Abstract. We show how Fresnel transform computations can be simplified by using the diffraction properties of periodic objects. Such a simplification occurs at locations along the propagation axis which are defined by the fractional Talbot order. An extension to non periodic objects can be obtained by approximations compatible with those defining the domain of the Fresnel diffraction. Such considerations determine the theoretical framework for the fractional Fresnel transform, the main practical advantage of which is the existence of fast algorithms for computing the diffracted fields at given locations along the propagation axis.

Print publication: Issue 2 (March 1995)