Ptychography has risen as a reference X-ray imaging technique: it achieves resolutions of one billionth of a meter, macroscopic field of view, or the capability to retrieve chemical or magnetic contrast, among other features. A ptychographic reconstruction is normally formulated as a blind phase retrieval problem, where both the image (sample) and the probe (illumination) have to be recovered from phaseless measured data. In this article we address a nonlinear least squares model for the blind ptychography problem with constraints on the image and the probe by maximum likelihood estimation of the Poisson noise model. We formulate a variant model that incorporates the information of phaseless measurements of the probe to eliminate possible artifacts. Next, we propose a generalized alternating direction method of multipliers designed for the proposed nonconvex models with convergence guarantee under mild conditions, where their subproblems can be solved by fast el-ementwise operations. Numerically, the proposed algorithm outperforms state-of-the-art algorithms in both speed and image quality.

In order to determine the 3D structure of a thick sample, researchers have recently combined ptychography (for high resolution) and tomography (for 3D imaging) in a single experiment. 2-step methods are usually adopted for reconstruction, where the ptychography and tomography problems are often solved independently. In this paper, we provide a novel model and ADMM-based algorithm to jointly solve the ptychography-tomography problem iteratively, also employing total variation regularization. The proposed method permits large scan stepsizes for the ptychography experiment, requiring less measurements and being more robust to noise with respect to other strategies, while achieving higher reconstruction quality results.

Coherent ptychographic imaging experiments often discard the majority of the flux from a light source to define the coherence of the illumination. Even when the coherent flux is sufficient, the stability required during an exposure is another important limiting factor. Partial coherence analysis can considerably reduce these limitations. A partially coherent illumination can often be written as the superposition of a single coherent illumination convolved with a separable translational kernel. This article proposes the gradient decomposition of the probe (GDP), a model that exploits translational kernel separability, coupling the variances of the kernel with the transverse coherence. An efficient first-order splitting algorithm (GDP-ADMM) for solving the proposed nonlinear optimization problem is described. Numerical experiments demonstrate the effectiveness of the proposed method with Gaussian and binary kernel functions in fly-scan measurements. Remarkably, GDP-ADMM using nanoprobes produces satisfactory results even when the ratio between the kernel width and the beam size is more than one, or when the distance between successive acquisitions is twice as large as the beam width.

Spectroscopic ptychography is a powerful technique to determine the chemical composition of a sample with high spatial resolution. In spectro-ptychography, a sample is rastered through a focused X-ray beam with varying photon energy so that a series of phaseless diffraction data are recorded. Each chemical component in the material under investigation has a characteristic absorption and phase contrast as a function of photon energy. Using a dictionary formed by the set of contrast functions of each energy for each chemical component, it is possible to obtain the chemical composition of the material from high-resolution multi-spectral images. This paper presents SPA (spectroscopic ptychography with alternating direction method of multipliers), a novel algorithm to iteratively solve the spectroscopic blind ptychography problem. First, a nonlinear spectro-ptychography model based on Poisson maximum likelihood is designed, and then the proposed method is constructed on the basis of fast iterative splitting operators. SPA can be used to retrieve spectral contrast when considering either a known or an incomplete (partially known) dictionary of reference spectra. By coupling the redundancy across different spectral measurements, the proposed algorithm can achieve higher reconstruction quality when compared with standard state-of-the-art two-step methods. It is demonstrated how SPA can recover accurate chemical maps from Poisson-noised measurements, and its enhanced robustness when reconstructing reduced-redundancy ptychography data using large scanning step sizes is shown.

Tomographic imaging has benefited from advances in X-ray sources, detectors and optics to enable novel observations in science, engineering and medicine. These advances have come with a dramatic increase of input data in the form of faster frame rates, larger fields of view or higher resolution, so high performance solutions are currently widely used for analysis. Tomographic instruments can vary significantly from one to another, including the hardware employed for reconstruction: from single CPU workstations to large scale hybrid CPU/GPU supercomputers. Flexibility on the software interfaces and reconstruction engines are also highly valued to allow for easy development and prototyping. This paper presents a novel software framework for tomographic analysis that tackles all aforementioned requirements. The proposed solution capitalizes on the increased performance of sparse matrix-vector multiplication and exploits multi-CPU and GPU reconstruction over MPI. The solution is implemented in Python and relies on CuPy for fast GPU operators and CUDA kernel integration, and on SciPy for CPU sparse matrix computation. As opposed to previous tomography solutions that are tailor-made for specific use cases or hardware, the proposed software is designed to provide flexible, portable and high-performance operators that can be used for continuous integration at different production environments, but also for prototyping new experimental settings or for algorithmic development. The experimental results demonstrate how our implementation can even outperform state-of-the-art software packages used at advanced X-ray sources worldwide.

Tomographic imaging has benefited from advances in X-ray sources, detectors and optics to enable novel observations in science, engineering and medicine. These advances have come with a dramatic increase of input data in the form of faster frame rates, larger fields of view or higher resolution, so high performance solutions are currently widely used for analysis. Tomographic instruments can vary significantly from one to another, including the hardware employed for reconstruction: from single CPU workstations to large scale hybrid CPU/GPU supercomputers. Flexibility on the software interfaces and reconstruction engines are also highly valued to allow for easy development and prototyping. This paper presents a novel software framework for tomographic analysis that tackles all aforementioned requirements. The proposed solution capitalizes on the increased performance of sparse matrix-vector multiplication and exploits multi-CPU and GPU reconstruction over MPI. The solution is implemented in Python and relies on CuPy for fast GPU operators and CUDA kernel integration, and on SciPy for CPU sparse matrix computation. As opposed to previous tomography solutions that are tailor-made for specific use cases or hardware, the proposed software is designed to provide flexible, portable and high-performance operators that can be used for continuous integration at different production environments, but also for prototyping new experimental settings or for algorithmic development. The experimental results demonstrate how our implementation can even outperform state-of-the-art software packages used at advanced X-ray sources worldwide.

Ptychography has rapidly grown in the fields of X-ray and electron imaging for its unprecedented ability to achieve nano or atomic scale resolution while simultaneously retrieving chemical or magnetic information from a sample. A ptychographic reconstruction is achieved by means of solving a complex inverse problem that imposes constraints both on the acquisition and on the analysis of the data, which typically precludes real-time imaging due to computational cost involved in solving this inverse problem. In this work we propose PtychoNN, a novel approach to solve the ptychography reconstruction problem based on deep convolutional neural networks. We demonstrate how the proposed method can be used to predict real-space structure and phase at each scan point solely from the corresponding far-field diffraction data. The presented results demonstrate how PtychoNN can effectively be used on experimental data, being able to generate high quality reconstructions of a sample up to hundreds of times faster than state-of-the-art ptychography reconstruction solutions once trained. By surpassing the typical constraints of iterative model-based methods, we can significantly relax the data acquisition sampling conditions and produce equally satisfactory reconstructions. Besides drastically accelerating acquisition and analysis, this capability can enable new imaging scenarios that were not possible before, in cases of dose sensitive, dynamic and extremely voluminous samples.

The success of ptychographic imaging experiments strongly depends on achieving high signal-to-noise ratio. This is particularly important in nanoscale imaging experiments when diffraction signals are very weak and the experiments are accompanied by significant parasitic scattering (background), outliers or correlated noise sources. It is also critical when rare events, such as cosmic rays, or bad frames caused by electronic glitches or shutter timing malfunction take place. In this paper, we propose a novel iterative algorithm with rigorous analysis that exploits the direct forward model for parasitic noise and sample smoothness to achieve a thorough characterization and removal of structured and random noise. We present a formal description of the proposed algorithm and prove its convergence under mild conditions. Numerical experiments from simulations and real data (both soft and hard X-ray beamlines) demonstrate that the proposed algorithms produce better results when compared to state-of-the-art methods.

The analysis of chemical states and morphology in nanomaterials is central to many areas of science. We address this need with an ultrahigh-resolution scanning transmission soft x-ray microscope. Our instrument provides multiple analysis tools in a compact assembly and can achieve few-nanometer spatial resolution and high chemical sensitivity via x-ray ptychography and conventional scanning microscopy. A novel scanning mechanism, coupled to advanced x-ray detectors, a high-brightness x-ray source, and high-performance computing for analysis provide a revolutionary step forward in terms of imaging speed and resolution. We present x-ray microscopy with 8-nm full-period spatial resolution and use this capability in conjunction with operando sample environments and cryogenic imaging, which are now routinely available. Our multimodal approach will find wide use across many fields of science and facilitate correlative analysis of materials with other types of probes.