A multiresolution (multiscale) analysis based on wavelet transform is applied to the problem of optical phase retrieval from the intensity measured in the in-line geometry (lens-free). The transport-of-intensity equation and the Fresnel diffraction integral are approximated in terms of a wavelet basis. A solution to the phase retrieval problem can be efficiently found in both cases using the multiresolution concept. Due to the hierarchical nature of wavelet spaces, wavelets are well suited to multiresolution methods that contain multigrid algorithms. Appropriate wavelet bases for the best solution approximation are discussed. The proposed approach reduces the computational complexity and accelerates the convergence of the solution. It is robust and reliable, and successful on both simulated and experimental images obtained with hard x rays.
In the present work the X-ray optical anisotropy of 5CB type liquid crystals has been investigated based on the method of X-ray interferometry. In this way Moire fringes have been obtained both in the absence and presence of specimens with different orientations of optical axes. The relative displacement of Moire fringes enabled us to observe and immediately ascertain the presence of X-ray optical anisotropy, to measure the values of refractive indices n o and n e for this specimen (n o is the refractive index for radiation with polarization normal to the principal plain, n e is that for radiation with polarization in the principal plain parallel to the optical axis). X-ray optical anisotropy of 5CB type liquid crystal was observed using the proposed method and values of refractive indices n o and n e for this specimen were measured. It was found out that 5CB type nematic liquid crystal was X-ray anisotropic optically positive medium.
We presents the results of study of focusing and imaging properties of double-lens system for hard x-ray radiation consisting of two Fresnel zone plates (ZP) made from silicon.We demonstrate for the first time the phenomenon of focusing by two crystal ZP located at significant distance from each other. We investigate by both theoretically and experimentally the peculiarities of intensity distribution at the focal plane during a scan by second ZP normally to the optical axis of the system. We investigate as well the intensity distribution along the optical axis for our double-lens system from crystal ZP.We realize experimentally a registration of the focused image of the object by means of double-lens system based on ZP. Measurements are performed on the beam line BM-5 of the European Synchrotron Radiation Facility (ESRF) at the x-ray energy 9.4 keV. We elaborate a computer program for theoretical simulation of the optical properties of x-ray double-lens system based on ZPs. A calculation is made by convolution of transmission function and Kirchhoff propagator in paraxial approximation by means of Fast Fourier Transformation.
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