Coherence properties of focused X-ray beams at high-brilliance synchrotron sources

Singer, Andrej; Vartanyants, Ivan A.

doi:10.1107/s1600577513023850

Cited by 32 publications

(21 citation statements)

References 36 publications

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“…1(a)] was performed at the coherence beamline P10 of the PETRA III facility at DESY. The x rays with the photon energy of 13 keV were focused by compound refractive lenses (CRLs) [20,21] to a spot about 3 μm (FWHM) at the sample. A 2D detector (Pilatus 1M with 981 × 1043 pixels and a pixel size of 172 × 172 μm 2 ) was positioned at 263 mm distance downstream from the sample.…”

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confidence: 99%

X-ray cross-correlation analysis of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition

et al. 2013

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We present an x-ray study of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition by means of angular x-ray cross-correlation analysis. By applying two-point angular-intensity cross-correlation functions to the measured series of diffraction patterns the parameters of bond-orientational (BO) order in hexatic phase were directly determined. The temperature dependence of the positional correlation lengths was analyzed as well. The obtained correlation lengths show larger values for the higher-order Fourier components of BO order. These findings indicate a strong coupling between BO and positional order. About 30 years ago it was realized that the phase transition between a two-dimensional (2D) crystal and the liquid phase can proceed through an intermediate hexatic phase [1]. The corresponding mechanism involves dissociation of dislocation pairs. The 2D hexatic phase is characterized by a sixfold quasilong-range bond-orientational (BO) order, while the positional order is short range and the shear modulus is zero. Phases with hexatic order have been found in several systems, such as electrons at the surface of helium [2], charged polymer colloids [3,4], and smectic liquid crystals (LCs) [5][6][7]. In the last case a hexatic phase was experimentally observed quite unexpectedly in three-dimensional (3D) stacked molecular systems [8]. In the 3D hexatic phase the positional order is short range, while the BO order persists over a long range. However, the mere existence of a hexatic phase does not imply a specific melting mechanism, and the origin of hexatic order and its relation to the defect-mediated melting transition is still controversial. Smectic liquid crystals are particularly suitable to investigate these problems, as they can be suspended over an opening in a solid frame. Such smectic membranes are substrate-free and have a controlled thickness ranging from two to more than thousands of layers [9].Smectic-A membranes can be described as stacks of liquid layers. The in-plane structure is liquidlike with positional correlations between the molecules decaying exponentially with a correlation length ξ 0 . While cooling a hexatic phase may occur, which shows a long-range BO order. This leads to a sixfold rotational symmetry and the BO correlations are characterized by the local ordering field ψ(r) ∝ exp[i6θ (r)], where θ (r) is the angle between the "bonds" and some reference axis. Upon decreasing the temperature, the width of the radial-intensity peak decreases simultaneously with a further development of the BO order. This indicates a coupling * Present address: The University of California, San Diego, La Jolla, CA 92093, USA.† Corresponding author: ivan.vartaniants@desy.de between the positional correlations and the BO order [10]. Additionally, at even lower temperatures a 3D crystalline phase appears with a hexagonal in-plane lattice or a rectangular lattice with a so-called herringbone order [6,7]. The common way to study the BO order is to perform x-ray or electron diffraction me...

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X-ray cross-correlation analysis of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition

et al. 2013

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“…Propagation of the X-rays to the nanofocusing optic Equation (6) has the Gaussian structure of a so-called Gaussian shell model (Vartanyants & Singer, 2010;Singer & Vartanyants, 2014). This model has been analyzed in detail by I. Vartanyants and A.…”

Section: ðR; Qþmentioning

confidence: 99%

Hard X-ray nanofocusing at low-emittance synchrotron radiation sources

Schroer

Falkenberg

2014

J Synchrotron Radiat

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X-ray scanning microscopy relies on intensive nanobeams generated by imaging a highly brilliant synchrotron radiation source onto the sample with a nanofocusing X-ray optic. Here, using a Gaussian model for the central cone of an undulator source, the nanobeam generated by refractive X-ray lenses is modeled in terms of size, flux and coherence. The beam properties are expressed in terms of the emittances of the storage ring and the lateral sizes of the electron beam. Optimal source parameters are calculated to obtain efficient and diffraction-limited nanofocusing. With decreasing emittance, the usable fraction of the beam for diffraction-limited nanofocusing experiments can be increased by more than two orders of magnitude compared with modern storage ring sources. For a diffraction-limited storage ring, nearly the whole beam can be focused, making these sources highly attractive for X-ray scanning microscopy.

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“…The Monte Carlo Green's function formalism (Fischer et al, 2008;Prahl et al, 2009) is also applied to X-ray optics by combining with raytracing . Recently, an analytical approach describing the propagation of partially coherent radiation through focusing optics has been developed (Singer & Vartanyants, 2014).…”

Section: Introductionmentioning

confidence: 99%

“…To include the partial coherence of the synchrotron radiation source, theories and simulation tools have been developed based on coherent mode decomposition (Vartanyants & Singer, 2010;Singer & Vartanyants, 2011;Hua et al, 2013) and Gaussian superposition . On the other hand, geometrical raytracing codes like SHADOW assume that the X-ray source is either completely incoherent or coherent.…”

Section: Introductionmentioning

confidence: 99%

A hybrid method for X-ray optics simulation: combining geometric ray-tracing and wavefront propagation

Shi

Reininger

Río

et al. 2014

J Synchrotron Radiat

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A new method for beamline simulation combining ray-tracing and wavefront propagation is described. The 'Hybrid Method' computes diffraction effects when the beam is clipped by an aperture or mirror length and can also simulate the effect of figure errors in the optical elements when diffraction is present. The effect of different spatial frequencies of figure errors on the image is compared with SHADOW results pointing to the limitations of the latter. The code has been benchmarked against the multi-electron version of SRW in one dimension to show its validity in the case of fully, partially and non-coherent beams. The results demonstrate that the code is considerably faster than the multi-electron version of SRW and is therefore a useful tool for beamline design and optimization.

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Coherence properties of focused X-ray beams at high-brilliance synchrotron sources

Cited by 32 publications

References 36 publications

X-ray cross-correlation analysis of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition

X-ray cross-correlation analysis of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition

Hard X-ray nanofocusing at low-emittance synchrotron radiation sources

A hybrid method for X-ray optics simulation: combining geometric ray-tracing and wavefront propagation

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