Signal-to-noise and spatial resolution in in-line imaging. 1. Basic theory, numerical simulations and planar experimental images.

Signal-to-noise ratio and spatial resolution are quantitatively analysed in the context of in-line (propagation based) X-ray phase-contrast imaging. It is known that free-space propagation of a coherent X-ray beam from the imaged object to the detector plane, followed by phase retrieval in accordance with Paganin's method, can increase the signal-to-noise in the resultant images without deteriorating the spatial resolution. This results in violation of the noise-resolution uncertainty principle and demonstrates `unreasonable' effectiveness of the method. On the other hand, when the process of free-space propagation is performed in software, using the detected intensity distribution in the object plane, it cannot reproduce the same effectiveness, due to the amplification of photon shot noise. Here, it is shown that the performance of Paganin's method is determined by just two dimensionless parameters: the Fresnel number and the ratio of the real decrement to the imaginary part of the refractive index of the imaged object. The relevant theoretical analysis is performed first, followed by computer simulations and then by a brief test using experimental images collected at a synchrotron beamline. More extensive experimental tests will be presented in the second part of this paper.

X-ray phase and dark-field computed tomography without optical elements.

X-ray diffusive dark-field imaging, which allows spatially unresolved microstructure to be mapped across a sample, is an increasingly popular tool in an array of settings. Here, we present a new algorithm for phase and dark-field computed tomography based on the x-ray Fokker-Planck equation. Needing only a coherent x-ray source, sample, and detector, our propagation-based algorithm can map the sample density and dark-field/diffusion properties of the sample in 3D. Importantly, incorporating dark-field information in the density reconstruction process enables a higher spatial resolution reconstruction than possible with previous propagation-based approaches. Two sample exposures at each projection angle are sufficient for the successful reconstruction of both the sample density and dark-field Fokker-Planck diffusion coefficients. We anticipate that the proposed algorithm may be of benefit in biomedical imaging and industrial settings.

Mask design, fabrication, and experimental ghost imaging applications for patterned X-ray illumination.

A set of non-configurable transversely-displaced masks has been designed and fabricated to generate high-quality X-ray illumination patterns for use in imaging techniques such as ghost imaging (GI), ghost projection, and speckle tracking. The designs include a range of random binary and orthogonal patterns, fabricated through a combination of photolithography and gold electroplating techniques. We experimentally demonstrated that a single wafer can be used as an illumination mask for GI, employing individual illumination patterns and also a mixture of patterns, using a laboratory X-ray source. The quality of the reconstructed X-ray ghost images has been characterized and evaluated through a range of metrics.

Shot-to-shot two-dimensional photon intensity diagnostics within megahertz pulse-trains at the European XFEL.

Characterizing the properties of X-ray free-electron laser (XFEL) sources is a critical step for optimization of performance and experiment planning. The recent availability of MHz XFELs has opened up a range of new opportunities for novel experiments but also highlighted the need for systematic measurements of the source properties. Here, MHz-enabled beam imaging diagnostics developed for the SPB/SFX instrument at the European XFEL are exploited to measure the shot-to-shot intensity statistics of X-ray pulses. The ability to record pulse-integrated two-dimensional transverse intensity measurements at multiple planes along an XFEL beamline at MHz rates yields an improved understanding of the shot-to-shot photon beam intensity variations. These variations can play a critical role, for example, in determining the outcome of single-particle imaging experiments and other experiments that are sensitive to the transverse profile of the incident beam. It is observed that shot-to-shot variations in the statistical properties of a recorded ensemble of radiant intensity distributions are sensitive to changes in electron beam current density. These changes typically occur during pulse-distribution to the instrument and are currently not accounted for by the existing suite of imaging diagnostics. Modulations of the electron beam orbit in the accelerator are observed to induce a time-dependence in the statistics of individual pulses - this is demonstrated by applying radio-frequency trajectory tilts to electron bunch-trains delivered to the instrument. We discuss how these modifications of the beam trajectory might be used to modify the statistical properties of the source and potential future applications.

A Method for High-Resolution Three-Dimensional Reconstruction with Ewald Sphere Curvature Correction from Transmission Electron Images.

A method for three-dimensional reconstruction of objects from defocused images collected at multiple illumination directions in high-resolution transmission electron microscopy is presented. The method effectively corrects for the Ewald sphere curvature by taking into account the in-particle propagation of the electron beam. Numerical simulations demonstrate that the proposed method is capable of accurately reconstructing biological molecules or nanoparticles from high-resolution defocused images under conditions achievable in single-particle electron cryo-microscopy or electron tomography with realistic radiation doses, non-trivial aberrations, multiple scattering, and other experimentally relevant factors. The physics of the method is based on the well-known Diffraction Tomography formalism, but with the phase-retrieval step modified to include a conjugation of the phase (i.e., multiplication of the phase by a negative constant). At each illumination direction, numerically backpropagating the beam with the conjugated phase produces maximum contrast at the location of individual atoms in the molecule or nanoparticle. The resultant algorithm, Conjugated Holographic Reconstruction, can potentially be incorporated into established software tools for single-particle analysis, such as, for example, RELION or FREALIGN, in place of the conventional contrast transfer function correction procedure, in order to account for the Ewald sphere curvature and improve the spatial resolution of the three-dimensional reconstruction.

Hybrid refractive-diffractive axicons for Bessel-beam multiplexing and resolution improvement.

Optical elements rely on refraction, diffraction, or reflection for light manipulation. Fusing diffractive and refractive functions in a single element provides an extra layer of control over the wave propagation, allowing complex beam shaping through self-aligned, monolithic and miniaturized optics. Using gray-scale lithography with high-current focused Xe ion-beams, we realized hybrid refractive-diffractive micro-axicons that feature diffractive gratings engraved on their conical surfaces. Furthermore, we fabricated these devices in lithium niobate, which is a challenging piezo/optoelectronic material for processing with an as-yet unexploited potential in optical applications. The curvilinear surfaces of fabricated micro-axicons with a 230-µm diameter were engraved with diffraction linear and circular gratings of various depths (<400 nm), and the optical performance of these components was characterized, showing excellent agreement with theoretical expectations. The fusing of diffractive elements with carrier refractive surfaces introduces additional or enhanced device functionalities, such as beam multiplexing and resolution improvement. The potential applications of such monolithic and miniaturized hybrid micro-optical components include beamshaping for fluorescence microscopy.

Photon-counting, energy-resolving and super-resolution phase contrast X-ray imaging using an integrating detector.

This work demonstrates the use of a scientific-CMOS (sCMOS) energy-integrating detector as a photon-counting detector, thereby eliminating dark current and read-out noise issues, that simultaneously provides both energy resolution and sub-pixel spatial resolution for X-ray imaging. These capabilities are obtained by analyzing visible light photon clouds that result when X-ray photons produce fluorescence from a scintillator in front of the visible light sensor. Using low-fluence monochromatic X-ray projections to avoid overlapping photon clouds, the centroid of individual X-ray photon interactions was identified. This enabled a tripling of the spatial resolution of the detector to 6.71 ± 0.04 µm. By calculating the total charge deposited by this interaction, an energy resolution of 61.2 ± 0.1% at 17 keV was obtained. When combined with propagation-based phase contrast imaging and phase retrieval, a signal-to-noise ratio of up to 15 ± 3 was achieved for an X-ray fluence of less than 3 photons/mm2.

Ring artifact suppression in X-ray computed tomography using a simple, pixel-wise response correction.

We present a pixel-specific, measurement-driven correction that effectively reduces errors in detector response that give rise to the ring artifacts commonly seen in X-ray computed tomography (CT) scans. This correction is easy to implement, suppresses CT artifacts significantly, and is effective enough for use with both absorption and phase contrast imaging. It can be used as a standalone correction or in conjunction with existing ring artifact removal algorithms to further improve image quality. We validate this method using two X-ray CT data sets acquired using monochromatic sources, showing post-correction signal-to-noise increases of up to 55%, and we define an image quality metric to use specifically for the assessment of ring artifact suppression.

Nodal-line dynamics via exact polynomial solutions for coherent waves traversing aberrated imaging systems.

We obtain exact polynomial solutions for two-dimensional coherent complex scalar fields propagating through arbitrary aberrated shift-invariant linear imaging systems. These solutions are used to model nodal-line dynamics of coherent fields output by such systems.

Vortex Thermometry for Turbulent Two-Dimensional Fluids.

We introduce a new method of statistical analysis to characterize the dynamics of turbulent fluids in two dimensions. We establish that, in equilibrium, the vortex distributions can be uniquely connected to the temperature of the vortex gas, and we apply this vortex thermometry to characterize simulations of decaying superfluid turbulence. We confirm the hypothesis of vortex evaporative heating leading to Onsager vortices proposed in Phys. Rev. Lett. 113, 165302 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.165302, and we find previously unidentified vortex power-law distributions that emerge from the dynamics.

On the "unreasonable" effectiveness of transport of intensity imaging and optical deconvolution.

The effectiveness of reconstructive imaging using the homogeneous transport of intensity equation may be regarded as "unreasonable," because it has been shown to significantly increase signal-to-noise ratio while preserving spatial resolution, compared to equivalent conventional absorption-based imaging techniques at the same photon fluence. We reconcile this surprising behavior by analyzing the propagation of noise in typical in-line holography experiments. This analysis indicates that novel imaging techniques may be designed that produce high signal-to-noise images at low radiation doses without sacrificing spatial resolution.

On the van Cittert-Zernike theorem for intensity correlations and its applications.

A reciprocal relationship between the autocovariance of the light intensity in the source plane and in the far-field detector plane is presented in a form analogous to the classical van Cittert-Zernike theorem, but involving intensity correlation functions. A "classical" version of the reciprocity relationship is considered first, based on the assumption of circular Gaussian statistics of the complex amplitudes in the source plane. The result is consistent with the theory of Hanbury Brown-Twiss interferometry, but it is shown to be also applicable to estimation of the source size or the spatial resolution of the detector from the noise power spectrum of flat-field images. An alternative version of the van Cittert-Zernike theorem for intensity correlations is then derived for a quantized electromagnetic beam in a coherent state, which leads to Poisson statistics for the intrinsic intensity of the beam.

Generalised Cornu spirals: an experimental study using hard x-rays.

The Cornu spiral is a graphical aid that has been used historically to evaluate Fresnel integrals. It is also the Argand-plane mapping of a monochromatic complex scalar plane wave diffracted by a hard edge. We have successfully reconstructed a Cornu spiral due to diffraction of hard x-rays from a piece of Kapton tape. Additionally, we have explored the generalisation of the Cornu spiral by observing the Argand-plane mapping of complex scalar electromagnetic fields diffracted by a cylinder and a sphere embedded within a cylinder.

Capturing and visualizing transient X-ray wavefront topological features by single-grid phase imaging.

The detection, localisation and characterisation of stationary and singular points in the phase of an X-ray wavefield is a challenge, particularly given a time-evolving field. In this paper, the associated difficulties are met by the single-grid, single-exposure X-ray phase contrast imaging technique, enabling direct measurement of phase maxima, minima, saddle points and vortices, in both slowly varying fields and as a means to visualise weakly-attenuating samples that introduce detailed phase variations to the X-ray wavefield. We examine how these high-resolution vector measurements can be visualised, using branch cuts in the phase gradient angle to characterise phase features. The phase gradient angle is proposed as a useful modality for the localisation and tracking of sample features and the magnitude of the phase gradient for improved visualization of samples in projection, capturing edges and bulk structure while avoiding a directional bias. In addition, we describe an advanced two-stage approach to single-grid phase retrieval.

Singularimetry of local phase gradients using vortex lattices and in-line holography.

We have developed a differential form of singularimetry, which utilizes phase vortices or intensity gradient singularities as topological fiducial markers in a structured illumination context. This approach analytically measures phase gradients imparted by refracting specimens, yielding quantitative information that is both local and deterministic. We have quantified our phase gradient experiments to demonstrate that lattices of wave field singularities can be used to detect subtle phase gradients imparted by a spherical specimen and fiber optic cylinders.

Experimental X-Ray Ghost Imaging.

We report an experimental proof of principle for ghost imaging in the hard-x-ray energy range. We use a synchrotron x-ray beam that is split using a thin crystal in Laue diffraction geometry. With an ultrafast imaging camera, we are able to image x rays generated by isolated electron bunches. At this time scale, the shot noise of the synchrotron emission process is measurable as speckles, leading to speckle correlation between the two beams. The integrated transmitted intensity from a sample located in the first beam is correlated with the spatially resolved intensity measured in the second, empty, beam to retrieve the shadow of the sample. The demonstration of ghost imaging with hard x rays may open the way to protocols to reduce radiation damage in medical imaging and in nondestructive structural characterization using free electron lasers.

Erratum: Experimental X-Ray Ghost Imaging [Phys. Rev. Lett. 117, 113902 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.117.113902.

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

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.

Live small-animal X-ray lung velocimetry and lung micro-tomography at the Australian Synchrotron Imaging and Medical Beamline.

The high flux and coherence produced at long synchrotron beamlines makes them well suited to performing phase-contrast X-ray imaging of the airways and lungs of live small animals. Here, findings of the first live-animal imaging on the Imaging and Medical Beamline (IMBL) at the Australian Synchrotron are reported, demonstrating the feasibility of performing dynamic lung motion measurement and high-resolution micro-tomography. Live anaesthetized mice were imaged using 30 keV monochromatic X-rays at a range of sample-to-detector propagation distances. A frame rate of 100 frames s(-1) allowed lung motion to be determined using X-ray velocimetry. A separate group of humanely killed mice and rats were imaged by computed tomography at high resolution. Images were reconstructed and rendered to demonstrate the capacity for detailed, user-directed display of relevant respiratory anatomy. The ability to perform X-ray velocimetry on live mice at the IMBL was successfully demonstrated. High-quality renderings of the head and lungs visualized both large structures and fine details of the nasal and respiratory anatomy. The effect of sample-to-detector propagation distance on contrast and resolution was also investigated, demonstrating that soft tissue contrast increases, and resolution decreases, with increasing propagation distance. This new capability to perform live-animal imaging and high-resolution micro-tomography at the IMBL enhances the capability for investigation of respiratory diseases and the acceleration of treatment development in Australia.

Physical unsharp mask with structured detection.

We present a method to implement physically an unsharp mask filter in an imaging system. The idea is based on the use of a spatially periodic variation in the detection efficiency of an area detector. Such a "structured detection" introduces harmonic peaks in the Fourier spectrum associated with the image, enabling the use of higher spatial frequencies that would otherwise be inaccessible, due to the system point spread function. The result is an effective deblurring of the image implemented in hardware, i.e., before the detection noise occurs. The method is first demonstrated via a numerical simulation and then validated using experimental neutron imaging data.