The electric field in the temporal and spectral domain of coherent
diffraction-limited transition radiation is studied. An electron bunch,
with arbitrary longitudinal momentum distribution, propagating at
normal incidence to a sharp metal-vacuum boundary with finite
transverse dimension is considered. A general expression for the
spatiotemporal electric field of the transition radiation is derived,
and closed-form solutions for several special cases are given. The
influence of parameters such as radial boundary size, electron momentum
distribution, and angle of observation on the waveform (e.g., radiation
pulse length and amplitude) are discussed. For a Gaussian electron
bunch, the coherent radiation waveform is shown to have a single-cycle
profile. Application to a novel THz source based on a laser-driven
accelerator is discussed.