Machine Learning Enables PPM-Level CO₂ Isotopologue Quantification

Researchers from the University of Adelaide, working across the Australian Institute for Machine Learning (AIML) and the Institute for Photonics and Advanced Sensing, and the ARC Centre of Excellence in Optical Microcombs for Breakthrough Science (COMBS) have developed a new approach that combines modern machine learning with direct frequency comb spectroscopy to achieve highly precise detection of the CO₂ isotopologues ¹²C¹⁶O₂ and ¹³C¹⁶O₂. Using a Menlo Systems FC1500 optical frequency comb as the light source, the team demonstrated that data-driven models can largely outperform traditional fitting routines, achieving mean absolute errors on the order of parts-per-million. The results show how intelligent data processing can unlock the full power of frequency comb spectroscopy and opens the door to new possibilities in gas sensing, particularly in settings where overlapping absorption features traditionally limit accuracy [1].

Direct comb spectroscopy is a simple but powerful technique [2,3]. It involves a broadband frequency comb probing an absorbing sample after which the transmission is analyzed by a spectrometer. Because the comb consists of evenly spaced, precisely known optical lines that can be tuned via its two degrees of freedom, f_rep and f_ceo, it provides an ideal light source for high-precision spectroscopy. While well-established for many applications, one particularly challenging use case remains: the analysis of complex gas mixtures. This capability can be crucial for industrial process control, breath analysis or environmental monitoring.

At the core of the experiment addressing this challenge is a Menlo Systems frequency comb, capable of probing a wide spectral region in a single shot. The comb light is split into reference and sample paths and then sent through a virtually imaged phased array (VIPA) spectrometer. The VIPA disperses the light into characteristic curved interference fringes, each containing detailed molecular absorption information.

For gas mixtures containing molecules with heavily overlapping absorption features, such as the two naturally abundant CO₂ isotopologues studied here, standard curve fitting can become unreliable. Traditional fitting routines depend on assumed line shapes, usually based on idealized Voigt profiles or related models. These profiles often fail to capture subtle collisional effects and instrument-specific line-shape distortions, which introduces systematic errors. This makes it difficult to extract accurate concentrations, especially when absorption bands blend together or when background structure is imperfectly corrected.

The team investigated whether machine learning could bypass these limitations by learning the mapping between measured spectra and molecular concentrations directly from thousands of labeled data points (i.e. spectral data and corresponding known CO₂ isotopologue concentration levels). Each measurement produced both a full VIPA image and a one-dimensional spectrum unwrapped from the image, which reveals the depth and shape of absorption features across the frequency range of interest. This allowed the researchers to test machine-learning approaches on both forms of data. Additionally, two data augmentation methods were combined with the original data to test how the models’ performance degraded with less training data.

On the image-processing side, they evaluated several pretrained computer vision models, including ResNet and VGG. These models have been trained on millions of natural images and are designed to recognize edges, textures and shapes. However, VIPA images differ significantly from typical photographic inputs. They contain repeated spectral orders because the VIPA image spans more than one free spectral range, meaning that regions can carry redundant information that does not contribute new absorption features. As a result, image-based models must learn not only the underlying molecular signatures, but also which parts of the image can safely be ignored.

On the spectral side, the team tested multilayer perceptrons (MLPs), convolutional neural networks (CNNS) and, most notably, a transformer model adapted for one-dimensional signals. Transformers work by dividing the spectrum into small segments (tokens) and then using an attention mechanism to learn how these segments relate to each other. Originally designed for language processing, the attention mechanism excels at capturing contextual and long-range relationships. In the context of spectroscopy, this means that the model can learn how different parts of the spectrum are relevant to one another, even when one region may be distorted or partially obscured.

Because modern AI models typically perform best when trained on large datasets, the team additionally implemented two methods of data augmentation, to test how size of the training set affects the outcomes. One augmentation strategy involved adding small amounts of Gaussian noise to the spectra. This makes the model more robust to the natural noise present in real measurements and encourages it to focus on meaningful absorption features rather than memorizing incidental fluctuations. The second strategy, called shifted spectra augmentation, is rooted in the fact that in practical spectrometers, the precise mapping between pixel index and optical frequency can shift by small amounts due to temperature variations or mechanical drift. By cropping each spectrum at slightly different starting positions within a narrow window where no important absorption structures are lost, the researchers generated slight horizontal shifts of the spectrum, reflecting realistic variations of each measurement. This allowed the transformer to learn that the underlying absorption patterns remain the same even when slightly displaced.

Among the tested architectures, the transformer model stood out as the best performer for the one-dimensional spectra. Without any augmentation, it reached mean absolute errors of about 131 ppm for the dominant isotopologue (¹²C¹⁶O₂) and roughly 4 ppm for the less abundant isotopologue (¹³C¹⁶O₂), dropping down to 15 ppm and 0.3 ppm respectively after the addition of shifted spectra data augmentation. These errors are roughly three orders of magnitude smaller than those obtained through the curve-fitting method used in earlier work on the same spectrometer, which reported average errors of 15,694 ppm for ¹²C¹⁶O₂ and 617 ppm for ¹³C¹⁶O₂. While not on par with the results obtained from spectral data, the models trained directly on VIPA images also showed improvements over curve fitting methods. ResNet, for example, achieved a few thousand ppm for ¹²C¹⁶O₂ and a few tens of ppm for ¹³C¹⁶O₂, which is still significantly better than curve fitting on both fronts.

Beyond raw performance, the team considered the interpretability of the models. Using class activation maps (CAMs), they identified which parts of each VIPA image the networks relied on for their predictions. The models consistently focused on the regions where the absorption features appear in the dispersed pattern, confirming that the predictions were driven by physically meaningful spectral structure rather than incidental image details. For the transformer, they used an approach called LIME to identify the most important parts of the spectrum for each prediction. These regions lined up with known CO₂ absorption bands, again reinforcing confidence that the model was using legitimate spectroscopic cues to inform its predictions.

This combination of accuracy and interpretability strengthens the case for machine learning in scientific instrumentation, where confidence in the measurement process is essential. Models that can justify their predictions and rely on physically meaningful spectral features are well suited for applications such as environmental monitoring or breath analysis.

For the photonics community, the message is clear. Direct frequency comb spectroscopy offers exceptional resolution, but its data can be challenging to analyze with traditional methods. Machine learning, when guided by domain knowledge, helps overcome these limitations. It enables frequency-comb and VIPA-based systems to reach higher precision without hardware changes and broadens their usability in scenarios where conventional analysis would be too slow or too restrictive.

As frequency-comb platforms evolve, intelligent data processing will play an increasingly critical role. This work demonstrates how transformers, data augmentation and explainable AI can form a reliable analysis pipeline that fully leverages comb spectroscopy. Their approach points toward future gas sensors capable of delivering precise, stable and trustworthy ppm-level estimates even in complex spectral conditions.

Menlo Systems is proud to be a partner of the ARC Centre of Excellence in Optical Microcombs for Breakthrough Science (COMBS) in Australia and to collaborating on such rapid advancements in science and technology.

Author: Emma Caldwell

Original Publications:

[1] M. Cochrane, S. K. Scholten, C. Perrella, A. van den Hengel, K. Dholakia, A. N. Luiten, Z. Liao, and J. W. Verjans, “CO₂ isotopologue quantification using direct frequency comb spectroscopy and machine learning,” ACS Omega 10 (43), 51443–51454 (2025).

[2] N. Picqué and T. W. Hänsch, “Frequency comb spectroscopy,” Nature Photonics 13, 146–157 (2019). DOI: 10.1038/s41566-018-0347-5.

[3] F. C. Roberts, H. J. Lewandowski, B. F. Hobson, and J. H. Lehman, “A rapid, spatially dispersive frequency comb spectrograph aimed at gas-phase chemical reaction kinetics,” Molecular Physics 118(16), e1733116 (2020). DOI: 10.1080/00268976.2020.1733116.