A highly accurate method for calculating X-ray propagation is developed. Within this approach, the propagating wave is represented as a superposition of oriented Gaussian beams. The direction of wave propagation in each Gaussian beam agrees with the local direction of propagation of the X-ray wavefront. When calculating the propagation of X-ray waves through lenses, the thin lens approximation is applied. In this approximation, the wave parameters change discontinuously when the wave passes through a lens; the corresponding explicit formulae are derived. The theory is applied to highly accurate calculation of the focusing of X-rays by a system of many beryllium lenses. Fine structure of the wave electric field on the focal plane is revealed and studied. The fine structure is formed due to the diffraction of waves at the edges of the lens apertures. Tools for controlling the calculation accuracy are proposed. The amplitude of the electric field on the focal plane and the focal spot width are shown to be very sensitive to the quality of the calculation, while the best focus position can be obtained even from simple calculations.research papers

The propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. For solving the problem for an electromagnetic wave, a finite-difference method is applied. The error of simulation is analytically estimated and investigated. It was found that a very detailed difference grid is required for reliable and accurate calculations of the propagation of X-ray waves through a multi-lens system. The reasons for using a very detailed difference grid are investigated. It was shown that the wave phase becomes a function, very quickly increasing with increasing distance from the optical axis, after the wave has passed through the multi-lens system. If the phase is a quickly increasing function of the coordinates perpendicular to the optical axis, then the electric field of the wave is a quickly oscillating function of these coordinates, and thus a very detailed difference grid becomes necessary to describe such a wavefield. To avoid this difficulty, an equation for the phase function is proposed as an alternative to the equation of the electric field. This allows reliable and accurate simulations to be carried out when using the multi-lens system. An equation for the phase function is derived and used for accurate simulations. The numerical error of the suggested method is estimated. It is shown that the equation for the phase function allows efficient simulations to be fulfilled for the multi-lens system.

This paper reports a special device called a 'speckle suppressor', which contains a highly porous nanoberyllium plate squeezed between two beryllium windows. The insertion of the speckle suppressor in an X-ray beam allows manipulation of the spatial coherence length, thus changing the effective source size and removing the undesirable speckle structure in X-ray imaging experiments almost without beam attenuation. The absorption of the nanoberyllium plate is below 1% for 1 mm thickness at 12 keV. The speckle suppressor was tested on the ID06 ESRF beamline with X-rays in the energy range from 9 to 15 keV. It was applied for the transformation of the phase-amplitude contrast to the pure amplitude contrast in full-field microscopy.

This study develops anew theory of nonlinear acoustics investigating interactions between acoustical and other non-acoustical modes, such as vorticity modes, in afl uid. The ideas proposed by the authors makep ossible to derive instantaneous equations describing interaction between different modes in arelaxing Maxwell fluid. The procedure of deriving of anew dynamic equation governing the vorticity mode which is generated by sound, is discussed in details. It uses only instantaneous quantities and does not include averaging oversound period. The resulting equation applies to both periodic and aperiodic sound of anyw aveform as the origin of the vorticity mode. The theory is illustrated by tworepresentative examples of generation of the vorticity mode in arelaxing Maxwell fluid, caused by periodic sound beam and asound beam with astationary butaperiodic waveform. PACS no. 43.25.-x, 43.25.Nm ©S.Hirzel Verlag · EAA 807 ACTA ACUSTICA UNITED WITH ACUSTICA Perelomova,W ojda: Generation of vorticity mode Vol. 96 (2010)