Theory of edge radiation. Part I: Foundations and basic applications

We formulate a complete theory of edge radiation based on a novel method relying on Fourier Optics techniques. Special attention is payed in discussing the validity of approximations upon which the theory is built. Our study makes consistent use of both similarity techniques and comparisons with numerical results from simulation. We discuss both near and far zone. Physical understanding of many asymptotes is discussed. As an example of application we discuss the case of Transition Undulator Radiation, which can be conveniently treated with our formalism.