Spectral µCT with an energy resolving and interpolating pixel detector.

A main challenge in x-ray µCT with laboratory radiation derives from the broad spectral content, which in contrast to monochromatic synchrotron radiation gives rise to reconstruction artifacts and impedes quantitative reconstruction. Due to the low spectral brightness of these sources, monochromatization is unfavorable and parallel recording of a broad bandpath is practically indispensable. While conventional CT sums up all spectral components into a single detector value, spectral CT discriminates the data in several spectral bins. Here we show that a new generation of charge integrating and interpolating pixel detectors is ideally suited to implement spectral CT with a resolution in the range of 10 µm. We find that the information contained in several photon energy bins largely facilitates automated classification of materials, as demonstrated for of a mouse cochlea. Bones, soft tissues, background and metal implant materials are discriminated automatically. Importantly, this includes taking a better account of phase contrast effects, based on tailoring reconstruction parameters to specific energy bins.

Erratum: X-Ray Optics on a Chip: Guiding X Rays in Curved Channels [Phys. Rev. Lett. 115, 203902 (2015)].

This corrects the article DOI: 10.1103/PhysRevLett.115.203902.

Using sparsity information for iterative phase retrieval in x-ray propagation imaging.

For iterative phase retrieval algorithms in near field x-ray propagation imaging experiments with a single distance measurement, it is indispensable to have a strong constraint based on a priori information about the specimen; for example, information about the specimen's support. Recently, Loock and Plonka proposed to use the a priori information that the exit wave is sparsely represented in a certain directional representation system, a so-called shearlet system. In this work, we extend this approach to complex-valued signals by applying the new shearlet constraint to amplitude and phase separately. Further, we demonstrate its applicability to experimental data.

Holographic imaging with a hard x-ray nanoprobe: ptychographic versus conventional phase retrieval.

We have performed near-field x-ray imaging with simultaneous object and probe reconstruction. By an advanced ptychographic algorithm based on longitudinal and lateral translations, full-field images of nanoscale objects are reconstructed with quantitative contrast values, along with the extended wavefronts used to illuminate the objects. The imaging scheme makes idealizing assumptions on the probe obsolete, and efficiently disentangles phase shifts related to the object from the imperfections in the illumination. We validate this approach by comparison to the conventional reconstruction scheme without simultaneous probe retrieval, based on the contrast transfer function algorithm. To this end, a set of semiconductor nanowires with controlled chemical composition (InP core, insulating SiO2 layer, and indium tin oxide cover) is imaged using the quasi-point source illumination realized by the hard x-ray nanofocus (26 nm×39 nm spot size) of the ID16A Nano-Imaging beamline at the European Synchrotron Radiation Facility.

New X-Ray Tomography Method Based on the 3D Radon Transform Compatible with Anisotropic Sources.

In this work, we propose a novel computed tomography (CT) approach for three-dimensional (3D) object reconstruction, based on a generalized tomographic geometry with two-dimensional angular sampling (two angular degrees of freedom). The reconstruction is based on the 3D Radon transform and is compatible with anisotropic beam conditions. This allows isotropic 3D imaging with a source, which can be extended along one direction for increased flux, while high resolution is achieved by a small source size only in the orthogonal direction. This novel scheme for analytical CT is demonstrated by numerical simulations and proof-of-concept experiments. In this way high resolution and coherence along a single direction determines the reconstruction quality of the entire 3D data set, opening up, for example, new opportunities to achieve nanoscale resolution and/or phase contrast with low brilliance sources such as laboratory x-ray or neutron sources.

Actin bundles cross-linked with α-actinin studied by nanobeam X-ray diffraction.

We have performed scanning nano-beam small-angle X-ray scattering (nano-SAXS) experiments on in vitro-formed actin filaments cross-linked with [Formula: see text]-actinin. The experimental method combines a high resolution in reciprocal space with a real space resolution as given by the spot-size of the nano-focused X-ray beam, and opens up new opportunities to study local super-molecular structures of actin filaments. In this first proof-of-concept, we show that the local orientation of actin bundles formed by the cross-linking can be visualized by the X-ray darkfield maps. The filament bundles give rise to highly anisotropic diffraction patterns showing distinct streaks perpendicular to the bundle axes. Interestingly, some diffraction patterns exhibit a fine structure in the form of intensity modulations allowing for a more detailed analysis of the order within the bundles. A first empirical quantification of these modulations is included in the present work.

Myelinated mouse nerves studied by X-ray phase contrast zoom tomography.

We have used X-ray phase contrast tomography to resolve the structure of uncut, entire myelinated optic, saphenous and sciatic mouse nerves. Intrinsic electron density contrast suffices to identify axonal structures. Specific myelin labeling by an osmium tetroxide stain enables distinction between axon and surrounding myelin sheath. Utilization of spherical wave illumination enables zooming capabilities which enable imaging of entire sciatic internodes as well as identification of sub-structures such as nodes of Ranvier and Schmidt-Lanterman incisures.

X-Ray Optics on a Chip: Guiding X Rays in Curved Channels.

We study the propagation of hard x rays in single curved x-ray waveguide channels and observe waveguide effects down to surprisingly small radii of curvature R≃10 mm and a large contour length s≃5 mm, deflecting beams up to 30°. At these high angles, about 2 orders of magnitude above the critical angle of total reflection θ(c), most radiation modes are lost by "leaking" into the cladding, while certain "survivor" modes persist. This may open up a new form of integrated x-ray optics "on a chip," requiring curvatures mostly well below the extreme values studied here, e.g., to split and to delay x-ray pulses.

X-ray holographic imaging of hydrated biological cells in solution.

We demonstrate nanoscale x-ray holographic imaging using optimized illumination wave fronts emitted by x-ray waveguide channels. Mode filtering minimizes wave-front distortions and artifacts encountered in most hard x-ray focusing schemes, enabling quantitative reconstruction of the projected density, as evidenced by a test pattern imaged with a field of view of about 20×40 µm and at 22 nm resolution. The dose efficiency and contrast sensitivity make the optical scheme compatible with samples of intrinsically low contrast, typical for hydrated soft matter. This is demonstrated by imaging bacteria in the hydrated and living state, with quantitative phase contrast revealing dense structures of the bacterial nucleoids associated with compactified DNA. In response to continued irradiation, characteristic changes in these dense structures are observed.

Reconstruction of wave front and object for inline holography from a set of detection planes.

We illustrate the errors inherent in the conventional empty beam correction of full field X-ray propagation imaging, i.e. the division of intensities in the detection plane measured with an object in the beam by the intensity pattern measured without the object, i.e. the empty beam intensity pattern. The error of this conventional approximation is controlled by the ratio of the source size to the smallest feature in the object, as is shown by numerical simulation. In a second step, we investigate how to overcome the flawed empty beam division by simultaneous reconstruction of the probing wavefront (probe) and of the object, based on measurements in several detection planes (multi-projection approach). The algorithmic scheme is demonstrated numerically and experimentally, using the defocus wavefront of the hard X-ray nanoprobe setup at the European Synchrotron Radiation Facility (ESRF).

Collective lipid bilayer dynamics excited by surface acoustic waves.

We use standing surface acoustic waves to induce coherent phonons in model lipid multilayers deposited on a piezoelectric surface. Probing the structure by phase-controlled stroboscopic x-ray pulses we find that the internal lipid bilayer electron density profile oscillates in response to the externally driven motion of the lipid film. The structural response to the well-controlled motion is a strong indication that bilayer structure and membrane fluctuations are intrinsically coupled, even though these structural changes are averaged out in equilibrium and time integrating measurements. Here the effects are revealed by a timing scheme with temporal resolution on the picosecond scale in combination with the sub-nm spatial resolution, enabled by high brilliance synchrotron x-ray reflectivity.

Transport of intensity phase reconstruction to solve the twin image problem in holographic x-ray imaging.

We have implemented a deterministic method for solving the phase problem in hard x-ray in-line holography which overcomes the twin image problem. The phase distribution in the detector plane is retrieved by using two images with slightly different Fresnel numbers. We then use measured intensities and reconstructed phases in the detection plane to compute the exit wave in the sample plane. No further a priori information like a limited support or the assumption of pure phase objects is necessary so that it can be used for a wide range of complex samples. Using a nano-focused hard x-ray beam half period resolutions better than 30 nm are achieved.

Phase retrieval for object and probe using a series of defocus near-field images.

Full field x-ray propagation imaging can be severely deteriorated by wave front aberrations. Here we present an extension of ptychographic phase retrieval with simultaneous probe and object reconstruction suitable for the near-field diffractive imaging setting. Update equations used to iteratively solve the phase problem from a set of near-field images in view of reconstruction both object and probe are derived. The algorithm is tested based on numerical simulations including photon shot noise. The results indicate that the approach provides an efficient way to overcome restrictive idealizations of the illumination wave in the near-field (propagation) imaging.

Sub-5 nm hard x-ray point focusing by a combined Kirkpatrick-Baez mirror and multilayer zone plate.

Compound optics such as lens systems can overcome the limitations concerning resolution, efficiency, or aberrations which fabrication constraints would impose on any single optical element. In this work we demonstrate unprecedented sub-5 nm point focusing of hard x-rays, based on the combination of a high gain Kirkpatrick-Baez (KB) mirror system and a high resolution W/Si multilayer zone plate (MZP) for ultra-short focal length f. The pre-focusing allows limiting the MZP radius to below 2 µm, compatible with the required 5 nm structure width and essentially unlimited aspect ratios, provided by enabling fabrication technology based on pulsed laser deposition (PLD) and focused ion beam (FIB).

Single pulse coherence measurements in the water window at the free-electron laser FLASH.

The spatial coherence of free-electron laser radiation in the water window spectral range was studied, using the third harmonic (λ<(3rd) = 2.66 nm) of DESY's Free-electron LASer in Hamburg (FLASH). Coherent single pulse diffraction patterns of 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC) multilamellar lipid stacks have been recorded. The intensity histogram of the speckle pattern around the first lamellar Bragg peak, corresponding to the d = 5 nm periodicity of the stack, reveals an average number of transverse modes of M¯ = 3.0 of the 3rd harmonic. Using the lipid stack as a 'monochromator', pulse-to-pulse fluctuations in the third harmonic λ(3rd) have been determined to be 0.033 nm.

Nonequilibrium collective dynamics in photoexcited lipid multilayers by time resolved diffuse x-ray scattering.

We study the nonequilibrium shape fluctuations in fluorescence labeled phospholipid multibilayers composed of the model lipid DOPC and the well-known lipid dye Texas red, driven out of equilibrium by short laser pulses. The temporal evolution of the lipid bilayer undulations after excitation was recorded by time resolved x-ray diffraction. Already at moderate peak intensities (Pp≤10(5) W/cm2), pulsed laser illumination leads to significant changes of the undulation modes in a well-defined lateral wavelength band. The observed phenomena evolve on nano- to microsecond time scales after optical excitation, and can be described in terms of a modulation instability in the lipid multilamellar stack.

Structure and Volta potential of lipid multilayers: effect of X-ray irradiation.

The effect of hard X-ray radiation on the structure and electrostatics of solid-supported lipid multilayer membranes is investigated using a scanning Kelvin probe (SKP) integrated with a high-energy synchrotron beamline to enable in situ measurements of the membranes' local Volta potential (V(p)) during X-ray structural characterization. The undulator radiation employed does not induce any detectable structural damage, but the V(p) of both bare and lipid-modified substrates is found to undergo strong radiation-induced shifts, almost immediately after X-ray exposure. Sample regions that are macroscopically distant (~cm) from the irradiated region experience an exponential V(p) growth with a characteristic time constant of several minutes. The V(p) variations occurring upon periodic on/off X-ray beam switching are fully or partially reversible depending on the location and time-scale of the SKP measurement. The general relevance of these findings for synchrotron-based characterization of biomolecular thin films is critically reviewed.

Sub-10 nm beam confinement by X-ray waveguides: design, fabrication and characterization of optical properties.

The propagation of hard X-ray synchrotron beams in waveguides with guiding layer diameters in the 9-35 nm thickness range has been studied. The planar waveguide structures consist of an optimized two-component cladding. The presented fabrication method is suitable for short and leak-proof waveguide slices with lengths (along the optical axis) in the sub-500 µm range, adapted for optimized transmission at photon energies of 11.5-18 keV. A detailed comparison between finite-difference simulations of waveguide optics and the experimental results is presented, concerning transmission, divergence of the waveguide exit beam, as well as the angular acceptance. In a second step, two crossed waveguides have been used to create a quasi-point source for propagation-based X-ray imaging at the new nano-focus endstation of the P10 coherence beamline at Petra III. By inverting the measured Fraunhofer diffraction pattern by an iterative error-reduction algorithm, a two-dimensional focus of 10 nm × 10 nm is obtained. Finally, holographic imaging of a lithographic test structure based on this optical system is demonstrated.

Hard X-ray imaging of bacterial cells: nano-diffraction and ptychographic reconstruction.

Ptychographic coherent X-ray diffractive imaging (PCDI) has been combined with nano-focus X-ray diffraction to study the structure and density distribution of unstained and unsliced bacterial cells, using a hard X-ray beam of 6.2keV photon energy, focused to about 90nm by a Fresnel zone plate lens. While PCDI provides images of the bacteria with quantitative contrast in real space with a resolution well below the beam size at the sample, spatially resolved small angle X-ray scattering using the same Fresnel zone plate (cellular nano-diffraction) provides structural information at highest resolution in reciprocal space up to 2nm(-1). We show how the real and reciprocal space approach can be used synergistically on the same sample and with the same setup. In addition, we present 3D hard X-ray imaging of unstained bacterial cells by a combination of ptychography and tomography.

Spatial and temporal coherence properties of single free-electron laser pulses.

The experimental characterization of the spatial and temporal coherence properties of the free-electron laser in Hamburg (FLASH) at a wavelength of 8.0 nm is presented. Double pinhole diffraction patterns of single femtosecond pulses focused to a size of about 10×10 µm(2) were measured. A transverse coherence length of 6.2 ± 0.9 µm in the horizontal and 8.7 ± 1.0 µm in the vertical direction was determined from the most coherent pulses. Using a split and delay unit the coherence time of the pulses produced in the same operation conditions of FLASH was measured to be 1.75 ± 0.01 fs. From our experiment we estimated the degeneracy parameter of the FLASH beam to be on the order of 10(10) to 10(11), which exceeds the values of this parameter at any other source in the same energy range by many orders of magnitude.