Imaging extended single crystal lattice distortion fields with multi-peak Bragg ptychography.

Recent advances in phase-retrieval-based x-ray imaging methods have demonstrated the ability to reconstruct 3D distortion vector fields within a nanocrystal by using coherent diffraction information from multiple crystal Bragg reflections. However, these works do not provide a solution to the challenges encountered in imaging lattice distortions in crystals with significant defect content that result in phase wrapping. Moreover, these methods only apply to isolated crystals smaller than the x-ray illumination, and therefore cannot be used for imaging of distortions in extended crystals. We introduce multi-peak Bragg ptychography which addresses both challenges via an optimization framework that combines stochastic gradient descent and phase unwrapping methods for robust image reconstruction of lattice distortions and defects in extended crystals. Our work uses modern automatic differentiation toolsets so that the method is easy to extend to other settings and easy to implement in high-performance computers. This work is particularly timely given the broad interest in using the increased coherent flux in fourth-generation synchrotrons for innovative material research.

Counting on the future: fast charge-integrating detectors for X-ray nanoimaging.

A fast charge-integrating detector has been showcased for high-resolution X-ray ptychography. The advancement in developing detectors of this kind, with rapid framing capabilities, holds paramount significance in harnessing the full potential of emerging diffraction-limited synchrotron sources for X-ray nanoimaging.

Fast and noise-tolerant determination of the center of rotation in tomography.

High-quality tomographic reconstruction is not possible without the accurate localization of the center of rotation. Poor localization leads to artifacts in the data and can even cause reconstructions to fail. There are many approaches to solving this problem, some of which involve the collection of full sinograms, or even provisional tomographic reconstructions, in order to determine the center of rotation. Here, a simple method based on the expected symmetry of the Fourier transform of summed projections approximately 180° apart is presented; unlike cross-correlation methods, it requires only a single Fourier transform to compute, and uses mainly low spatial frequency information which is less susceptible to noise. This approach is shown to be fast, and robust against poor signal-to-noise as well as to projection images acquired at angles that are not exactly 180° apart. This rapid method can be useful as a first step in the processing of tomographic data.

Fast scanning in x-ray microscopy: the effects of offset in the central stop position.

Scanning of lightweight circular diffractive optics, separate from central stops and apertures, is emerging as an approach to exploit advances in synchrotron x-ray sources. We consider the effects in a scanning microscope of offsets between the optic and its central stop and find that scan ranges of up to about half the diameter of the optic are possible with only about a 10% increase in the focal spot width. For large scanning ranges, we present criteria for the working distance between the last aperture and the specimen to be imaged.

Using a modified double deep image prior for crosstalk mitigation in multislice ptychography.

Multislice ptychography is a high-resolution microscopy technique used to image multiple separate axial planes using a single illumination direction. However, multislice ptychography reconstructions are often degraded by crosstalk, where some features on one plane erroneously contribute to the reconstructed image of another plane. Here, the use of a modified `double deep image prior' (DDIP) architecture is demonstrated in mitigating crosstalk artifacts in multislice ptychography. Utilizing the tendency of generative neural networks to produce natural images, a modified DDIP method yielded good results on experimental data. For one of the datasets, it is shown that using DDIP could remove the need of using additional experimental data, such as from X-ray fluorescence, to suppress the crosstalk. This method may help X-ray multislice ptychography work for more general experimental scenarios.

Fast digital lossy compression for X-ray ptychographic data.

Increases in X-ray brightness from synchrotron light sources lead to a requirement for higher frame rates from hybrid pixel array detectors (HPADs), while also favoring charge integration over photon counting. However, transfer of the full uncompressed data will begin to constrain detector design, as well as limit the achievable continuous frame rate. Here a data compression scheme that is easy to implement in a HPAD's application-specific integrated circuit (ASIC) is described, and how different degrees of compression affect image quality in ptychography, a commonly employed coherent imaging method, is examined. Using adaptive encoding quantization, it is shown in simulations that one can digitize signals up to 16383 photons per pixel (corresponding to 14 bits of information) using only 8 or 9 bits for data transfer, with negligible effect on the reconstructed image.

Efficient ptychographic phase retrieval via a matrix-free Levenberg-Marquardt algorithm.

The phase retrieval problem, where one aims to recover a complex-valued image from far-field intensity measurements, is a classic problem encountered in a range of imaging applications. Modern phase retrieval approaches usually rely on gradient descent methods in a nonlinear minimization framework. Calculating closed-form gradients for use in these methods is tedious work, and formulating second order derivatives is even more laborious. Additionally, second order techniques often require the storage and inversion of large matrices of partial derivatives, with memory requirements that can be prohibitive for data-rich imaging modalities. We use a reverse-mode automatic differentiation (AD) framework to implement an efficient matrix-free version of the Levenberg-Marquardt (LM) algorithm, a longstanding method that finds popular use in nonlinear least-square minimization problems but which has seen little use in phase retrieval. Furthermore, we extend the basic LM algorithm so that it can be applied for more general constrained optimization problems (including phase retrieval problems) beyond just the least-square applications. Since we use AD, we only need to specify the physics-based forward model for a specific imaging application; the first and second-order derivative terms are calculated automatically through matrix-vector products, without explicitly forming the large Jacobian or Gauss-Newton matrices typically required for the LM method. We demonstrate that this algorithm can be used to solve both the unconstrained ptychographic object retrieval problem and the constrained "blind" ptychographic object and probe retrieval problems, under the popular Gaussian noise model as well as the Poisson noise model. We compare this algorithm to state-of-the-art first order ptychographic reconstruction methods to demonstrate empirically that this method outperforms best-in-class first-order methods: it provides excellent convergence guarantees with (in many cases) a superlinear rate of convergence, all with a computational cost comparable to, or lower than, the tested first-order algorithms.

Adorym: a multi-platform generic X-ray image reconstruction framework based on automatic differentiation.

We describe and demonstrate an optimization-based X-ray image reconstruction framework called Adorym. Our framework provides a generic forward model, allowing one code framework to be used for a wide range of imaging methods ranging from near-field holography to fly-scan ptychographic tomography. By using automatic differentiation for optimization, Adorym has the flexibility to refine experimental parameters including probe positions, multiple hologram alignment, and object tilts. It is written with strong support for parallel processing, allowing large datasets to be processed on high-performance computing systems. We demonstrate its use on several experimental datasets to show improved image quality through parameter refinement.

Comparison of distributed memory algorithms for X-ray wave propagation in inhomogeneous media.

Calculations of X-ray wave propagation in large objects are needed for modeling diffractive X-ray optics and for optimization-based approaches to image reconstruction for objects that extend beyond the depth of focus. We describe three methods for calculating wave propagation with large arrays on parallel computing systems with distributed memory: (1) a full-array Fresnel multislice approach, (2) a tiling-based short-distance Fresnel multislice approach, and (3) a finite difference approach. We find that the first approach suffers from internode communication delays when the transverse array size becomes large, while the second and third approaches have similar scaling to large array size problems (with the second approach offering about three times the compute speed).

Effect of tilt on circular zone plate performance.

Fresnel zone plates are frequently used as focusing and imaging optics in x-ray microscopy, as they provide the ease of use of normal incidence optics. We consider here the effects of tilt misalignment on their optical performance, both in the thin optics limit and in the case of zone plates that are sufficiently thick so that volume diffraction effects come into play. Using multislice propagation, we show that simple analytical models describe the tilt sensitivity of thin zone plates and the thickness at which volume diffraction must be considered, and examine numerically the performance of example zone plates for soft x-ray focusing at 0.5 keV and hard x-ray focusing at 10 keV.

Using automatic differentiation as a general framework for ptychographic reconstruction.

Coherent diffraction imaging methods enable imaging beyond lens-imposed resolution limits. In these methods, the object can be recovered by minimizing an error metric that quantifies the difference between diffraction patterns as observed, and those calculated from a present guess of the object. Efficient minimization methods require analytical calculation of the derivatives of the error metric, which is not always straightforward. This limits our ability to explore variations of basic imaging approaches. In this paper, we propose to substitute analytical derivative expressions with the automatic differentiation method, whereby we can achieve object reconstruction by specifying only the physics-based experimental forward model. We demonstrate the generality of the proposed method through straightforward object reconstruction for a variety of complex ptychographic experimental models.

More are better, but the details matter: combinations of multiple Fresnel zone plates for improved resolution and efficiency in X-ray microscopy.

Fresnel zone plates used for X-ray nanofocusing face high-aspect-ratio nanofabrication challenges in combining narrow transverse features (for high spatial resolution) along with extended optical modulation along the X-ray beam direction (to improve efficiency). The stacking of multiple Fresnel zone plates along the beam direction has already been shown to offer improved characteristics of resolution and efficiency when compared with thin single zone plates. Using multislice wave propagation simulation methods, here a number of new schemes for the stacking of multiple Fresnel zone plates are considered. These include consideration of optimal thickness and spacing in the axial direction, and methods to capture a fraction of the light otherwise diffracted into unwanted orders, and instead bring it into the desired first-order focus. The alignment tolerances for stacking multiple Fresnel zone plates are also considered.

Tomosaic: efficient acquisition and reconstruction of teravoxel tomography data using limited-size synchrotron X-ray beams.

X-rays offer high penetration with the potential for tomography of centimetre-sized specimens, but synchrotron beamlines often provide illumination that is only millimetres wide. Here an approach is demonstrated termed Tomosaic for tomographic imaging of large samples that extend beyond the illumination field of view of an X-ray imaging system. This includes software modules for image stitching and calibration, while making use of existing modules available in other packages for alignment and reconstruction. The approach is compatible with conventional beamline hardware, while providing a dose-efficient method of data acquisition. By using parallelization on a distributed computing system, it provides a solution for handling teravoxel-sized or larger datasets that cannot be processed on a single workstation in a reasonable time. Using experimental data, the package is shown to provide good quality three-dimensional reconstruction for centimetre-sized samples with sub-micrometre pixel size.

Relaxation of the Crowther criterion in multislice tomography.

For objects larger than the depth of focus of an imaging system, one must account for wavefield propagation effects within the object as is done in diffraction tomography, diffraction microscopy, and multislice ptychographic tomography. We show here that if the imaging method used reconstructs Na planes along each viewing direction, one can reduce the number of illumination directions required to fill Fourier space by a factor of 1/Na, relaxing the usual Crowther criterion for tomography. This provides a conceptual basis to explain two recent experiments where multiple axial planes were imaged per viewing direction, and tomographic images were obtained with good 3D spatial resolution, even though fewer illumination directions were used than one would have expected from the Crowther criterion.

X-ray tomography of extended objects: a comparison of data acquisition approaches.

The penetration power of x rays allows one to image large objects, while their short wavelength allows for high spatial resolution. As a result, with synchrotron sources, one has the potential to obtain tomographic images of centimeter-sized specimens with sub-micrometer pixel sizes. However, limitations on beam and detector size make it difficult to acquire such data of this sort in a single take, necessitating strategies for combining data from multiple regions. One strategy is to acquire a tiled set of local tomograms by rotating the specimen around each of the local tomogram center positions. Another strategy, sinogram oriented acquisition, involves the collection of projections at multiple offset positions from the rotation axis followed by data merging and reconstruction. We have carried out a simulation study to compare these two approaches in terms of radiation dose applied to the specimen, and reconstructed image quality. Local tomography acquisition involves an easier data alignment problem, and immediate viewing of subregions before the entire dataset has been acquired. Sinogram oriented acquisition involves a more difficult data assembly and alignment procedure, and it is more sensitive to accumulative registration error. However, sinogram oriented acquisition is more dose efficient, involves fewer translation motions of the object, and avoids certain artifacts of local tomography.

Simultaneous cryo X-ray ptychographic and fluorescence microscopy of green algae.

Trace metals play important roles in normal and in disease-causing biological functions. X-ray fluorescence microscopy reveals trace elements with no dependence on binding affinities (unlike with visible light fluorophores) and with improved sensitivity relative to electron probes. However, X-ray fluorescence is not very sensitive for showing the light elements that comprise the majority of cellular material. Here we show that X-ray ptychography can be combined with fluorescence to image both cellular structure and trace element distribution in frozen-hydrated cells at cryogenic temperatures, with high structural and chemical fidelity. Ptychographic reconstruction algorithms deliver phase and absorption contrast images at a resolution beyond that of the illuminating lens or beam size. Using 5.2-keV X-rays, we have obtained sub-30-nm resolution structural images and ∼90-nm-resolution fluorescence images of several elements in frozen-hydrated green algae. This combined approach offers a way to study the role of trace elements in their structural context.

Strategies for high-throughput focused-beam ptychography.

X-ray ptychography is being utilized for a wide range of imaging experiments with a resolution beyond the limit of the X-ray optics used. Introducing a parameter for the ptychographic resolution gain Gp (the ratio of the beam size over the achieved pixel size in the reconstructed image), strategies for data sampling and for increasing imaging throughput when the specimen is at the focus of an X-ray beam are considered. The tradeoffs between large and small illumination spots are examined.

Multislice does it all-calculating the performance of nanofocusing X-ray optics.

We describe an approach to calculating the optical performance of a wide range of nanofocusing X-ray optics using multislice scalar wave propagation with a complex X-ray refractive index. This approach produces results indistinguishable from methods such as coupled wave theory, and it allows one to reproduce other X-ray optical phenomena such as grazing incidence reflectivity where the direction of energy flow is changed significantly. Just as finite element analysis methods allow engineers to compute the thermal and mechanical responses of arbitrary structures too complex to model by analytical approaches, multislice propagation can be used to understand the properties of the real-world optics of finite extent and with local imperfections, allowing one to better understand the limits to nanoscale X-ray imaging.

Joint reconstruction of x-ray fluorescence and transmission tomography.

X-ray fluorescence tomography is based on the detection of fluorescence x-ray photons produced following x-ray absorption while a specimen is rotated; it provides information on the 3D distribution of selected elements within a sample. One limitation in the quality of sample recovery is the separation of elemental signals due to the finite energy resolution of the detector. Another limitation is the effect of self-absorption, which can lead to inaccurate results with dense samples. To recover a higher quality elemental map, we combine x-ray fluorescence detection with a second data modality: conventional x-ray transmission tomography using absorption. By using these combined signals in a nonlinear optimization-based approach, we demonstrate the benefit of our algorithm on real experimental data and obtain an improved quantitative reconstruction of the spatial distribution of dominant elements in the sample. Compared with single-modality inversion based on x-ray fluorescence alone, this joint inversion approach reduces ill-posedness and should result in improved elemental quantification and better correction of self-absorption.

Preserving elemental content in adherent mammalian cells for analysis by synchrotron-based x-ray fluorescence microscopy.

Trace metals play important roles in biological function, and x-ray fluorescence microscopy (XFM) provides a way to quantitatively image their distribution within cells. The faithfulness of these measurements is dependent on proper sample preparation. Using mouse embryonic fibroblast NIH/3T3 cells as an example, we compare various approaches to the preparation of adherent mammalian cells for XFM imaging under ambient temperature. Direct side-by-side comparison shows that plunge-freezing-based cryoimmobilization provides more faithful preservation than conventional chemical fixation for most biologically important elements including P, S, Cl, K, Fe, Cu, Zn and possibly Ca in adherent mammalian cells. Although cells rinsed with fresh media had a great deal of extracellular background signal for Cl and Ca, this approach maintained cells at the best possible physiological status before rapid freezing and it does not interfere with XFM analysis of other elements. If chemical fixation has to be chosen, the combination of 3% paraformaldehyde and 1.5 % glutaraldehyde preserves S, Fe, Cu and Zn better than either fixative alone. When chemically fixed cells were subjected to a variety of dehydration processes, air drying was proved to be more suitable than other drying methods such as graded ethanol dehydration and freeze drying. This first detailed comparison for x-ray fluorescence microscopy shows how detailed quantitative conclusions can be affected by the choice of cell preparation method.