# Improved calibrations of the stellar occultation data accumulated by the SPICAV UV onboard Venus Express

Daria Evdokimova, Denis Belyaev, Franck Montmessin, Jean-Loup Bertaux, Oleg Korablev

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Daria Evdokimova, Denis Belyaev, Franck Montmessin, Jean-Loup Bertaux, Oleg Korablev. Improved calibrations of the stellar occultation data accumulated by the SPICAV UV onboard Venus Express. Planetary and Space Science, 2020, 184 (May), pp.art. 104868. 10.1016/j.pss.2020.104868. insu-02472151

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Distributed under a Creative Commons Attribution 4.0 International License
1 Improved calibrations of the stellar occultation data accumulated by the SPICAV UV

2 onboard Venus Express.

3 Daria Evdokimova¹, ², *, Denis Belyaev¹, Franck Montmessin², Jean-Loup Bertaux¹, ², Oleg

4 Korablev¹.

5 ¹ Space Research Institute of the Russian Academy of Sciences (IKI), 84/32 Profsoyuznaya Str,

6 117997 Moscow, Russia

7 ² LATMOS/IPSL, UVSQ Université Paris-Saclay, UPMC Univ. Paris 06, CNRS, 78990

8 Guyancourt, France

9 * evd.dar@yandex.ru

**Abstract:** Stellar occultation is a powerful method to study vertical structure of the Venus night mesosphere. The UV channel of SPICAV spectrometer, operated in 2006-2014 on board ESA's Venus Express orbiter, allowed retrieval profiles of atmospheric gases (CO₂, SO₂, and O₃) and aerosols. It was also able to register different UV emissions around Venus (nitric oxide airglow, Lyman-α) overlapping the absorption features at 120-300 nm. Several calibration steps convert the raw data to atmospheric transmission spectra used for the retrievals. The systematic errors of resulted gaseous concentrations mainly relate to: (i) an uncertainty of the wavelength to pixel assignment; (ii) a portion of emitting light contaminating the analyzed transmission spectra. In the present paper, we have tested a new method of the wavelength-to-pixel assignment based on the spectral features of measured stars. Secondly, using imaging capabilities of the instrument, we have demonstrated an accurate separation between different kinds of registered signal: extended UV nightglow, light from a point star, transmitted through the atmosphere, and, sometimes, solar light, scattered by Venus dusk. The efficiency of two approaches performing the separation was studied. As a result, corrected transmission spectra provided retrievals of gaseous concentrations with 20-40% higher precision respectively to those processed in previous SPICAV stellar occultation studies (Montmessin et al., 2011, Icarus 216, 82; Piccialli et al., 2015, Planet. Space Sci. 113-114, 321; Belyaev et al., 2017, Icarus 294, 58).
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**Keywords:** Venus mesosphere, Stellar occultation, Wavelength assignment, Transmission spectrum processing.

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# 1. Introduction

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Orbital stellar occultation experiment of the Venus' atmosphere was implemented for the first time by the ultraviolet (UV) channel of the SPICAV (SPectroscopy for Investigation and Characterizations of Atmosphere of Venus) spectrometer onboard the ESA's Venus Express orbiter (VEX) in 2006-2014 (Bertaux et al., 2007). The instrument detects transmitted light containing spectral features of absorbing components (gases, aerosol particles) integrated along the instrument line of sight (LOS) while a star is occulted by atmospheric layers. It is an efficient way to study the vertical structure of the mesosphere at altitudes from 140 km down to 85 km where the aerosol extinction becomes too strong in the UV. The method is self-calibrated since a stellar reference spectrum is extracted from the same orbital session while the LOS is above the atmosphere. The transmission to be analyzed is a ratio of the transmitted spectrum to the reference one.

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The SPICAV UV range of 118-320 nm covers absorption bands of the most abundant molecule CO₂ (at λ<200 nm) and some minor species as SO₂ (180-235 nm, 250-340 nm) and O₃ (around 250 nm), detected by the instrument (Montmessin et al., 2011; Piccialli et al., 2015; Belyaev et al., 2017). A retrieval of gaseous and aerosol concentrations from transmission spectra was performed by resolving spectral and vertical inversion problems. The algorithms were described in details by Quemerais et al. (2006).

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In addition of absorption signatures, SPICAV also registered UV emissions produced by different sources. The first was nitric oxide (NO) night airglow at wavelengths of 190-270 nm (the δ- and γ-bands) (Barth et al., 1967). The layer of maximum emission with 400 kR located at altitude about 115 km was observed in stellar occultations (Royer et al., 2010) and night limb observations (Stiepen et al., 2012). The NO glow varying in time and in space was presented in the whole SPICAV stellar occultation database. The second source was hydrogen Lyman-α
53 emission at 121.6 nm having intensity of 1-3 kR in the night mesosphere (Chaufray et al., 2015).

54 This radiance was registered at occultations of weak stars and was totally absorbed by CO₂ in
55 lower layers of mesosphere: 80-100 km. The third type of considering emissions was the sun
56 light reflected at cloud top on the Venus crescent. It had significant intensity at 200-300 nm
57 overlapping the range of NO emission. These illuminations are parasitic for the retrieval of
58 absorbing quantities since they contaminate transmission spectra preventing a precise solution of
59 the spectral inversion problem.

60 Goal of the present paper is to distinguish all types of the emissions and to compare two different
61 methods for their subtraction from the transmitted light. These two approaches are based on
62 imaging capabilities of the spectrometer, where the useful and spurious signals spread over the
detector matrix differently. The methods were separately described by Royer et al. (2010) and
64 Belyaev et al. (2017). However, so far their precision and influence on the gaseous absorption
65 retrievals were never analyzed. In parallel, we propose an improved algorithm for the
66 wavelength to pixel assignment providing a better fit between measured and synthetic
67 transmission spectra. The algorithm fits the observed stellar spectrum to correspondent catalogue
68 one, while previously spectral features of the atmospheric CO₂ were used for that (Quemerais et
69 al., 2006).

## 2. The instrument description

70 The SPICAV UV channel, a spectrometer with imaging capabilities, operated in a spectral range
71 of 118-320 nm with a spectral resolution about 1.5 nm (see Bertaux et al., 2007 for details). The
72 spectrometer features a concave holographic grating that provides a light dispersion along 384
73 spectral points of the CCD while the other matrix coordinate (289 pixels) represents spatial
74 distribution of an observed scene. The scheme includes a narrow slit providing the specified
75 spectral resolution covering 3 pixels with the sampling of ~0.5 nm per each one. During a star
76 observation the slit was mechanically removed that allowed to accumulate more photons from
77 such a weak point source. The point-spread function (PSF) of the instrument distributes an
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element of stellar spectrum over a few tens of pixels in both, spectral and spatial, coordinates (Fig. 1A). This function is based on the Voigt profile with the half-magnitude width of ~3 pixels and rather wide wings. Thus, the convolved stellar spectrum was spread among several CCD rows in the spatial direction. In order to reduce the data volume transferred to the Earth a spatial binning of sequential spectral rows was applied onboard. One data package consisted of 5 bins (bands) composed by 4, 8, 16 or 32 spectra summed per bin (Fig. 1B). Targeting a star, the major portion of its light remained in the 3rd, i.e. central, bin while the rest was spread among other four ones.

<figure><img src="image_2.png" /><figcaption>Figure 1. A. A measured image represents spreading of star light among several CCD rows at the occultation #0668A05. B. An example of 5 spectra transferred to the Earth after onboard summing within different bins where the colors of lines corresponds to bin areas highlighted at Fig. 1A.</figcaption></figure>

Our algorithm of the stellar occultation data processing works with the raw spectra of stars cleaned from the dark current. The stellar spectra were then passed through a wavelength to pixel assignment. Totally, 690 sessions of stellar occultation were succeeded. The dataset covers mostly middle latitudes in both Venus hemispheres and, generally, the coordinates of observed target points corresponds to the latitude range of 80°S-80°N. On the other hand, the entire longitude range was observed for 8 years of the mission. The mesosphere layer studied by the SPICAV UV instrument on the night side corresponded to the altitudes from 85 km to 140 km.
Vertical resolution of the experiment varied from 0.5 to 8 km according to the distance to the
Venus limb.

3. The wavelength to pixel assignment

The experimental transmission spectra are modeled by the Beer-Lambert law where the
absorption parameters depend on wavelengths. This dependence determines the importance of a
precise wavelength to pixel assignment. The preceding algorithm performing this calibration was
based on an alignment of the CO₂ absorption band position (Fig. 2A) in observed spectra. It was
described in Quemerais et al. (2006) for the Mars atmosphere which is 10-5 times less dense than
the Venus one. The CO₂ absorption band at the wavelengths shorter than 170 nm is detectable by
SPICAV only between 120 and 140 km (Fig. 2A). Below it becomes fully saturated to zero
signal, making a transmission spectrum useless for the wavelength calibration in this spectral
interval. Due to the geometry of the VEX stellar occultation the altitude step between two
consequent spectra, measured at one matrix bin, is about 8 km. It implies to have 3-4 points for
the proper wavelength to pixel assignment for each bin.

A new approach is not based on gas absorption and considers the features of the stellar spectrum
measured outside of the atmosphere. Hundreds of pure star spectra are measured for every
observation depending on the occultation duration. For each of these spectra the correspondence
of stellar spectral lines positions is established in comparison with the catalog spectra. The
catalog is taken from data obtained by the International Ultraviolet Explorer (IUE) operated on
the Earth orbit in 1978-1996 (Boggess et al., 1978). IUE channels covered wavelengths from 115
to 320 nm that was consistent with the SPICAV UV range and the spectral resolution achieved
the value of 0.02 nm.

During the SPICAV ground calibrations a parabolic law describing the wavelength (λ) to pixel
number (Nₚₓ) assignment (Eq. 1) was defined (Villard, 2008). For the in-flight conditions
wavelengths were shifted by a value Δλ needed to be retrieved:

$$
\lambda(N_{pix}, \Delta\lambda) = \Delta\lambda + 325.48 - 0.54596 \cdot (N_{pix} + 9) - 4.9096 \cdot 10^{-6} \cdot (N_{pix} + 9)^2 \quad (1)
$$
<figure><img src="image_3.png" /><figcaption>Figure 2. Wavelength-to-pixel assignment for occultation #3098A02. A. A transmission spectrum measured by SPICAV UV ($T_{SPICAV}$) at 133.43 km which displays the CO$_2$ absorption band shape ($T_{model}$) used previously for the older wavelength assignment. B. Wavelength alignment by a star spectrum (HR6175). (Top) The SPICAV UV spectrum ($S_{SPICAV}$) and the IUE one convolved with the SPICAV UV resolution ($S_{IUE}^{convolved}$). Their corresponding continuums ($C_{SPICAV}$ and $C_{IUE}$) are calculated by smoothing the $S_{SPICAV}$ and $S_{IUE}$ with an interval of 21 spectral points, i.e. ~11 nm. (Bottom) SPICAV UV and IUE relative spectra S/C normalized by their smoothed curves and aligned by wavelengths. The blue line displays the range of fitted points.</figcaption></figure>

It was found that a good way to determine $\Delta\lambda$ was an alignment between observed SPICAV spectra with those of IUE, retaining only the higher frequency features of the spectra and removing the effect of the continuum supposed to be specific to each instrument due to their absolute calibration function. To achieve that, we computed a relative spectrum out of the ratio between the measured signal and its smoothed version, applying a simple low-pass filter. The shapes of SPICAV and IUE spectra ($S_{SPICAV}$ and $S_{IUE}$) and the corresponding continuums ($C_{SPICAV}$ and $C_{IUE}$) are shown on Fig. 2B (top) while relative spectra S/C are shown in the bottom plot of Fig. 2B. The smoothing interval was chosen to perform the best extraction of star lines positions considering current spectral resolution. It was equal to 21 spectral points corresponding to a spectral interval of ~11 nm. One occultation contains hundreds of stellar spectra that are free of atmospheric absorption. This number allows to increase the accuracy of the $\lambda(N_{pix})$ function

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compared to the CO₂ alignment approach. Moreover, an absence of Δλ-shift temporal evolution was proved. The resulting Δλ-shift is defined with an error of 1-10% of one-pixel width while the method based on the CO₂ alignment provides an uncertainty comparable with the one-pixel width.

An improvement obtained from this other spectral alignment method is a correction of systematic error in the resulting CO₂ slant density profiles. Since the CO₂ absorption band is saturated below 120 km the spectral inversion problem becomes sensitive to wavelengths determined for each pixel of a spectrum. For instance, an error of one-pixel width corresponding to 0.54 nm is considered for the wavelength calibration of observation #1269A03. This observation has a vertical resolution of 1.2 km and is used to gauge the slant density uncertainty caused by the wavelength shift at different altitudes. The estimated error reaches 20% for the deep mesosphere (Fig. 3). The wavelength to pixel assignment shift affects even more the volume mixing ratio (VMR) profiles of trace gases (SO₂, O₃) because the VMR is calculated as the ratio of the trace gas density with that of CO₂, both being retrieved from the same observation.

<figure><img src="image_4.png" /><figcaption>Figure 3. Differences in percentage of the CO₂ slant density profiles retrieved from the same observation #1269A03 using two different approaches for the wavelength to pixel assignment. The reference is chosen to be a CO₂ profile retrieved from spectra calibrated with the stellar line alignment method. A. A negative shift of one-pixel width (-0.54 nm) is applied to the stellar lines alignment method. B. A positive shift of one-pixel width (0.54 nm) is applied.</figcaption></figure>
4. Signal contamination by the emission of extended sources

The measured signal after the dark current correction ($S^{SPICAV}$) is composed of the following components:

$$S^{SPICAV} = S^{STAR} + \underbrace{S^{NO} + S^{LY-A} + S^{SUN}}_{S^{STRL}} = S^{STAR} + \underbrace{S^{STRL}}_{S^{STRL}} \quad (2)$$

All types of the UV emission as the nitric oxide airglow ($S^{NO}$), the Lyman-a scattered light ($S^{LY-A}$), the sun light in the UV ($S^{SUN}$) contained in spectra obtained by the SPICAV UV are considered by us as a stray light ($S^{STRL}$) regarding to the spectral inversion problem. A behavior of this illumination in spectra depends on the observation geometry and on the condition of whether the observation was carried out using an additional slit. While the spectrum of a star being a point source is not changed by the slit presence, the spectral resolution and the spectrum shape of extended sources light depend on the instrument FOV value. The whole FOV exposition smooths the emission spectrum features over the entire pixel range. The most intense emission is produced by the NO molecules and it dominates in each stellar occultation session. Its vertical distribution in the Venus atmosphere is non-uniform, thus, the CCD illumination depends on the emitting layer position in the FOV (Royer et al., 2010). The Venus Lyman-α light is detectable only for observations of weak stars performed with high gain values. High gain observations correspond to setting the pre-amplifier to high values in order to increase the flux of electrons on the photodetector (>100 in the digital range of 0-255, see Bertaux et al., 2007 for details). The Lyman-α line is well-distinguishable in spectra measured using additional slit. Otherwise, it is integrated in the entire FOV and the signal is spread among more than 250 pixels. Finally, the Sun in the UV range might be registered in the stellar occultations performed at low phase angles where the light reflected on the crescent gets into the FOV.

The stray light spreads among all of the detectors rows, thus, the resulting spectrum of each bin ($S_i^{SPICAV}$) in addition to a portion of transmitted stellar light defined by the PSF function contains a stray light contamination ($S_i^{STRL}$) and this is represented by the following formula:

$$S_i^{SPICAV}(\lambda) = \alpha_i S^{ref}(\lambda)T(\lambda) + S_i^{STRL}(\lambda), i = 1 \dots 5 \quad (3)$$
where $\alpha_i$ is the fraction of the PSF occupying the i-th bin, $S^{ref}$ is a star spectrum multiplied by the atmospheric transmission ($T$). Nominally a star is focused to the central or 3rd bin and 90% of its signal is contained in this bin. Extended sources illuminate the whole CCD and tend to evolve more slowly in time than the stellar signal. Their emission spectrum can be inferred from consideration of the bins containing the wings of the PSF distribution. This assumption was used in two different approaches allowing the stray light separation in the stellar occultation data and their respective efficiency was studied.

## 4.1. Stray light elimination: method 1.

The first considered method was introduced in Royer et al. (2010) and presented in greater details in Picciali et al. (2015). The algorithm estimates stray light spectrum on the 3rd bin ($S_3^{STRL}$) as a linear combination of stray light spectra on other bins ($S_i^{STRL}$).

$$S_3^{STRL} = \sum_{i=1,2,4,5} k_i S_i^{STRL}(\lambda) \qquad (4)$$

The correct determination of the linear coefficients $k_i$ is key to the proper subtraction of the emission from the transmittance spectra. It is possible to obtain a reliable estimation using occultation altitudes where the star light is absent, typically below 60 km. For these spectra the resulting coefficients release the best fit of the Eq. 3 and the minimum of the following $\chi^2$ function:

$$\chi^2(k_1, k_2, k_4, k_5) = \sum_{z=-200 \text{ km}}^{z=60 \text{ km}} \sum_{\lambda} \left( \frac{S_3^{STRL} - \sum k_i S_i^{STRL}(\lambda)}{\sigma^{STRL}(\lambda)} \right)^2 \qquad (5)$$

where $\sigma^{STRL}(\lambda)$ reflects experimental uncertainties established below 60 km.

The resulting values are then used in the occultation region (85-140 km) to determine the transmission spectra by Eq. 3 considering the PSF spreading only a few percent of the incoming stellar light to edge bins.

$$T(\lambda, z) = \frac{S_3^{SPICAV}(\lambda,z) - \sum k_i S_i^{SPICAV}(\lambda,z)}{S^{ref}(\lambda)} \qquad (6)$$

## 4.2. Stray light elimination: method 2.
The second method is also based on the determination of the stray light fraction contained in the central (the 3rd) bin. It is mentioned above that this bin generally contains about 90% of the stellar signal and the 1st and 5th bins retain just about 1-3% due to the PSF distribution (Fig. 1). Therefore, one is capable to build a stray light template while averaging the 1st and 5th bins spectra. The spectral inversion problem for each measurement within the considering altitude range is resolved by a minimization of the $\chi^2$-function. The latter (Eq. 7) depends on an additional variable parameter k which scales the stray light template to avoid overestimation of the modeled transmission:

$$ \chi^2(k, N_g, \tau_\alpha) = \sum_{\lambda} \left( \frac{S_3^{SPICAV}(\lambda) - [T^{MODEL}(\lambda, N_g, \tau_\alpha) + k \cdot S_{template}^{STRL}(\lambda)]^2}{\sigma(\lambda)} \right) \quad (7) $$

where $\sigma(\lambda)$ corresponds to experimental uncertainties of the $S_3^{SPICAV}(\lambda)$ spectrum.

$T^{MODEL}$ is a synthetic transmission calculated using the following parameters: a slant density of the gaseous compound along the spectrometer LOS ($N_g$) and an aerosol optical depth ($\tau_\alpha$). In this case the extracted transmission spectrum evaluates by the formula:

$$ T(\lambda, z) = \frac{S_3^{SPICAV}(\lambda, z) - k \cdot S_{template}^{STRL}(\lambda, z)}{S^{ref}(\lambda)} \quad (8) $$

### 4.3. Comparison of the methods

Both methods determine a stray light template and, thus, show comparative results. Each orbit of the SPICAV UV dataset was treated by two ways to study their efficiencies. An example of correct treatment by both algorithms is shown on the Fig. 4 where the raw data has a bright red signature of the NO emission at 200-250 nm that distorts the transmission values.

<figure><img src="image_5.png" /><figcaption>Figure 4. Altitude dependence of transmission spectra for orbit #3071A02. From the left to the right: the raw data, the data treated by the method 1, the data treated by the method 2, and a</figcaption></figure>
residual between transmissions retrieved by both methods. The residual represents an underestimation of the NO emission in the method 2.

The transmission decreases from 1 to 0 while the instrument LOS is going deeper in the atmosphere. The CO₂ absorption band becomes saturated quickly reducing the atmospheric transmission to zero below 120 km at wavelengths shorter than 150 nm. Longward of 180 nm, there is no absorption by either minor species or aerosol at altitudes down to 115 km and the spectrum remains equal to one. Due to this behavior, the results of the treatment were studied within three different spectral intervals relating to three molecules absorbing in the SPICAV UV range: the CO₂ absorption band (130-150 nm), one of the SO₂ bands (200-230 nm) and the O₃ one (250-270 nm). The considered SO₂ absorption band is interesting because it corresponds to the maximum of the nitric oxide emission and therefore differences in the two methods will probably be highlighted in that range.

Systematic errors in the retrieved profiles of atmospheric components caused by overestimation of the transmission while extracting the NO emission are significant. They are comparable with the one originating from the wavelength to pixel assignment. To examine the influence of transmission uncertainties on the trace gases profiles, one considers a negative deviation of -0.005 of transmission averaged within the spectral ranges to be studied. In Fig. 5 we show the estimated uncertainties. Thus, the CO₂ slant densities do not change significantly (Fig. 5A). However, if one considers relative values of minor gases abundances, which are the VMRs, there is a resulting decrease of a factor of two of their VMRs (Fig. 5B and 5C).

<figure><img src="image_6.png" /></figure>
Figure 5. Influence of underestimated transmission values on the resulting slant density profiles of CO₂ (A) and the resulting volume mixing ratio (VMR) profiles of SO₂ (B) and O₃ (C) depending on the altitude.

The comparative efficiency of the algorithms is estimated by examining transmissions averaged within the three spectral intervals presented above and at varying altitudes (Fig. 6). The uncertainties of the two methods cause some statistical distribution around expected values of transmission: 0 (Fig. 6A) or 1 (Fig. 6B, 6C). Transmission at 130-150 nm turns to zero below 120 km since the CO₂ absorption band becomes saturated. Besides, transmission is equal to one at longer wavelengths over 115 km due to a small aerosol and trace gases absorptions. The considering altitude ranges are highlighted on Fig. 6. For each profile, considering statistical distribution is expressed by a histogram of the probability density function (PDF) with mean value and dispersion. In intervals of the maximum NO emission (Fig. 6B) and the ozone absorption band (Fig. 6C) it is well fitted by the Gaussian law. The nitric oxide airglow band is characterized by mean transmission value μ₀ close to 1 that corresponds to expectations (Fig. 6.1B and 6.2B). The resulting deviation is covered by this experimental uncertainty. The transmission deviations from 1 also might be related to atmospheric absorbers variations in addition to inaccurate estimation of emission component. The range of carbon dioxide absorption band (Fig. 6A) shows the most precise result of the transmission extraction quality. However, CO₂ in the mesosphere causes partial to total absorption of the UV light within its absorption band that eventually results in transmission equal to zero. Thus, any deviations visible on histograms are related strictly to methods errors (Fig. 6.1A and 6.2A). The Gaussian profile does not match the derived histograms and the best coincidence is given by a bimodal normal distribution. Bimodality is the most obvious in the method 2 (Fig. 6.2A) where the maxima of the PDF are obtained at transmission values μ₀ ≈ 0 and μ₁ = 0.0054. Results of Method 1 are also characterized by a bimodal distribution, however, it is less pronounced and is only used to describe the distribution tail (Fig. 6.1A).
<figure><img src="image_7.png" /><figcaption>Figure 6. Retrieved profiles of transmission averaged within different spectral intervals: a range of the CO₂ absorption band (130-150 nm), the maximum of the NO emission (200-230 nm matching to the SO₂ absorption band) and a range of the O₃ absorption band (250-270 nm). At altitude ranges of 120-140 km for the CO₂ band and 85-115 km for other intervals distributions of values were built. The points that are used to build histograms correspond to highlighted areas of the transmission profiles. There are probability dense functions for resulted transmissions averaged within CO₂ band at 1A and 2A, averaged in range of NO emission at 1B and 2B and averaged within O₃ band at 1C and 2C. The black dashed line represents modeled distributions with estimated parameters presented in Table 1.</figcaption></figure>

<table><caption>Table 1. Parameters of fitted distributions.</caption><thead><tr><th></th><th>Method 1</th><th>Method 2</th></tr></thead><tbody><tr><td>CO₂ band range</td><td>μ₀ = (69.5 ± 0.2) e-05, σ₀ = 0.0020 ± 3.1e-06<br>μ₁ = 0.0049 ± 2.2e-05, σ₁ = 0.0106 ± 1.7e-05</td><td>μ₀ = (8.2 ± 0.7) e-05, σ₀ = 0.0021 ± 1.1e-05<br>μ₁ = 0.0054 ± 1.4e-05, σ₁ = 0.0095 ± 1.5e-05</td></tr><tr><td>NO band range</td><td>μ₀ = 0.9989 ± 0.0003, σ₀ = 0.0087 ± 0.0002</td><td>μ₀ = 1.0009 ± 0.0003, σ₀ = 0.0085 ± 0.0002</td></tr><tr><td>O₃ band range</td><td>μ₀ = 0.9823 ± 0.0005, σ₀ = 0.0156 ± 0.0003</td><td>μ₀ = 0.9829 ± 0.0006, σ₀ = 0.0180 ± 0.0004</td></tr></tbody></table>

In most cases, both methods lead to nearly identical results. Analysis of the Method 2 has shown that CO₂ density values were more frequently underestimated in the lower atmosphere (<100 km) and bimodality in statistical distribution of transmissions around zero is more pronounced. At these altitudes the aerosol absorption is significant and the transmission is less than one for
301 the whole SPICAV UV wavelength range. For these spectra, Method 2 yields an inaccurate 302 determination of the aerosol absorption due to $\chi^2$ minimization procedure that leaves residual 303 signal. Therefore, the average value of the transmission in the range of the CO$_2$ band remains 304 greater than zero. We can conclude that the Method 1 is more efficient than Method 2 in frames 305 of statistical comparison of its results.

### 5. Conclusions

307 We have analyzed impacts of systematic errors onto gaseous concentration retrievals in stellar 308 occultation experiment made by the SPICAV UV spectrometer on board Venus Express orbiter. 309 The considered uncertainties are mainly related to two calibration aspects: (i) a wavelength to 310 pixel assignment, and (ii) a portion of emitting atmospheric light contaminating the analyzed 311 transmission spectra. The wavelength displacement along a pixel number may result in both 312 either underestimation or overestimation of retrieved concentrations. For instance, an uncertainty 313 of one-pixel width corresponding to 0.54 nm leads to the retrieved CO$_2$ slant density change of 314 20% in lower mesosphere (85-100 km). In the present paper, we have tested a new method of the 315 pixel-to-wavelength assignment based on the spectral features of measured stars. The method 316 compares star spectra measured by SPICAV with reference ones taken from the well-resolved 317 IUE data. As a result, the higher assignment accuracy was achieved versus the previous 318 approach, based on wavelength alignment by CO$_2$ absorption band at $\lambda<200$ nm. Deriving the 319 wavelength assignment from the CO$_2$ absorption band at 120-170 nm is constrained by a quick 320 increase of the mesosphere optical thickness. It allowed nominally to measure just 3-4 spectra 321 with non-saturated CO$_2$ band at one occultation session. In contrast, hundreds of pure star 322 spectra, measured out of the atmosphere before (or after) each occultation, were used for the 323 wavelength calibrations. Thus, the uncertainty of the wavelength to pixel assignment was 324 reduced at least by 10 times and was estimated to be 1-10% of the width of the pixel.

325 The possible underestimation of gaseous and aerosol abundances is also an effect of different 326 kinds of emission light in the UV registered by SPICAV. That emission was considered as a
stray light, which overlaps a star spectrum making an atmospheric transmission overestimated.

Currently, two methods were considered in order to distinguish the emission component (coming mainly from the nitric oxide airglow around Venus) and the light from the star. The spectra obtained by SPICAV UV were treated by both methods and the resulted transmissions were compared to establish the most efficient way extracting the total emission component. For instance, an overestimation of transmission at 0.005 gives a 15% decrease of CO₂ slant densities.

Mixing ratio of minor species as a relative value is more sensible to transmission uncertainties.

Such a systematic error may change the VMR by a factor of two. To apply both methods, we used imaging capabilities of the instrument, where the stray light pattern was determined as a linear combination of spectra registered within edge bins according to the star focus position on the matrix. In the first algorithm the coefficients defining the linear combination are computed at the atmospheric shadow and they remain fixed for the occultation altitude range. The second approach considers the stray light template included to a spectral inversion equation with a free scaling parameter. This parameter is calculated for each spectrum separately. The analysis of altitude transmission profiles shows that the first method is more effective to subtract the emission component from the stellar one. That is related to underestimation of the aerosol absorption (Fig. 6.1A and Fig. 6.2A). The statistical analysis of the entire SPICAV dataset allows to conclude that the emission component is estimated more accurately by the first method.

The atmospheric transmission spectra retrieved by this method are less subjected to have overestimated values. That decreases the systematic errors of resulted vertical profiles of CO₂ and other atmospheric components. Consequently, the algorithm is accepted to calibrate the entire SPICAV dataset. The resulted transmission spectra are used for the spectral inversion problem to retrieve gaseous and aerosols vertical profiles and for further investigations.

The described data processing improvements might be also applied for future stellar occultation measurements in the similar spectral range, to be performed by the PHEBUS spectrometer on
board ESA/JAXA BepiColombo mission (lunched in October, 20th, 2018 to Mercury) during
Venus flybys (Mangano et al., 2018).

Acknowledgments

Daria Evdokimova and Denis Belyaev acknowledge a support of the RSF grant #16-12-10453.

References

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