A general integral formalism based on multiple plane wave scattering theory for acousto-optic and holographic Bragg diffraction is developed. The formalism, which is a modification of earlier work, is applicable to dynamic gratings created by sound waves as well as static (holographic) gratings of any modulation strength over a wide range of Bragg angles. Numerical results for light beams incident on moving gratings are then obtained for three different beam profiles by employing this formalism. Straightforward extensions to the case of holographic gratings, with or without tilt, are also presented, and the results are compared, wherever feasible, with other known approaches.