Phase retrieval based on wave-front relay and modulation

We report and demonstrate experimentally an approach to retrieving the phase of a general complex-valued wave field from a single diffraction pattern. The approach employs a modulator in its data acquisition, which greatly reduces the dynamic range requirement of the detector and also greatly facilitates the inverse calculation. The new algorithm, involving a nonlinear modulus constraint, is free from ambiguities and robust to noise; it converges rapidly even with a rather loose support constraint. This approach provides a practical solution to coherent imaging with a broad range of radiations and at all wavelengths.