The measurements acquired with the OP3 setup consist of background-subtracted spectra. The telluric signatures were then fitted to the HITRAN15 model (considering a temperature of 296 K and a pressure of 1 atmosphere) to provide their absolute spectral positions. This approach provides a very accurate spectral source independent of the setup spectral performances. This leads to high accuracy on the absolute calibration data for strong signatures (< 0.5 nm).
More specifically, the methodology for calibrating the spectral central wavelengths of the instrument consisted of the following steps. A background spectrum was acquired with no gas in the optical path and subtracted from the raw data. The HITRAN15 model data were convoluted to a Gaussian window with an FWHM of 3.5 nm for the VISNIR channel and 6.0 nm for the IR channel to match the average instrument spectral FWHM. Wavelength ranges exhibiting strong absorption features were selected based on the convoluted HITRAN data. The continuum was subtracted from the data on these intervals, allowing a match between the instrument data and the HITRAN data to determine the spectral central wavelengths.
The matching procedure is automatically performed using the algorithm presented in the following. For the selected wavelength range and spectels, which correspond to one or more absorption signatures, two parameters are optimized: the central wavelength of the first spectel and the sampling between the relevant spectels (i.e., the constant wavelength step between successive spectels). The objective (or cost) function of the optimization algorithm associates a wavelength to each pixel using these two parameters and interpolates the model transmittance at these wavelengths. It then calculates the Sum of Squared Differences (SSD) between the measured and interpolated transmittance. The optimization goal is to find values for the optimization parameters that minimize the SSD. The initial values and boundary settings of the algorithm have been selected 19 based on theoretical models and preliminary analyses.

The solver uses a Broyden–Fletcher–Goldfarb–Shanno algorithm to minimize the cost function21. This processing is expected to find values for the optimization parameters that provide a good match between the model and measured datasets while ensuring that successive spectels are separated by a constant wavelength step, which is a reasonable approximation over spectral ranges of a few tens of µm (the relevance of this approximation is checked afterward with the actual spectral variations of this wavelength step, see Fig. 13). However, in practice, this algorithm is often applied to a small number of signatures to simplify the problem and avoid any overfitting artifacts (Fig. 8 (A)). The quantification of errors on the spectral positions is not straightforward due to a large number of factors such as the noise and uncertainty in the measured data, the accuracy of the model data, the assumptions made by the optimization algorithm, the quality of the cost function, and the accuracy of the initial guess and boundaries of the optimization procedure. Nevertheless, we assess these errors by using a bootstrapping approach. Bootstrapping is a statistical method that generates resampled data to evaluate the error margin. Multiple bootstrap samples are first randomly generated from the original dataset. The optimization algorithm described previously is then run on each of these resampled datasets, and the distribution of results can be used to estimate the variability or uncertainty statistically. To estimate the error margin on the original result, the standard deviation of the resampled distributions is calculated for each spectel (Fig. 8).

[Figure: Fig. 8. Panel A: Example of a best-fit match of the OP3 data with the HITRAN-generated transmission spectra near the 1.365 µm water vapor signatures. See text for the explanation on how the error bar on the spectral position is derived for each spectel. Panel B: Same as Panel A but for the IR channel and the 2.65 µm water vapor signatures.]