Retrieval of a Complex-Valued Object from its Diffraction Pattern

It is commonly understood that the retrieval of a complex-valued object from its diffraction pattern using a support constraint is a difficult problem, the more so if the support is symmetric. In this Letter we show that, for just such a symmetric support, use of an iterative algorithm in which the basic iteration is specified by a difference map converges routinely. All that is required is sufficient oversampling in the diffraction pattern coupled with judicious choices of the parameters defining the difference map.