Quantitative millimetre wave spectroscopy .3. Theory of spectral detection and quantitative analysis in a millimetre wave confocal Fabry-Perot cavity spectrometer

The quantitative response of a confocal millimetre wave Fabry-Perot cavity spectrometer is described theoretically. The treatment is based on consideration of the cavity as a lossy resonator, with the gas sample acting as an additional loss with a frequency dependence due to its spectral profile. Frequency modulation of the source frequency causes a variation of the transmitted signal due to the changing power level in the cavity as well as that caused by power absorption by the sample as the source is swept across the resonant frequency of each. Fourier analysis of the resulting cavity signals leads to a rather straightforward relationship between the modulated power output from the cavity integrated over the spectral range scanned and the product of the fractional abundance (concentration) of the absorbing species in the cavity with the peak absorption coefficient of a pure sample. The integrated spectral line power absorption was tested as an indicator of gas concentration within the cavity, using as trial samples vibrationally excited states of (NNO)-N-14-N-14-O-16 and naturally abundant (0.365%) (NNO)-N-14-N-15-O-16, each of which display absorptions in the neighbourhood of 176 GHz. The results obtained were at first surprisingly poor, the integration algorithm showing anomalous behaviour at low sample pressures. This was demonstrated to be caused by the integration interval (in this case a frequency increment) being too large to support a 256 point trapezium or Simpson's rule numerical integration procedure. Only when these were replaced by a 8096 point Romberg interathe spectral features, but suffer from the inherent problem that those that remove the background also set the integral over these features to zero. Further studies are addressing this dilemma. In spite of its imperfections, the theoretical model used has enabled the definition of an operating regime in which absorption signals are almost independent of the instrument parameters. It also accounts correctly for the observed amplitudes and shapes of these spectra over a wide range of modulation depths and sample pressures.ctive integration process based on the theoretically computed line profile did the area algorithm become stable at all linewidths tested. Experiments on the modulation depth dependence of the integrated spectral line absorption displayed further anomalies in the line area to cavity background ratio possibly caused by the pulling of a cavity resonance containing a spectral line during our frequency sweep. These effects were intriguing rather than serious, and the experiments did indicate a region for which the ratio was almost independent of the modulation depth at a constant pressure of 7 Pa, varying for a range of modulation from 0.132 MHz to 1.32 MHz by only a factor of 4 in the worst case ((NNO)-N-14-N-15-O-16) and 1.4 in the best ((NNO)-N-14-N-14-O-16 in the 01(-1)0 state). Measurements were conducted by diluting N2O at 7 Pa by addition of air up to 92 Pa. The integrated spectral line absorption for the mixtures rose gradually from a value of 0.99 for the pure sample to 1.92 for a sample containing 7 Pa N2O + 32 Pa air, and then dropped to 1.64 again in the high pressure limit (7 Pa N2O + 92 Pa air). This drop can be explained by the frequency scan not encompassing the broadened wings of the spectral line, but the initial increase in the lower pressure range is not readily explained. Various procedures and algorithms were essayed to improve the signal to noise and background ratios. Savitzky-Golay, Gaussian and derivative Gaussian convolutions all serve to highlight the spectral features, but suffer from the inherent problem that those that remove the background also set the integral over these features to zero. Further studies are addressing this dilemma. In spite of its imperfections, the theoretical model used has enabled the definition of an operating regime in which absorption signals are almost independent of the instrument parameters. It also accounts correctly for the observed amplitudes and shapes of these spectra over a wide range of modulation depths and sample pressures.