In the past few years, X-ray phase-contrast and dark-field imaging have evolved to be invaluable tools for non-destructive sample visualisation, delivering information inaccessible by conventional absorption imaging. X-ray phase-sensing techniques are furthermore increasingly used for at-wavelength metrology and optics characterisation. One of the latest additions to the group of differential phase-contrast methods is the X-ray speckle-based technique. It has drawn significant attention due to its simple and flexible experimental arrangement, cost-effectiveness and multimodal character, amongst others. Since its first demonstration at highly brilliant synchrotron sources, the method has seen rapid development, including the translation to polychromatic laboratory sources and extension to higher-energy X-rays. Recently, different advanced acquisition schemes have been proposed to tackle some of the main limitations of previous implementations. Current applications of the speckle-based method range from optics characterisation and wavefront measurement to biomedical imaging and materials science. This review provides an overview of the state of the art of the X-ray speckle-based technique. Its basic principles and different experimental implementations as well as the the latest advances and applications are illustrated. In the end, an outlook for anticipated future developments of this promising technique is given.

State of the Art of X-ray Speckle-Based Phase-Contrast and Dark-Field Imaging

We previously demonstrated near-field speckle-scanning-based x-ray imaging to be an easy-to-implement phase-sensing method capable of providing both high sensitivity and high resolution. Yet this performance combination could only be achieved at the cost of a significant number of sample exposures and of extensive data acquisition time, thus tempering its implementation for tomography applications. Here we show ways of drastically lowering the number of exposures for the speckle scanning method to become attractive for computed tomography imaging. As the method presented can cope with a high divergence beam, it is also expected to attract the attention of the laboratory sources community.

Near-field speckle-scanning-based x-ray tomography

Compared to the grating or crystal-based X-ray phase contrast imaging, the speckle-tracking method has the advantages of a simple setup and two-dimensional imaging. However, the edge-enhancement effect prevents the application of the speckle-tracking imaging to a large variety of samples. In this letter, an image reconstruction method is proposed to solve this problem. The experimental results from phantom, a biomedical sample, and a sample with a speckle-resembling structure demonstrated that the proposed method is efficacious in eliminating the effect of edge enhancement. The proposed method may greatly expand the application of the speckle-tracking method to most biomedical and material samples.

Speckle-tracking X-ray phase-contrast imaging for samples with obvious edge-enhancement effect

X-ray phase contrast enables weakly-attenuating structures to be imaged, with bright synchrotron sources adding the ability to capture time sequences and analyse sample dynamics. Here, we describe the translation of dynamical differential phase contrast imaging from the synchrotron to a compact x-ray source, in order to achieve this kind of time sequence imaging in the laboratory. We formulate broadly-applicable set-up guidelines for the single-grid, single-exposure imaging technique using a divergent source, exploring the experimental factors that restrict set-up size, imaging sensitivity and sample size. Experimental images are presented using the single-grid phase contrast technique with a steel attenuation grid and a liquid-metal-jet x-ray source, enabling exposure times as short as 0.5 s for dynamic imaging. Differential phase contrast images were retrieved from phantoms, incorporating noise filtering to improve the low-count images encountered when imaging dynamics using short exposures.

Requirements for dynamical differential phase contrast x-ray imaging with a laboratory source

The beam diffusing properties of stacked layers of diffuser material were evaluated experimentally and compared to a Gaussian random phase screen model The model was found to give promising accuracy in combination with a Lorentzian auto-correlation model The tail behaviour of the angular scattering distribution as a function of number of diffusing layers was particularly well described by the model, and in the case of an amorphous carbon diffuser, the model could describe the whole of the scattering distribution convincingly

Experimental investigation of Gaussian random phase screen model for x-ray diffusers.

Phase-contrast X-ray imaging using a paper analyzer enables the visualization of X-ray transparent biological structures using the refractive properties of the sample. The technique measures the sample-induced distortions of a spatially random reference pattern to retrieve quantitative sample information. This phase-contrast method is promising for biomedical application due to both a simple experimental set-up and a capability for real-time imaging. The authors explore the experimental configuration required to achieve robustness and accuracy in terms of (i) the paper analyzer feature size, (ii) the sample-to-detector distance, and (iii) the exposure time. Results using a synchrotron source confirm that the technique achieves accurate phase retrieval with a range of paper analyzers and at exposures as short as 0.5 ms. These exposure times are sufficiently short relative to characteristic physiological timescales to enable real-time dynamic imaging of living samples. A theoretical guide to the choice of sample-to-detector distance is also derived. While the measurements are specific to the set-up, these guidelines, the example speckle images, the strategies for analysis in the presence of noise and the experimental considerations and discussion will be of value to those who wish to use the speckle-tracking paper analyzer technique.

Exploring experimental parameter choice for rapid speckle-tracking phase-contrast X-ray imaging with a paper analyzer.

Modelling the dynamics of open quantum systems with strong correlations is fundamental to problems in materials science, quantum chemistry, and condensed matter physics [1, 2]. Strong coupling between a system and a complex environment can result in non-Markovian dynamics, where environment-mediated memory effects lead to correlations across multiple times. So then, exactly how complex are non-Markovian processes? Answering this challenging question informs our ability to simulate such systems on hardware and extract useful information about their dynamical properties. In this work, we examine the complexity of sampling a system coupled to an environment at successive points in time, and argue that there exist quantum stochastic processes that cannot be efficiently simulated on a classical computer. We formally extend the notion of sampling the output distribution of a quantum state to quantum processes. We show that, surprisingly, spatial complexity of the system-environment state is necessary, but not sufficient, to guarantee temporal complexity of the reduced open system dynamics. We then present a dynamical process where we ‘inject’ complexity through operations on the system alone, suggesting an avenue for demonstrating complex quantum dynamics on devices with only a small number of qubits. Moreover, our framework allows us to examine the complexity of noisy dynamics, which too constitute quantum stochastic processes. If these processes can be truly computationally complex, then this opens the possibility of engineering noise as a resource to demonstrate useful quantum advantage. Finally, we study the dynamics of a system and environment evolving according to a random Hamiltonian, and show that multi-time sampling of the system generates a probability distribution that displays Porter-Thomas statistics, which are characteristic of quantum chaos and conjectured to be classically hard to sample from [3]. Our results confirm that complex system-environment interactions, where long-time dynamics or memory effects are important, are likely to be temporally complex. The comparison of the complexity of multi-time sampling with that of only two-time correlation functions provides a pathway for understanding the complexity of the master equation description

Characterizing The Complexity Of Non-Markovian Processes

Open quantum systems are ubiquitous in the physical sciences, with widespread applications in the areas of chemistry, condensed matter physics, material science, optics, and many more. Not surprisingly, there is significant interest in their efficient simulation. However, direct classical simulation quickly becomes intractable with coupling to an environment whose effective dimension grows exponentially. This raises the question: can quantum computers help model these complex dynamics? A first step in answering this question requires understanding the computational complexity of this task. Here, we map the temporal complexity of a process to the spatial complexity of a many-body state using a computational model known as the process tensor framework. With this, we are able to explore the simulation complexity of an open quantum system as a dynamic sampling problem: a system coupled to an environment can be probed at successive points in time -- accessing multi-time correlations. The complexity of multi-time sampling, which is an important and interesting problem in its own right, contains the complexity of master equations and stochastic maps as a special case. Our results show how the complexity of the underlying quantum stochastic process corresponds to the complexity of the associated family of master equations for the dynamics. We present both analytical and numerical examples whose multi-time sampling is as complex as sampling from a many-body state that is classically hard. This also implies that the corresponding family of master equations are classically hard. Our results pave the way for studying open quantum systems from a complexity-theoretic perspective, highlighting the role quantum computers will play in our understanding of quantum dynamics.

Isobel A. Aloisio

Papers

Exploring experimental parameter choice for rapid speckle-tracking phase-contrast X-ray imaging with a paper analyzer.

Characterizing The Complexity Of Non-Markovian Processes

Sampling Complexity of Open Quantum Systems