X-ray phase contrast imaging: Transmission functions separable in cylindrical coordinates.

A Fresnel–Kirchhoff integral can be used to calculate x-ray phase contrast images when the transmission function is known. Here expressions for image intensity are derived for objects with axial symmetry for an x-ray source with non-vanishing dimensions. An expression for the image intensity is given for an x-ray source whose intensity distribution is described by a Gaussian function, from which an expression for the limiting case of a point source of radiation is found. The expressions for image intensity are evaluated for cases where the magnification is substantially greater than one, as would be employed in biological imaging. Experiments using a microfocus x-ray tube and charge coupled device camera are reported to determine the capability of the method for imaging small spherical objects, such as gold particles, which might find application as contrast agents in biomedical imaging. [ABSTRACT FROM AUTHOR]