Iterative phase retrieval without support

An iterative phase retrieval method for nonperiodic objects has been developed from the charge-f lipping algorithm proposed in crystallography. A combination of the hybrid input–output (HIO) algorithm and the f lipping algorithm has greatly improved performance. In this combined algorithm the f lipping algorithm serves to find the support (object boundary) dynamically, and the HIO part improves convergence and moves the algorithm out of local minima. It starts with a single intensity measurement in the Fourier domain and does not require a priori knowledge of the support in the image domain. This method is suitable for general image recovery from oversampled diffuse elastic x-ray and electron-diffraction intensities. The relationship between this algorithm and the output–output algorithm is elucidated.