Long-range, open path CO2 measurements using tunable diode laser absorption spectroscopy: analytical, numerical, and experimental comparison

Tunable Diode Laser Absorption Spectroscopy (TDLAS) is a well-established technique for sensitive gas detection based on wavelength-selective absorption. In recent years, it has gained increasing relevance for long-range atmospheric measurements of greenhouse gases such as CO₂. This work presents an analytical, numerical, and experimental investigation of wavelength-modulated TDLAS applied to long open-path CO₂ sensing over kilometer-scale distances.

A distributed feedback diode laser is sinusoidally modulated in injection current to generate a periodic wavelength sweep across a selected CO₂ absorption line. The transmitted signal, strongly attenuated after propagation over approximately 2 km, is detected and demodulated using phase-sensitive lock-in amplification to extract the first, second, and third harmonic components (1f, 2f, and 3f). This approach enables the reliable retrieval of extremely weak absorption signals under low signal-to-noise conditions. Harmonic amplitude ratios, particularly 2f/1f and 3f/1f, are analyzed as functions of the CO₂ mixing ratio under controlled laboratory conditions.

To interpret the measured harmonic signals, an analytical formulation based on the Beer–Lambert law and a parameterized description of laser wavelength tuning and optical power modulation is developed, and it is compared with numerical simulations and experimental results. We demonstrate that at elevated CO₂ concentrations, the commonly used 2f/1f ratio exhibits saturation, while higher-order ratios, such as 3f/1f, retain sensitivity and provide improved robustness for long-range measurements.

Furthermore, we illustrate that even small offsets between the modulation center and the absorption line center introduce systematic odd–even harmonic mixing, increase temperature sensitivity, and compromise the stability of harmonic-based retrievals. The combined analytical, numerical, and experimental analysis provides practical guidance for optimizing wavelength-modulated TDLAS systems that employ lock-in detection for long-range atmospheric CO₂ monitoring.