Ptychography

Fourier Ptychographic Coherent Anti-Stokes Raman Scattering Microscopy with Point-Scanning for Super-Resolution Imaging

Fourier ptychography (FP) is a high resolution wide-field imaging method based on the extended aperture in the Fourier space, which is synthesized from raw images with varying illumination angles. If FP is extended to coherent nonlinear optical imaging, the resolution could be further improved due to the increase of the cutoff frequency of the synthesized coherent optical transfer function (C-OTF) with respect to the order of nonlinear optical processes. However, there is a fundamental conflict between wide-field FP and nonlinear optical imaging, whereby the nonlinear optical imaging typically requires a focused excitation laser beam with high power density. To tackle the problem, in this work, a unique point-scanning FP (PS-FP) method is presented for super-resolution nonlinear optical imaging, in which the nonlinear optical signal is obtained by using focused laser beam, while the conventional FP algorithm can still be used to retrieve the super-resolution image. PS-FP coherent anti-Stokes Raman scattering (PS-FP-CARS) imaging on a variety of samples, where a 1.8-fold expansion of the OTF is achieved experimentally for enhancing vibrational imaging. Further theoretical calculation shows that the C-OTF of PS-FP higher-order CARS (PS-FP-HO-CARS) can be expanded up to ≈4.9-fold, thereby improving the spatial resolution by ≈3-fold in comparison with conventional point-scanning CARS with under tightly focused beams. The generality of PS-FP method developed in this work can be adapted to other coherent nonlinear optical imaging modalities for super-resolution imaging in tissue and cells.

New achievements in orbital angular momentum beam characterization using a Hartmann wavefront sensor and the Kirkpatrick-Baez active optical system KAOS

Advances in physics have been significantly driven by state-of-the-art technology, and in photonics and X-ray science this calls for the ability to manipulate the characteristics of optical beams. Orbital angular momentum (OAM) beams hold substantial promise in various domains such as ultra-high-capacity optical communication, rotating body detection, optical tweezers, laser processing, super-resolution imaging etc. Hence, the advancement of OAM beam-generation technology and the enhancement of its technical proficiency and characterization capabilities are of paramount importance. These endeavours will not only facilitate the use of OAM beams in the aforementioned sectors but also extend the scope of applications in diverse fields related to OAM beams. At the FERMI Free-Electron Laser (Trieste, Italy), OAM beams are generated either by tailoring the emission process on the undulator side or, in most cases, by coupling a spiral zone plate (SZP) in tandem with the refocusing Kirkpatrick-Baez active optic system (KAOS). To provide a robust and reproducible workflow to users, a Hartmann wavefront sensor (WFS) is used for both optics tuning and beam characterization. KAOS is capable of delivering both tightly focused and broad spots, with independent control over vertical and horizontal magnification. This study explores a novel non-conventional `near collimation' operational mode aimed at generating beams with OAM that employs the use of a lithographically manufactured SZP to achieve this goal. The article evaluates the mirror's performance through Hartmann wavefront sensing, offers a discussion of data analysis methodologies, and provides a quantitative analysis of these results with ptychographic reconstructions.

Ptycho-endoscopy on a lensless ultrathin fiber bundle tip

Synthetic aperture radar (SAR) utilizes an aircraft-carried antenna to emit electromagnetic pulses and detect the returning echoes. As the aircraft travels across a designated area, it synthesizes a large virtual aperture to improve image resolution. Inspired by SAR, we introduce synthetic aperture ptycho-endoscopy (SAPE) for micro-endoscopic imaging beyond the diffraction limit. SAPE operates by hand-holding a lensless fiber bundle tip to record coherent diffraction patterns from specimens. The fiber cores at the distal tip modulate the diffracted wavefield within a confined area, emulating the role of the 'airborne antenna' in SAR. The handheld operation introduces positional shifts to the tip, analogous to the aircraft's movement. These shifts facilitate the acquisition of a ptychogram and synthesize a large virtual aperture extending beyond the bundle's physical limit. We mitigate the influences of hand motion and fiber bending through a low-rank spatiotemporal decomposition of the bundle's modulation profile. Our tests demonstrate the ability to resolve a 548-nm linewidth on a resolution target. The achieved space-bandwidth product is ~1.1 million effective pixels, representing a 36-fold increase compared to that of the original fiber bundle. Furthermore, SAPE's refocusing capability enables imaging over an extended depth of field exceeding 2 cm. The aperture synthesizing process in SAPE surpasses the diffraction limit set by the probe's maximum collection angle, opening new opportunities for both fiber-based and distal-chip endoscopy in applications such as medical diagnostics and industrial inspection.

A correlated ferromagnetic polar metal by design

Polar metals have recently garnered increasing interest because of their promising functionalities. Here we report the experimental realization of an intrinsic coexisting ferromagnetism, polar distortion and metallicity in quasi-two-dimensional Ca3Co3O8. This material crystallizes with alternating stacking of oxygen tetrahedral CoO4 monolayers and octahedral CoO6 bilayers. The ferromagnetic metallic state is confined within the quasi-two-dimensional CoO6 layers, and the broken inversion symmetry arises simultaneously from the Co displacements. The breaking of both spatial-inversion and time-reversal symmetries, along with their strong coupling, gives rise to an intrinsic magnetochiral anisotropy with exotic magnetic field-free non-reciprocal electrical resistivity. An extraordinarily robust topological Hall effect persists over a broad temperature-magnetic field phase space, arising from dipole-induced Rashba spin-orbit coupling. Our work not only provides a rich platform to explore the coupling between polarity and magnetism in a metallic system, with extensive potential applications, but also defines a novel design strategy to access exotic correlated electronic states.

An Efficient Electron Ptychography Method for Retrieving the Object Spectrum from Only a Few Iterations

We present an efficient approach for electron ptychography based on a mathematical relationship that differs from that underlying the established algorithms of the ptychography iterative engine or the noniterative algorithms like the Wigner-distribution-deconvolution or the single-side-band method. Three variables are handled in this method-the transfer function of the objective lens, the object spectrum, and the diffraction wave whose phase is unknown. In the case of an aberration-corrected electron microscope, one is able to obtain a well-estimated transfer function of the lens. After reducing the number of three variables down to two, we construct an iterative loop between the object spectrum and the diffraction wave, which retrieves the object spectrum within a small number of iterations. We tested this object spectrum retrieval method on both a calculated and an experimental 4D-STEM datasets. By applying this method, we explore the influence of sampling, dose, and the size of illumination aperture on the reconstructed phase images.

Ptychographic Nanoscale Imaging of the Magnetoelectric Coupling in Freestanding BiFeO3

Understanding the magnetic and ferroelectric ordering of magnetoelectric multiferroic materials at the nanoscale necessitates a versatile imaging method with high spatial resolution. Here, soft X-ray ptychography is employed to simultaneously image the ferroelectric and antiferromagnetic domains in an 80 nm thin freestanding film of the room-temperature multiferroic BiFeO3 (BFO). The antiferromagnetic spin cycloid of period 64 nm is resolved by reconstructing the corresponding resonant elastic X-ray scattering in real space and visualized together with mosaic-like ferroelectric domains in a linear dichroic contrast image at the Fe L3 edge. The measurements reveal a near perfect coupling between the antiferromagnetic and ferroelectric ordering by which the propagation direction of the spin cycloid is locked orthogonally to the ferroelectric polarization. In addition, the study evinces both a preference for in-plane propagation of the spin cycloid and changes of the ferroelectric polarization by 71° between multiferroic domains in the epitaxial strain-free, freestanding BFO film. The results provide a direct visualization of the strong magnetoelectric coupling in BFO and of its fine multiferroic domain structure, emphasizing the potential of ptychographic imaging for the study of multiferroics and non-collinear magnetic materials with soft X-rays.

Direct observation of single-atom defects in monolayer two-dimensional materials by using electron ptychography at 200 kV acceleration voltage

Electron ptychography has emerged as a popular technology for high-resolution imaging by combining the high coherence of electron sources with the ultra-fast scanning electron coil. However, the limitations of conventional pixelated detectors, including poor dynamic range and slow data readout speeds, have posed restrictions in the past on conducting electron ptychography experiments. We used the Gatan STELA pixelated detector to capture sequential diffraction data of monolayer two-dimensional (2D) materials for ptychographic reconstruction. By using the pixelated detector and electron ptychography, we demonstrate the observation of the radiation damage at atomic resolution in Transition Metal Dichalcogenides (TMDs).

Artificial intelligence-enabled quantitative phase imaging methods for life sciences

Quantitative phase imaging, integrated with artificial intelligence, allows for the rapid and label-free investigation of the physiology and pathology of biological systems. This review presents the principles of various two-dimensional and three-dimensional label-free phase imaging techniques that exploit refractive index as an intrinsic optical imaging contrast. In particular, we discuss artificial intelligence-based analysis methodologies for biomedical studies including image enhancement, segmentation of cellular or subcellular structures, classification of types of biological samples and image translation to furnish subcellular and histochemical information from label-free phase images. We also discuss the advantages and challenges of artificial intelligence-enabled quantitative phase imaging analyses, summarize recent notable applications in the life sciences, and cover the potential of this field for basic and industrial research in the life sciences.

Extreme ultraviolet pellicle wrinkles influence on mask 3D effects: experimental demonstration

Extreme ultraviolet (EUV) lithography uses reflective optics and a thick mask absorber, leading to mask 3D (M3D) effects. These M3D effects cause disparities in the amplitudes and phases of EUV mask diffractions, impacting mask imaging performance and reducing process yields. Our findings demonstrate that wrinkles in the EUV pellicle can exacerbate M3D effects. This imbalance results in critical dimension variation, image contrast loss, and pattern shift in mask images. Therefore, the use of a pellicle material with thermodynamic characteristics that minimize wrinkles when exposed to EUV rays is imperative.

Soft X-ray spectro-ptychography of boron nitride nanobamboos, carbon nanotubes and permalloy nanorods

Spectro-ptychography offers improved spatial resolution and additional phase spectral information relative to that provided by scanning transmission X-ray microscopes. However, carrying out ptychography at the lower range of soft X-ray energies (e.g. below 200 eV to 600 eV) on samples with weakly scattering signals can be challenging. Here, results of soft X-ray spectro-ptychography at energies as low as 180 eV are presented, and its capabilities are illustrated with results from permalloy nanorods (Fe 2p), carbon nanotubes (C 1s) and boron nitride bamboo nanostructures (B 1s, N 1s). The optimization of low-energy X-ray spectro-ptychography is described and important challenges associated with measurement approaches, reconstruction algorithms and their effects on the reconstructed images are discussed. A method for evaluating the increase in radiation dose when using overlapping sampling is presented.

Spatial- and Fourier-domain ptychography for high-throughput bio-imaging

First envisioned for determining crystalline structures, ptychography has become a useful imaging tool for microscopists. However, ptychography remains underused by biomedical researchers due to its limited resolution and throughput in the visible light regime. Recent developments of spatial- and Fourier-domain ptychography have successfully addressed these issues and now offer the potential for high-resolution, high-throughput optical imaging with minimal hardware modifications to existing microscopy setups, often providing an excellent trade-off between resolution and field of view inherent to conventional imaging systems, giving biomedical researchers the best of both worlds. Here, we provide extensive information to enable the implementation of ptychography by biomedical researchers in the visible light regime. We first discuss the intrinsic connections between spatial-domain coded ptychography and Fourier ptychography. A step-by-step guide then provides the user instructions for developing both systems with practical examples. In the spatial-domain implementation, we explain how a large-scale, high-performance blood-cell lens can be made at negligible expense. In the Fourier-domain implementation, we explain how adding a low-cost light source to a regular microscope can improve the resolution beyond the limit of the objective lens. The turnkey operation of these setups is suitable for use by professional research laboratories, as well as citizen scientists. Users with basic experience in optics and programming can build the setups within a week. The do-it-yourself nature of the setups also allows these procedures to be implemented in laboratory courses related to Fourier optics, biomedical instrumentation, digital image processing, robotics and capstone projects.

Near-field multi-slice ptychography: quantitative phase imaging of optically thick samples with visible light and X-rays

Ptychography is a form of lens-free coherent diffractive imaging now used extensively in electron and synchrotron-based X-ray microscopy. In its near-field implementation, it offers a route to quantitative phase imaging at an accuracy and resolution competitive with holography, with the added advantages of extended field of view and blind deconvolution of the illumination beam profile from the sample image. In this paper we show how near-field ptychography can be combined with a multi-slice model, adding to this list of advantages the unique ability to recover high-resolution phase images of larger samples, whose thickness places them beyond the depth of field of alternative methods.

PtyLab.m/py/jl: a cross-platform, open-source inverse modeling toolbox for conventional and Fourier ptychography

Conventional (CP) and Fourier (FP) ptychography have emerged as versatile quantitative phase imaging techniques. While the main application cases for each technique are different, namely lens-less short wavelength imaging for CP and lens-based visible light imaging for FP, both methods share a common algorithmic ground. CP and FP have in part independently evolved to include experimentally robust forward models and inversion techniques. This separation has resulted in a plethora of algorithmic extensions, some of which have not crossed the boundary from one modality to the other. Here, we present an open source, cross-platform software, called PtyLab, enabling both CP and FP data analysis in a unified framework. With this framework, we aim to facilitate and accelerate cross-pollination between the two techniques. Moreover, the availability in Matlab, Python, and Julia will set a low barrier to enter each field.

Upgraded imaging capabilities at the BAMline (BESSY II)

The BAMline at the BESSY II synchrotron X-ray source has enabled research for more than 20 years in widely spread research fields such as materials science, biology, cultural heritage and medicine. As a nondestructive characterization method, synchrotron X-ray imaging, especially tomography, plays a particularly important role in structural characterization. A recent upgrade of key equipment of the BAMline widens its imaging capabilities: shorter scan acquisition times are now possible, in situ and operando studies can now be routinely performed, and different energy spectra can easily be set up. In fact, the upgraded double-multilayer monochromator brings full flexibility by yielding different energy spectra to optimize flux and energy resolution as desired. The upgraded detector (based on an sCMOS camera) also allows exploiting the higher flux with reduced readout times. Furthermore, an installed slip ring allows the sample stage to continuously rotate. The latter feature enables tomographic observation of processes occurring in the time scale of a few seconds.

High-throughput digital pathology via a handheld, multiplexed, and AI-powered ptychographic whole slide scanner

The recent advent of whole slide imaging (WSI) systems has moved digital pathology closer to diagnostic applications and clinical practices. Integrating WSI with machine learning promises the growth of this field in upcoming years. Here we report the design and implementation of a handheld, colour-multiplexed, and AI-powered ptychographic whole slide scanner for digital pathology applications. This handheld scanner is built using low-cost and off-the-shelf components, including red, green, and blue laser diodes for sample illumination, a modified stage for programmable sample positioning, and a synchronized image sensor pair for data acquisition. We smear a monolayer of goat blood cells on the main sensor for high-resolution lensless coded ptychographic imaging. The synchronized secondary sensor acts as a non-contact encoder for precisely tracking the absolute object position for ptychographic reconstruction. For WSI, we introduce a new phase-contrast-based focus metric for post-acquisition autofocusing of both stained and unstained specimens. We show that the scanner can resolve the 388-nm linewidth on the resolution target and acquire gigapixel images with a 14 mm × 11 mm area in ∼70 seconds. The imaging performance is validated with regular stained pathology slides, unstained thyroid smears, and malaria-infected blood smears. The deep neural network developed in this study further enables high-throughput cytometric analysis using the recovered complex amplitude. The reported do-it-yourself scanner offers a portable solution to transform the high-end WSI system into one that can be made widely available at a low cost. The capability of high-throughput quantitative phase imaging may also find applications in rapid on-site evaluations.

Blood-Coated Sensor for High-Throughput Ptychographic Cytometry on a Blu-ray Disc

The Blu-ray drive is an engineering masterpiece that integrates disc rotation, pickup head translation, and three lasers in a compact and portable format. Here, we integrate a blood-coated image sensor with a modified Blu-ray drive for high-throughput cytometric analysis of various biospecimens. In this device, samples are mounted on the rotating Blu-ray disc and illuminated by the built-in lasers from the pickup head. The resulting coherent diffraction patterns are then recorded by the blood-coated image sensor. The rich spatial features of the blood-cell monolayer help down-modulate the object information for sensor detection, thus forming a high-resolution computational biolens with a theoretically unlimited field of view. With the acquired data, we develop a lensless coherent diffraction imaging modality termed rotational ptychography for image reconstruction. We show that our device can resolve the 435 nm line width on the resolution target and has a field of view only limited by the size of the Blu-ray disc. To demonstrate its applications, we perform high-throughput urinalysis by locating disease-related calcium oxalate crystals over the entire microscope slide. We also quantify different types of cells on a blood smear with an acquisition speed of ∼10,000 cells per second. For in vitro experiments, we monitor live bacterial cultures over the entire Petri dish with single-cell resolution. Using biological cells as a computational lens could enable new intriguing imaging devices for point-of-care diagnostics. Modifying a Blu-ray drive with the blood-coated sensor further allows the spread of high-throughput optical microscopy from well-equipped laboratories to citizen scientists worldwide.

Accurate and Robust Calibration of the Uniform Affine Transformation Between Scan-Camera Coordinates for Atom-Resolved In-Focus 4D-STEM Datasets

Accurate geometrical calibration between the scan coordinates and the camera coordinates is critical in four-dimensional scanning transmission electron microscopy (4D-STEM) for both quantitative imaging and ptychographic reconstructions. For atomic-resolved, in-focus 4D-STEM datasets, we propose a hybrid method incorporating two sub-routines, namely a J-matrix method and a Fourier method, which can calibrate the uniform affine transformation between the scan-camera coordinates using raw data, without a priori knowledge of the crystal structure of the specimen. The hybrid method is found robust against scan distortions and residual probe aberrations. It is also effective even when defects are present in the specimen, or the specimen becomes relatively thick. We will demonstrate that a successful geometrical calibration with the hybrid method will lead to a more reliable recovery of both the specimen and the electron probe in a ptychographic reconstruction. We will also show that, although the elimination of local scan position errors still requires an iterative approach, the rate of convergence can be improved, and the residual errors can be further reduced if the hybrid method can be firstly applied for initial calibration. The code is made available as a simple-to-use tool to correct affine transformations of the scan-camera coordinates in 4D-STEM experiments.

Dynamical diffraction of high-energy electrons investigated by focal series momentum-resolved scanning transmission electron microscopy at atomic resolution

We report a study of scattering dynamics in crystals employing momentum-resolved scanning transmission electron microscopy under varying illumination conditions. As we perform successive changes of the probe focus, multiple real-space signals are obtained in dependence of the shape of the incident electron wave. With support from extensive simulations, each signal is shown to be characterised by an optimum focus for which the contrast is maximum and which differs among different signals. For instance, a systematic focus mismatch is found between images formed by high-angle scattering, being sensitive to thickness and chemical composition, and the first moment in diffraction space, being sensitive to electric fields. It follows that a single recording at one specific probe focus is usually insufficient to characterise materials comprehensively. Most importantly, we demonstrate in experiment and simulation that the second moment μ20+μ02=〈p2〉 of the diffracted intensity exhibits a contrast maximum when the electron probe is focused at the top and bottom faces of the specimen, making the presented concept attractive for measuring local topography. Given the versatility of 〈p2〉, we furthermore present a detailed study of its large-angle convergence both analytically using the Mott scattering approach, and by dynamical simulations using the multislice algorithm including thermal diffuse scattering. Both approaches are in very good agreement and yield logarithmic divergence with increasing scattering angle.

Factors limiting quantitative phase retrieval in atomic-resolution differential phase contrast scanning transmission electron microscopy using a segmented detector

Quantitative differential phase contrast imaging of materials in atomic-resolution scanning transmission electron microscopy using segmented detectors is limited by various factors, including coherent and incoherent aberrations, detector positioning and uniformity, and scan-distortion. By comparing experimental case studies of monolayer and few-layer graphene with image simulations, we explore which parameters require the most precise characterisation for reliable and quantitative interpretation of the reconstructed phases. Coherent and incoherent lens aberrations are found to have the most significant impact. For images over a large field of view, the impact of noise and non-periodic boundary conditions are appreciable, but in this case study have less of an impact than artefacts introduced by beam deflections coupling to beam scanning (imperfect tilt-shift purity).

Optofluidic ptychography on a chip

We report the implementation of a fully on-chip, lensless microscopy technique termed optofluidic ptychography. This imaging modality complements the miniaturization provided by microfluidics and allows the integration of ptychographic microscopy into various lab-on-a-chip devices. In our prototype, we place a microfluidic channel on the top surface of a coverslip and coat the bottom surface with a scattering layer. The channel and the coated coverslip substrate are then placed on top of an image sensor for diffraction data acquisition. Similar to the operation of a flow cytometer, the device utilizes microfluidic flow to deliver specimens across the channel. The diffracted light from the flowing objects is modulated by the scattering layer and recorded by the image sensor for ptychographic reconstruction, where high-resolution quantitative complex images are recovered from the diffraction measurements. By using an image sensor with a 1.85 μm pixel size, our device can resolve the 550 nm linewidth on the resolution target. We validate the device by imaging different types of biospecimens, including C. elegans, yeast cells, paramecium, and closterium sp. We also demonstrate a high-resolution ptychographic reconstruction at a video framerate of 30 frames per second. The reported technique can address a wide range of biomedical needs and engenders new ptychographic imaging innovations in a flow cytometer configuration.

A Parameter Refinement Method for Ptychography Based on Deep Learning Concepts

X-ray ptychography is an advanced computational microscopy technique, which is delivering exceptionally detailed quantitative imaging of biological and nanotechnology specimens, which can be used for high-precision X-ray measurements. However, coarse parametrisation in propagation distance, position errors and partial coherence frequently threaten the experimental viability. In this work, we formally introduce these actors, solving the whole reconstruction as an optimisation problem. A modern deep learning framework was used to autonomously correct the setup incoherences, thus improving the quality of a ptychography reconstruction. Automatic procedures are indeed crucial to reduce the time for a reliable analysis, which has a significant impact on all the fields that use this kind of microscopy. We implemented our algorithm in our software framework, SciComPty, releasing it as open-source. We tested our system on both synthetic datasets, as well as on real data acquired at the TwinMic beamline of the Elettra synchrotron facility.

Single-particle cryo-EM: alternative schemes to improve dose efficiency

Imaging of biomolecules by ionizing radiation, such as electrons, causes radiation damage which introduces structural and compositional changes of the specimen. The total number of high-energy electrons per surface area that can be used for imaging in cryogenic electron microscopy (cryo-EM) is severely restricted due to radiation damage, resulting in low signal-to-noise ratios (SNR). High resolution details are dampened by the transfer function of the microscope and detector, and are the first to be lost as radiation damage alters the individual molecules which are presumed to be identical during averaging. As a consequence, radiation damage puts a limit on the particle size and sample heterogeneity with which electron microscopy (EM) can deal. Since a transmission EM (TEM) image is formed from the scattering process of the electron by the specimen interaction potential, radiation damage is inevitable. However, we can aim to maximize the information transfer for a given dose and increase the SNR by finding alternatives to the conventional phase-contrast cryo-EM techniques. Here some alternative transmission electron microscopy techniques are reviewed, including phase plate, multi-pass transmission electron microscopy, off-axis holography, ptychography and a quantum sorter. Their prospects for providing more or complementary structural information within the limited lifetime of the sample are discussed.

Lensless Reflection Imaging of Obliquely Illuminated Objects I: Choosing a Domain for Phase Retrieval and Ptychography

Ptychography is a lensless imaging technology that is validated from hard X-rays to terahertz spectral range. It is most attractive for extreme ultraviolet (EUV) and X-rays as optical elements are expensive and often not available. Typically, the set up involves coherently illuminated object that directs the scattered radiation normally to detector which is parallel to the object plane. Computer processing of diffraction patterns obtained when scanning the object gives the image, more precisely, the distribution of intensity and phase on its surface. However, this scheme is inefficient for EUV and X-rays due to poor reflectivity and low penetration in all materials. Reflection mode ptychography solves the problem if illumination angles do not exceed the critical angle of object material. Changing the geometry of experiment changes physical and mathematical model of image formation. Including: diffraction integral describing beam propagation from object to detector, inverse problem, optimization of object illumination angle, position and orientation of detector, choosing size and grid of coordinate and frequency computer domains. This paper considers the wavefield scattered to detector by obliquely illuminated object and determines a domain for processing of obtained scans. Solution of inverse problem with phase retrieval and resulting numerical images will be presented in the next paper.

Scattering Matrix Determination in Crystalline Materials from 4D Scanning Transmission Electron Microscopy at a Single Defocus Value

Recent work has revived interest in the scattering matrix formulation of electron scattering in transmission electron microscopy as a stepping stone toward atomic-resolution structure determination in the presence of multiple scattering. We discuss ways of visualizing the scattering matrix that make its properties clear. Through a simulation-based case study incorporating shot noise, we shown how regularizing on this continuity enables the scattering matrix to be reconstructed from 4D scanning transmission electron microscopy (STEM) measurements from a single defocus value. Intriguingly, for crystalline samples, this process also yields the sample thickness to nanometer accuracy with no a priori knowledge about the sample structure. The reconstruction quality is gauged by using the reconstructed scattering matrix to simulate STEM images at defocus values different from that of the data from which it was reconstructed.

Complex wavefront sensing based on coherent diffraction imaging using vortex modulation

Phase retrieval seeks to reconstruct the phase from the measured intensity, which is an ill-posed problem. A phase retrieval problem can be solved with physical constraints by modulating the investigated complex wavefront. Orbital angular momentum has been recently employed as a type of reliable modulation. The topological charge l is robust during propagation when there is atmospheric turbulence. In this work, topological modulation is used to solve the phase retrieval problem. Topological modulation offers an effective dynamic range of intensity constraints for reconstruction. The maximum intensity value of the spectrum is reduced by a factor of 173 under topological modulation when l is 50. The phase is iteratively reconstructed without a priori knowledge. The stagnation problem during the iteration can be avoided using multiple topological modulations.

Ptychographic optical coherence tomography

Ptychography is a robust computational imaging technique that can reconstruct complex light fields beyond conventional hardware limits. However, for many wide-field computational imaging techniques, including ptychography, depth sectioning remains a challenge. Here we demonstrate a high-resolution three-dimensional (3D) computational imaging approach, which combines ptychography with spectral-domain imaging, inspired by optical coherence tomography (OCT). This results in a flexible imaging system with the main advantages of OCT, such as depth-sectioning without sample rotation, decoupling of transverse and axial resolution, and a high axial resolution only determined by the source bandwidth. The interferometric reference needed in OCT is replaced by computational methods, simplifying hardware requirements. As ptychography is capable of deconvolving the illumination contributions in the observed signal, speckle-free images are obtained. We demonstrate the capabilities of ptychographic optical coherence tomography (POCT) by imaging an axially discrete lithographic structure and an axially continuous mouse brain sample.

Soft X-ray Ptychography Chemical Imaging of Degradation in a Composite Surface-Reconstructed Li-Rich Cathode

The capability in spatially resolving the interactions between components in lithium (Li)-ion battery cathodes, especially correlating chemistry and electronic structure, is challenging but critical for a better understanding of complex degradation mechanisms for rational developments. X-ray spectro-ptychography and conventional synchrotron-based scanning transmission X-ray microscopy image stacks are the most powerful probes for studying the distribution and chemical state of cations in degraded Li-rich cathodes. Herein, we propose a chemical approach with a spatial resolution of around 5.6 nm to imaging degradation heterogeneities and interplay among components in degraded Li-rich cathodes. Through the chemical imaging reconstruction of the degraded Li-rich cathodes, fluorine (F) ions incorporated into the lattice during charging/discharging processes are proved and strongly correlate with the manganese (Mn) dissolution and oxygen loss within the secondary particles and impact the electronic structure. Otherwise, the electrode-electrolyte interphase component, scattered LiF particles (100-500 nm) along with the MnF₂ layer, is also visualized between the primary particles inside the secondary particles of the degraded cathodes. The results provide direct visual evidence for the Li-rich cathode degradation mechanisms and demonstrate that the low-energy ptychography technique offers a superior approach for high-resolution battery material characterization.

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.

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.

Multi-layered full-field phase imaging using continuous-wave terahertz ptychography

Due to the unique properties of terahertz (THz) waves, THz phase imaging has been widely investigated to retrieve the absorption and phase modulation of dielectric two-dimensional thin samples, as well as multiple stacked samples. In this Letter, we apply the three-dimensional ptychographic iterative engine algorithm for continuous-wave THz full-field multi-layered phase imaging. The complex-valued transmission function of two-layered polypropylene thin plates and the corresponding probe function are reconstructed, respectively, which are immune to crosstalk of different layers. The phenomenon of the field-of-view enlargement at the second object layer is observed. This lensless compact imaging method can be potentially used for THz three-dimensional imaging.