Inversion of time domain signals from a Balle–Flygare type microwave spectrometer

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The method of sine and cosine Fourier transforms with a phase correction, well known in NMR and traveling wave Fourier transform microwave spectroscopy, is examined for the pulsed beam Fabry–Perot cavity. The validity of this approach is closely related to the result, noted previously elsewhere [J.-L. Le Gouët and P. R. Berman, Phys. Rev. A 20, 1105 (1979), and F. Rohart and B. Macke, J. Phys. 41, 837 (1980)] that only the polarization spatial harmonic that projects onto the driven fundamental mode of the cavity contributes appreciably to the free induction decay signal. When the full signal is recorded after a short polarization pulse, an absorption line shape function in the low power limit for a single nondegenerate transition can be recovered as an angular distribution weighted integral over the coordinate θ between the nozzle axis and a point on the cavity axis of Doppler-shifted Voight profiles. Passage of the beam through the transverse Gaussian profile of a TEM00q mode contributes an effective line broadening temperature. These results are a direct extension of a semiclassical derivation given earlier [E. J. Campbell, L. W. Buxton, T. J. Balle, and W. H. Flygare, J. Chem. Phys. 74, 813 (1981), and E. J. Campbell, L. W. Buxton, T. J. Balle, M. R. Keenan, and W. H. Flygare, J. Chem. Phys. 74, 829 (1981)]. Analytical results are derived using simplified cavity mode functional forms. Calculations using the exact mode expressions are reported. The relation between this approach and the direct absorption method is discussed.