## 2 CLaDS Basic Operation Principles
The latter can significantly benefit remote sensing applications that rely on multiple optical paths of different lengths to perform tomographic measurements of atmospheric constituents [16, 17]. Despite the fundamental advantages of direct CLaDS, previous studies have revealed some limitations in this technique. Although theory suggests that the CLaDS signal is baseline-free, in practice a weak baseline can be observed when the interferometer in the direct CLaDS setup is not perfectly balanced and the chirp rate is not truly linear (both can occur in practical implementations) [9]. Moreover, with chirp rates typically between \(10^{12}\) and \(10^{15}\) Hz/s, the acquisition bandwidth (BW) required to capture the dispersion spectrum must be very broadband, which leads to an increase in the FM-demodulation noise (proportional to BW\({}^{2}\)). On the other hand, with lower chirp rates the CLaDS signal amplitude is proportionally reduced and the signal-to-noise ratio (SNR) decreases [18]. Hence, direct CLaDS requires the chirp rate and acquisition bandwidth to be carefully optimized for the best performance. In order to overcome the identified limitations in direct CLaDS, a CM-CLaDS technique that is based on a harmonic detection scheme has been developed [19]. In the QCL-based CM-CLaDS the laser frequency is chirped with a fast sinusoidal waveform added to the injection current. The heterodyne detection followed by the FM-demodulation is similar as in direct CLaDS. However, the CM-CLaDS signal is recovered in the post-processing of the time series of the FM-demodulated beat-note frequency. The beat-note frequency time-series undergoes Fourier analysis and the amplitude of the 2 nd harmonic component of the chirp modulation frequency is recorded as the CM-CLaDS signal. Narrowband analysis of the 2f signal allows reduction of the acquisition bandwidth, which leads to reduction of the FM-noise and increases the SNR. Moreover, it has been shown in [19] that in CM-CLaDS only the first harmonic is affected by the imbalance of the interferometer arms. Therefore, the 2 nd harmonic signal is baseline-free which allows for convenient operation of CM-CLaDS system in a line-locked mode (laser frequency is locked to the peak of the transition) without the need for laser frequency scanning and spectroscopic data fitting for concentration retrieval. A transition from direct CLaDS to CM-CLaDS is analogous to the transition from DLAS to WMS that also allows for continuous monitoring of the sample concentration in a line-locked mode. Figure 1: Schematic diagram of mid-IR CLaDS setup (M-mirror, BS-beam splitter). However, in WMS the 2f signal must be corrected for the laser power/sample transmission fluctuations [20; 21; 22]. Such corrections might be challenging or even not possible in the presence of large changes in the received optical power levels, especially when using mid-infrared photodetectors that usually have nonlinear response. Moreover, such nonlinearities can create a baseline in the WMS spectrum that generates additional errors in 2f/1f normalization. These issues are not affecting CM-CLaDS signal due to its immunity to optical power variations [19].