Film grain is a highly valued characteristic of analog images, thus realistic digital film grain synthesis is an important objective for many modern photographers and film-makers. We carry out a theoretical analysis of a physically realistic film grain model, based on a Boolean model, and derive expressions for the expected value and covariance of the film grain texture. We approximate these quantities using a Monte Carlo simulation, and use them to propose a film grain synthesis algorithm based on Gaussian textures. With numerical and visual experiments, we demonstrate the correctness and subjective qualities of the proposed algorithm