## 1 Introduction  
Nowadays, the concentration of greenhouse gases (such as carbon dioxide (CO\({}_{2}\)), methane (CH\({}_{4}\)), nitrous oxide (N\({}_{2}\)O), etc.) in the atmosphere is increasing due to the anthropogenic emissions. Thus, there is a need to determine the anthropogenic contribution against the natural background and to recognize emissions from various industries [1; 2; 3]. One possibility for doing this is via the carbon isotope (\({}^{12}\)C and \({}^{13}\)C) ratio measurements of carbon dioxide (CO\({}_{2}\)) and methane (CH\({}_{4}\)) in the atmospheric air [4; 5]. So far, the isotope ratio Raman spectroscopy of CO\({}_{2}\) has been addressed in several research works. In [6], the authors have found a way for determining the isotope-delta values (the relative difference of isotope ratios with respect to the reference material) \(\delta^{13}\)C using micro-Raman spectroscopy. A technique for monitoring \({}^{13}\)CO\({}_{2}\) by cavity-enhanced Raman spectroscopy was developed in [7]. Quantitative analysis of carbon isotopic composition in CO\({}_{2}\) with the estimation of the measurement uncertainty was performed in [8]. A detailed experimental and theoretical study on isotopic surface-enhanced Raman spectroscopy was done in [9]. Defining the isotopic composition of greenhouse gases helps to constrain global budgets and to study sink and source processes [10]. CH\({}_{4}\) is an important anthropogenic and natural greenhouse gas and, moreover, it participates in atmospheric chemistry through its reaction with the hydroxyl radical [11]. Since individual CH\({}_{4}\) sources have characteristic isotope signatures, carbon and hydrogen isotope ratios of CH\({}_{4}\) (e.g., \(\delta^{13}\)C-CH\({}_{4}\)) have been useful in constraining the global methane budget [12]. By precisely measuring the ratio of \({}^{13}\)C to \({}^{12}\)C, one is able to determine the source of methane [13]. The individual values depend on the mechanisms of the CH\({}_{4}\) formation and consumption prior to its release into the atmosphere. It was shown [14] that it is possible to accurately measure the methane content in natural gases using Raman spectroscopy. The results of this work show the possibility of isotope-ratio analysis of methane. Nowadays, isotope ratio measurement systems based on optical spectrometers are used because of several advantages. The first one is the fundamental possibility to distinguish the isotopologues (molecules that differ only in their isotope composition) with the same molecular weight but different isotopic composition such as \({}^{16}\)O\({}^{13}\)C\({}^{16}\)O and \({}^{16}\)O\({}^{12}\)C\({}^{17}\)O (both representing carbon dioxide) [15]. Second, it is possible to perform calibration-free absolute measurements of isotopologues based on ab initio calculations of line intensities [16]. This is a relevant possibility in the metrology of isotope ratios because the International Committee for Weights and Measures (CIPM) encourages the development of absolute isotope ratio measurement values for reference materials [17]. Third, such systems are relatively easy to use, field deployable and low cost. They require no complicated sample preparation, provide real-time data, and allow for in situ monitoring with a spectroscopic selectivity. The disadvantage of the isotope ratio optical spectrometers compared to mass spectrometers is still low accuracy [18]. Raman spectroscopy has advantages over traditional methods in the analysis of pure isotopologues. Due to different selection rules, Raman spectroscopy can detect even diatomic homonuclear molecules such as O\({}_{2}\) or N\({}_{2}\)[19; 20; 21; 22]. The development of Raman-based gas analyzers was presented in several papers [23; 24]. A system for analysis of mixtures of CO and H\({}_{2}\) (synthesis gas) was proposed in [25]. The Purcell enhanced Raman scattering (PERS) device was used for isotopic gas analysis in [26]. A Raman analyzer for sensitive natural gas composition analysis was described in [27].