Dynamic imaging using ptychography

Wavelength-multiplexed multi-mode EUV reflection ptychography based on automatic differentiation

Ptychographic extreme ultraviolet (EUV) diffractive imaging has emerged as a promising candidate for the next generationmetrology solutions in the semiconductor industry, as it can image wafer samples in reflection geometry at the nanoscale. This technique has surged attention recently, owing to the significant progress in high-harmonic generation (HHG) EUV sources and advancements in both hardware and software for computation. In this study, a novel algorithm is introduced and tested, which enables wavelength-multiplexed reconstruction that enhances the measurement throughput and introduces data diversity, allowing the accurate characterisation of sample structures. To tackle the inherent instabilities of the HHG source, a modal approach was adopted, which represents the cross-density function of the illumination by a series of mutually incoherent and independent spatial modes. The proposed algorithm was implemented on a mainstream machine learning platform, which leverages automatic differentiation to manage the drastic growth in model complexity and expedites the computation using GPU acceleration. By optimising over 200 million parameters, we demonstrate the algorithm's capacity to accommodate experimental uncertainties and achieve a resolution approaching the diffraction limit in reflection geometry. The reconstruction of wafer samples with 20-nm high patterned gold structures on a silicon substrate highlights our ability to handle complex physical interrelations involving a multitude of parameters. These results establish ptychography as an efficient and accurate metrology tool.

Mathematical uniqueness of multimode ptychographic imaging

By writing diffracted intensities as a set of linear equations with the self-correlation of sample's Fourier components as unknown terms and the self-correlation of illumination's Fourier components as coefficients, it was found that the number of unknown terms to be determined is much larger in partially coherent PIE than that in purely coherent PIE. When a partially coherent illumination composed of N modes was applied a unique reconstruction can be determined by scanning the sample to at least 4N positions and recording 4N frames of diffraction patterns. While mathematically illustrating the physical mechanism of multimode ptychography and numerically demonstrating its capability in generating unique reconstruction under partially coherent illumination, this study showed for the first time that multimode ptychography could be an analytic imaging method.

Automatic parameter selection for electron ptychography via Bayesian optimization

Electron ptychography provides new opportunities to resolve atomic structures with deep sub-angstrom spatial resolution and to study electron-beam sensitive materials with high dose efficiency. In practice, obtaining accurate ptychography images requires simultaneously optimizing multiple parameters that are often selected based on trial-and-error, resulting in low-throughput experiments and preventing wider adoption. Here, we develop an automatic parameter selection framework to circumvent this problem using Bayesian optimization with Gaussian processes. With minimal prior knowledge, the workflow efficiently produces ptychographic reconstructions that are superior to those processed by experienced experts. The method also facilitates better experimental designs by exploring optimized experimental parameters from simulated data.

High-resolution ptychographic imaging enabled by high-speed multi-pass scanning

As a coherent diffraction imaging technique, ptychography provides high-spatial resolution beyond Rayleigh's criterion of the focusing optics, but it is also sensitively affected by the decoherence coming from the spatial and temporal variations in the experiment. Here we show that high-speed ptychographic data acquisition with short exposure can effectively reduce the impact from experimental variations. To reach a cumulative dose required for a given resolution, we further demonstrate that a continuous multi-pass scan via high-speed ptychography can achieve high-resolution imaging. This low-dose scan strategy is shown to be more dose-efficient, and has potential for radiation-sensitive sample studies and time-resolved imaging.

Broadband X-ray ptychography using multi-wavelength algorithm

Ptychography is a rapidly developing scanning microscopy which is able to view the internal structures of samples at a high resolution beyond the illumination size. The achieved spatial resolution is theoretically dose-limited. A broadband source can provide much higher flux compared with a monochromatic source; however, it conflicts with the necessary coherence requirements of this coherent diffraction imaging technique. In this paper, a multi-wavelength reconstruction algorithm has been developed to deal with the broad bandwidth in ptychography. Compared with the latest development of mixed-state reconstruction approach, this multi-wavelength approach is more accurate in the physical model, and also considers the spot size variation as a function of energy due to the chromatic focusing optics. Therefore, this method has been proved in both simulation and experiment to significantly improve the reconstruction when the source bandwidth, illumination size and scan step size increase. It is worth mentioning that the accurate and detailed information of the energy spectrum for the incident beam is not required in advance for the proposed method. Further, we combine multi-wavelength and mixed-state approaches to jointly solve temporal and spatial partial coherence in ptychography so that it can handle various disadvantageous experimental effects. The significant relaxation in coherence requirements by our approaches allows the use of high-flux broadband X-ray sources for high-efficient and high-resolution ptychographic imaging.

Dynamic coherent diffractive imaging using unsupervised identification of spatiotemporal constraints

Dynamic coherent diffractive imaging (CDI) reveals the fine details of structural, chemical, and biological processes occurring at the nanoscale but imposes strict constraints on the object distribution and illumination. Ptychographic CDI relaxes these constraints by exploiting redundant information in data obtained from overlapping regions of an object, but its time resolution is inherently limited. We have extended ptychographic redundancy into the spatiotemporal domain in dynamic CDI, automatically identifying redundant information in time-series coherent diffraction data obtained from dynamic systems. Simulated synchrotron experiments show that high spatiotemporal resolution is achieved without a priori knowledge of the object or its dynamics.

Multi-beam X-ray ptychography for high-throughput coherent diffraction imaging

X-ray ptychography is a rapidly developing coherent diffraction imaging technique that provides nanoscale resolution on extended field-of-view. However, the requirement of coherence and the scanning mechanism limit the throughput of ptychographic imaging. In this paper, we propose X-ray ptychography using multiple illuminations instead of single illumination in conventional ptychography. Multiple locations of the sample are simultaneously imaged by spatially separated X-ray beams, therefore, the obtained field-of-view in one scan can be enlarged by a factor equal to the number of illuminations. We have demonstrated this technique experimentally using two X-ray beams focused by a house-made Fresnel zone plate array. Two areas of the object and corresponding double illuminations were successfully reconstructed from diffraction patterns acquired in one scan, with image quality similar with those obtained by conventional single-beam ptychography in sequence. Multi-beam ptychography approach increases the imaging speed, providing an efficient way for high-resolution imaging of large extended specimens.

Ptychography at the Linac Coherent Light Source in a parasitic geometry

X-ray free-electron lasers (FELs) are being recognized as a powerful tool in an ever-increasing number of research fields, but are very limited as to the number of experiments that they can support. This work shows that more beamtime could be made available by using `parasitic' geometries, where a secondary experiment uses the X-ray beam that the primary experiment does not utilize. The first successful ptychography experiment, a scanning coherent diffractive imaging technique, in a parasitic geometry at an X-ray FEL is demonstrated. Utilizing the CXI hutch at the Linac Coherent Light Source (LCLS), it is shown that the obtained data are of high quality and that characterizing the beam using ptychography can be much faster than traditional imprinting methods.

Combining Laue diffraction with Bragg coherent diffraction imaging at 34-ID-C

Measurement modalities in Bragg coherent diffraction imaging (BCDI) rely on finding a signal from a single nanoscale crystal object which satisfies the Bragg condition among a large number of arbitrarily oriented nanocrystals. However, even when the signal from a single Bragg reflection with (hkl) Miller indices is found, the crystallographic axes on the retrieved three-dimensional (3D) image of the crystal remain unknown, and thus localizing in reciprocal space other Bragg reflections becomes time-consuming or requires good knowledge of the orientation of the crystal. Here, the commissioning of a movable double-bounce Si (111) monochromator at the 34-ID-C endstation of the Advanced Photon Source is reported, which aims at delivering multi-reflection BCDI as a standard tool in a single beamline instrument. The new instrument enables, through rapid switching from monochromatic to broadband (pink) beam, the use of Laue diffraction to determine crystal orientation. With a proper orientation matrix determined for the lattice, one can measure coherent diffraction patterns near multiple Bragg peaks, thus providing sufficient information to image the full strain tensor in 3D. The design, concept of operation, the developed procedures for indexing Laue patterns, and automated measuring of Bragg coherent diffraction data from multiple reflections of the same nanocrystal are discussed.

Mixed-state electron ptychography enables sub-angstrom resolution imaging with picometer precision at low dose

Both high resolution and high precision are required to quantitatively determine the atomic structure of complex nanostructured materials. However, for conventional imaging methods in scanning transmission electron microscopy (STEM), atomic resolution with picometer precision cannot usually be achieved for weakly-scattering samples or radiation-sensitive materials, such as 2D materials. Here, we demonstrate low-dose, sub-angstrom resolution imaging with picometer precision using mixed-state electron ptychography. We show that correctly accounting for the partial coherence of the electron beam is a prerequisite for high-quality structural reconstructions due to the intrinsic partial coherence of the electron beam. The mixed-state reconstruction gains importance especially when simultaneously pursuing high resolution, high precision and large field-of-view imaging. Compared with conventional atomic-resolution STEM imaging techniques, the mixed-state ptychographic approach simultaneously provides a four-times-faster acquisition, with double the information limit at the same dose, or up to a fifty-fold reduction in dose at the same resolution.

With conventional scanning transmission electron microscopy, some sensitive materials are difficult to image with atomic resolution. The authors present a method of mixed-state electron ptychography that enables picometer precision with fast acquisition and low dosage.

Multibeam ptychography with synchrotron hard X-rays

We report the first demonstration of multibeam ptychography using synchrotron hard X-rays, which can enlarge the field of view of the reconstructed image of objects by efficiently using partially coherent X-rays. We measured the ptychographic diffraction patterns of a Pt test sample and MnO particles using three mutually incoherent coherent beams with a high intensity that were produced by using both the multiple slits and a pair of focusing mirrors. We successfully reconstructed the phase map of the samples at a spatial resolution of 25 nm in a field of view about twice as wide as that in the single-beam ptychography. We also computationally simulated a feasible experimental setup using random modulators to further enlarge the field of view by increasing the number of available beams. The present method has the potential to enable the high spatial resolution and large field-of-view observation of specimens in materials science and biology.

Three-dimensional optical trapping and orientation of microparticles for coherent X-ray diffraction imaging

Optical trapping has been implemented in many areas of physics and biology as a noncontact sample manipulation technique to study the structure and dynamics of nano- and mesoscale objects. It provides a unique approach for manipulating microscopic objects without inducing undesired changes in structure. Combining optical trapping with hard X-ray microscopy techniques, such as coherent diffraction imaging and crystallography, provides a nonperturbing environment where electronic and structural dynamics of an individual particle in solution can be followed in situ. It was previously shown that optical trapping allows the manipulation of micrometer-sized objects for X-ray fluorescence imaging. However, questions remain over the ability of optical trapping to position objects for X-ray diffraction measurements, which have stringent requirements for angular stability. Our work demonstrates that dynamic holographic optical tweezers are capable of manipulating single micrometer-scale anisotropic particles in a microfluidic environment with the precision and stability required for X-ray Bragg diffraction experiments-thus functioning as an "optical goniometer." The methodology can be extended to a variety of X-ray experiments and the Bragg coherent diffractive imaging of individual particles in solution, as demonstrated here, will be markedly enhanced with the advent of brighter, coherent X-ray sources.

Simultaneous nanostructure and chemical imaging of intact whole nematodes

Accurately locating biologically relevant elements at high resolution: simultaneous ptychography and fluorescence imaging of large specimens comes of age.

3D X-Ray Imaging of Continuous Objects beyond the Depth of Focus Limit

X-ray ptychography is becoming the standard method for sub-30 nm imaging of thick extended samples. Available algorithms and computing power have traditionally restricted sample reconstruction to 2D slices. We build on recent progress in optimization algorithms and high performance computing to solve the ptychographic phase retrieval problem directly in 3D. Our approach addresses samples that do not fit entirely within the depth of focus of the imaging system. Such samples pose additional challenges because of internal diffraction effects within the sample. We demonstrate our approach on a computational sample modeled with 17 million complex variables.

Arbitrary-path fly-scan ptychography

Ptychography is a coherent diffractive imaging method that can provide a diffraction-limited, robust reconstruction of the sample's complex transmission function without the use of high-quality optics. However, the scanning nature of conventional X-ray ptychography unavoidably requires the mechanical motion of either the illumination probe or the sample. In order to avoid overhead related to breaking and acceleration for every scan position, so-called fly-scan methods were developed. Here, we present an improved variant that removes the limitation of continuous scanning along a linear scanning path and allows for ptychographic reconstruction of scans taken along an arbitrary 2D continuous trajectory. We also demonstrate numerically and experimentally that our method provides significantly improved robustness against noise, particularly for larger fly-scan steps, i.e. sample shift during an exposure, which will gain importance with the advent of 4th generation synchrotron sources, where the available coherent flux may be increased by orders of magnitude. Finally, we show that the use of a spiral scan continuous trajectory alleviates significantly raster grid artifacts.

Beam drift and partial probe coherence effects in EUV reflective-mode coherent diffractive imaging

While the industrial implementation of extreme ultraviolet lithography for upcoming technology nodes is becoming ever more realistic, a number of challenges have yet to be overcome. Among them is the need for actinic mask inspection. We report on reflective-mode lensless imaging of a patterned multi-layer mask sample at extreme ultraviolet wavelength that provides a finely structured defect map of the sample under test. Here, we present the imaging results obtained using ptychography in reflection mode at 6° angle of incidence from the surface normal and 13.5 nm wavelength. Moreover, an extended version of the difference map algorithm is employed that substantially enhances the reconstruction quality by taking into account both long and short-term variations of the incident illumination.

Low-dose cryo electron ptychography via non-convex Bayesian optimization

Electron ptychography has seen a recent surge of interest for phase sensitive imaging at atomic or near-atomic resolution. However, applications are so far mainly limited to radiation-hard samples, because the required doses are too high for imaging biological samples at high resolution. We propose the use of non-convex Bayesian optimization to overcome this problem, and show via numerical simulations that the dose required for successful reconstruction can be reduced by two orders of magnitude compared to previous experiments. As an important application we suggest to use this method for imaging single biological macromolecules at cryogenic temperatures and demonstrate 2D single-particle reconstructions from simulated data with a resolution up to 5.4 Å at a dose of 20e⁻/Ų. When averaging over only 30 low-dose datasets, a 2D resolution around 3.5 Å is possible for macromolecular complexes even below 100 kDa. With its independence from the microscope transfer function, direct recovery of phase contrast, and better scaling of signal-to-noise ratio, low-dose cryo electron ptychography may become a promising alternative to Zernike phase-contrast microscopy.

Compensation for the setup instability in ptychographic imaging

The high-frequency vibration of the imaging system degrades the quality of the reconstruction of ptychography by acting as a low-pass filter on ideal diffraction patterns. In this study, we demonstrate that by subtracting the deliberately blurred diffraction patterns from the recorded patterns and adding the properly amplified subtraction to the original data, the high-frequency components lost by the vibration of the setup can be recovered, and thus the image quality can be distinctly improved. Because no prior knowledge regarding the vibrating properties of the imaging system is needed, the proposed method is general and simple and has applications in several research fields.

A computational framework for ptychographic reconstructions

Ptychography is now a well-established X-ray microscopy tool for synchrotron end-stations equipped with a scanning stage and a pixelated detector. Ptychographic phasing algorithms use information from coherent diffraction to deliver quantitative images of the specimen at a resolution higher than the scanning resolution. These algorithms have traditionally been implemented in software on a per-instrument basis in various degrees of user-friendliness and sophistication. Here, we present Ptypy, a ptychography software written with the intention to serve as a framework across the diverse sets of available instruments and usage cases. A distinctive feature of the software is its formalism, which provides a convenient abstraction of the physical model, thus allowing for concise algorithmic implementations and portability across set-up geometries. We give an overview of the supported usage cases, explain the abstraction layer and design principles, and provide a step-by-step guide describing how an algorithm may be realized in a concise and readable manner. The software capabilities are illustrated with reconstructions from visible light and X-ray data.

Dark-field X-ray ptychography: Towards high-resolution imaging of thick and unstained biological specimens

The phase shift of light or electrons in objects is now necessary for probing weak-phase objects such as unstained biological specimens. Optical microscopy (OM) and transmission electron microscopy (TEM) have been used to observe weak-phase objects. However, conventional OM has low spatial resolution and TEM is limited to thin specimens. Here, we report on the development of dark-field X-ray ptychography, which combines X-ray ptychography and X-ray in-line holography, to observe weak-phase objects with a phase resolution better than 0.01 rad, a spatial resolution better than 15 nm, and a field of view larger than 5 μm. We apply this method to the observation of both the outline and magnetosomes of the magnetotactic bacteria MO-1. Observation of thick samples with high resolution is expected to find broad applications in not only biology but also materials science.

Simultaneous X-ray fluorescence and scanning X-ray diffraction microscopy at the Australian Synchrotron XFM beamline

Owing to its extreme sensitivity, quantitative mapping of elemental distributions via X-ray fluorescence microscopy (XFM) has become a key microanalytical technique. The recent realisation of scanning X-ray diffraction microscopy (SXDM) meanwhile provides an avenue for quantitative super-resolved ultra-structural visualization. The similarity of their experimental geometries indicates excellent prospects for simultaneous acquisition. Here, in both step- and fly-scanning modes, robust, simultaneous XFM-SXDM is demonstrated.

Multiple defocused coherent diffraction imaging: method for simultaneously reconstructing objects and probe using X-ray free-electron lasers

The sample size must be less than the diffraction-limited focal spot size of the incident beam in single-shot coherent X-ray diffraction imaging (CXDI) based on a diffract-before-destruction scheme using X-ray free electron lasers (XFELs). This is currently a major limitation preventing its wider applications. We here propose multiple defocused CXDI, in which isolated objects are sequentially illuminated with a divergent beam larger than the objects and the coherent diffraction pattern of each object is recorded. This method can simultaneously reconstruct both objects and a probe from the coherent X-ray diffraction patterns without any a priori knowledge. We performed a computer simulation of the prposed method and then successfully demonstrated it in a proof-of-principle experiment at SPring-8. The prposed method allows us to not only observe broad samples but also characterize focused XFEL beams.

Breaking ambiguities in mixed state ptychography

Recent advances in ptychographic imaging have shown how the technique extends naturally to mixed state experiments, for example when the illuminating radiation is partially coherent or when the object being imaged is laterally vibrating. To date, experiments using this mixed-state form of ptychography have relied on decomposition of the illumination 'probe' into multiple modes. In this paper we demonstrate, for the first time, ptychographic imaging with the simultaneous presence of both multiple probe and multiple object states. Our results prompt a discussion of uniqueness in the reconstructed images, and we show mathematically how ambiguities can arise. This leads us to extend the reconstruction process to include additional constraints that break these ambiguities, allowing interpretation of mixed object states that are not orthogonal.

Molar concentration from sequential 2-D water-window X-ray ptychography and X-ray fluorescence in hydrated cells

Recent developments in biological X-ray microscopy have allowed structural information and elemental distribution to be simultaneously obtained by combining X-ray ptychography and X-ray fluorescence microscopy. Experimentally, these methods can be performed simultaneously; however, the optimal conditions for each measurement may not be compatible. Here, we combine two distinct measurements of ultrastructure and elemental distribution, with each measurement performed under optimised conditions. By combining optimised ptychography and fluorescence information we are able to determine molar concentrations from two-dimensional images, allowing an investigation into the interactions between the environment sensing filopodia in fibroblasts and extracellular calcium. Furthermore, the biological ptychography results we present illustrate a point of maturity where the technique can be applied to solve significant problems in structural biology.

3D visualization of XFEL beam focusing properties using LiF crystal X-ray detector

Here, we report, that by means of direct irradiation of lithium fluoride a (LiF) crystal, in situ 3D visualization of the SACLA XFEL focused beam profile along the propagation direction is realized, including propagation inside photoluminescence solid matter. High sensitivity and large dynamic range of the LiF crystal detector allowed measurements of the intensity distribution of the beam at distances far from the best focus as well as near the best focus and evaluation of XFEL source size and beam quality factor M². Our measurements also support the theoretical prediction that for X-ray photons with energies ~10 keV the radius of the generated photoelectron cloud within the LiF crystal reaches about 600 nm before thermalization. The proposed method has a spatial resolution ~ 0.4–2.0 μm for photons with energies 6–14 keV and potentially could be used in a single shot mode for optimization of different focusing systems developed at XFEL and synchrotron facilities.

Quantitative electron phase imaging with high sensitivity and an unlimited field of view

As it passes through a sample, an electron beam scatters, producing an exit wavefront rich in information. A range of material properties, from electric and magnetic field strengths to specimen thickness, strain maps and mean inner potentials, can be extrapolated from its phase and mapped at the nanoscale. Unfortunately, the phase signal is not straightforward to obtain. It is most commonly measured using off-axis electron holography, but this is experimentally challenging, places constraints on the sample and has a limited field of view. Here we report an alternative method that avoids these limitations and is easily implemented on an unmodified transmission electron microscope (TEM) operating in the familiar selected area diffraction mode. We use ptychography, an imaging technique popular amongst the X-ray microscopy community; recent advances in reconstruction algorithms now reveal its potential as a tool for highly sensitive, quantitative electron phase imaging.

Opportunities and limitations for combined fly-scan ptychography and fluorescence microscopy

X-ray fluorescence offers unparalleled sensitivity for imaging the nanoscale distribution of trace elements in micrometer thick samples, while x-ray ptychography offers an approach to image light element containing structures at a resolution beyond that of the x-ray lens used. These methods can be used in combination, and in continuous scan mode for rapid data acquisition when using multiple probe mode reconstruction methods. We discuss here the opportunities and limitations of making use of additional information provided by ptychography to improve x-ray fluorescence images in two ways: by using position-error-correction algorithms to correct for scan distortions in fluorescence scans, and by considering the signal-to-noise limits on previously-demonstrated ptychographic probe deconvolution methods. This highlights the advantages of using a combined approach.

Fly-scan ptychography

We report an experimental ptychography measurement performed in fly-scan mode. With a visible-light laser source, we demonstrate a 5-fold reduction of data acquisition time. By including multiple mutually incoherent modes into the incident illumination, high quality images were successfully reconstructed from blurry diffraction patterns. This approach significantly increases the throughput of ptychography, especially for three-dimensional applications and the visualization of dynamic systems.

Continuous motion scan ptychography: characterization for increased speed in coherent x-ray imaging

Ptychography is a coherent diffraction imaging (CDI) method for extended objects in which diffraction patterns are acquired sequentially from overlapping coherent illumination spots. The object's complex transmission function can be reconstructed from those diffraction patterns at a spatial resolution limited only by the scattering strength of the object and the detector geometry. Most experiments to date have positioned the illumination spots on the sample using a move-settle-measure sequence in which the move and settle steps can take longer to complete than the measure step. We describe here the use of a continuous "fly-scan" mode for ptychographic data collection in which the sample is moved continuously, so that the experiment resembles one of integrating the diffraction patterns from multiple probe positions. This allows one to use multiple probe mode reconstruction methods to obtain an image of the object and also of the illumination function. We show in simulations, and in x-ray imaging experiments, some of the characteristics of fly-scan ptychography, including a factor of 25 reduction in the data acquisition time. This approach will become increasingly important as brighter x-ray sources are developed, such as diffraction limited storage rings.

Evaluation of partial coherence correction in X-ray ptychography

Coherent X-ray Diffraction Imaging (CDI) and X-ray ptychography both heavily rely on the high degree of spatial coherence of the X-ray illumination for sufficient experimental data quality for reconstruction convergence. Nevertheless, the majority of the available synchrotron undulator sources have a limited degree of partial coherence, leading to reduced data quality and a lower speckle contrast in the coherent diffraction patterns. It is still an open question whether experimentalists should compromise the coherence properties of an X-ray source in exchange for a higher flux density at a sample, especially when some materials of scientific interest are relatively weak scatterers. A previous study has suggested that in CDI, the best strategy for the study of strong phase objects is to maintain a high degree of coherence of the illuminating X-rays because of the broadening of solution space resulting from the strong phase structures. In this article, we demonstrate the first systematic analysis of the effectiveness of partial coherence correction in ptychography as a function of the coherence properties, degree of complexity of illumination (degree of phase diversity of the probe) and sample phase complexity. We have also performed analysis of how well ptychographic algorithms refine X-ray probe and complex coherence functions when those variables are unknown at the start of reconstructions, for noise-free simulated data, in the case of both real-valued and highly-complex objects.

Partially coherent ultrafast spectrography

Modern ultrafast metrology relies on the postulate that the pulse to be measured is fully coherent, that is, that it can be completely described by its spectrum and spectral phase. However, synthesizing fully coherent pulses is not always possible in practice, especially in the domain of emerging ultrashort X-ray sources where temporal metrology is strongly needed. Here we demonstrate how frequency-resolved optical gating (FROG), the first and one of the most widespread techniques for pulse characterization, can be adapted to measure partially coherent pulses even down to the attosecond timescale. No modification of experimental apparatuses is required; only the processing of the measurement changes. To do so, we take our inspiration from other branches of physics where partial coherence is routinely dealt with, such as quantum optics and coherent diffractive imaging. This will have important and immediate applications, such as enabling the measurement of X-ray free-electron laser pulses despite timing jitter.

Continuous scanning mode for ptychography

We outline how ptychographic imaging can be performed without the need for discrete scan positions. Through an idealized experiment, we demonstrate how a discrete-position scan regime can be replaced with a continuously scanned one with suitable modification of the reconstruction scheme based on coherent modes. The impact of this is that acquisition times can be reduced, significantly aiding ptychographic imaging with x rays, electrons, or visible light.

Optimization of overlap uniformness for ptychography

We demonstrate the advantages of imaging with ptychography scans that follow a Fermat spiral trajectory. This scan pattern provides a more uniform coverage and a higher overlap ratio with the same number of scan points over the same area than the presently used mesh and concentric [13] patterns. Under realistically imperfect measurement conditions, numerical simulations show that the quality of the reconstructed image is improved significantly with a Fermat spiral compared with a concentric scan pattern. The result is confirmed by the performance enhancement with experimental data, especially under low-overlap conditions. These results suggest that the Fermat spiral pattern increases the quality of the reconstructed image and tolerance to data with imperfections.