Transition radiation from a relativistic electron obliquely incident on a thin metal plate of finite transverse dimensions

The problem of transition radiation generated by the oblique motion of a relativistic electron through a thin metal plate of finite transverse dimensions is considered. The expressions for the spectral and angular densities of radiation emitted forward and backward are obtained. It is shown that, in the millimeter and the submillimeter range, the spectra of both forward and backward radiation for targets of finite transverse dimensions can differ substantially from the corresponding spectra for an infinite plate.