Ab initio nonrigid X-ray nanotomography

High-performance 4-nm-resolution X-ray tomography using burst ptychography

Advances in science, medicine and engineering rely on breakthroughs in imaging, particularly for obtaining multiscale, three-dimensional information from functional systems such as integrated circuits or mammalian brains. Achieving this goal often requires combining electron- and photon-based approaches. Whereas electron microscopy provides nanometre resolution through serial, destructive imaging of surface layers1, ptychographic X-ray computed tomography2 offers non-destructive imaging and has recently achieved resolutions down to seven nanometres for a small volume3. Here we implement burst ptychography, which overcomes experimental instabilities and enables much higher performance, with 4-nanometre resolution at a 170-times faster acquisition rate, namely, 14,000 resolution elements per second. Another key innovation is tomographic back-propagation reconstruction4, allowing us to image samples up to ten times larger than the conventional depth of field. By combining the two innovations, we successfully imaged a state-of-the-art (seven-nanometre node) commercial integrated circuit, featuring nanostructures made of low- and high-density materials such as silicon and metals, which offer good radiation stability and contrast at the selected X-ray wavelength. These capabilities enabled a detailed study of the chip's design and manufacturing, down to the level of individual transistors. We anticipate that the combination of nanometre resolution and higher X-ray flux at next-generation X-ray sources will have a revolutionary impact in fields ranging from electronics to electrochemistry and neuroscience.

2D vs. 3D Evaluation of Osteocyte Lacunae - Methodological Approaches, Recommended Parameters, and Challenges: A Narrative Review by the European Calcified Tissue Society (ECTS)

PURPOSE OF REVIEW

Quantification of the morphology of osteocyte lacunae has become a powerful tool to investigate bone metabolism, pathologies and aging. This review will provide a brief overview of 2D and 3D imaging methods for the determination of lacunar shape, orientation, density, and volume. Deviations between 2D-based and 3D-based lacunar volume estimations are often not sufficiently addressed and may give rise to contradictory findings. Thus, the systematic error arising from 2D-based estimations of lacunar volume will be discussed, and an alternative calculation proposed. Further, standardized morphological parameters and best practices for sampling and segmentation are suggested.

RECENT FINDINGS

We quantified the errors in reported estimation methods of lacunar volume based on 2D cross-sections, which increase with variations in lacunar orientation and histological cutting plane. The estimations of lacunar volume based on common practice in 2D imaging methods resulted in an underestimation of lacunar volume of up to 85% compared to actual lacunar volume in an artificial dataset. For a representative estimation of lacunar size and morphology based on 2D images, at least 400 lacunae should be assessed per sample.

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.

Towards routine 3D characterization of intact mesoscale samples by multi-scale and multimodal scanning X-ray tomography

Non-invasive multi-scale and multimodal 3D characterization of heterogeneous or hierarchically structured intact mesoscale samples is of paramount importance in tackling challenging scientific problems. Scanning hard X-ray tomography techniques providing simultaneous complementary 3D information are ideally suited to such studies. However, the implementation of a robust on-site workflow remains the bottleneck for the widespread application of these powerful multimodal tomography methods. In this paper, we describe the development and implementation of such a robust, holistic workflow, including semi-automatic data reconstruction. Due to its flexibility, our approach is especially well suited for on-the-fly tuning of the experiments to study features of interest progressively at different length scales. To demonstrate the performance of the method, we studied, across multiple length scales, the elemental abundances and morphology of two complex biological systems, Arabidopsis plant seeds and mouse renal papilla samples. The proposed approach opens the way towards routine multimodal 3D characterization of intact samples by providing relevant information from pertinent sample regions in a wide range of scientific fields such as biology, geology, and material sciences.

Environmental control for X-ray nanotomography

The acquisition speed and spatial resolution of X-ray nanotomography have continuously improved over the last decades. Coherent diffraction-based techniques breach the 10 nm resolution barrier frequently and thus pose stringent demands on sample positioning accuracy and stability. At the same time there is an increasing desire to accommodate in situ or operando measurements. Here, an environmental control system for X-ray nanotomography is introduced to regulate the temperature of a sample from room temperature up to 850°C in a controlled atmospheric composition. The system allows for a 360° sample rotation, permitting tomographic studies in situ or operando free of missing wedge constraints. The system is implemented and available at the flOMNI microscope at the Swiss Light Source. In addition to the environmental control system itself, the related modifications of flOMNI are described. Tomographic measurements of a nanoporous gold sample at 50°C and 600°C at a resolution of sub-20 nm demonstrate the performance of the device.

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.

Joint iterative reconstruction and 3D rigid alignment for X-ray tomography

X-ray tomography is widely used for three-dimensional structure determination in many areas of science, from the millimeter to the nanometer scale. The resolution and quality of the 3D reconstruction is limited by the availability of alignment parameters that correct for the mechanical shifts of the sample or sample stage for the images that constitute a scan. In this paper we describe an algorithm for marker-free, fully automated and accurately aligned and reconstructed X-ray tomography data. Our approach solves the tomographic reconstruction jointly with projection data alignment based on a rigid-body deformation model. We demonstrate the robustness of our method on both synthetic phantom and experimental data and show that our method is highly efficient in recovering relatively large alignment errors without prior knowledge of a low resolution approximation of the 3D structure or a reasonable estimate of alignment parameters.

Adjoint image warping using multivariate splines with application to four-dimensional computed tomography

Purpose

Adjoint image warping is an important tool to solve image reconstruction problems that warp the unknown image in the forward model. This includes four‐dimensional computed tomography (4D‐CT) models in which images are compared against recorded projection images of various time frames using image warping as a model of the motion. The inversion of these models requires the adjoint of image warping, which up to now has been substituted by approximations. We introduce an efficient implementation of the exact adjoints of multivariate spline based image warping, and compare it against previously used alternatives.

Methods

Using symbolic computer algebra, we computed a list of 64 polynomials that allow us to compute a matrix representation of trivariate cubic image warping. By combining an on‐the‐fly computation of this matrix with a parallelized implementation of columnwise matrix multiplication, we obtained an efficient, low memory implementation of the adjoint action of 3D cubic image warping. We used this operator in the solution of a previously proposed 4D‐CT reconstruction model in which the image of a single subscan was compared against projection data of multiple subscans by warping and then projecting the image. We compared the properties of our exact adjoint with those of approximate adjoints by warping along inverted motion.

Results

Our method requires halve the memory to store motion between subscans, compared to methods that need to compute and store an approximate inverse of the motion. It also avoids the computation time to invert the motion and the tunable parameter of the number of iterations used to perform this inversion. Yet, a similar and often better reconstruction quality was obtained in comparison with these more expensive methods, especially when the motion is large. When compared against a simpler method that is similar to ours in computational demands, our method achieves a higher reconstruction quality in general.

Conclusions

Our implementation of the exact adjoint of cubic image warping improves efficiency and provides accurate reconstructions.

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.

Improving image quality in fast, time-resolved micro-CT by weighted back projection

Time-resolved micro-CT is an increasingly powerful technique for studying dynamic processes in materials and structures. However, it is still difficult to study very fast processes with this technique, since fast scanning is typically associated with high image noise levels. We present weighted back projection, a technique applicable in iterative reconstruction methods using two types of prior knowledge: (1) a virtual starting volume resembling the sample, for example obtained from a scan before the dynamic process was initiated, and (2) knowledge on which regions in the sample are more likely to undergo the dynamic process. Therefore, processes on which this technique is applicable are preferably occurring within a static grid. Weighted back projection has the ability to handle small errors in the prior knowledge, while similar 4D micro-CT techniques require the prior knowledge to be exactly correct. It incorporates the prior knowledge within the reconstruction by using a weight volume, representing for each voxel its probability of undergoing the dynamic process. Qualitative analysis on a sparse subset of projection data from a real micro-CT experiment indicates that this method requires significantly fewer projection angles to converge to a correct volume. This can lead to an improved temporal resolution.

In-Situ X-ray Imaging Of Sublimating Spin-Frozen Solutions

Spin-freeze-drying is a promising technique to enable long-term storage of pharmaceutical unit doses of aqueous drug solutions. To investigate the sublimation of the ice during the primary phase of freeze-drying, X-ray imaging can yield crucial temporally resolved information on the local dynamics. In this paper, we describe a methodology to investigate the sublimation front during single unit-dose freeze-drying using 4D in-situ X-ray imaging. Three spin-frozen samples of different solutions were imaged using this methodology and the process characteristics were analysed and reduced to two-dimensional feature maps.

Alignment methods for nanotomography with deep subpixel accuracy

As the resolution of X-ray tomography improves, the limited long-term stability and accuracy of nanoimaging tools does not allow computing artifact-free three-dimensional (3D) reconstructions without an additional step of numerical alignment of the measured projections. However, the common iterative alignment methods are significantly more computationally demanding than a simple tomographic reconstruction of the acquired volume. Here, we address this issue and present an alignment toolkit, which exploits methods with deep-subpixel accuracy combined with a multi-resolution scheme. This leads to robust and accurate alignment with significantly reduced computational and memory requirements. The performance of the presented methods is demonstrated on simulated and measured datasets for tomography and also laminography acquisition geometries. A GPU accelerated implementation of our alignment framework is publicly available.