**1. Introduction**

Measuring the isotope ratio of chemical substances (carbon, water, chlorine and so on) has a large variety of applications in environmental sciences [1–5]. Providing a monitor of the emission in the atmosphere of greenhouse gases has potential application in global climate warnings, as well as in general monitoring [6–9], water cycle studies [10–12], and in general for establishing formation mechanisms and strategies [13–17]. Additionally, biomedical applications benefit from accurate fractional isotopic ratio measurements, particularly in human breath analysis [18,19], where it is possible to detect biomarkers related to specific diseases or metabolic processes, or even in pharmacological research [20]. Finally, isotopic ratio measurements are employed in space research, in star dynamics and planet studies [21]; the particular measurement of the <sup>13</sup>*C*/12*C* ratio, which we consider in this work, has additional interests in carbon capture and storage monitoring [22] and in volcanic gas processes studies [23]. According to the type of application, the desirable target for accuracy and precision in such measurements could be different. For example, in very demanding biomedical applications (i.e., breath test for disease diagnosis or metabolic status monitoring), the accuracy and precision level for the R<sup>13</sup>*C*/12*<sup>C</sup>* isotopic ratio could be lower than 0.5% [24,25]

Broadband spectroscopic techniques that use optical frequency combs (OFC) as an interaction laser source have become very popular for multiplexed detection of molecular species. Among all molecular parameters measurable with such techniques, the accu-

**Citation:** Siciliani de Cumis, M.; Eramo, R.; Jiang, J.; Fermann, M.E.; Cancio Pastor, P. Direct Comb Vernier Spectroscopy for Fractional Isotopic Ratio Determinations. *Sensors* **2021**, *21*, 5883. https://doi.org/10.3390/ s21175883

Academic Editor: Krzysztof M. Abramski

Received: 30 June 2021 Accepted: 25 August 2021 Published: 31 August 2021

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rate determination of the isotopic composition of a gas sample is surely one of the most challenging applications.

OFC-based spectroscopic techniques with dual comb [26], Fourier transform [27] and spatially dispersive [28–31] detection schemes, sometimes combined with Fabry–Perot enhanced spectroscopy [29–32], are widely used for trace gas detection [19,30,31,33–37]. However, the most accurate results regarding fractional isotopic ratio measurements were obtained by direct frequency comb dispersive spectroscopy (DFCDS) [25,38]. Bailey and coworkers [38] used a MIR-FC-based cross-dispersed spectrometer to measure a fractional isotopic abundance of nitrous oxide (N2O) with a precision of 6.7 × <sup>10</sup>−<sup>6</sup> in 1 s of acquisition time. Such measurements can be used to determine sources, skins and mechanisms of formation of this potent greenhouse gas and ozone-depleting agent, helping to improve current mitigation strategies. Similarly, accurate optical number density of <sup>12</sup>*C* and <sup>13</sup>*C* single substituted isotopic variants of C16O2 gas with a precision of, respectively, 0.03% and 1.24%, were measured by using DFCDS in the near-IR [25]. These kinds of measurements open the way for environmental monitoring and biomedical sciences applications of this OFC-based technology. DFCDS exploits the broadband coverage and spectroscopic resolution and irradiance of the laser source to allow simultaneous detection of almost all isotopic components of the targeted gas with short acquisition times and with a compact technology. The accuracy of the resulting fractional isotopic ratio measurements are comparable to single-frequency-laser-based spectrometers [7,8,18,39–42] and to the mass spectrometry performance currently used for these kinds of measurements. Such accuracy is ensured by a not-trivial calibration of the spectral instrumental response of the DFCDS apparatus in order to identify the contribution of each interacting frequency of the comb with the sample gas. In this article, we report the capabilities of a slightly modified DFCDS approach, called direct comb Vernier spectroscopy (DCVS) [29,35], to perform fractional ratio isotopic measurements in 12C16O2 and 13C16O2 components of a CO2 gas sample around 5005 cm<sup>−</sup>1.

Our DCVS combines efficient comb filtering by using interferometric Fabry–Perot (FP) techniques in an adequate Vernier configuration with the spectral resolution of the FP-transmitted comb by using a high-resolution dispersive spectrometer. In addition, our spectrometer well isolates each of the sample-interacting teeth of the OFC from the others, and their spectral contribution can be extracted by using a simpler instrumental response approach, opening the way to very accurate lineshape studies. As a drawback, the detected OFC portions are quite limited compared to DFCDS, reducing the possibilities to reach a larger number of isotopologues of the gas in a single acquisition. Nevertheless, the reported fractional 13C/12C at 3% of precision is a proof of the principle of the capabilities of this technique for these kinds of measurements.
