Fresnel tomography: a novel approach to wave-function reconstruction based on the Fresnel representation of tomograms

We introduce a new type of tomographic probability distribution containing complete information about the density matrix (wave function) related to the Fresnel transform of the complex wave function. We elucidate the relation to the symplectic tomographic probability distribution. We present a multimodegeneralization of the Fresnel tomography and give examples of applications of the present approach.