Image Formation by Incoherent and Coherent Transition Radiation from Flat and Rough Surfaces

In this paper we derive equations for the image formation of transverse profile of a relativistic beam obtained by means of optical transition radiation (OTR) from flat and rough metal surfaces. The motivation behind this study lies in the desire to suppress coherent transition radiation (COTR) observed in experiments at modern free electron lasers. The physical mechanism behind the problem of COTR is that the OTR is predominantly radiated at small angles of order of 1/{gamma} where {gamma} is the relativistic factor of the beam. This means that the transverse formation size of the image is of order of {bar {lambda}}{gamma} where {bar {lambda}} = {lambda}/2{pi} with {lambda} the radiation wavelength. For relativistic beams this can be comparable or even exceed the transverse size of the beam, which would mean that the image of the beam has very little to do with its transverse profile. It is fortuitous, however, that the incoherent image is formed by adding radiation energy of electrons and results in the transverse formation size being of order of {bar {lambda}}/{theta}{sub a}, with {theta}{sub a} is the aperture angle of the optical system. The COTR image, in contrast, is formed by adding electromagnetic field of electrons, and leads to the formation size {bar {lambda}}{gamma}. In situations when the COTR intensity exceeds that of OTR the COTR imaging makes the diagnostic incapable of measuring the beam profile