Perfect X-ray focusing via fitting corrective glasses to aberrated optics

Wavefront analysis and phase correctors design using SHADOW

Knife-edge imaging is a successful method for determining the wavefront distortion of focusing optics such as Kirkpatrick-Baez mirrors or compound refractive lenses. In this study, the wavefront error of an imperfect elliptical mirror is predicted by developing a knife-edge program using the SHADOW/OASYS platform. It is shown that the focusing optics can be aligned perfectly by minimizing the parabolic and cubic coefficients of the wavefront error. The residual wavefront error provides precise information about the figure/height errors of the focusing optics suggesting it as an accurate method for in situ optical metrology. A Python program is developed to design a customized wavefront refractive corrector to minimize the residual wavefront error. Uniform beam at and out of focus and higher peak intensity are achieved by the wavefront correction in comparison with ideal focusing. The developed code provides a quick way for wavefront error analysis and corrector design for non-ideal optics especially for the new-generation diffraction-limited sources, and saves considerable experimental time and effort.

Ultracompact mirror device for forming 20-nm achromatic soft-X-ray focus toward multimodal and multicolor nanoanalyses

Nanoscale soft-X-ray microscopy is a powerful analysis tool in biological, chemical, and physical sciences. To enhance its probe sensitivity and leverage multimodal soft-X-ray microscopy, precise achromatic focusing devices, which are challenging to fabricate, are essential. Here, we develop an ultracompact Kirkpatrick-Baez (ucKB) mirror, which is ideal for the high-performance nanofocusing of broadband-energy X-rays. We apply our advanced fabrication techniques and short-focal-length strategy to realize diffraction-limited focusing over the entire soft-X-ray range. We achieve a focus size of 20.4 nm at 2 keV, which represents a significant improvement in achromatic soft-X-ray focusing. The ucKB mirror extends soft-X-ray fluorescence microscopy by producing a bicolor nanoprobe with a 1- or 2-keV photon energy. We propose a subcellular chemical mapping method that allows a comprehensive analysis of specimen morphology and the distribution of light elements and metal elements. ucKB mirrors will improve soft-X-ray nanoanalyses by facilitating photon-hungry, multimodal, and polychromatic methods, even with table-top X-ray sources.

Femtosecond Reduction of Atomic Scattering Factors Triggered by Intense X-Ray Pulse

X-ray diffraction of silicon irradiated with tightly focused femtosecond x-ray pulses (photon energy, 11.5 keV; pulse duration, 6 fs) was measured at various x-ray intensities up to 4.6×10^{19}  W/cm^{2}. The measurement reveals that the diffraction intensity is highly suppressed when the x-ray intensity reaches of the order of 10^{19}  W/cm^{2}. With a dedicated simulation, we confirm that the observed reduction of the diffraction intensity can be attributed to the femtosecond change in individual atomic scattering factors due to the ultrafast creation of highly ionized atoms through photoionization, Auger decay, and subsequent collisional ionization. We anticipate that this ultrafast reduction of atomic scattering factor will be a basis for new x-ray nonlinear techniques, such as pulse shortening and contrast variation x-ray scattering.

Alvarez varifocal X-ray lens

Visible light optical elements such as lenses and mirrors have counterparts for X-rays. In the visible regime, a variable focusing power can be achieved by an Alvarez lens which consists of a pair of inline planar refractors with a cubic thickness profile. When the two refractors are laterally displaced in opposite directions, the parabolic component of the wavefront is changed resulting in a longitudinal displacement of the focus. This paper reports an implementation of this concept for X-rays using two planar microfabricated refractive elements. The Alvarez X-ray lens can vary the focal distance of an elliptical X-ray mirror or a planar compound X-ray lens over several millimetres. The study presents the first demonstration of an Alvarez X-ray lens which adaptively corrects defocus and astigmatism aberrations of X-ray optics. In addition, the Alvarez X-ray lens eliminates coma aberration in an elliptical mirror, to the lowest order, when combining the lens with an adjustment of the pitch angle of the mirror.

Preparation and testing of laterally graded multilayer with a double genetic algorithm and root mean square error optimization in differential deposition

Lateral graded multilayer can realize reflection, collimation and focusing of hard X-ray, and are currently the research frontier and hotspot of synchrotron radiation and high-performance X-ray sources. To reduce the d-spacing error of graded multilayers, a root mean square error optimization method based on double genetic algorithm (DGA-RMSE) is proposed. The theoretical d-spacing distribution is obtained by optical design, and the range is 1.9 ∼ 3.1 nm. The optimized d-spacing distribution is obtained by convolution of particle beam function and continuous monotonic rate distribution line (RDL) which is constructed in the form of a polynomial. The GA is applied to optimize variables from the polynomial twice, and the RMSE of thickness error is optimized and converged to 0.0065 nm. The final thickness error which is measured by the grazing incidence X-ray reflectivity (GIXRR) is consistent with the theoretical calculation. The results show that DGA-RMSE can precisely select polynomial function of RDL, reducing the error in high-precision magnetron sputtering and mask technology.

Single-Slice XRF Mapping of Light Elements in Frozen-Hydrated Allium schoenoprasum via a Self-Absorption-Corrected Hyperspectral Tomographic Reconstruction Approach

3D and 2D-cross-sectional X-ray fluorescence analysis of biological material is a powerful tool to image the distribution of elements and to understand and quantify metal homeostasis and the distribution of anthropogenic metals and nanoparticles with minimal preparation artifacts. Using tomograms recorded on cryogenically prepared leaves of Allium schoenoprasum, the cross-sectional distribution of physiologically relevant elements like calcium, potassium, manganese, and zinc could be tomographically reconstructed by peak fitting followed by a conventional maximum-likelihood algorithm with self-absorption correction to reveal the quantitative cross-sectional element distribution. If light elements such as S and P are located deep in the sample compared to the escape depth of their characteristic X-ray fluorescence lines, the quantitative reconstruction becomes inaccurate. As a consequence, noise is amplified to a magnitude where it might be misinterpreted as actual concentration. We show that a tomographic MCA hyperspectral reconstruction in combination with a self-absorption correction allows for fitting of the XRF spectra directly in real space, which significantly improves the qualitative and quantitative analysis of the light elements compared to the conventional method as noise and artifacts in the tomographic reconstruction are reduced. This reconstruction approach can substantially improve the quantitative analysis of trace elements as it allows the fitting of summed voxel spectra in anatomical regions of interest. The presented method can be applied to XRF 2D single-slice tomography data and 3D tomograms and is particularly relevant for, but not limited to, biological material in order to help retrieve self-absorption corrected quantitative reconstructions of the spatial distribution of light elements and ultra-trace-elements.

Direct high-resolution X-ray imaging exploiting pseudorandomness

Owing to its unique penetrating power and high-resolution capability, X-ray imaging has been an irreplaceable tool since its discovery. Despite the significance, the resolution of X-ray imaging has largely been limited by the technical difficulties on X-ray lens making. Various lensless imaging methods have been proposed, but are yet relying on multiple measurements or additional constraints on measurements or samples. Here we present coherent speckle-correlation imaging (CSI) using a designed X-ray diffuser. CSI has no prerequisites for samples or measurements. Instead, from a single shot measurement, the complex sample field is retrieved based on the pseudorandomness of the speckle intensity pattern, ensured through a diffuser. We achieve a spatial resolution of 13.9 nm at 5.46 keV, beating the feature size of the diffuser used (300 nm). The high-resolution imaging capability is theoretically explained based on fundamental and practical limits. We expect the CSI to be a versatile tool for navigating the unexplored world of nanometer.

Direct LiF imaging diagnostics on refractive X-ray focusing at the EuXFEL High Energy Density instrument

The application of fluorescent crystal media in wide-range X-ray detectors provides an opportunity to directly image the spatial distribution of ultra-intense X-ray beams including investigation of the focal spot of free-electron lasers. Here the capabilities of the micro- and nano-focusing X-ray refractive optics available at the High Energy Density instrument of the European XFEL are reported, as measured in situ by means of a LiF fluorescent detector placed into and around the beam caustic. The intensity distribution of the beam focused down to several hundred nanometers was imaged at 9 keV photon energy. A deviation from the parabolic surface in a stack of nanofocusing Be compound refractive lenses (CRLs) was found to affect the resulting intensity distribution within the beam. Comparison of experimental patterns in the far field with patterns calculated for different CRL lens imperfections allowed the overall inhomogeneity in the CRL stack to be estimated. The precise determination of the focal spot size and shape on a sub-micrometer level is essential for a number of high energy density studies requiring either a pin-size backlighting spot or extreme intensities for X-ray heating.

The synchrotron radiation source PETRA III and its future ultra-low-emittance upgrade PETRA IV

PETRA III at DESY is one of the brightest synchrotron radiation sources worldwide. It serves a broad international multidisciplinary user community from academia to industry at currently 25 specialised beamlines. With a storage-ring energy of 6 GeV, it provides mainly hard to high-energy X-rays for versatile experiments in a very broad range of scientific fields. It is ideally suited for an upgrade to the ultra-low emittance source PETRA IV, owing to its large circumference of 2304 m. With a targeted storage ring emittance of 20 × 5 pm 2 rad 2 , PETRA IV will reach spectral brightnesses two to three orders of magnitude higher than today. The unique beam parameters will make PETRA IV the ultimate in situ 3D microscope for biological, chemical, and physical processes helping to address key questions in health, energy, mobility, information technology, and earth and environment.

Rapid aberration correction for diffractive X-ray optics by additive manufacturing

Diffraction-limited hard X-ray optics are key components for high-resolution microscopy, in particular for upcoming synchrotron radiation sources with ultra-low emittance. Diffractive optics like multilayer Laue lenses (MLL) have the potential to reach unprecedented numerical apertures (NA) when used in a crossed geometry of two one-dimensionally focusing lenses. However, minuscule fluctuations in the manufacturing process and technical limitations for high NA X-ray lenses can prevent a diffraction-limited performance. We present a method to overcome these challenges with a tailor-made refractive phase plate. With at-wavelength metrology and a rapid prototyping approach we demonstrate aberration correction for a crossed pair of MLL, improving the Strehl ratio from 0.41(2) to 0.81(4) at a numerical aperture of 3.3 × 10^-3. This highly adaptable aberration-correction scheme provides an important tool for diffraction-limited hard X-ray focusing.

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.

Two-dimensional wavefront characterization of adaptable corrective optics and Kirkpatrick-Baez mirror system using ptychography

Aberrations introduced during fabrication degrade the performance of X-ray optics and their ability to achieve diffraction limited focusing. Corrective optics can counteract these errors by introducing wavefront perturbations prior to the optic which cancel out the distortions. Here we demonstrate two-dimensional wavefront correction of an aberrated Kirkpatrick-Baez mirror pair using adaptable refractive structures. The resulting two-dimensional wavefront is measured using hard X-ray ptychography to recover the complex probe wavefield with high spatial resolution and model the optical performance under coherent conditions. The optical performance including the beam caustic, focal profile and wavefront error is examined before and after correction with both mirrors found to be diffraction limited after correcting. The results will be applicable to a wide variety of high numerical aperture X-ray optics aiming to achieve diffraction limited focussing using low emittance sources.

Sub-micrometer focusing setup for high-pressure crystallography at the Extreme Conditions beamline at PETRA III

Scientific tasks aimed at decoding and characterizing complex systems and processes at high pressures set new challenges for modern X-ray diffraction instrumentation in terms of X-ray flux, focal spot size and sample positioning. Presented here are new developments at the Extreme Conditions beamline (P02.2, PETRA III, DESY, Germany) that enable considerable improvements in data collection at very high pressures and small scattering volumes. In particular, the focusing of the X-ray beam to the sub-micrometer level is described, and control of the aberrations of the focusing compound refractive lenses is made possible with the implementation of a correcting phase plate. This device provides a significant enhancement of the signal-to-noise ratio by conditioning the beam shape profile at the focal spot. A new sample alignment system with a small sphere of confusion enables single-crystal data collection from grains of micrometer to sub-micrometer dimensions subjected to pressures as high as 200 GPa. The combination of the technical development of the optical path and the sample alignment system contributes to research and gives benefits on various levels, including rapid and accurate diffraction mapping of samples with sub-micrometer resolution at multimegabar pressures.

Multi-beam X-ray ptychography using coded probes for rapid non-destructive high resolution imaging of extended samples

Imaging large areas of a sample non-destructively and with high resolution is of great interest for both science and industry. For scanning coherent X-ray diffraction microscopy, i. e., ptychography, the achievable scan area at a given spatial resolution is limited by the coherent photon flux of modern X-ray sources. Multibeam X-ray ptychography can improve the scanning speed by scanning the sample with several parallel mutually incoherent beams, e. g., generated by illuminating multiple focusing optics in parallel by a partially coherent beam. The main difficulty with this scheme is the robust separation of the superimposed signals from the different beams, especially when the beams and the illuminated sample areas are quite similar. We overcome this difficulty by encoding each of the probing beams with its own X-ray phase plate. This helps the algorithm to robustly reconstruct the multibeam data. We compare the coded multibeam scans to uncoded multibeam and single beam scans, demonstrating the enhanced performance on a microchip sample with regular and repeating structures.

An achromatic X-ray lens

Diffractive and refractive optical elements have become an integral part of most high-resolution X-ray microscopes. However, they suffer from inherent chromatic aberration. This has to date restricted their use to narrow-bandwidth radiation, essentially limiting such high-resolution X-ray microscopes to high-brightness synchrotron sources. Similar to visible light optics, one way to tackle chromatic aberration is by combining a focusing and a defocusing optic with different dispersive powers. Here, we present the first successful experimental realisation of an X-ray achromat, consisting of a focusing diffractive Fresnel zone plate (FZP) and a defocusing refractive lens (RL). Using scanning transmission X-ray microscopy (STXM) and ptychography, we demonstrate sub-micrometre achromatic focusing over a wide energy range without any focal adjustment. This type of X-ray achromat will overcome previous limitations set by the chromatic aberration of diffractive and refractive optics and paves the way for new applications in spectroscopy and microscopy at broadband X-ray tube sources.

X-ray diffractive and refractive optical elements suffer from chromatic aberrations, limiting high-resolution X-ray microscopes mainly to bright synchrotron sources. Here, the authors experimentally realise an achromatic X-ray lens by combing a focusing diffractive Fresnel zone plate and a defocusing refractive lens.

Advances in laboratory-scale ptychography using high harmonic sources [Invited]

Extreme ultraviolet microscopy and wavefront sensing are key elements for next-generation ultrafast applications, such as chemically-resolved imaging, focal spot diagnostics in pump-and-probe experiments, and actinic metrology for the state-of-the-art lithography node at 13.5 nm wavelength. Ptychography offers a robust solution to the aforementioned challenges. Originally adapted by the electron and synchrotron communities, advances in the stability and brightness of high-harmonic tabletop sources have enabled the transfer of ptychography to the laboratory. This review covers the state of the art in tabletop ptychography with high harmonic generation sources. We consider hardware options such as illumination optics and detector concepts as well as algorithmic aspects in the analysis of multispectral ptychography data. Finally, we review technological application cases such as multispectral wavefront sensing, attosecond pulse characterization, and depth-resolved imaging.

Adiabatically focusing X-rays to the nanometer scale by one dimensional long kinoform lenses: comparison between an ideal Cartesian oval refocusing lens and a parabolic lens

The nano-focusing performance of adiabatically designed Cartesian oval refocusing lenses is compared with other well known compound refractive lenses with parabolic profiles (both simple concave and kinoform types). Using beam propagation method (BPM) simulation, it is shown that our design based on oval lenses does significantly improve the focusing properties compared to other parabolic lens based designs, e.g. adiabatically focusing lenses (AFLs), which doesn't take into account of the refocusing effect. This points to the importance of optimizing complex lens design in improving nano-focusing lens performance.

Beam and sample movement compensation for robust spectro-microscopy measurements on a hard X-ray nanoprobe

Static and in situ nanoscale spectro-microscopy is now routinely performed on the Hard X-ray Nanoprobe beamline at Diamond and the solutions implemented to provide robust energy scanning and experimental operation are described. A software-based scheme for active feedback stabilization of X-ray beam position and monochromatic beam flux across the operating energy range of the beamline is reported, consisting of two linked feedback loops using extremum seeking and position control. Multimodal registration methods have been implemented for active compensation of drift during an experiment to compensate for sample movement during in situ experiments or from beam-induced effects.

High-resolution achromatic X-ray optical systems for broad-band imaging and for focusing attosecond pulses

Achromatic focusing systems for hard X-rays are examined which consist of a refractive lens paired with a diffractive lens. Compared with previous analyses, we take into account the behaviour of thick refractive lenses, such as compound refractive lenses and waveguide gradient index refractive lenses, in which both the focal length and the position of the principal planes vary with wavelength. Achromatic systems formed by the combination of such a thick refractive lens with a multilayer Laue lens are found that can operate at a focusing resolution of about 3 nm, over a relative bandwidth of about 1%. With the appropriate distance between the refractive and diffractive lenses, apochromatic systems can also be found, which operate over relative bandwidth greater than 10%. These systems can be used to focus short pulses without distorting them in time by more than several attoseconds. Such systems are suitable for high-flux scanning microscopy and for creating high intensities from attosecond X-ray pulses.

Pump-probe X-ray holographic imaging of laser-induced cavitation bubbles with femtosecond FEL pulses

Cavitation bubbles can be seeded from a plasma following optical breakdown, by focusing an intense laser in water. The fast dynamics are associated with extreme states of gas and liquid, especially in the nascent state. This offers a unique setting to probe water and water vapor far-from equilibrium. However, current optical techniques cannot quantify these early states due to contrast and resolution limitations. X-ray holography with single X-ray free-electron laser pulses has now enabled a quasi-instantaneous high resolution structural probe with contrast proportional to the electron density of the object. In this work, we demonstrate cone-beam holographic flash imaging of laser-induced cavitation bubbles in water with nanofocused X-ray free-electron laser pulses. We quantify the spatial and temporal pressure distribution of the shockwave surrounding the expanding cavitation bubble at time delays shortly after seeding and compare the results to numerical simulations.

The Hard X-ray Nanoprobe beamline at Diamond Light Source

The Hard X-ray Nanoprobe beamline, I14, at Diamond Light Source is a new facility for nanoscale microscopy. The beamline was designed with an emphasis on multi-modal analysis, providing elemental mapping, speciation mapping by XANES, structural phase mapping using nano-XRD and imaging through differential phase contrast and ptychography. The 185 m-long beamline operates over a 5 keV to 23 keV energy range providing a ≤50 nm beam size for routine user experiments and a flexible scanning system allowing fast acquisition. The beamline achieves robust and stable operation by imaging the source in the vertical direction and implementing horizontally deflecting primary optics and an overfilled secondary source in the horizontal direction. This paper describes the design considerations, optical layout, aspects of the hardware engineering and scanning system in operation as well as some examples illustrating the beamline performance.

Nanosecond timing and synchronization scheme for holographic pump-probe studies at the MID instrument at European XFEL

Single-pulse holographic imaging at XFEL sources with 1012 photons delivered in pulses shorter than 100 fs reveal new quantitative insights into fast phenomena. Here, a timing and synchronization scheme for stroboscopic imaging and quantitative analysis of fast phenomena on time scales (sub-ns) and length-scales (≲100 nm) inaccessible by visible light is reported. A fully electronic delay-and-trigger system has been implemented at the MID station at the European XFEL, and applied to the study of emerging laser-driven cavitation bubbles in water. Synchronization and timing precision have been characterized to be better than 1 ns.

Materials Imaging and Dynamics (MID) instrument at the European X-ray Free-Electron Laser Facility

The Materials Imaging and Dynamics (MID) instrument at the European X-ray Free-Electron Laser (EuXFEL) facility is described. EuXFEL is the first hard X-ray free-electron laser operating in the MHz repetition range which provides novel science opportunities. The aim of MID is to enable studies of nano-structured materials, liquids, and soft- and hard-condensed matter using the bright X-ray beams generated by EuXFEL. Particular emphasis is on studies of structure and dynamics in materials by coherent scattering and imaging using hard X-rays. Commission of MID started at the end of 2018 and first experiments were performed in 2019.

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.

Single-pulse phase-contrast imaging at free-electron lasers in the hard X-ray regime

X-ray free-electron lasers (XFELs) have opened up unprecedented opportunities for time-resolved nano-scale imaging with X-rays. Near-field propagation-based imaging, and in particular near-field holography (NFH) in its high-resolution implementation in cone-beam geometry, can offer full-field views of a specimen's dynamics captured by single XFEL pulses. To exploit this capability, for example in optical-pump/X-ray-probe imaging schemes, the stochastic nature of the self-amplified spontaneous emission pulses, i.e. the dynamics of the beam itself, presents a major challenge. In this work, a concept is presented to address the fluctuating illumination wavefronts by sampling the configuration space of SASE pulses before an actual recording, followed by a principal component analysis. This scheme is implemented at the MID (Materials Imaging and Dynamics) instrument of the European XFEL and time-resolved NFH is performed using aberration-corrected nano-focusing compound refractive lenses. Specifically, the dynamics of a micro-fluidic water-jet, which is commonly used as sample delivery system at XFELs, is imaged. The jet exhibits rich dynamics of droplet formation in the break-up regime. Moreover, pump-probe imaging is demonstrated using an infrared pulsed laser to induce cavitation and explosion of the jet.

Review of in vivo optical molecular imaging and sensing from x-ray excitation

SIGNIFICANCE

Deep-tissue penetration by x-rays to induce optical responses of specific molecular reporters is a new way to sense and image features of tissue function in vivo. Advances in this field are emerging, as biocompatible probes are invented along with innovations in how to optimally utilize x-ray sources.

AIM

A comprehensive review is provided of the many tools and techniques developed for x-ray-induced optical molecular sensing, covering topics ranging from foundations of x-ray fluorescence imaging and x-ray tomography to the adaptation of these methods for sensing and imaging in vivo.

APPROACH

The ways in which x-rays can interact with molecules and lead to their optical luminescence are reviewed, including temporal methods based on gated acquisition and multipoint scanning for improved lateral or axial resolution.

RESULTS

While some known probes can generate light upon x-ray scintillation, there has been an emergent recognition that excitation of molecular probes by x-ray-induced Cherenkov light is also possible. Emission of Cherenkov radiation requires a threshold energy of x-rays in the high kV or MV range, but has the advantage of being able to excite a broad range of optical molecular probes. In comparison, most scintillating agents are more readily activated by lower keV x-ray energies but are composed of crystalline inorganic constituents, although some organic biocompatible agents have been designed as well. Methods to create high-resolution structured x-ray-optical images are now available, based upon unique scanning approaches and/or a priori knowledge of the scanned x-ray beam geometry. Further improvements in spatial resolution can be achieved by careful system design and algorithm optimization. Current applications of these hybrid x-ray-optical approaches include imaging of tissue oxygenation and pH as well as of certain fluorescent proteins.

CONCLUSIONS

Discovery of x-ray-excited reporters combined with optimized x-ray scan sequences can improve imaging resolution and sensitivity.

X-Ray Single-Grating Interferometry for Wavefront Measurement and Correction of Hard X-Ray Nanofocusing Mirrors

X-ray single-grating interferometry was applied to conduct accurate wavefront corrections for hard X-ray nanofocusing mirrors. Systematic errors in the interferometer, originating from a grating, a detector, and alignment errors of the components, were carefully examined. Based on the measured wavefront errors, the mirror shapes were directly corrected using a differential deposition technique. The corrected X-ray focusing mirrors with a numerical aperture of 0.01 attained two-dimensionally diffraction-limited performance. The results of the correction indicate that the uncertainty of the wavefront measurement was less than λ/72 in root-mean-square value.

Submicron focusing of high-energy X-rays with silicon saw-tooth refractive lenses: fabrication and aberrations

Saw-tooth refractive lenses are extremely well-suited to focus high energy X-rays (>50 keV). These lenses have properties of being continuously tunable (in energy or focal length), effectively parabolic, in-line, and attenuation-free on-axis. Vertical focusing of 60 keV synchrotron X-rays to 690 nm at a focal length f = 1.3 m with silicon saw-tooth lenses at a high-energy undulator radiation beamine is demonstrated, with discussion of relevant fabrication and mounting considerations and of geometrical aberrations unique to these devices. Aberration corrections towards further progress into the diffraction-limited nanofocusing regime are suggested. The versatility of such optics, combined with the attainability of smaller spot sizes at these penetrating photon energies, should continue to enhance material microstructure investigations at increasingly higher spatial resolutions.

Metrology of a Focusing Capillary Using Optical Ptychography

The focusing property of an ellipsoidal monocapillary has been characterized using the ptychography method with a 405 nm laser beam. The recovered wavefront gives a 12.5×10.4μm2 focus. The reconstructed phase profile of the focused beam can be used to estimate the height error of the capillary surface. The obtained height error shows a Gaussian distribution with a standard deviation of 1.3 μm. This approach can be used as a quantitative tool for evaluating the inner functional surfaces of reflective optics, complementary to conventional metrology methods.

Correction of the X-ray wavefront from compound refractive lenses using 3D printed refractive structures

A refractive phase corrector optics is proposed for the compensation of fabrication error of X-ray optical elements. Here, at-wavelength wavefront measurements of the focused X-ray beam by knife-edge imaging technique, the design of a three-dimensional corrector plate, its fabrication by 3D printing, and use of a corrector to compensate for X-ray lens figure errors are presented. A rotationally invariant corrector was manufactured in the polymer IP-S^TM using additive manufacturing based on the two-photon polymerization technique. The fabricated corrector was characterized at the B16 Test beamline, Diamond Light Source, UK, showing a reduction in r.m.s. wavefront error of a Be compound refractive Lens (CRL) by a factor of six. The r.m.s. wavefront error is a figure of merit for the wavefront quality but, for X-ray lenses, with significant X-ray absorption, a form of the r.m.s. error with weighting proportional to the transmitted X-ray intensity has been proposed. The knife-edge imaging wavefront-sensing technique was adapted to measure rotationally variant wavefront errors from two different sets of Be CRL consisting of 98 and 24 lenses. The optical aberrations were then quantified using a Zernike polynomial expansion of the 2D wavefront error. The compensation by a rotationally invariant corrector plate was partial as the Be CRL wavefront error distribution was found to vary with polar angle indicating the presence of non-spherical aberration terms. A wavefront correction plate with rotationally anisotropic thickness is proposed to compensate for anisotropy in order to achieve good focusing by CRLs at beamlines operating at diffraction-limited storage rings.

Ronchi shearing interferometry for wavefronts with circular symmetry

Ronchi testing of a focused electromagnetic wave has in the last few years been used extensively at X-ray free-electron laser (FEL) facilities to qualitatively evaluate the wavefront of the beam. It is a quick and straightforward test, is easy to interpret on the fly, and can be used to align phase plates that correct the focus of aberrated beams. In general, a single Ronchigram is not sufficient to gain complete quantitative knowledge of the wavefront. However the compound refractive lenses that are commonly used at X-ray FELs exhibit a strong circular symmetry in their aberration, and this can be exploited. Here, a simple algorithm that uses a single recorded Ronchigram to recover the full wavefront of a nano-focused beam, assuming circular symmetry, is presented, and applied to experimental measurements at the Matter in Extreme Conditions instrument at the Linac Coherent Light Source.

Wavelet-transform-based speckle vector tracking method for X-ray phase imaging

We introduce a new X-ray speckle-vector tracking method for phase imaging, which is based on the wavelet transform. Theoretical and experimental results show that this method, which is called wavelet-transform-based speckle-vector tracking (WSVT), has stronger noise robustness and higher efficiency compared with the cross-correlation-based method. In addition, the WSVT method has the controllable noise reduction and can be applied with fewer scan steps. These unique features make the WSVT method suitable for measurements of large image sizes and phase shifts, possibly under low-flux conditions, and has the potential to broaden the applications of speckle tracking to new areas requiring faster phase imaging and real-time wavefront sensing, diagnostics, and characterization.

Single-shot ptychography with highly tilted illuminations

A single-shot ptychographic iterative engine (PIE) using highly tilted illumination is proposed to realize accurate phase retrieval from a single frame of multiple and non-overlapping sub-diffraction patterns generated by a bunch of laser beams propagating at greater angles with respect to the optical axis. A non-paraxial reconstruction algorithm is developed to numerically propagate these highly tilted laser beams in back and forth iterative computations. Faster data acquisition and higher reconstruction quality are achieved in the proposed method by recording non-overlapping sub-diffraction patterns in a single frame and eliminating usual reconstruction errors arising from paraxial approximations.

Single-shot characterization of strongly focused coherent XUV and soft X-ray beams

In this Letter, we present a novel, to the best of our knowledge, single-shot method for characterizing focused coherent beams. We utilize a dedicated amplitude-only mask, in combination with an iterative phase retrieval algorithm, to reconstruct the amplitude and phase of a focused beam from a single measured far-field diffraction pattern alone. In a proof-of-principle experiment at a wavelength of 13.5 nm, we demonstrate our new method and obtain an RMS phase error of better than λ/70. This method will find applications in the alignment of complex optical systems, real-time feedback to adaptive optics, and single-shot beam characterization, e.g., at free-electron lasers or high-order harmonic beamlines.

Hard X-ray wavefront correction via refractive phase plates made by additive and subtractive fabrication techniques

Modern subtractive and additive manufacturing techniques present new avenues for X-ray optics with complex shapes and patterns. Refractive phase plates acting as glasses for X-ray optics have been fabricated, and spherical aberration in refractive X-ray lenses made from beryllium has been successfully corrected. A diamond phase plate made by femtosecond laser ablation was found to improve the Strehl ratio of a lens stack with a numerical aperture (NA) of 0.88 × 10-3 at 8.2 keV from 0.1 to 0.7. A polymer phase plate made by additive printing achieved an increase in the Strehl ratio of a lens stack at 35 keV with NA of 0.18 × 10-3 from 0.15 to 0.89, demonstrating diffraction-limited nanofocusing at high X-ray energies.

PtyNAMi: ptychographic nano-analytical microscope

Ptychographic X-ray imaging at the highest spatial resolution requires an optimal experimental environment, providing a high coherent flux, excellent mechanical stability and a low background in the measured data. This requires, for example, a stable performance of all optical components along the entire beam path, high temperature stability, a robust sample and optics tracking system, and a scatter-free environment. This contribution summarizes the efforts along these lines to transform the nanoprobe station on beamline P06 (PETRA III) into the ptychographic nano-analytical microscope (PtyNAMi).

Confocal Bragg ptychography for bulk specimens: a numerical demonstration

We report on a new X-ray imaging method, which generalizes Bragg ptychography to 3D mapping of embedded crystalline volumes within thick specimens. The sample is probed by a pencil X-ray beam. The diffracted beam is magnified by an objective and passes through a slit in the image plane to be monitored by a 2D detector in the far-field of the image plane. The dimensions of the incoming beam and the slit opening define a confocal Bragg volume. Scanning the sample with respect to this probe volume, an iterative oversampling routine is used to reconstruct the shape and projected displacement field of extended internal volumes. This routine takes into account the pupil function and known aberrations of the lens. We demonstrate the method by a numerical study of a 3.5 µm grain comprising a wall of edge dislocations. With a probe volume of ∼0.12 µm³ and a compound refractive lens with a numerical aperture of 0.49×10^-3 as the objective, the dislocations are fully resolved with a displacement sensitivity of ∼10 pm. The spatial resolution is 26×27×123 nm³ (rms), with the poor resolution along the optical axis being limited by the probe size. With a four times larger numerical aperture, the resolution becomes 16×8×123 nm³ (rms). The lens aberrations are found to be not critical.

Focusing with saw-tooth refractive lenses at a high-energy X-ray beamline

The Advanced Photon Source 1-ID beamline, operating in the 40-140 keV X-ray energy range, has successfully employed continuously tunable saw-tooth refractive lenses to routinely deliver beams focused in both one and two dimensions to experiments for over 15 years. The practical experience of implementing such lenses, made of silicon and aluminium, is presented, including their properties, control, alignment, and diagnostic methods, achieving ∼1 µm focusing (vertically). Ongoing development and prospects towards submicrometre focusing at these high energies are also mentioned.

Nanofocusing Optics for an X-Ray Free-Electron Laser Generating an Extreme Intensity of 100 EW/cm2 Using Total Reflection Mirrors

A nanofocusing optical system—referred to as 100 exa—for an X-ray free-electron laser (XFEL) was developed to generate an extremely high intensity of 100 EW/cm2 (1020 W/cm2) using total reflection mirrors. The system is based on Kirkpatrick-Baez geometry, with 250-mm-long elliptically figured mirrors optimized for the SPring-8 Angstrom Compact Free-Electron Laser (SACLA) XFEL facility. The nano-precision surface employed is coated with rhodium and offers a high reflectivity of 80%, with a photon energy of up to 12 keV, under total reflection conditions. Incident X-rays on the optics are reflected with a large spatial acceptance of over 900 μm. The focused beam is 210 nm × 120 nm (full width at half maximum) and was evaluated at a photon energy of 10 keV. The optics developed for 100 exa efficiently achieved an intensity of 1 × 1020 W/cm2 with a pulse duration of 7 fs and a pulse energy of 150 μJ (25% of the pulse energy generated at the light source). The experimental chamber, which can provide different stage arrangements and sample conditions, including vacuum environments and atmospheric-pressure helium, was set up with the focusing optics to meet the experimental requirements.

Conception of diffractive wavefront correction for XUV and soft x-ray spectroscopy

We present a simple and precise method to minimize aberrations of mirror-based, wavelength-dispersive spectrometers for the extreme ultraviolet (XUV) and soft x-ray domain. The concept enables an enhanced resolving power $ E/\Delta E $E/ΔE, in particular, close to the diffraction limit over a spectral band of a few percent around the design energy of the instrument. Our optical element, the "diffractive wavefront corrector" (DWC), is individually shaped to the form and figure error of the mirror profile and might be written directly with a laser on a plane and even strongly curved substrates. Theory and simulations of various configurations, like Hettrick-Underwood or compact, highly efficient all-in-one setups for $ {{\rm TiO}_2} $TiO₂ spectroscopy with $ E/\Delta E \mathbin{\lower.3ex\hbox{$\buildrel{\displaystyle{\lt}}\over{\smash{\displaystyle\sim}\vphantom{_x}}$}} 4.5 \times {10^4} $E/ΔE∼_x<4.5×10⁴, are addressed, as well as aspects of their experimental realization.

X-ray optics and beam characterization using random modulation: theory

X-ray near-field speckle-based phase-sensing approaches provide efficient means of characterizing optical elements. Presented here is a theoretical review of several of these speckle methods within the framework of optical characterization, and a generalization of the concept is provided. As is also demonstrated experimentally in a parallel paper [Berujon, Cojocaru, Piault, Celestre, Roth, Barrett & Ziegler (2020), J. Synchrotron Rad. 27, (this issue)], the methods theoretically developed here can be applied to different beams and optics and within a variety of situations where at-wavelength metrology is desired. By understanding the differences between the various processing methods, it is possible to find and implement the most suitable approach for each metrology scenario.

Modelling phase imperfections in compound refractive lenses

A framework based on physical optics for simulating the effect of imperfect compound refractive lenses (CRLs) upon an X-ray beam is described, taking into account measured phase errors obtained from at-wavelength metrology. A CRL stack is modelled, with increasing complexity, as a single thin phase element, then as a more realistic compound element including absorption and thickness effects, and finally adding realistic optical imperfections to the CRL. Coherent and partially coherent simulations using Synchrotron Radiation Workshop (SRW) are used to evaluate the different models, the effects of the phase errors and to check the validity of the design equations and suitability of the figures of merit.

X-ray fluorescence analysis of metal distributions in cryogenic biological samples using large-acceptance-angle SDD detection and continuous scanning at the Hard X-ray Micro/Nano-Probe beamline P06 at PETRA III

A new Rococo 2 X-ray fluorescence detector was implemented into the cryogenic sample environment at the Hard X-ray Micro/Nano-Probe beamline P06 at PETRA III, DESY, Hamburg, Germany. A four sensor-field cloverleaf design is optimized for the investigation of planar samples and operates in a backscattering geometry resulting in a large solid angle of up to 1.1 steradian. The detector, coupled with the Xspress 3 pulse processor, enables measurements at high count rates of up to 106 counts per second per sensor. The measured energy resolution of ∼129 eV (Mn Kα at 10000 counts s-1) is only minimally impaired at the highest count rates. The resulting high detection sensitivity allows for an accurate determination of trace element distributions such as in thin frozen hydrated biological specimens. First proof-of-principle measurements using continuous-movement 2D scans of frozen hydrated HeLa cells as a model system are reported to demonstrate the potential of the new detection system.

Angular X-Ray Cross-Correlation Analysis (AXCCA): Basic Concepts and Recent Applications to Soft Matter and Nanomaterials

Angular X-ray cross-correlation analysis (AXCCA) is a technique which allows quantitative measurement of the angular anisotropy of X-ray diffraction patterns and provides insights into the orientational order in the system under investigation. This method is based on the evaluation of the angular cross-correlation function of the scattered intensity distribution on a two-dimensional (2D) detector and further averaging over many diffraction patterns for enhancement of the anisotropic signal. Over the last decade, AXCCA was successfully used to study the anisotropy in various soft matter systems, such as solutions of anisotropic particles, liquid crystals, colloidal crystals, superlattices composed by nanoparticles, etc. This review provides an introduction to the technique and gives a survey of the recent experimental work in which AXCCA in combination with micro- or nanofocused X-ray microscopy was used to study the orientational order in various soft matter systems.

Refractive hard x-ray vortex phase plates

In this Letter, we report on the creation of hard x-ray beams carrying orbital angular momentum of topological charge -ℏ and -3ℏ at a photon energy of 8.2 keV via spiral phase plates made out of fused silica by ultrashort-pulsed laser ablation. The phase plates feature a smooth phase ramp with a 0.5 μm nominal step height and a surface roughness of 0.5 μm. The measured vortex beams show submicrometer-sized donut rings and agree well with numerical modeling. Fused silica phase plates are potentially suited to manipulate the electromagnetic field in highly intense x-ray beams at x-ray free-electron laser sources.

A versatile nanoreactor for complementary in situ X-ray and electron microscopy studies in catalysis and materials science

Two in situ `nanoreactors' for high-resolution imaging of catalysts have been designed and applied at the hard X-ray nanoprobe endstation at beamline P06 of the PETRA III synchrotron radiation source. The reactors house samples supported on commercial MEMS chips, and were applied for complementary hard X-ray ptychography (23 nm spatial resolution) and transmission electron microscopy, with additional X-ray fluorescence measurements. The reactors allow pressures of 100 kPa and temperatures of up to 1573 K, offering a wide range of conditions relevant for catalysis. Ptychographic tomography was demonstrated at limited tilting angles of at least ±35° within the reactors and ±65° on the naked sample holders. Two case studies were selected to demonstrate the functionality of the reactors: (i) annealing of hierarchical nanoporous gold up to 923 K under inert He environment and (ii) acquisition of a ptychographic projection series at ±35° of a hierarchically structured macroporous zeolite sample under ambient conditions. The reactors are shown to be a flexible and modular platform for in situ studies in catalysis and materials science which may be adapted for a range of sample and experiment types, opening new characterization pathways in correlative multimodal in situ analysis of functional materials at work. The cells will presently be made available for all interested users of beamline P06 at PETRA III.

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

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.

Wavefront sensing at X-ray free-electron lasers

Here a direct comparison is made between various X-ray wavefront sensing methods with application to optics alignment and focus characterization at X-ray free-electron lasers (XFELs). Focus optimization at XFEL beamlines presents unique challenges due to high peak powers as well as beam pointing instability, meaning that techniques capable of single-shot measurement and that probe the wavefront at an out-of-focus location are desirable. The techniques chosen for the comparison include single-phase-grating Talbot interferometry (shearing interferometry), dual-grating Talbot interferometry (moiré deflectometry) and speckle tracking. All three methods were implemented during a single beam time at the Linac Coherent Light Source, at the X-ray Pump Probe beamline, in order to make a direct comparison. Each method was used to characterize the wavefront resulting from a stack of beryllium compound refractive lenses followed by a corrective phase plate. In addition, difference wavefront measurements with and without the phase plate agreed with its design to within λ/20, which enabled a direct quantitative comparison between methods. Finally, a path toward automated alignment at XFEL beamlines using a wavefront sensor to close the loop is presented.

Characterization of high spatial resolution lithium fluoride X-ray detectors

The response of lithium fluoride (LiF) crystal detectors to monochromatic X-rays is measured in the multi-kilo-electron-volt range. This response, as a function of the X-ray dose, is independent of photon energy with no saturation level found. The response, as a function of the incident energy flux, is found to increase for photons of lower energy due to the differing attenuation lengths of X-ray photons within the crystal. Small differences are seen between different confocal microscopes used to scan the data, suggesting the need for absolute calibration. The spatial resolution of the LiF is also measured (1.19-1.36 μm) and is found to be independent of incident photon energy. Finally, a photometric study is performed in order to assess the feasibility of using these detectors at current X-ray free electron laser and laser facilities worldwide.

Towards optimized illumination for high-resolution ptychography

We present a systematic study, where effects of the illumination probe design on ptychography reconstruction quality are evaluated under well-controlled conditions. The illumination probe was created using Fresnel zone-plate (FZP) optics with locally displaced zones to provide a fine control over perturbations of the illumination wavefront. We show that optimally designed wavefront modulations not only reduce bias and variance in the reconstruction of the lowest spatial frequencies but also lead to improved imaging resolution and reduction of artefacts compared to a conventional FZP. Both these factors are important for quantitative accuracy and resolution of ptychographic tomography. Our work furthers the understanding of the important characteristics of an optimal illumination for high-resolution X-ray ptychography and how to design optimal FZP wavefront modulations for different applications of ptychographic imaging. These findings are applicable and relevant for ptychography using optical, EUV, and X-ray photons as well as electrons.