**4. Discussion**

Abundances of 12C16O2 and 13C16O2 are measured with a precision of 2.1% and 2.7%, respectively, in agreement with the HITRAN values. Consequently, a fractional isotope ratio R<sup>13</sup>*C*/12*<sup>C</sup>* = 0.0116 (4) is determined, as expected for a CO2 gas sample with the current natural isotopic content [44]. The present measurements can be considered a proof of principle of the DCVS applied to fractional isotopic ratio determinations, even if the experiment was performed at only one pressure, which was selected for giving the best precision performance for both isotopes in a single OFC scan. The final uncertainty is due to several issues: S/N ratio of each transmittance spectrum, limited scan of the full spectral profile of the transitions, and saturated absorption effects. The last two issues are particularly present in the 12C16O2 transition, which shows a quasi total saturation of the absorption, and the high frequency side is unrecorded. The final precision of *a* <sup>12</sup>*C* determination is strongly limited by these experimental issues, which must be avoided to obtain the determinations for this isotope that are comparable to those achieved in other DFCDS [25]. Measurements at lower pressures could avoid saturation effects for this transition, paying for a decrease in the S/N ratio of the 13C16O2 transition by considering that the gas sample and absorption path are shared for both transitions. We are confident that measurements with gas sample pressure between 10 and 55 mbar could lead to a result that is compatible with the present uncertainties of the *a*13*<sup>C</sup>* . In addition, detection of the complete transition profiles would allow a significant improvement of the spectral parameters determination, including *a* <sup>12</sup>*C*, even at the gas pressure of the experiment. A more accurate choice of the frequency parameters of the OFC and FP could allow to center both transitions in the present maximum continuous scan of the OFC frequency for a single acquisition. Alternatively, consecutive OFC-shifted scans could be combined to increase the scan range. Through global fits, spectra recorded at different gas pressures, and

involving other transitions of the sample gas, could be considered all together, increasing the final precision. Finally, combining detection and scan schemes as those described in [30,31] with the high Vernier filtering of our DCVS spectrometer, would allow faster broadband acquisitions.

Besides the fractional isotopic ratio, other spectral parameters of the targeted transitions are determined in our measurements. We find the transition frequencies to be in agreement with the HITRAN values, considering one standard deviation uncertainty. Their absolute value is reported with a precision of 1×10−<sup>8</sup> and 4×10−<sup>8</sup> for the 12C16O2 and 13C16O2 transitions, respectively. Instead, a small disagreement with the HITRAN values of the collisional broadening coefficients should be noted. Nevertheless, we believe that for our single pressure measurement, such discrepancies could be expected for a parameter that is just measuring a pressure-induced effect.

The present results show the capabilities of DCVS for precise measurements of the fractional isotopic ratios in a sample gas, with potential applicability in the detection of rare isotopologues [46], where absorption background from the others must be avoided. In principle, our technique could be applied to different kinds of OFC (ICL and QCL combs) in order to realize a compact setup toward the mid-infrared region.

**Author Contributions:** Conceptualization and methodology, R.E., M.S.d.C. and P.C.P.; comb laser development, J.J. and M.E.F., experimental data recording, M.S.d.C. and P.C.P.; formal analysis and software, R.E.; data analysis, P.C.P.; writing—original draft preparation, P.C.P.; writing—review and editing, M.S.d.C. and R.E. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the project Extreme Light Infrastructure-Italy (ELI-Italy) and by the QOMBS project (FET Flagship on Quantum Technologies grant No. 820419).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data supporting this paper are available from the corresponding authors upon reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **References**

