Phase-retrieval stagnation problems and solutions

The iterative Fourier-transform algorithm has been demonstrated to be a practical method for reconstructing an object from the modulus of its Fourier transform (i.e., solving the problem of recovering phase from a single intensity measurement). In some circumstances the algorithm may stagnate. New methods are described that allow the algorithm to overcome three different modes of stagnation: those characterized by (1) twin images, (2) stripes, and (3) truncation of the image by the support constraint. Curious properties of Fourier transforms of images are also described: the zero reversal for the striped images and the relationship between the zero lines of the real and imaginary parts of the Fourier transform. A detailed description of the reconstruction method is given to aid those employing the iterative transform algorithm.