The optical layout of the FIRMOS interferometer is composed by double-input and double-output Mach–Zehnder configuration. The setup allows full tilt compensation by employing a movable unit with roof-top mirrors (RTMU). Additional flat mirrors are used on the right arm of the interferometer to compensate for slit yaw. Parabolic mirrors (45∘ off axis) enable light focusing on the detectors, encapsulated with caesium iodide windows. The reference source is a 785.9 nm single-mode thermally stabilised laser (Thorlabs). The latter is driven with a constant current from a controller developed in-house and already employed within the previous REFIR-PAD instrument. The reference laser follows the same optical path as the infrared beam, with dedicated optics joined to the same mountings as for the main measurement.

Radiometric accuracy is achieved by employing three blackbody sources, the hot (HBB) and the cold (CBB) calibration blackbodies, and the reference blackbody (RBB). A rotating mirror (PM0) located at the interferometer first input can select either the HBB, the CBB, or the sample scene (Fig. ); the contribution of this mirror to the instrument response is therefore accounted for in the calibration procedure (see Sect. ). The RBB, located at the second input, is in thermal equilibrium with the other optical components. At every measurement cycle, the calibration procedure is performed before and after the sample scene.

The FIRMOS setup was designed to maximize the optical throughput by employing 76.2 mm diameter optics while maintaining a field of view of 22 mrad. In addition, the optical system is image forming at the detector, although the latter is a single pixel (diameter of 2 mm). The above features are meant to enhance the observed scene selectivity while maintaining good signal-to-noise ratio, and therefore to facilitate the development of software tools for geophysical parameters retrieval.

The field of view in FIRMOS is defined by the optical path length of the instrument, the internal pupil radius, and the detector area, the latter being the main limiting factor in the current design. The optical specifications of the instrument are listed in Table .

To cover the IR spectral range from 100 to 1000 cm-1, the instrument adopts wideband germanium-coated biaxially-oriented polyethylene terephthalate (BoPET) beam splitters (BS) and room temperature deuterated L-alanine doped triglycene sulfate (DLATGS) pyroelectric detectors. The absorption of the BoPET BS substrate causes some degradation in efficiency in some narrow bands around 730, 850, 873, and 973 cm−1, as can be seen in Fig.  which shows the typical 4RT efficiency. The instrument spectral range is limited at low wavenumbers by the absorbance of the detector CsI windows and at high wavenumbers by degradation of the optical performance due to BSs flatness errors (see Figs. b and ).

The BS samples were manufactured at INO-CNR and tested with a Newton interferometer, to select those with maximum flatness. The interferometer is capable of detecting flatness anomalies with 0.1 µm precision by employing a reference surface with a flatness of λ/20, a monochromatic source, and a digital camera. The pattern observed in the case of membranes with a divergence from flatness of a few micrometres is of the saddle or multi-saddle type, especially close to the edge. The saddle peak-valley distance is evaluated through the measurements of the number of fringes on the main saddle along a track (Fig. b). The best two BS samples, with flatness error of less than 2.5 µm peak-valley, were integrated on FIRMOS to guarantee good performance over the 100–1000 cm−1 range.

A lightweight and compact linear stage model (Zaber model X-LSM025A; mass: <0.5 kg, height: 20 mm, centred load capacity: 100 N) was used, installed within a notch of the breadboard below the RTMU to perform the interferometric scan. A scanning speed of 0.25 mm s-1 in a 30–60 s acquisition time for a single scan is used. The typical standard deviation of speed over a scan was obtained experimentally as 0.043 mm s-1 at a 0.25 mm s-1 scan speed, sufficiently stable to be accounted for during the signal analysis.

The RTMU was manufactured from a monolithic aluminium piece (see Fig. b). The mirrors are placed in a roof-top configuration and fixed by a system of springs and screws.

The instrument was designed for easy transportation and deployment. Its size is 85×95×50 cm, it weighs 80 kg, and the power consumption is 60 W. A plastic enclosure was used to protect against environmental conditions, an 8 cm diameter aperture with a motorized shutter was used for observation.

The instrument breadboard was realized as a monolithic aluminium slab with a mass of 17.5 kg and dimension of 520×540×45 mm (L×W×H). Rods spacing and tightening points were initially designed balancing dimensions, mass, and stiffness of the framework. The final layout was identified through an iterative design process carried out with CAD software that evaluated static loads.

In order to perform a calibrated radiometric measurement, at least two known radiation sources are required. In FIRMOS the HBB and a CBB are located at the instrument entrance. The scene mirror allows the acquisition of the external view of the instrument (zenith or nadir) or one of the two BBs. The axial rotation is obtained through a stepper motor (NEMA 17 stepper), that also supports the mirror, surrounded by a plastic guard in order to prevent stray light from other instrument components. The support was assembled out of 3D-printed high strength co-polyester plastic parts.

Monte Carlo numerical calculations were performed to optimize the cavity geometry of the BBs, in order to maximize normal emissivity, a 34∘ angle was chosen for both the HBB and CBB inner cones (see Fig. ) achieving an emissivity >0.9985.

The CBB was assembled in a 3D-printed co-polyester plastic shell and the HBB was assembled in a 3D-printed heat-resistant carbon fibre-reinforced Nylon plastic shell, they were both designed to minimize thermal dispersion. The BBs cavities were fabricated in aluminium, internally coated using NEXTEL velvet coating 811-21. Some layers of thermal superinsulation foils were placed inside the plastic shells, in order to minimize the thermal exchange between the aluminium structure and its plastic supports.

The BBs controllers are two modular drivers for temperature reading and stabilization, developed in-house. The temperature of the RBB is monitored by a supplementary module of the HBB driver. Each BB controller simultaneously records the temperature of four sensors: one high-accuracy (30 mK) resistance temperature detector (PT100 sensor) for the measurement of the BB temperature, one high-resolution (500 µK) negative temperature coefficient (NTC) sensor for active thermal stabilization, and two one-wire digital thermometers (Dallas DS18B20). The position of the sensors inside the BBs is shown in Fig. .

Due to the sensor high accuracy, the PT100 is employed to measure the BB temperature value used in the L1 data analysis. The PT100 temperature reading by the FIRMOS controller and by a commercial temperature monitor (Lakeshore; model 218, with a temperature equivalent accuracy of 68 mK) were compared to estimate the contribution of the readout electronics to the accuracy of the BB temperature. The comparison showed a maximum positive offset of 200 mK between the two, this value was conservatively assumed as the BB temperature total accuracy.

The NTC temperature is used for the thermal stabilization of the BB. Each stabilization controller is equipped with a proportional integral derivative (PID) circuitry to maintain the temperature read from the NTC, equal to a selected value. The HBB controller operates in heating-only mode by driving a heater resistor mounted inside the HBB. The CBB controller operates in cooling/heating mode by driving a Peltier element placed inside the CBB.

Two Dallas sensors, located at the opposite extremities of the BB, are used to monitor the BB thermal homogeneity.

For the field campaign, the CBB and the HBB were typically stabilized at a temperature of 15 and 60 ∘C, respectively. In order to find the precision of the BB thermal stabilization, the difference between the PT100 reading and the set point (the so-called temperature stabilization error) was recorded for some hours. Figure  shows the PT100 measurements after stabilization was activated, for the HBB (Fig. a) and the CBB (Fig. c). Figure b and d shows the temperature stabilization error after the set point is reached, respectively, for the HBB and the CBB. The HBB reached the temperature of 60 ∘C in approximately 2 h, and the CBB reached 15 ∘C in approximately 30 min. To infer the precision of the temperature stabilization, assumed as the standard deviation of the stabilization error after the set temperature is reached, we calculated the standard deviation of the signals reported in Fig. b and d. The HBB controller provides a stabilization precision of 8.3 mK, and the CBB controller provides a stabilization precision of 1.1 mK.

The BBs temperature homogeneity was estimated from the time evolution of the difference between the readings of the two Dallas thermometers placed at the extremities of the BBs. Figure  shows the Dallas1 and Dallas2 measurements after stabilization was activated for the HBB (Fig. a) and the CBB (Fig. c), and the temperature difference between the two Dallas sensors after thermal stabilization was reached (Fig. b for the HBB and d for the CBB). After the set temperature was reached, the HBB Dallas thermal difference did not show a significant variation, and the thermal gradient remained constant with a mean value of 250 mK. The Dallas thermal difference for CBB showed only a slight decrease of about 30 mK h-1, and the mean value of the thermal gradient during 4 h resulted in 300 mK. The mean value of the temperature difference between Dallas2 and Dallas1, after temperature stabilization was reached, was assumed to be the thermal gradient of the BB. The BB thermal homogeneity was thus conservatively considered to be about 300 mK for both.

The BB controllers performance is summarized in Table .

One of FIRMOS enabling technologies is the adoption of two room-temperature pyroelectric DLATGS detectors covering the mid-infrared and the far-infrared region. The detectors are uncooled (model: Selex P5180) and have a noise equivalent power NEP ≡A/D* of 1.4 and 1.6×10-10 W /Hz, where A and D* are, respectively, the detector area (3.14 mm2) and the detectivity. The pyroelectric preamplifiers were prepared at INO-CNR, and the electric scheme follows a classic design, previously tested for the REFIR-PAD instrument . The original scheme was optimized, miniaturizing as much as possible the amplifier to reduce the wiring length, in order to increase immunity to electromagnetic interference noise.

The slow response of pyroelectric detectors requires compensation for the acquired signals with digital processing in order to remove amplitude and phase distortions. For this purpose, the frequency response of the detector and of the pre-amplifier subsystem were characterized, measuring their frequency response to a laser-beam step excitation for both output channels (Fig. ). An empirical model was successively derived from the measurements with a fitting procedure and then used to digitally compensate for the detector response during the L1a analysis (described in Sect. ).

The FIRMOS detectors observe signal variations in the range of 5–100 Hz depending on the scanning conditions.

Five dedicated balloon launches were carried out by a team from the Forschungszentrum Jülich at the Institut für Meteorologie und Klimaforschung (IMK-IFU; part of the Karlsruher Institut für Technologie, KIT) in Garmisch–Partenkirchen, 8.6 km north-east of the summit. The balloons were launched at 18:03, 19:03, and 23:00 CET on 5 February and at 18:33 and 23:33 CET the following day.

Air temperature and water vapour mixing ratio from standard Vaisala RS41-SGP radiosondes were compared to the three individual FIRMOS L2 data nearest in time, in order to evaluate the retrieval products quality. Table  lists the measurement time of the FIRMOS data used in the comparison and the corresponding balloon launch.

The RS41 temperature measurement has accuracy of 0.3 K and precision of 0.15 K, the humidity sensor accuracy is 10 % and precision is 2 %, and the quality of the radiosonde water vapour measurements were checked with an accompanied high accurate frostpoint hygrometer CFH; for details see.

Figure  shows the radiosonde flight trajectories while their altitude was between 3 and 10 km. The radiosoundings launched on 6 February were under thin cirrus cloud conditions and much farther from Zugspitze, so they were not included in the comparison. The radiosonde profiles have a fine vertical resolution. Therefore, to compare with FIRMOS L2 products, their readings were convolved with the FIRMOS averaging kernels AK.

Each radio sounding acquired on 5 February was compared to the average of the three profiles of water vapour and temperature retrieved from FIRMOS closest in time (Figs.  and ). Each plot refers to a different radiosonde acquisition, the local time is also reported. The retrieved products are the red curves, and radiosonde profiles before and after the convolution with the FIRMOS AK are the orange and green curves, respectively, a priori profiles are in grey. FIRMOS and a priori retrieval errors are also reported.

Figure  shows how the water vapour profiles retrieved from FIRMOS observations agree with the convolved radiosonde profiles within the retrieval errors. The third radiosonde at the surface is an exception that is probably related to the different boundary conditions experienced by the radiosonde during its trajectory relative to those measured by FIRMOS above the Zugspitze site. Similar to water vapour, the comparison between the temperature obtained from FIRMOS and the convolved radiosonde profiles shows good agreement within the FIRMOS retrieval errors.

On 5 and 6 February 2019, a total of four water vapour measurements was carried out with a high-power Raman lidar at UFS. In this period, the stratospheric aerosol lidar was continuously recording backscatter profiles in order to detect the presence of thin cirrus clouds . The lidar systems are described in detail by (; see also for more technical details). For water vapour the system features a range from 3 to 20 km a.m.s.l. for a measurement time of 1 h. The data evaluation procedure was recently refined, yielding a better agreement than described by with the reference measurements of the campaign. A range extension of up to 25 km could be achieved for measurements with minimal background noise.

The water vapour mixing ratios retrieved from the lidar were calibrated by balloon-borne cryogenic sensors (CFH) of the Forschungszentrum Jülich. The agreement of the lidar measurement with the CFH data was outstanding below 5 km and in the upper troposphere and lower stratosphere in the case of the best time overlap. Between 5 and 8 km, the water vapour mixing ratio exhibited an increasingly spiky humidity structure that was different for lidar and sonde. This is explained by several spatially confined and highly variable dry layers of stratospheric air, unprecedented in spatial inhomogeneity in our lidar sounding over several decades e.g.and references therein, making the instrument comparison particularly difficult see.

The best agreement can be expected for the vertical measurement on the summit and at UFS since the observation volumes almost match. For the lidar, we assume an uncertainty of the order of 5 % on the first 2 d, given the excellent specifications for the CFH sondes. On the third day, the uncertainty can be higher because of the rather distant calibration source.

The lidar acquisitions were compared to water vapour profiles retrieved from FIRMOS coincident measurements. The comparison was performed averaging the profiles from five FIRMOS observations for each Raman profile. Given the finer vertical resolution of the Raman profiles, they were convolved with the AK to compare them with FIRMOS L2 products.

Figure  shows the comparison between the profiles from FIRMOS L2 water vapour and Raman profiles. Each plot refers to one of the FIRMOS–lidar pairs. The retrieved products are plotted in red, the original Raman profiles in orange, and the green curve is the result of the convolution of the Raman profile with the FIRMOS AK. A priori profiles are shown in grey. FIRMOS, Raman, and a priori retrieval errors are also reported. From Fig.  we can conclude that the water vapour profiles retrieved from the FIRMOS observation agreed with the convolved Raman profiles within the retrieval error.

The E-AERI spectrometer at Zugspitze measured in the range 400–1800 cm−1 with a resolution of 0.48215 cm−1 and was positioned 4 m above FIRMOS. To accurately account for the spectral and geometrical differences, the technique described by was employed to compare the spectra acquired by the two instruments, calculating the residuals between the observed and the calculated spectra of each instrument, the residuals were then convolved by the other's instrument spectral response function (SRF). Equation () defines the radiance differences as follows: 6RDIFF=RFIRMOS∗SRFAERI-RFIRMOS′∗SRFAERI-RAERI∗SRFFIRMOS-RAERI′∗SRFFIRMOS. RFIRMOS and RAERI are the mean radiance spectrum for FIRMOS and AERI, respectively; RFIRMOS′ and RAERI′ are the mean simulated radiances; the symbol ∗ denotes the spectral convolution. In RDIFF the residuals are reduced to the lowest common spectral resolution; since the radiance calculations were performed using the same atmospheric state, and forward model physics for both instruments, this results in systematic errors that are common to both sets of calculations, and to first order removes the effects of altitude from the comparison .

Figure  shows the radiance differences RDIFF, the spectral quantity calculated as in Eq. () over 252 coincident spectra, in the range used for the retrieval of IWV (see Sect. ). The spectrum in the plot starts at 450, as a suitable number of spectral points are needed to avoid wraparound effects when calculating the convolution. The mean of RDIFF indicates a small positive bias of 0.17 mW m-2 sr-1 cm and a standard deviation of 1.13 mW m-2 sr-1 cm, the total NESR shown in red in the figure is the sum in quadrature of the instruments' individual NESR. The analysis of the radiance differences demonstrates the very good agreement of the two instruments.

The KIT algorithm for the retrieval of IWV was applied to both the FIRMOS and E-AERI datasets for comparison. IWV is retrieved by minimizing E-AERI (or FIRMOS) versus the line-by-line radiative transfer model LBLRTM; spectral residuals in the range from 400 to 600 cm-1 seefor details. The dominant contribution to IWV precision error is the retrieval noise: the higher uncertainty value for FIRMOS precision (0.027 mm) compared to E-AERI (0.020 mm) is related to the higher NESR of FIRMOS compared to E-AERI: ∼2 and ∼0.5 mW m-2 sr-1 cm, respectively.

Note that the lower NESR in E-AERI spectra may be explained by E-AERI using a cooled detector (67 K), while FIRMOS uses a room-temperature detector. H2O continuum and line parameters used in the forward calculation and a priori assumptions on the shape of the H2O profile (the NCEP reanalysis as for the FIRMOS L2 data) are factors impacting the accuracy of the IWV retrieval; however, they are common to E-AERI and FIRMOS retrievals and can therefore be disregarded for the IWV intercomparison. Other factors are specific to the instruments and can cause biases between E-AERI and FIRMOS:

altitude difference of 4 m between the E-AERI and FIRMOS location;

The impact of the altitude difference on IWV (E-AERI: 2961 m a.s.l., FIRMOS: 2957 m a.m.s.l.) was corrected by calculating IWV at the two altitudes from the NCEP profile used as retrieval a priori. The resulting difference used for the altitude correction is 0.002 mm for the mean atmospheric state of the campaign, and therefore the error introduced by this altitude correction should be ≪0.002 mm.

In addition, FTS measurements can show small errors in the frequency scale due to tiny drifts of the calibration laser. As the measured spectrum is fitted to a theoretical spectrum, such frequency errors can propagate to IWV errors in the retrieval process. In fact, direct comparison of coincident FIRMOS and E-AERI spectra (Δt≤4 min) showed evidence of a small discrepancy in frequency scales. Therefore, we implemented a joint fit of a frequency scale factor =1+ frequency shift within our IWV retrieval. The resulting mean wavenumber scale factor is 1.0000555 for FIRMOS and 0.9999513 for E-AERI.

The impact from this joint frequency scale retrieval on IWV is shown in Fig. . The IWV retrievals with the original spectra are displayed as red squares and there is a bias of δIWV(FIRMOS-AERI) =0.0045 mm. For IWV retrievals with joint frequency scale fit (blue crosses), the bias is practically eliminated to δIWV(FIRMOS-AERI) =0.0002 mm. This bias of 0.0002 mm is negligible compared to the level of measured atmospheric IWV states (from 0.2 to 2 mm H2O); i.e. there are no indications of significant calibration errors in the spectral domain of the H2O rotational band.