X-ray Irradiance Distribution for an Interferometer with a Curved Biprism Array

Abstract

The development of interferometry-based X-ray phase contrast imaging systems that provide highly resolved X-rays with spatially-modulated intensity is enabling the full potential of X-ray optics to image phase, attenuation, and small angle scatter properties of soft tissue. In this work we present analytical formulations of a new hardware concept for X-ray phase contrast imaging wherein the phase grating is replaced with an array of Fresnel biprisms. We derive expressions for the irradiance distribution pattern of a biprism interferometer composed of a curved biprism array with multiple biprisms and multiple point sources. These expressions are used to plot fringe patterns for X-ray design parameters, including 1) size, number, and period of X-ray point sources; 2) biprism parameters of material composition, angle, number, and period; and 3) biprism array to X-ray source and detector distances. Analytical results show that the biprism interferometer provides a longitudinally-nonperiodic pattern of spatially modulated intensity different from the Talbot longitudinally-periodic pattern common in grating interferometry. The curvature of the biprism array brings a sharper longitudinal fringe pattern. Experiments are being performed to verify the analytical calculations for a biprism plastic material of SU-8 using a synchrotron source. X-ray biprism material has widely varied indexes of refraction relative to wavelength and thus the separation of the virtual sources and resulting interference fringe period also varies with X-ray wavelength. Our aim is to develop biprism interferometry imaging systems with excellent polychromatic performance that produce high-contrast fringes with spatially incoherent X-ray illumination. Biprism interferometry will potentially provide higher fringe visibility with better image quality to that of diffraction grating interferometry.