Abstract
Subject and Purpose. The frequency modulation (FM)combined with lock-in detection, the technique which is used in microwave spectroscopy for enhancing the sensitivity of measurements, as well as the effects due to standing wavesinthe measuring absorption cell can lead to distortions in the spectral line shapes observed. To ensure the highest possible accuracy derivable from the experimental data, these distortions needto be taken into account. A way of improving theaccuracy is to approximate to the experimental line contour with a theoretical line shape that would account for the observable distortion effects.The relevant literature sources suggest examples of theoretical expressions for the line shape in the case of a sinusoidal frequency modulation. This work has been aimed at derivingsimilar expressions for the case of a square-wave frequency modulation that shall allow increasing the accuracy of measurements. Methods and Methodology.The square-wave-FM signalsare obtained with the aid of a direct digital frequency synthesizer thatcan provide switching between two frequencies known to a high accuracy. This technical solution permits generating FM signals with precisely specified parameters. Results. A closed-form expression has been suggested, based on numerically evaluated line shape derivatives, whichallows taking into considerationthe basic types of distortions encountered in the spectral line records. The cases that have been considered concern a variety of experimental conditions, including sub-Doppler measurements with Lamb-dip observations. Conclusions. The approach that has been proposed allows one to properly take into account the distortions of spectral line shapes resulting from the use of a square-wave-FM signal, as well as those due to standing wave effects in the spectrometer cell. As has been found, application of this approach to experimental spectra with a variety of modulation parameters permits reducing the errors of frequency determination to ±0.001MHz, provided the signal-to-noise ratios are reasonably high.
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