Emmanuel Marcq
email: emmanuel.marcq@latmos.ipsl.fr

Kandis Lea Jessup

Lucio Baggio

Thérèse Encrenaz

Yeon Joo Lee

Franck Montmessin

Denis Belyaev

Oleg Korablev

Jean-Loup Bertaux

Climatology of SO 2 and UV absorber at Venus' cloud top from SPICAV-UV nadir dataset

Keywords: Venus, atmosphere, Ultraviolet, observations, Atmospheres, composition

, we have updated our forward radiative transfer code and processed the whole SPICAV-UV/Venus Express nadir dataset (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014) in order to retrieve SO 2 abundance at cloud top -assuming a SO 2 decreasing scale height of 3 km and a ratio SO/SO 2 tied to 10% -as well as the imaginary index of scattering mode 1 particles, representative of the remaining UV absorption : ,

Introduction

Sulphur dioxide is arguably the most variable species in Venus' cloud top atmosphere, on a large range of temporal and spatial time scales. The first attempt to detect it in UV only yielded a 0.1 ppmv upper limit [START_REF] Jenkins | Rocket Spectra of Venus and Jupiter from 2000 TO 3000 Å[END_REF]). Yet, a decade later, Barker (1979) found between 0.1 and 0.5 ppmv of SO 2 using the same UV spectral range. The most extensive data set before Venus Express was acquired with UVIS onboard Pioneer Venus [START_REF] Esposito | Sulfur dioxide in the Venus atmosphere -Distribution and implications[END_REF][START_REF] Esposito | Sulfur dioxide -Episodic injection shows evidence for active Venus volcanism[END_REF][START_REF] Esposito | Sulfur dioxide at the Venus cloud tops, 1978-1986[END_REF], and revealed an important short term variability, as well as a long term decrease between 1978 and 1988.

These long-term variations were interpreted as possible evidence for active volcanism, which would alter the thermal buoyancy of the lower atmosphere and allow for an intermittent resupply of SO 2 above Venus' clouds, where it is photochemically destroyed. Meanwhile, IR measurements from Venera 15 [START_REF] Zasova | SO 2 in the Middle Atmosphere of Venus: IR Measurements from Venera-15 and Comparison to UV Data[END_REF] and UV measurements from rockets [START_REF] Na | Sulfur dioxide in the atmosphere of Venus. 2: Modeling results[END_REF] also evidenced a latitudinal gradient, with SO 2 increasing with increasing latitude, consistent with a photochemical control of SO 2 since photolysis is less effective at higher latitudes.

After a blank decade (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005), Venus exploration (including cloud top SO 2 monitoring) resumed with ESA Venus Express. Occultation measurements from SOIR (Belyaev et al., 2008) allowed for a retrieval of SO 2 scale height above the clouds, confirmed that SO 2 had returned to the relatively high values of the early 1980s, and evidenced a reversal in the latitudinal gradient of SO 2 . These features were confirmed by our first SPICAV-UV nadir measurements [START_REF] Marcq | An investigation of the SO 2 content of the venusian mesosphere using SPICAV-UV in nadir mode[END_REF][START_REF] Marcq | Variations of sulphur dioxide at the cloud top of Venus's dynamic atmosphere[END_REF], along with a long-term decrease of low latitude SO 2 similar to the one observed by Pioneer Venus. In parallel, high spectral resolution measurements in the thermal IR using NASA IRTF [START_REF] Encrenaz | HDO and SO 2 thermal mapping on Venus: evidence for strong SO 2 variability[END_REF][START_REF] Encrenaz | HDO and SO 2 thermal mapping on Venus. III. Short-term and long-term variations between 2012 and 2016[END_REF][START_REF] Encrenaz | HDO and SO 2 thermal mapping on Venus. IV. Statistical analysis of the SO 2 plumes[END_REF], or in the UV using STIS/HST [START_REF] Jessup | Coordinated Hubble Space Telescope and Venus Express Observations of Venus' upper cloud deck[END_REF] have confirmed and supported this trend, with two possible SO 2 regimes above the clouds: a high abundance regime more prevalent in the early 1980s or late 2000s, with a large number of SO 2 plumes located at lower latitudes and a negative latitudinal gradient, and a low abundance regime with little to no SO 2 convective plumes, and a reversed latitudinal gradient more typical of the early 1990s or mid-2010s. The transition between these regimes can occur within a few Earth days [START_REF] Jessup | Coordinated Hubble Space Telescope and Venus Express Observations of Venus' upper cloud deck[END_REF], and accounts for the large short-term dispersion of the measurements. ::::

The ::::::::::

long-term :::::::: change :: in :::: the ::::::::: relative ::::::::::: prevalence ::: of :::::: these :::: two ::::::::: regimes :::::::: explain :::: the ::::::::::

long-term :::::::: change ::: in :::: the :::::::: average ::::: SO 2 :::::::::::: latitudinal ::::::::: gradient :::::: that ::: we :::::::::: observed ::

in :::: our ::::::::: previous ::::::: study :::::::::::::::::::::::::::: (Marcq et al., 2013, Fig. 2) : . : Nevertheless, the physical processes ruling both these regimes are still poorly known. Convective mix-ing with the lower atmosphere where SO 2 is always abundant -more than 100 ppmv near 30-40 km [START_REF] Bézard | The abundance of sulfur dioxide below the clouds of Venus[END_REF][START_REF] Marcq | A latitudinal survey of CO, OCS, H 2 O, and SO 2 in the lower atmosphere of Venus: Spectroscopic studies using VIRTIS-H[END_REF]Arney et al., 2014) is most certainly involved, but the reasons behind these variations of the convective mixing intensity are still debated, including possible episodic volcanism or other atmospheric processes.

Following the recent progress in our knowledge of Venus clouds and hazes [START_REF] Luginin | Aerosol properties in the upper haze of Venus from SPICAV IR data[END_REF], as well as in our processing of SPICAV-UV nadir spectra, we have completely rewritten our analysis pipeline and processed the whole of SPICAV-UV archive in order to complete and update our SO 2 climatology, as well as other derived observable parameters such as the mean UV brightness of the clouds. A short description of our data set in given in §2, and of our forward radiative transfer model in §3, since both were already extensively described in a previous paper [START_REF] Marcq | Discovery of cloud top ozone on Venus[END_REF].

Our results about SO 2 and UV absorber variability is detailed in §4 and their scientific implications further commented in §5, before we summarize and conclude in §6.

Observations

Our data set and processing is detailed in our previous paper [START_REF] Marcq | Discovery of cloud top ozone on Venus[END_REF]. For the convenience of the reader, we summarize the main points below.

Data set

Our data set consists in the whole archive of SPICAV-UV [START_REF] Bertaux | SPICAV on Venus Express: Three spectrometers to study the global structure and composition of the Venus atmosphere[END_REF] nadir or near-nadir spectra, from 170 to 320 nm at a spectral resolution along ::::: the :::::::: orbbital ::::::: track).

Processing

The first steps of data processing are unchanged since [START_REF] Marcq | An investigation of the SO 2 content of the venusian mesosphere using SPICAV-UV in nadir mode[END_REF], namely cosmic :::: ray : hit removal, dark subtraction, correction of electronic readout artifact, flat-fielding, wavelength assignment. Most recent progress come from a better knowledge of the instrument PSF ::::: Point :::::::: Spread :::::::::: Function ::::::

(PSF), especially at large distances from the center (far wings). Richardson-Lucy deconvolution is now performed in order to clean the far wing contribution, which enables the scientific use of spectra from 200 nm instead of 215 nm in our first analyses, which in turn enables to retrieve more observable parameters relative to Venus' clouds and SO 2 .

Photometric calibration of the spectral radiance spectra was performed from the CALSPEC catalog of bright UV stars observed in-flight [START_REF] Bohlin | Techniques and review of absolute flux calibration from the ultraviolet to the mid-infrared[END_REF]. From these calibrated spectral radiances, we computed the corresponding radiance factors β(λ) = I(λ)×π sr

F (λ)
where I(λ) is the spectral radiance and F (λ) a reference top-of-atmosphere solar spectral irradiance.

These solar spectral irradiance were extracted from the SOLSTICE II database [START_REF] Mcclintock | Solar-Stellar Irradiance Comparison Experiment II (SOLSTICE II): Instrument Concept and Design[END_REF] at the corresponding date to account for the solar cycle variations. We also corrected a spectral feature in these solar spectra near 230-240 nm that our forward radiative transfer model was unable to reproduce, no matter the prescribed values of the atmospheric parameters.

Forward Model

Overview

A detailed description of the forward radiative transfer we use is available in [START_REF] Marcq | Discovery of cloud top ozone on Venus[END_REF]. For the sake of convenience, we present below a summary of its features and free parameters. The radiative transfer equation solver we use is the pseudo-spherical version of DISORT [START_REF] Dahlback | A new spherical model for computing the radiation field available for photolysis and heating at twilight[END_REF]) using 16 streams.

Aerosols

The model encompasses the 50-110 km altitude range. We consider a bimodal log-normal size distribution (r eff = 0.12 and 0.8 µm respectively, with an effective dimensionless variance of ν eff = 0.15) of aerosol particles following [START_REF] Luginin | Aerosol properties in the upper haze of Venus from SPICAV IR data[END_REF].

The vertical profiles for both modes that we consider are simplified from the same reference [START_REF] Luginin | Aerosol properties in the upper haze of Venus from SPICAV IR data[END_REF] : a :::::::::::::: simplification :::::: from :::: the :::::::::: retrieved ::::::

Below :::: this :::::::::: altitude, ::: we ::::: have :: a :::::::::: constant, ::::::: capped :::::: value ::::::::::::::::::::::::::::::::: n 2 (z < Z 2 ) = 10 8 ) particles/m 3 . the ::::::: above :::::::::: described ::::::::::: extinction :::::::: profiles.

The real refractive index of both modes is taken from Hummel et al.

(1988) for a 75%-25% H 2 SO 4 -H 2 O mixture. Imaginary indices for both modes are discussed in §3.2, the imaginary index of mode 1 particles at 250 nmbeing a : , ::::::::::::: m i (250 nm), :::::: being ::::::::: another : free parameter.

Gaseous Species

The gaseous species involved in absorption and/or scattering are displayed in Fig. 2. CO 2 Rayleigh and absorption cross-section is unchanged since [START_REF] Marcq | Variations of sulphur dioxide at the cloud top of Venus's dynamic atmosphere[END_REF]. SO 2 and SO cross-sections were compiled from various sources by [START_REF] Jessup | Coordinated Hubble Space Telescope and Venus Express Observations of Venus' upper cloud deck[END_REF], and we use the same. New gaseous species that we consider is O 3 and OCS, whose UV absorption cross-sections are taken from [START_REF] Sander | Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies[END_REF].

CO 2 vertical profile is computed from hydrostatic equilibrium assuming VIRA-2 temperature profile [START_REF] Moroz | VIRA-2: a review of inputs for updating the Venus International Re ference Atmosphere[END_REF]. at :::::::::::::: SPICAV-UV :::::::: spectral ::::::::::: resolution, :::: we ::::: have ::: to ::::::: assume ::::: that : SO vertical profile is tied at :: to 10% of SO 2 : , :::::::::: according ::: to :::: the :::::::: average ::::::: values :::::::: dervied :::::: from ::::::: higher ::::::::

spectral ::::::::::: resolution :::::::::::: HST/STIS ::::::::::::::: measurements ::::::::::::::::::::: [START_REF] Jessup | Coordinated Hubble Space Telescope and Venus Express Observations of Venus' upper cloud deck[END_REF]. OCS vertical profile is taken from [START_REF] Haus | Radiative heating and cooling in the middle and lower atmosphere of Venus and responses to atmospheric and spectroscopic parameter variations[END_REF], and O 3 is considered uniformly mixed between 55 and 70 km. Its mixing ratio in this range is an optional free parameter of the model.

CO 2 (T=200 K) CO 2 (Rayleigh) SO 2 (T=200 K) SO O 3 OCS

Model Sensitivity

The modeled effect of varying SO 2 (Fig. 3) is easy to understand: since SO 2 has two broad electronic absorption bands peaking near 215 and 280 nm, respectively, these two absorption bands have a relative depth that becomes more pronounced with increasing SO 2 abundance. However, it is noteworthy that the SO 2 influence extends throughout the whole spectrum, even though the cross-section is a continuum between 240 and 270; nm reaching a local minimum near 240 nm. Sensitivity of the inferred radiance factor to SO 2 absorption in the 240-270 nm region is a telltale sign that multiple scattering is prevalent, so that most backscattered photons have traveled through long enough optical paths into deep, SO 2 -rich atmospheric layers that its smaller absorption cross-section is partially offset. This is important when considering SO 2 measurement proxies such as image ratios between 280 and 240 nm: gas : absorption, is also not independent from the spatial SO 2 variations.

At Venus' cloud top, the observed SO 2 absorption band is primarily related to the column density above the cloud top [START_REF] Marcq | An investigation of the SO 2 content of the venusian mesosphere using SPICAV-UV in nadir mode[END_REF][START_REF] Marcq | Variations of sulphur dioxide at the cloud top of Venus's dynamic atmosphere[END_REF].

Thus, altering the cloud top altitude results in a change in the total SO 2 column density above the cloud top, according to the assumed vertical profile of SO 2 number density. The primary effects of altering the cloud top altitude while making no change to SO 2 vertical profile would therefore be very similar to the results displayed in Fig. 3, because the direct outcome of the change in the cloud top altitude is a change in the SO 2 column density above that altitude. However, as Fig. 4 shows, changing the cloud top altitude will impact the total absorption occuring in the two SO 2 electronic absorption Altering the imaginary part ::: m i : of the refractive index of mode 1 particles yields the expected outcome, namely lowering the albedo when particles are darker (Fig. 5). However, altering the spectral slope of this mode 1 absorption results in a spectral distortion very much alike that of changing the cloud top altitude. This resulted in a fitting degeneracy when : if : we tried to fit both the mode-1 absorption spectral slope and cloud top altitude together. We therefore chose to keep ::::: only : the cloud top altitude as a fitted parameter, and adopted a spectral dependency ::::: fixed ::::::::: spectral :::::: slope :::: for

m i (λ) = m i (250 nm) × exp λ-250 nm 40 nm
where the exponential function : , ::::::: fitting :::: only :::::::::::::: m i (250 nm). ::::: The :::::: 40 nm :::::: slope : accounts for the decreasing mode 1 singlescattering albedo with increasing wavelength. Using this relationship ::::: fixed :::::: 40 nm ::::::: value, our low latitude cloud top average altitude near 250 nm was ::::: then : in agreement with the most recent IR measurements [START_REF] Ignatiev | Altimetry of the Venus cloud tops from the Venus Express observations[END_REF] that do not suffer from this degeneracy. The ::::: This : 40 nm value is slightly less steep than our previous estimate of about 34 nm [START_REF] Marcq | An investigation of the SO 2 content of the venusian mesosphere using SPICAV-UV in nadir mode[END_REF], which can be explained by our updates to the spectral calibration of radiance factors [START_REF] Marcq | Discovery of cloud top ozone on Venus[END_REF]. At first, we assumed that this dependency applied to both particle modes, but this assumption resulted in spurious correlations between effective airmass and cloud top altitude as well as imaginary refractive index retrievals -mode 2 particles contribute more to backscattering at smaller airmass since they dominate at lower altitudes.

Empirically, we found that assuming a constant, fixed imaginary refractive index of 10 -3 for mode 2 particles minimized such spurious correlations.

Since this fixed value is much larger than the imaginary refractive index of pure H 2 SO 4 -H 2 O solutions in this wavelength range, this may be indicative of two different UV absorbers: one, well mixed with mode 2 and mode 1 particles and with little spectral dependency between 200 and 300 nm, and the other one, mixed with mode 1 particles only and horizontally variable, absorbing more towards longer wavelengths. This latter absorber is likely the same absorber than the infamous near UV-blue absorber peaking

i(250 nm) = 1 × 10 -3 mi(250 nm) = 3 × 10 -3 mi(250 nm) = 1 × 10 -2 mi(250 nm) = 3 × 10 -2 mi(250 nm) = 1 × 10 -1
near 365 nm, our retrieved imaginary indexes in the 10 -2 -10 -1 range and spectral slope being in agreement with recent determinations of this imaginary refractive index over a larger spectral range extending to the visible range [START_REF] Pérez-Hoyos | Venus Upper Clouds and the UV Absorber From MESSENGER/MASCS Observations[END_REF]. We will further discuss the scientific implications in §5.1.

Results

4.1.

::::::::: Retrieval :::::::::::::: uncertainties ::::

The ::::::: above :::::::::: described ::::::::: forward :::::::: model ::: is ::::: then ::::::::::: compared :::: to ::::: 30-s :::::::: binned ::::::::::::: SPICAV-UV ::::::::::::: observations ::::::::: through : a ::::::::::::::::::::::: Levenberg-Marquardt ::::::::: iterative ::::::::::: algorithm :::::::::::::::::::::: [START_REF] Newville | LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python[END_REF] . ::::::: Three :::::::::::: parameters :::: are :::::::: always ::::::: fitted, ::::::::: namely: :::::: SO 2 ::::::: mixing :::::: ratio ::: at :::::::: 70 km, ::: Z 2 :::: and :::::::::::::: m i (250 nm). ::: O 3 :::::::: mixing :::::: ratio :: is ::::: also :::::: fitted :::::: when :::: its :::::::::: inclusion ::::::: results

::

in :: a ::::::::::: significant ::::::::::: reduction ::: in :::::::: residual :::: χ 2 ::

-:::: the ::::::::::: interested ::::::: reader :::::::: should ::::: refer :: (which ::::::::: indicates ::::: that :::::::::::: systematic :::::: errors ::: do :::::: exist, :::::::: and/or :::: that :::: the :::::::::::::: observatoinal :::::::::::: uncertainity :::::: may ::: be :::::::::::::::::: underestimated). :::::::::::: Hereafter, :::: we ::::: only :::::::::: consider :::: our :::: fits ::::: valid :: if :::::: their ::: χ 2 ::

is ::::: less ::::: than :: 3 :::::: times ::::: this :::::::: median :::::: value ::::::::::: (χ 2 < 50). : ::

In :::: this ::::: valid ::::::::: dataset, :::: the :::::::: median :::::::: relative ::::: 1 • σ :::::::::::: uncertainty ::: on ::::: SO 2 ::::::::: retrievals ::

is ::::: 38%, :::::::::::::: substantially :::: less ::::: than :::: the :::::::: 3-order ::: of ::::::::::: magnitude :::::::: spatial :::: and :::::::::: temporal

Temporal variability

The long term evolution over the whole extent of Venus Express of our retrieved cloud top SO 2 and imaginary index of mode 1 particles are shown respectively on Fig. 6 and7. We restricted the analysis of :::::

Since :::::: most : SO 2 temporal variability to lower latitudes only so that we do not encompass any bias in latitude , since SO 2 and latitude are correlated in our data set :::::::: content ::

is :::::::: actually :::::::: located ::::::: below :::::: ±20 • ::

in ::::::::: latitude : (see §4. Regarding UV darkness (as measured through mode 1 imaginary index at 250 nm), the long term trend can be divided in two time periods: first a 5fold increase from 2006 (∼ 10 -2 ) until 2010 (∼ 5 • 10 -2 ), and then a constant, darker plateau from 2011 onward until the end of the mission in late 2014.

These variations are most pronounced at lower and mid-latitudes, latitudes above 60 • seem less affected by this trend. Here also, these results compare well with our previous results [START_REF] Marcq | Variations of sulphur dioxide at the cloud top of Venus's dynamic atmosphere[END_REF] where we accounted for this UV darkening through a fitted scaling factor, but also with the 40% UV albedo darkening observed in 2006-2011 by Venus Express/VMC at 365 nm [START_REF] Lee | Long-term variations of the UV contrast on Venus observed by the Venus Monitoring Camera on board Venus Express[END_REF]. This agreement between two diffrent instruments (VMC and SPICAV) and the fact that the albedo latitude variation trends inferred from either the VMC and SPICAV data sets are consistent, even though the binning and the reduction of the two data sets is ::: are : unique lead us to believe that this darkening is genuine, and not an artifact from the aging of the SPICAV UV detector. The SO 2 variations observed in Fig. 6 suggest they may exhibit some periodicity. In order to discuss them more quantitatively, we computed a Lomb-Scargle periodogram of both SO 2 mixing ratio as well as its logarithm (since we present all of our SO 2 results in a logarithmic scale). Lomb-Scargle periodograms are well suited when the temporal sampling of measurements is uneven (as it is the case here), but may exhibit "ghost" harmonics for integer multiple values of the genuine frequency.

These periodograms are shown in Fig. 8. Assuming that genuine frequencies would show up in both SO 2 and log(SO 2 ) periodograms, we find that our frequency signal is dominated by a 400 Earth day period (and its ghost harmonics near 200, 135 and 100 days) component, that can be seen between the SO 2 surges in Fig. 6. A 110-day long component is also visible, We present the correlation between topography and SO 2 in more detail in §4.3.1.

Other possible periods that are significantly above noise include a 155 Earth day component, as well as medium term components (40, 17 and 6 Earth days). Noticeably, a 4-day period is absent, implying that SO 2 patches are shorter lived than the super-rotation period at cloud top.

Spatial variability

SO 2

The binned latitudinal distribution of our SO 2 retrievals is shown in Fig. 9.

The main features from our previous analyses [START_REF] Marcq | Variations of sulphur dioxide at the cloud top of Venus's dynamic atmosphere[END_REF][START_REF] Marcq | An investigation of the SO 2 content of the venusian mesosphere using SPICAV-UV in nadir mode[END_REF] are still valid, namely: (i) there is a large dispersion, spanning more than two orders of magnitude at lower latitudes and about one order of magnitude at higher latitudes (ii) the median SO 2 value is larger at lower latitudes (typically 5 to 100 ppbv, median 20 ppbv below 30 • ), due to the occurrence of SO 2 "plumes" (above 100 ppbv) that do not occur at higher latitudes. The observed latitudinal pattern remains consistent with the SO 2 gas distribution being dominantly controlled by a Hadley-cell type circulation as reported previously [START_REF] Jessup | On Venus' Cloud Top Chemistry, Convective Activity and Topography: A Perspective from HST[END_REF]Vandaele et al., 2017b;[START_REF] Jessup | Coordinated Hubble Space Telescope and Venus Express Observations of Venus' upper cloud deck[END_REF][START_REF] Marcq | Variations of sulphur dioxide at the cloud top of Venus's dynamic atmosphere[END_REF][START_REF] Marcq | An investigation of the SO 2 content of the venusian mesosphere using SPICAV-UV in nadir mode[END_REF] -thus is linked to large-scale (or deep) convective mixing process. The broad range of SO 2 abundance values observed at each latitude points to the perpetual competition between general circulation and the LST dependent photochemical destruction of SO 2 [START_REF] Marcq | Variations of sulphur dioxide at the cloud top of Venus's dynamic atmosphere[END_REF] which may produce order of magnitude changes in the cloud top abundances on a time scale of several Earth days (corresponding to 1-2 hours of LST considering the zonal super-rotation at cloud top) particularly at low latitudes. The SPICAV-observed variability patterns are fully consistent with other measurements in UV from HST/STIS [START_REF] Jessup | Coordinated Hubble Space Telescope and Venus Express Observations of Venus' upper cloud deck[END_REF] or in IR with IRTF/TEXES [START_REF] Encrenaz | HDO and SO 2 thermal mapping on Venus: evidence for strong SO 2 variability[END_REF][START_REF] Encrenaz | HDO and SO 2 thermal mapping on Venus. III. Short-term and long-term variations between 2012 and 2016[END_REF].

Our comprehensive data set also allows us to study the variability of SO 2 with respect to local solar time as shown in Fig. 10. A local minimum near noon (between 10am and 2pm) is evidenced. Interestingly, TEXES measurements also confirm the inefficiency of upwelling SO 2 plumes in the 10h to 14h local time interval [START_REF] Encrenaz | HDO and SO 2 thermal mapping on Venus. IV. Statistical analysis of the SO 2 plumes[END_REF]. We further discuss the SO 2 and overall UV brightness variations with respect to local solar time in §5.2.

The SO 2 periodgram ( §4.2.1) suggest that SO 2 and surface topography may be correlated. Therefore, we have mapped our SO 2 retrievals with respect to latitude and geographic longitude in Fig. 11. Besides the latitudinal trend already discussed, we notice a possible SO 2 enhancement located downwind of the western edge of ::: the :::::: large :::::::::: equatorial :::::::::::::: high-altitude ::::::::: plateau ::::::: known ::

as : Aphrodite Terra in the 30 • -45 • range. Similarly, the SO 2 volume mixing ratio observed by HST at low latitudes in the 0 • -45 • E longitude range was an order of magnitude higher than directly over Aphrodite Terra (Jessup and is distinctly evident in the TEXES data (Encrenaz et al., 2019, their Fig. 8). One should also note that the polar orbit of Venus Express implies that diffrent longitudes were observed at different dates, so that longitudinal and temporal variablity cannot be retrieved separately from these maps.

UV brightness

We have also investigated the correlation between topography and the retrieved absorption of mode 1 particles shown in Fig. 12 to determine if SO 2 vmr @ 70 km [ppbv] relationships between the albedo and the underlying topography proposed by [START_REF] Bertaux | Influence of Venus topography on the zonal wind and UV albedo at cloud top level: The role of stationary gravity waves[END_REF] are supported by our data, and to determine how the observed albedo trends might relate to the retrieved SO 2 abundances.

:::

We :::: are :::::: able ::: to ::: do :::: so, :::::: since :::: the :::::::::: 12 : also indicates that high m i values are retrieved at lower latitudes, which is expected since convective activity is strongest at these latitudes due to the enhanced solar heating [START_REF] Peralta | Cloud brightness distribution and turbulence in Venus using Galileo violet images[END_REF][START_REF] Titov | Atmospheric structure and dynamics as the cause of ultraviolet markings in the clouds of Venus[END_REF][START_REF] Titov | Morphology of the cloud tops as observed by the Venus Express Monitoring Camera[END_REF]. However, strong longitudinal variability in the cloud top brightness is observed within the low latitude region sampled by SPICAV; and the inferred brightness distribution is not symmetric with respect to the equator.

Additionally, as already mentioned, the polar orbit of Venus :::::::: Express leads to an uneven longitudinal sampling with respect to observation date, so that the observed distribution pattern may also be linked to :::::::::: long-term : temporal variability.

In terms of local time and latitudinal variability, Fig. 13 shows that (i)

UV brightness increases with increasing latitude, reaching a high plateau near 60 • N; and (ii) UV brightness is lower between 10:00 and 16:00 at lower [START_REF] Titov | Atmospheric structure and dynamics as the cause of ultraviolet markings in the clouds of Venus[END_REF][START_REF] Titov | Morphology of the cloud tops as observed by the Venus Express Monitoring Camera[END_REF][START_REF] Lee | Long-term variations of the UV contrast on Venus observed by the Venus Monitoring Camera on board Venus Express[END_REF]. These already known trends, plus the fact that minimum UV brightness (correlated with maximum m i values) is reached near 14:00 and not exactly at noon lead us to discard a spurious correlation of our retrievals with respect to airmass, which may occur if the assumed extinction vertical profiles are not representative of the real ones.

Cloud top altitude

Variations of cloud top altitude with respect to latitudes are shown in Fig. 14. The average low latitude cloud top altitude (defined as τ (250 nm) = 1 nadir level) we find is 73 ± 2 km in good agreement with already known values [START_REF] Ignatiev | Altimetry of the Venus cloud tops from the Venus Express observations[END_REF][START_REF] Pérez-Hoyos | Venus Upper Clouds and the UV Absorber From MESSENGER/MASCS Observations[END_REF]. This is not surprising, since we adjusted the spectral slope of the UV absorber precisely to match this mean value (see §3.2). The already known decrease of cloud top altitude towards higher latitudes [START_REF] Ignatiev | Altimetry of the Venus cloud tops from the Venus Express observations[END_REF] is also observed, although the amplitude -about 10 km from equator to pole here instead of about 3 km according to [START_REF] Ignatiev | Altimetry of the Venus cloud tops from the Venus Express observations[END_REF] -is somewhat larger, and starts at lower latitudes (30 • instead of 50 • ). Nevertheless, due to the aforementioned degeneracy between the spectral slope and cloud top altitude, reaching a qualitative agreement for this poorly constrained parameter retrieval is satisfactory, considering the need to keep as few free fitted parameters as possible in our forward model. ::::::

Please :::::: note ::::: that ::::::::::::: simultaneous ::::: and ::::::::::: co-loacted We already reported ( §4.3) that low SO 2 abundances were observed within 2 hours of the subsolar point, and similarly the lowest UV brightness (minimum absorber abundance) was detected in the afternoon hours. The longterm trends are opposite too, with an observed secular decrease for SO 2 , and secular increase of the UV absorption, see §4.2). This points to an anticorrelation between SO 2 and UV absorption that is confirmed in Fig. 15:

although the statistical dispersion for both SO 2 and the imaginary refractive index m i (250 nm) is large, there is an average decrease of one order magnitude for m i relative to an increase of SO 2 of two orders of magnitude.

Such an anti-correlation using VMC 365 nm observations with respect to our previous estimates of SO 2 [START_REF] Marcq | Variations of sulphur dioxide at the cloud top of Venus's dynamic atmosphere[END_REF] was reported by [START_REF] Lee | Long-term variations of the UV contrast on Venus observed by the Venus Monitoring Camera on board Venus Express[END_REF], as well as using high spectral resolution (line-resolving) retrievals of SO 2 and SO with HST/STIS from [START_REF] Jessup | Coordinated Hubble Space Telescope and Venus Express Observations of Venus' upper cloud deck[END_REF]. Therefore, we can safely dismiss that correlation would be a spurious artifact due to parasitic trends in the photometric calibration of SPICAV-UV spectra. There are two The prevalence of Venus' cloud top SO 2 abundance to peak at low latitudes was already noticed in our first analysis [START_REF] Marcq | An investigation of the SO 2 content of the venusian mesosphere using SPICAV-UV in nadir mode[END_REF][START_REF] Marcq | Variations of sulphur dioxide at the cloud top of Venus's dynamic atmosphere[END_REF], and was then linked to the general meridional circulation causing upwelling at lower latitudes and downwelling at higher latitudes. Therefore, the combined SPICAV, TEXES and HST results confirm that the mechanism driving transient plume formation differs distinctely from shallow sub-solar mixing and deep Hadley-cell circulation processes.

The observed increase in SO 2 abundance in the 0 • to 40 • S latitude region at longitudes intersecting Aphrodite Terra relative to what is observed at similar latitudes upwind provides further evidence to the unexpected connection between surface topography and cloud top [START_REF] Bertaux | Influence of Venus topography on the zonal wind and UV albedo at cloud top level: The role of stationary gravity waves[END_REF][START_REF] Peralta | Stationary waves and slowly moving features in the night upper clouds of Venus[END_REF]. In general, the current analysis shows that statistically on average SO 2 is high at low latitudes from 40 • to 120 • E relative to other longitudes except at 30 • -45 • E (downwind from Aphrodite) where the SO 2 abundance is on average higher than at Aphrodite. We still do not completely understand what controls the overall SO 2 longitudinal variation (provided it is genuine and not an artifact from our temporal-longitudinal sampling). Nevertheless, the relative increase in SO 2 between the region downwind of Aphrodite and directly over Aphrodite are consistent with the differences in wind speed within those two specific regions and the anticipated vertical wind speed response proposed by [START_REF] Bertaux | Influence of Venus topography on the zonal wind and UV albedo at cloud top level: The role of stationary gravity waves[END_REF], ::: as :::: we :::::::: already ::::::::::: suggested :: in ::::::: §4.2.1

:::::

while ::::::::::: discussing :::: the ::::::::: possible ::::::::: 110-day ::::::: period ::: in ::::: SO 2 . The differences in wind speed between these two regions are likely linked to the impact of gravity waves [START_REF] Navarro | Atmospheric mountain wave generation on Venus and its influence on the solid planet's rotation rate[END_REF] momentum deposition on cloud top zonal wind speeds as proposed by [START_REF] Bertaux | Influence of Venus topography on the zonal wind and UV albedo at cloud top level: The role of stationary gravity waves[END_REF].

Interestingly, [START_REF] Encrenaz | HDO and SO 2 thermal mapping on Venus. III. Short-term and long-term variations between 2012 and 2016[END_REF] does not see any SO 2 plume over this location (see Fig. 11), which highlights that while the discussed SO 2 enhance-ment over the western slopes of Aphrodite Terra is on average higher than other longitude regions, other transient phenomena may also be relevant, Express at some point in the late 2020s to early 2030s.

  of 1 nm. There are 1508 such observations, from2006-06-01 up to 2014-11- 20. Coverage in local time and latitude is extensive except for the south polar region[START_REF] Marcq | Discovery of cloud top ozone on Venus[END_REF] Fig. 1), with southern hemisphere observations dominated by near nadir tracking ::::::::: pointing mode observations over single spots :::: spot :::::::: targets :::::::::: (implying :::::::::::::: continuously :::::::::: changing ::::::::: emission ::::: and :::::: phase :::::: angles ::::::: along :::: the :::::: orbit), whereas northern hemisphere observations consisted mainly in nadir latitudinal scans ::::::: (where ::::::::: emission ::::::: angle :: is :::::::::::: essentially ::::: zero :::::

  ::::::: derived ::: by ::::::::::::::::::::::: Luginin et al. (2016) and can be seen in Fig. 1. Number density is capped for both particles at in the lower part the model (respectively 2 • 10 8 and 10 8 particles/m 3 for mode 1 and mode :::::: Above :: a :::::::: altitude :::::::: named ::: Z 2 :::::::::: hereafter, :::::: mode 2 ), and the number density ratio n 1 /n 2 = 1000 is fixed in the upper :::::::: particle :::::::: number :::::::: density :::::::::: decreases :::::::::: following :::::::::::::::::::::::::::::::::::::::::::: n 2 (z > Z 2 ) = 10 8 exp Z 2 -z 4.5 km particles/m 3 .

Figure 1 ::

 1 Figure 1: Synthetic number density profiles for both particle modes. Z 2 is a free parameter ::in ::: our ::::::: model, ::::: which :::::::: captures :::::: cloud ::: top :::::::: altitude :::::::::: variations.

  :::::::::: Following ::::::: recent :::::::::::::::: intercomparison ::::::::: between ::::::::::::: observations ::::: and ::::::: models ::::::::::::::::::::::::::::::::::::::::::::: (Vandaele et al., 2017a; Marcq et al., 2018) : , ::: we :::::::::: consider ::::: that : SO 2 vertical profile is capped at 150 ppmv in the lower part of the model, and decreases according to a scale height of 3 km in the upper part of the model. Its mixing ratio at 70 km is a free parameter of our model. ::::: Since :::: we :::::::: cannot ::::::::::: distinguish :::::::::::: individual ::: SO ::::: and ::::: SO 2 :::::::::::: absorption ::::: lines ::

O 3

 3 measurements is the main topic addressed by[START_REF] Marcq | Discovery of cloud top ozone on Venus[END_REF]. O 3 absorption is considered only when including it yields a substantial reduction in the reduced χ 2 (namely, 5.5). We adopt the same criterion in the present study. Example of a fitted spectrum with and without O 3 can be found in[START_REF] Marcq | Discovery of cloud top ozone on Venus[END_REF] Fig. 2) ::::::::::::::::::::::::::::::::: Marcq et al. (2019, their Fig. 3).

Figure 2 :

 2 Figure 2: UV cross-sections of considered gaseous species

Figure 3 :

 3 Figure 3: Synthetic radiance factors for a cloud top altitude of 74 km, m i (250 nm) = 10 -2 and varying SO 2 abundances. The considered geometry is pure nadir viewing, with a solar zenith angle of 30 • .

Figure 4 :

 4 Figure 4: Synthetic radiance factors for m i (250 nm) = 10 -2 , and varying SO 2 abundances as well as cloud top altitudes et :: at : 250 nm. The considered geometry is pure nadir viewing, with a solar zenith angle of 30 • .

Figure 5 :

 5 Figure 5: Synthetic radiance factors for a cloud top altitude of 74 km, SO 2 volume mixing ratio of 50 ppbv at 70 km and varying m i (250 nm). The considered geometry is pure nadir viewing, with a solar zenith angle of 30 • .

  to ::::::::::::::::::::: Marcq et al. (2019) ::: for :::::::: further ::::::: details ::::::: about :::: O 3 :: in :::: the :::::::::::::: SPICAV-UV :::::: nadir ::::: data :::: set. : :::: The ::::::::::::::::::::::: Levenberg-Marquardt ::::::::::: algorithm ::::::: yields ::: a ::::::::::: covariance ::::::::: matrix, :::::: from :::::: which ::::: 1 • σ ::::::::::: statistical :::::::::::::: uncertainties :::: are ::::::::: derived ::: for :::::: each :::: fit, :::::: along :::::: with :::: the :::::::: residual ::::::::: reduced :::: χ 2 . :::::: The :::::::: median ::::::::: reduced :::: χ 2 ::: of :::: the ::::::: whole :::::::: dataset ::: is ::::: 16.6 :::::::

:

  ::::::::: variability ::: of ::::: SO 2 ::::::: ( §4.2, :::::::: §4.3.1): ::::: the ::::::: lowest ::::: 3 • σ ::::::::::: detection ::: of ::::: SO 2 :: is ::::::: about :::::::: 0.6 ppb, ::::: and :::: the ::::::::: highest ::::::: values ::: on ::::: the :::::: order ::: of :::::::::::: 1000 ppbv. :::::::::::: Similarly, :::: the ::::::: median ::::::::: relative ::::: 1 • σ ::::::::::::: uncertainty ::: on :::: m i :::::::::: retrievals :: is :::::: 25%, ::::: also :::::::::::::: substantially :::: less ::::: than :::: its :::::::: spatial ::::: and :::::::::: temporal :::::::::::: variability ::::::: ( §4.2, ::::::::: §4.3.2). ::::::::: Finally, ::::: the ::::::: median ::::::::: relative ::::::::::::: uncertainty ::: on ::::: our :::::: cloud ::::: top ::::::::: altitude :::::::::: retrievals ::: is :::: on :::: the ::::: order ::: of ::::::: 1 km. :

  3) : , ::: we ::::: will ::::::: discuss :::::::::: hereafter ::: the :::::::::: temporal ::::::::::: variabilty :: of ::::: SO 2 :::::::::: temporal ::::::::::: variability :::::: only :: in ::::: this ::::::::::::: low-latitude ::: bin. The most striking features in both retrieved parameters are: (i) shortterm dispersion is much larger than retrieval uncertainties, and spans two orders of magnitude for SO 2 and one for the imaginary index; (ii) despite this short-term variability, longer term trends can be observed.For SO 2 , the overall trend consists in an overall decline by a factor 5 to 10 from 2007 (about 80 ppbv) :::::::: 80 ppbv in median) to 2014 (about 10 ppbv). This steady decline is not monotonous though: after the peak in 2007, surges in SO 2 can observed in 2009, 2012, and late 2013. This trend is consistent with our previous findings for 2006-2012 (Marcq et al., 2013), except for the 2009 peak that was not noticed at the time, probably due to an insufficient number of analyzed observations compared to our extensive analysis presented here. Comparison with STIS/HST retrievals[START_REF] Jessup | Coordinated Hubble Space Telescope and Venus Express Observations of Venus' upper cloud deck[END_REF] and with TEXES retrievals[START_REF] Encrenaz | HDO and SO 2 thermal mapping on Venus: evidence for strong SO 2 variability[END_REF][START_REF] Encrenaz | HDO and SO 2 thermal mapping on Venus. III. Short-term and long-term variations between 2012 and 2016[END_REF], : extrapolated at 70 km assuming a scale height of 3 kmis excellent, and : , :::: are ::::: fully :::::::::::: consistent ::::: with ::: the ::::::::::: statistical ::::::::::: dispersion ::: of ::::::::::::: SPICAV-UV ::::::::::: retrievals, ::::::: which highlights the fact that these "snapshot" observations are actually representative of the median state of cloud top SO 2 as observed statistically by SPICAV. More generally, these variations are in agreement with the inter-comparison of available SO 2 measurements detailed by Vandaele et al. (2017b), as well as recent UVI/Akatsuki results (Lee et al., 2017).

Figure 6 :

 6 Figure 6: Temporal evolution of SO 2 mixing ratio at 70 km for latitudes lower than 30 • . The red line stands for the moving median value, and white diamondsare TEXES ::::::: /squares :::: show ::::: other : SO 2 mixing ratios from Encrenaz et al. (2016) ::::::::::::: measurements :: in :::: the :::: same ::::: time :::::::interval.

Figure 7 :

 7 Figure 7: Temporal evolution of mode 1 imaginary refractive index at 250 nm. The red line stands for the moving median value. Absolute latitude is color-coded.

Figure 8 :

 8 Figure 8: Lomb-Scargle periodogram of low-latitude SO 2 in log and linear scales. Periods discussed in the main text are shown in dashed, with the 400-day period and its ghost harmonics shown in dashed black.

Figure 9 :

 9 Figure 9: SO 2 mixing ratio at 70 km with respect to latitude :: for ::: all :::: LSt :::::: values. The red line stands for the moving :::::::::: 10 • -moving ::::::: boxcar : median value, and red error bars for the 1 • σ statistical dispersion.

Figure 10 :

 10 Figure 10: SO 2 mixing ratio at 70 km ::: for :::::::: latitudes :::::: below ::: 20 • : with respect to local solar time. The red line stands for the :::::: 1-hour : moving :::::: boxcar median value, and red error bars for the 1 • σ statistical dispersion.

Figure 11 :

 11 Figure 11: Map (latitude vs. longitude) of SO 2 mixing ratio at 70 km. The contour lines follow topographic elevation : -::::::::: Aphrodite ::::: Terre : is :::::::: peaking ::::: near ::::::: 90 • E-0 • . Crossed hatching indicated lack of meaningful data. Red diamonds show co-located day side TEXES retrievals : , :::: with :::: red :::::: crosses :::::::: showing ::: the :::::::: TEXES ::::::::::: observations :::::::: footprint.

  retrieved ::::::: values ::: of ::::::::::::: m i (250 nm) ::::::::: exhibit ::: an :::::::::::::::: anti-correlation ::::: with :::: the :::: UV ::::::::::: brightness :: of :::: the :::::: cloud :::: top :::::: (once ::::: SO 2 ::::::::::: absorption :: is :::::: taken ::::: into ::::::::::: account). :: Comparison of Figures 11 and 12 highlights that directly over Aphrodite Terra (60 • -140 • E, 15 • S) where relatively SO 2 VMRs have been retrieved, the m i values are low, suggesting a bright cloud topthis results confirms that the cloud top is brighter over Aphrodite but the anti-correlation between the cloud top albedo and the SO 2 gas abundance does not support that the abundance of both components (SO 2 and UV absorber) is controlled solely by linked vertical transport process (see §5).

Fig

  Fig. 11 ::12 : also indicates that high m i values are retrieved at lower lati-

Figure 12 :

 12 Figure 12: Map (latitude vs. longitude) of mode 1 imaginary refractive index at 250 nm.The contour lines follow topographic elevation :-::::::::: Aphrodite ::::: Terre : is :::::::: peaking :::: near :::::::90 • E-0 • .Crossed hatching indicates lack of meaningful data.

Figure 13 :

 13 Figure 13: Pseudo-map (latitude vs. local solar time) of mode 1 imaginary refractive index at 250 nm. Hatched areas indicate lack of meaningful data

  IR :::::: cloud :::: top ::::::::::::::: measurements ::::::: would ::::::::: remove ::::: such :: a ::::::::::::: degeneracy, :::: and :::::: allow :::: for : a ::::::::: detailed :::::::::::::: investigation :: of :::: the :::::::: spatial :::: and :::::::::: temporal :::::::::::: variability :: of :::: the :::::::: aerosol :::::::: spectral ::::::: slope. : 1. Nature of UV absorber As already mentioned in §3.2, we suspect that our retrievals of the imaginary refractive index of mode 1 particles is directly related to the local abundance of the infamous UV absorber. Unfortunately, the only spectropscopic :::::::::::::: spectroscopic constraint we were able to derive is the spectral slope-related parameter of 40 nm. Such an : a : decrease of UV single scattering albedo with increasing wavelength in the SPICAV UV range is compatible with a large number of candidates for the UV absorber, including the most recent mix-

Figure 14 :

 14 Figure 14: Cloud top altitude with respect to latitude. The red line stands for the ::: 10 • :::::: binned : moving :::::: boxcar : median value, and red error bars for the 1 • σ statistical dispersion.

Figure 15 :

 15 Figure 15: Scatter plot between imaginary index of mode 1 particles at 250 nm and SO 2 mixing ratio at 70 km

  complex :::::::: spatial ::::::::: patterns : are likely more readily discernible in the SPICAV data, because these data may be used to distinguish between different particle modes (effectively segregating :::::::::::::: distinguishing ::::::::: between : mode 2 H 2 SO 4 particles mostly conservative scatter-ing from :::: and mode 1 absorption), while VMC traces only the total absorption in the 365 nm band, thus likely to include both mode 1 and mode 2 contributions. :::::::::: Moreover, :::::::::: SPICAV :::::::::::::: reconstructed :::::: maps :::::::: include ::::::::::: long-term :::::::::: temporal :::::::::: variations ::::: due ::: to :::: the ::::: slow :::::::: Venus :::::::: Express ::::::: orbital ::::::: swath ::::::::::: precession ::::::::: relative ::to ::::::::::: longitude :::::::: and/or ::::: local :::::: solar :::::: time, ::::::: which :::::: may :::::::: explain :::: the :::::::: overall ::::::: larger :::::::::: variability ::::: seen :::: by ::::::::: SPICAV ::::::::::: compared ::: to ::::::::::::::: instantaneous :::::: VMC ::::::: maps. :5.2. Requirements for deep vertical mixingSince SO 2 transient enhancements and correlated UV brightenings are caused by local upwellings -also called "plumes" by e.g. Encrenaz et al. (2016)), clues to the processes that support the observed SO 2 spatial distributions and the impact of SO 2 enhancement plumes can be derived by considering the LST, latitude and longitude patterns revealed in the statistically averaged data. As described in §4.3 and shown in Fig. 11, regions of SO 2 enhancements have been observed primarily at latitudes smaller than 30 • except at Aphrodite Terra longitudes (60 • -140 • E) where the SO 2 enhancement extends to 40 • S so that on average the SO 2 abundance from 0 • tp 40 • S is higher than observed at the same latitudes in the 160 • -240 • E region. Additionally, on average a very strong enhancement region is typically observed downwind from Aphrodite at 30-45 • E. On the other hand, depletion of SO 2 noted between 10:00 to 14:00 local solar time ::::: (Fig. :::: 10) : implies that at these local solar times replenishment of the cloud top SO 2 abundance via largescale mixing cannot keep up with the high rate of photochemical loss that would dominate at these local solar times at low latitude.

  such as local time effects shown in Fig.13. In fact, TEXES measurements were acquired above Aphrodite Terra at 13:30 local time, further confirming that transient plume activity is suppressed directly over Aphrodite near local noon. Similarly, STIS observations from[START_REF] Jessup | On Venus' Cloud Top Chemistry, Convective Activity and Topography: A Perspective from HST[END_REF] show that increased 245 nm cloud top darkening occurs over regions of low elevation 2 hours LST prior to local noon, but these increases are not observed at similar local times directly over Aphrodite Terra.6. ConclusionOur analysis of the full SPICAV-UV nadir data set has been performed by fitting the observed radiance factors with respect to SO 2 abundance at cloud top and UV absorption of mode 1 particles. Our previous conclusions about SO 2[START_REF] Marcq | An investigation of the SO 2 content of the venusian mesosphere using SPICAV-UV in nadir mode[END_REF][START_REF] Marcq | Variations of sulphur dioxide at the cloud top of Venus's dynamic atmosphere[END_REF] are mostly confirmed: in average, SO 2 is found to be decreasing with increasing latitude, from typically 5-100 ppbv at 70 km near the equator to 2-20 ppbv polewards of 60 • N and S. Statistical dispersion is therefore much larger at lower latitudes, consistent with the location of transient SO 2 plumes as seen by other observers[START_REF] Encrenaz | HDO and SO 2 thermal mapping on Venus. III. Short-term and long-term variations between 2012 and 2016[END_REF]. The 5-fold secular decrease in equatorial SO 2 reported by[START_REF] Marcq | Variations of sulphur dioxide at the cloud top of Venus's dynamic atmosphere[END_REF] between 2007 and 2011 is now found to extend until 2015 at least, albeit with a previously unreported secondary maximum in 2009. A minimum near subsolar point is also found in average, likely caused by the locally higher photochemical depletion rate. UV absorption :::::: (Fig. :::: 13) : displays the familiar pattern of comparatively

  possible, non-mutually exclusive physical explanations already reported[START_REF] Esposito | Sulfur dioxide -Episodic injection shows evidence for active Venus volcanism[END_REF][START_REF] Jessup | Coordinated Hubble Space Telescope and Venus Express Observations of Venus' upper cloud deck[END_REF] and supported by this study: (i) injections of SO 2 and H 2 O from the deep atmosphere lead to an increased formation rate of uncontaminated H 2 SO 4 , UV-bright haze particles above the UV absorber; and (ii) on longer time scales, SO 2 is a precursor species to the UV absorber, so that there is a possible conversion of SO 2 into a sulfur-bearing UV absorber -SO 2 and the UV absorber being competing reservoirs of sulfur in such a case. Similarly, the latitude variation at southern latitudes is more complex than what is seen in VMC at southern latitudes. On the other hand, the latitudinal variations inferred from the SPICAV analysis at northern latitudes shows the expected pattern of low latitudes darker than high at

5.1.3. Comparison with VMC

Our SPICAV retrievals of m i (mode 1 imaginary index) show a greater level of longitudinal variation of the unknown UV absorber than inferred from VMC

[START_REF] Lee | Long-term variations of the UV contrast on Venus observed by the Venus Monitoring Camera on board Venus Express[END_REF][START_REF] Bertaux | Influence of Venus topography on the zonal wind and UV albedo at cloud top level: The role of stationary gravity waves[END_REF]

; for example, Fig.

12

does not indicate that Aphrodite is a region where the cloud top albedo is uniquely bright compared to all other longitudes, unlike what is indicated by

[START_REF] Bertaux | Influence of Venus topography on the zonal wind and UV albedo at cloud top level: The role of stationary gravity waves[END_REF]

. ::: for almost all longitudes. These complexities ::::::::

Acknowledgements

We wish to acknowledge the support of CNES and ESA for this work. As a result from this support, it is planned to deliver to ESA Planetary Science Archives (PSA) both the day side nadir UV albedo spectra and the columns of SO 2 and ozone derived from SPICAV/Venus Express mission. EM, JLB, FL and FM acknowledge support Programme National de Plantologie (AT-MARVEN grant) during this analysis. DB, OK and JLB wish to acknowledge the support of the Ministry of Education and Science of Russian Federation grant 14.W03.31.0017. KLJ acknowledges support for her contributions to this work were provided through NASA Venus Climate Orbiter, Participating Scientist Program grant number NNX16AK82G. Arney, G., Meadows, V., Crisp, D., Schmidt, S.J., Bailey, J., Robinson, T., 2014. Spatially resolved measurements of H 2 O, HCl, CO, OCS, SO 2 , cloud opacity, and acid concentration in the Venus near-infrared spectral windows. Journal of Geophysical Research (Planets) 119, 1860-1891.

Barker, E.S., 1979. Detection of SO 2 in the UV spectrum of Venus. Geophys. Res. Lett. 6, 117-120. Belyaev, D., Korablev, O., Fedorova, A., Bertaux, J., Vandaele, A., Montmessin, F., Mahieux, A., Wilquet, V., Drummond, R., 2008. First observations of SO 2 above Venus' clouds by means of Solar Occultation in the Infrared. Journal of Geophysical Research (Planets) 113, 1-10.

brighter mid-to-high latitudes compared to lower latitudes [START_REF] Titov | Clouds and Hazes of Venus[END_REF], along with an already known darkening in the 12:00-14:00 local time range at low latitudes [START_REF] Titov | Morphology of the cloud tops as observed by the Venus Express Monitoring Camera[END_REF]. Long-term evolution of UV darkness :::::: (Fig. Venus : Express, namely VMC [START_REF] Lee | Long-term variations of the UV contrast on Venus observed by the Venus Monitoring Camera on board Venus Express[END_REF][START_REF] Lee | Long-term variations of Venus' 365-nm albedo observed by Venus Express, Akatsuki, MESSEN-GER and Hubble Space Telescope[END_REF].

We have also investigated possible correlations with topography. [START_REF] Bertaux | Influence of Venus topography on the zonal wind and UV albedo at cloud top level: The role of stationary gravity waves[END_REF] and SO 2 behavior as seen by STIS/HST [START_REF] Jessup | Coordinated Hubble Space Telescope and Venus Express Observations of Venus' upper cloud deck[END_REF], and explained through coupled variations in vertical mixing and zonal wind speed through momentum deposition from topography-induced gravity waves over the western edge of Aphrodite Terra.

In any case, the high temporal and spatial variability of both SO 2 and UV absorption over a large span of temporal (from days to decades) and spatial (from regional to planetary) scales highlight the need to continue the monitoring of Venus after the end of Venus Express, from orbiters like Akatsuki and Earth-based observations, at least until the next generation of UV instruments on board Venus orbiters may take over the legacy of Venus


Laure Lagny

Mathieu Secail-Geraud

Julien Le Meur

Silvio Montresor

Kevin Heggarty

Charles Pezerat

Pascal Picart
email: pascal.picart@univ-lemans.fr

Visualization of travelling waves propagating in a plate equipped with 2D ABH using wide-field holographic vibrometry

This paper presents a method for wide-field vibrometry based on high-speed digital holographic interferometry. We demonstrate the possibility of measuring transient vibrations of structures at 100kHz frame rate when providing 46600 quantitative data on 380cm 2 rectangular spot at the object surface. Investigation of traveling acoustic waves propagating in alloy plate equipped with a two-dimensional acoustic black hole (ABH) is considered. Such a structure leads to localized vibrations of high amplitude and constitutes a good candidate for methodology testing. The wave front is generated by a short shock with duration about 50µs.

The time sequence of the vibration field obtained after the shock is depicted and exhibits the propagation of the wave front in the plate and inside the ABH. It follows that the observation of the modification of the wave propagation can be observed at very short time scale. The modification of the wave front due to the gradient in elastic properties related to the ABH area is also highlighted.

1.

Introduction

The development of lightweight structures is a field of research with many issues and significant impacts. At present, several main reasons lead manufacturers to move towards a reduction of weight in automobile, aeronautics, railway, etc., in order to reduce their energy consumption. In this context, lightweight structures build with wave traps such as acoustic black holes (ABH) are serious candidates to develop non-resonant structures without adding any mass. The ABH concept was first proposed by Mironov [START_REF] Mironov | Propagation of a flexural wave in a plate whose thickness decreases smoothly to zero in a finite interval[END_REF] and Krylov [START_REF] Krylov | Acoustic 'black holes' for flexural waves as effective vibration dampers[END_REF]. In the past years, several research groups have developed research on the analysis, modelling and the characterization of ABH performance. Experimental evidence of the vibration reduction induced by 1D ABH (beam termination) or 2D ABH (pit of power law profile embedded in a plate) have been shown in [START_REF] Bowyer | Experimental investigation of damping flexural vibrations in plates containing tapered indentations of power-law profile[END_REF][START_REF] Georgiev | Damping of structural vibrations in beams and elliptical plates using the acoustic black hole effect[END_REF]. The main features of the 1D ABH effect can be investigated from the measurement of the reflection coefficient of a beam termination [START_REF] Denis | Measurement and modelling of the reflection coefficient of an Acoustic Black Hole termination[END_REF] and from its modelling based on wave expansion [START_REF] Denis | Scattering effects induced by imperfections on an acoustic black hole placed at a structural waveguide termination[END_REF], or wavelets expansion [START_REF] Tang | Characterization of acoustic black hole effect using a one-dimensional fully-coupled and wavelet-decomposed semi-analytical model[END_REF]. Spiral ABH have also 2 been proposed to reduce the size of the tapered region [START_REF] Lee | Vibration damping using a spiral acoustic black hole[END_REF]. The 2D ABH trap effect linked to the capture of the ray trajectories of flexural waves and the focalization effect has been investigated in [START_REF] Huang | Analysis of ray trajectories of flexural waves propagating over generalized acoustic black hole indentations[END_REF][START_REF] Huang | Wave energy focalization in a plate with imperfect two-dimensional acoustic black hole indentation[END_REF] and the scattering of the 2D ABH has been modeled in [START_REF] Bowyer | Damping of flexural vibrations in turbofan blades using the acoustic black hole effect[END_REF]. The wave propagation in plates with multiple ABH indentations or ABH grids have also been modelled and measured in [START_REF] Aklouche | Scattering of flexural waves by a pit of quadratic profile inserted in an infinite thin plate[END_REF][START_REF] Bayod | Application of elastic wedge for vibration damping of turbine blade[END_REF]. Taking advantage of the vibration damping induced by ABH without adding mass, first propositions of transfer of the ABH concept towards industrial applications have been made [START_REF] Denis | Improvement of the acoustic black hole effect by using energy transfer due to geometric nonlinearity[END_REF][START_REF] Li | A vibro-impact acoustic black hole for passive damping of flexural beam vibrations[END_REF]. More recently, geometrical [START_REF] Conlon | Numerical analysis of the vibroacoustic properties of plates with embedded grids of acoustic black holes[END_REF] and impact [START_REF] Aklouche | Dispersion curves for bending waves in a meta-plate made with a periodic lattice of abh like scatterers[END_REF] non linearity inside the ABH have been exploited to transfer energy from the low frequency range (defined as being below the ABH cut-on frequency, ∼500-600Hz) to high frequencies. Such strategy improves the ABH performance in the low frequency domain, in which ABH is not active. Such nonlinear systems require analysis in the time domain, in which the present metrological tool can be useful. Especially, one might be interested by characterizing their global behavior when submitted to transient excitation or to investigate their nonlinear properties. From the point of view of measurement and metrology, the challenge is to get characterization at both the time and space scale of the involved phenomena. Generally, in the domains of acoustics, vibro-acoustics, vibrations of structures or flow-induced vibrations, Laser Doppler Vibrometer (LDV) is the most used tool for dynamic measurements [START_REF] Drain | The laser Doppler technique[END_REF][START_REF] Scruby | Laser-ultrasonics: techniques and applications[END_REF][START_REF] Monchalin | Progress towards the application of laser-ultrasonics in industry[END_REF][START_REF] Castellini | Laser doppler vibrometry: a review of advances and applications[END_REF].

Its main drawback is that the measurement is pointwise and a collection of data points at the surface of the object has to be obtained using scanning. Such scanning may be quite long, typically about 4h to scan a surface with 41×41 points. In order to overcome scanning, multipoint vibrometers were developed to simultaneously yield a collection of data points at the surface of the inspected object [START_REF] Macpherson | Multipoint laser vibrometer for modal analysis[END_REF][START_REF] Sun | Scanning laser-line source technique for nondestructive evaluation of cracks in human teeth[END_REF][START_REF] Connelly | Multipoint laser Doppler vibrometry using holographic optical elements and a CMOS digital camera[END_REF][START_REF] Fu | Multipoint laser Doppler vibrometry with single detector: principles, implementations, and signal analyses[END_REF][START_REF] Fu | Spatially encoded multibeam laser Doppler vibrometry using a single photodetector[END_REF]. Nevertheless, a high density of data points can be obtained by digital holographic techniques. By this way, the required measurement time can be reduced when simultaneously getting high number of data points. In the past, timeaveraging in digital holography was discussed as an efficient tool for vibration analysis [START_REF] Picart | Time averaged digital holography[END_REF][START_REF] Asundi | Amplitude and phase analysis in digital dynamic holography[END_REF][START_REF] Leclercq | Evaluation of surface acoustic waves on the human skin using quasi-time-averaged digital Fresnel holograms[END_REF][START_REF] Thomas | Investigation on vibration excitation of debonded sandwich structures using time-average digital holography[END_REF][START_REF] Thomas | Digital holographic study on the dynamic response of plates with geometric and material discontinuities simulating potted-insert metallic honeycomb sandwich structures[END_REF][START_REF] Stipčević | Effective procedure for determination of unknown vibration frequency and phase using time-averaged digital holography[END_REF][START_REF] Kirkove | Determination of vibration amplitudes from binary phase patterns obtained by phase-shifting time-averaged speckle shearing interferometry[END_REF][START_REF] Languy | vibration mode shapes visualization in industrial by real-time time-averaged phase-stepped electronic speckle pattern interferometry at 10.6µm and shearographie at 532nm[END_REF]. Full object movement was also demonstrated through stroboscopic recordings [START_REF] Picart | Tracking high amplitude auto-oscillations with digital Fresnel holograms[END_REF][START_REF] Pedrini | Pulsed digital holography combined with laser vibrometry for 3D measurements of vibrating objects[END_REF][START_REF] Alexeenko | Separate recording of rationally related vibration frequencies using digital stroboscopic holographic interferometry[END_REF][START_REF] De Greef | Digital stroboscopic holography setup for deformation measurement at both quasi-static and acoustic frequencies[END_REF][START_REF] Pérez-López | Very high speed cw digital holographic interferometry[END_REF][START_REF] Khaleghi | Simultaneous full-field 3-D vibrometry of the human eardrum using spatial-bandwidth multiplexed holography[END_REF][START_REF] Bortolozzo | Selfadaptive vibrometry with CMOS-LCOS digital holography[END_REF][START_REF] Redding | Measuring vibrational motion in the presence of speckle using off-axis holography[END_REF][START_REF] Ney | Three wavelengths parallel phase-shift interferometry for real-time focus tracking and vibration measurement[END_REF][START_REF] Kakue | Digital holographic high-speed 3D imaging for the vibrometry of fast-occurring phenomena[END_REF].

However, in most of these studies, the excitation of structures was performed in the stationary regime. As mentioned before, studying complex structures equipped with wave traps requires analysis at both their time and space scales. It follows that providing a real-time follow-up of the vibration amplitude under arbitrary excitation conditions is a challenge for full-field optical metrology.

During the past years, the performances of continuous wave lasers with power larger than 5W, and high-speed imaging sensors (frame rate up to 1MHz) have been significantly improved. Merging these technologies into holographic techniques yields an adapted approach for real-time and multi-point recording of transient phenomena in complex media.

When recording digital holograms with a high-speed sensor, recording transient phenomena at both their time and space scales becomes possible. Recently [START_REF] Poittevin | Multi-point vibrometer based on high-speed digital in-line holography[END_REF][START_REF] Poittevin | Quality assessment of combined quantization shot-noise-induced decorrelation noise in high-speed digital holographic metrology[END_REF], the authors demonstrated the ability of digital holography as an accurate multipoint vibrometer. Identification of the force distribution at the surface of a vibrating object, by solving a regularized inverse problem, was discussed when exciting with monochromatic signals [START_REF] Poittevin | Combined digital-DOE holographic interferometer for force identification in vibroacoustics[END_REF]. In this paper, we aim at considering the case of transient excitations of structures and observation over a large field of view, typically larger than 350cm 2 . In literature, there does not exist any experimental setup to provide the wide-field visualization of the interaction between transient waves and 2D ABH. Indeed, the use of a scanning laser Doppler vibrometer is not adapted to this case because it requires spatial scanning and a perfect reproduction of the impact to the structure for each scan. In the case of scanning with 41×41 data points, that would require 1681 impacts. A perfect repeatability for such a number of impacts is really not possible. When recording the wave front propagation at its time and space scale by wide-field and timeresolved digital holography, the problem of the reproducibility of impact is naturally bypassed.

However, the spatial resolution in measurement results is also a key parameter. When increasing the frame rate of any high-speed sensor, the available spatial resolution has to be decreased consequently. In addition, the spatial resolution in the reconstructed images from holograms closely depends on the number of useful pixels at recording and on the sensor-toscene distance. So, there is contradiction between wide-field (the scene has to be far from sensor) and high spatial resolution (the frame rate has to be decreased). In this paper, on-line configuration for digital holography is optimized so as to make the most of the capabilities of both sensor and digital holography. A negative zoom is designed in order to fulfill the Shannon requirements of holographic recording, and to provide the maximum occupation of the reconstructed image of the scene in the field of view. From the reconstructed images, the Doppler phase can be extracted and yields data related to the transient wave front propagation. Furthermore, the light efficiency is optimized by using a dedicated diffractive optical element for the surface illumination, providing a maximization of photon collection at the sensor plane. Digital holography is an appropriate measurement method for capturing vibrations varying rapidly with space and time. Such configuration is the one of an ABH which justify the application case discussed in this paper. In the case presented in this paper, one aims at visualizing the transient acoustic wave front propagating in a plate equipped with a 2D ABH, and excited by a 50µs short shock from an impact hammer. The interest for the ABH leads in the fact that it is an efficient way to damp the structure without adding mass. This is a promising approach, having high applicative potential at long term. Nevertheless, creating well controlled local damping requires understanding in details its behavior. In the case of the ABH, wide-field observation of the interaction with an incident wave front contributes to a better understanding of what is not. Another specificity of the ABH is that it exhibits a large vibration dynamics with high variability in its central area. It also follows that ABH is a good candidate to test experimental measurement methods.

The paper is organized as follows: Section II gives the basics fundamentals of wide-field vibrometry based on digital holography, Section III describes the experimental holographic set-up and Section IV discusses on the complex structure of the study. In Section V experimental results are provided whereas Section VI draws the conclusion of the paper.

Wide-field vibrometry

Wide-field vibrometry provides new opportunities for studying vibrations and acoustic phenomena at both their time and space scales and is based on high-speed digital holographic interferometry. Digital holograms are produced from the large-field illumination of the object surface to be studied. Since the complex-valued optical field is recorded in any digital holograms, the optical phase, and then, the optical path difference, can be retrieved and yields the measurement of the displacement field at the illuminated surface. Basically, the digital holograms are obtained by recording, with an image sensor organized as a matrix of pixels, the coherent mixing of the diffracted optical wave from the object surface and a known reference wave. If we note O the wave front from the illuminated object and R the wave front from the reference wave, then the digital hologram can be expressed by Eq. (1) (*means complex conjugate) [START_REF] Schnars | Direct recording of holograms by a CCD target and numerical reconstruction[END_REF][START_REF] Picart | General theoretical formulation of image formation in digital Fresnel holography[END_REF]:

. * * 2 2 RO O R O R H + + + = (1)
The reference wave is generally written as R(x,y)=aRexp[2iπ(u0x+v0y)] with {u0,v0} its spatial frequencies and aR is a constant. In this paper, the specificity of high-speed holographic vibrometry is that the spatial frequencies of R can be set to {u0,v0}={0,0}, corresponding to the on-axis configuration. This point is discussed in detail in [START_REF] Poittevin | Quality assessment of combined quantization shot-noise-induced decorrelation noise in high-speed digital holographic metrology[END_REF] and the reader is invited to have a look at the paper for further details. The illuminated object surface is generally at distance d0 from the recording sensor which is used without any imaging lens (arrangement known as the Fresnel configuration). The object wave diffracted to the sensor plane can be expressed with the Fresnel approximations by Eq. ( 2) [START_REF] Picart | General theoretical formulation of image formation in digital Fresnel holography[END_REF][START_REF] Goodman | Introduction to Fourier optics[END_REF] (i=√-1):

( ) ( ) ( ) ( ) ( ) . 2 exp exp exp 2 exp 0 2 2 0 2 2 0 0 0 0 dXdY yY + xX λd i Y + X λd i Y X, A y + x λd i d i d i = d y, x, O         -         ×               - ∫ ∫ π π π λ π λ (2)
The object wave front at the object plane is

A(X,Y)=A0(X,Y)exp[iψ0(X,Y)],
λ is the wavelength of light, A0 is related to the object reflectance and ψ0 is the optical phase related to the object surface profile and roughness.

From the digitally recorded holograms, the reconstruction of the object field at any distance dr from the recording plane is given by the discrete Fresnel transform [START_REF] Schnars | Direct recording of holograms by a CCD target and numerical reconstruction[END_REF]. From the hologram, the numerically reconstructed complex-valued image can be obtained from Eq. ( 3) [START_REF] Schnars | Direct recording of holograms by a CCD target and numerical reconstruction[END_REF][START_REF] Picart | General theoretical formulation of image formation in digital Fresnel holography[END_REF]:

[ ] F F r h H FFT h A × × = , ( 3
)
where FFT means two-dimensional Fast Fourier Transform and hF is the Fresnel kernel defined by Eq. ( 4), ( )

( )       +         - = 2 2 exp 4 exp 1 , y x d i i d i d y x h r r r F λ π π λ π λ . ( 4
)
From the numerical computation of Eq. ( 3), the amplitude and phase of the diffracted field Ar can be evaluated. When the reconstruction distance is dr=-d0 the initial object plane is recovered and the phase variation from the time sequence is related to the displacement field at the surface. When considering two consecutive time-instants in the hologram sequence, the phase variation is given by Eq. ( 5) and is similar to the Doppler effect, but from the point of view of the optical phase. The phase change is thus related to the displacement field U rather than the velocity.

( )

o e K K U. - = ∆ λ π ϕ 2 . ( 5
)
In Eq. ( 5), Ke is the normalized illumination vector from the light source to the object and Ko is the observation vector (also normalized) from the object to the sensor, both defined in a set of reference axis (i,j,k) attached to the object surface, with k being perpendicular to the surface. In the approach described in this paper, the observation vector is parallel to k and the illumination vector is quasi-oriented along -k. Thus, the sensitivity of the phase measurement is oriented along k so that the out-of-plane movement at the surface of the object, uz, can be measured. Generally, the phase variation in Eq. ( 5) is obtained modulo 2π and requires phase unwrapping to yield uz [START_REF] Ghiglia | Two-dimensional phase unwrapping: theory, algorithms and software[END_REF].

Thanks to the coherent mixing by heterodyning with the reference wave (Eq. ( 1)), the object wave O is amplified by the reference wave R, because of the term R * O included in the recorded hologram (third term of Eq. ( 1)). So, a weak object wave, due to a non-cooperative target, may be balanced by a strong reference wave, if |R| 2 >>|O| 2 . In addition, the reference wave is directly impacting the sensor and this makes it easier to get large amount of photons for optimizing light detection. In the approach described in this paper, measurements are possible with about 40% of the full sensor dynamics and ratio |R| 2 /|O| 2 at about 100, thus yielding suitable phase maps for visualization or metrology purposes.

Image reconstruction according to Eq. ( 3) imposes the spatial resolution in the image plane. It depends on the sensor-to-object distance, on the pixel pitch of the sensor (px) and on the number of pixels of the recorded hologram. If we note {M,N} the number of pixels along respectively the vertical and horizontal direction of the sensor plane, then the spatial resolutions achieved using Eq. ( 4) are given by [START_REF] Picart | General theoretical formulation of image formation in digital Fresnel holography[END_REF]:

       = = x y x x Mp d Np d 0 0 λ ρ λ ρ . ( 6
)
It follows that if the recording matrix is not square, the spatial resolution in the image plane is anisotropic. Typically, at frame rate 100kHz, the sensor of the set-up provides N=384 and M=264 pixels.

Experimental set-up

The experimental set-up is described in Fig. 1(a). The light is emitted from a continuous DPSS laser at λ=532nm with maximum power at 6W. The laser is separated into a reference wave and an object wave by using a polarizing beam splitter (PBS). The half-wave plate at the output of the laser is used to adjust the power in both object and reference paths to get adequate |R| 2 /|O| 2 ratio. This ratio is an important parameter of the experimental set-up. In [START_REF] Poittevin | Quality assessment of combined quantization shot-noise-induced decorrelation noise in high-speed digital holographic metrology[END_REF] was demonstrated that in order to minimize the influence of measurement noise and to get contrasted phase fringe patterns, the ratio has to be adjusted at around 100. The way to adjust the ratio is as follows: the power meter in Fig. 1(a) placed near the 50% beam splitter cube is used to measure the optical power in the reference beam and in the object beam (by blocking one after the other). Using the half wave plate at the output of the laser, the ratio can be set to around 100 when splitting light in the two arms. The polarization of the object wave is then rotated 90° to be parallel with that of the reference wave, so that interferences may occur. The reference wave is expanded, spatially filtered using a spatial filter (microscope objective and pinhole), and collimated to produce a smooth plane reference wave impacting the sensor at normal incidence. So, the carrier spatial frequencies along the reference beam are {u0,v0}≈{0,0}, giving the on-line configuration [START_REF] Poittevin | Multi-point vibrometer based on high-speed digital in-line holography[END_REF]. The object wave is spatially expanded to illuminate the structure by using a dedicated DOE (Diffractive Optical Element). The DOE inserted in the illumination path is an optical component that transforms the incident wave front into a desired wave front. It was designed to produce several spot shapes, with 8 subareas, each of them producing a particular laser beam shape. Figure 1(b) illustrates the diversity of shapes that can be produce with the DOE: square area, elliptical areas, narrow and large rectangular beams (vertical and horizontal). Such beam shaping increases the photometric efficiency of the set-up by avoiding wasting light with classical lenses and mirror assembly. In practice, a DOE consists of a substrate (a glass plate for example) on which a photoresist is deposited by spin-coating. The photoresist S1800 series from Micro Resist Technology was used, which is a positive photoresist. This series has different viscosities and therefore permits to put down photoresist layers with different thicknesses ranging from a few hundred nm to above 10microns. The error in the uniformity of the photoresist layer in the spin-coating process is about 20nm. Within this photoresist, micro or nano diffractive structures are engraved [START_REF] Goodman | Introduction to Fourier optics[END_REF]. For application in vibroacoustics, centrosymmetric diffractive patterns are required (see Fig. 1(b)). They can be obtained through binary phase DOEs (phase shift of π between the 2 levels), the simplest to produce. The spin-coating speed should be chosen so that the thickness of the photoresist layer is e=λ/2(n-1), where n is the refractive index of the photoresist material at the DOE working wavelength λ [START_REF] O'shea | Diffractive optics: Design, Fabrication, and Test[END_REF]. In this paper, the illuminating wavelength is 532nm and the photoresist thickness is close to 405nm. To solve the inverse diffractive problem, diffractive structures are modelled using an Iterative Fourier-Transform Algorithm (IFTA) optimization algorithm [START_REF] Wyrowski | Diffractive optical elements: iterative calculation of quantized, blazed phase structures[END_REF][START_REF] Wyrowski | Iterative Fourier-transform algorithm applied to computer holography[END_REF]. Once simulated, the DOEs are fabricated in a clean room using a micro-photolithography system developed at IMT Atlantique [START_REF] Kessels | Versatile stepper based maskless microlithography using a liquid crystal display for direct write of binary and multilevel microstructures[END_REF].

In the fabrication process, the parallel direct-write photo-plotter uses a programmable liquid crystal spatial light modulator (SLM) as a reconfigurable mask. The photoresist is then exposed to a pattern (corresponding to the modelled diffractive structures) of intense light with a wavelength of 436nm to which the photoresist is active. A reduction lens is used to image the pattern at LCD into the photoresist layer. The resolution limit of the direct-write photo-plotter is about 750nm. The pattern can be replicated along x and y axes by moving a nano-precision 2D translational stage. This fabrication process has been shown to be cost-effective and particularly adapted to DOE prototyping. After exposure, the substrate is put into a developer solution (Microposit TM 351 developer, Rohm and Haas)

to etch the exposed pattern into the photoresist layer. The fabricated structures are then measured with an interferometric microscope, where the lateral dimensions and the etching depth can be verified. The quality of a DOE is assessed depending on the application, usually by diffraction efficiency, uniformity and/or mean-square-error [START_REF] Kress | Applied digital optics: from micro-optics to nanophotonics[END_REF][START_REF] Herzig | Micro-optics: elements, systems and applications[END_REF].

In the set-up, the illumination angle is about θ=15°. From Eq. ( 5), the out-of-plane displacement field at the surface of the object is given by Eq. ( 7) [START_REF] Picart | Tracking high amplitude auto-oscillations with digital Fresnel holograms[END_REF]:

( ) θ ϕ π λ cos 1 2 + ∆ = z u . ( 7
)
The object and reference waves are combined by the 50% beam splitter cube placed just in front of the high-speed sensor. In the optical path from the object surface to the sensor plane, a negative zoom is inserted, in front of the cube. The negative zoom is a divergent optical system having a negative focal length. The image produced by such optical system is not located in the sensor plane, but at shorter distance from the sensor. This negative zoom produces a smaller image of the object when reducing the object-to-sensor distance [START_REF] Schnars | Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum[END_REF][START_REF] Mundt | Digital holographic recording and reconstruction of large scale objects for metrology and display[END_REF].

This provides a smaller virtual object facing the sensor at smaller distance d'0. By this way, the dimensions of the virtual object are compatible with the requirement from the Shannon conditions for recording digital holograms [START_REF] Picart | General theoretical formulation of image formation in digital Fresnel holography[END_REF]. Basically, from the hologram, the virtual image can be computed when setting dr=-d'0. And the physical plane is obtained by scaling the set of reference coordinates attached to the image plane. If we note gopt the optical magnification (0<gopt<1) produced by the negative zoom, then the spatial resolutions in the final image are given by

       = = opt x y opt x x g Mp d g Np d 0 0 ' ' λ ρ λ ρ . ( 8
)
The sensor is a high-speed camera from Photron, with pixel pitch at px=20μm and maximum spatial resolution including 1024×1024 pixels. At the full spatial resolution, the maximum frame rate is 12500Hz. When increasing the frame rate, the spatial resolution is degraded, that is 328×768 at 50kHz and 264×384 at 100kHz. The exposure time can be set from 380ns to few ms. In this paper, the exposure time was set at 1µs and the laser power was adjusted at 3W. When adjusting the negative zoom to capture holograms from a rectangular area sized 27cm×14cm, about 380cm 2 , the focal length was set to -42.8mm, leading to the reconstruction distance at d'0=-160mm. In this set-up, the distance between the initial object plane and the sensor plane is about 2.45m and the optical magnification is gopt=0.0152. So, at 100kHz, with the experimental parameters the spatial resolutions are respectively given along the x and y direction by

   = = mm m y x 06 . 1 792 ρ µ ρ . ( 9
)

Plate equipped with a 2D ABH

Wide-field holographic vibrometry is applied to the visualization of travelling waves propagating in a plate equipped with a 2D ABH, when exciting using an impact hammer.

From Mironov [START_REF] Mironov | Propagation of a flexural wave in a plate whose thickness decreases smoothly to zero in a finite interval[END_REF] and Krylov [START_REF] Krylov | Acoustic 'black holes' for flexural waves as effective vibration dampers[END_REF], the ABH is known to provide an efficient vibration damper for flexural waves on panels when the wave trap is made with a local variation of the thickness. Generally, the truncation effect near the ABH extremity can be overcome by adding a thin damping layer in its vicinity [START_REF] Krylov | Acoustic 'black holes' for flexural waves as effective vibration dampers[END_REF]. For building panels with damping properties, the circular geometry of ABH was proposed and developed in [START_REF] Bowyer | Experimental investigation of damping flexural vibrations in plates containing tapered indentations of power-law profile[END_REF][START_REF] Georgiev | Damping of structural vibrations in beams and elliptical plates using the acoustic black hole effect[END_REF]. We manufactured a 2D

ABH in alloy plate sized 900mm×540mm with 1.5mm thickness. The ABH zone is φ=59mm in diameter and is located at 196mm from the left edge and 375mm from the top of the plate.

The center of the ABH is open with 9mm diameter. The plate equipped with the ABH and the thickness profile of typical 2D ABH are depicted in Fig. 2. The principle of the ABH effect is as follows: the extremity of the structure is shaped so that the local phase velocity of flexural wave decreases progressively to 0. The consequence is that the ABH area behaves as a trap for the wave propagating through, leading to energy absorption and thus avoiding reflection phenomenon from the ABH. Figure 2(a) shows an overview of the plate equipped with the 2D ABH and its location in the plane of the plate. In the ABH area, the local thickness decreases with a power law profile as proposed by Mironov (quadratic profile) [START_REF] Mironov | Propagation of a flexural wave in a plate whose thickness decreases smoothly to zero in a finite interval[END_REF]. This means that the center of the ABH area is shaped so that its thickness h(x) progressively decreases to 0 according to Eq. ( 9):

( ) ( )      ≤ - - = not if if 0 0 2 0 0 2 / e x x x x e x h φ . (9)
In Eq. ( 9), x0 is the center of the ABH area and φ its diameter, whereas e0 is the initial thickness of the plate. A thin viscoelastic damping layer (a viscoelastic tape having a thickness at few 20-50µm) has been added in the center of the ABH area. The system constituted by the ABH and the viscoelastic layer is what is usually called a "practical ABH": in the studied case, preliminary tests show that it is able to damp vibration from a cut-on frequency of about 500-600Hz.

Experimental results

In the case presented in this paper, one aims at visualizing the transient acoustic waves

propagating in the structure equipped with the 2D ABH, and excited by transient signal.

Therefore, the plate was excited with an impact hammer from PCB Piezotronics (ref.

086E80), equipped with a force sensor, the tip being equipped with a stiff PVC tip. The hammer is used to provide shocks to the structure. The stiff tip permits to get a broad range of frequency, typically up to 10kHz. The impact of the hammer is localized at 170mm from the right edge of the plate and 292mm from its top, thus 38mm above the illuminated area. Figure 3(a) shows the force signal recorded with the set-up. The maximal force is about 8N. The duration of the shock is about 50µs (estimated at half width). The power spectrum density of the force signal injected in the plate is provided in Fig. 3(b). As can be seen, the spectrum is The digital holograms are reconstructed using the algorithm described in Eq. ( 3) with computation over 1024×1024 data points [START_REF] Picart | General theoretical formulation of image formation in digital Fresnel holography[END_REF]. Figure 4(a) shows a picture of the plate illuminated with the horizontal rectangular laser shape. The ABH area is indicated by a dashed red line and the position of the impact hammer is marked by the red spot. Note that, in the plate, there is a screw in the illuminated area, which was used to clamp a mechanical shaker in previous experiments and which does not have specific role in the proposed set-up.

Interestingly, the influence of this small screw can be seen by the measurement method. With the spatial resolution evaluation from Eq. ( 8), the dashed red lined area in Fig. 4(b) is covered by 353×132 independent data points, thus providing a collection of 46600 measurement points at the surface of the plate. From the complex valued data computed from the reconstruction algorithm, the optical phase at each time instant can be extracted and the phase difference can be obtained. Optical phase differences are obtained modulo 2π and they need to be unwrapped [START_REF] Ghiglia | Two-dimensional phase unwrapping: theory, algorithms and software[END_REF] to get the scaled physical displacement field according to Eq. ( 7).

However, modulo 2π phase variations are helpful for visualizing the interaction between the 2D ABH and the wave front emitted from the shock with the impact hammer. Indeed, the phase is wrapped in the interval [-π,+π] and that permits to keep the dynamic range of display constant over the set of figures, even if the wave amplitude is weak. But, in order to also provide amplitude maps, the wave amplitude was calculated and displayed after unwrapping the modulo 2π phase data according to Eq. ( 7) with λ=532nm and θ=15°. In the followings, Figure 5 to Fig. 9 show several sets of modulo 2π phase maps extracted from the phase variation sequence after computation from the recorded digital holograms. In Fig. 5 to Fig. 9, the dashed black circle indicates the ABH area. Fig. 10 to Fig. 12 show amplitude maps from Fig. 6 to Fig. 8, with the dynamic range adjusted to ±220nm. The vanguard of the wave front impacts the area 0.19ms after the shock. Considering the gradient of velocity in the ABH area, this part of the wave front has its velocity decreased.

The wave front is then distorted and this can be observed in the sequence of pictures in Fig. 7.

In Fig. 7(c), 0.21ms after the shock, the incident wave front is deformed by the velocity gradient in the ABH area: the local curvature of the wave front in the ABH area changes its sign. In Fig. 7(e) and Fig. 7(f), respectively 0.23ms and 0.24ms after the shock, one can observe the dislocation of the wave front in the ABH zone. Note that one observes concentrated phase jumps in the ABH center which indicate that the local vibration amplitude increases. These phase jumps are not spatially resolved. It follows that in Fig. 10 to Fig. 12 displaying the amplitude of the vibration, the quantitative data are not relevant in the ABH circled area. This is well correlated with works at LAUM demonstrating the high concentration of vibration energy at the edges of the 2D ABH [START_REF] Aklouche | Scattering of flexural waves by a pit of quadratic profile inserted in an infinite thin plate[END_REF]. Note that in order to observe the wave front dislocation with better spatial resolution, one would have to change the experimental optical parameter in order to get a more focused imaged area, to yield resolved phase jumps in the ABH center. Figure 8 shows a set of modulo 2π phase maps showing the vibration field few instants after the wave front passed through the ABH area, in between 0.31ms and 0.36ms after the shock. The deformation of the wave front in the lowerleft part of the field of view can be observed, whereas the ABH center part exhibits non resolved phase jumps which indicate local high vibration amplitude. After a while, about 16ms after the shock, at the periphery of the ABH, a vibration field with lower amplitude is observable, whereas the center still exhibits phase jumps indicating local high vibration amplitude. This is highlighted in Fig. 9(a) to Fig. 9(f) which show the sequence of pictures 15.95ms to 16ms after the shock. The set of sequences, provided through Fig. 5 to Fig. 9, Fig. 10 to Fig. 12, and supplementary material, yields an operational analysis through highlighting the wave front propagating in this complex environment. High-speed digital holographic vibrometry experimentally demonstrates such complex phenomena, at both its time (0∼16ms, and later if needed) and space scale (∼380cm 2 ). As a result, the wide-field and real-time investigation of the propagation of waves in ABH inhomogeneous wave guide can be envisaged in the near future.

Conclusion

This paper presents and discusses the application of a robust and efficient digital holographic set-up including a compact interferometer with the Fresnel configuration equipped with a negative zoom and a diffractive optical element (DOE) to improve the photometric efficiency of the set-up for illuminating large surfaces. We demonstrate the possibility of measuring transient vibrations of structures at 100kHz frame rate when providing quantitative data on 380cm 2 rectangular spot at the object surface. This is the best performance ever achieved for such area and frame rate, to the best of our knowledge. This paper provides the investigation of traveling acoustic waves propagating in alloy plate equipped with a two-dimensional Acoustic Black Hole (ABH). The wave front is generated by an impact hammer to yield 8N

force with duration about 50µs. The time sequence of the vibration field obtained after the shock is depicted and exhibits the propagation of the wave front in the complex structure made of the plate equipped with the ABH, and containing a screw. It follows that the observation of the modification of the wave propagation can be observed at very short time scale. Diffraction and reflection phenomena can be clearly seen when the wave front reaches the screw. The modification of the wave front due to the gradient in elastic properties related to the ABH area is also highlighted. Observations are well correlated to theoretical approaches of literature.

The approach presented in the paper opens the way to a thorough analysis of physical phenomena existing in and around the ABH, such as for example non-linear behavior in the center of the ABH, or qualifying the efficiency of the wave trap by evaluating its reflection coefficient. In addition, one might be able to address other problems which cannot be addressed by classical experimental means such as vibrations of panels induced by hydro or aero-acoustic sources, structural vibration induced by squeak and rattle noise.

Fig. 1 .

 1 Fig. 1. (a) Experimental set-up for wide-field holographic vibrometry (PBS: polarizing beam splitter, DOE: diffractive optical element, λ/2 half-wave plate), (b) set of beam shape structures that can be produced by the DOE for illuminating the object surface

Fig. 2 .

 2 Fig. 2. (a) Scheme of the plate equipped with the 2D ABH, (b) profile of the plate equipped with the 2D ABH with details of the shape of the structure and the thin viscoelastic layer (in orange color) stuck at the ABH center

  broad and flat up to almost 10kHz. The force sensor is used to trig the sensor in order to record a hologram sequence. A sequence including 37600 digital holograms was recorded at the sensor frame rate of 100kHz that is duration about 0.376s, with time shift between two consecutive holograms at 10µs. Considering the frequency bandwidth in Fig.1(b), the Shannon conditions are fulfilled for the hologram temporal recording. Indeed, the frame rate of the sensor is at 100kHz and the bandwidth of the shock is 20kHz. So, the temporal recording provides at least 5 sampling points for the maximum frequency in the temporal excitation signal.

Fig. 3 .

 3 Fig. 3. (a) Force signal injected in the plate, (b) power spectrum density of the force signal

Figure 4 (

 4 Figure 4(b) shows the amplitude image reconstructed from digital holograms. The illuminated

Fig. 4 .

 4 Fig. 4. (a) Picture of the plate illuminated with the rectangular laser shape, the ABH area is indicated by a dashed red line and the position of the impact hammer is marked by the red spot, (b) amplitude image reconstructed from digital holograms, the illuminated area is marked with the dashed red line

Figure 5 (

 5 Figure 5(a) to Fig. 5(f) show six phase maps corresponding to the time interval [0ms; 0.05ms] and showing the first instants of the wave front arrival in the region of interest illuminated by the laser. The spherical wave front emitted from the impact point and propagating through the plate at the early first instants can be observed. After 0.12ms the wave front reaches the screw screwed to the plate.Figure 6(a) to Fig. 6(f) exhibit the interaction between the wave front

Figure 6 (

 6 a) to Fig.6(f) exhibit the interaction between the wave front and the screw. One can clearly observe both phenomena: reflection and diffraction of the wave by the screw.

Figure 6 (

 6 b) to Fig. 6(e) show the diffraction by the screw.

Figure 7 (

 7 Figure 7(a) to Fig. 7(f) provides pictures of the wave front when entering in the ABH area.

Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .Fig. 10 .Fig. 12 .

 56781012 Fig. 5. Extracted modulo 2π phase maps over time interval [0ms; 0.05ms] showing the first instants of the wave front arrival in the region of interest illuminated by the laser

Acknowledgments

The authors would like to express their appreciation to Prof. François Gautier and Dr. Adrien Pelat from LAUM CNRS at Le Mans University for very fruitful discussion and comments. This study is part of the Chair program VIBROLEG (Vibroacoustics of Lightweight structures) supported by IRT Jules Verne (French Institute in Research and Technology in Advanced Manufacturing Technologies for Composite, Metallic and Hybrid Structures). The authors wish to associate the industrial and academic partners of this project; respectively