On x-ray phase imaging with a point source

Abstract

A theoretical analysis of the in-line method of x-ray phase-contrast imaging with a small (microfocus) source is presented. By applying the stationary-phase formula to the Fresnel integral, we derive a new variant of the transport of intensity equation (TIE) that explicitly takes image magnification into account and does not require the distance between the two observation planes to be infinitesimally small. The new derivation method provides a uniform technique for obtaining the TIE’s with incident waves of different types and also leads to new practically convenient validity conditions. A new boundary problem for the TIE, which is particularly suitable for the in-line imaging, is defined a..