Refractive X-ray Lenses Research Articles

Tilting refractive x-ray lenses for fine-tuning of their focal length.

In this work, we measure and model tilted x-ray refractive lenses to investigate their effects on an x-ray beam. The modelling is benchmarked against at-wavelength metrology obtained with x-ray speckle vector tracking experiments (XSVT) at the BM05 beamline at the ESRF-EBS light source, showing very good agreement. This validation permits us to explore possible applications of tilted x-ray lenses in optical design. We conclude that while tilting 2D lenses does not seem interesting from the point of view of aberration-free focusing, tilting 1D lenses around their focusing direction can be used for smoothly fine-tuning their focal length. We demonstrate experimentally this continuous change in the apparent lens radius of curvature R: a reduction up to a factor of two and beyond is achieved and possible applications in beamline optical design are proposed.

Design optimization of one-dimensional aberration-free x-ray gradually focusing lenses

In our previous work, we proposed a new design method for an aberration-free x-ray refractive focusing lens based on an ideal Cartesian oval shape to solve the aberration problem in x-ray compound refractive focusing. In this paper, we propose an optimization method for this new lens. By reducing the aperture of each lens, we achieve the objective of increasing the effective aperture and improving the focusing performance of the lens. The simulation of the beam propagation method shows that the focusing performance of the optimized lenses is better in compound refractive lens shape but worse in the kinoform shape. This is different from the results obtained with the conventional kinoform lens. After further comparison, we found that this is because the step height of the kinoform lens is small when the lens aperture is very small, resulting in a strong diffraction effect that weakens the focusing performance of the lens. Further modifications to the structure of the kinoform lens are needed to improve this phenomenon.

Erratum to: Refractive X-Ray Lenses Made by the Two-Photon Laser Lithography Method

An Erratum to this paper has been published: https://doi.org/10.3103/S1541308X22060085

Refractive X-Ray Lenses Made by the Two-Photon Laser Lithography Method

Refractive X-Ray Lenses Made by the Two-Photon Laser Lithography Method

Signatures of misalignment in x-ray cavities of cavity-based x-ray free-electron lasers

Cavity-based x-ray free-electron lasers (CBXFEL) will allow use of optical cavity feedback to support generation of fully coherent x-rays of high brilliance and stability by electrons in undulators. CBXFEL optical cavities comprise Bragg-reflecting flat crystal mirrors, which ensure x-rays circulation on a closed orbit, and x-ray refractive lenses, which stabilize the orbit and refocus the x-rays back on the electrons in the undulator. Depending on the cavity design, there are tens of degrees of freedom of the optical elements, which can never be perfectly aligned. Here, we study signatures of misalignment of the optical components and of the undulator source with the purposes of understanding the effects of misalignment on x-ray beam dynamics, understanding misalignment tolerances, and developing cavity alignment procedures. Betatron oscillations of the x-ray beam trajectory (both symmetric and asymmetric) are one of the characteristic signatures of cavity misalignment. The oscillation period is in the general case a non-integer number of round-trip passes of x-rays in the cavity. This period (unlike the amplitude and offset of the oscillations) is independent of the type of misalignment and is defined by cavity parameters. The studies are performed on an example of a four-crystal rectangular cavity using analytical and numerical wave optics as well as ray-tracing techniques. Both confocal and generic stable cavity types are studied.

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 byadditive 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.

Liquid compound refractive X-ray lens.

We introduce the concept of a liquid compound refractive X-ray zoom lens. The lens is generated by pumping a suitable liquid lens material like water, alcohol or heated lithium through a line of nozzles each forming a jet with the cross section of lens elements. The system is housed, so there is a liquid-circulation. This lens can be used in white beam at high brilliance synchrotron sources, as radiation damages are cured by the continuous reformation of the lens. The focal length can be varied by closing nozzles, thus reducing the number of lens elements in the beam.

Development of a Tandem Nano-Focusing Optics with X-ray Refractive Lens and Kirkpatric-Baez Mirror

Development of a Tandem Nano-Focusing Optics with X-ray Refractive Lens and Kirkpatric-Baez Mirror

Impact of beryllium microstructure on the imaging and optical properties of X-ray refractive lenses.

Beryllium is one of the most transparent materials to hard X-ray radiation and, as a direct consequence, it is the main material for the fabrication of X-ray refractive optics and instrumentation for synchrotron radiation sources and free-electron laser facilities. However, it is known that almost all beryllium currently in use is polycrystalline material. In this paper, the influence of the microstructure of different beryllium grades on the optical properties of X-ray refractive lenses is studied. The experiments were performed at the ESRF ID06 beamline in X-ray coherent transmission microscopy mode in the near- and far-fields. Two sets of refractive lenses made of beryllium O-30-H and IS-50M grades with different internal microstructure were used. It was found that both beryllium grades have a strongly inhomogeneous structure, which inevitably produces speckle patterns under coherent illumination in imaging experiments. It was shown that fine-grained beryllium O-30-H is better suited for imaging applications, whereas beryllium IS-50M with a relatively large grain microstructure is more appropriate for focusing and collimation of X-rays. A discussion on the requirements for X-ray optical materials used at the third- and fourth-generation synchrotrons is also presented.

Diamond nanofocusing refractive X-ray lenses made by planar etching technology.

The manufacturing steps and first tests of a refractive lens made of polycrystalline diamond are described. A fabrication process based on electron-beam lithography and deep reactive ion etching is introduced. Experimental tests on beamline ID13 at the ESRF have been performed. A spot size of 360 nm (FWHM) at an energy E = 24.3 keV is observed.

Zooming X-rays with a single rotation in X-ray prism zoom lenses (XPZL).

Prism arrays arranged to form a slightly open alligator mouth were found to focus incident X-rays, as with increasing distance from the object symmetry axis these rays hit an increasing number of refracting prism tips. Such an object is then formally a refractive lens. Due to the strong energy dependence of the refractive index of material for X-rays a refractive X-ray lens is chromatically focusing. The attractive feature of the alligator lens is the inherent zoomability possible as the mouth can easily be opened or closed. However, the required tolerances for the jaw rotations and the jaw positioning are so stringent, that the routine use of such systems has not been reported yet. This study will show that the related technical problems can be overcome by proper object fabrication. In fact the here presented objects can already be aligned in the production stage. Then the assembly can be made with simple tools. And the zooming is achieved by just a simple rotation. The transmission through the devices was found to be as expected, and thus performance-wise these objects can directly compete with other refractive X-ray focusing systems.

Investigation of `glitches' in the energy spectrum induced by single-crystal diamond compound X-ray refractive lenses.

Single-crystal diamond stands out among all the candidate materials that could be exploited to fabricate compound refractive lenses (CRLs) owing to its extremely stable properties. Among all related experimental features, beam divergence, χ-angles relative to the incoming beam in Eulerian geometry and different positions of the X-ray beam relative to the lens geometry may influence the transmission energy spectrum of CRLs. In addition, the orientation of the single-crystal diamond sample may also affect the glitches significantly. To verify these initial assumptions, two experiments, an energy scan and an ω-scan, were set up by employing a polished diamond plate consisting of five biconcave lenses. The results show that beam divergence does not affect the spectrum, nor do χ-angles when ω is set to zero. Nevertheless, different incident positions have an appreciable effect on the transmission spectrum, in particular the `strengths' of the glitches. This is attributed to absorption. The ω-scan setup is capable of determining the so-called orientation matrix, which may be used to predict both `energy positions' and `strengths' of the glitches.

Kinoform and saw-tooth X-ray refractive lenses development at SSRF

Here we describe the effort made at Shanghai Synchrotron Radiation Facility (SSRF) to develop X-ray refractive lenses for real beamline applications. Fabrication process of silicon and germanium based kinoform lenses are optimized to increase the height-width aspect ratio and decrease the roughness. Saw-tooth lenses made with a new fabrication process based on dry etching are also described. Focusing effect for both kinoform and saw-tooth lenses are tested at Shanghai Synchrotron.

Simultaneous 8.2 keV phase-contrast imaging and 24.6 keV X-ray diffraction from shock-compressed matter at the LCLS

In this work, we demonstrate simultaneous phase-contrast imaging (PCI) and X-ray diffraction from shock compressed matter at the Matter in Extreme Conditions endstation, at the Linac Coherent Light Source (LCLS). We utilize the chromaticity from compound refractive X-ray lenses to focus the 24.6 keV 3rd order undulator harmonic of the LCLS to a spot size of 5 μm on target to perform X-ray diffraction. Simultaneous PCI from the 8.2 keV fundamental X-ray beam is used to visualize and measure the transient properties of the shock wave over a 500 μm field of view. Furthermore, we demonstrate the ability to extend the reciprocal space measurements by 5 Å−1, relative to the fundamental X-ray energy, by utilizing X-ray diffraction from the 3rd harmonic of the LCLS.

A Shack-Hartmann Sensor for Single-Shot Multi-Contrast Imaging with Hard X-rays

An array of compound refractive X-ray lenses (CRL) with 20 × 20 lenslets, a focal distance of 20cm and a visibility of 0.93 is presented. It can be used as a Shack-Hartmann sensor for hard X-rays (SHARX) for wavefront sensing and permits for true single-shot multi-contrast imaging the dynamics of materials with a spatial resolution in the micrometer range, sensitivity on nanosized structures and temporal resolution on the microsecond scale. The object’s absorption and its induced wavefront shift can be assessed simultaneously together with information from diffraction channels. In contrast to the established Hartmann sensors the SHARX has an increased flux efficiency through focusing of the beam rather than blocking parts of it. We investigated the spatiotemporal behavior of a cavitation bubble induced by laser pulses. Furthermore, we validated the SHARX by measuring refraction angles of a single diamond CRL, where we obtained an angular resolution better than 4 μ rad.

Beryllium Materials and Their Application in Energetics of Future

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At-wavelength optics characterisation via X-ray speckle- and grating-based unified modulated pattern analysis.

The current advances in new generation X-ray sources are calling for the development and improvement of high-performance optics. Techniques for high-sensitivity phase sensing and wavefront characterisation, preferably performed at-wavelength, are increasingly required for quality control, optimisation and development of such devices. We here show that the recently proposed unified modulated pattern analysis (UMPA) can be used for these purposes. We characterised two polymer X-ray refractive lenses and quantified the effect of beam damage and shape errors on their refractive properties. Measurements were performed with two different setups for UMPA and validated with conventional X-ray grating interferometry. Due to its adaptability to different setups, the ease of implementation and cost-effectiveness, we expect UMPA to find applications for high-throughput quantitative optics characterisation and wavefront sensing.

Nanofocusing with aberration-corrected rotationallyparabolic 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.

Refraction and ultra-small-angle scattering of X-rays in a single-crystal diamond compound refractive lens.

In this work a double-crystal setup is employed to study compound refractive lenses made of single-crystal diamond. The point spread function of the lens is calculated taking into account the lens transmission, the wavefront aberrations, and the ultra-small-angle broadening of the X-ray beam. It is shown that, similarly to the wavefront aberrations, the ultra-small-angle scattering effects can significantly reduce the intensity gain and increase the focal spot size. The suggested approach can be particularly useful for the characterization of refractive X-ray lenses composed of many tens of unit lenses.

Generalized pupil function of a compound X-ray refractive lens.

Quality of a refractive compound X-ray lens can be limited by imperfections in surfaces of unit lenses and stacking precision. In general case both the lens transmission and optical aberrations define properties of a beam in the lens exit plane; together they can be expressed in terms of the generalized pupil function. In this work we measure this function for a diamond single crystal compound refractive lens. Consequently, we apply the pupil function to evaluate the performance of the examined compound refractive X-ray lens. A number of practically important conclusions can be drawn from such analysis.