  We have developed a novel method based on vector electromagnetic theory and
Schellkunoff's principles to calculate the spectral and angular distributions
of transtion radiation (TR) and diffraction radiation (DR) produced by a
charged particle interacting with an arbitrary target. The vector method
predicts the polarization and spectral angular distributions of the radiation
at an arbitrary distance form the source, i.e. in both the near and far fields,
and in any direction of observation. The radiation fields of TR and DR
calculated with the commonly used scalar Huygens model are shown to be limiting
forms of those predicted by the vector theory and the regime of validity of the
scalar theory is explicitly shown. Calculations of TR and DR done using the
vector model are compared to results available in the literature for various
limiting cases and for cases of more general interest. Our theory has important
applications in the design of TR and DR diagnostics particularly those that
utilize coherent TR or DR to infer the longitudinal bunch size and shape. A new
technique to determine the bunch length using the angular distribution of
coherent TR or DR is proposed.
