Hard-x-ray phase-imaging microscopy using the self-imaging phenomenon of a transmission grating

Abstract

We report on a hard-x-ray imaging microscope consisting of a lens, a sample, and a transmission grating. After the theoretical framework of self-imaging phenomenon by the grating in the system is presented, equations for the electric field on the image plane are derived for ideal and real lenses and an equation for the intensity on the image plane for partially coherent illumination is derived. The equations are simple and similar to those applying to a projection microscope consisting of a transmission grating except that there is no defocusing effect, regardless of whether the grating is in front of or behind the lens. This means that x-ray phase-imaging microscopy can be done without the defocusing effect. It is also shown that, by resolving the self-image on the image plane, high-sensitive x-ray phase-imaging microscopy can be attained without degradation in the spatial resolution due to diffraction by the grating. Experimental results obtained using partially coherent illumination from a synchrotron x-ray source confirm that hard-x-ray phase-imaging microscopy can be quantitatively performed with high sensitivity and without the spatial resolution degradation.