LAN EFFECT - NON-PARAXIAL ANALYSIS

A non-paraxial analysis based on optical coherence theory is carried o ut to determine the far-zone diffraction pattern of a double-grating s et-up (gratings of period d, axial separation Delta z) illuminated by spatially incoherent light of wavelength lambda. In the paraxial limit the formalism describes the Lau effect, and a close analogy with the Talbot effect is established if the first grating is a Ronchi ruling w ith narrow slits; when Delta z = z(T) = 2d(2)/lambda, the second grati ng is self-imaged into the far zone irrespective of its profile. In an alogy with the fractional Talbot effect, a binary phase grating in the Lau setup generates a binary-amplitude profile in the far zone when z = z(T)/4. The accuracy of these paraxial predictions is evaluated num erically for different values of d/lambda using the non-paraxial forma lism. It is shown that better-quality profiles are obtained if the sli ts of the first grating are not infinitely narrow but have a finite wi dth, which depends on the parameters of the set-up.