In attempting a unified treatment of the field of X-ray, neutron and electron diffraction, including electron microscopy and other imaging techniques based on diffraction, we are faced with the task of bringing together a number of theoretical treatments developed for convenience in handling particular topics. Often the "popular" treatment used by experimentalists is not just a simplification of the more rigorous methods of the theorist. It may have a different basis which is more conceptually pleasing but less tractable mathematically or is easier to visualize as in the geometric optics approximation for imaging theory.