The NO 2 camera based on Gas Correlation Spectroscopy

. Monitoring of NO 2 is in the interest of public health, because NO 2 contributes to the decline of air quality in 5 many urban regions. Its abundance can be a direct cause of asthmatic and cardiovascular diseases and plays a significant part in forming other pollutants such as ozone or particulate matter. Spectroscopic methods have proven to be reliable and of high selectivity by utilizing the characteristic spectral absorption signature of trace gasses (cid:58)(cid:58)(cid:58)(cid:58)(cid:58) gases such as NO 2 . However, they typically lack the spatio-temporal resolution required for real-time imaging measurements of NO 2 emissions. We propose imaging measurements of NO 2 in the visible spectral range using a novel instrument, an NO 2 camera based on the principle 10 of Gas Correlation Spectroscopy (GCS). For this purpose two gas cells (cuvettes) are placed in front of two camera modules. One gas cell is empty, while the other is filled with a high concentration of the target gas. The filled gas cell operates as a non-dispersive spectral filter to the incoming light, maintaining the two-dimensional imaging capability of the sensor arrays. NO 2 images are generated on the basis of the signal ratio between the two images in the spectral window between 430 and 445 nm, where the NO 2 absorption cross section is strongly structured. The capabilities and limits of

interest occur on small spatial (sub-meter) and temporal (sub-second) scales, e.g. when measuring the emissions of moving point sources, such as cars, ships, or air planes. At the same time examinations of plume geometries, mass fluxes, and chemical reactions that take place in plumes require spatial coverage of the scene. Overall, an imaging method for NO 2 with high spatio-temporal resolution could reveal more insight into the quantity and the dynamics of NO 2 emissions. 30 In polluted regions NO x emissions are mainly of anthropogenic origin. Combustion processes, which occur e.g. in car motors or industrial power plants, generate NO x , which, at the time of emission, consists mostly of NO (typically with NO 2 /NO x ratios as low as 5-10 %, see e.g. Kenty et al. (2007); Carslaw (2005)). Through oxidization processes, such as There are different remote sensing methods for monitoring of atmospheric trace gasses such as NO 2 . The state of the art method is Differential Optical Absorption Spectroscopy (DOAS, Platt and Stutz (2008)), where the absorption cross sections of the target gasses are fitted to the spectrally resolved differential optical depths along a light path. Then the column densities of the target gasses are retrieved as fit parameters. DOAS measurements can be based on either natural light sources, such as scattered sunlight, or on artificial ones. Modern DOAS spectrographs typically have a spectral resolution of < 1 nm and 45 operate in the UV and visible spectral range. The benefits of analysing spectrally resolved data are high selectivity and low detection limits. However, grating spectrographs are less suited for imaging, because spectral mapping leads to a reduced light throughput. Therefore measurements with sufficient spatial and spectral resolution require rather long acquisition times of many minutes (Bobrowski et al. (2006); Louban et al. (2009)). Imaging DOAS (I-DOAS) is typically realized using a pushbroom technique, where one detector dimension is used for spatial resolution and the other for spectral mapping. Consequently 50 I-DOAS requires to scan a field of view (FOV) column by column or row by row. This strategy was used, for example, by Manago et al. (2018), who report on an imaging DOAS instrument for NO 2 , based on a hyperspectral camera with a spatial resolution of 640 × 480 pixels, a 13 • × 9 • FOV and a frame rate of 0.2 FPS. Although modern hyperspectral cameras can reach adequate spatio-temporal resolution, problems like the immanent asynchrony of the push-broom scheme, as well as portability and price of the instrumental setup remain. 55 We propose an imaging instrument for NO 2 based on Gas Correlation Spectroscopy (GCS, see e.g. Ward and Zwick (1975); Drummond et al. (1995); Wu et al. (2018)) and demonstrate that an instrument designed to measure only a single trace gas can work by using reduced but specific spectral information in order to maximize spatio-temporal resolution. This is achieved  by the use of two 2D-photosensors, each equipped with a lens and a glass cell: one filled with air (the "empty" cell), and one filled with a high concentration of NO 2 . Figure 1 shows a photograph of an instrument prototype. The NO 2 cell functions as a 60 spectral filter to the incoming light, while the empty cell has ideally no effect on the incoming light and serves as a reference.
At the same time, the cameras fully resolve the light in two spatial dimensions. This way we obtain image data with only two spectral channels (in contrast to about 100 spectral channels used for typical DOAS fitting windows). The NO 2 column density measured by each pixel of the instrument can then be obtained by application of the Lamber-Beer law to the two channels. This principle is explained in more detail in sect. 2.1. The method is therefore similar to the recently developed filter 65 correlation based SO 2 camera (Mori and Burton (2006)), the imaging Fabry-Perot interferometer correlation spectroscopy technique (IFPICS, see e.g. Kuhn et al. (2019); Fuchs et al. (2021)) or the acousto-optical tunable filter (AOTF) based NO 2 camera (Dekemper et al. (2016)). However, using a gas cell has substantial advantages compared to the listed techniques.
While the filter correlation approach through its reduced selectivity only works for large volcanic SO 2 emissions, Fabry-Perot interferometers and AOTFs require collimated light beams within the lens setup, largely reducing the light throughput. In order 70 to further increase selectivity to NO 2 , we use an additional bandpass filter with transmission in the region of 425 nm to 450 nm, where the absorption cross section of NO 2 shows strong characteristic features. An instrument of this kind requires that NO 2 can be stably contained in glass cells. The instrument prototype we present fulfils this requirement. The chemistry of NO 2 gas cells is explained in detail by Platt and Kuhn (2019).
measurements of NO 2 . We introduce an instrument forward model, which allows to predict instrument responses, detection limits, and cross sensitivities of a GCS-based NO 2 camera under different circumstances. Section 3 presents a prototype of the instrument and lists its detailed technical specifications. Section 4 shows the results of two measurements that have been taken with that instrument prototype. The first is a proof-of-concept measurement with reference cells in an optical laboratory. The purpose of this measurement is to verify the functionality of the instrument and to validate the predictions of the instrument 80 forward model in sect. 2.2. The second is a measurement of the emissions of the German coal power plant Großkraftwerk Mannheim (GKM). Section 5 concludes.

Gas Correlation Spectroscopy
The absorption of light is described by the Lambert-Beer law. It states that for a given incident spectral radiance L 0 (λ) the 85 spectral radiance L(λ) after travelling along a light path s through absorbing media with absorption cross sections σ k (λ) and concentrations c k is given by: Here, S k = c k (s) ds in units of [molec cm −2 ] denotes the column density of the absorbing medium k in the atmosphere and τ is the resulting optical depth. In our application, L 0 denotes the radiance spectrum of scattered sunlight. The Lambert-Beer law can be applied to radiances, denoted with L in units [W nm −1 m −2 sr −1 ], as well as to irradiances, denoted with I in The pixels of a photosensor do not resolve spectrally. Let µ p (λ) be the number of photons per wavelength interval and 95 time period in units of [ph nm −1 s −1 ], that a photosensor is exposed to. It will then measure a detector signal J in units of photoelectrons ([phe]), given by the spectral and temporal integral where η in units of [phe ph −1 ] denotes the quantum efficiency of the photosensor. The wavelength dependence of η typically restricts the integration to the near ultra violet (UV), the visible, and near infrared regions of the electromagnetic spectrum. 100 µ p (λ) can be expressed as and (d) demonstrate the principle of GCS: Given a hypothetical absorption cross section (here assumed to be of sinoidal shape, displayed in (c)), the spectral absorption can be derived from the Lambert-Beer law for different choices of S (here S = 0, "Low S", "High S"). A photosensor is only sensitive to the spectrally integrated radiance that it is exposed to, i.e. the gray-coloured areas displayed in (d).
where L 0 denotes the radiance spectrum of the light source, T denotes the transmission of the instrumental setup, e −τ ( Figure 2 explains the principle of GCS, assuming (for the sake of simplicity) that the target gas with column density S and absorption cross section σ(λ) is the sole absorber and thus τ = σ(λ) · S. Two camera modules are placed behind two gas cells, of which one is filled with air (the "empty" cell) and one is filled with a high concentration of the target gas (see Fig. 1). For a 110 detector pixel with the indices (i, j), the camera with the empty cell will measure and the camera with the cell containing the target gas will measure where S (i,j) denotes the column density of the target gas in the FOV of the pixel with indices (i, j) and S c the column density 115 of the target gas in the gas cell of the instrument. In imaging GCS, the instrument response (instrument signal) is computed for each individual pixel.τ (i,j) is the logarithmic signal ratio between the two spectral channels of the instrument and functions as a measure of S (i,j) : When S (i,j) is small, incoming light will be only slightly attenuated before it reaches the cells, and thus the signal ratio J c,(i,j) /J (i,j) will be smaller compared to a scenario in which S (i,j) is large and thus the 120 atmospheric target gas has already attenuated a larger portion of the light, that else would have been absorbed by the gas cell.
It therefore follows directly thatτ (i,j) grows monotonically with S (i,j) .
When using two camera modules with distinct optical setups, the resulting detector signals are highly sensitive to imperfections in the optical path. For example, small differences in the focal lengths of the camera lenses or dust particles on the lenses or gas cells can induce significant false signals, contributing toτ . Furthermore, vignetting is immanent to imaging measure-125 ments and manifests itself in increasing false signal gradients towards the corners of the image. These effects can be partly corrected by recording reference signals J ref, (i,j) for the channel with the empty cell and J c,ref, (i,j) for the channel with the filled cell in zenith direction, where S = 0 is assumed. In reality this latter condition need not be perfectly fulfilled, although it is important that S is approximately constant throughout the FOV for the reference images. In analogy to eq. (7) and (8) the reference signals are given by and The measurement signal ratio is then divided by the reference signal ratio, i.e.

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This procedure is also referred to as flat field correction. In the following section it will be shown that in good approximatioñ τ ∝ S holds.

Instrument model calculation
A numerical forward model was implemented to predict characteristics of a GCS-based NO 2 camera. Specifically we investigate the shape of the instrument response, the calibration curve, and the signal-to-noise ratio (SNR) as a function of S and S c , 140 as well as cross sensitivities to other atmospheric trace gasses. This section discusses specifically the application of GCS to measurements of NO 2 . Other trace gasses may, for example, require to operate in a different spectral range. Overall, the simulation of realistic conditions of daytime measurements in the atmosphere is the aim. For this a spectrum of scattered sunlight is used as the light source and atmospheric NO 2 column densities are considered in the range from 10 16 to 10 18 molec cm −2 , as well as integration times on the scale of seconds. The relevant detector signals are modelled according to eq. (7), (8), (10),

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and (11). In this instrument model, we assume T (λ) = T f (λ) · T l (λ), where T f denotes the transmission of the bandpass filter and T l denotes the transmission of the camera lens. Since t exp is realistically small enough that I 0 (λ) is constant throughout exposure and the transmission of the bandpass filter used is effectively a cut-off function outside its transmission band from 430 nm to 445 nm, the detector signals can be simplified to

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The choice of of this particular bandpass filter is motivated by the strong, characteristic absorption features, that NO 2 shows in its transmission range. The absorption cross section of NO 2 (Vandaele et al. (2002)) is displayed in Fig. 3 (a) with a zoomed-in region close to the transmission band of the bandpass filter. The model requires a light source radiance spectrum L 0 . For realistic applications of the instrument the light source will almost exclusively be an atmospheric background spectrum, i.e. a radiance spectrum of scattered sunlight. We use a highly resolved irradiance spectrum in units of [W nm −1 m −2 ] (Chance and Kurucz 155 (2010)), and scale it with a low-resolution radiance spectrum at 400 nm (Pissulla et al. (2009) This way we obtain a radiance spectrum that represents the typical spectral shape of scattered sunlight, but maintain the high spectral resolution of the irradiance spectrum. We argue that this is the most realistic general estimation of the background spectrum that we can make. The radiance spectrum used for scaling was recorded at Thessaloniki, Greece, at a sun zenith angle of 21 • . The transmission lines of the bandpass filter T f (λ) and the camera lenses T l (λ), as well as the quantum efficiency 160 of the camera sensors η(λ) are provided by the manufacturers. An étendue of E ≈ 10 −5 sr mm 2 was assumed throughout, which was computed on the basis of a fully opened aperture (f-number 1.6). Figure 3 Figure 4 shows the modelled instrument responseτ (see eq. (12)) as a function of the column density S in the range from 10 16 to 10 18 molec cm −2 for different choices of the 165 column density S c within the NO 2 cell of the instrument. The instrument response is in good approximation proportional to S.
The instrument calibration factor k can be obtained for any fixed value of S c by sampling the instrument signalτ for different choices of S and fitting a linear function of the form The radiance spectrum, as well as the transmission lines of the filter T f and the lens T l , the quantum efficiency of the camera sensor η and the total throughput T f · T l · η, that are assumed in the instrument model.
to the samples. In order to convert the unitless instrument signalτ to column densities, the inverse k −1 in units [molec cm −2 ] 170 is used.
With this model we can also quantify the signal-to-noise ratio (SNR) in order to estimate the detection limit of the instrument under typical atmospheric conditions. An SNR of 1 is assumed to be the lower limit at which atmospheric column densities of the target gas can be resolved. Photoelectron counting follows Poissonian statistics, i.e. the uncertainty ∆J of a signal measured by a photosensor is ∆J = √ J. Thus, the uncertainty ∆τ of the instrument signal ∆τ can be expressed in closed 175 form by application of Gaussian uncertainty propagation: In practice the uncertainties of the reference signals will be comparably small, because the exposure time for the recording of  This instrument model only accounts for the photon shot noise and disregards additional possible sources of noise such as dark noise and read-out noise of the photosensors. This is on purpose in order to make the model applicable to different instrumental setups. In practice the shot noise is by far the dominating source of noise due to the large light throughput of the setup, and 185 both dark current as well as dark noise can be neglected (see sect. 3 for a more detailed explanation). Figure 5 (a) shows the modelled SNR as a function of the cell column density S c for different choices of the column density of the target gas S.
The highest SNR is reached at approximately S c ≈ 4 · 10 18 molec cm −2 with a slight dependence on the observed target gas column density S. Figure 5 (b) shows the modelled SNR as a function of the target gas column density S. The red horizontal line marks the resulting detection limit, where SNR = 1. With an ideal choice of S c ≈ 4 · 10 18 molec cm −2 , a detection limit 190 of approximately 2 · 10 16 molec cm −2 is reached with an exposure time of 2 s.
The instrument model also allows to study the selectivity of the instrument. Equation (13) holds under the assumption that the target gas is the sole absorber. In a realistic measuring scenario many different trace gasses other than NO 2 could be present in the atmosphere. Cross sensitivities to other trace gasses can be determined on the basis of the instrument model. We define τ X , the false signal of a species X, as the additional contribution to the overall instrument signalτ , that is due to the absorption    When expressed in NO 2 signal equivalents, the false signal of O 4 is comparably small, reaching around −2 · 10 15 molec cm −2 assuming the maximal column. The false signal of H 2 O is an order of magnitude larger, reaching up to −3.2·10 16 molec cm −2 assuming the maximal column. As discussed, we treat these false signals and the column densities that have generated them as an overestimate of a realistic expectation. In addition, the naturally abundant water vapour of the atmosphere is typically 215 distributed much more homogeneously than strong NO 2 concentration gradients from a point source. Under this circumstance false signal induced by water vapour should be easily separable from the NO 2 signal of interest. Water vapour inside the plume of a point source emission, which can not be separated from NO 2 signal by the argument above, is contained within much shorter light paths (typically on the order of 100 -200 m) and is not expected to induce relevant false signals.

Analytic instrument model 220
The instrument model presented in sect. 2.2 allows forward modelling of the measuring process with highly resolved radiance spectra and absorption cross sections. However, the integral terms that occur in the instrument response do not allow for a closed-form expression ofτ . Starting from eq. (12), we simplify the expression for the instrument response by assuming a constant radiance spectrum, L 0 (λ, t) = const and quantum efficiency η(λ) = const. We restrict the model to some spectral range ∆λ = [λ min , λ max ] and define λ mid = (λ max + λ min )/2. The final assumption is that the cross section of the target gas 225 consists of only two representative absorption strengths, σ strong and σ weak . To determine both, we compute the median of σ NO2 and define σ weak and σ strong as the mean absorption strength below and above the median respectively. The absorption cross section can then be expressed as where 1 I is the indicator function on an interval I. The instrument responseτ then only depends on the integrals of transmission Equation (12) then takes the form This equation can be applied to arbitrary absorption cross sections, however σ weak and σ strong must be estimated anew for each absorption cross section. The analytical term in eq. (23) could be further simplified, if a gas without broadband contribution to its absorption cross section were considered. In that case, σ weak ≈ 0 and the column in the gas cell S c could be chosen, so that 240 T Sc,strong ≈ 0. The approximation of the instrument signal would then simplify tõ τ ≈ ln 2 The true instrument signalτ , as obtained in sect. 2.1, and the analytical approximation in eq. (23) are plotted in Fig. 8. The spectral range of choice was 430 -445 nm. The analytical approximation underestimates the true instrument response by around 25%, but is equally linear in S besides. The deviation can be corrected by tweaking the choice of σ weak and σ strong , 245 although good candidates can not be known a priori. The derived analytical expression allows for quick approximation of the sensitivity of a GCS measurement.

Instrument prototype
We have built an instrument prototype based on commercially available hardware. The camera modules use a monochrome progressive scan CMOS sensor in a 1/1.2 " format with a pixel size of 5.86 µm × 5.86 µm and a global shutter. They record images with 1920 × 1200 (height × width) pixels. A charge signal is digitized by a 16-Bit analog-digital converter (ADC).
The cameras connect via USB 3.0 to a controlling computer equipped with corresponding camera software. Image acquisition rates depend on the selected exposure time and the read-out time t read = 24.39 ms of the camera sensors. The instrument is therefore limited to a frame rate of 41 FPS at best. However, the read-out time t read can be reduced by using windowing, a feature where the cameras are advised to only read out a subrange of their sensor arrays. The usability of windowing depends 255 on the imaged scene and whether large parts of the FOV can be neglected. The camera modules have a read-out noise of 7 phe.
The thermal dark signal of the camera modules was determined experimentally according to the EMVA (see Jähne, B. (2010)).
A thermal dark signal of (24 ± 9) phe s −1 at a sensor temperature of 50 • C and a doubling temperature of (6.1 ± 0.1) • C were found. The camera modules have a full-well depth of 34,000 phe. Given that in bright daylight the exposure times for images within the dynamic range of the camera are typically far below 1 s, the contribution of the dark signal to the total measured 260 camera signal is negligibly small (e.g. below 0.05 % for an exposure time of 30 ms and a sensor saturation of 50 %). Also the total dark noise (meaning read-out noise + thermal noise) is negligible compared to the photon shot noise of around 130 phe at 50 % saturation. Each camera is equipped with a lens with a focal length of f = 25 mm. The full diagonal, vertical, and horizontal opening angles amount to 30 • , 16.1 • , and 25.5 • , respectively. For each camera a bandpass filter with transmission in the range from 430 -445 nm was placed between the camera lens and the camera sensor. The gas cells of the instrument are 265 cylindrical with a diameter of 50 mm and a thickness of 10 mm. The NO 2 cell was filled from a large reservoir to contain an NO 2 column density of 4 · 10 18 molec cm −2 (which is the ideal value according to the results shown in sect. 2.2, specifically Fig. 5 (a)). The camera behind the NO 2 cell is mounted to a tiltable stage, which can be used to adjust its optical axis in vertical and horizontal orientation with mrad precision using two thumb screws. This adjustment is scene-dependent and of crucial importance in order to eliminate shifts in the FOVs of the two cameras. All parts are placed inside a closable plastic 270 case. Overall, the instrument is portable and compact, while maintaining a reasonable cost of below 2,000 Euro. A control software with graphical user interface was developed in the Python programming language.

Proof-of-concept measurement with gas cells
In order to validate the instrument model described in sect. 2.2 we performed a simple laboratory experiment. Four glass cells 275 were filled with different concentrations of NO 2 and measured with both the NO 2 camera and a conventional DOAS setup.
The light source for the camera measurement was a halogen lamp inside an integrating sphere in front of which the cells were mounted onto a stand with a clamp. An additional series of images was recorded without a cell in the lightpath, whose average serves as the reference image (J ref , J c,ref , see eq. (12)). When evaluating the images taken by the NO 2 camera, an in-cell pixel set and a background pixel set were defined. The in-cell pixel set contained the pixels inside the cell, while the background 280 pixel set contained pixels of the illuminated entrance of the integrating sphere, not covered by the cell. Due to the varying size of the test cells, the in-cell and background pixel sets were different for each cell. The total acquisition time of the NO 2 camera was set to 3 minutes for each cell, and the exposure time of each camera was chosen such that the camera sensors saturated to approximately 50 %.
First, the column density inside the gas cell of the NO 2 camera was estimated as where J bg and J c,bg are the camera signals of the camera with empty cell and the one with the filled cell respectively, averaged over the background pixels of all images. σ ≈ 5.1 · 10 −19 cm 2 molec −1 is the absorption cross section of NO 2 , averaged over the spectral range from 430 to 445 nm. A cell column density of S c = (3.89 ± 0.03) · 10 18 molec cm −2 was obtained. The cell was originally filled with S c = 4 · 10 18 molec cm −2 , but this deviation can be explained by the temperature-dependent 290 NO 2 ⇌ N 2 O 4 equilibrium. The lower the temperature, the lower the NO 2 concentration within the gas cell. The calibration of the instrument was obtained from the instrument model as explained in sect. 2.2. The fit procedure yielded a calibration factor of k −1 = (2.69 ± 0.02) · 10 19 molec cm −2 . Additionally, the signal offsetτ 0 of the instrument was calculated from the background pixels, which was defined as 295 Subtraction ofτ 0 from the instrument signalτ set the average background pixel to zero. The instrument signal of a test cell was determined by averaging over the pixels that were covered by the cell, i.e.
where J and J c denote the camera signal with the empty cell and with the filled gas cell respectively in the in-cell pixel region.
The uncertainty of these measurements is given by Gaussian error propagation according to eq. (16). The uncertainties ∆J c 300 and ∆J are obtained by computing the standard deviation of the detector signal in the in-cell region for the two channels respectively. Figure 9 (a) shows an exemplary image of this measurement. In the center foreground of the image the outline of test cell no. 4 and the stand and clamp, used to hold it, are shown. The offsetτ 0 was subtracted and the flat field correction was (1.00 ± 0.02) · 10 18 (1.10 ± 0.08) · 10 18 0.04092 ± 0.00290 0.03717 ± 0.00036 1 applied using the reference images according to eq. (12). The camera measures a signal ofτ = (4.09±0.29)·10 −2 in the in-cell region of the test cell. Using the calibration factor k −1 , a column density of S = (1.10±0.08)·10 18 molec cm −2 was obtained.

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Within the uncertainty of the measurement this result coincides with that of the DOAS instrument, which measured a column density of S = (1.00 ± 0.02) · 10 18 molec cm −2 . Table 1 lists the column densities measured for each cell by the DOAS setup and the NO 2 camera. The measurements taken with the NO 2 camera show significant uncertainties. For cell no. 1, the relative uncertainty is as large as 231 % and the detection limits, ranging from 2.29 · 10 16 molec cm −2 to 8 · 10 16 molec cm −2 , are larger than the prediction of the instrument model, which was 2 · 10 16 molec cm −2 at 2 seconds of exposure. The reason for 310 this deviation is the use of a different light source: While the instrument model assumed scattered sunlight as the light source, a halogen lamp inside an integrating sphere was used for this experiment. The detection limit is mainly determined by the overall intensity of the light source, which is much lower for such a halogen lamp in the blue spectral range. This increased the statistical uncertainty of the measurement. Additionally systematic false signals were observed, which were not considered in the instrument model: Due to the small diameter of the test cells and the limited interior space of typical optical laboratories 315 there are inevitable perspective shifts between the images of the two cameras, when they are oriented so that the test cells are in the center of their FOVs. Small dust particles on the test cell or condensed droplets on its inside can then introduce false signals.
In order to smooth out these false signals, the images were convoluted with a rectangle filter of the same size as the average diameter of the observed structures. Table 1 lists the chosen filter size for each cell. The filter sizes were chosen differently for each cell, because larger cells require less smoothing. The cell image shown in Fig. 9 required no smoothing at all (which 320 corresponds to a filter size of 1 pixel). Figure 10 shows  (2017)). The NO 2 camera was set up at ms. The exposure times were chosen, so that the camera sensors were read out, once they were saturated to about 50 %. In order to increase image rate and reduce data volume, 100 consecutive frames were averaged, and these averages were saved.
We refer to them as images consisting of 100 frames. This way an image acquisition time of 2 seconds per 100 frames was was subtracted in order to account for the fact that all four images were acquired with different exposure times.
Secondly, a background imageτ background was subtracted, for which the procedure and reasoning is described in the following. The background image was obtained by fitting a 1D-polynomial of degree n to each column of a manually selected set of background pixels, obtained by using a free-hand selection tool on the images. This was required, because the camera 355 signal images showed large signal gradients across the FOV. We suspect that these gradients are a side-effect of the flat field correction, possibly because the sky, against which the reference images were taken, is generally not radiometrically uniform.
An exemplary background correction procedure with n = 2 is shown in Fig. 12 which can be seen in panel (e). A weak temporal dependence of the background image was observed, possibly due to changes in the relative position of the sun (see Fig. 13).
Thirdly, a scalar signal offsetτ 0 was subtracted. The purpose of this correction was to account for slight variations of S c 365 over the course of the measurement. The instrument model in sect. 2.2 showed, that the instrument signalτ is sensitive to the cell column density S c , which again is expected to vary with ambient temperature and irradiance. For studying time-series it is important that this effect is accounted for, i.e. the signal in an off-plume reference region is forced to remain constant, which can be achieved by subtraction of a suitable offsetτ 0 . Here,τ 0 was computed by averaging the signalτ over a small rectangle in the off-plume region (the patterned rectangle in Fig. 14) for each image individually.

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Finally the resulting signal images were multiplied with the calibration factor k −1 , which was obtained from the instrument model (see sect. 2.2). This required knowledge of S c . S c was therefore estimated according to eq. (25), considering the same background rectangle as in the calculation ofτ 0 and a value of S c = (2.72 ± 0.04) · 10 18 molec cm −2 was obtained. With all corrections included, a single camera image was computed via where each pixel value S (i,j) corresponds to the NO 2 slant column density (SCD) measured at pixel (i, j). Figure 14 shows the first camera image of the series, calculated according to eq. (29). To obtain this image, the first 6 consecutive images of the series were averaged. A background fitting routine with polynomial degree n = 2 and the same fit mask as displayed in Fig. 12 (a) were used (the choice of this fit mask is discussed further at the end of this section). A positive 380 NO 2 plume signal equalling approximately 5 · 10 16 molec cm −2 was observed to be emitted from the chimney of block 7. At the point of emission, i.e. directly above the chimney (at width = 1000 m), the plume was in a fully condensed phase and the instrument signal image shows structures of strong negative and positive signal. This effect can be explained as a consequence of the optical setup inside the instrument: The optical axes of the two cameras inside of the instrument were adjusted, so that there was no displacement of the imaged objects (i.e. the uncondensed part of the plume) in the center of the FOV. However 385 displacements towards the corners of the FOV could not be avoided. These displacements manifest as strong false signals, when the signal ratio of the two cameras is computed. Given that in this measurement they occurred in an image region of low interest, they were deemed as unavoidable and not concerned with any further.

Evaluation of an individual camera image
To obtain the NO 2 SCDs and the diameter d of the plume systematically, each column of the NO 2 camera signal image was considered as an individual vertical cross section through the plume. It was observed that the shapes of the measured 390 NO 2 SCDs along these cross sections coarsely followed that of a Gaussian. Figure 15 (a) shows this observation for an exemplary column at y-pixel 660. To each image column i, a Gaussian with amplitude A i , mean µ i and standard deviation σ i was fitted. The NO 2 slant column density and the diameter of the plume at column i were then associated with A i and 2 · σ i respectively. Columns for which the fit routine did not converge well were ignored. This was considered the case when either the fit failed to converge entirely or the retrieved fit parameters were outside a realistic range (A i = S i > 8 · 10 16 molec cm −2 395 or 2 · σ i = d i > 100 m), which was the case for approximately 50 % of the columns. The resulting NO 2 SCDs and plume diameters are shown in Fig. 15 (b). The ensemble of all column fits allows to calculate an average in-plume NO 2 SCD of S = (4.74 ± 1.21) · 10 16 molec cm −2 and an average plume diameter of d = (78 ± 17) m. These values are represented by the red marker in Fig. 15 (b). It is necessary to discuss the uncertainties of such an evaluation procedure. It was explained in sect. 2.2 (see specifically eq. (16)) that the measurement has an intrinsic uncertainty ∆τ of the uncalibrated camera signal due 400 to the Poissonian error of photon counting. This uncertainty propagates directly onto the NO 2 SCDs, that are obtained upon calibration of the instrument using k −1 (S c ) as described in eq. (29) and was estimated by computing the standard deviation  of the measured NO 2 SCDs in an off-plume region of a camera image, e.g. the patterned rectangle in Fig. 14. A value of ∆S = 1.89 · 10 16 molec cm −2 was obtained. This is the detection limit of the instrument prototype. In the next step the plume SCDs and diameters were obtained in a Gaussian fit routine for the vertical plume cross sections of all image columns. For a 405 single column i, this introduced additional uncertainties ∆A i , ∆µ i , and ∆σ i , which were given by the covariances of the fit parameters of that column. These uncertainties propagate into those of the means over all columns, producing the uncertainties used above (∆S = 1.21 · 10 16 molec cm −2 and ∆d = 17 m). Finally the uncertainties of the background fitting routine as described in sect. 4.2.1 were investigated. The camera image shown in Fig. 14 was calculated according to eq. (29), wherẽ τ background was computed using a polynomial of degree n = 2 and the same fit mask as displayed in Fig. 12 (a). Given that 410 this choice of n and the fit mask are subject to our personal assessment, it was investigated, how much the obtained NO 2 SCD and diameter of the plume vary with different choices of n and the fit mask. Figure 16 shows the results of this analysis.
Subfigures (a-h) show the process of the background fitting routine using the freehand fit mask that was described earlier.
Subfigure (c, e, g) show the resulting background imagesτ background for n = 2, 3, 4 respectively. Subfigures (d, f, h) show the corresponding scatter plots of NO 2 SCD and plume diameters as obtained from the Gaussian fit routine. Subfigures (i-p) 415 show the same procedure with a different fit mask, namely one that makes no assumptions of the plume position and covers the entire FOV. The case n = 1 was dismissed, seeing that the background signal is clearly not linear (see Fig. 12 and Fig.   13). Intercomparison of subfigures (d), (f), and (h) as well as (l), (n), and (p) shows, that for a given fit mask the average NO 2 SCD and plume diameter do not vary significantly with the choice of n. Using a full-FOV fit mask yields significantly smaller average values of NO 2 SCD and plume diameter. Furthermore, image objects such as the condensed plumes at y-420 pixel 400 and 1200 lead to vertical fragments in the background image (see subfigure (j)). Overall, the background fitting procedure with n = 2 and a freehand selection of the plume as displayed in subfigure (c) and (d) seems to be a sensible choice, because the resulting background image does not suffer from vertical fragments and shows less signal variations in the off-plume region. In addition the fit is fastest to compute for n = 2. Table 2 contains a quantitative summary of these (2.97−0.92)·10 16 molec cm −2 = 2.05·10 16 molec cm −2 to (5.03+1.01)·10 16 molec cm −2 = 6.04·10 16 molec cm −2 . The mean is 4.04 · 10 16 molec cm −2 . Therefore, the overall uncertainty can be estimated as ∆S = 2 · 10 16 molec cm −2 . In analogy an uncertainty of ∆d = 34 m for the plume diameter is obtained, which will be used throughout the rest of this chapter. With this method an estimate of the overall uncertainty of the evaluation is obtained, by including not only the statistical uncertainty of the measurement (noisy data), but also the systematic uncertainty that is immanent to the evaluation method.

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A series of camera images was assembled into a video (see video supplement), which shows the movement of the plume in wind direction from 08:53 to 09:05.

Optical flow and mass flux analysis
A mass flux analysis was carried out on the basis of image sequences. Given a camera image as shown in Fig. 14, the mass flux through a vertical cross section of the plume can be computed as where M NO2 = 46.0055 g mol −1 is the molar weight of NO 2 , N A = 6.022 · 10 23 mol −1 the Avogadro number, v the wind speed in horizontal direction and S the column density, which is integrated along the vertical (height) axis. v was obtained by running a Farnebäck optical flow retrieval (Farnebäck (2003)) on the in-plume region of consecutive camera images. The optical flow was then divided by the time difference ∆t between the images. Figure 17 (2018)). Therefore the GKM should have been running at approximately 6.3 % of its average power. Assuming that the NO x emission scales linearly with the power produced, a NO x mass flux of F m = 182 tons yr −1 is expected. The mean mass flux obtained from the camera data is significantly lower, and amounts only to about one third of this reference value. Given that the reference is a NO x mass flux and the NO 2 camera can only detect the NO 2 mass flux, such deviations are expected.

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It should be taken into account that this analysis contains two further uncertainties: Firstly, although the most recent available data were used, there may be differences in the reference values between 2017 and 2021 (e.g. total mass of yearly emitted NO x or mean power production). The E-PRTR data show a decline in total yearly emitted NO x from 2007 to 2017 and it can be expected that this trend has continued until 2021. It should be taken into account, that a comparison between a mean flux observed in a time frame of 30 minutes and a yearly average reference flux is hardly indicative for the accuracy of our measurement. Secondly, GKM block 7, of which the emitted plume column densities were used for this analysis, was not the only active block at the time of the measurement. During the measurement, emissions from GKM blocks 6 and 8 were observed as well, but the FOV of the NO 2 camera was too small to record the plumes emitted from all blocks simultaneously.
It is plausible to assume additional emissions of NO 2 from GKM block 6 and 8, which could not be examined on the basis of our measurement.

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Although the discussed uncertainties do not allow for a definite conclusion on the overall accuracy of the mass flux analysis, we present the results as a demonstration that flux analyses on the basis of image data with high spatio-temporal resolution are a feasible concept.

Estimation of [NO 2 ]/[NO x ] ratios
The camera images can be used to investigate the conversion of NO to NO 2 by the reaction of NO with ambient ozone (see eq.

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(R1)) and direct oxidization by molecular oxygen (see eq. (R2)). The NO 2 /NO x ratio can be modelled according to Janssen  and v the wind speed, as well as another parameter A = J/k, where J is the photodissociation frequency of NO 2 . The rate constant k(T ) is temperature dependent. Lippmann et al. (1980) find the empirical relationship k(T ) = 4.3 · 10 −12 · e −1598 K/T cm 3 molec −1 s −1 with temperature T . The photolysis frequency J is often cited as approximately J = 8 · 10 −3 s −1 in full sunshine (see e.g. (2019)), but varies strongly with irradiance (Parrish et al. (1983)). Figure 19 shows an approach to compare . This is in accordance with the Janssen model, which predicts an initial concentration ratio of 0 with an exponential convergence towards a concentration ratio of ≤ 1, depending on the model parameters. Figure 19 shows these obtained ratios as black dots, plotted against the distance downwind, measured from the point, where the fully condensed part of the plume ended (see Fig. 14 (2021)). Parrish et al. (1983) report similar values of J at solar zenith angles of approximately 60 • , while the solar zenith angle at the beginning of our measurement was 77.7 • .

Platt and Kuhn
Overall, the data points in Fig. 19 coarsely resemble the shape of the Janssen model. However, they oscillate around the prediction of the best fit (red dotted line in Fig. 19). The cause of these oscillations is possibly the alignment of the optical 510 axes of the cameras inside the instrument. It was explained earlier, that the camera axes were aligned so that no shifts occur in the center of the FOV due to the displacement of the two cameras. However, shifts towards the corners of the FOV are then inevitable. It was observed, that such shifts typically lead to patterns of consecutively increased and decreased false signal in the signal ratio image. The plateau after 400 m of downwind distance agrees with Janssen models assuming ozone mixing ratios of 15 -30 ppb. Although such mixing ratios are relatively low for typical polluted urban areas, they are within a realistic 515 order of magnitude. Overall, the obtained fit parameters agree well with the reference values we have listed. It should be taken into consideration that more recent studies have found initial NO 2 /NO x concentration ratios of 5 -10 % to be more realistic for the emission from most combustion processes (see e.g. Kenty et al. (2007); Carslaw (2005)). This is neglected by the Janssen model, which predicts an initial NO 2 /NO x ratio of zero. Furthermore, as discussed in sect. 4.2.2, the NO 2 camera is incapable of measuring the NO 2 SCD of the plume directly after its emission, when it is still in a fully condensed phase (see Fig. 14). 520 Figure 19 shows the concentration ratio against the distance downwind, which is measured from the point, where the fully condensed part of the plume ended (at a width of 840 m in Fig. 14). The evaluation shown here neglects the plume chemistry of this early phase. To conclude, a crucial uncertainty is the mapping of the column-wise vertical SCD integrals onto the interval

Comparison of camera images and MAX-DOAS elevation scans
A comparison between the NO 2 column densities measured by the NO 2 camera and the results from elevation scans with the MAX-DOAS instrument was carried out. The MAX-DOAS instrument and the NO 2 camera operated simultaneously from   to the measured optical depth in a fit window from 400.6 to 425 nm. Spectra recorded at 90 • were used as reference. Elevation scans taken over polluted regions typically show a strong anthropogenic NO 2 background, caused by the combined emission of 535 the many NO 2 sources (e.g. fuel burning in traffic, in households or on industrial sites) in these regions. For reference, similar backgrounds were measured e.g. by Manago et al. (2018) and Peters et al. (2019). In order to extract the NO 2 signal attributed to the emission of GKM block 7, the anthropogenic background signal (the red line in Fig. 20 (a)) was estimated and subtracted from the total signal (the black line in Fig. 20 (a)). The procedure is similar to the background fit described in sect. 4.2.1, although here the intention was to separate two sources of true NO 2 signal (plume and background), whereas the background 540 fit procedure for the camera data intended to additionally separate plume signal and false signal due to imperfections of the optical setup. For ideal comparability the DOAS background signal was extracted using the same background estimation routine that was used for the camera data (see sect. 4.2.1). Here a cubic function (polynomial of degree n = 3) was used for both camera and DOAS data. Additionally, the elevation angles that were masked out in the camera data by choice of the fit mask were masked out in the DOAS fit as well. In practice, this means that here the elevation angles 2-4 • were excluded from 545 the fit. The plume signal was then extracted by subtraction of the obtained background signal from the total signal, as shown in Fig. 20 (b), leaving a clear signal spike at an elevation angle of 3 • . resolution of the NO 2 camera data, it was nonetheless still higher than that of the MAX-DOAS instrument. This is because the MAX-DOAS instrument only samples one elevation angle at a time, while the NO 2 camera captures a full-frame image, yielding a higher overall information content. Also the MAX-DOAS measurements do not continuously cover the range of elevation angles, because the FOV is smaller than the steps of the elevation scan. The resulting camera image is displayed 555 in Fig. 21 (a) along with some coloured vertical and horizontal lines indicating the regions in which the comparison to the MAX-DOAS elevation scans was carried out (see figure description). Figure 21 (b) shows plots of the camera signal along the vertical plume cross sections indicated by the coloured vertical lines in Fig. 21 (a). Compared to the results shown in Fig. 14, the overall plume signal is much lower, peaking at around 1.5 · 10 16 molec cm −2 (see purple line in Fig. 21 (b)). The average plume signal amounts to around 1 · 10 16 molec cm −2 (see thick red line in Fig. 21 (b)). The plume was located at a for some DOAS elevation scans, a negative plume signal of up to −0.8 · 10 16 molec cm −2 is obtained after subtraction of the background fit. As a consequence, in the average DOAS elevation scan (see thick red line in Fig. 21) the measured NO 2 SCD 565 is largely reduced. These deviations from the camera measurements require discussion.
In order to compare the elevation angles, at which both instruments registered the target plume signal, an elevation calibration method is required for both instruments. The elevation calibration for the NO 2 camera is straightforward. Using the chimney height of 200 m and a distance between the NO 2 camera and the GKM of 3.6 km, the chimney top is at an elevation angle of arctan(200/3600) ≈ 3.2 • . Both chimney height and distance to the scene are known very accurately and thus we take 570 this calibration as reliable. MAX-DOAS instruments are typically calibrated by scanning the horizon in small elevation steps and identifying the elevation angle of 0 • by the sudden jump of measured intensity that is expected to occur at the horizon line. From the perspective of our measurement location, the rooftops of the GKM buildings were reaching over the horizon, meaning that the MAX-DOAS calibration has registered the intensity jump that occurred between the sky and the rooftops at a height of 120 m or 1.9 • elevation (as opposed to the horizon at 0 m height or 0 • elevation). This reference allows for full 575 elevation calibration of the MAX-DOAS instrument. Because time was running short, the horizon scan was performed with relatively coarse elevation steps of around 1 • . Combined with the extended FOV of ±0.2 • of the MAX-DOAS instrument, the uncertainty of the elevation angle can be assumed to be on the order of 1 • .
As explained, a difference in the overall magnitude of the measured plume signals is observed as well. While the NO 2 camera measures an average plume signal of approximately 1 · 10 16 molec cm −2 , the corresponding average values measured 580 by the MAX-DOAS instrument are much lower. Two possible reasons can be identified for this deviation: Firstly, the background fitting routine is a critical step for both instruments. It was shown in sect. 4.2.2, that the uncertainty of the overall plume signal is around 2 · 10 16 molec cm −2 . This uncertainty was mainly constituted by the detection limit of the instrument due to the uncertainty of photon counting, the variance in measured signal at different distances downwind and the uncertainty of which background fit function to use (see Fig. 16). Here, because the camera data was averaged over a time of 1 · 10 16 molec cm −2 must be separated from a background signal gradient on the scale of at least 5 · 10 16 molec cm −2 (see Fig. 20). Figure 21 (c) demonstrates, that the distinction between plume and background signal is so uncertain, that a for a few elevation scans the routine even returns negative plume signal.
Secondly, and more importantly, the two instruments achieve spatio-temporal sampling of the plume on very different scales.
The NO 2 camera is capable of full-frame imaging with acquisition times on the scale of seconds and can measure the plume 595 regardless of its position and shape, given a high enough plume column density. The MAX-DOAS on the other hand requires around 2 minutes for a single elevation scan of 14 individual elevation angles, meaning it effectively yields a point measurement every 8.5 seconds. The temporal sampling in the plume region is therefore rather low. Specifically, the MAX-DOAS samples the plume region for only around 20 % of the measuring time. It is very likely that during the elevation scans, the MAX-DOAS FOV missed the plume center, where the highest SCD would be measured, or even missed the plume entirely. Additionally, 600 variations of the vertical plume position during sampling may have further decreased the obtained signal or even led to negative signals.
Figure 21 (c) shows, that some MAX-DOAS elevation scans measured an enhanced signal at an elevation angle of 3.7 • , which is close to where the NO 2 camera located the plume at around 3.3 • (see subfigure (b)). One of these MAX-DOAS scans, scan no. 9, was taken from 10:20 to 10:22. Figure 22 shows a direct comparison between that elevation scan and the camera 605 results, averaged over that respective time frame (as opposed to Fig. 21 (a) and (b), which show the camera signal averaged over the entire measurement from 10:15 to 10:50). The dotted blue lines show the upper and lower edge of the uncertainty of the MAX-DOAS elevation calibration, here assumed to be ±1 • . Within the uncertainty, a reasonable agreement with the camera data is possible in the region around 3.3 • elevation. Overall the data shown in Fig. 22 yields the best agreement between MAX-DOAS and NO 2 camera results that we could find.

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To conclude, the agreement between camera and MAX-DOAS data is fair at best. For future measurements the MAX-DOAS elevation scans should be carried out in smaller elevation steps and longer acquisition times per step to accommodate for its poor spatio-temporal resolution. If possible, emission plumes with higher NO 2 concentrations and less turbulent atmospheric conditions should be chosen.

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We present a prototype of a novel NO 2 imaging instrument based on Gas Correlation Spectroscopy: the GCS NO 2 camera.
It operates by recording images with two cameras, each with a gas cell (cuvette) in front of it, where one is filled with air and the other filled with a high concentration of NO 2 . The instrument acquires images at high spatio-temporal resolutions of up to 1/2 FPS and 1920 × 1200 pixels. The instrument response to a wide range of target column densities, ranging up to 1 · 10 18 molec cm −2 , has been examined in a numerical instrument model. A linear instrument response has been observed 620 within that range, making the instrument easy to calibrate. An examination of the signal-to-noise ratio has shown that the ideal NO 2 column density in the gas cell of the instrument is approximately 4 · 10 18 molec cm −2 . Furthermore, under realistic conditions, a detection limit of about 2·10 16 molec cm −2 is expected. A study on the cross sensitivity to trace gasses other than NO 2 was carried out for water vapour and O 4 . Under assumption of realistic column densities of these species the magnitude of the cross sensitivity of the instrument was predicted to be below an instrument signal equalling −3.2 · 10 16 molec cm −2 625 of NO 2 . The predictions of the instrument model were verified in a proof-of-concept laboratory measurement, where four test cells were filled with different concentrations of NO 2 . Then their column densities were measured with a conventional DOAS setup and the NO 2 camera. We noticed agreement between both instrumental setups within their uncertainties for all test cells and between the camera results and the predictions of the instrument model. The average relative deviation between model prediction and camera result amounted to 18.2%. We present the results of a field measurement at the coal power 630 plant Großkraftwerk Mannheim. The camera measured an average NO 2 plume SCD of (4.74 ± 2.00) · 10 16 molec cm −2 and an average plume diameter of (78 ± 34) m. By examination of an off-plume area the detection limit of this measurement was estimated to be at ∆S = 1.89·10 16 molec cm −2 , however, the uncertainties of the evaluation procedure, mainly the background estimation, increased the overall uncertainty to ∆S = 2.00·10 16 molec cm −2 . A mass flux analysis was carried out on the basis of image sequences. For this purpose, the optical flow between pairs of consecutive images was estimated with a Farnebäck 635 algorithm, which yielded average horizontal wind speeds of (0.94 ± 0.33) m s −1 and a resulting mean NO 2 mass flux of (7.41 ± 4.23) kg h −1 ( = (64.5 ± 36.8) tons yr −1 ).
Finally, the camera data were compared to elevation scans performed by a MAX-DOAS instrument. We found fair agreement in magnitude and position of the plume signal, as measured by both instruments and identified the elevation calibration and the poor spatio-temporal sampling of the MAX-DOAS in combination with the dynamic variability of the plume position as 640 the main uncertainty. Future measurements with these aspects in mind may yield more satisfying results. An improved optical setup within the instrument could be considered. By including a beam splitter, the light for both sensor arrays could be collected from a mutual lens, thus eliminating the need to correct for differences in the otherwise two lenses as a potential error source, especially the cumbersome background fitting routine. Furthermore, this would make alignment of the cameras' optical axes obsolete. In its current form the instrument is easily transportable and highly cost efficient with a build price of less than 2,000 645 Euro.
Data availability. All data is available from the authors upon request.
Video supplement. A series of camera images was assembled into a video sequence. It shows consecutive NO2 camera images of the GKM measurement from 08:53 to 09:05, where the observed NO2 signal was especially strong. See Kuhn (2021).