We introduce a fast, dependable algorithm to solve for the exit surface wave of a specimen in coherent diffractive imaging for a set of illumination conditions that are not unduly restrictive. It is shown that a direct solution of the phase problem from a diffraction pattern is obtained efficiently and uniquely. The algorithm is deterministic and is known a priori to converge to the correct solution in less than a predetermined number of steps. It is based on the conjugate gradient least-squares method implemented with Fourier transforms and offers the possibility of real-time solutions. We also extend the formulation to allow for imaging of extended objects in a manner similar to ptychography.

• Received 22 November 2011

DOI:https://doi.org/10.1103/PhysRevA.85.013816