  The generation and properties of transition radiation (TR) are thoroughly
treated. The spectral energy density, as described by the Ginzburg-Frank
formula, is computed analytically, and the modifications caused by the finite
size of the TR screen and by near-field diffraction effects are carefully
analyzed. The principles of electron bunch shape reconstruction using coherent
transition radiation are outlined. Spectroscopic measure- ments yield only the
magnitude of the longitudinal form factor but not its phase. Two phase
retrieval methods are investigated and illustrated with model calculations:
analytic phase computation by means of the Kramers- Kronig dispersion relation,
and iterative phase retrieval. Particular attention is paid to the ambiguities
which are unavoidable in the reconstruction of longitudinal charge density
profiles from spectroscopic data. The origin of these ambiguities has been
identified and a thorough mathematical analysis is presented. The experimental
part of the paper comprises a description of our multichannel infrared and THz
spectrometer and a selection of measurements at FLASH, comparing the bunch
profiles derived from spectroscopic data with those determined with a
transversely deflecting microwave structure. A rigorous derivation of the
Kramers-Kronig phase formula is presented in Appendix A. Numerous analytic
model calculations can be found in Appendix B. The differences between normal
and truncated Gaussians are discussed in Appendix C. Finally, Appendix D
contains a short description of the propagation of an electromagnetic wave
front by two-dimensional fast Fourier transformation. This is the basis of a
powerful numerical Mathematica code THzTransport, which permits the propagation
of electromagnetic wave fronts through a beam line consisting of drift spaces,
lenses, mirrors and apertures.

Accelerator Physics