Vector diffraction theory and coherent transition radiation interferometry in electron linacs

Electrons impinging on a thin metallic foil produce small bursts of transition radiation (TR) as they cross the boundary from one medium to the next. A popular diagnostic application is found for compact electron bunches. In this case they will emit radiation more or less coherently with an enhancement of the intensity on wavelengths comparable to or larger than the bunch size, generating coherent transition radiation (CTR). Several detailed analytical descriptions have been proposed for describing the resulting spectral distribution, often making different simplifying assumptions. Given that bunches tenths of millimeters long can generate measurable spectra into the millimeter range, concern may arise as to weak diffraction effects produced by optical interference devices containing elements with dimensions in the centimeter range