Diffractive–refractive optics: X‐ray splitter

The possibility of splitting a thin (e.g. undulator) X‐ray beam based on diffraction–refraction effects is discussed. The beam is diffracted from a crystal whose diffracting surface has the shape of a roof with the ridge lying in the plane of diffraction. The crystal is cut asymmetrically. One half of the beam impinges on the left‐hand part of the roof and the other half impinges on the right‐hand side of the roof. Owing to refraction the left part of the beam is deviated to the left whereas the right part is deviated to the right. The device proposed consists of two channel‐cut crystals with roof‐like diffraction surfaces; the crystals are set in a dispersive position. The separation of the beams after splitting is calculated at a distance of 10 m from the crystals for various asymmetry and inclination angles. It is shown that such a splitting may be utilized for long beamlines. Advantages and disadvantages of this method are discussed.     

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.     

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.     

Diffraction of partially coherent X‐rays in clessidra prism arrays

When small triangular prisms are arranged in arrays which have an overall appearance like an hourglass (in Italian: clessidra) they can focus X‐rays owing to a combined action of diffraction and refraction. From the optical point of view these objects can be regarded as a Fresnel variant of concave transmission lenses. Consequently they can provide larger apertures than purely refractive lenses. However, one has to recognize that clessidra lenses will strongly diffract as the lens structure is periodic in the direction perpendicular to the incident beam. In experiments the diffraction is reduced because it is difficult to illuminate the large apertures with a full spatially coherent wavefront. So the illumination is at best partially coherent. In order to interpret available experimental data for this condition, diffraction theory has been applied appropriately to the clessidra structure, taking into account the limited spatial coherence. The agreement between the theoretical simulations and experimental data is very good, keeping the lens properties at their projected values and allowing for only two free model parameters. The first is the lateral spatial coherence; the second is a lens defect, a rounding of all edges and tips in the structure. Both values obtained from the simulations have been found to be in agreement with expectations.     

Diffractive–refractive optics: (+,−,−,+) X‐ray crystal monochromator with harmonics separation

A new kind of two channel‐cut crystals X‐ray monochromator in dispersive (+,?,?,+) position which spatially separates harmonics is proposed. The diffracting surfaces are oriented so that the diffraction is inclined. Owing to refraction the diffracted beam is sagittally deviated. The deviation depends on wavelength and is much higher for the first harmonics than for higher harmonics. This leads to spatial harmonics separation. The idea is supported by ray‐tracing simulation.     

非线性光栅的自适应光限幅

首次采用液晶为自聚焦媒质,夹在内表面刻有光栅的两玻璃片间,以Ar离子激光514.5nm波长的激光束垂直入射到光栅上,实验验证了该光栅的自适应光限幅特征。     

Hard X‐ray microbeam lithography using a Fresnel zone plate with a long focal length

Focused hard X‐ray microbeams for use in X‐ray nanolithography have been investigated. A 7.5 keV X‐ray beam generated at an undulator was focused to about 3 µm using a Fresnel zone plate fabricated on silicon. The focused X‐ray beam retains a high degree of collimation owing to the long focal length of the zone plate, which greatly facilitates hard X‐ray nanoscale lithography. The focused X‐ray microbeam was successfully utilized to fabricate patterns with features as small as 100 nm on a photoresist.     

Energy‐dispersive diffraction with synchrotron radiation and a germanium detector

The response of an intrinsic Ge detector in energy‐dispersive diffraction measurements with synchrotron radiation is studied with model calculations and diffraction from perfect Si single‐crystal samples. The high intensity and time‐structure of the synchrotron radiation beam leads to pile‐up of the output pulses, and the energy distribution of the pile‐up pulses is characteristic of the fill pattern of the storage ring. The pile‐up distribution has a single peak and long tail when the interval of the radiation bunches is small, as in the uniform fill pattern, but there are many pile‐up peaks when the bunch distance is a sizable fraction of the length of the shaping amplifier output pulse. A model for the detecting chain response is used to resolve the diffraction spectrum from a perfect Si crystal wafer in the symmetrical Laue case. In the 16‐bunch fill pattern of the ESRF storage ring the spectrum includes a large number of `extra reflections' owing to pile‐up, and the model parameters are refined by a fit to the observed energy spectrum. The model is used to correct for the effects of pile‐up in a measurement with the 1/3 fill pattern of the storage ring. Si reflections (2h,2h,0) are resolved up to h = 7. The pile‐up corrections are very large, but a perfect agreement with the integrated intensities calculated from dynamical diffraction theory is achieved after the corrections. The result also demonstrates the convergence of kinematical and dynamical theories at the limit where the extinction length is much larger than the effective thickness of the perfect crystal. The model is applied to powder diffraction using different fill patterns in simulations of the diffraction pattern, and it is demonstrated that the regularly spaced pile‐up peaks might be misinterpreted to arise from superlattices or phase transitions. The use of energy‐dispersive diffraction in strain mapping in polycrystalline materials is discussed, and it is shown that low count rates but still good statistical accuracy are needed for reliable results.     

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.     

Coherence and wavefront characterization of Si‐111 monochromators using double‐grating interferometry

A study of the coherence and wavefront properties of a pseudo‐channel‐cut monochromator in comparison with a double‐crystal monochromator is presented. Using a double‐grating interferometer designed for the hard X‐ray regime, the complex coherence factor was measured and the wavefront distortions at the sample position were analyzed. A transverse coherence length was found in the vertical direction that was a factor of two larger for the channel‐cut monochromator owing to its higher mechanical stability. The wavefront distortions after different optical elements in the beam, such as monochromators and mirrors, were also quantified. This work is particularly relevant for coherent diffraction imaging experiments with synchrotron sources.     

Study of X-ray diffraction processes in ADP crystals under the influence of temperature gradient

The influence of temperature gradient on the intensity of X-ray beam reflected from atomic planes of antiferroelectric crystal of ammonium dihydro-phosphate (ADP) was studied. It was found that under the influence of temperature gradient on ADP crystal, the intensity of diffracted X-ray beam initially decreases at small values of gradient and then monotonously increases with increasing gradient. It is assumed that in the initial period of the action of temperature gradient the crystal domains have no time to orient in the same direction, and the intensity of beam decreases owing to the scattering of X-rays in different directions when reflected from the walls of boundaries of domains. After the alignment of domains, their arrangement in the same direction, separate areas of unidirectional domains are formed under the action of temperature gradient and the intensity of diffracted X-ray beam increases, as confirm the experimental data. The specified mechanism is supposed to occur also in other crystals having the domain structure.     

Linear effect of doubling of the laser pulse repetition rate in the laue geometry of bragg diffraction in a photonic crystal

It has been theoretically shown that, during Bragg diffraction of a picosecond laser pulse in the Laue geometry in a linear photonic crystal, the pulse, entering the crystal structure, may be split into two transmitted and two diffracted pulses. The time interval between these pulses can be controlled by varying the crystal thickness and the modulation depth of the refractive index.     

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.     

Time‐ and spatial‐resolved XAFS spectroscopy in a single shot: new analytical possibilities for in situ material characterization

A new concept that comprises both time‐ and lateral‐resolved X‐ray absorption fine‐structure information simultaneously in a single shot is presented. This uncomplicated set‐up was tested at the BAMline at BESSY‐II (Berlin, Germany). The primary broadband beam was generated by a double multilayer monochromator. The transmitted beam through the sample is diffracted by a convexly bent Si (111) crystal, producing a divergent beam. This, in turn, is collected by either an energy‐sensitive area detector, the so‐called color X‐ray camera, or by an area‐sensitive detector based on a CCD camera, in θ–2θ geometry. The first tests were performed with thin metal foils and some iron oxide mixtures. A time resolution of lower than 1 s together with a spatial resolution in one dimension of at least 50 µm is achieved.     

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.     

Utilizing broadband X‐rays in a Bragg coherent X‐ray diffraction imaging experiment

A method is presented to simplify Bragg coherent X‐ray diffraction imaging studies of complex heterogeneous crystalline materials with a two‐stage screening/imaging process that utilizes polychromatic and monochromatic coherent X‐rays and is compatible with in situ sample environments. Coherent white‐beam diffraction is used to identify an individual crystal particle or grain that displays desired properties within a larger population. A three‐dimensional reciprocal‐space map suitable for diffraction imaging is then measured for the Bragg peak of interest using a monochromatic beam energy scan that requires no sample motion, thus simplifying in situ chamber design. This approach was demonstrated with Au nanoparticles and will enable, for example, individual grains in a polycrystalline material of specific orientation to be selected, then imaged in three dimensions while under load.     

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.     

Characterization of spatial coherence of synchrotron radiation with non‐redundant arrays of apertures

A method to characterize the spatial coherence of soft X‐ray radiation from a single diffraction pattern is presented. The technique is based on scattering from non‐redundant arrays (NRAs) of slits and records the degree of spatial coherence at several relative separations from 1 to 15 µm, simultaneously. Using NRAs the spatial coherence of the X‐ray beam at the XUV X‐ray beamline P04 of the PETRA III synchrotron storage ring was measured as a function of different beam parameters. To verify the results obtained with the NRAs, additional Young's double‐pinhole experiments were conducted and showed good agreement.     

Angular vibrations of cryogenically cooled double‐crystal monochromators

The effect of angular vibrations of the crystals in cryogenically cooled monochromators on the beam performance has been studied theoretically and experimentally. A simple relation between amplitude of the vibrations and size of the focused beam is developed. It is shown that the double‐crystal monochromator vibrations affect not only the image size but also the image position along the optical axis. Several methods to measure vibrations with the X‐ray beam are explained and analyzed. The methods have been applied to systematically study angular crystal vibrations at monochromators installed at the PETRA III light source. Characteristic values of the amplitudes of angular vibrations for different monochromators are presented.     

Effect of the spatial structure of an acoustic field on Bragg’s acoustooptic diffraction under strong acoustic anisotropy conditions

Bragg’s acoustooptic diffraction in an acoustically anisotropic medium is considered taking into account the two-dimensional spatial diffraction structure of the acoustic beam. The conditions are determined under which reverse transfer of optical power from the diffracted to the transmitted beam in the regime of 100% efficiency of diffraction is considerably suppressed. It is shown that this effect is due to diffraction bending of wave fronts of the acoustic beam in the acoustooptic diffraction plane. The problem of optimization of the piezoelectric transducer size and the spatial position of the input light beam is solved using the criterion of the minimal required power of the acoustic field. The results of simulation in a wide range of the acoustooptic interaction parameters for a Gaussian light beam are reported. The correctness of the model is confirmed experimentally. Recommendations for designers of acoustooptic devices are formulated.