Quantitative imaging of volcanic SO2 plumes with Fabry Pérot Interferometer Correlation Spectroscopy

We present first measurements with a novel imaging technique for atmospheric trace gases in the UV spectral range. Imaging Fabry Pérot Interferometer Correlation Spectroscopy (IFPICS), employs a Fabry Pérot Interferometer (FPI) as wavelength selective element. Matching the FPIs distinct, periodic transmission features to the characteristic differential absorption structures of the investigated trace gas allows to measure differential atmospheric column density (CD) distributions of numerous trace gases, e.g. sulphur dioxide (SO2), bromine monoxide (BrO), or nitrogen dioxide (NO2), with high spatial and 5 temporal resolution. The high specificity in the spectral detection of IFPICS minimises cross interferences to other trace gases and aerosol extinction allowing precise determination of gas fluxes. Furthermore, the instrument response can be modelled using absorption cross sections and a solar atlas spectrum from the literature, thereby avoiding additional calibration procedures, e.g. using gas cells. In a field campaign, we recorded the temporal CD evolution of SO2 in the volcanic plume of Mt. Etna with an integration time of 1s and 400× 400 pixels spatial resolution. The first IFPICS prototype can reach a detection limit 10 of 2.1×1017 molec cm−2 s−1/2, which is comparable to traditional and much less selective volcanic SO2 imaging techniques.

two) wavelength channels by using wavelength selective optical elements for the entire image frame, thereby usually strongly reducing the spectral resolution (e.g. Mori and Burton, 2006;Dekemper et al., 2016). The high spectral resolution of the first two approaches allows the accurate and simultaneous identification of several trace gases, however, the light throughput and the scanning process severely limit the temporal resolution. The third approach can be quite fast, the trace gas selectivity, however, strongly depends on the correlation of trace gas absorption with the wavelength selective elements and usually is rather marginal.

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Fabry Pérot Interferometers (FPIs) exhibit a periodic spectral transmission pattern, which can be matched to periodic spectral features (typically due to rotational or vibrational structures of electronic transitions) of the trace gas absorption, thereby yielding very high correlation for some trace gases. Imaging Fabry Pérot Interferometer Correlation Spectroscopy (IFPICS) thus essentially combines the advantage of fast image acquisition with selective spectral identification of the target trace gas. IFPICS was proposed by Kuhn et al. (2014) and discussed in Platt et al. (2015) for volcanic SO 2 . Kuhn et al. (2019) demonstrated the 35 feasibility with a one-pixel prototype for volcanic SO 2 and evaluated its applicability to other trace gases.
Here we present first imaging measurements (at a resolution of 400×400 pixels, 1 s exposure time) performed with IFPICS and confirm its high selectivity and sensitivity. A prototype instrument for SO 2 was tested at Mt. Etna volcano, Italy, showing a noise equivalent signal between 2.1 × 10 17 − 5.5 × 10 17 molec cm −2 s −1/2 . Furthermore, we show that the instrument response can be modelled and thereby intrinsically calibrated, using a solar atlas spectrum and literature trace gas absorption cross sec-40 tions.
Existing interference filter based SO 2 cameras used for e.g. the quantification of volcanic trace gas emission fluxes into the atmosphere (Mori and Burton, 2006;Bluth et al., 2007;Kern et al., 2015), exhibit strong cross interferences to aerosol scattering extinction and other trace gases (Lübcke et al., 2013;Kuhn et al., 2014). Furthermore, these techniques require in field calibration. Besides the thereby induced systematic errors that propagate into the emission flux quantification, the detection 45 limit is mostly determined by these cross interferences. Thus, the applicability of the technique is limited to strong emitters with respective plume and weather conditions. The much higher selectivity of IFPICS largely extends the range of applicable conditions (e.g. to ship emissions and weaker emitting volcanoes) and significantly reduces the systematic errors. Furthermore, the extension of the technique to other trace gases e.g. bromine monoxide (BrO), formaldehyde (HCHO) or nitrogen dioxide (NO 2 ) can give new important insights into short scale chemical conversion processes in the atmosphere. Similarly to the SO 2 camera principle (e.g. Mori and Burton, 2006;Bluth et al., 2007), IFPICS uses an apparent absorbance (AA)τ = τ A − τ B , i.e. the difference between two measured optical densities τ A and τ B , to quantify the column density (CD) S = L 0 c(l) dl, i.e. the integrated concentration c of the measured gas along a light path L for each pixel of the image. The AA is calculated from two (or more) spectral settings that yield a maximum correlation difference to the gas absorption spectrum.

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Ideally the periodicity of the FPI fringes are matched to periodic spectral absorption features as shown in Fig. 1 ×10 18 Figure 1. Spectral variation of: (a) The SO2 absorption cross section σSO 2 (black drawn, left axis, according to Bogumil et al. (2003)) and the scattered skylight radiance I0(λ) (gray drawn, right axis in relative units), given by Eq. 2. (b) The FPI transmissions in settings A and B yielding the maximum AA detectable (best correlation/anti-correlation to σSO 2 ) in the spectral range specified by the used band pass filter (BPF). Shown are: The BPF transmission TBP F (λ) (black) and the FPI transmission spectrum for a single beam approach according to Eq. 6 in on-band TF P I,A(λ) (dashed blue, correlation with σSO 2 ) and off-band TF P I,B (λ) setting (dashed orange, anti-correlation with σSO 2 ).
The effective FPI transmission spectrum including an incident angle distribution according to Eq. 7 in on-band T ef f F P I,A (λ)(drawn blue) and off-band T ef f F P I,B (λ) setting (drawn orange).
coincide with the SO 2 absorption maxima and hence correlating with the differential absorption structures of SO 2 . Setting B, uses an off-band position where the FPI transmission maxima anti-correlate with the differential SO 2 absorption structures (see Fig. 1). The spectral separation between setting A and B is thereby reduced by a factor of ≈ 30 (in the case of SO 2 ) to only 60 ≈ 0.5 nm in contrast to ≈ 10−15 nm for traditional SO 2 cameras (see Lübcke et al., 2013;Kern et al., 2015), which minimises broad band interferences due to e.g. scattering and extinction by aerosols or other absorbing gases. This application of an FPI is similar to approaches reported by Wilson et al. (2007) and Vargas-Rodríguez and Rutt (2009), for the detection of carbon monoxide, carbon dioxide and methane in the infrared spectral range.
By measuring the optical density τ A = ln(I A /I 0,A ) and τ B = ln(I B /I 0,B ) in both spectral settings A and B respectively, the 65 relation between the AAτ (S) with the CD S is given bỹ where I A , I B denote the radiances with and I 0,A , I 0,B the radiance without the presence of the target trace gas in the absorption light path. The absorber free reference radiances I 0,A and I 0,B can be determined from e.g. a reference region within the image. The differential weighted effective trace gas absorption cross section ∆σ(S) becomes independent of S for small 70 AAs (τ 1). At higher AAs saturation effects occur due to the non-linearity of Lambert-Beer's law, however knowledge of the absorption cross sections, the background radiation spectrum, and the instrument transmission allows to calculateτ for arbitrary CDs S using a numerical model.

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The AAτ is modelled for given target trace gas CDs S by simulating the incoming radiances I A , I B and I 0,A , I 0,B . As incident radiation a high-resolution, top of atmosphere (TOA) solar atlas spectrum I 0,T OA (λ) is used according to Chance and Kurucz (2010). The TOA spectrum is scaled by the wavelength λ −4 approximating a Rayleigh scattering atmosphere. Since our measurement wavelength range, of 304-313 nm for SO 2 , overlaps with absorption of ozone (O 3 ), the TOA spectrum is corrected for the stratosperhic O 3 absorption by multiplying all intensities with the Lambert-Beer's term e −σO 3 (λ)·SO 3 . Where 80 S O3 denotes the total atmospheric ozone slant column density, e.g. according to TEMIS Database, (Veefkind et al., 2006), and σ O3 the O 3 absorption cross section according to Serdyuchenko et al. (2014). This yields the scattered skylight radiance I 0 (λ) Based on I 0 (λ) the radiances measured by the instrument for the two respective spectral settings are calculated with the absorption of trace gases and the spectral instrument transfer function T instr (λ). The investigated target trace gas j (in this 85 work SO 2 ) and potentially interfering trace gas species k (in this work O 3 ) are added according to Lambert-Beer's law. In the following we use the index i, denoting the FPI settings A and B, respectively. The quantity I 0,i thereby denotes the reference radiance excluding the target trace gas j from the light path.
The spectral instrument transfer functions T instr,i (λ) for the two spectral settings consists of the measured band pass filter (BPF) transmission spectrum T BP F (λ), the spectral (i.e. wavelength dependent) quantum efficiency Q(λ) of the detector, and a spectral loss factor η(λ) of the employed optical components (e.g. by reflections).
Considering only a single, parallel beam of light traversing the instrument the FPI transmission spectrum T F P I,i (λ) is defined 95 by the Airy function (Perot and Fabry, 1899) with the light beam incidence angle α i for the two spectral settings onto the FPI, the FPI mirror separation d, the refractive index n of the medium inside the FPI, and the FPI reflectivity R (see Tab. 1, Fig. 1 and Fig. 2, (c)).
However, in reality a spectral setting will always contain a range of incidence angles onto the FPI. In this work we assume cone 100 4 https://doi.org/10.5194/amt-2020-263 Preprint. Discussion started: 21 July 2020 c Author(s) 2020. CC BY 4.0 License.
shaped light beams, with half cone opening angles ω c , where the entire cone can be tilted by α i relative to the normal of the FPI mirrors (see Fig. 2, (c)). From this assumption follows that the incidence angles α i are distributed over a cone with the incidence angle distribution γ(α i , ω c , ϑ, ϕ), where ϑ and ϕ are the polar and azimuth angles, respectively. Hence, the single beam FPI transmission spectrum T F P I,i (λ) of Equation 6 is extended by a weighted average over T F P I,i (λ; γ(α i , ω c , ϑ, ϕ), d, n, R), Thereby, N (γ(α i , ω c )) denotes the weighting function, ϑ the polar angle and ϕ the azimuth angle of the spherical integration within boundaries defined by the tilted cone shaped light beams. E.g.: for a non-tilted FPI (α i = 0) the integration boundaries are ϑ ∈ [0, ω c ] and ϕ ∈ [0, 2π], for a tilted FPI however, the transformation of γ(α i , ω c , ϑ, ϕ) is more complex and requires several case analyses.

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The incidence angle distribution γ(α i , ω c ) will affect the shape of the FPI transmission spectrum by decreasing the effective finesse F of the FPI leading to a blurring of the FPI fringes (see Fig. 1).

The IFPICS prototype
The IFPICS prototype is a newly developed instrument, designed to function under harsh environmental conditions in remote locations like e.g. in the proximity to volcanoes. Hence, the prototype is designed to be small with dimensions of 115 200 mm × 350 mm × 130 mm, lightweight with 4.8 kg (see Fig. 2, (a)) and has a power consumption < 10 W, thus can be battery-operated for several hours. A 2D UV-sensitive CMOS sensor (SCM2020-UV provided by EHD imaging) is used to acquire images. However, we found that the software of the SCM2020-UV image sensor does not allow sufficiently precise triggering. Therefore ≈ 0.6 seconds are lost in each image acquisition, which severely limits the operation of the IFPICS camera. Replacement of the sensor by a scientific-grade UV detector array will solve this problem in future studies.

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The internal camera optics is highly modular and easily adjustable. The IFPICS prototype employs an image side telecentric optical setup as proposed in Kuhn et al. (2014Kuhn et al. ( , 2019. A photograph and a schematic drawing are shown in Fig. 2. An aperture and a lens (lens 1) parallelise incoming light from the imaging field of view (FOV) before it traverses the FPI and the BPF.
A second lens (lens 2) focusses the light onto the 2D UV-sensitive sensor. Thereby, in good approximation, all the pixels of the image experience the same spectral instrument transfer function T instr,i (λ) for the two wavelength settings. The static 125 air-spaced FPI (d, n and R fixed, provided by SLS Optics Ltd.) can be tilted within the parallelised light path in order to tune its spectral transmission T ef f F P I between setting A and B via variation of the incidence angle α (see Section 2.1). The half cone opening angle ω c is determined by the entrance aperture a and the focal length f of lens 1 and can be calculated by ω c = arctan(a/2f ). The physical properties of the optical components and the instrument are listed in Tab. 1 and were mostly chosen according to the dimensioning assumed in the calculations of Kuhn et al. (2019).

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The FPI design with fixed d, n and R (see Fig. 2, (c)) in particular is chosen to inherently generate a transmission spectrum matching the differential absorption structures of SO 2 . This includes the basic idea that the untilted FPI (α i = 0 • ) al- (drawn red) with incidence angle α is reflected multiple times between the FPI mirrors with reflectance R and separation d. Visualisation of an incoming cone shaped beam (red dash-dotted) with half cone opening angle ωc and incidence angle α of the cone axis. ready matches the on-band position A. In our case however, the manufacturing accuracy of d lies within one free spectral range (≈ 2 nm for SO 2 ) yielding that α B = 0 • , corresponds to a off-band (B) position (T ef f F P I,B ) and the on-band (A) position (T ef f F P I,A ) is reached by a small tilt of α A = 4.5 • .The basic advantages of using small incident angles α i are, that they keep the 135 spread of the incidence angle distribution γ(α i , ω c ) (see Section 2.1) low and thereby retain the FPIs effective finesse F high (since the reflectivity R of the FPI-mirror coating is somewhat dependent on the angle of incidence so is the finesse F ). This leads to a much weaker blurring of the FPI fringes in the FPI transmission spectrum T ef f F P I,i resulting in a higher sensitivity of the instrument (see Fig. 1). With the prototype setup, however, we encountered disturbing reflections for low FPI incidence angles. For that reason we used the subsequent correlating order of the FPI transmission with α A = 8.17 • for an on-band and 140 α B = 6.45 • for an off-band setting (see Tab. 1), thereby making a compromise between sensitivity and accurate evaluable images. the FPI tilt angles α i for tuning T ef f F P I,i (λ) between on-band i = A and off-band setting i = B were selected according to Tab. 1. The exposure time was set to 1 s for all acquired images. entering the IFPICS instrument and the flat-field images are obtained by the arithmetic mean over five images acquired in a plume free sky region. The flat field images thereby directly including the reference measurement I 0,i , making a later correction for the atmospheric background unnecessary. In the same viewing direction I i is measured for each gas cell and FPI setting i in order to calculate the AA according to Eq. 1. Figure 3 shows the gas cell measurements (red) including uncertainties (error-bars, 1-σ). The uncertainties directly arise from the errors of the DOAS measurement and due to variations in optomechanical settings of the IFPICS prototype.

Validation of the instrument model
The instrument model (Eq. 2 -7) was used to calculate the IFPICSs AAτ SO2 (S SO2 ) from a given SO 2 CD S SO2 . The model parameters are mostly fixed by the IFPICS prototype optics as given in Tab for noon conditions. High SZAs lead to an increase of stratospheric O 3 absorption which alters the spectral shape of the scattered skylight radiance I 0 (λ) (see Eq. 2) which is used in the forward model. I. e. for high O 3 absorption, lower wavelength radiance, where the differential SO 2 absorption features are stronger, will contribute less to the integrated radiances I i , I 0,i (Eq. 3, 4). The thereby induced SZA dependence of the sensitivity can easily be accounted for in the model. Note, that this influence of strong O 3 absorption only occurs at our chosen wavelength range for the SO 2 measurement. When applying IFPICS to other 180 trace gases, e.g. BrO or NO 2 at higher wavelength, this effect will be negligible.

Results of the field measurements
Volcanic plume measurements were performed on July 22, 2019, 08:50 -09:10 CET. The instrument was pointing towards the plume of Mt. Etna's South East crater with a constant viewing direction (azimuth 204 • N, elevation 5 • , see Fig. 4). The wind direction was ≈ 5 • N with a velocity of ≈ 6 m s −1 (wind data from UWYO). Hence, the plume was partly covered by the crater 185 flank. The frame rate during the measurement was 0.2 Hz for a pair (I A and I B ) of images.
The flat-field correction was performed as described in section 3.2, using the arithmetic mean over five dark images and flatfield images, obtained in a plume free sky region. An exemplary set of volcanic plume SO 2 images, obtained with the IFPICS instrument in on-band setting I A and off-band setting I B , are shown in   The volcanic plume of Mt. Etna's South East crater is clearly visibly and reaches SO 2 CDs higher than 3 × 10 18 molec cm −2 .
The atmospheric background is S SO2,bg = 4.3 × 10 16 molec cm −2 and was determined by the arithmetic mean over a plume free area within the evaluated image (white square, 100 × 100 pixel, in Fig. 6, (a)). The S SO2,bg was subtracted from the displayed image in the final step of the evaluation. The similar plume free area (white square, 100 × 100 pixel, in Fig. 6, (a)) 205 is further used to give an estimation for the SO 2 detection limit of the IFPICS prototype by calculating the 1-σ pixel-pixel standard deviation. The obtained detection limit is 5.5 × 10 17 molec cm −2 s −1/2 given by the noise equivalent signal. The measurements were performed in the morning with an SZA of 78 • and therefore reduced sensitivity and under relatively low light conditions. For decreasing SZA the sensitivity will increase according to Fig. 3 and the increasing sky radiance will reduce the photon shot noise. I.e. the gas cell measurements (taken at SZA of 53 • , with approximately twice the sky radiance compared to 210 SZA of 78 • ) show a detection limit of 2.1 × 10 17 molec cm −2 s −1/2 . For ideal measurement conditions (lowest SZA, highest sky radiance) the detection limit will be further improved.

Conclusion
By imaging and quantifying the SO 2 distribution in the volcanic plume of Mt. Etna we successfully demonstrate the feasibility of the IFPICS technique proposed by Kuhn et al. (2014). We were able to unequivocally resolve the dynamical evolution of 215 SO 2 in a volcanic plume with a high spatial and temporal resolution (400 × 400 pixel, 1 s integration time). The retrieved detection limit for the SO 2 measurement is 5.5 × 10 17 molec cm −2 s −1/2 . The detection limit however varies with the SZA and can reach values below 2 × 10 17 molec cm −2 s −1/2 under ideal conditions, comparable to traditional SO 2 imaging techniques (see Kern et al., 2015).
The specific spectral detection scheme of IFPICS allows to use a numerical instrument model to directly convert the mea-220 sured AAτ into CD S distributions. This inherent calibration method makes in-field calibrations methods, e.g. by gas cells, unnecessary. The accuracy of the instrument model could be demonstrated using SO 2 cells with a known CD, determined by simultaneous DOAS measurements.
Our IFPICS instrument is still an early stage prototype. The employed optics are highly modular allowing easy adjustments even outside a laboratory. The physical dimensions of < 10 litres, and < 5 kg and the low power consumption of < 10 W 225 combined with the fact that no maintenance and in-field calibration is needed, make it already a close to ideal field instrument.
Furthermore, the temporal resolution of the instrument can further be increased by replacing the employed sensor as it does not allow for time-optimised control of image acquisition.
Compared to traditional SO 2 cameras the minimised cross interferences to broad band plume extinction increases selectivity and thus should allow to apply the IFPICS technique to much weaker SO 2 sources. Furthermore, the small interference to