The development of modeling algorithms for adaptive optics systems is important for evaluating both performance and design parameters prior to system construction. Two of the most critical subsystems to be modeled are the binary optic design and the adaptive control system. Since these two are intimately related, it is beneficial to model them simultaneously. Optic modeling techniques have some significant limitations. Diffraction effects directly limit the utility of geometrical ray-tracing models, and transform techniques such as the fast Fourier transform can be both cumbersome and memory intensive. We have developed a hybrid system incorporating elements of both ray-tracing and Fourier transform techniques. In this paper we present an analytical model of wavefront propagation through a binary optic lens system developed and implemented at Sandia National Laboratories. This model is unique in that it solves the transfer function for each portion of a diffractive optic analytically. The overall performance is obtained by a linear superposition of each result. The model has been successfully used in the design of a wide range of binary optics, including an adaptive optic for a beam combining system consisting of an array of rectangular mirrors, each controllable in tip/tilt and piston. Wavefront sensing and the control models for a beam combining system have been integrated and used to predict overall systems performance. Applicability of the model for design purposes is demonstrated with several lens designs through a comparison of model predictions with actual adaptive optics results.