Talbot effect for periodical objects limited by finite apertures: a new interpretation

The paper presents a new interpretation of the Talbot effect for periodical objects limited by finite apertures. According to the proposed approach, a self-image of a real, finite object is a superposition of deformed images of an elementary cell. The singular elementary cell image is equivalent to that formed in a proper optical system. Two possible optical arrangements are discussed. The theoretical description makes possible to define a structure of self-images. Particularly, the approach enables a determination of apertures' dimensions, which lead to self-images of a reasonable quality in a desired region of an image plane. The theory is illustrated and verified by numerical simulations.