Ptychographic X-ray speckle tracking with multi-layer Laue lens systems

X-ray focusing below 3 nm with aberration-corrected multilayer Laue lenses

Multilayer Laue lenses are volume diffractive optical elements for hard X-rays with the potential to focus beams to sizes as small as 1 nm. This ability is limited by the precision of the manufacturing process, whereby systematic errors that arise during fabrication contribute to wavefront aberrations even after calibration of the deposition process based on wavefront metrology. Such aberrations can be compensated by using a phase plate. However, current high numerical aperture lenses for nanometer resolution exhibit errors that exceed those that can be corrected by a single phase plate. To address this, we accumulate a large wavefront correction by propagation through a linear array of 3D-printed phase correcting elements. With such a compound refractive corrector, we report on a point spread function with a full-width at half maximum area of 2.9 × 2.8 nm2 at a photon energy of 17.5 keV.

X-ray-to-visible light-field detection through pixelated colour conversion

Light-field detection measures both the intensity of light rays and their precise direction in free space. However, current light-field detection techniques either require complex microlens arrays or are limited to the ultraviolet-visible light wavelength ranges^1-4. Here we present a robust, scalable method based on lithographically patterned perovskite nanocrystal arrays that can be used to determine radiation vectors from X-rays to visible light (0.002-550 nm). With these multicolour nanocrystal arrays, light rays from specific directions can be converted into pixelated colour outputs with an angular resolution of 0.0018°. We find that three-dimensional light-field detection and spatial positioning of light sources are possible by modifying nanocrystal arrays with specific orientations. We also demonstrate three-dimensional object imaging and visible light and X-ray phase-contrast imaging by combining pixelated nanocrystal arrays with a colour charge-coupled device. The ability to detect light direction beyond optical wavelengths through colour-contrast encoding could enable new applications, for example, in three-dimensional phase-contrast imaging, robotics, virtual reality, tomographic biological imaging and satellite autonomous navigation.

High-speed processing of X-ray wavefront marking data with the Unified Modulated Pattern Analysis (UMPA) model

Wavefront-marking X-ray imaging techniques use e.g., sandpaper or a grating to generate intensity fluctuations, and analyze their distortion by the sample in order to retrieve attenuation, phase-contrast, and dark-field information. Phase contrast yields an improved visibility of soft-tissue specimens, while dark-field reveals small-angle scatter from sub-resolution structures. Both have found many biomedical and engineering applications. The previously developed Unified Modulated Pattern Analysis (UMPA) model extracts these modalities from wavefront-marking data. We here present a new UMPA implementation, capable of rapidly processing large datasets and featuring capabilities to greatly extend the field of view. We also discuss possible artifacts and additional new features.

Robust ptychographic X-ray speckle tracking with multilayer Laue lenses

In recent years, X-ray speckle tracking techniques have emerged as viable tools for wavefront metrology and sample imaging applications, and have been actively developed for use at synchrotron light sources. Speckle techniques can recover an image free of aberrations and can be used to measure wavefronts with a high angular sensitivity. Since they are compatible with low-coherence sources they can be also used with laboratory X-ray sources. A new implementation of the ptychographic X-ray speckle tracking method, suitable for the metrology of highly divergent wavefields, such as those created by multilayer Laue lenses, is presented here. This new program incorporates machine learning techniques such as Huber and non-parametric regression and enables robust and quick wavefield measurements and data evaluation even for low brilliance X-ray beams, and the imaging of low-contrast samples. To realize this, a software suite was written in Python 3, with a C back-end capable of concurrent calculations for high performance. It is accessible as a Python module and is available as source code under Version 3 or later of the GNU General Public License.

Precise wavefront characterization of x-ray optical elements using a laboratory source

Improvements in x-ray optics critically depend on the measurement of their optical performance. The knowledge of wavefront aberrations, for example, can be used to improve the fabrication of optical elements or to design phase correctors to compensate for these errors. At present, the characterization of such optics is made using intense x-ray sources, such as synchrotrons. However, the limited access to these facilities can substantially slow down the development process. Improvements in the brightness of lab-based x-ray micro-sources in combination with the development of new metrology methods, particularly ptychographic x-ray speckle tracking, enable characterization of x-ray optics in the lab with a precision and sensitivity not possible before. Here, we present a laboratory setup that utilizes a commercially available x-ray source and can be used to characterize different types of x-ray optics. The setup is used in our laboratory on a routine basis to characterize multilayer Laue lenses of high numerical aperture and other optical elements. This typically includes measurements of the wavefront distortions, optimum operating photon energy, and focal length of the lens. To check the sensitivity and accuracy of this laboratory setup, we compared the results to those obtained at the synchrotron and saw no significant difference. To illustrate the feedback of measurements on performance, we demonstrated the correction of the phase errors of a particular multilayer Laue lens using a 3D printed compound refractive phase plate.

Coherent Diffractive Imaging with Diffractive Optics

We present a novel approach to x-ray microscopy based on a multilayer zone plate which is positioned behind a sample similar to an objective lens. However, unlike transmission x-ray microscopy, we do not content ourselves with a sharp intensity image; instead, we incorporate the multilayer zone plate transfer function directly in an iterative phase retrieval scheme to exploit the large diffraction angles of the small layers. The presence of multiple diffraction orders, which is conventionally a nuisance, now comes as an advantage for the reconstruction and photon efficiency. In a first experiment, we achieve sub-10-nm resolution and a quantitative phase contrast.

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.

Analysis of X-ray multilayer Laue lenses made by masked deposition

Multilayer Laue lenses are diffractive optics for hard X-rays. To achieve high numerical aperture and resolution, diffracting structures of nanometer periods are required in such lenses, and a thickness (in the direction of propagation) of several micrometers is needed for high diffracting efficiency. Such structures must be oriented to satisfy Bragg's law, which can only be achieved consistently over the entire lens if the layers vary in their tilt relative to the incident beam. The correct tilt, for a particular wavelength, can be achieved with a very simple technique of using a straight-edge mask to give the necessary gradient of the layers. An analysis of the properties of lenses cut from such a shaded profile is presented and it is shown how to design, prepare, and characterize matched pairs of lenses that operate at a particular wavelength and focal length. It is also shown how to manufacture lenses with ideal curved layers for optimal efficiency.

speckle-tracking: a software suite for ptychographic X-ray speckle tracking

The program speckle-tracking is described, an open-source software suite for performing wavefront metrology and sample imaging from projection in-line holograms of a sample.

In recent years, X-ray speckle-tracking techniques have emerged as viable tools for wavefront metrology and sample imaging applications. These methods are based on the measurement of near-field images. Thanks to their simple experimental setup, high angular sensitivity and compatibility with low-coherence sources, these methods have been actively developed for use with synchrotron and laboratory light sources. Not only do speckle-tracking techniques give the potential for high-resolution imaging, but they also provide rapid and robust characterization of aberrations of X-ray optical elements, focal spot profiles, and sample position and transmission properties. In order to realize these capabilities, software implementations are required that are equally rapid and robust. To address this need, a software suite has been developed for the ptychographic X-ray speckle-tracking technique, an X-ray speckle-based method suitable for highly divergent wavefields. The software suite is written in Python 3, with an OpenCL back end for GPU and multi-CPU core processing. It is accessible as a Python module, through the command line or through a graphical user interface, and is available as source code under Version 3 or later of the GNU General Public License.

Ptychographic X-ray speckle tracking

A method is presented for the measurement of the phase gradient of a wavefront by tracking the relative motion of speckles in projection holograms as a sample is scanned across the wavefront. By removing the need to obtain an undistorted reference image of the sample, this method is suitable for the metrology of highly divergent wavefields. Such wavefields allow for large magnification factors that, according to current imaging capabilities, will allow for nanoradian angular sensitivity and nanoscale sample projection imaging. Both the reconstruction algorithm and the imaging geometry are nearly identical to that of ptychography, except that the sample is placed downstream of the beam focus and that no coherent propagation is explicitly accounted for. Like other X-ray speckle tracking methods, it is robust to low-coherence X-ray sources, making it suitable for laboratory-based X-ray sources. Likewise, it is robust to errors in the registered sample positions, making it suitable for X-ray free-electron laser facilities, where beam-pointing fluctuations can be problematic for wavefront metrology. A modified form of the speckle tracking approximation is also presented, based on a second-order local expansion of the Fresnel integral. This result extends the validity of the speckle tracking approximation and may be useful for similar approaches in the field.