1. Introduction

The instrument described in this paper is a complementary development activity of the Atmospheric Limb Tracker for the Investigation of the Upcoming Stratosphere (ALTIUS) project. ALTIUS is a Belgian initiative to propose a microsatellite-borne spectral imager aimed at measuring atmospheric trace gas concentration profiles from a sun-synchronous orbit. It will make measurements of the light radiance scattered by the sunlit earth’s atmosphere (also referred to as limb), and will also observe solar, stellar and planetary occultations. Its main concept relies on three independent hyperspectral imagers that will perform simultaneous measurements: one in the ultraviolet (UV, 250–450 nm), one in the visible (vis, 450–900 nm), and one in the near-infrared (NIR, 900–1800 nm). Each spectral channel is based on the same concept: a telecentric objective focuses incoming light into a spectral filter where the desired wavelength is selected. The focal plane is re-imaged by a back-end optics onto a sensor array. The spectrometer is an acousto-optical tunable filter (AOTF) that separates the selected wavelength from the incoming beam and rotates its polarization by 90° [1]. This project successfully passed a feasibility review in June 2010 and is currently in phase B (conceptual design consolidation).

Among the different observation geometries, bright limb measurements are the most challenging. For solar, stellar or planetary occultations, the light source is spatially well defined, allowing for easier tangent altitude registration and providing a transmittance measurement by dividing the attenuated radiance by its reference acquired above the atmosphere. On the contrary, the Earth’s limb is a bright, diffuse source where photons can be scattered more than once (especially at lower altitudes where optical thickness increases). This situation makes the determination of the sounded vertical domain more complex. Existing instruments that use grating spectrometers such as the scanning imaging absorption spectrometer for atmospheric chartography (SCIAMACHY) [2]) or the optical spectrograph and infrared imaging system (OSIRIS) [3]), map a single spatial dimension on their detector. As a consequence, they need to scan the atmosphere and assess the tangent altitude from a radiometric model or platform attitude parameters. The imaging capability of ALTIUS allows for accurate altitude registration by taking advantage of the instant two-dimensional (2D) spatial sampling of the total geophysical scene and by cross-calibrating attitude sensors with stars in the background. Since the innovative concept of ALTIUS is based on the use of an AOTF inserted in the optical path to spectrally filter the image, and because there is currently no space application of an AOTF-based spectral imager, we decided to build a breadboard of the visible channel to assess the imaging and spectral performances of the proposed measurement technique.

A prototype matching the current optical specifications of the visible spectral channel was designed by the company Optique et Instruments de Précision (OIP), and manufactured by the Belgian Institute for Space Aeronomy (BIRA-IASB). The only differences with ALTIUS are the use of commercial, off-the-shelf (COTS) parts and a linear optical design made of lenses instead of a folded optical path made of mirrors. This visible channel breadboard (referred to as “breadboard” or “instrument” hereafter) was tested from September 2010 to January 2011 against compliance to requirements by OIP. A final review of the tests results took place at the European Space Agency (ESA), which led to acceptance of the breadboard. Since then, it has been delivered to BIRA-IASB to carry on with more detailed calibration campaigns. As a complementary objective, we decided to demonstrate the measurement capabilities of atmospheric trace gas concentration.

In the first section, we describe the optical design and the optical parts constituting the breadboard along with its control and acquisition software. Particular attention is paid to a description of the AOTF working principle, the core element of this instrument. Then we present an application in real conditions: the detection of ${\mathrm{NO}}_2$ within the dense and turbulent plume exhausted by a waste incinerator. The underlying radiative transfer theory is exposed and, finally, the results are presented and discussed.

2. Instrument Description

A. Optics Description and Performances

The breadboard is a simplified version of the visible channel of the ALTIUS instrument as designed during the feasibility study of the project. It contains refractive optical COTS instead of mirrors, a detector, and a ${\mathrm{TeO}}_2$ AOTF. It is designed to simulate ALTIUS measurements in the bright limb observation mode. The characteristics of the breadboard are shown in Table 1.

Table 1. Visible Channel Breadboard Characteristics

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The breadboard consists of front-end optics (FEO) and back-end optics (BEO), as shown in Fig. 1. The FEO is designed as a telecentric confocal system, optimized for high uniformity. The BEO is a relay system that images the AOTF selected order (see Subsection 2.B.) onto the detector. The large $f$-number of the breadboard ensures a large depth of focus at the detector focal plane position. The detector is a commercial PIXIS 512B from Princeton Instruments that includes a back-illuminated CCD array, sensitive from the UV to the NIR spectral range and cooled down to $-70°\mathrm{C}$. The Glan–Taylor polarizers in the FEO and BEO are cross-oriented to achieve highest extinction ratios of the rejected spectrum. Their use in combination with the BEO pupil ensure efficient stray light reduction.

 

Fig. 1. Breadboard optical design: the front-end optics (FEO) is composed of a telecentric stop, a lens doublet, a calcite Glan-Taylor polarizer, and the ${\mathrm{TeO}}_2$ AOTF; the back-end optics (BEO) is composed of a Glan–Taylor polarizer, a lens doublet, an aperture stop, a second lens doublet, and the pixel array. Polarization state of the incident beam and the selected order is represented after each polarizer. The acoustic wave propagating through the crystal is represented by the pale gray region. Neither the relative dimensions of the optical elements nor the focal lengths are representative of the real dimensions.

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The modulation transfer function (MTF) performance of the optics was simulated for different points in the field of view (FOV) and at different wavelengths. The system is diffraction limited on axis. Points located in the central part of the detector always have a MTF higher than 0.3 at the Nyquist frequency. A tolerance analysis confirmed the relative immunity of the instrument optical design to misalignment and lens tilt.

The instrument opto-mechanical assembly is composed of an optical baseplate manufactured at BIRA-IASB and holders made from black anodized aluminum. On top of this structure, commercial Thorlabs assemblies are mounted for optics integration and alignment. Provisions to tilt lenses and to align the assembly in $X$-, $Y$-, and $Z$-directions allow for compensation of possible misalignments for optimum MTF performance. The detector is mounted on a bracket that can be moved in the $Z$-direction (height) by using adjusting screws. This adjustable bracket is mounted on two motorized translation stages for $X$- and $Y$-movement. This assembly ensures accurate positioning of the detector CCD and allows for the correction of the chromatic aberrations within the 400–800 nm operational spectral range.

The AOTF and the detector are controlled by LabVIEW software. It allows for a wide range of different acquisition sequences and saves the images together with the corresponding housekeeping data. A functional scheme of the breadboard operating system is represented in Fig. 2.

 

Fig. 2. Functional scheme of the breadboard electronics and acquisition software.

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B. Acousto-optic Tunable Filter

The instrument we describe is a spectral imager. One advantage of taking fast snapshots at particular wavelengths is to easily emphasize the presence of absorbing molecules in the light path by using differential methods. At the same time, the 2D-nature of our measurements provides knowledge of possible concentration gradients in the observed scene. From requirements in terms of spectral resolution, spatial sampling, field of view, and acquisition speed, an AOTF-based solution was selected. It has the advantage of being small (a few tens of ${\mathrm{cm}}^3$, lightweight (a few hundred grams), low power consuming (1–2 W), rapidly tunable (millisecond timescale), and contains no moving parts. The improvements in noncollinear optical and acoustic waves propagation in birefringent media [4] allowed for the design of AOTF-based imaging systems with large angular aperture [5,6]. In the context of a space application (ALTIUS), a ${\mathrm{TeO}}_2$ AOTF has proven to survive in space conditions for years in the Solar Occultation at Infrared (SOIR) channel of the Spectroscopy for Investigation of Characteristics of the Atmosphere of Venus (SPICAV) instrument onboard Venus Express. However, it was only used to reduce the spectrum of the incoming radiance before it enters the grating spectrometer to avoid multiple orders of diffraction [7].

An AOTF consists of a piezo-electric transducer (PT) bonded to a birefringent crystal. RF waves applied to the transducer generate acoustic wavefronts that propagate in the medium, creating a periodic modulation of the refractive index. The optical and acoustic waves couple if the momentum matching condition is fulfilled (also called the Bragg-matching condition):

 

Fig. 3. Vector diagram of the momentum-matching condition in ${\mathrm{TeO}}_2$. The acoustic wave ($\mathbf{K}$) and the incident (${\mathit{k}}_{\mathit{i}}$) and diffracted (${\mathit{k}}_{\mathit{d}}$) light beams are represented.

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In the Bragg regime (i.e., no momentum mismatch, $\mathrm{\Delta }k=k_i+K-k_d=0$), up to 100% of the corresponding light intensity $I_1(\lambda )$ can be diffracted by an angle ${\theta }_d$ with its polarization rotated by 90° [9]. For this reason a beam stop together with cross-oriented polarizers were used to remove the undiffracted order $I_0(\lambda )$ (Fig. 1). Slight momentum mismatch ($\mathrm{\Delta }k\ne 0$) makes the diffraction efficiency ($\mathrm{DE}=I_1(\lambda )/I_0(\lambda )$) decrease as the wings of a ${\mathrm{sinc}}^2$ function [9]. A drawback of this behavior is that small sidelobes are observed close to the main peak. This spectral leakage (accounting for not more than 10% of the total signal) is certainly to be addressed when performing absolute measurements, but less important when applying differential methods as for this work. The spectral bandwidth ($\mathrm{\Delta }\lambda$) is the FWHM of this ${\mathrm{sinc}}^2$ function and can be measured by tuning the acoustic frequency around the value providing the best DE for a monochromatic light source. It is proportional to ${\lambda }^2$ and $1/L$, $L$ being the interaction path length (i.e., the transducer length) [4].

Whereas the noncollinear interaction geometry offers large acceptance angles at the cost of a spectral gradient across the FOV in an afocal layout, our AOTF was used in a telecentric confocal design to overcome this effect by ensuring an identical beam incidence angle over the entire crystal aperture [10]. For a fixed acoustic frequency, a change in ${\theta }_i$ induces a change of the diffracted wavelength $\lambda$, Eq. (2). However, one drawback of this design is the sensitivity of the final image to impurities and DE patterns standing inside the crystal. These patterns appear like quasi-periodic modulation of the image intensity with a dependence on temperature and acoustic frequency. By keeping the intermediate focal plane a few millimeters behind the AOTF, this effect was partly reduced: the bundle of rays focusing behind the filter have crossed different portions of the crystal with different DE (averaging out part of the modulation amplitude), which is not the case when they focus right on the acoustic field. Nevertheless, it has to be accounted for by flat field correction.

The AOTF we used was a Gooch & Housego (model number TF625-350-2-12-BR1A) together with its associated 16-channel RF driver (R64060-150-10DFS-16X1-CDI3). This AOTF was based on a noncollinear design operating at the parallel tangents condition (thus it was optimized to have a relatively wide field of view [4]). The configuration was compatible with the requirements of a spectral imaging system; in particular, the aperture was large ($10\times 10\mathrm{mm}$) so as to maximize the light throughput and the interaction length was long enough to minimize the effects of acousto-optic blur. The design has been described elsewhere [11,12]. From laboratory measurements, it was found that DE close to 100% could be reached over the full wavelength range. Using laser sources, we measured a spectral bandwidth from 0.65 nm at 457.9 nm to 3.5 nm at 800 nm.

3. Ground-Based Test Campaign

During the fourth week of January 2012, an airborne campaign in Toulouse, France, was prepared in collaboration with the Service des Avions Français Instrumentés pour la Recherche en Environnement (SAFIRE). The measurement campaign consisted of a three-hour flight during which limb-scattered light and a solar occultation could be observed. The analysis of the flight data is still ongoing. However, on January 24 (the day before the flight), the airplane containing the breadboard was driven outside of its hangar for testing. Fortunately, the waste incinerator smokestack in Toulouse can be seen from the tarmac of the Francazal airport, about 3.5 km away. By orienting the airplane in such a way that the breadboard could observe the smokestack, spectral snapshots of the smoke plume could be taken. It was an unexpected test for our instrument with rather limited control on the experimental setup, but it was definitely an excellent opportunity to demonstrate the capabilities of a fast AOTF-based spectral imager.

A. Experimental Conditions

The instrument was mounted on a rack fixed in the airplane cabin in front of a quartz window through which the scene can be observed. The Francazal airport is located at 43.5413 °N, 1.3616 °E and the smokestack is located at 43.5569 °N, 1.3991 °E. The distance between the instrument and the stack is about 3485 m and the mean line of sight azimuth angle with respect to North is 60°. At this distance, the measured instrument FOV of $0.097\times 0.097{\mathrm{rad}}^2$ embraces a scene of $338\times 338{\mathrm{m}}^2$ ($0.44\times 0.44{\mathrm{m}}^2$ per pixel). Figure 4 shows an image taken by the breadboard with the AOTF tuned to the central wavelength of 645 nm (offering better visibility than shorter wavelengths). Due to the telecentric optical design, all perspective effects have disappeared, which gives the impression that the stack belongs to the building in the foreground, which is actually much closer than the incinerator. The image was taken at $10\text{:}20\text{:}54$ (UT) with an integration time of 1 second. At that time, the sky was partly cloudy with moderate wind (estimated to about $10\mathrm{km}/\mathrm{h}$ from the smoke displacement in successive pictures). Contrary to the impression given by this grayscale picture, the smoke actually appeared white, mainly because the cleaning processes of combustion smokes involve water vapor flushing.

 

Fig. 4. Image taken by the breadboard with the AOTF tuned at the central wavelength of 645 nm. The color bar shows the number of counts per pixel. The integration time was one second. Stray light has been removed and the image was corrected for flat field non-uniformities, which is the reason why the lower right corner is noisy (region of rather poor diffraction efficiency). Axes indicate pixel number.

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The experimental conditions were not optimal for the measurement of ${\mathrm{NO}}_2$ concentrations by means of backscattered sunlight: a partly cloudy sky prevented us from taking reference measurements at zenith and the plume was dense, contained lots of different gases and particles, and was blown by a moderate wind.

By comparison, the experimental conditions described in the reference paper by Lohberger, et al. [13] about imaging differential optical absorption spectroscopy (DOAS) were more favorable: they observed the exhaust gases of a gas cogeneration plant with a perfectly blue sky, in the absence of wind, and whose smoke was transparent. It was actually the only possible experimental condition for them because the imaging system used in their study was a scanning spectrometer, which took several minutes to complete the picture. On the other side, they managed to measure accurately the ${\mathrm{NO}}_2$ concentration at the outlet of the stack with uncertainties of about 10% only (but neglecting temperature effects on the differential ${\mathrm{NO}}_2$ absorption cross-section).

B. Measurement Principle

This instrument is designed to capture fast snapshots with moderate spectral resolution. It is not designed to sample large spectral windows the way other DOAS instruments do because it would take too much time, especially when observing moving targets. We therefore chose to apply the simplest measurement principle: by quickly taking pictures at two well-chosen wavelengths [a strongly absorbing one (${\lambda }_s$) and a weakly absorbing one (${\lambda }_w$)], one can emphasize the presence of a small absorber in the light path by detecting a variation of light intensity as long as other species do not spectrally interfere.

Figure 5 illustrates the radiative transfer problem and the assumptions made in the frame of this simple test case: the photons reaching the instrument have crossed the entire atmosphere to reach the boundary layer where they are scattered in our FOV. Some of them have penetrated the plume, while others have been scattered far behind the stack. The main difference is that the former have experienced strong extinction by the smoke, while the latter have traveled a larger distance in the boundary layer (if we assume single scattering approximation). Describing the extinction of light intensity by a Beer–Lambert law, one can write for the “smoke” pixels:

 

Fig. 5. Illustration of two photons trajectories. One is backscattered by the plume; the other one by the neutral air density (and passes close to the plume but not through). A simple single-scattering process is assumed. One notices the difference in path length in the boundary layer.

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The choice of the two wavelengths is critical for the method. By choosing them close, the difference in aerosol extinction can be neglected. Moreover, as other absorbing trace gases are present (with possibly comparable or larger extinction capacity), the selected spectral range should be kept away from differential structures in their spectrum. By doing so, one can estimate the extinction due to ${\mathrm{NO}}_2$ within the smoke by computing the following ratios: for the smoke pixels,

C. Data Acquisition and Correction

A standard doublet of wavelengths for ${\mathrm{NO}}_2$ measurements are 448 nm and 453 nm (see SAGE II instrument, for instance [14]). Unfortunately, the instrument could not be calibrated down to these wavelengths and another pair at ${\lambda }_s=463.3\mathrm{nm}$ and ${\lambda }_w=468.5\mathrm{nm}$ was selected instead. They have the advantage of being close ($\mathrm{\Delta }\lambda =5.2\mathrm{nm}$), corresponding to a negligibly different ${\mathrm{O}}_3$ absorption cross section amplitude, and benefiting from a narrow 0.65 nm FWHM AOTF spectral response function.

Between 10:12 AM and 10:20 AM, six sequences of two pictures were acquired with an integration time of two seconds. The wavelength was tuned to 463.3 nm and 468.5 nm alternatively with an average dwell time of six seconds between each picture, with a partial change of the shape of the plume during this interval. Among the six sequences, the last one shows the best overlap of the plumes, as illustrated in Fig. 6. Stray light and flat field measurements were also performed during and after the acquisition sequence.

 

Fig. 6. First two images (cropped from the initial ones) capture the plume at 463.3 nm and 468.5 nm. The color scale units are arbitrary. The last image shows $\ln (I(468.5)/I(463.3))$ where one can observe that most of the signal in the main body of the plume and its tail comes from the poor correspondence of the two plume images. Clearly, as the plume has moved down in the second picture, the ratio is sometimes computed between a brighter background pixel and a plume pixel, instead of two plume pixels. Only the very beginning of the plume is consistent from one image to the other.

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Flat field. The smokestack pictures acquisition was followed by flat field measurements. The technique is based on imaging uniform extended light source at each target wavelength in the same environmental conditions (i.e., temperature and humidity) as the measurements. The acquired picture forms the instrument imaging transfer function, which includes the effects of the optics aberrations, the non-constant DE over the AOTF aperture and the detector pixel response non-uniformity (PRNU). Any picture ($P(\lambda )$) can then be corrected by performing a pixel-to-pixel division by the normalized flat field response ($F(\lambda )$).

The spatially uniform light source was provided by the cloudy sky. With a sufficiently large number of pictures of moving clouds in the FOV, one can get as close as desired to a perfect flat scene. In our case, the cloud coverage was almost 100% with a moderate wind. Twenty consecutive pictures were averaged to construct the true flat field.

As the retrieval method uses ratios of spectral pictures (Eq. 8), particular attention was paid to not introducing any bias along with the subsequent ratio of flat fields. In absence of coincident calibrated measurements of the zenith cloudy sky radiance, radiative transfer simulations (using MODTRAN 5 [15]) provided the missing information. It was found that the radiances at 463.3 nm and 468.5 nm are almost equal for similar conditions (urban pollution, stratus clouds, same time, date and location, convolved by the instrumental spectral response function), requiring no further correction of the computed ratios. Though, a 1% $1\sigma$ standard deviation on the flat field ratio correction factor is considered in the total error budget.

Stray light. Due to the combined effect of an imperfect cross-orientation of the two polarizers surrounding the AOTF and the scattering of the residual undiffracted beam by the BEO diaphragm, pictures are contaminated by a non-negligible amount of stray light. To remove its contribution to the total intensity, some pictures must be acquired with the AOTF turned off ($P^{\text{OFF}}$). By doing so, nothing but residual undiffracted photons can reach the detector, which also happens when the AOTF is turned on but superimposed to the image made from the diffracted beam. Figure 7 shows how residual, undiffracted photons contaminate the picture, together with an image taken with the AOTF turned off.

 

Fig. 7. Left drawing shows part of the optical design as seen from above. Stray light is generated by the scattering of the unwanted order ($I_0$) by the diaphragm. The right picture is an image acquired when observing in the direction of the smokestack with the AOTF turned off. Integration time was two seconds.

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Altogether, the image correction follows a two-step procedure. First, the stray light is removed by subtraction (which is also applied to the flat field pictures), then it is normalized by the mean flat field: $P^{\text{corr}}(\lambda )=(P^{\text{ON}}(\lambda )-P^{\text{OFF}})/({\overline{F}}^{\text{ON}}(\lambda )-{\overline{F}}^{\text{OFF}})$.

D. Results

To solve Eq. (8) and to find the ${\mathrm{NO}}_2$ smoke SCD, $I^{\text{cl}}(\lambda )$ and ${\tau }_{{\mathrm{NO}}_2}^{\text{trop}}(\lambda )$ must be determined. From the spectral convolution of the ${\mathrm{NO}}_2$ absorption cross-section with the instrument response function, we have ${\sigma }_{{\mathrm{NO}}_2}(463.3)=5.45\pm 0.22\times {10}^{-19}{\mathrm{cm}}^2{\text{molecule}}^{-1}$ and ${\sigma }_{{\mathrm{NO}}_2}(468.5)=3.49\pm 0.14\times {10}^{-19}{\mathrm{cm}}^2{\text{molecule}}^{-1}$ (data from Vandaele, et al. [16], at 294 K , neglecting the small uncertainties due to the different temperatures of the local air masses). As can be observed in the third image of Fig. 6, $\ln (I(468.5)/I(463.3))$ is almost constant and close to 0 for the air imaged by the pixels looking at the left side of the stack (the “clear air” pixels). By computing the natural logarithm of the average ratio of intensities registered between rows 100 and 200 and columns 50 and 100, we find $\ln (I^{\text{cl}}(468.5)/I^{\text{cl}}(463.3))=0.0783\pm 0.0010$ (which seems consistent with the presence of a background atmospheric ${\mathrm{NO}}_2$ absorption in a polluted region).

The last term of Eq. (8) corrects the “smoke” and “clear air” intensity ratio for their difference of light path length in the boundary layer. In our case, ${\tau }_{{\mathrm{NO}}_2}^{\text{trop}}(463.3)$ and ${\tau }_{{\mathrm{NO}}_2}^{\text{trop}}(468.5)$ can only be determined indirectly.

By definition, ${\tau }_{{\mathrm{NO}}_2}(\lambda )={\sigma }_{{\mathrm{NO}}_2}(\lambda )·n_{{\mathrm{NO}}_2}·L$, where $n_{{\mathrm{NO}}_2}$ is the ${\mathrm{NO}}_2$ concentration in the air and $L$ is the optical path length. Information on the hourly concentrations of pollution-related species like ${\mathrm{NO}}_2$ could be obtained from the Observatoire Régional de l’Air en Midi-Pyrénées (ORAMIP) [17], the official institution responsible for air quality monitoring in the Toulouse region. From their in-situ measurements in different places of the city, an average ${\mathrm{NO}}_2$ mass concentration of $55\pm 7\mathrm{\mu g}{\mathrm{m}}^{-3}$ at this time of the day could be estimated. The fact that the first 15 km of the instrument’s line of sight cover the city area is an argument for only using urban measurement stations.

The estimation of $L$ is less straightforward. We assume that $L$ is the visual range (visibility) as defined by the Koschmieder formula [18]: ${\text{vis}}_{550}=3.912/\beta (550)$, where $\beta (\lambda )$ is the light extinction coefficient at a given wavelength in the air mass, mainly due to aerosols. A number of studies have shown a significant correlation between particulate matter (${\mathrm{PM}}_{10}$ or ${\mathrm{PM}}_{2.5}$, particles whose diameter is smaller than 10 or 2.5 μm) and the total aerosol optical thickness (AOT, represented by ${\tau }_a(\lambda )=\beta (\lambda )·H$, where $H$ is the light path length). Chu et al. [19] derived a relation between ${\mathrm{PM}}_{10}$ concentrations and the AOT at 550 nm from co-registered, ground-based aerosol robotic network (AERONET) data [20]: ${\mathrm{PM}}_{10}=54.7\times {\tau }_a+8$, ($R^2=0.82$). The ORAMIP data show a ${\mathrm{PM}}_{10}$ mass concentration of $22\pm 1\mathrm{\mu g}{\mathrm{m}}^{-3}$ on average at the time of our measurements, leading to ${\tau }_a(550)=0.26\pm 0.07$. Assuming that most of the aerosols observed by the AERONET Sun photometer are found in the boundary layer (box distribution profile), and according to the NOAA meteorological model real-time environmental applications and display system (READY) [21], which gives a boundary layer thickness of $H=700\mathrm{m}$ at the time and place of our measurements, we find a mean aerosol extinction coefficient at 550 nm in the boundary layer: $\beta (550)={\tau }_a(550)/H=0.37\pm 0.09{\mathrm{km}}^{-1}$. Using the Angström law to derive $\beta (466)$ (mean measurements wavelength) with a mean Angström coefficient of $1.55\pm 0.34$ (taken from measurements by Melin and Zibordi [22] in similar pollution conditions in Ispra, Italy), we find $\beta (466)=0.37·{(466/550)}^{-1.55}=0.48\pm 0.12{\mathrm{km}}^{-1}$. From these values, we estimate a visual range of $8.2\pm 2.1\mathrm{km}$ at our wavelengths. Subtracting the 3.5 km distance between the instrument and the stack from the visual range, we finally obtain ${\tau }_{{\mathrm{NO}}_2}^{\text{trop}}(463.3)-{\tau }_{{\mathrm{NO}}_2}^{\text{trop}}(468.5)=0.067\pm 0.033$.

Equation (8) can now be solved and the ${\mathrm{NO}}_2$ SCD in the plume close to the stack outlet is represented by a color map superimposed on the initial grayscale picture in Fig. 8. The location of the small subset of selected pixels for the SCD computation corresponds to the region where the plume remains stable within the six-second interval (Fig. 6). The standard deviation on the SCD values at the pixel level are shown in the right panel of Fig. 8. The relatively large uncertainty on the SCD is due to the somewhat reduced signal-to-noise ratio of the initial pictures (a consequence of the small integration time) and to the uncertainty on the optical thickness in the boundary layer [last term of Eq. (8)]. However, observing a bell-shaped distribution of the SCD values, we can decrease the uncertainty by computing a mean value for the SCD at the beginning of the plume: $6.0\pm 0.4\times 10^{17}\text{molecules}{\mathrm{cm}}^{-2}$. This value doesn’t take into account the effect of the temperature on the differential absorption cross-section of ${\mathrm{NO}}_2$ [23,24]. From computations on different data sets [16,25], convolved by our instrument spectral transfer function, we estimated a relative effect of $-0.3\%{\mathrm{K}}^{-1}$ in the cross-section amplitude difference between 463.3 nm and 468.5 nm. However, no valuable information could be found on the temperature of the plume released in the atmosphere by such incinerators. A few tens of degrees above the ambient temperature can quickly lead to an underestimation of more than 10% in SCD. This aspect was eluded in Lohberger’s work and, in absence of reliable information, we cannot do much more than mention it.

 

Fig. 8. Left panel: ${\mathrm{NO}}_2$ slant column density at the beginning of the plume, as computed with Eq. (8) for individual pixels. Right panel: Standard deviation of the computed SCD value. The large uncertainty at the pixel level arises from a relatively low signal-to-noise ratio of the pictures and, to a lesser extent, to uncertainties on the optical thickness in the boundary layer.

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To get an insight of the mass concentration of ${\mathrm{NO}}_2$ within the plume, the optical path length inside the smoke must be determined. The large optical thickness of this white plume is in favor of an accurate treatment involving multiple scattering. Though, as the accurate determination of ${\mathrm{NO}}_2$ emissions of such incinerator is not the target of this work, we obtained an estimated value by making two rough assumptions. The first one supposes an effective optical path length equal to twice the radius of the disk section of a conic envelope of the plume (i.e., photons undergo a single scattering at the core of the plume). The second one assumes a homogeneous distribution of the ${\mathrm{NO}}_2$ molecules within the plume conic volume. In the middle of the triangle-shaped subset of selected pixels (Fig. 8), the diameter of the cone is approximately nine pixels, equivalent to a length of four $\mathrm{m}$. The concentration of ${\mathrm{NO}}_2$ at the beginning of the plume would then be about $115\mathrm{mg}{\mathrm{m}}^{-3}$. This estimation, although a rough one, is at least in line with the official threshold of $200\mathrm{mg}{\mathrm{m}}^{-3}$ [26], and with the emission rates published by Veolia, the incinerator administrator: for 24 January 2012, an average of $151.8\mathrm{mg}{\mathrm{m}}^{-3}$ of ${\mathrm{NO}}_x(=\mathrm{NO}+{\mathrm{NO}}_2)$ were emitted.

4. Conclusion and Prospects

We have described a tunable spectral imager working in the visible domain that has been designed from the current specifications of the ALTIUS visible channel. Taking advantage of the moderate spectral resolution of the AOTF and its fast tuning capabilities (which outperform filter-based solutions), this instrument is well suited for acquiring sharp monochromatic pictures that allow for atmospheric trace gases remote sensing. It can offer valuable data, especially when spatial information is needed, and inherently solves the problem of pointing knowledge common to one-dimensional (1D) measurement systems.

The breadboard’s remote sensing capabilities were tested in harsh conditions by observing the turbulent plume of a waste incinerator at a distance of 3.5 km. From successive pictures at two well-chosen wavelengths, we could detect the presence of ${\mathrm{NO}}_2$ within the smoke and estimate its concentration nearby the stack outlet. The total measurement time was 10 s.

A number of possible improvements are considered to turn this breadboard of a space-borne instrument channel into a real ground-based or even airborne remote sensing instrument for the measurement of ${\mathrm{NO}}_2$ or ozone concentrations along with some spatial information. The reduction of the stray light, the decrease of the time interval between two snapshots and the improvement of the flat fielding method and the spectral calibration are currently under consideration.