This paper is devoted to the development of a two-dimensional computer-simulation model that is based on the rigid constraints of optical diffraction theory with careful attention paid to the generation of sample realizations of Gaussian-distributed, spatially random, isotropic wave fronts that have zero-mean and prescribed-covariance functions. Given a sample realization of the wave front, the corresponding centered point-spread function and optical-transfer function are evaluated. A detailed study is made of the statistics of random wave-front tilt, point-spread function, modulus squared of transfer function, and phase of transfer function.