Wavefront reconstruction for in-line holograms formed by pure amplitude objects

A recursive algorithm is described which gives a numerical solution to the twin image problem of in-line holography for pure amplitude objects. This algorithm combines the benefits of the Fraunhofer method and the Gerchberg-Saxton type algorithm, so that the applicability is extended to include features whose Fresnel numbers are significantly larger than one. A solution to the wavefront reconstruction problem from a single hologram formed by a general object is found to be impossible, due to non-uniqueness of the solution.