At present, ptychography seems to be the most natural and efficient method for approaching the diffraction-limited optical resolution. The general setup of a ptychoscope does not contain refracting or focusing elements and includes a coherent illumination source, a translation stage for displacement of a macroscopic object, and a detector for recording transmitted or reflected radiation from the object, which is connected to a computer for processing diffractograms. In classical optics, the main problem with achieving high spatial resolution is the correction and elimination of aberrations in optical systems, whereas the spatial resolution in ptychography mainly depends on the reliability of recording and computer processing diffractograms with large numerical apertures. After a brief introduction to the history and current state of ptychography, the wave-packet method for calculating the wave field on a detector in the far field and for a large numerical aperture is considered in detail. This gives a relation between fields on the object and on the detector, which underlies the ePIE (extended Ptychography Iterative Engine) algorithms for recovering images used in practice. The realization of algorithms involves operations with functions defined in certain domains (coordinate networks) of the direct space and Fourier space related to the object and detector. The size of and steps involved in such networks are strictly related to the object size, its distance from the detector, and the numerical aperture. The programs developed in this paper are used to refine the limits of applicability of the paraxial approximation (Fresnel integrals) in calculations of the field on the detector. Simulations of images obtained by the ptychography method are presented.
The paper deals with an analytical study of the problem of pore detection and certification in bulk materials by means of X-ray radiography. The optimum thickness of a sample under X-ray absorption investigation of the pores is found, that can be used for an improvement of the signal-to-noise ratio by the proper X-ray photon energy. In the case of low absorption an X-ray coherent beam can be used for production of phase contrast in the radiographic experiments. We present a simple model to calculate the complex value of the wave field formed by the sample. The model includes two dimensionless parameters: the Fresnel number F= a 2 (λz), where a is the pore radius, λ is the wavelength, z is the sampleto-detector distance and the phase number Φ = akδ, where k = 2π λ and δ is the decrement of the real part of material's relative permittivity. The detailed analysis of the field structure is given with an estimation of the optimal position of the detector. The numerical simulation results are presented as well, which were obtained for the Gaussian type of the pore shape function. The stationary phase method of higher orders has been proven to simplify the Fresnel integral. The developed qualitative visualization of the pores with the help of phase contrast X-ray imaging complements other modern methods of monitoring porous-sensitive materials.
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