X-ray multilens interferometer based on Si refractive lenses

On the theory of synchrotron radiation nanofocusing with planar compound refractive lenses

Two new methods of computer simulation of synchrotron radiation nanofocusing with planar compound refractive lenses (PCRLs) are presented. The methods are based on the results of analytical theory. In contrast to previous works, the new methods take into account the PCRL aperture. It is especially important at high photon energies, when absorption is low and the calculations based on analytical theory, i.e. without taking into account the aperture, give incorrect results. A computer program was created and specific results were obtained for a silicon PCRL having an aperture of 50 µm, element length of 102 µm and minimum thickness of 2 µm. For an energy of 50 keV and number of elements 300, it focuses the beam to 31 nm size at a distance of one and a half times its length. Analysis of the calculation accuracy for the proposed methods is performed, as well as a demonstration of the capabilities of the computer program.

Coherent X-ray beam expander based on a multilens interferometer

A coherent X-ray beam expander based on a multilens interferometer is proposed in this paper. The multilens interferometer allows efficient generation of a highly diverging coherent beam up to several milliradians in the hard X-ray energy range. The optical properties of the interferometer were experimentally demonstrated at the ESRF ID13 undulator beamline (Grenoble, France), using 12.4 keV X-rays. The beam expander allowed us to control the angular size and photon flux density of the formed beam and enabled operation in both coherent and incoherent modes. The experimental results were fully consistent with the theoretical concepts and appropriate computer simulations. Future design improvements and related applications are also discussed.

Staircase array of inclined refractive multi-lenses for large field of view pixel super-resolution scanning transmission hard X-ray microscopy

Owing to the development of X-ray focusing optics during the past decades, synchrotron-based X-ray microscopy techniques allow the study of specimens with unprecedented spatial resolution, down to 10 nm, using soft and medium X-ray photon energies, though at the expense of the field of view (FOV). One of the approaches to increase the FOV to square millimetres is raster-scanning of the specimen using a single nanoprobe; however, this results in a long data acquisition time. This work employs an array of inclined biconcave parabolic refractive multi-lenses (RMLs), fabricated by deep X-ray lithography and electroplating to generate a large number of long X-ray foci. Since the FOV is limited by the pattern height if a single RML is used by impinging X-rays parallel to the substrate, many RMLs at regular intervals in the orthogonal direction were fabricated by tilted exposure. By inclining the substrate correspondingly to the tilted exposure, 378000 X-ray line foci were generated with a length in the centimetre range and constant intervals in the sub-micrometre range. The capability of this new X-ray focusing device was first confirmed using ray-tracing simulations and then using synchrotron radiation at BL20B2 of SPring-8, Japan. Taking account of the fact that the refractive lens is effective for focusing high-energy X-rays, the experiment was performed with 35 keV X-rays. Next, by scanning a specimen through the line foci, this device was used to perform large FOV pixel super-resolution scanning transmission hard X-ray microscopy (PSR-STHXM) with a 780 ± 40 nm spatial resolution within an FOV of 1.64 cm × 1.64 cm (limited by the detector area) and a total scanning time of 4 min. Biomedical implant abutments fabricated via selective laser melting using Ti-6Al-4V medical alloy were measured by PSR-STHXM, suggesting its unique potential for studying extended and thick specimens. Although the super-resolution function was realized in one dimension in this study, it can be expanded to two dimensions by aligning a pair of presented devices orthogonally.

Feasibility of X-ray beam nanofocusing with compound refractive lenses

A more general analytical theory of X-ray beam propagation through compound refractive lenses (CRLs) than the earlier study by Kohn [(2003). JETP, 97, 204-215] is presented. The problem of nanofocusing with CRLs is examined in detail. For a CRL with a relatively large aperture the focusing efficiency is limited by the radiation absorption in the lens material. The aperture does not affect the focusing process and it is replaced by the effective aperture. The X-ray transverse beam size at the focus is then by a factor of γ = β/δ times smaller than the transverse beam size just behind the CRL. Here, δ and β are the real and imaginary parts of the CRL material refractive index n = 1 - δ + iβ. In this instance, to improve focusing efficiency, it is advantageous to decrease the CRL aperture and increase the photon energy E. However, with increasing photon energy, the material absorption decreases, which results in the CRL aperture impact on the transverse beam size. The latter leads to the fact that with a proper CRL length the beam size is independent of both the aperture and photon energy but depends only on the CRL material electron density and is approximately equal to w_c = λ/(8δ)^1/2, where λ denotes the radiation wavelength, as predicted by Bergemann et al. [(2003). Phys. Rev. Lett, 91, 204801].

X-ray phase-sensitive imaging using a bilens interferometer based on refractive optics

The phase-sensitive X-ray imaging technique based on the bilens interferometer is developed. The essence of the method consists of scanning a sample, which is set upstream of the bilens across the beam of one lens of the interferometer by recording changes in the interference pattern using a high-resolution image detector. The proposed approach allows acquiring the absolute value of a phase shift profile of the sample with a fairly high phase and spatial resolution. The possibilities of the imaging technique were studied theoretically and experimentally using fibres with different sizes as the test samples at the ESRF ID06 beamline with 12 keV X-rays. The corresponding phase shift profile reconstructions and computer simulations were performed. The experimental results are fully consistent with theoretical concepts and appropriate numerical calculations. Applications of the interferometric imaging technique are discussed, as well as future improvements.

Synchrotron Radiation-Based Three-Dimensional Visualization of Angioarchitectural Remodeling in Hippocampus of Epileptic Rats

Characterizing the three-dimensional (3D) morphological alterations of microvessels under both normal and seizure conditions is crucial for a better understanding of epilepsy. However, conventional imaging techniques cannot detect microvessels on micron/sub-micron scales without angiography. In this study, synchrotron radiation (SR)-based X-ray in-line phase-contrast imaging (ILPCI) and quantitative 3D characterization were used to acquire high-resolution, high-contrast images of rat brain tissue under both normal and seizure conditions. The number of blood microvessels was markedly increased on days 1 and 14, but decreased on day 60 after seizures. The surface area, diameter distribution, mean tortuosity, and number of bifurcations and network segments also showed similar trends. These pathological changes were confirmed by histological tests. Thus, SR-based ILPCI provides systematic and detailed views of cerebrovascular anatomy at the micron level without using contrast-enhancing agents. This holds considerable promise for better diagnosis and understanding of the pathogenesis and development of epilepsy.

CRL-based ultra-compact transfocator for X-ray focusing and microscopy

A new ultra-compact transfocator (UCTF) based on X-ray compound refractive lenses (CRLs) is presented. The device can be used to change the number of one- and two-dimensional focusing CRLs by moving the individual parabolic lenses one-by-one independently, thus providing permanent energy and focal-length tunability for scanning and full-field X-ray microscopy applications. The small overall size and light weight of the device allow it to be integrated in any synchrotron beamline, while even simplifying the experimental layout. The UCTF was tested at the Excillium MetalJet microfocus X-ray source and at the P14 EMBL (PETRA-III) beamline, demonstrating high mechanical stability and lens positioning repeatability.

Nanofocusing with aberration-corrected rotationally parabolic refractive X-ray lenses

Wavefront errors of rotationally parabolic refractive X-ray lenses made of beryllium (Be CRLs) have been recovered for various lens sets and X-ray beam configurations. Due to manufacturing via an embossing process, aberrations of individual lenses within the investigated ensemble are very similar. By deriving a mean single-lens deformation for the ensemble, aberrations of any arbitrary lens stack can be predicted from the ensemble with \bar{\sigma} = 0.034λ. Using these findings the expected focusing performance of current Be CRLs are modeled for relevant X-ray energies and bandwidths and it is shown that a correction of aberrations can be realised without prior lens characterization but simply based on the derived lens deformation. The performance of aberration-corrected Be CRLs is discussed and the applicability of aberration-correction demonstrated over wide X-ray energy ranges.

Polymer X-ray refractive nano-lenses fabricated by additive technology

The present work demonstrates the potential applicability of additive manufacturing to X-Ray refractive nano-lenses. A compound refractive lens with a radius of 5 µm was produced by the two-photon polymerization induced lithography. It was successfully tested at the X-ray microfocus laboratory source and a focal spot of 5 μm was measured. An amorphous nature of polymer material combined with the potential of additive technologies may result in a significantly enhanced focusing performance compared to the best examples of modern X-ray compound refractive lenses.

30-Lens interferometer for high-energy X-rays

A novel high-energy multi-lens interferometer consisting of 30 arrays of planar compound refractive lenses is reported. Under coherent illumination each lens array creates a diffraction-limited secondary source. Overlapping such coherent beams produces an interference pattern demonstrating strong longitudinal functional dependence. The proposed multi-lens interferometer was tested experimentally at the 100 m-long ID11 ESRF beamline in the X-ray energy range from 30 to 65 keV. The interference pattern generated by the interferometer was recorded at fundamental and fractional Talbot distances. An effective source size (FWHM) of the order of 15 µm was determined from the first Talbot image, proving the concept that the multi-lens interferometer can be used as a high-resolution tool for beam diagnostics.

Lens coupled tunable Young's double pinhole system for hard X-ray spatial coherence characterization

We have implemented a modified Young's double slit experiment using pinholes with tunable separation distance coupled with compound refractive lens for hard X-ray spatial coherence characterization. Varying distance between the apertures provides a high sensitivity to the determination of spatial coherence across a wide range of experimental parameters. The use of refractive lenses as a Fourier transformer ensures far field registration conditions and allows the realization of a very compact experimental setup in comparison with the classical Young technique and its derivatives. The tunable double aperture interferometer was experimentally tested at the ESRF ID06 beamline in the energy range from 8 to 25 keV. The spatial coherence and the source size were measured by evaluating the visibility of the interference fringes at various separation distances between the apertures and this value agrees very well with the data obtained by other techniques. The proposed scheme can be used for comprehensive characterization of the coherence properties of the source on low emittance synchrotrons in the hard X-ray region.

Hard x-ray single crystal bi-mirror

We report a novel hard x-ray interferometer consisting of two parallel channels manufactured in a single Si crystal by means of microfabrication technology. The sidewall surfaces of the channels, similar to mirrors, scatter at very small incident angles, acting equivalently to narrow micrometer size slits as in the Young double-slit interferometer. Experimental tests of the interferometer were performed at the ESRF ID06 beamline in the energy range from 12 to 16 keV. The interference patterns at different grazing incidence angles were recorded in the near- and far-field. Evaluation of the influence of the channel surface roughness on the visibility of interference fringes was performed. The proposed interferometer design allows the arrangement of mirrors at different split distances.