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.     

Optical performance of materials for X‐ray refractive optics in the energy range 8–100 keV

A quantitative analysis of the crucial characteristics of currently used and promising materials for X‐ray refractive optics is performed in the extended energy range 8–100 keV. According to the examined parameters, beryllium is the material of choice for X‐ray compound refractive lenses (CRLs) in the energy range 8–25 keV. At higher energies the use of CRLs made of diamond and the cubic phase of boron nitride (c‐BN) is beneficial. It was demonstrated that the presence of the elements of the fourth (or higher) period has a fatal effect on the functional X‐ray properties even if low‐Z elements dominate in the compound, like in YB₆₆. Macroscopic properties are discussed: much higher melting points and thermal conductivities of C and c‐BN enable them to be used at the new generation of synchrotron radiation sources and X‐ray free‐electron lasers. The role of crystal and internal structure is discussed: materials with high density are preferable for refractive applications while less dense phases are suitable for X‐ray windows. Single‐crystal or amorphous glass‐like materials based on Li, Be, B or C that are free of diffuse scattering from grain boundaries, voids and inclusions are the best candidates for applications of highly coherent X‐ray beams.     

Focusing synchrotron radiation using a polycapillary half‐focusing X‐ray lens for imaging

An imaging system based on a polycapillary half‐focusing X‐ray lens (PHFXRL) and synchrotron radiation source has been designed. The focal spot size and the gain in power density of the PHFXRL were 22 µm (FWHM) and 4648, respectively, at 14.0 keV. The spatial resolution of this new imaging system was better than 5 µm when an X‐ray charge coupled device with a pixel size of 10.9 × 10.9 µm was used. A fossil of an ancient biological specimen was imaged using this system.     

Spectrometer for hard X‐ray free‐electron laser based on diffraction focusing

X‐ray free‐electron lasers (XFELs) generate sequences of ultra‐short spatially coherent pulses of X‐ray radiation. A diffraction focusing spectrometer (DFS), which is able to measure the whole energy spectrum of the radiation of a single XFEL pulse with an energy resolution of ΔE/E? 2 × 10^?6, is proposed. This is much better than for most modern X‐ray spectrometers. Such resolution allows one to resolve the fine spectral structure of the XFEL pulse. The effect of diffraction focusing occurs in a single‐crystal plate due to dynamical scattering, and is similar to focusing in a Pendry lens made from a metamaterial with a negative refraction index. Such a spectrometer is easier to operate than those based on bent crystals. It is shown that the DFS can be used in a wide energy range from 5 keV to 20 keV.     

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.     

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.     

An alternative scheme of angular‐dispersion analyzers for high‐resolution medium‐energy inelastic X‐ray scattering

The development of medium‐energy inelastic X‐ray scattering optics with meV and sub‐meV resolution has attracted considerable efforts in recent years. Meanwhile, there are also concerns or debates about the fundamental and feasibility of the involved schemes. Here the central optical component, the back‐reflection angular‐dispersion monochromator or analyzer, is analyzed. The results show that the multiple‐beam diffraction effect together with transmission‐induced absorption can noticeably reduce the diffraction efficiency, although it may not be a fatal threat. In order to improve the efficiency, a simple four‐bounce analyzer is proposed that completely avoids these two adverse effects. The new scheme is illustrated to be a feasible alternative approach for developing meV‐ to sub‐meV‐resolution inelastic X‐ray scattering spectroscopy.     

Effective aperture of X‐ray compound refractive lenses

A new definition of the effective aperture of the X‐ray compound refractive lens (CRL) is proposed. Both linear (one‐dimensional) and circular (two‐dimensional) CRLs are considered. It is shown that for a strongly absorbing CRL the real aperture does not influence the focusing properties and the effective aperture is determined by absorption. However, there are three ways to determine the effective aperture in terms of transparent CRLs. In the papers by Kohn [(2002). JETP Lett. 76 , 600–603; (2003). J. Exp. Theor. Phys. 97 , 204–215; (2009). J. Surface Investig. 3 , 358–364; (2012). J. Synchrotron Rad. 19 , 84–92; Kohn et al. (2003). Opt. Commun. 216 , 247–260; (2003). J. Phys. IV Fr, 104 , 217–220], the FWHM of the X‐ray beam intensity just behind the CRL was used. In the papers by Lengeler et al. [(1999). J. Synchrotron Rad. 6 , 1153–1167; (1998). J. Appl. Phys. 84 , 5855–5861], the maximum intensity value at the focus was used. Numerically, these two definitions differ by 50%. The new definition is based on the integral intensity of the beam behind the CRL over the real aperture. The integral intensity is the most physical value and is independent of distance. The new definition gives a value that is greater than that of the Kohn definition by 6% and less than that of the Lengeler definition by 41%. A new approximation for the aperture function of a two‐dimensional CRL is proposed which allows one to calculate the two‐dimensional CRL through the one‐dimensional CRL and to obtain an analytical solution for a complex system of many CRLs.     

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.     

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.     

A sagittally focusing double‐multilayer monochromator for ultrafast X‐ray imaging applications

The development of a sagittally focusing double‐multilayer monochromator is reported, which produces a spatially extended wide‐bandpass X‐ray beam from an intense synchrotron bending‐magnet source at the Advanced Photon Source, for ultrafast X‐ray radiography and tomography applications. This monochromator consists of two W/B₄C multilayers with a 25 Å period coated on Si single‐crystal substrates. The second multilayer is mounted on a sagittally focusing bender, which can dynamically change the bending radius of the multilayer in order to condense and focus the beam to various points along the beamline. With this new apparatus, it becomes possible to adjust the X‐ray beam size to best match the area detector size and the object size to facilitate more efficient data collection using ultrafast X‐ray radiography and tomography.     

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.     

Silicon nitride transmission X‐ray mirrors

Transmission X‐ray mirrors have been fabricated from 300–400 nm‐thick low‐stress silicon nitride windows of size 0.6 mm × 85 mm. The windows act as a high‐pass energy filter at grazing incidence in an X‐ray beam for the beam transmitted through the window. The energy cut‐off can be selected by adjusting the incidence angle of the transmission mirror, because the energy cut‐off is a function of the angle of the window with respect to the beam. With the transmission mirror at the target angle of 0.22°, a 0.3 mm × 0.3 mm X‐ray beam was allowed to pass through the mirror with a cut‐off energy of 10 keV at the Cornell High Energy Synchrotron Source. The energy cut‐off can be adjusted from 8 to 12 keV at an angle of 0.26° to 0.18°, respectively. The observed mirror transmittance was above 80% for a 300 nm‐thick film.     

Spatial structure of a focused X‐ray beam diffracted from crystals

The spatial structure of a beam focused by a planar refractive lens and Bragg diffracted from perfect silicon crystals was experimentally studied at the focal plane using a knife‐edge scan and a high‐resolution CCD camera. The use of refractive lenses allowed for a detailed comparison with theory. It was shown that diffraction leads to broadening of the focused beam owing to the extinction effect and, for a sufficiently thin crystal, to the appearance of a second peak owing to reflection from the back surface. It was found that the spatial structure of the diffracted beam depends on whether the crystal diffracts strongly (dynamically) or weakly (kinematically). The results help to understand the physical origin of the diffracted intensity recorded in a typical microbeam diffraction experiment.     

Focusing femtosecond X‐ray free‐electron laser pulses by refractive lenses

The possibility of using a parabolic refractive lens with initial X‐ray free‐electron laser (XFEL) pulses, i.e. without a monochromator, is analysed. It is assumed that the measurement time is longer than 0.3 fs, which is the time duration of a coherent pulse (spike). In this case one has to calculate the propagation of a monochromatic wave and then perform an integration of the intensity over the radiation spectrum. Here a general algorithm for calculating the propagation of time‐dependent radiation in free space and through various objects is presented. Analytical formulae are derived describing the properties of the monochromatic beam focused by a system of one and two lenses. Computer simulations show that the European XFEL pulses can be focused with maximal efficiency, i.e. as for a monochromatic wave. This occurs even for nanofocusing lenses.     

Analysis of tapered front‐coupling X‐ray waveguides

The coupling and propagation of electromagnetic waves through planar X‐ray waveguides (WG) with vacuum gap and Si claddings are analyzed in detail, starting from the source and ending at the detector. The general case of linearly tapered WGs (i.e. with the entrance aperture different from the exit one) is considered. Different kinds of sources, i.e. synchrotron radiation and laboratory desk‐top sources, have been considered, with the former providing a fully coherent incoming beam and the latter partially coherent beams. It is demonstrated that useful information about the parameters of the WG can be derived, comparing experimental results with computer simulation based on analytical solutions of the Helmholtz equation which take into account the amplitude and phase matching between the standing waves created in front of the WG, and the resonance modes propagating into the WG.     

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.     

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.     

Design and performance of an X‐ray scanning microscope at the Hard X‐ray Nanoprobe beamline of NSLS‐II

A hard X‐ray scanning microscope installed at the Hard X‐ray Nanoprobe beamline of the National Synchrotron Light Source II has been designed, constructed and commissioned. The microscope relies on a compact, high stiffness, low heat dissipation approach and utilizes two types of nanofocusing optics. It is capable of imaging with ～15 nm × 15 nm spatial resolution using multilayer Laue lenses and 25 nm × 26 nm resolution using zone plates. Fluorescence, diffraction, absorption, differential phase contrast, ptychography and tomography are available as experimental techniques. The microscope is also equipped with a temperature regulation system which allows the temperature of a sample to be varied in the range between 90 K and 1000 K. The constructed instrument is open for general users and offers its capabilities to the material science, battery research and bioscience communities.     

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.