This paper discusses algorithms for phase retrieval where the measurements follow independent Poisson distributions. We developed an optimization problem based on maximum likelihood estimation (MLE) for the Poisson model and applied Wirtinger flow algorithm to solve it. Simulation results with a random Gaussian sensing matrix and Poisson measurement noise demonstrated that the Wirtinger flow algorithm based on the Poisson model produced higher quality reconstructions than when algorithms derived from Gaussian noise models (Wirtinger flow, Gerchberg Saxton) are applied to such data, with significantly improved computational efficiency.