more robust to noise than its l2-based counterpart. We also introduce an extremely fast general purpose restricted domain calculation method for Fourier transform based iterative algorithms operating on sparse data.

Recent advances in point spread function engineering and related computational microscopy approaches: from one viewpoint

This personal hybrid review piece, written in light of my recipience of the UIPAB 2020 young investigator award, contains a mixture of my scientific biography and work so far. This paper is not intended to be a comprehensive review, but only to highlight my contributions to computation-related aspects of super-resolution microscopy, as well as their origins and future directions.

Improved ptychographic inspection of EUV reticles via inclusion of prior information

The development of actinic mask metrology tools represents one of the major challenges to be addressed on the roadmap of extreme ultraviolet (EUV) lithography. Technological advancements in EUV lithography result in the possibility to print increasingly fine and highly resolved structures on a silicon wafer; however, the presence of fine-scale defects, interspersed in the printable mask layout, may lead to defective wafer prints. Hence, the development of actinic methods for review of potential defect sites becomes paramount. Here, we report on a ptychographic algorithm that makes use of prior information about the object to be retrieved, generated by means of rigorous computations, to improve the detectability of defects whose dimensions are of the order of the wavelength. The comprehensive study demonstrates that the inclusion of prior information as a regularizer in the ptychographic optimization problem results in a higher reconstruction quality and an improved robustness to noise with respect to the standard ptychographic iterative engine (PIE). We show that the proposed method decreases the number of scan positions necessary to retrieve a high-quality image and relaxes requirements in terms of signal-to-noise ratio (SNR). The results are further compared with state-of-the-art total variation-based ptychographic imaging.

Influence of the Local Scattering Environment on the Localization Precision of Single Particles

We study the fundamental limit on the localization precision for a subwavelength scatterer embedded in a strongly scattering environment, using the external degrees of freedom provided by wavefront shaping. For a weakly scattering target, the localization precision improves with the value of the local density of states at the target position. For a strongly scattering target, the localization precision depends on the dressed polarizability that includes the backaction of the environment. This numerical study provides new insights for the control of the information content of scattered light by wavefront shaping, with potential applications in sensing, imaging, and nanoscale engineering.

Quantifying bio-filament morphology below the diffraction limit of an optical microscope using out-of-focus images

A method to measure the dimensions of objects below the optical diffraction limit using diffraction analysis of out-of-focus bright-field images is presented. The method relies on the comparison of the diffraction patterns of an object of unknown size to those of calibration objects of known size. Correlative scanning electron microscope measurements are used to demonstrate the applicability of this method to measure 100 nm microbeads as well as objects with a geometry different from the calibration objects. This technique is important in the context of tethered particle experiments, in which bio-filaments are bound between a substrate and a microbead. This procedure is applied to obtain the diameters of axonal extensions or neurites that are mechanically created in samples of rat hippocampal neurons. The dependence of neurite geometry on mechanical pull speed is investigated, and the diameter is found to be rate independent.

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

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

Improving techniques for diagnostics of laser pulses by compact representations

We propose and demonstrate, numerically and experimentally, use of sparsity as prior information for extending the capabilities and performance of techniques and devices for laser pulse diagnostics. We apply the concept of sparsity in three different applications. First, we improve a photodiode-oscilloscope system's resolution for measuring the intensity structure of laser pulses. Second, we demonstrate the intensity profile reconstruction of ultrashort laser pulses from intensity autocorrelation measurements. Finally, we use a sparse representation of pulses (amplitudes and phases) to retrieve measured pulses from incomplete spectrograms of cross-correlation frequency-resolved optical gating traces.

Deep learning-based super-resolution in coherent imaging systems

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. The capabilities of this approach are experimentally validated by super-resolving complex-valued 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-based holographic imaging system that was limited in resolution by the numerical aperture of its objective lens. This deep learning-based super-resolution framework can be broadly applied to enhance the space-bandwidth product of coherent imaging systems using image data and convolutional neural networks, and provides a rapid, non-iterative method for solving inverse image reconstruction or enhancement problems in optics.

Far-field super-focusing by a feedback-based wavefront shaping method

Abbe diffraction limit has always been an important subject in conventional far-field focusing and imaging systems, where the resolution of an image is usually limited to 0.5λ/NA. Recently, the studies of the optical super-oscillation lens (SOL) enable us to break the limitation in both theory and practice successfully. Here a genetic algorithm was introduced to design the SOL phase more controllably and precisely obtain much better focusing such as the focal spot with 0.105λ/NA (or 79.0% minification) in the simulation and 65.5% minification in the experimental demonstration. This technique is of great significance in advanced optical lithography or biology microscopy, because it promises non-invasive unlabelled imaging from the far field.

Single-shot coherent power-spectrum imaging of objects hidden by opaque scattering media

We report coherent imaging of objects behind opaque scattering media with only one piece of the power spectrum pattern. We solve the unique solution and improve algorithm speed for the inverse problem. Based on the proposed scattering-disturbance model, with only one piece of the Fourier transform power spectrum pattern under coherent illumination, we successfully reconstruct clear images of the objects fully hidden by an opaque diffuser. The experimental results demonstrate the feasibility of the reconstruction method and the scattering-disturbance model. Our method makes it possible to carry out snapshot coherent imaging of the objects obscured by scattering media, which extends the methodology of x-ray crystallography to visible-light scattering imaging for underwater and living biomedical imaging.

Computational multifocal microscopy

Despite recent advances, high performance single-shot 3D microscopy remains an elusive task. By introducing designed diffractive optical elements (DOEs), one is capable of converting a microscope into a 3D "kaleidoscope," in which case the snapshot image consists of an array of tiles and each tile focuses on different depths. However, the acquired multifocal microscopic (MFM) image suffers from multiple sources of degradation, which prevents MFM from further applications. We propose a unifying computational framework which simplifies the imaging system and achieves 3D reconstruction via computation. Our optical configuration omits optical elements for correcting chromatic aberrations and redesigns the multifocal grating to enlarge the tracking area. Our proposed setup features only one single grating in addition to a regular microscope. The aberration correction, along with Poisson and background denoising, are incorporated in our deconvolution-based fully-automated algorithm, which requires no empirical parameter-tuning. In experiments, we achieve spatial resolutions of 0.35um (lateral) and 0.5um (axial), which are comparable to the resolution that can be achieved with confocal deconvolution microscopy. We demonstrate a 3D video of moving bacteria recorded at 25 frames per second using our proposed computational multifocal microscopy technique.

Real-time coherent diffraction inversion using deep generative networks

Phase retrieval, or the process of recovering phase information in reciprocal space to reconstruct images from measured intensity alone, is the underlying basis to a variety of imaging applications including coherent diffraction imaging (CDI). Typical phase retrieval algorithms are iterative in nature, and hence, are time-consuming and computationally expensive, making real-time imaging a challenge. Furthermore, iterative phase retrieval algorithms struggle to converge to the correct solution especially in the presence of strong phase structures. In this work, we demonstrate the training and testing of CDI NN, a pair of deep deconvolutional networks trained to predict structure and phase in real space of a 2D object from its corresponding far-field diffraction intensities alone. Once trained, CDI NN can invert a diffraction pattern to an image within a few milliseconds of compute time on a standard desktop machine, opening the door to real-time imaging.

Sparsity-based super-resolution microscopy from correlation information

For more than a century, the wavelength of light was considered to be a fundamental limit on the spatial resolution of optical imaging. Particularly in light microscopy, this limit, known as Abbe's diffraction limit, places a fundamental constraint on the ability to image sub-cellular organelles with high resolution. However, modern microscopy techniques such as STED, PALM, and STORM, manage to recover sub-wavelength information, by relying on fluorescence imaging. Specifically, PALM/STORM acquire large sequences of fluorescence images from molecules attached to the organelles within the imaged specimen, such that in each frame only a small set of fluorophores are active. The position of each fluorophore can be found accurately in each frame, and the image is recovered by superimposing the points from all frames. The resulting grainy image is subsequently smoothed to produce the final super-resolved image with a resolution of tens of nano-meters. However, because PALM/STORM rely on many (>10,000) exposures, they suffer from poor temporal resolution. To address that, super-resolution optical fluctuation imaging (SOFI) was shown to produce sub-diffraction images with increased temporal resolution, by allowing for higher fluorophore density and exploiting the temporal statistics of the emissions. However, the improved temporal resolution of SOFI comes at the expense of its spatial resolution, which is not as high as that of PALM/STORM. Here, we present a new method called SPARCOM: sparsity-based super-resolution correlation microscopy, which combines a shorter integration time than previously reported with spatial resolution comparable to PALM and STORM. SPARCOM relies on sparsity in the correlation domain, exploiting the sparse distribution of fluorescent molecules and the lack of correlation between different emitters. We demonstrate our technique in simulations and in experiments and provide comparisons to state-of-the-art high density methods.

Planar Diffractive Lenses: Fundamentals, Functionalities, and Applications

Traditional objective lenses in modern microscopy, based on the refraction of light, are restricted by the Rayleigh diffraction limit. The existing methods to overcome this limit can be categorized into near-field (e.g., scanning near-field optical microscopy, superlens, microsphere lens) and far-field (e.g., stimulated emission depletion microscopy, photoactivated localization microscopy, stochastic optical reconstruction microscopy) approaches. However, they either operate in the challenging near-field mode or there is the need to label samples in biology. Recently, through manipulation of the diffraction of light with binary masks or gradient metasurfaces, some miniaturized and planar lenses have been reported with intriguing functionalities such as ultrahigh numerical aperture, large depth of focus, and subdiffraction-limit focusing in far-field, which provides a viable solution for the label-free superresolution imaging. Here, the recent advances in planar diffractive lenses (PDLs) are reviewed from a united theoretical account on diffraction-based focusing optics, and the underlying physics of nanofocusing via constructive or destructive interference is revealed. Various approaches of realizing PDLs are introduced in terms of their unique performances and interpreted by using optical aberration theory. Furthermore, a detailed tutorial about applying these planar lenses in nanoimaging is provided, followed by an outlook regarding future development toward practical applications.

Single-shot 3D coherent diffractive imaging of core-shell nanoparticles with elemental specificity

We report 3D coherent diffractive imaging (CDI) of Au/Pd core-shell nanoparticles with 6.1 nm spatial resolution with elemental specificity. We measured single-shot diffraction patterns of the nanoparticles using intense x-ray free electron laser pulses. By exploiting the curvature of the Ewald sphere and the symmetry of the nanoparticle, we reconstructed the 3D electron density of 34 core-shell structures from these diffraction patterns. To extract 3D structural information beyond the diffraction signal, we implemented a super-resolution technique by taking advantage of CDI’s quantitative reconstruction capabilities. We used high-resolution model fitting to determine the Au core size and the Pd shell thickness to be 65.0 ± 1.0 nm and 4.0 ± 0.5 nm, respectively. We also identified the 3D elemental distribution inside the nanoparticles with an accuracy of 3%. To further examine the model fitting procedure, we simulated noisy diffraction patterns from a Au/Pd core-shell model and a solid Au model and confirmed the validity of the method. We anticipate this super-resolution CDI method can be generally used for quantitative 3D imaging of symmetrical nanostructures with elemental specificity.

In situ coherent diffractive imaging

Coherent diffractive imaging (CDI) has been widely applied in the physical and biological sciences using synchrotron radiation, X-ray free-electron laser, high harmonic generation, electrons, and optical lasers. One of CDI’s important applications is to probe dynamic phenomena with high spatiotemporal resolution. Here, we report the development of a general in situ CDI method for real-time imaging of dynamic processes in solution. By introducing a time-invariant overlapping region as real-space constraint, we simultaneously reconstructed a time series of complex exit wave of dynamic processes with robust and fast convergence. We validated this method using optical laser experiments and numerical simulations with coherent X-rays. Our numerical simulations further indicated that in situ CDI can potentially reduce radiation dose by more than an order of magnitude relative to conventional CDI. With further development, we envision in situ CDI could be applied to probe a range of dynamic phenomena in the future.

Coherent diffractive imaging (CDI) allows for high resolution imaging without lenses. Here, Lo et al. develop in situ CDI with real-time imaging and a corresponding low-dose requirement, with expected applications in the physical and life sciences.

Phase recovery and holographic image reconstruction using deep learning in neural networks

Phase recovery from intensity-only measurements forms the heart of coherent imaging techniques and holography. In this study, we demonstrate that a neural network can learn to perform phase recovery and holographic image reconstruction after appropriate training. This deep learning-based approach provides an entirely new framework to conduct holographic imaging by rapidly eliminating twin-image and self-interference-related spatial artifacts. This neural network-based method is fast to compute and reconstructs phase and amplitude images of the objects using only one hologram, requiring fewer measurements in addition to being computationally faster. We validated this method by reconstructing the phase and amplitude images of various samples, including blood and Pap smears and tissue sections. These results highlight that challenging problems in imaging science can be overcome through machine learning, providing new avenues to design powerful computational imaging systems.

Super-resolution imaging by metamaterial-based compressive spatial-to-spectral transformation

We present a new far-field super-resolution imaging approach called compressive spatial to spectral transformation microscopy (CSSTM). The transformation encodes the high-resolution spatial information to a spectrum through illuminating sub-diffraction-limited and wavelength-dependent patterns onto an object. The object is reconstructed from scattering spectrum measurements in the far field. The resolution of the CSSTM is mainly determined by the materials used to perform the spatial to spectral transformation. As an example, we numerically demonstrate sub-15 nm resolution by using a practically achievable Ag/SiO₂ multilayer hyperbolic metamaterial.

Sparsity-Based Super Resolution for SEM Images

The scanning electron microscope (SEM) is an electron microscope that produces an image of a sample by scanning it with a focused beam of electrons. The electrons interact with the atoms in the sample, which emit secondary electrons that contain information about the surface topography and composition. The sample is scanned by the electron beam point by point, until an image of the surface is formed. Since its invention in 1942, the capabilities of SEMs have become paramount in the discovery and understanding of the nanometer world, and today it is extensively used for both research and in industry. In principle, SEMs can achieve resolution better than one nanometer. However, for many applications, working at subnanometer resolution implies an exceedingly large number of scanning points. For exactly this reason, the SEM diagnostics of microelectronic chips is performed either at high resolution (HR) over a small area or at low resolution (LR) while capturing a larger portion of the chip. Here, we employ sparse coding and dictionary learning to algorithmically enhance low-resolution SEM images of microelectronic chips-up to the level of the HR images acquired by slow SEM scans, while considerably reducing the noise. Our methodology consists of two steps: an offline stage of learning a joint dictionary from a sequence of LR and HR images of the same region in the chip, followed by a fast-online super-resolution step where the resolution of a new LR image is enhanced. We provide several examples with typical chips used in the microelectronics industry, as well as a statistical study on arbitrary images with characteristic structural features. Conceptually, our method works well when the images have similar characteristics, as microelectronics chips do. This work demonstrates that employing sparsity concepts can greatly improve the performance of SEM, thereby considerably increasing the scanning throughput without compromising on analysis quality and resolution.

Two noise-robust axial scanning multi-image phase retrieval algorithms based on Pauta criterion and smoothness constraint

We proposed two noise-robust iterative methods for phase retrieval and diffractive imaging based on the Pauta criterion and the smoothness constraint. The work is to address the noise issue plaguing the application of iterative phase retrieval algorithms in coherent diffraction imaging. It is demonstrated by numerical analysis and experimental results that our proposed algorithms have higher retrieval accuracy and faster convergence speed at a high shot noise level. Moreover, they are proved to hold the superiority to cope with other kinds of noises. Due to the inconvenience of conventional iteration indicators in experiments, a more reliable retrieval metric is put forward and verified its effectiveness. It should be noted that the proposed methods focus on exploiting the longitudinal diversity. It is anticipated that our work can further expand the application of iterative multi-image phase retrieval methods.

Spatial-domain filter enhanced subtraction microscopy and application to mid-IR imaging

We have experimentally investigated the enhancement in spatial resolution by image subtraction in mid-infrared central solid-immersion lens (c-SIL) microscopy. The subtraction exploits a first image measured with the c-SIL point-spread function (PSF) realized with a Gaussian beam and a second image measured with the beam optically patterned by a silicon π-step phase plate, to realize a centrally hollow PSF. The intense sides lobes in both PSFs that are intrinsic to the SIL make the conventional weighted subtraction methods inadequate. A spatial-domain filter with a kernel optimized to match both experimental PSFs in their periphery was thus developed to modify the first image prior to subtraction, and this resulted in greatly improved performance, with polystyrene beads 1.4 ± 0.1 µm apart optically resolved with a mid-IR wavelength of 3.4 µm in water. Spatial-domain filtering is applicable to other PSF pairs, and simulations show that it also outperforms conventional subtraction methods for the Gaussian and doughnut beams widely used in visible and near-IR microscopy.

Ptychographic ultrahigh-speed imaging

We propose and demonstrate numerically a simple method for ultrahigh-speed imaging of complex (amplitude and phase) samples. Our method exploits redundancy in single-shot ptychography (SSP) for reconstruction of multiple frames from a single camera snapshot. We term the method Time-resolved Imaging by Multiplexed Ptychography (TIMP). We demonstrate TIMP numerically-reconstructing 15 frames of a complexed-valued dynamic object from a single noisy camera snapshot. Experimentally, we demonstrate SSP with single pulse illumination with pulse duration of 150 psec, where its spectral bandwidth can support 30 fsec pulses.

Photoacoustic imaging beyond the acoustic diffraction-limit with dynamic speckle illumination and sparse joint support recovery

In deep tissue photoacoustic imaging the spatial resolution is inherently limited by the acoustic wavelength. Recently, it was demonstrated that it is possible to surpass the acoustic diffraction limit by analyzing fluctuations in a set of photoacoustic images obtained under unknown speckle illumination patterns. Here, we purpose an approach to boost reconstruction fidelity and resolution, while reducing the number of acquired images by utilizing a compressed sensing computational reconstruction framework. The approach takes into account prior knowledge of the system response and sparsity of the target structure. We provide proof of principle experiments of the approach and demonstrate that improved performance is obtained when both speckle fluctuations and object priors are used. We numerically study the expected performance as a function of the measurement's signal to noise ratio and sample spatial-sparsity. The presented reconstruction framework can be applied to analyze existing photoacoustic experimental data sets containing dynamic fluctuations.

Subsampled phase retrieval for temporal resolution enhancement in lensless on-chip holographic video

On-chip holographic video is a convenient way to monitor biological samples simultaneously at high spatial resolution and over a wide field-of-view. However, due to the limited readout rate of digital detector arrays, one often faces a tradeoff between the per-frame pixel count and frame rate of the captured video. In this report, we propose a subsampled phase retrieval (SPR) algorithm to overcome the spatial-temporal trade-off in holographic video. Compared to traditional phase retrieval approaches, our SPR algorithm uses over an order of magnitude less pixel measurements while maintaining suitable reconstruction quality. We use an on-chip holographic video setup with pixel sub-sampling to experimentally demonstrate a factor of 5.5 increase in sensor frame rate while monitoring the in vivo movement of Peranema microorganisms.

Doubling the far-field resolution in mid-infrared microscopy

The spatial resolution in far-field mid-infrared (λ>2.5 µm) microscopy and micro-spectroscopy remains limited with the full-width at half maximum of the point-spread function ca. λ/1.3; a value that is very poor in comparison to that commonly accessible with visible and near-infrared optics. Hereafter, it is demonstrated however that polymer beads that are centre-to-centre spaced by λ/2.6 can be resolved in the mid-infrared. The more than 2-fold improvement in resolution in the far-field is achieved by exploiting a newly constructed scanning microscope built around a mid-infrared optical parametric oscillator and a central solid-immersion lens, and by enforcing the linear polarization unidirectional resolution enhancement with a novel and robust specimen error minimization based on a particle swarm optimization. The method is demonstrated with specimens immersed in air and in water, and its robustness shown by the analysis of dense and complex self-assembled bead islands.

Two-photon tomography using on-chip quantum walks

We present an approach to quantum tomography based on first expanding a quantum state across extra degrees of freedom and then exploiting the introduced sparsity to perform reconstruction. We formulate its application to photonic circuits and show that measured spatial photon correlations at the output of a specially tailored discrete-continuous quantum walk can enable full reconstruction of any two-photon spatially entangled and mixed state at the input. This approach does not require any tunable elements, so it is well suited for integration with on-chip superconducting photon detectors.

Sparsity-Based Pixel Super Resolution for Lens-Free Digital In-line Holography

Lens-free digital in-line holography (LDIH) is a promising technology for portable, wide field-of-view imaging. Its resolution, however, is limited by the inherent pixel size of an imaging device. Here we present a new computational approach to achieve sub-pixel resolution for LDIH. The developed method is a sparsity-based reconstruction with the capability to handle the non-linear nature of LDIH. We systematically characterized the algorithm through simulation and LDIH imaging studies. The method achieved the spatial resolution down to one-third of the pixel size, while requiring only single-frame imaging without any hardware modifications. This new approach can be used as a general framework to enhance the resolution in nonlinear holographic systems.

Undersampled Phase Retrieval with Outliers

This paper proposes a general framework for reconstructing sparse images from undersampled (squared)-magnitude data corrupted with outliers and noise. This phase retrieval method uses a layered approach, combining repeated minimization of a convex majorizer (surrogate for a nonconvex objective function), and iterative optimization of that majorizer using a preconditioned variant of the alternating direction method of multipliers (ADMM). Since phase retrieval is nonconvex, this implementation uses multiple initial majorization vectors. The introduction of a robust 1-norm data fit term that is better adapted to outliers exploits the generality of this framework. The derivation also describes a normalization scheme for the regularization parameter and a known adaptive heuristic for the ADMM penalty parameter. Both 1D Monte Carlo tests and 2D image reconstruction simulations suggest the proposed framework, with the robust data fit term, reduces the reconstruction error for data corrupted with both outliers and additive noise, relative to competing algorithms having the same total computation.

High dynamic range coherent imaging using compressed sensing

In both lensless Fourier transform holography (FTH) and coherent diffraction imaging (CDI), a beamstop is used to block strong intensities which exceed the limited dynamic range of the sensor, causing a loss in low-frequency information, making high quality reconstructions difficult or even impossible. In this paper, we show that an image can be recovered from high-frequencies alone, thereby overcoming the beamstop problem in both FTH and CDI. The only requirement is that the object is sparse in a known basis, a common property of most natural and manmade signals. The reconstruction method relies on compressed sensing (CS) techniques, which ensure signal recovery from incomplete measurements. Specifically, in FTH, we perform compressed sensing (CS) reconstruction of captured holograms and show that this method is applicable not only to standard FTH, but also multiple or extended reference FTH. For CDI, we propose a new phase retrieval procedure, which combines Fienup's hybrid input-output (HIO) method and CS. Both numerical simulations and proof-of-principle experiments are shown to demonstrate the effectiveness and robustness of the proposed CS-based reconstructions in dealing with missing data in both FTH and CDI.

Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects

Phase-retrieval problems of one-dimensional (1D) signals are known to suffer from ambiguity that hampers their recovery from measurements of their Fourier magnitude, even when their support (a region that confines the signal) is known. Here we demonstrate sparsity-based coherent diffraction imaging of 1D objects using extreme-ultraviolet radiation produced from high harmonic generation. Using sparsity as prior information removes the ambiguity in many cases and enhances the resolution beyond the physical limit of the microscope. Our approach may be used in a variety of problems, such as diagnostics of defects in microelectronic chips. Importantly, this is the first demonstration of sparsity-based 1D phase retrieval from actual experiments, hence it paves the way for greatly improving the performance of Fourier-based measurement systems where 1D signals are inherent, such as diagnostics of ultrashort laser pulses, deciphering the complex time-dependent response functions (for example, time-dependent permittivity and permeability) from spectral measurements and vice versa.

In measurements that employ phase retrieval algorithms, such as coherent diffraction imaging, reconstruction of one-dimensional signals is challenging due to ambiguity issues. Here, the authors demonstrate super-resolution coherent imaging of one-dimensional objects by utilizing sparsity prior information.

Sparsity-based Ankylography for Recovering 3D molecular structures from single-shot 2D scattered light intensity

Deciphering the three-dimensional (3D) structure of complex molecules is of major importance, typically accomplished with X-ray crystallography. Unfortunately, many important molecules cannot be crystallized, hence their 3D structure is unknown. Ankylography presents an alternative, relying on scattering an ultrashort X-ray pulse off a single molecule before it disintegrates, measuring the far-field intensity on a two-dimensional surface, followed by computation. However, significant information is absent due to lower dimensionality of the measurements and the inability to measure the phase. Recent Ankylography experiments attracted much interest, but it was counter-argued that Ankylography is valid only for objects containing a small number of volume pixels. Here, we propose a sparsity-based approach to reconstruct the 3D structure of molecules. Sparsity is natural for Ankylography, because molecules can be represented compactly in stoichiometric basis. Utilizing sparsity, we surpass current limits on recoverable information by orders of magnitude, paving the way for deciphering the 3D structure of macromolecules.

X-ray laser holds promise for deciphering three-dimensional structures of organic molecules, which constitutes a major goal in structural biology. Mutzafi et al. propose an algorithm to overcome the issue of laser-induced sample damage based on prior knowledge of the atoms that comprise the molecules.

New modes in label-free super resolution based on photo-modulated reflectivity

The recent advances in far-field super-resolution (SR) microscopy rely on, and therefore are limited by the ability to control the fluorescence of label molecules. We demonstrated a far field label-free SR methodology that relies on the nonlinear response of the reflectance to photo-modulation by a pump laser. Here we extend our approach in two directions. We show that the method can be further simplified and improved by using a single beam rather than a pump and probe or by adding spatial probe modulation to improve resolution. Additionally, we demonstrate SR in sectioning and further investigate the dynamics of non-linearity in photo-modulated reflectance. These new modalities of nonlinear photo-modulated reflectivity (NPMR) enhance its applicability using lower orders of nonlinear response.

Super resolution methodology based on temperature dependent Raman scattering

The recent advances in far-field super-resolution (SR) microscopy rely on, and therefore are limited by the ability to control the fluorescence of label molecules. We suggest a new, label-free, far-field SR microscopy based on temperature dependence of Raman scattering. Here, we present simulation and experimental characterization of the method. In an ultrafast pump-probe scheme, a spatial temperature profile is optically excited throughout the diffraction-limited spot; the Raman spectrum is probed with an overlapping laser. Thermally induced shifts, recorded in a specific spectral region of interest (ROI), enable spatial discrimination between areas of different temperature. Our simulations show spatial resolution that surpasses the diffraction limit by more than a factor of 2. Our method is compatible with material characterization in ambient, vacuum and liquid, thin and thick samples alike.

Dictionary-based image reconstruction for superresolution in integrated circuit imaging

Resolution improvement through signal processing techniques for integrated circuit imaging is becoming more crucial as the rapid decrease in integrated circuit dimensions continues. Although there is a significant effort to push the limits of optical resolution for backside fault analysis through the use of solid immersion lenses, higher order laser beams, and beam apodization, signal processing techniques are required for additional improvement. In this work, we propose a sparse image reconstruction framework which couples overcomplete dictionary-based representation with a physics-based forward model to improve resolution and localization accuracy in high numerical aperture confocal microscopy systems for backside optical integrated circuit analysis. The effectiveness of the framework is demonstrated on experimental data.

Beyond crystallography: diffractive imaging using coherent x-ray light sources

X-ray crystallography has been central to the development of many fields of science over the past century. It has now matured to a point that as long as good-quality crystals are available, their atomic structure can be routinely determined in three dimensions. However, many samples in physics, chemistry, materials science, nanoscience, geology, and biology are noncrystalline, and thus their three-dimensional structures are not accessible by traditional x-ray crystallography. Overcoming this hurdle has required the development of new coherent imaging methods to harness new coherent x-ray light sources. Here we review the revolutionary advances that are transforming x-ray sources and imaging in the 21st century.

Super-resolution in label-free photomodulated reflectivity

We demonstrate a new, label-free, far-field super-resolution method based on an ultrafast pump-probe scheme oriented toward nanomaterial imaging. A focused pump laser excites a diffraction-limited spatial temperature profile, and the nonlinear changes in reflectance are probed. Enhanced spatial resolution is demonstrated with nanofabricated silicon and vanadium dioxide nanostructures. Using an air objective, resolution of 105 nm was achieved, well beyond the diffraction limit for the pump and probe beams and offering a novel kind of dedicated nanoscopy for materials.

Far-field imaging beyond diffraction limit using single sensor in combination with a resonant aperture

Far-field imaging beyond the diffraction limit is a long sought-after goal in various imaging applications, which requires usually mechanical scanning or an array of antennas. Here, we propose to solve this challenging problem using a single sensor in combination with a spatio-temporal resonant aperture antenna. We theoretically and numerically demonstrate that such resonant aperture antenna is capable of converting part evanescent waves into propagating waves and delivering them to far fields. The proposed imaging concept provides the unique ability to achieve super resolution for real-time data when illuminated by broadband electromagnetic waves, without the harsh requirements such as near- field scanning, mechanical scanning, or antenna arrays. We expect the imaging methodology to make breakthroughs in super-resolution imaging in microwave, terahertz, optical, and ultrasound regimes.

Exact modeling of cylindrical metal-dielectric multilayers beyond the effective medium approximation

We present a semi-analytical method for accurate modeling of wave propagation in cylindrically symmetric subwavelength metal-dielectric multilayers. Utilizing a cylindrical transfer matrix method, we compute the amplitude transfer function of cylindrical hyperlens, simulate the exact field distribution and propagation for a given source and compare it to that in effective hyperbolic medium. We investigate the conditions under which the effective medium theory (EMT) is valid and show that in cylindrical configuration, a new degree of freedom is present in the applicability of the EMT-the ratio between the inner radius of the structure and the unit cell size.