Reconstructing a complex field from a series of its near-field diffraction patterns

We propose a method for reconstructing a complex field from a series of its near-field diffraction patterns. This method is based on the paraxial Fresnel diffraction equation without making further approximations. Numerical simulations are presented showing that a complex field can even be reconstructed with moderate qualities from its two near-field diffraction patterns and almost exact reconstructions can be obtained when three or more diffraction patterns are used. We also show by numerical simulation that the correct diffraction distances can be recovered in case only coarsely measured values are available. This method may be applied to phase imaging of weak-absorption objects.