Precomputable (Cramer-Rao) lower bounds for the integrated mean-square error are presented for the phase retrieval problem. The results are based upon the assumption that the phase is a sample function of a Gaussian random process and that the intensity measurements include additive white Gaussian noise. The bound, which is obtained from an information kernel which is the solution to a Fredholm integral equation, clearly demonstrates the effect of prior statistics, measurement noise and the nature of the linear transformation introduced prior to detection. Several examples are given; in particular, the role of diffraction is shown to be quite important for successful phase retrieval. Finally, the results are extended to include independent measurements of intensity in several planes.