X‐ray focusing by the system of refractive lens(es) placed inside asymmetric channel‐cut crystals

An X‐ray one‐dimensionally focusing system, a refracting–diffracting lens (RDL), composed of Bragg double‐asymmetric‐reflecting two‐crystal plane parallel plates and a double‐concave cylindrical parabolic lens placed in the gap between the plates is described. It is shown that the focal length of the RDL is equal to the focal distance of the separate lens multiplied by the square of the asymmetry factor. One can obtain RDLs with different focal lengths for certain applications. Using the point‐source function of dynamic diffraction, as well as the Green function in a vacuum with parabolic approximation, an expression for the double‐diffracted beam amplitude for an arbitrary incident wave is presented. Focusing of the plane incident wave and imaging of a point source are studied. The cases of non‐absorptive and absorptive lenses are discussed. The intensity distribution in the focusing plane and on the focusing line, and its dependence on wavelength, deviation from the Bragg angle and magnification is studied. Geometrical optical considerations are also given. RDLs can be applied to focus radiation from both laboratory and synchrotron X‐ray sources, for X‐ray imaging of objects, and for obtaining high‐intensity beams. RDLs can also be applied in X‐ray astronomy.     

On the use of clessidra prism arrays in long‐focal‐length X‐ray focusing

Clessidra (hour‐glass) X‐ray lenses have an overall shape of an old hour glass, in which two opposing larger triangular prisms are formed of smaller identical prisms or prism‐like objects. In these lenses, absorbing and otherwise optically inactive material was removed with a material‐removal strategy similar to that used by Fresnel in the lighthouse lens construction. It is verified that when the single prism rows are incoherently illuminated they can be operated as independent micro‐lenses with coinciding image positions for efficient X‐ray beam concentration. Experimental data for the line width and the refraction efficiency in one‐dimensional focusing are consistent with the expectations. Imperfections in the structures produced by state‐of‐the‐art deep X‐ray lithography directed only 35% of the incident intensity away from the image and widened it by just 10% to 125 µm. An array of micro‐lenses with easily feasible prism sizes is proposed as an efficient retrofit for the refocusing optics in an existing beamline, where it would provide seven‐fold flux enhancement.     

On aberrations in saw‐tooth refractive X‐ray lenses and on their removal

The X‐ray lens, which is composed of opposing canted saw‐tooth structures, originally assembled from cut‐out pieces from long‐playing records, is understood by recognizing that an incident plane X‐ray wave will traverse a varying number of triangular prisms in them. The refraction will deflect any beam towards the prism tips and the variation of the deflection angle, which grows linearly with the number of traversed prisms, can result in X‐ray focusing. The structure offers focusing flexibility by simply changing the taper angle. This report will discuss the aberrations arising in the saw‐tooth structure in its simplest form with identical prisms. It is found that the saw‐tooth structures in low‐Z materials with focal length below 1 m provide less flux density in the focal spot than stacks of one‐dimensionally focusing refractive lenses with identical transmission function. This is due to excessive aberrations in the regular structure, which are absent in stacks of concave lenses, and which limit the focusing to spot sizes of just submicrometre dimensions, as measured experimentally for some lenses. It will be shown that this limitation can be overcome by appropriately modifying the prism shape. Then the image size could be reduced by about an order of magnitude to the diffraction limit with competitive numbers even below 0.1 µm. Microfabrication techniques are identified as the appropriate means for producing the structures.     

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.     

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.     

Efficiency and coherence preservation studies of Be refractive lenses for XFELO application

Performance tests of parabolic beryllium refractive lenses, considered as X‐ray focusing elements in the future X‐ray free‐electron laser oscillator (XFELO), are reported. Single and double refractive lenses were subject to X‐ray tests, which included: surface profile, transmissivity measurements, imaging capabilities and wavefront distortion with grating interferometry. Optical metrology revealed that surface profiles were close to the design specification in terms of the figure and roughness. The transmissivity of the lenses is >94% at 8 keV and >98% at 14.4 and 18 keV. These values are close to the theoretical values of ideal lenses. Images of the bending‐magnet source obtained with the lenses were close to the expected ones and did not show any significant distortion. Grating interferometry revealed that the possible wavefront distortions produced by surface and bulk lens imperfections were on the level of ～λ/60 for 8 keV photons. Thus the Be lenses can be succesfully used as focusing and beam collimating elements in the XFELO.     

Large‐aperture prism‐array lens for high‐energy X‐ray focusing

A new prism‐array lens for high‐energy X‐ray focusing has been constructed using an array of different prisms obtained from different parabolic structures by removal of passive parts of material leading to a multiple of 2π phase variation. Under the thin‐lens approximation the phase changes caused by this lens for a plane wave are exactly the same as those caused by a parabolic lens without any additional corrections when they have the same focal length, which will provide good focusing; at the same time, the total transmission and effective aperture of this lens are both larger than those of a compound kinoform lens with the same focal length, geometrical aperture and feature size. This geometry can have a large aperture that is not limited by the feature size of the lens. Prototype nickel lenses with an aperture of 1.77 mm and focal length of 3 m were fabricated by LIGA technology, and were tested using CCD camera and knife‐edge scan method at the X‐ray Imaging and Biomedical Application Beamline BL13W1 at Shanghai Synchrotron Radiation Facility, and provided a focal width of 7.7 µm and a photon flux gain of 14 at an X‐ray energy of 50 keV.     

Point focusing with flat and wedged crossed multilayer Laue lenses

Point focusing measurements using pairs of directly bonded crossed multilayer Laue lenses (MLLs) are reported. Several flat and wedged MLLs have been fabricated out of a single deposition and assembled to realise point focusing devices. The wedged lenses have been manufactured by adding a stress layer onto flat lenses. Subsequent bending of the structure changes the relative orientation of the layer interfaces towards the stress‐wedged geometry. The characterization at ESRF beamline ID13 at a photon energy of 10.5 keV demonstrated a nearly diffraction‐limited focusing to a clean spot of 43 nm × 44 nm without significant side lobes with two wedged crossed MLLs using an illuminated aperture of approximately 17 µm × 17 µm to eliminate aberrations originating from layer placement errors in the full 52.7 µm × 52.7 µm aperture. These MLLs have an average individual diffraction efficiency of 44.5%. Scanning transmission X‐ray microscopy measurements with convenient working distances were performed to demonstrate that the lenses are suitable for user experiments. Also discussed are the diffraction and focusing properties of crossed flat lenses made from the same deposition, which have been used as a reference. Here a focal spot size of 28 nm × 33 nm was achieved and significant side lobes were noticed at an illuminated aperture of approximately 23 µm × 23 µm.     

Theoretical consideration of an X‐ray Bragg‐reflection lens using the eikonal approximation

On the basis of the eikonal approximation, X‐ray Bragg‐case focusing by a perfect crystal with parabolic‐shaped entrance surface is considered theoretically. Expressions for focal distances, intensity gain and distribution around the focus spot as well as for the focus spot sizes are obtained. The condition of point focusing is presented. The experiment can be performed using X‐ray synchrotron radiation sources (particularly free‐electron lasers).     

Kinoform optics applied to X‐ray photon correlation spectroscopy

Moderate‐demagnification higher‐order silicon kinoform focusing lenses have been fabricated to facilitate small‐angle X‐ray photon correlation spectroscopy (XPCS) experiments. The geometric properties of such lenses, their focusing performance and their applicability for XPCS measurements are described. It is concluded that one‐dimensional vertical X‐ray focusing via silicon kinoform lenses significantly increases the usable coherent flux from third‐generation storage‐ring light sources for small‐angle XPCS experiments.     

Application of kinoform lens for X‐ray reflectivity analysis

In this paper the first practical application of kinoform lenses for the X‐ray reflectivity characterization of thin layered materials is demonstrated. The focused X‐ray beam generated from a kinoform lens, a line of nominal size ～50 µm × 2 µm, provides a unique possibility to measure the X‐ray reflectivities of thin layered materials in sample scanning mode. Moreover, the small footprint of the X‐ray beam, generated on the sample surface at grazing incidence angles, enables one to measure the absolute X‐ray reflectivities. This approach has been tested by analyzing a few thin multilayer structures. The advantages achieved over the conventional X‐ray reflectivity technique are discussed and demonstrated by measurements.     

A high‐accuracy complex‐phase method of simulating X‐ray propagation through a multi‐lens system

The propagation of X‐ray waves through an optical system consisting of many X‐ray refractive lenses is considered. For solving the problem for an electromagnetic wave, a finite‐difference method is applied. The error of simulation is analytically estimated and investigated. It was found that a very detailed difference grid is required for reliable and accurate calculations of the propagation of X‐ray waves through a multi‐lens system. The reasons for using a very detailed difference grid are investigated. It was shown that the wave phase becomes a function, very quickly increasing with increasing distance from the optical axis, after the wave has passed through the multi‐lens system. If the phase is a quickly increasing function of the coordinates perpendicular to the optical axis, then the electric field of the wave is a quickly oscillating function of these coordinates, and thus a very detailed difference grid becomes necessary to describe such a wavefield. To avoid this difficulty, an equation for the phase function is proposed as an alternative to the equation of the electric field. This allows reliable and accurate simulations to be carried out when using the multi‐lens system. An equation for the phase function is derived and used for accurate simulations. The numerical error of the suggested method is estimated. It is shown that the equation for the phase function allows efficient simulations to be fulfilled for the multi‐lens system.     

High‐energy X‐ray optics with silicon saw‐tooth refractive lenses

Silicon saw‐tooth refractive lenses have been in successful use for vertical focusing and collimation of high‐energy X‐rays (50–100 keV) at the 1‐ID undulator beamline of the Advanced Photon Source. In addition to presenting an effectively parabolic thickness profile, as required for aberration‐free refractive optics, these devices allow high transmission and continuous tunability in photon energy and focal length. Furthermore, the use of a single‐crystal material (i.e. Si) minimizes small‐angle scattering background. The focusing performance of such saw‐tooth lenses, used in conjunction with the 1‐ID beamline's bent double‐Laue monochromator, is presented for both short (～1:0.02) and long (～1:0.6) focal‐length geometries, giving line‐foci in the 2 µm–25 µm width range with 81 keV X‐rays. In addition, a compound focusing scheme was tested whereby the radiation intercepted by a distant short‐focal‐length lens is increased by having it receive a collimated beam from a nearer (upstream) lens. The collimation capabilities of Si saw‐tooth lenses are also exploited to deliver enhanced throughput of a subsequently placed small‐angular‐acceptance high‐energy‐resolution post‐monochromator in the 50–80 keV range. The successful use of such lenses in all these configurations establishes an important detail, that the pre‐monochromator, despite being comprised of vertically reflecting bent Laue geometry crystals, can be brilliance‐preserving to a very high degree.     

X‐ray focusing scheme with continuously variable lens

A novel hybrid X‐ray focusing scheme was developed for operation of the X‐ray streak camera at the Advanced Photon Source: an X‐ray lens focuses vertically from a long distance of 16 m and produces an extended focus that has a small footprint on an inexpensive sagittal mirror. A patented method is used to continuously adjust the focal length of the lens and compensate for chromatic dispersion in energy scans.     

The first microbeam synchrotron X‐ray fluorescence beamline at the Siam Photon Laboratory

The first microbeam synchrotron X‐ray fluorescence (µ‐SXRF) beamline using continuous synchrotron radiation from Siam Photon Source has been constructed and commissioned as of August 2011. Utilizing an X‐ray capillary half‐lens allows synchrotron radiation from a 1.4 T bending magnet of the 1.2 GeV electron storage ring to be focused from a few millimeters‐sized beam to a micrometer‐sized beam. This beamline was originally designed for deep X‐ray lithography (DXL) and was one of the first two operational beamlines at this facility. A modification has been carried out to the beamline in order to additionally enable µ‐SXRF and synchrotron X‐ray powder diffraction (SXPD). Modifications included the installation of a new chamber housing a Si(111) crystal to extract 8 keV synchrotron radiation from the white X‐ray beam (for SXPD), a fixed aperture and three gate valves. Two end‐stations incorporating optics and detectors for µ‐SXRF and SXPD have then been installed immediately upstream of the DXL station, with the three techniques sharing available beam time. The µ‐SXRF station utilizes a polycapillary half‐lens for X‐ray focusing. This optic focuses X‐ray white beam from 5 mm × 2 mm (H × V) at the entrance of the lens down to a diameter of 100 µm FWHM measured at a sample position 22 mm (lens focal point) downstream of the lens exit. The end‐station also incorporates an XYZ motorized sample holder with 25 mm travel per axis, a 5× ZEISS microscope objective with 5 mm × 5 mm field of view coupled to a CCD camera looking to the sample, and an AMPTEK single‐element Si (PIN) solid‐state detector for fluorescence detection. A graphic user interface data acquisition program using the LabVIEW platform has also been developed in‐house to generate a series of single‐column data which are compatible with available XRF data‐processing software. Finally, to test the performance of the µ‐SXRF beamline, an elemental surface profile has been obtained for a piece of ancient pottery from the Ban Chiang archaeological site, a UNESCO heritage site. It was found that the newly constructed µ‐SXRF technique was able to clearly distinguish the distribution of different elements on the specimen.     

Suppression of Bragg reflection glitches of a single‐crystal diamond anvil cell by a polycapillary half‐lens in high‐pressure XAFS spectroscopy

In combination with a single‐crystal diamond anvil cell (DAC), a polycapillary half‐lens (PHL) re‐focusing optics has been used to perform high‐pressure extended X‐ray absorption fine‐structure measurements. It is found that a large divergent X‐ray beam induced by the PHL leads the Bragg glitches from single‐crystal diamond to be broadened significantly and the intensity of the glitches to be reduced strongly so that most of the DAC glitches are efficiently suppressed. The remaining glitches can be easily removed by rotating the DAC by a few degrees with respect to the X‐ray beam. Accurate X‐ray absorption fine‐structure (XAFS) spectra of polycrystalline Ge powder with a glitch‐free energy range from ?200 to 800 eV relative to the Ge absorption edge are obtained using this method at high pressures up to 23.7 GPa, demonstrating the capability of PHL optics in eliminating the DAC glitches for high‐pressure XAFS experiments. This approach brings new possibilities to perform XAFS measurements using a DAC up to ultrahigh pressures.     

A method of hard X‐ray phase‐shifting digital holography

A new method of phase‐shifting digital holography is demonstrated in the hard X‐ray region. An in‐line‐type phase‐shifting holography setup was installed in a 6.80 keV hard X‐ray synchrotron beamline. By placing a phase plate consisting of a hole and a band at the focusing point of a Fresnel lens, the relative phase of the reference and objective beams could be successfully shifted for use with a three‐step phase‐shift algorithm. The system was verified by measuring the shape of a gold test pattern and a silica sphere.     

Feasibility of in‐line instruments for high‐resolution inelastic X‐ray scattering

Inelastic X‐ray scattering instruments in operation at third‐generation synchrotron radiation facilities are based on backreflections from perfect silicon crystals. This concept reaches back to the very beginnings of high‐energy‐resolution X‐ray spectroscopy and has several advantages but also some inherent drawbacks. In this paper an alternate path is investigated using a different concept, the `M⁴ instrument'. It consists of a combination of two in‐line high‐resolution monochromators, focusing mirrors and collimating mirrors. Design choices and performance estimates in comparison with existing conventional inelastic X‐ray scattering instruments are presented.     

Diffraction theory applied to X‐ray imaging with clessidra prism array lenses

Clessidra (hourglass) lenses, i.e. two large prisms each composed of smaller identical prisms or prism‐like objects, can focus X‐rays. As these lenses have a periodic structure perpendicular to the incident radiation, they will diffract the beam like a diffraction grating. Refraction in the prisms is responsible for blazing, i.e. for the concentration of the diffracted intensity into only a few diffraction peaks. It is found that the diffraction of coherent radiation in clessidra lenses needs to be treated in the Fresnel, or near‐field, regime. Here, diffraction theory is applied appropriately to the clessidra structure in order to show that blazing in a perfect structure with partly curved prisms can indeed concentrate the diffracted intensity into only one peak. When the lens is entirely composed of identical perfect prisms, small secondary peaks are found. Nevertheless, the loss in intensity in the central peak will not lead to any significant widening of this peak. Clessidras with perfect prisms illuminated by full coherent X‐ray radiation can then provide spatial resolutions, which are consistent with the increased aperture, and which are far below the height of the single small prisms.     

A desktop X‐ray monochromator for synchrotron radiation based on refraction in mosaic prism lenses

Focusing planar refractive mosaic lenses based on triangular prism microstructures have been used as an alternative approach for wide‐bandpass monochromatization of high‐energy X‐rays. The strong energy dependence of the refractive index of the lens material leads to an analogous energy dependence of the focal length of the lens. The refractive mosaic lens, in comparison with the refractive lens of continuous parabolic profile, is characterized by a higher aperture because of reduced passive material. In combination with a well defined pinhole aperture in the focal plane, the transmittance of photons of an appropriate energy can be relatively high and photons of deviating energy can be efficiently suppressed. The photon energy can be tuned by translating the pinhole along the optical axis, and the bandwidth changed by selecting appropriate pinhole aperture and beam stop. This method of monochromatization was realised at the ANKA FLUO beamline using a mosaic lens together with a 20 µm pinhole and beam stop. An energy resolution of 2.0% at 16 keV has been achieved.