Talbot images formed with an arbitrary incidence wave

When a plane wave illuminates a spatially periodic structure (grating), the resulting diffracted field reproduces images of the diffracting structure at special (Talbot) distances behind the grating. In practice however the finite extent of the grating and non-ideal plane wave illumination, lead to deviations between the reproduced Talbot image and the original input. In this paper we propose a novel analytical technique for describing the diffraction pattern formed behind a grating that allows us to account for both of these effects, thereby providing new insight into the diffraction process. The theoretical predictions of our model are confirmed with numerical simulations. Some applications of our technique to estimate the wave-front of an optical field are discussed.