QUANTITATIVE MILLIMETER-WAVE SPECTROSCOPY .3. THEORY OF SPECTRAL DETECTION AND QUANTITATIVE-ANALYSIS IN A MILLIMETER-WAVE CONFOCAL FABRY-PEROT CAVITY SPECTROMETER

The quantitative response of a confocal millimetre wave Fabry-Perot ca vity spectrometer is described theoretically. The treatment is based o n consideration of the cavity as a lossy resonator, with the gas sampl e 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 straightfo rward relationship between the modulated power output from the cavity integrated over the spectral range scanned and the product of the frac tional abundance (concentration) of the absorbing species in the cavit y with the peak absorption coefficient of a pure sample. The integrate d spectral line power absorption was tested as an indicator of gas con centration within the cavity, using as trial samples vibrationally exc ited states of (NNO)-N-14-N-14-O-16 and naturally abundant (0.365%) (N NO)-N-14-N-15-O-16, each of which display absorptions in the neighbour hood of 176 GHz. The results obtained were at first surprisingly poor, the integration algorithm showing anomalous behaviour at low sample p ressures. This was demonstrated to be caused by the integration interv al (in this case a frequency increment) being too large to support a 2 56 point trapezium or Simpson's rule numerical integration procedure. Only when these were replaced by a 8096 point Romberg interathe spectr al features, but suffer from the inherent problem that those that remo ve the background also set the integral over these features to zero. F urther studies are addressing this dilemma. In spite of its imperfecti ons, the theoretical model used has enabled the definition of an opera ting regime in which absorption signals are almost independent of the instrument parameters. It also accounts correctly for the observed amp litudes and shapes of these spectra over a wide range of modulation de pths and sample pressures.ctive integration process based on the theor etically 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 anomalie s in the line area to cavity background ratio possibly caused by the p ulling of a cavity resonance containing a spectral line during our fre quency sweep. These effects were intriguing rather than serious, and t he experiments did indicate a region for which the ratio was almost in dependent of the modulation depth at a constant pressure of 7 Pa, vary ing for a range of modulation from 0.132 MHz to 1.32 MHz by only a fac tor 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 conduct ed by diluting N2O at 7 Pa by addition of air up to 99 Pa. The integra ted spectral line absorption for the mixtures rose gradually from a va lue of 0.99 for the pure sample to 1.92 for a sample containing 7 Pa N 2O + 32 Pa air, and then dropped to 1.64 again in the high pressure li mit (7 Pa N2O + 92 Pa air). This drop can be explained by the frequenc y scan not encompassing the broadened wings of the spectral line, but the initial increase in the lower pressure range is not readily explai ned. Various procedures and algorithms were essayed to improve the sig nal to noise and background ratios. Savitzky-Golay, Gaussian and deriv ative Gaussian convolutions all serve to highlight the spectral featur es, but suffer from the inherent problem that those that remove the ba ckground also set the integral over these features to zero. Further st udies are addressing this dilemma. In spite of its imperfections, the theoretical model used has enabled the definition of an operating regi me in which absorption signals are almost independent of the instrumen t parameters. It also accounts correctly for the observed amplitudes a nd shapes of these spectra over a wide range of modulation depths and sample pressures.