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.     

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.     

A tunable wedge‐shaped absorber for hard X‐ray synchrotron applications

The concept of a concave aluminium wedge‐shaped absorber for hard X‐ray synchrotron beamlines is presented. Unlike the commonly used absorber types (fixed‐thickness absorber sheets or binary exchangers of individual fixed absorbers), this concept allows a compact system, controlled with a single linear positioner, and provides a wide attenuation range as well as a precise tunability over a large energy range. Data were recorded at the Nanofocus Endstation of the MINAXS beamline, PETRA III, Hamburg, Germany.     

Development of new apertures for coherent X‐ray experiments

When one performs a coherent small‐angle X‐ray scattering experiment, the incident beam must be spatially filtered by slits on a length scale smaller than the transverse coherence length of the source which is typically around 10 µm. The Fraunhofer diffraction pattern of the slit is one of the important sources of background in these experiments. New slits which minimize this parasitic background have been designed and tested. The slit configuration apodizes the beam by the use of partially transmitting inclined slit jaws. A model is presented which predicts that the high wavevector tails of the diffraction pattern fall as the inverse fourth power of the wavevector instead of the inverse second power that is observed for standard slits. Using cleaved GaAs single‐crystal edges, Fraunhofer diffraction patterns from 3 and 5.5 keV X‐rays were measured, in agreement with the theoretical model proposed. A novel phase‐peak diffraction pattern associated with phase variations of the transmitted electric field was also observed. The model proposed adequately accounts for this phenomenon.     

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.     

Comparative study of multilayers used in monochromators for synchrotron‐based coherent hard X‐ray imaging

A systematic study is presented in which multilayers of different composition (W/Si, Mo/Si, Pd/B₄C), periodicity (from 2.5 to 5.5 nm) and number of layers have been characterized. In particular, the intrinsic quality (roughness and reflectivity) as well as the performance (homogeneity and coherence of the outgoing beam) as a monochromator for synchrotron radiation hard X‐ray micro‐imaging are investigated. The results indicate that the material composition is the dominating factor for the performance. By helping scientists and engineers specify the design parameters of multilayer monochromators, these results can contribute to a better exploitation of the advantages of multilayer monochromators over crystal‐based devices; i.e. larger spectral bandwidth and high photon flux density, which are particularly useful for synchrotron‐based micro‐radiography and ‐tomography.     

A soft X‐ray beamline for transmission X‐ray microscopy at ALBA

The MISTRAL beamline is one of the seven phase‐I beamlines at the ALBA synchrotron light source (Barcelona, Spain) that will be opened to users at the end of 2010. MISTRAL will be devoted to cryotomography in the water window and multi‐keV spectral regions for biological applications. The optics design consists of a plane‐grating monochromator that has been implemented using variable‐line‐spacing gratings to fulfil the requirements of X‐ray microscopy using a reflective condenser. For instance, a fixed‐focus condition independent of the included angle, constant magnification as well as coma and spherical aberration corrections are achieved with this system. The reported design is of wider use.     

Multivariate analysis of hyperspectral hard X‐ray images

This article describes methods to analyse and process hyperspectral hard X‐ray imaging data. We focus on the use of multivariate techniques that exploit the spectral information to make informed decisions on the material content within each pixel of an X‐ray image. These analysis methods have the ability to auto‐segment data without prior knowledge of the sample composition or structure, and are particularly useful for studying completely unknown, diluted or complex specimens. We demonstrate the methods on a variety of hard X‐ray images including X‐ray fluorescence and absorption data recorded using a hard X‐ray imaging spectrometer. The multivariate methods described are very powerful with the ability to segment, distinguish and, in some cases, identify different materials within a single X‐ray image. Potential uses of hyperspectral X‐ray imaging are discussed varying from materials science to industrial or security applications. Copyright © 2013 John Wiley & Sons, Ltd.     

Picosecond‐resolved X‐ray absorption spectroscopy at low signal contrast using a hard X‐ray streak camera

A picosecond‐resolving hard‐X‐ray streak camera has been in operation for several years at Sector 7 of the Advanced Photon Source (APS). Several upgrades have been implemented over the past few years to optimize integration into the beamline, reduce the timing jitter, and improve the signal‐to‐noise ratio. These include the development of X‐ray optics for focusing the X‐rays into the sample and the entrance slit of the streak camera, and measures to minimize the amount of laser light needed to generate the deflection‐voltage ramp. For the latter, the photoconductive switch generating the deflection ramp was replaced with microwave power electronics. With these, the streak camera operates routinely at 88 MHz repetition rate, thus making it compatible with all of the APS fill patterns including use of all the X‐rays in the 324‐bunch mode. Sample data are shown to demonstrate the performance.     

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.     

Sapphire hard X‐ray Fabry–Perot resonators for synchrotron experiments

Hard X‐ray Fabry–Perot resonators (FPRs) made from sapphire crystals were constructed and characterized. The FPRs consisted of two crystal plates, part of a monolithic crystal structure of Al₂O₃, acting as a pair of mirrors, for the backward reflection (0 0 0 30) of hard X‐rays at 14.3147 keV. The dimensional accuracy during manufacturing and the defect density in the crystal in relation to the resonance efficiency of sapphire FPRs were analyzed from a theoretical standpoint based on X‐ray cavity resonance and measurements using scanning electron microscopic and X‐ray topographic techniques for crystal defects. Well defined resonance spectra of sapphire FPRs were successfully obtained, and were comparable with the theoretical predictions.     

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.     

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.     

X‐ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility

An X‐ray grating interferometer was installed at the BL13W beamline of Shanghai Synchrotron Radiation Facility (SSRF) for biomedical imaging applications. Compared with imaging results from conventional absorption‐based micro‐computed tomography, this set‐up has shown much better soft tissue imaging capability. In particular, using the set‐up, the carotid artery and the carotid vein in a formalin‐fixed mouse can be visualized in situ without contrast agents, paving the way for future applications in cancer angiography studies. The overall results have demonstrated the broad prospects of the existing set‐up for biomedical imaging applications at SSRF.     

Confocal full‐field X‐ray microscope for novel three‐dimensional X‐ray imaging

A confocal full‐field X‐ray microscope has been developed for use as a novel three‐dimensional X‐ray imaging method. The system consists of an X‐ray illuminating `sheet‐beam' whose beam shape is micrified only in one dimension, and an X‐ray full‐field microscope whose optical axis is normal to the illuminating sheet beam. An arbitral cross‐sectional region of the object is irradiated by the sheet‐beam, and secondary X‐ray emission such as fluorescent X‐rays from this region is imaged simultaneously using the full‐field microscope. This system enables a virtual sliced image of a specimen to be obtained as a two‐dimensional magnified image, and three‐dimensional observation is available only by a linear translation of the object along the optical axis of the full‐field microscope. A feasibility test has been carried out at beamline 37XU of SPring‐8. Observation of the three‐dimensional distribution of metallic inclusions in an artificial diamond was performed.     

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.     

Fresnel zone plate with apodized aperture for hard X‐ray Gaussian beam optics

Fresnel zone plates with apodized apertures [apodization FZPs (A‐FZPs)] have been developed to realise Gaussian beam optics in the hard X‐ray region. The designed zone depth of A‐FZPs gradually decreases from the center to peripheral regions. Such a zone structure forms a Gaussian‐like smooth‐shouldered aperture function which optically behaves as an apodization filter and produces a Gaussian‐like focusing spot profile. Optical properties of two types of A‐FZP, i.e. a circular type and a one‐dimensional type, have been evaluated by using a microbeam knife‐edge scan test, and have been carefully compared with those of normal FZP optics. Advantages of using A‐FZPs are introduced.     

X‐ray tube spectral measurement method for quantitative analysis of X‐ray fluorescence analysis

Lα and Lβ X‐ray fluorescence spectra of a lead metallic sheet were measured using an energy dispersive X‐ray spectrometer by changing the X‐ray tube voltage and the material of the primary filter. The Lα to Lβ intensity ratio changed from Lα: Lβ = 3: 1 at 15 kV to Lα: Lβ = 1: 1 at 50 kV depending on the X‐ray tube voltage and the filter. The scattered X‐ray spectra of an acrylic slab instead of the sample in the sample holder were measured by changing the applied voltage and the material of the primary filter. The calculated values of the Pb Lα/Lβ intensity ratio of the metallic sheet using the Shiraiwa–Fujino formula by inserting the scattered X‐ray spectra of an acrylic plate as incident X‐ray spectra and the fundamental parameters taken from the Elam database were in good agreement with the experimental ones. We conclude that we can obtain an incident X‐ray spectrum approximately by measuring the scattered X‐ray spectrum without measuring the direct incident beam. Copyright © 2010 John Wiley & Sons, Ltd.