Ghostbuster: A phase retrieval diffraction tomography algorithm for cryo-EM

Ewald sphere curvature correction, which extends beyond the projection approximation, stretches the shallow depth of field in cryo-EM reconstructions of thick particles. Here we show that even for previously assumed thin particles, reconstruction artifacts which we refer to as ghosts can appear. By retrieving the lost phases of the electron exitwaves and accounting for the first Born approximation scattering within the particle, we show that these ghosts can be effectively eliminated. Our simulations demonstrate how such ghostbusting can improve reconstructions as compared to existing state-of-the-art software. Like ptychographic cryo-EM, our Ghostbuster algorithm uses phase retrieval to improve reconstructions, but unlike the former, we do not need to modify the existing data acquisition pipelines.

Quantitative phase contrast X-ray tomography of aluminium metal matrix composite

The quantitative assessment of micro-structure and load-induced damages in Al-SiC metal matrix composites (MMC) is important for its design optimization, performance evaluation and structure-property correlation. X-ray Phase contrast micro-tomography is potentially used for evaluation of its 3 dimensional micro-structure manifested in the form of voids, cracks, embedded particles, and load-induced damages. However, the contrast between Al matrix and SiC particles is insufficient for their clear morphological identification and quantitative assessment. In the present study, we have proposed and applied single image-based phase retrieval as a pre-processing step to micro-tomography reconstruction for improved assessment of micro-structure and cohesion-induced damages in Al-SiC MMC. The advantages of applying different phase retrieval techniques in the enhancement of image quality and morphological quantification of SiC particles, pores and cohesion damages are discussed. It is observed that the Paganin method offers the best improvement in contrast to noise ratio for the measurement of SiC particles embedded in the Al matrix.

On the connection between uniqueness from samples and stability in Gabor phase retrieval

Gabor phase retrieval is the problem of reconstructing a signal from only the magnitudes of its Gabor transform. Previous findings suggest a possible link between unique solvability of the discrete problem (recovery from measurements on a lattice) and stability of the continuous problem (recovery from measurements on an open subset of R 2 ). In this paper, we close this gap by proving that such a link cannot be made. More precisely, we establish the existence of functions which break uniqueness from samples without affecting stability of the continuous problem. Furthermore, we prove the novel result that counterexamples to unique recovery from samples are dense in L 2 ( R ) . Finally, we develop an intuitive argument on the connection between directions of instability in phase retrieval and certain Laplacian eigenfunctions associated to small eigenvalues.

Phase retrieval for X-ray differential phase contrast radiography with knowledge transfer learning from virtual differential absorption model

Grating-based X-ray phase contrast radiography and computed tomography (CT) are promising modalities for future medical applications. However, the ill-posed phase retrieval problem in X-ray phase contrast imaging has hindered its use for quantitative analysis in biomedical imaging. Deep learning has been proved as an effective tool for image retrieval. However, in practical grating-based X-ray phase contrast imaging system, acquiring the ground truth of phase to form image pairs is challenging, which poses a great obstacle for using deep leaning methods. Transfer learning is widely used to address the problem with knowledge inheritance from similar tasks. In the present research, we propose a virtual differential absorption model and generate a training dataset with differential absorption images and absorption images. The knowledge learned from the training is transferred to phase retrieval with transfer learning techniques. Numerical simulations and experiments both demonstrate its feasibility. Image quality of retrieved phase radiograph and phase CT slices is improved when compared with representative phase retrieval methods. We conclude that this method is helpful in both X-ray 2D and 3D imaging and may find its applications in X-ray phase contrast radiography and X-ray phase CT.

Reliable phase quantification in focused probe electron ptychography of thin materials

Electron ptychography provides highly sensitive, dose efficient phase images which can be corrected for aberrations after the data has been acquired. This is crucial when very precise quantification is required, such as with sensitivity to charge transfer due to bonding. Drift can now be essentially eliminated as a major impediment to focused probe ptychography, which benefits from the availability of easily interpretable simultaneous Z-contrast imaging. However challenges have remained when quantifying the ptychographic phases of atomic sites. The phase response of a single atom has a negative halo which can cause atoms to reduce in phase when brought closer together. When unaccounted for, as in integrating methods of quantification, this effect can completely obscure the effects of charge transfer. Here we provide a new method of quantification that overcomes this challenge, at least for 2D materials, and is robust to experimental parameters such as noise, sample tilt.

Phase imaging in scanning transmission electron microscopy using bright-field balanced divergency method

We introduce a phase imaging mechanism for scanning transmission electron microscopy that exploits the complementary intensity changes of transmitted disks at different scattering angles. For scanning transmission electron microscopy, this method provides a straightforward, dose-efficient, and noise-robust phase imaging, from atomic resolution to intermediate length scales, as a function of scattering angles and probe defocus. At atomic resolution, we demonstrate that the phase imaging using the method can detect both light and heavy atomic columns. Furthermore, we experimentally apply the method to the imaging of nanoscale magnetic phases in FeGe samples. Compared with conventional methods, phase retrieval using the new method has higher effective spatial resolution and robustness to non-phase background contrast. Our method complements traditional phase imaging modalities in electron microscopy and has the potential to be extended to other scanning transmission techniques and to characterize many emerging material systems.

Reconstruction of 3D density from solution scattering

Ab initio modeling methods have proven to be powerful means of interpreting solution scattering data. In the absence of atomic models, or complementary to them, ab initio modeling approaches can be used for generating low-resolution particle envelopes using only solution scattering profiles. Recently, a new ab initio reconstruction algorithm has been introduced to the scientific community, called DENSS. DENSS is unique among ab initio modeling algorithms in that it solves the inverse scattering problem, i.e., the 1D scattering intensities are directly used to determine the 3D particle density. The reconstruction of particle density has several advantages over conventional uniform density modeling approaches, including the ability to reconstruct a much wider range of particle types and the ability to visualize low-resolution density fluctuations inside the particle envelope. In this chapter we will discuss the theory behind this new approach, how to use DENSS, and how to interpret the results. Several examples with experimental and simulated data will be provided.

A modular software framework for the design and implementation of ptychography algorithms

Computational methods are driving high impact microscopy techniques such as ptychography. However, the design and implementation of new algorithms is often a laborious process, as many parts of the code are written in close-to-the-hardware programming constructs to speed up the reconstruction. In this article, we present SciComPty, a new ptychography software framework aiming at simulating ptychography datasets and testing state-of-the-art and new reconstruction algorithms. Despite its simplicity, the software leverages GPU accelerated processing through the PyTorch CUDA interface. This is essential for designing new methods that can readily be employed. As an example, we present an improved position refinement method based on Adam and a new version of the rPIE algorithm, adapted for partial coherence setups. Results are shown on both synthetic and real datasets. The software is released as open-source.

Quantitative reconstruction of the complex-valued object based on complementary phase modulations

In the coherent diffraction imaging (CDI) techniques, a key point is to reconstruct the complex-valued object from the far-field intensity measurements, i.e., solving the phase retrieval problem. However, due to this ill-posed problem, traditional phase retrieval algorithms often encounter some problems associated with the iteration convergence. In this work, complementary phase modulations (CPM) are introduced to generate different far-field intensity measurements. The namely CPM-based method aims to find out the global optimal solution by imposing multi-dimensional constraints, including the diverse intensity images at the Fourier plane and the CPM at the object plane. It is proved by the numerical simulations and the optical experiments that the convergence speed and the recovery accuracy could be greatly improved. Furthermore, the shifting complementary phase modulations (SCPM)-based method is proposed by introducing more CPMs. The reconstruction performance is further improved even when the phase range is larger, and the support constraints are not required. In addition, the SCPM-based method is more robust to the Poisson noise. With the outstanding reconstruction performance, the CPM-based methods may be helpful to phase imaging in the application of visible-light microscopy and X-ray imaging.

Quantifying the data quality of focal series for inline electron holography

Inline electron holography, the recovery of amplitude and phase of an electron wave function having passed through a thin specimen from a focal series recorded in a transmission electron microscope is being applied in many labs worldwide. At medium range magnification (i.e. typically ≥0.8 nm where the lattice of small unit cell crystals such as silicon is not resolved), where the defocus needs to be varied over a rather large range of several hundred nm or even μm, the retrieval of low spatial frequency information is severely affected by the choice of experimental parameters as well as the way of data normalization. Methods to quantitatively analyze the reliability of phase maps obtained by inline electron holography are presented, and data recorded and processed in different ways are compared. While, even under optimized conditions, the phase reconstructed from an experimental focal series still lacks very low spatial frequency components, regularization schemes exist and are demonstrated to effectively hide artifacts associated with this lack of information.

Efficient large field of view electron phase imaging using near-field electron ptychography with a diffuser

Most implementations of ptychography on the electron microscope operate in scanning transmission (STEM) mode, where a small focussed probe beam is rapidly scanned across the sample. In this paper we introduce a different approach based on near-field ptychography, where the focussed beam is replaced by a wide-field, structured illumination, realised through a purpose-designed etched Silicon Nitride window. We show that fields of view as large as 100 μm² can be imaged using the new approach, and that quantitative electron phase images can be reconstructed from as few as nine near-field diffraction pattern measurements.

The Potential of Utilizing Mid-Energy X-Rays for In-Line Phase Sensitive Breast Cancer Imaging

OBJECTIVE

The objective of this study is to demonstrate the potential of utilizing mid-energy x-rays for in-line phase-sensitive breast cancer imaging by phantom studies.

METHODS

The midenergy (50-80kV) in-line phase sensitive imaging prototype was used to acquire images of the contrast-detail mammography (CDMAM) phantom, an ACR accreditation phantom, and an acrylic edge phantom. The low-dose mid-energy phase-sensitive images were acquired at 60 kV with a radiation dose of 0.9 mGy, while the high-energy phase-sensitive images were acquired at 90 kV with a radiation dose of 1.2 mGy. The Phase-Attenuation Duality (PAD) principle for soft tissue was used for the phase retrieval. A blind observer study was conducted and paired-sample T-test were performed to compare the mean differences in the two imaging systems.

RESULTS

The correct detection ratio for the CDMAM phantom for phase-contrast images acquired by the low-dose mid-energy system was 56.91%, whereas images acquired by the high-energy system correctly revealed only 40.97% of discs. The correct detection ratios were 57.88% and 43.41% for phase-retrieved images acquired by the low-dose mid-energy and high-energy imaging systems, respectively. The reading scores for all three groups of objects in the ACR phantom were higher for the mid energy imaging system as compared to the high-energy system for both phase-contrast and phase- retrieved images. The calculated edge enhancement index (EEI) from the acrylic edge phantom image for the mid-energy system was higher than that calculated for the high-energy imaging system. The quantitative analyses showed a higher Contrast to Noise Ratio (CNR) as well as a higher Figure of Merit (FOM) in images acquired by the low-dose mid-energy imaging system.

CONCLUSION

The PAD based retrieval method can be applied in mid-energy system without remarkably affecting the image quality, and in fact, it improves the lesion detectability with a patient dose saving of 25%.

Modulator refinement algorithm for coherent modulation imaging

Coherent modulation imaging (CMI) has been shown to be an effective lensless diffraction approach to imaging general extended samples with fast algorithmic convergence and high robustness to data imperfection. In the reported phasing algorithms of CMI, an exact knowledge of modulator is used as a priori. Extra characterization of the modulator is thus required before the CMI experiments are conducted and this can be cumbersome. Here we propose a modulator refinement algorithm that allows for modulator refinement in the same iterative process of image reconstruction. We demonstrate the method for both near-field and far-field geometries in simulations and for a far-field experiment. A relaxed requirement on exactly knowing the modulator would turn CMI into a standalone technique and make it much easier to implement, thus open up its wider applications in biology and materials science.

High-quality reconstruction of coherent modulation imaging using weak cascade modulators

Coherent modulation imaging (CMI) has been shown to be an effective lensless diffraction approach to imaging general extended samples with fast algorithmic convergence and high robustness to data imperfection. Being a single-shot technique, CMI holds a high potential for imaging dynamics with ultrafast pulses like the ones from free-electron lasers. In the reported work, strong modulators have been suggested for CMI to have the optimal performance, which may be an obstacle for the wide adoption of the method. Here we show that with our improved reconstruction algorithm the requirements on the modulation depth and feature size of a modulator can be relaxed. Furthermore, we demonstrate that when cascade configuration is used, the modulators can be even weaker while providing lower image errors in reconstruction than the case of a single modulator. Detailed numerical studies in both far-field and near-field experiment geometry are given via simulation. A relaxed requirement on modulators in CMI could pave the way for its wide use in biology and materials science.

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

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

Fourier phase retrieval with a single mask by Douglas-Rachford algorithms

The Fourier-domain Douglas-Rachford (FDR) algorithm is analyzed for phase retrieval with a single random mask. Since the uniqueness of phase retrieval solution requires more than a single oversampled coded diffraction pattern, the extra information is imposed in either of the following forms: 1) the sector condition on the object; 2) another oversampled diffraction pattern, coded or uncoded. For both settings, the uniqueness of projected fixed point is proved and for setting 2) the local, geometric convergence is derived with a rate given by a spectral gap condition. Numerical experiments demonstrate global, power-law convergence of FDR from arbitrary initialization for both settings as well as for 3 or more coded diffraction patterns without oversampling. In practice, the geometric convergence can be recovered from the power-law regime by a simple projection trick, resulting in highly accurate reconstruction from generic initialization.

Detectability comparison of simulated tumors in digital breast tomosynthesis using high-energy X-ray inline phase sensitive and commercial imaging systems

This study compared the detectability of simulated tumors using a high-energy X-ray inline phase sensitive digital breast tomosynthesis (DBT) prototype and a commercial attenuation-based DBT system. Each system imaged a 5-cm thick modular breast phantom with 50-50 adipose-glandular percentage density containing contrast-detail (CD) test objects to simulate different tumor sizes. A commercial DBT system acquired 15 projection views over 15 degrees (15d-15p) was used to acquire the attenuation-based projection views and to reconstruct the conventional DBT slices. Attenuation-based projection views were acquired at 32 kV, 46 mAs with a mean glandular dose (D_g) of 1.6 mGy. For acquiring phase sensitive projection views, the prototype utilized two acquisition geometries: 11 projection views were acquired over 15 degrees (15d-11p), and 17 projection views were acquired over 16 degrees (16d-17p) at 120 kV, 5.27 mAs with 1.51 mGy under the magnification (M) of 2. A phase retrieval algorithm based on the phase-attenuation duality (PAD) was applied to each projection view, and a modified Feldkamp-Davis-Kress (FDK) algorithm was used to reconstruct the phase sensitive DBT slices. Simulated tumor margins were rated as more conspicuous and better visualized for both phase sensitive acquisition geometries versus conventional DBT imaging. The CD curves confirmed the improvement in both contrast and spatial resolutions with the phase sensitive DBT imaging. The superiority of the phase sensitive DBT imaging was further endorsed by higher contrast to noise ratio (CNR) and figure-of-merit (FOM) values. The CNR improvements provided by the phase sensitive DBT prototype were sufficient to offset the noise reduction provided by the attenuation-based DBT imaging.

Optical projection tomography via phase retrieval algorithms

We describe a computational method for accurate, quantitative tomographic reconstructions in Optical Projection Tomography, based on phase retrieval algorithms. Our method overcomes limitations imposed by light scattering in opaque tissue samples under the memory effect regime, as well as reduces artifacts due to mechanical movements, misalignments or vibrations. We make use of Gerchberg-Saxton algorithms, calculating first the autocorrelation of the object and then retrieving the associated phase under four numerically simulated measurement conditions. By approaching the task in such a way, we avoid the projection alignment procedure, exploiting the fact that the autocorrelation sinogram is always aligned and centered. We thus propose two new, projection-based, tomographic imaging flowcharts that allow registration-free imaging of opaque biological specimens and unlock three-dimensional tomographic imaging of hidden objects. Two main reconstruction approaches are discussed in the text, focusing on their efficiency in the tomographic retrieval and discussing their applicability under four different numerical experiments.

SYRMEP Tomo Project: a graphical user interface for customizing CT reconstruction workflows

When considering the acquisition of experimental synchrotron radiation (SR) X-ray CT data, the reconstruction workflow cannot be limited to the essential computational steps of flat fielding and filtered back projection (FBP). More refined image processing is often required, usually to compensate artifacts and enhance the quality of the reconstructed images. In principle, it would be desirable to optimize the reconstruction workflow at the facility during the experiment (beamtime). However, several practical factors affect the image reconstruction part of the experiment and users are likely to conclude the beamtime with sub-optimal reconstructed images. Through an example of application, this article presents SYRMEP Tomo Project (STP), an open-source software tool conceived to let users design custom CT reconstruction workflows. STP has been designed for post-beamtime (off-line use) and for a new reconstruction of past archived data at user's home institution where simple computing resources are available. Releases of the software can be downloaded at the Elettra Scientific Computing group GitHub repository https://github.com/ElettraSciComp/STP-Gui.

Iterative reconstruction of magnetic induction using Lorentz transmission electron tomography

Intense ongoing research on complex nanomagnetic structures requires a fundamental understanding of the 3D magnetization and the stray fields around the nano-objects. 3D visualization of such fields offers the best way to achieve this. Lorentz transmission electron microscopy provides a suitable combination of high resolution and ability to quantitatively visualize the magnetization vectors using phase retrieval methods. In this paper, we present a formalism to represent the magnetic phase shift of electrons as a Radon transform of the magnetic induction of the sample. Using this formalism, we then present the application of common tomographic methods particularly the iterative methods, to reconstruct the 3D components of the vector field. We present an analysis of the effect of missing wedge and the limited angular sampling as well as reconstruction of complex 3D magnetization in a nanowire using simulations.

Holography and coherent diffraction with low-energy electrons: A route towards structural biology at the single molecule level

The current state of the art in structural biology is led by NMR, X-ray crystallography and TEM investigations. These powerful tools however all rely on averaging over a large ensemble of molecules. Here, we present an alternative concept aiming at structural analysis at the single molecule level. We show that by combining electron holography and coherent diffraction imaging estimations concerning the phase of the scattered wave become needless as the phase information is extracted from the data directly and unambiguously. Performed with low-energy electrons the resolution of this lens-less microscope is just limited by the De Broglie wavelength of the electron wave and the numerical aperture, given by detector geometry. In imaging freestanding graphene, a resolution of 2Å has been achieved revealing the 660.000 unit cells of the graphene sheet from a single data set. Once applied to individual biomolecules the method shall ultimately allow for non-destructive imaging and imports the potential to distinguish between different conformations of proteins with atomic resolution.