New theoretical and experimental results in Fresnel optics with applications to matter-wave and X-ray interferometry

New methods and formulas for calculating the image amplitude and image spatial power spectral density produced by monochromatic point-source illumination of a finite (and/or infinite) periodic complex transmission grating are presented. In the Fresnel domain the self-images are generalizations of the Talbot and von Lau effects, while in the Fraunhofer to Fresnel transition domain, the present formulas demonstrate the formation of these structures from Fraunhofer diffraction order side-lobes. Design criteria are provided for constructing lens-free three-grating interferometers with spatially diffuse illumination and detection. The present results demonstrate interference and image aliasing in such a device with spatially diffuse illumination and detection.