Coherent pore-scale imaging: phase contrast and ptychography

Abstract

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.