Phase Retrieval with Random Phase Illumination

This paper presents a detailed, numerical study on the performance of the standard phasing algorithms with random phase illumination (RPI). Phasing with high resolution RPI and the oversampling ratio $\sigma=4$ determines a unique phasing solution up to a global phase factor. Under this condition, the standard phasing algorithms converge rapidly to the true solution without stagnation. Excellent approximation is achieved after a small number of iterations, not just with high resolution but also low resolution RPI in the presence of additive as well multiplicative noises. It is shown that RPI with $\sigma=2$ is sufficient for phasing complex-valued images under a sector condition and $\sigma=1$ for phasing nonnegative images. The Error Reduction algorithm with RPI is proved to converge to the true solution under proper conditions.