DOI: https://doi.org/10.15407/rpra27.04.299

E. A. Alekseev, V. V. Ilyushin, R. A. Motiyenko


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


1. De Lucia, F.C., 2010. The submillimeter: A spectroscopist’s view. J. Mol. Spectrosc., 261(1), pp. 1—17. DOI:https://doi.org/10.1016/j.jms.2010.01.002

2. Nagourney, W., 1978. Baseline suppression in microwave spectroscopy frequency modulation and harmonic detection. Rev. Sci. Instrum., 49, pp. 1072—1076. DOI:https://doi.org/10.1063/1.1135516

3. Alekseev, E.A., Zakharenko, V.V., 2004. Direct digital synthesizer as a reference source of a millimeter-wave frequency synthesizer. In: Proc. V Int. Kharkov Symp. “Physics and engineering of millimeter and submillimeter waves”. Kharkov, Ukraine, 21—26 June 2004, pp. 782—784. DOI:https://doi.org/10.1109/MSMW.2004.1346148

4. Alekseev, E.A., Zakharenko, V.V., 2007. Direct Digital Synthesizer at the Microwave Spectroscopy. Radio Phys. Radio Astron., 12(2), pp. 205—214 (in Russian).

5. Alekseev, E.A., 2011. Direct Digital Frequency Synthesizers: Potentialities and Limitations for Microwave Spectroscopy Applications. Radio Phys. Radio Astron., 2(4), pp. 369—378. DOI:https://doi.org/10.1615/RadioPhysicsRadioAstronomy.v2.i4.100

6. Zakharenko, O., Motiyenko, R.A., Margulès, L., Huet, T.R., 2015. Terahertz spectroscopy of deuterated formaldehyde using a frequency multiplication chain. J. Mol. Spectrosc., 317, pp. 41—46. DOI:https://doi.org/10.1016/j.jms.2015.09.005

7. Alekseev, E.A., Motiyenko, R.A., Margulès, L., 2012. Millimeter- and Submillimeter-Wave Spectrometers on the Basis of Direct Digital Frequency Synthesizers. Radio Phys. Radio Astron., 3(1), pp. 75—88. DOI: https://doi.org/10.1615/RadioPhysicsRadioAstronomy.v3.i1.100

8. Alekseev, E.A., Ilyushin, V.V., Mescheryakov, A.A., 2014. High-Precision Microwave Spectrometer with Sub-Doppler Spectral Resolution. Radio Phys. Radio Astron., 19, pp. 364—374 (in Russian). DOI: https://doi.org/10.15407/rpra19.04.364

9. Daly, A.M., Kolesniková, L., Mata, S., Alonso, J.L., 2014. The millimeter and submillimeter wave spectrum of cis-methyl vinyl ether. J. Mol. Spectrosc., 306, pp. 11—18. DOI: https://doi.org/10.1016/j.jms.2014.10.003

10. Pickett, H.M., 1980. Determination of collisional linewidths and shifts by a convolution method. Appl. Optics. Roy. Soc. London, 19(16), pp. 2745—2749. DOI:https://doi.org/10.1364/AO.19.002745

11. Winnewisser, G., Belov, S.P., Klaus, Th., Schieder, R., 1997. Sub-Doppler measurements of the rotational transitions of carbon monoxide. J. Mol. Spectrosc., 184(2), pp. 468—472. DOI:https://doi.org/10.1006/jmsp.1997.7341

12. Cazzoli, G., Puzzarini, C., Stopkowicz, S., Gauss, J., 2010. Hyperfine structure in the rotational spectra of trans-formic acid: Lambdip measurements and quantum-chemical calculations, Astron. Astrophys., 520, id. A64. DOI:https://doi.org/10.1051/0004-6361/201014787

13. Melosso, M., Dore, L., Gauss, J., Puzzarini, C., 2020. Deuterium hyperfine splittings in the rotational spectrum of NH2D as revealed by Lamb-dip spectroscopy. J. Mol. Spectrosc., 370, id. 111291. DOI:https://doi.org/10.1016/j.jms.2020.111291

14. Belov, S.P., Golubiatnikov, G.Yu., Lapinov, A.V., Ilyushin, V.V., Alekseev, E.A., Mescheryakov, A.A., Hougen, J.T., and Li-Hong Xu, 2016. Torsionally mediated spin-rotation hyperfine splittings at moderate to high J values in methanol. J. Chem. Phys., 145, id. 024307. DOI:https://doi.org/10.1063/1.4954941

15. Dore, L., 2003. Using Fast Fourier Transform to compute the line shape of frequency-modulated spectral profi les. J. Mol. Spectrosc., 221(1), pp. 93—98. DOI:https://doi.org/10.1016/S0022-2852(03)00203-0

16. Karplus, R., 1948. Frequency modulation in microwave spectroscopy. Phys. Rev., 73(9), pp. 1027—1034. DOI:https://doi.org/10.1103/PhysRev.73.1027

17. De Vreede, J.P.M., Gillis, M.P.W., Dijkerman, H.A., 1988. Linewidth, Lineshift, and Lineshape Measurements on Rotational Transitions of OCS Using Frequency Modulation. J. Mol. Spectrosc., 128(2), pp. 509—520. DOI:https://doi.org/10.1016/0022-2852(88)90166-X

18. Nguyen, L., Buldyreva, J., Colmont, J.-M., Roharth, F., Wlodarczak, G., Alekseev, E.A., 2006. Detailed profile analysis of millimetre 502 and 602 GHz N 2O-N2(O2) lines at room temperature for collisional linewidth determination. Mol. Phys., 104(16–17), pp. 2701—2710. DOI:https://doi.org/10.1080/03067310600833534

19. Savitzky, A., Golay, M.J.E., 1964. Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Anal. Chem., 36(8), pp. 1627—1639. DOI:https://doi.org/10.1021/ac60214a047

20. Gordy, W., Cook, R.L., 1984. Microwave Molecular Spectra. New York: John Wiley & Sons. ISNB 0471086819

21. Di Rocco, H.O., 2005. The exact expression of the Voigt profile function. J. Quant. Spectrosc. Radiat. Transf., 92, pp. 231—237. DOI: https://doi.org/10.1016/j.jqsrt.2004.08.002

22. McLean, A.B., Mitchell, C.E.J., Swanston, D.M., 1994. Implementation of an efficient analytical approximation to the Voigt function for photoemission lineshape analysis. J. Electron Spectrosc. Relat. Phenom., 69, pp. 125—132. DOI: https://doi.org/10.1016/0368-2048(94)02189-7

23. Di Rocco, H.O., Cruzado, A., 2012. The Voigt Profile as a Sum of a Gaussian and a Lorentzian Functions, when the Weight Coefficient Depends Only on the Widths Ratio. Acta Phys. Pol. A, 122, pp. 666—669. DOI: https://doi.org/10.12693/APhysPolA.122.666

Full Text:


Creative Commons License
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0)