Modelling the power threshold and optimum thermal deformation of indirectly liquid-nitrogen cryo-cooled Si monochromators.

Maximizing the performance of crystal monochromators is a key aspect in the design of beamline optics for diffraction-limited synchrotron sources. Temperature and deformation of cryo-cooled crystals, illuminated by high-power beams of X-rays, can be estimated with a purely analytical model. The analysis is based on the thermal properties of cryo-cooled silicon crystals and the cooling geometry. Deformation amplitudes can be obtained, quickly and reliably. In this article the concept of threshold power conditions is introduced and defined analytically. The contribution of parameters such as liquid-nitrogen cooling efficiency, thermal contact conductance and interface contact area of the crystal with the cooling base is evaluated. The optimal crystal illumination and the base temperature are inferred, which help minimize the optics deformation. The model has been examined using finite-element analysis studies performed for several beamlines of the Diamond-II upgrade.

Cryo-cooled silicon crystal monochromators: a study of power load, temperature and deformation.

Crystal monochromators are often the primary optics in hard X-ray synchrotron beamlines. Management of power load is central to their design. Strict requirements on stability and deformation are to be met, as new-generation synchrotron sources deliver brighter beams of X-rays. This article sets out to illustrate an overall picture of the deformation caused by heat load in a cryo-cooled Si crystal monochromator using first principles. A theoretical model has been developed to predict the temperature distribution and surface deformation by applying intrinsic properties of Si material and the cooling system parameters. The model explains the universal behaviour of crystal slope error versus absorbed power; it has been benchmarked against experimental data and used to interpret finite-element analysis of cryogenically cooled crystals.

The Hard X-ray Nanoprobe beamline at Diamond Light Source.

The Hard X-ray Nanoprobe beamline, I14, at Diamond Light Source is a new facility for nanoscale microscopy. The beamline was designed with an emphasis on multi-modal analysis, providing elemental mapping, speciation mapping by XANES, structural phase mapping using nano-XRD and imaging through differential phase contrast and ptychography. The 185 m-long beamline operates over a 5 keV to 23 keV energy range providing a ≤50 nm beam size for routine user experiments and a flexible scanning system allowing fast acquisition. The beamline achieves robust and stable operation by imaging the source in the vertical direction and implementing horizontally deflecting primary optics and an overfilled secondary source in the horizontal direction. This paper describes the design considerations, optical layout, aspects of the hardware engineering and scanning system in operation as well as some examples illustrating the beamline performance.

Hard X-ray ptychography for optics characterization using a partially coherent synchrotron source.

Ptychography is a scanning coherent diffraction imaging technique which provides high resolution imaging and complete spatial information of the complex electric field probe and sample transmission function. Its ability to accurately determine the illumination probe has led to its use at modern synchrotrons and free-electron lasers as a wavefront-sensing technique for optics alignment, monitoring and correction. Recent developments in the ptychography reconstruction process now incorporate a modal decomposition of the illuminating probe and relax the restriction of using sources with high spatial coherence. In this article a practical implementation of hard X-ray ptychography from a partially coherent X-ray source with a large number of modes is demonstrated experimentally. A strongly diffracting Siemens star test sample is imaged using the focused beam produced by either a Fresnel zone plate or beryllium compound refractive lens. The recovered probe from each optic is back propagated in order to plot the beam caustic and determine the precise focal size and position. The power distribution of the reconstructed probe modes also allows the quantification of the beams coherence and is compared with the values predicted by a Gaussian-Schell model and the optics exit intensity.

Aberration-free aspherical lens shape for shortening the focal distance of an already convergent beam.

The shapes of single lens surfaces capable of focusing divergent and collimated beams without aberration have already been calculated. However, nanofocusing compound refractive lenses (CRLs) require many consecutive lens surfaces. Here a theoretical example of an X-ray nanofocusing CRL with 48 consecutive surfaces is studied. The surfaces on the downstream end of this CRL accept X-rays that are already converging toward a focus, and refract them toward a new focal point that is closer to the surface. This case, so far missing from the literature, is treated here. The ideal surface for aberration-free focusing of a convergent incident beam is found by analytical computation and by ray tracing to be one sheet of a Cartesian oval. An `X-ray approximation' of the Cartesian oval is worked out for the case of small change in index of refraction across the lens surface. The paraxial approximation of this surface is described. These results will assist the development of large-aperture CRLs for nanofocusing.

Surface profiling of X-ray mirrors for shaping focused beams.

Grazing incidence mirrors are a standard optic for focusing X-rays. Active mirrors, whose surface profile can be finely adjusted, allow control of beam shape and size at the sample. However, progress towards their routine use for beam shaping has been hampered by the strong striations in reflected beams away from the focal plane. Re-entrant (partly concave and partly convex) surface modifications are proposed for shaping X-ray beams to a top-hat in the focal plane while reducing the striations caused by unavoidable polishing errors. A method for constructing such surfaces with continuous height and slope (but only piecewise continuous curvature) will be provided. Ray tracing and wave propagation calculations confirm its effectiveness. A mirror system is proposed allowing vertical beam sizes in the range 0.5 to 10µm. A prototype will be fabricated and is expected to have applications on many synchrotron X-ray beamlines.

Aberration-free short focal length x-ray lenses.

We treat the problem of defining the ideal x-ray refractive lens design for point focusing of low emittance x-ray beams at third- and fourth-generation synchrotron sources. The task is accomplished by using Fermat's principle to define a lens shape that is completely free from geometrical aberrations. Current microfabrication resolution limits are identified, and a design that tolerates the inherent fabrication imperfections is proposed. The refractive lens design delivers nanometer-sized focused x-ray beams and is compatible with current microfabrication techniques.

Aspherical lens shapes for focusing synchrotron beams.

Aspherical surfaces required for focusing collimated and divergent synchrotron beams using a single refractive element (lens) are reviewed. The Cartesian oval, a lens shape that produces perfect point-to-point focusing for monochromatic radiation, is studied in the context of X-ray beamlines. Optical surfaces that approximate ideal shapes are compared. Results are supported by ray-tracing simulations. Elliptical lenses, rather than parabolic, are preferred for nanofocusing X-rays because of the higher peak and lower tails in the intensity distribution. Cartesian ovals will improve the gain when using high-demagnification lenses of high numerical aperture.

A comment on 'A new ray-tracing program RIGTRACE for X-ray optical systems' [J. Synchrotron Rad. (2001), 8, 1047-1050].

Some points concerning the characteristics of the X-ray simulation code SHADOW [Welnak et al. (1994). Nucl. Instrum. Methods, A347, 344-347] are clarified which are not correctly mentioned by Yamada et al. [J. Synchrotron Rad. (2001), 8, 1047-1050]. It is shown that, contrary to the Authors' statement, some functionality of their new program is not original. In particular, we show that SHADOW can deal correctly with crystal monochromators.