In order to ensure a sufficient optical throughput at THz frequencies the MULTICHARME Chernin cell configuration employed uses two rectangular field mirrors (266 × 310 mm and 222 × 50 mm), and three circular objective mirrors (diameter 130 mm). As shown in Fig. 1b, we have opted for the modified version of the Chernin cell with the input and output windows on both sides of the field mirrors (Chernin, 2001). MULTICHARME has been designed in order to maximize the size of the mirrors to account for the large size of the beams and the strong divergences at longer wavelengths in the THz domain. We were nevertheless limited by the size of the flanges coupled to the DN 450 circular ports of the CHARME ASC. All mirrors have the same radius of curvature (ROC = 5000 mm) corresponding to the MULTICHARME base length. Fused silica substrates were used for the field mirrors, K9 for the objectives. To optimize the reflectivity from near-IR to THz domain, i.e. three frequency decades from 300 to 0.3 THz, a coating of 500 nm silver protected by 10 nm of Al2O3 was used. These relatively large mirrors were manufactured by the Anhui Institute of Optical and Fine Mechanics over a period of several months to build the substrates and to deposit the coatings. This institute has already successfully developed a Chernin cell for the detection of atmospheric radicals with Faraday rotation spectroscopy in the mid-IR (Fang et al., 2020).

The two optical mounts, equipped with the three objective mirrors and the two field mirrors, constitute the Chernin cell presented in Fig. 1. Using the DN 450 access ports (A1 and A2 in Fig. S1) and custom-made vacuum enclosures, they are located on opposite ends and placing the mirrors inside of the cylindrical chamber. Two aluminum optical mounts were constructed to hold the mirrors. The mass of the additional components added to CHARME was 160 kg for each of the two DN 450 ports located at opposite ends.

The total deformation of the Chernin cell and the corresponding mounting flanges were analyzed under static conditions. The forces that were considered were their own gravity and the atmospheric pressure on the outer surface of the flanges when the chamber was in a vacuum state. The maximum displacements have been estimated to be less than 30 µm. A picture of the five mirrors is given in Fig. S2. The characterization of their reflectivity in the IR and in the THz domains is described in Sect. 2.2.2 and 2.2.3, respectively. In order to accurately and easily control the optical alignment and the path length, both the field and objective mirrors are equipped with computer-controlled micrometric screws: MULTICHARME can be aligned with 18 compact linear motorized actuators TRA25PP from the MKS/Newport company (6 actuators are fixed on the field mount to adjust the 3 degrees of freedom of the 2 field mirrors; 12 actuators are on the objective mount: 9 to control the position of the 3 objective mirrors and 3 to adjust the relative orientation between field and objective blocks). The actuators are controlled by a home-made Arduino-based system located outside the cell (see Fig. S3). This system allows each actuator to be selected independently and to control their movement. The “5-mirror configuration” is easy to align, forms a matrix with an adjustable number of rows and even columns on the field mirrors and provides good vibration stability. Different spot patterns obtained with a He-Ne alignment laser are shown in Fig. S4 highlighting our ability to adjust matrix arrangement on the field mirror for different path lengths in MULTICHARME from 120 to 540 m.

The characterization in the near-IR has been performed using a continuous-wave external cavity diode laser (ECDL, Toptica DL pro) tunable from 1340 to 1450 nm with an output power of 80 mW, a spectral width of 100 kHz and a mode-hop free tuning range of 20 GHz. The ECDL source, the photodetector and the transfer optics were placed on an optical breadboard fixed to the field flange. The IR input and output were coupled to the CHARME ASC by two 76.2 mm diameter ZnSe windows with a 1∘ wedge giving a theoretical transmission of about 70 % at 1.4 µm.

The IR optical configuration is presented in Fig. 2b, an additional mirror was inserted into the beam path to coaxially inject a red MKS/Newport He-Ne laser (5 mW) with the IR beam axis in order to facilitate the alignment of the Chernin cell. This enables the IR path length in MULTICHARME to be evaluated by the observation of the matrix arrangement of the He-Ne spots on the field mirrors observed from a BK7 window placed on the objective transfer flange. All adjustments and path length changes can be made in situ, without venting CHARME, with the computer-controlled actuators. Once the laser was adjusted for the desired operating range, a wavelength calibration was performed (Burleigh WA-1500) with an accuracy better than 4 × 10-3 cm-1. An InGaAs detector (Thorlabs PDA400) with a typical bandwidth of 10 MHz was used for the detection. Spectra were obtained by applying a voltage ramp to the piezo actuator allowing an excursion of 0.17 cm-1 around the line center at a frequency of 1.3 Hz. The received photodiode signal was averaged by a digital oscilloscope (DSO-X 2002A Agilent Technologies, maximum frequency 70 MHz). The signal was typically accumulated over 16 ramp cycles with a sampling of 12.5 kHz (10 bits of vertical resolution).

To characterize the performance of MULTICHARME in the near-IR, we have examined the optical throughput in the modified Chernin multi-pass cell by measuring the output IR power for several different matrix arrangements (Glowacki et al., 2007a). It corresponds to 12 matrix configurations from 24 to 108 passes, for path lengths from 120 m (3 rows × 4 columns) to 540 m (9 rows × 6 columns), respectively. The output powers shown in Fig. 3 were measured with a PDA400 power-meter from Thorlabs with an accuracy of 1.2 µW. The variation of the output power with the number of reflections was modeled by a power law P=A×Reffn, where A is a constant corresponding to the received power with no reflection, Reff is the effective mirror reflectivity at 1.4 µm and n is the number of reflections. An effective reflectivity of the mirrors at 1.4 µm was adjusted to 95.98 ± 0.06 % (error given by the fit) with a weighted fit using the estimated error bars taking the accuracy of the IR photodetector into account. This value is relatively good considering the expected decrease of the IR reflectance at shorter wavelengths.

Several compact and versatile solid-state sub-THz sources are currently used in our laboratory for trace gas monitoring using high resolution rotational signatures of atmospheric pollutants in realistic media, e.g. industrial combustion (Mouret et al., 2013) or gas emitted in food packaging (Hindle et al., 2018). In this study, a commercial Virginia Diode Inc amplified multiplication chain (AMC) driven by a microwave synthesizer (Rhodes & Schwarz SMA 100B) was used (see Fig. 2c). Two Menlo systems TPX lenses of 50.8 mm diameter and 100 mm focal length were used to collimate the beam at the entrance of the chamber and refocus the output beam onto the detector. The propagation of the THz radiation in MULTICHARME was modeled as a Gaussian beam using a program developed by Lightmachinery inc. (Williams, 2019​​​​​​​) showing that the use of f = 100 mm lens provides the best results taking into account the beam properties (waist and divergence), the dimension of MULTICHARME and the different losses (transmission through the window & reflections on the field and objective mirrors). Two different AMC multiplication stages were used, the first (multiplication × 18) to cover the 140 to 220 GHz frequency region with an average power of 3 mW and the second (multiplication × 54) to cover the 440 to 660 GHz region with an output power of around 50 µW. To detect the MULTICHARME output THz signal, two VDI Schottky zero biased detectors (ZBD) WR5.1 and WR1.5 were chosen with typical responsivities of 1000 and 2400 V W-1, respectively for the first and the second stages. The typical noise equivalent power (NEP) of these Schottky diodes is estimated to be 10 pW Hz-1. Both amplitude modulation (AM) and frequency modulation (FM) schemes were employed. The simultaneous use of AM and FM as a function of frequency proved useful to minimize the effects of the standing waves in the baseline, (see Sect. 3). A computer-controlled Ametek 7230 lock-in amplifier recovered the measured signal as a function of the frequency. High resistivity float zone silicon windows with a theoretical transmission of more than 50 % were used for the entry and exit of MULTICHARME during the THz measurements. This material is opaque at the He-Ne laser wavelength, so the THz beam alignment in MULTICHARME was performed by superimposing the THz beam onto the IR beam at the entrance of MULTICHARME and on the objective mirrors.

As done with the IR radiation, we have measured the THz output power for different path lengths. These measurements presented in Fig. 3b were performed around 190 GHz corresponding to the maximum output power at the rank × 18 of the AMC. With a lower input power and a more divergent beam, only 5 matrix configurations corresponding to path lengths from 120 m (24 passes) to 280 m (56 passes) were accessible at this frequency. If we consider just the detector NEP, 50 pW should be detectable with a time constant of 1 s, i.e. four orders of magnitude below the power level measured for a 280 m path length. Here the strong limitation to reach larger path lengths is the divergence of the THz radiation and the size of the THz waist on the field mirrors. Reaching a path length of 280 m with an amplified frequency multiplication chain which is a highly divergent source, is a significant improvement compared to commonly used set-ups. Extending the path length further should be possible for higher frequencies or with more powerful THz sources. An overview of the best performance reached by rotational sub-mm-wave/THz long-path absorption spectroscopy is provided (Cuisset et al., 2021): the maximum THz path length in a White-cell was obtained with a weakly divergent and bright synchrotron source but it never exceeded 200 m (Brubach et al., 2010); longer interaction path lengths are accessible only in Fabry-Perot resonators with intracavity spectroscopic techniques (Hindle et al., 2019). By fitting, with the power law, the THz output power, an effective THz reflectivity of 94.2 ± 0.4 % (error given by the fit) has been found for MULTICHARME. This value is only slightly lower than the near-IR value found in Fig. 2a. Therefore, MULTICHARME guarantees a reflectivity better than 94 % on more than 3 decades of frequencies. With a unique modified Chernin type multi-pass cell, long path absorption spectroscopic measurements are now possible from the THz to the near-IR domain in an ASC such as CHARME.

The THz rotational spectroscopy is a powerful technique for detection at low pressure due to its great selectivity allowing discrimination between: (i) polar compounds in complex chemical mixture (Bigourd et al., 2006, 2007; Mouret et al., 2013); (ii) isomers and stable conformers amongst VOCs (Roucou et al., 2018, 2020) and (iii) isotopomers of small polar atmospheric compounds in natural abundance (Hindle et al., 2019). For this last point, it has been demonstrated that THz rotational spectroscopy is able to determine relative isotopic abundances of small polar compounds with accuracies of a few % (Lou et al., 2019). In order to highlight the selectivity of THz monitoring in MULTICHARME, we present in Fig. 6 some measurements of four different isotopomers of pure N2O, in natural abundance. Table 1 summarizes abundances, line frequencies and intensities tabulated in spectroscopic databases (Pickett et al., 1998; Gordon et al., 2022). For the four isotopomers, the differences between the observed and the JPL frequencies never exceed 500 kHz. In Fig. 6a, for each path length the absorption of the R(23) rotational transition of the most abundant 14N14N16O isotopomer is saturated. Nevertheless, the equivalent transition for the 14N15N16O expected to be only 43 MHz (1.4 × 10-3 cm-1) lower in frequency with an intensity around 260 times weaker is clearly observed and resolved. The other monosubstituted isotopomers 15N14N16O and 14N14N18O are also observed with the shortest path length L = 120 m at a pressure close to 1 mbar (Fig. 6b). An isotopic ratio [15N14N16O] / [14N14N18O] of 1.87 is deduced from the intensities of the two absorption lines plotted in Fig. 6b. This value is sufficiently close to the expected value of 1.83 deduced from the natural abundances in Table 1 to suggest the possibility to use THz spectroscopy with MULTICHARME for the analysis of the isotopic composition of atmospheric trace gases and to detect anomalous isotopic signatures, a powerful approach to identify sources and sinks of pollutants and/or greenhouse gases (Röckmann et al., 2001).

Finally the discrimination of the N2O isotopomer rotational lines (especially the lines of 14N15N16O and 14N14N16O on Fig. 6a) highlights the exceptional selectivity of the THz rotational spectroscopy. Indeed, when the measurements are performed at low pressure (typically stratospheric pressures) the line widths converge to the Doppler limit. For molecules such as N2O, the Doppler line widths, proportional to the line frequencies, typically vary from hundreds of kHz in the THz domain to hundreds of MHz in the IR and to several GHz in the UV visible domains. There is no doubt that THz high-resolution monitoring exhibits a significantly better selectivity compared to the IR/UV. In complex chemical mixtures studied in ASC, the THz method allows individual molecular signatures to be observed and resolved even for compounds with close molecular structures (isomers, conformers, isotopomers etc.). Moreover, the high-resolution THz method strongly limits the problem of interference substances in the gas monitoring. With photon detection in the IR/UV spectral domain, it is generally not possible to resolve individual rovibrational or rovibronic transitions with the typical instrumental resolutions (e.g resolutions of FTIR spectrometers coupled to ASC are limited to few GHz) and some corrections due to interferences with other species have to be taken into account in the trace gas quantification (Harris et al., 2020).

A priori all the polar compounds may be detected and quantified from their rotational signatures. In practice, for THz atmospheric monitoring at trace levels, we must opt for the lighter and the more strongly polar compounds with intense and resolved rotational transitions generally listed in the international databases. For these molecules, rotational line frequencies, line widths and line intensities are known with a good degree of accuracy allowing, if the line profile is preserved during the measurement, an absolute quantification without any standard of calibration.

In the present article, we demonstrate this statement in Fig. 7a by fitting the absorbance of the R(22) rotational line of N2O diluted in N2 at 1000 ppmv with a Voigt profile . Prior to the fit, two baseline treatments have be done in order to reduce the oscillations due to standing waves occurring in MULTICHARME: first of all, due to the capacities of the RF synthesizer, we have applied simultaneously to the amplitude modulation (AM) a rapid frequency modulation (FM) with a depth exceeding the FSR of the interaction length allowing a partial minimization of the effects of the standing waves. Next, during the posttreatment of the recorded signal leading to the absorbances shown in Fig. 7, an FFT filter was used to further reduce the rapid oscillations of the baseline. This treatment is described in Fig. S5. We have been careful that the postprocessing does not affect the line shape and hence the error of the resulting number density. The number density of absorbing N2O molecules in molec. cm-3 is directly deduced from the relation: N=∫A(ν)dνS×L with the numerator ∫A(ν)dν corresponding to the integral, in cm-1 units, of the fitted absorbance by a Voigt profile and for the denominator the product of the line intensity S in cm molecule-1 tabulated in HITRAN (Gordon et al., 2022) with the path length L in cm. Finally the mixing ratio χ is deduced by: χ=NPkBT with P and T, the pressure and the temperature in CHARME during the measurement.

In Fig. 7a, an integrated absorbance of 2.4 ± 0.3 MHz was fitted giving a N2O number density of N = (1.4 ± 0.2) × 1013 molec. cm-3 and a mixing ratio 1140 ± 160 ppmv. Taking into account the uncertainty of the fit, mainly due to the remaining baseline oscillations, the density number estimated by the absolute quantification procedure is in agreement with the value of the standard gas used. Based on the previous method, another example is given in Fig. 7b with the quantification of unknown quantity of ozone in CHARME. Ozone is a key compound in atmospheric chemistry, both in the troposphere and stratosphere (Finlayson-Pitts and Pitts Jr., 1999) and a real time in situ monitoring of reactive ozone is very interesting for numerous ozonolysis reactions occurring in our atmosphere especially with VOCs. In our study, ozone was produced at atmospheric pressure by a generator (Air Tree Ozone Technology C-L010-DTI), which converts O2 into O3 from zero air exposed to a high voltage corona discharge. Based on the calibration of the ozone generator, performed with a photometric O3 analyzer, and the injection time (90 min), the ozone volume ratio introduced in CHARME was estimated to be around 500 ppmv. Then the ASC was pumped down (in 45 min) to 1.5 mbar and the THz spectrometer was used to detect and quantify O3 traces from individual rotational transitions. The O3 wall losses occurring during the ozone introduction as well as during the pumping procedure contribute to reduce the ozone mixing ratio to an unknown lower value which is measured by THz spectroscopy. Ozone is an asymmetric top with a large number of rotational transitions in the THz domain and its rotational frequencies and intensities have been determined with accuracy in the THz domain (Colmont et al., 2005; Birk et al., 1994). The 251,25←240,24 transition centered around 610 GHz with a tabulated intensity of S = 4.035 × 10-22 cm molecule-1, the most intense on the source's band emission, was chosen for this reason. A mixing ratio of 258 ± 22 ppmv was deduced from the fit of a Voigt profile to the line presented in Fig. 7b. This value is around two times lower than the initial concentration injected in the ASC at atmospheric pressure. This difference is due to the losses on the chamber walls during the ozone injection and the pumping times from atmospheric pressure to 1.5 mbar (135 min). In Sect. 3.2.3, we show how to characterize at low pressure the kinetics of the O3 losses on the CHARME walls by THz monitoring.

In order to determine the limit of detection (LOD), we have considered the baseline oscillations as our detection noise and the LOD as the concentration obtained with a signal to noise (S/N) ratio equal to 1. Both for N2O and O3, the S/N of Fig. 7 are estimated to 15 by taking the maximum amplitude of the rotational line as signal and the maximum of the amplitude of the residual away from the line as noise. Therefore, an LOD of around 75 and 15 ppmv may be estimated respectively for N2O and O3. These LOD are slightly lower than the mixing ratio errors obtained with the uncertainties on the fitted area. For N2O, the LOD obtained by THz spectroscopy in this study are more than three orders of magnitude larger than the LOD on the strongest mid-IR rovibrational bands by tunable diode laser spectroscopy (TDLAS) even with measurements at low pressure (Hoor et al., 1999). With the THz method, for instance the LOD is limited to 15 ppmv. Using incoherent broad band cavity-enhanced absorption spectroscopy in the visible domain, an LOD of 120 ppbv was obtained in the Dunkirk ASC at atmospheric pressure (Wu et al., 2014). In order to improve the sensitivity of the THz method, we have to correctly model the baseline and to remove its variations due to multiple interfering stationary waves in MULTICHARME. Work is under progress to this goal.

In Fig. 8, we demonstrate the ability of the THz source coupled to MULTICHARME to monitor the ozone reactivity at low pressure in CHARME. To achieve the same O3 251,25←240,24 rotational transition centered at 610 365.35 MHz was targeted and measured during 12 h, over a frequency range of 60 MHz, every 3 min. Then 240 absorbance spectra were obtained and their time evolution as a 3D plot is shown in Fig. 8a. For each spectrum, we have repeated the baseline treatment and the line profile fit described in Fig. 7b. Then the data treatment to obtain the 240 absorbances of Fig. 8a and the 240 mixing ratios of Fig. 8b has been batch processed with the Origin Software. As shown in Fig. 8b, the ozone concentration decreases exponentially from 230 to 15 ppmv in 12 h. We have considered the first-order kinetics of the ozone decay due mainly to the ozone losses on the chamber walls. The concentration decrease was fitted using the exponential law [O3]t=[O3]0e-t/τO3. A lifetime τO3 of 3.4 ± 0.1 h was deduced from a fit weighted on the instrumental errors corresponding here to LODs estimated with the same method as explained in the previous subsection with the Fig. 7b. In the present case, we can see that for ozone concentrations lower than 50 ppmv, the lower error bars point to zero or negative values indicating that the LOD is reached at this level of concentration.

The losses of ozone in CHARME have already been investigated at atmospheric pressure with a UV-photometric analyzer (Thermo Scientific 49i; λ = 254 nm). Using several initial concentrations, from 0.7 to 4.8 ppmv, the O3 lifetimes τO3 were deduced from the first-order kinetics O3 wall loss reactions and varied from 6.2 to 13.8 h (Fayad, 2019), depending on the cleanliness of the chamber walls, which can change for different initial concentrations of ozone. Compared to the previous measurements performed in CHARME with a UV photometry analyzer, a shorter lifetime was determined by our low pressure THz measurements. Itoh et al. (2004, 2011)​​​​​​​ have developed and experimentally verified a physical model enabling understanding of the pressure and the wall material dependencies of the ozone-to-wall loss rate in a cylindrical tube (Itoh et al., 2004, 2011). They showed that the variation of the ozone lifetime with the pressure due to wall losses can be reproduced by the Eq. (1): 11τO3∼DePfα,l,β+kNP, where P is the pressure, N is the molecular density, f(α,l,β) is a function depending on geometrical and surface properties of the chamber (a and l are the radius and the length of the cylinder, respectively and β is a surface parameter), De is an equivalent diffusion coefficient giving the magnitude of the surface loss rate of ozone according to the material and k is a loss rate coefficient due to collisions with oxygen (Itoh et al., 2011). The pressure measurement conditions in THz rotational high-resolution spectroscopy are typical for chamber cleaning activities. Under these conditions it is known that the O3 loss in the chamber is dominated by wall reactions and not by reactions with O2. It corresponds to the first term of Eq. (1) and, therefore, as it is shown by our results, a decrease of the lifetime at low pressure was expected due to the reinforcement of the losses by the ozone diffusion on the chamber wall. That is why these conditions are chosen to get rid of impurities, such as VOCs, on the chamber wall.