X-ray nanointerferometer based on si refractive bilenses

Double-slit asymmetrical dynamical diffraction of X-rays in ideal crystals

The theoretical investigation of double-slit asymmetrical dynamical diffraction of X-rays in perfect crystals establishes that Young's interference fringes on the exit surface are formed. The position of the fringes in the cross section of the beam depends on deviation from the Bragg exact orientation and asymmetry angle. An equation for the period of the fringes is presented, according to which the period is polarization sensitive. The period increases with increasing the absolute value of the asymmetry angle. In its turn, the size of the interference region also increases with increasing the absolute value of the asymmetry angle. However, the ratio of interference region size to period, i.e. the number of observed fringes, decreases with increasing the absolute value of the asymmetry angle. The size of the interference region can be of the order of a few tens of mm, which can be used for obtaining Fourier dynamical diffraction holograms of a large size. This type of diffraction can also be used for obtaining double-slit dynamical diffraction contrast of defects and deformations. Due to the phase difference information, in comparison with single-slit diffraction, double-slit diffraction is more sensitive to the existence of objects and deformations in the path of the wave.

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.

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.

X-ray reflecto-interferometer based on compound refractive lenses

An X-ray amplitude-splitting interferometer based on compound refractive lenses, which operates in the reflection mode, is proposed and realized. The idea of a reflecto-interferometer is to use a very simplified experimental setup where a focused X-ray beam reflected from parallel flat surfaces creates an interference pattern in a wide angular range. The functional capabilities of the interferometer were experimentally tested at the European Synchrotron Radiation Facility (ESRF) ID06 beamline in the X-ray energy range from 10 keV to 15 keV. The main features of the proposed approach, high spatial and temporal resolution, were demonstrated experimentally. The reflections from free-standing Si3N4 membranes, gold and resist layers were studied. Experimentally recorded interferograms are in good agreement with our simulations. The main advantages and future possible applications of the reflecto-interferometer are discussed.

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.

Probing the spatial coherence of wide X-ray beams with Fresnel mirrors at BL25SU of SPring-8

Probing the spatial coherence of X-rays has become increasingly important when designing advanced optical systems for beamlines at synchrotron radiation sources and free-electron lasers. Double-slit experiments at various slit widths are a typical method of quantitatively measuring the spatial coherence over a wide wavelength range including the X-ray region. However, this method cannot be used for the analysis of spatial coherence when the two evaluation points are separated by a large distance of the order of millimetres owing to the extremely narrow spacing between the interference fringes. A Fresnel-mirror-based optical system can produce interference patterns by crossing two beams from two small mirrors separated in the transverse direction to the X-ray beam. The fringe spacing can be controlled via the incidence angles on the mirrors. In this study, a Fresnel-mirror-based optical system was constructed at the soft X-ray beamline (BL25SU) of SPring-8. The relationship between the coherence and size of the virtual source was quantitatively measured at 300 eV in both the vertical and horizontal directions using the beam. The results obtained indicate that this is a valuable method for the optimization of optical systems along beamlines.

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.

Miniaturized beamsplitters realized by X-ray waveguides

This paper reports on the fabrication and characterization of X-ray waveguide beamsplitters. The waveguide channels were manufactured by electron-beam lithography, reactive ion etching and wafer bonding techniques, with an empty (air) channel forming the guiding layer and silicon the cladding material. A focused synchrotron beam is efficiently coupled into the input channel. The beam is guided and split into two channels with a controlled (and tunable) distance at the exit of the waveguide chip. After free-space propagation and diffraction broadening, the two beams interfere and form a double-slit interference pattern in the far-field. From the recorded far-field, the near-field was reconstructed by a phase retrieval algorithm (error reduction), which was found to be extremely reliable for the two-channel setting. By numerical propagation methods, the reconstructed field was then propagated along the optical axis, to investigate the formation of the interference pattern from the two overlapping beams. Interestingly, phase vortices were observed and analysed.

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.

Characterizing transverse coherence of an ultra-intense focused X-ray free-electron laser by an extended Young's experiment

Characterization of transverse coherence is one of the most critical themes for advanced X-ray sources and their applications in many fields of science. However, for hard X-ray free-electron laser (XFEL) sources there is very little knowledge available on their transverse coherence characteristics, despite their extreme importance. This is because the unique characteristics of the sources, such as the ultra-intense nature of XFEL radiation and the shot-by-shot fluctuations in the intensity distribution, make it difficult to apply conventional techniques. Here, an extended Young's interference experiment using a stream of bimodal gold particles is shown to achieve a direct measurement of the modulus of the complex degree of coherence of XFEL pulses. The use of interference patterns from two differently sized particles enables analysis of the transverse coherence on a single-shot basis without a priori knowledge of the instantaneous intensity ratio at the particles. For a focused X-ray spot as small as 1.8 µm (horizontal) × 1.3 µm (vertical) with an ultrahigh intensity that exceeds 10(18) W cm(-2) from the SPring-8 Ångstrom Compact free-electron LAser (SACLA), the coherence lengths were estimated to be 1.7 ± 0.2 µm (horizontal) and 1.3 ± 0.1 µm (vertical). The ratios between the coherence lengths and the focused beam sizes are almost the same in the horizontal and vertical directions, indicating that the transverse coherence properties of unfocused XFEL pulses are isotropic. The experiment presented here enables measurements free from radiation damage and will be readily applicable to the analysis of the transverse coherence of ultra-intense nanometre-sized focused XFEL beams.

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.

Interaction between periodic structures of object and X-ray standing wave generated by wavefront-division interferometer

An x-ray imaging method that utilizes interaction between standing wave and periodic structure of object is proposed. When a periodic object is placed in a standing wave field, the interaction is modulated by relation between the periodic structure of object and the standing wave period. Then, the structure of object can be observed as a modulation of transmission image, and the existence of fine periodic structures can be detected with an imaging detector of low spatial resolution. Feasibility studies have been performed using a standing wave generated by a wavefront-division x-ray interferometer with refractive prism optics.

X-ray multilens interferometer based on Si refractive lenses

We report a multilens X-ray interferometer consisting of six parallel arrays of planar compound refractive lenses, each of which creates a diffraction limited beam under coherent illumination. Overlapping such coherent beams produces an interference pattern demonstrating substantially strong longitudinal functional dependence. The interference fringe pattern produced by multilens interferometer was described by Talbot imaging formalism. Theoretical analysis of the interference pattern formation was carried out and corresponding computer simulations were performed. The proposed multilens interferometer was experimentally tested at ID06 ESRF beamline in the X-ray energy range from 10 to 30 keV. The experimentally recorded fractional Talbot images are in a good agreement with computer simulations.

Intensity interferometry of single x-ray pulses from a synchrotron storage ring

We report on measurements of second-order intensity correlations at the high-brilliance storage ring PETRA III using a prototype of the newly developed adaptive gain integrating pixel detector. The detector records individual synchrotron radiation pulses with an x-ray photon energy of 14.4 keV and repetition rate of about 5 MHz. The second-order intensity correlation function is measured simultaneously at different spatial separations, which allows us to determine the transverse coherence length at these x-ray energies. The measured values are in a good agreement with theoretical simulations based on the Gaussian Schell model.

X-ray harmonics rejection on third-generation synchrotron sources using compound refractive lenses

A new method of harmonics rejection based on X-ray refractive optics has been proposed. Taking into account the fact that the focal distance of the refractive lens is energy-dependent, the use of an off-axis illumination of the lens immediately leads to spatial separation of the energy spectrum by focusing the fundamental harmonic at the focal point and suppressing the unfocused high-energy radiation with a screen absorber or slit. The experiment was performed at the ESRF ID06 beamline in the in-line geometry using an X-ray transfocator with compound refractive lenses. Using this technique the presence of the third harmonic has been reduced to 10(-3). In total, our method enabled suppression of all higher-order harmonics to five orders of magnitude using monochromator detuning. The method is well suited to third-generation synchrotron radiation sources and is very promising for the future ultimate storage rings.

High efficiency nano-focusing kinoform optics for synchrotron radiation

Modern synchrotron sources have provided for decades intense beams of photons over a large energy spectrum. The availability of improved optics and detectors has opened up new opportunities for the study of matter at the micrometre and nanometre scale in many disciplines. Whilst exploitation of micro-focused beams occurs almost daily in many beamlines, the production of beams of 100 nm is achieved on few instruments which use specialised optics. Refractive lenses, zone plates, curved mirrors, multilayers, and multilayer Laue lenses, can all focus x-rays to less than 50 nm under strict beam stability conditions. Focusing the synchrotron radiation to beam sizes smaller than 10 nm is considered the ultimate goal for the current decade. Silicon micro-technology has so far provided some of the most advanced x-ray refractive lenses; we report on design and characterisation of a novel silicon kinoform lens that is capable of delivering nano-beams with high efficiency.

Diffraction-enhanced beam-focusing for X-rays in curved multi-plate crystal cavity

Unusual x-ray focusing effect is reported for parabolic curved multi-plate x-ray crystal cavities of silicon consisting of compound refractive lenses (CRL). The transmitted beam of the (12 4 0) back reflection near 14.4388 keV from these monolithic silicon crystal devices exhibits extraordinary focusing enhancement, such that the focal length is reduced by as much as 18% for 2-beam and 56% for 24-beam diffraction from the curved crystal cavity. This effect is attributed to the presence of the involved Bragg diffractions, in which the wavevector of the transmitted beam is bent further when traversing several curved crystal surfaces.

Probing the transverse coherence of an undulator x-ray beam using brownian particles

We present a novel method to map the two-dimensional transverse coherence of an x-ray beam using the dynamical near-field speckles formed by scattering from colloidal particles. Owing to the statistical nature of the method, the coherence properties of synchrotron radiation from an undulator source is obtained with high accuracy. The two-dimensional complex coherence function is determined at the sample position and the imaging optical scheme further allowed us to evaluate the coherence factor at the undulator output despite the aberrations introduced by the focusing optics.