The Talbot effect, also referred to as self-imaging or lensless imaging, was originally discovered in the 1830s by H. F. Talbot. Over the years, investigators have come to understand different aspects of this phenomenon, and a theory of the Talbot effect based on classical diffraction theory has emerged which is capable of explaining the various observations. For a detailed description of the Talbot effect and related phenomena, as well as a historical perspective on the subject, the reader may consult references 3 and 4 and further references cited therein. Since many of the standard optics textbooks do not even mention the Talbot effect, it is worthwhile to bring to the reader's attention the essential features of this phenomenon.

Lensless imaging of a periodic pattern

The Talbot effect is observed when, under appropriate conditions, a beam of light is reflected from (or transmitted through) a periodic pattern. The pattern may have one-dimensional periodicity (as in traditional gratings), or it may exhibit periodicity in two dimensions (e.g., a surface relief structure or a photographic plate imprinted with identical features on a regular lattice).

In what follows we shall present the diffraction patterns obtained from a periodic array of cross-shaped apertures in an otherwise opaque screen. Because the diffraction pattern of a single aperture differs markedly from that of a periodic array of such apertures, we begin by examining the behavior of an individual aperture under coherent illumination.