Propagation of an X-ray beam modified by a photonic crystal

Feasibility of X-ray beam nanofocusing with compound refractive lenses

A more general analytical theory of X-ray beam propagation through compound refractive lenses (CRLs) than the earlier study by Kohn [(2003). JETP, 97, 204-215] is presented. The problem of nanofocusing with CRLs is examined in detail. For a CRL with a relatively large aperture the focusing efficiency is limited by the radiation absorption in the lens material. The aperture does not affect the focusing process and it is replaced by the effective aperture. The X-ray transverse beam size at the focus is then by a factor of γ = β/δ times smaller than the transverse beam size just behind the CRL. Here, δ and β are the real and imaginary parts of the CRL material refractive index n = 1 - δ + iβ. In this instance, to improve focusing efficiency, it is advantageous to decrease the CRL aperture and increase the photon energy E. However, with increasing photon energy, the material absorption decreases, which results in the CRL aperture impact on the transverse beam size. The latter leads to the fact that with a proper CRL length the beam size is independent of both the aperture and photon energy but depends only on the CRL material electron density and is approximately equal to w_c = λ/(8δ)^1/2, where λ denotes the radiation wavelength, as predicted by Bergemann et al. [(2003). Phys. Rev. Lett, 91, 204801].

Computer simulations of X-ray phase-contrast images and microtomographic observation of tubules in dentin

An investigation of the problems of X-ray imaging of dentinal tubules is presented. Two main points are addressed. In the first part of this paper, the problem of computer simulating tubule images recorded in a coherent synchrotron radiation (SR) beam has been discussed. A phantom material which involved a two-dimensional lattice of the tubules with parameters similar to those of dentin was considered. By a comparative examination of two approximations, it was found that the method of phase-contrast imaging is valid if the number of tubules along the beam is less than 100. Calculated images from a lattice of 50 × 50 tubules are periodic in free space but depend strongly on the distance between the specimen and the detector. In the second part, SR microtomographic experiments with millimetre-sized dentin samples in a partially coherent beam have been described. Tomograms were reconstructed from experimental projections using a technique for incoherent radiation. The main result of this part is the three-dimensional rendering of the directions of the tubules in a volume of the samples. Generation of the directions is possible because a tomogram shows the positions of the tubules. However, a detailed tubule cross-section structure cannot be restored.

Transmission of an X-ray beam through a two-dimensional photonic crystal and the Talbot effect

Results of computer simulations of the transmission of an X-ray beam through a two-dimensional photonic crystal as well as the propagation of an X-ray beam in free space behind the photonic crystal are reported. The photonic crystal consists of a square lattice of silicon cylinders of diameter 0.5 µm. The amount of matter in the path of the X-ray beam rapidly decreases at the sides of the cylinder projections. Therefore the transmission is localized near the boundaries, and appears like a channeling effect. The iterative method of computer simulations is applied. This method is similar to the multi-slice method that is widely used in electron microscopy. It allows a solution to be obtained with acceptable accuracy. A peculiarity in the intensity distribution inside the Talbot period z_T in free space was found when the intensity is approximately equal to the initial value at a distance 0.46z_T, and it is shifted by half a period at distance 0.5z_T. The reason for this effect is the existence of a periodic phase of the wavefunction of radiation inside the intensity peaks. Simulations with zero phase do not show this effect. Symmetry rules for the Talbot effect are discussed.

Ptychographic X-Ray Imaging of Colloidal Crystals

Ptychographic coherent X-ray imaging is applied to obtain a projection of the electron density of colloidal crystals, which are promising nanoscale materials for optoelectronic applications and important model systems. Using the incident X-ray wavefield reconstructed by mixed states approach, a high resolution and high contrast image of the colloidal crystal structure is obtained by ptychography. The reconstructed colloidal crystal reveals domain structure with an average domain size of about 2 µm. Comparison of the domains formed by the basic close-packed structures, allows us to conclude on the absence of pure hexagonal close-packed domains and confirms the presence of random hexagonal close-packed layers with predominantly face-centered cubic structure within the analyzed part of the colloidal crystal film. The ptychography reconstruction shows that the final structure is complicated and may contain partial dislocations leading to a variation of the stacking sequence in the lateral direction. As such in this work, X-ray ptychography is extended to high resolution imaging of crystalline samples.