RADIO PHYSICS AND RADIO ASTRONOMY

Subject and Purpose. Th e 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 waves in the 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 need to be taken into account. A way of improving the accuracy 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 deriving similar 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 signals are obtained with the aid of a direct digital frequency synthesizer that can 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, which allows taking into consideration the 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 0.001 MHz, provided the signal-to-noise ratios are reasonably high.

Keywords: microwave spectrometer, millimeter-wave spectrum, measurement accuracy, spectral lines

Manuscript submitted 11.09.2022

Radio phys. radio astron. 2022, 27(4):299-311

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