Microwave fourier transform spectroscopy: Linewidth effects in the low pressure limit

We describe theoretically the line shapes obtained with pulsed microwave Fourier Transform Spectroscopy carried out on a static gas at very low pressures in a waveguide absorption cell. A density-matrix formalism is used to study the interaction of a two-level quantum system with a classical, pulsed, travelling wave electric field in a rectangular waveguide. Neglecting intermolecular collisions, the effects of the molecular velocity distribution the linewidths of microwave transitions are considered, allowing for Doppler broadening, wall collisions and microwave-field inhomogeneities. General expressions for the decay function of sample polarisation are derived and examples for the resulting line shapes are given.