Talbot effect

Abstract: We have demonstrated the Talbot effect, the self-imaging of a periodic structure, with atom waves. We have measured the successive recurrence of these self-images as a function of the distance from the imaged grating. This is a near-field interference effect, which has several possible applications that are discussed.

Abstract: A theory of Fresnel images is presented. Only the Fresnel images of plane periodic objects viewed in monochromatic light are considered. The theory is in agreement with the experimental and computer research available in the literature. Photographs of Fresnel images of gratings are shown to verify certain aspects of the theory.

Abstract: Self-images of a grating with period a, illuminated by light of wavelength λ, are produced at distances z that are rational multiples p/q of the Talbot distance z T = a 2/λ; each unit cell of a Talbot image consists of q superposed images of the grating. The phases of these individual images depend on the Gauss sums studied in number theory and are given explicitly in closed form; this simplifies calculations of the Talbot images. In ‘transverse’ planes, perpendicular to the incident light, and with ζ = z/z T irrational, the intensity in the Talbot images is a fractal whose graph has dimension . In ‘longitudinal’ planes, parallel to the incident light, and almost all oblique planes, the intensity is a fractal whose graph has dimension . In certain special diagonal planes, the fractal dimension is . Talbot images are sharp only in the paraxial approximation λ/a → O and when the number N of illuminated slits tends to infinity. The universal form of the post-paraxial smoothing of the edge of the sli...

Abstract: The Talbot effect, also referred to as self-imaging or lensless imaging, is of the phenomena manifested by a periodic repetition of planar field distributions in certain types of wave fields. This phenomenon is finding applications not only in optics, but also in a variety of research fields, such as acoustics, electron microscopy, plasmonics, x ray, and Bose–Einstein condensates. In optics, self-imaging is being explored particularly in image processing, in the production of spatial-frequency filters, and in optical metrology. In this article, we give an overview of recent advances on the effect from classical optics to nonlinear optics and quantum optics. Throughout this review article there is an effort to clearly present the physical aspects of the self-imaging phenomenon. Mathematical formulations are reduced to the indispensable ones. Readers who prefer strict mathematical treatments should resort to the extensive list of references. Despite the rapid progress on the subject, new ideas and applications of Talbot self-imaging are still expected in the future.