Quentin Michalski
email: quentin.michalski@ensma.fr

Julien Sotton

Alain Claverie

Marc Bellenoue

An application of speckle-based background oriented schlieren for optical microcalorimetry

Keywords: Background Oriented Schlieren, Calorimetry, Spark, Ignition

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Ignition and flame stabilization in combustible mixtures are among the most challenging problems in fundamental and applied combustion research [START_REF] Glassman | Combustion, Fourth Edition[END_REF]. In particular, control of ignition in helicopter engines is a key point to achieve better performances. As an example, capability of a quick engine relight in case of a flameout at high altitudes and low combustor pressures is extremely desirable.

The first step in the ignition process is creation of a small-size flame kernel by the ignitor. Initial behaviors of this flame kernel depend on the energy release to the flow by the ignition system.

For this purpose, new ignition concepts are studied using laser ignition [START_REF] Tauer | Laser-initiated ignition[END_REF], corona discharge ignition [START_REF] Bellenoue | Spark plug and corona abilities to ignite stoichiometric and lean methane/air mixtures[END_REF], radiofrequency ignition, nanosecond repetitive pulse discharge (Grish and al. 2011) [START_REF] Pancheshnyi | Ignition for propane-air mixtures by a repetitively Pulsed Nanosecond Discharge[END_REF] [START_REF] Xu | Thermal and hydrodynamic effects of nanosecond discharges in air and application to plasmaassisted combustion[END_REF]. Some of them are still based on electrical discharges. Then energy released to the flow and electrical consumption must be determined in order to be able to really compare efficiency of such ignition system. Several methodologies are developed to quantify the thermal energy release to the flow like 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 -7, 2016 microcalorimetry [START_REF] Teets | Calorimetry of Ignition Sparks[END_REF], CARS diagnostics [START_REF] Grisch | Non-equilibrium kinetic studies of plasma assisted combustion using laser-based diagnostics[END_REF], Raman spectroscopy, LIF, etc.

Methodology described in the paper is the use of a quantitative Background Oriented Schlieren (BOS) (G. [START_REF] Meier | Hintergrund schlierenmessverfahren[END_REF] [START_REF] Dalziel | Synthetic schlieren[END_REF]. BOS is based on the refractive index variation of fluid due to density gradients. Variations of refractive index due to density gradient have been qualitatively used for a long time to perform visualizations, like shadowgraphy or schlieren, in compressible flow or reactive case.

Principles of implementation of the method are quite simple, as it only requires a single camera, a static structured background and a computer for processing. Images are taken with and without optical distortion. A numerical comparison of both images is done using cross-correlation algorithms and gives out the integrated displacement vector which then, through further calculation yields other physicals according to the measured medium properties.

On a quantitative level, numerous works illustrate BOS rendering capabilities and emphasize BOS qualitative measurement qualities as it provides a wide adaptable sensibility range and acquisition field size. BOS has been applied to most conventional schlieren case of application, as several studies shows. Quantitative measurement can also be achieved and physical field measurement of density [START_REF] Elsinga | Assessment and application of quantitative schlieren methods: Calibrated Color Schlieren and Background Oriented Schlieren[END_REF]) [START_REF] Hargather | A comparison of three quantitative schlieren techniques[END_REF] [START_REF] Meier | Density measurements using the Background Oriented Schlieren technique[END_REF]) [START_REF] Ota | Quantitative 3D density measurement of supersonic flow by colored grid background oriented schlieren (CGBOS) technique[END_REF] and temperature in reactive fluids [START_REF] Iffa | Gas Flame Temperature Measurement Using background Oriented Schlieren[END_REF] has been achieved. Elsinga [START_REF] Elsinga | Assessment and application of quantitative schlieren methods: Calibrated Color Schlieren and Background Oriented Schlieren[END_REF]) and Hargather [START_REF] Hargather | A comparison of three quantitative schlieren techniques[END_REF] works provide comparisons between BOS and other quantitative schlieren methods, with respectively calibrated colored schlieren and calibrated schlieren, and shows results within 2-3% of theory which sets BOS quantitative capabilities.

Recently, Meier [START_REF] Meier | Improved Background oriented schlieren imaging using laser spckle illumination[END_REF] proposed using the speckle of a laser as a background (SBOS). SBOS allows for fine dynamic tuning over background spatial resolution even at high optical magnification.

The objective here is first to achieve a quantitative measurement of the density and assess the temperature distribution in the electric discharge kernel. The integration of the temperature field over the kernel then yields a quantitative enthalpy measurement. The method is first applied on the analysis of a laminar low Reynolds CO2 jet. It provides results which allows for uncertainty and noise investigation of the method which is then applied to electric discharges where enthalpy measurement is performed.

18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 -7, 2016

Method

Optical configuration and signal origin

In this section we introduce the optical concepts and hypothesis that link the integrated refraction index to the measured displacement field. The optical configuration is similar to the one described in Meier [START_REF] Meier | Improved Background oriented schlieren imaging using laser spckle illumination[END_REF].

Schlieren method is based on the principle that when propagating through optically heterogeneous medium, the light ray trajectory bends according to refractive index gradient. Such a behavior is mathematically modeled by the eikonal equation. If one suppose the z-axis of a righthanded Cartesian 𝑥,𝑦,𝑧 coordinate system being the direction vector of the undisturbed light ray, the eikonal equation yields the resulting curvature which is then given by

$ % & $' % = ) * $* $& $ % + $' % = ) * $* $+ (1)
One can integrate those equations along the light path 𝒞 which yield the schlieren intrinsic angular ray deflection 𝜀 and its components along 𝑥 and 𝑦, 𝐺 is the Gladstone-Dale constant which can be found in tables or calculated based on refractive index measurement and volumic mass calculation in the respective conditions. The same variation on 𝑛 is thus observed on 𝐺 which depends mainly on both the fluid composition and the wavelength used. In BOS configuration, the angular intrinsic deflection is materialized on a screen through a mirage effect which is a function of the optical collection configuration and efficiency (Fig. 1). Where 𝑀 is the optical magnification of the optical system (i.e. the magnification measured in the in-focus field) and 𝑙 the « defocusing » distance. 𝐴 = 𝑙𝑀 can be considered as the optical amplification constant. Most published works have so far used Eq. ( 5). One should notice that doing so, one makes the hypothesis that the distortion happens in one unique refraction plan therefore that the radius of the schlieren object 𝑤 is negligeable compared to the defocusing distance. The recent work of van Hinsberg & Rösgen (van Hinsberg and Rösgen 2014) emphasize the importance of this hypothesis and shows that the error ratio between the measured, under the precedent hypothesis, angular deviation ε and the real deviation ε ?@ can be estimated by

𝜀 & = ) * $* $& 𝒞 𝑑𝑧 𝜀 + = ) * $* $+ 𝒞 𝑑𝑧 (2)
(ε BC -ε) ε = 𝑤 𝑙 (6)
When considering microscopic application or simply when increasing the spatial resolution of any BOS system, 𝑀 should increase. At a constant 𝐴, it implies that 𝑙 should decrease which then results in a loss of accuracy because of an increasing ε ε BC error ratio. As seen on most BOS picture the in-

𝑑 2E = F G H )IJ (7)
Where 𝑁 is the f-number of the optical system, N = f/𝐷 where 𝐷 is the optical system effective aperture diameter and 𝑓 the focal length of the aperture lens. 𝑀 is the absolute value of magnification. Depending on the optical configuration, 𝑑 2E may slightly differ from the optic blur observed considering focus rays traced back from the refractive plan.

When looking for optimal BOS configuration, one should then notice that the blur spatial averaging scales proportionally to the defocusing distance. One may then mitigate this effect by adjusting D, the aperture diameter. A direct consequence of that spatial averaging is that it put an upper limitation to BOS signal amplification value 𝐴 which would then depend on intrinsic schlieren signal 𝜀 and spatial dimension, w. Any BOS design at early design phase should observe Eq. (3) ( 5) and ( 7) as rough resolution limits of any system can then been easily estimated before engaging in any measurement.

18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 -7, 2016

Speckle-based Background Oriented Schlieren

Implementation of BOS is quite simple as it technically only requires a background and a camera to work. On a first approach, one should notice that because cross-correlation algorithm from PIV applications are used to determine displacement, therefore any background looking like a PIVseeded flow will give good results for BOS. For qualitative and visualization purposes, it is easily evidenced that any background with enough contrast will work for the algorithm. Several Speckle photography already used likewise configurations [START_REF] Fomin | Speckle Photography for Fluid Mechanics Measurements[END_REF]) except that computation capacity and algorithm as well were not in place at the time it was considered. Eq. ( 5) still stands in speckle configuration, furthermore this time, speckle being observed in the focal plan, one can work with negative value of defocusing distance. According to Meier [START_REF] Meier | Improved Background oriented schlieren imaging using laser spckle illumination[END_REF] compared to an equal but positive sign distance, working with negative distance greatly increases sensitivity. Such configuration proves to considerably reduce the distance needed to achieve equivalent sensitivity with positive distance.

Speckle patterns are of interferential nature and are formed when scattered, i.e. therefore spatially randomly phased, coherent light interfer on a sensor surface. It can be shown [START_REF] Fomin | Speckle Photography for Fluid Mechanics Measurements[END_REF]) that when collecting the speckle through an optic system, the speckle dot mean « diameter », i.e. characteristic size, Δ R is such as

Δ R ≈ 1.22𝜆𝑁 )IJ J ( 8
)
Where 𝜆 is the wavelength of the coherent light. As of Eq. ( 8), Δ R varies in regard of the collection system exit pupil diameter which is easily experimentally verified. PIV software criteria advices using dots of 2-5 pixel/dots to achieve optimum spatial resolution, then when looking at investigating small dimension, printing resolution can become an issue (looking at more than 1200dpi). When working with speckle this problem is overcome by increasing the diaphragm opening which indeed may result in a loss of gradient resolution given equation ( 7).

18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 -7, 2016

3. Experiments

Reference flow configuration and motivations

Our objective is to achieve a small enthalpy variation measurement in electrical discharges kernel by SBOS through refractive index measurement. In order to validate the SBOS configuration we ought to find a suitable configuration close in dimension and 𝜀 to discharge kernel conditions.

Discharge energy transfer efficiency and kernel dimensions found in literature [START_REF] Maly | Spark ignition its physics and effect on the internal combustion engine[END_REF] considering an energy deposit of 40mJ, under hypothesis for the kernel gas we extensively discuss in following sections and using Eq. ( 3) it yields 𝜀 12& ~3.4.10 Z[ which is relatively close in magnitude to CO2 observed in air at ambient conditions 𝜀 12&,]^_ ~-3.10 Z[ rad. Although the difference of density gradient direction may affect the overall physic of each phenomenon, following Eq. ( 5), the only noticeable difference, from the method perspective should only be in the displacement direction and should not affect the measurement. The validation is thus made on the resolution of density of a CO2 laminar jet.

Optical configuration

The coherent source is a diode-pumped continuous solid-state laser (MxL-F, 𝜆 = 532𝑛𝑚, 3W) which emission power is stabilized in steady conditions at 1%. The beam is expanded through a collimator. Parallel beams expanded to a 45mm diameter impact a 1mm width ground glass which produces the speckle by scattering effects (Fig. 4). in each case radius is the distance from the center of the nozzle.

Fig. 5 gives a quantitative idea of the overall image acquisition quality (Fig. 5a) obtained under no flow conditions and the mean displacement intensity (Fig. 5b) of the CO2 flow. The nozzle edge, at the bottom of the image, appears blurry and the speckle which constitutes the background, remains sharp as expected.

BOS processing

The acquisition is made on 100 images at a 0.2Hz camera frequency, the same reference image is being used for each of them. The CO2 jet acquisitions are processed with MatPIV (Sveen 2004).

Given a maximum displacement 𝛿 12& = 3𝑝𝑥, the MatPIV multipass interrogation windows starting at 32x32 and finishing at 16x16 is used with a 87.5% overlap. Based on the final interrogation window size the spatial resolution achieved is ∆𝑥 = 0.208𝑚𝑚. An important overlapping is used, which may not be an optimum, but prevents discretization issues in onwards gradient integrations. Overlapping does not yield truly independent vectors [START_REF] Raffel | Particle Image Velocimetry-A Practial Guide[END_REF], which even if they aren't proper individual measurements at least act as relevant and precise interpolations. Images of 1024x1024px yields a field of 505x505 vectors. A mean displacement field is then computed. Displacements field must then be integrated. Therefore two possibilities exists, one can solve the tomography problem, obtain the gradient field which is then integrated. The other way is to notice that because the derivation is orthogonal to the integration, one can first integrate, then solve the tomography problem. In respect of Leibniz integral rule, Eq. ( 2) coupled to Eqs. ( 4) and ( 5), then yields the following system to integrate Gladstone Dale constant is set from tables [START_REF] Fomin | Speckle Photography for Fluid Mechanics Measurements[END_REF] with 𝐺 = 0.229𝑐𝑚 n /𝑔 and refractive ambient air index is taken at 20°𝐶 and 𝑝 = 1𝑏𝑎𝑟, 𝑛 0 = 1.00027. Differentiation and sum of ( 9) system's equations yields the Poisson equation which is classically solved in BOS. A rather quicker way to solve this system is to directly integrate the displacement line by line which induces a lot less smoothing than the elliptical solution. Integration is performed along the direction which present best signal to noise ratio. The line of sight integrated density (projection) is then processed through the inverse Radon transform where the usual Ram-Lak ramp filter is modulated by an Hamming window. The window filtering greatly attenuates the projection high frequency spatial components which are assumed to be mainly noise related and may therefore be reduced to negligible values without affecting the density distribution [START_REF] Meier | Density measurements using the Background Oriented Schlieren technique[END_REF].

Additional filtering by directly truncating high frequency noises (up to the Nyquist) using a reduced windows width was not required.

Validation results

Flow is estimated to be laminar thus supposed to present relatively stable parallel and axisymmetric conditions at nozzle exit along several diameters. On the jet, one reference image is taken then a hundred acquisitions are made. For each, a displacement field is computed. BOS processing is then applied to the averaged displacement field. Left Fig. 6.a shows the density profile in the jet averaged along the axis on a one diameter (4mm) distance from the nozzle tip. As expected, consequences of the reconstruction filtering, the radius density profile are rather smooth and show no high frequencies. The mean difference of density measured at jet core on 4mm long is 2.3% less than expected, which yields a 0.8% error on CO2 density. The jet sides show gradients spread on a 1.77mm distance, measured for a variation from 10% to 90% of maximum density. This value should be compared to the spatial resolution superior limit calculated from Eq. ( 7) which yields 𝑑 2E = 0.86𝑚𝑚. Right Fig. 6b presents the reconstructed, on 4mm long, jet density at core.

Its presents clear stochastic oscillations of 3.5% around the mean value. These oscillations do not disappear after temporal averaging operations thus are not assumed to be related to any oscillating jet instability. should be zero and therefore before reconstruction, the field residual mean displacement is subtracted. A first approach on an estimation of the uncertainty on density profile measurement (Fig. 6a.) can be given by applying a logarithmic differentiation on integrated Eq. ( 9). On 𝛿 & it yields

∆𝐼 𝐼 = ∆𝑛 0 𝑛 0 + ∆𝐺 𝐺 + ∆𝑀 𝑀 + ∆𝑙 𝑙 + 𝐽 ( 10
)
Where 𝐽 is the term that accounts for the uncertainty on the integral of the displacement profile and is detailed hereafter. First four terms are easily estimated with the first one been negligible

and the uncertainty on the Gladstone-Dale constant too [START_REF] Bideau-Mehu | Interferometric determination of the refractive index of carbon dioxide in the ultraviolet region[END_REF]. The magnification M measurement is done, measuring an object in the focus plan, knowing its dimension (1.98 Z0 I0.0)11 ), measuring its size in pixel (153 ± 1𝑝𝑥) and converting it knowing the pixel size (0.013𝑚𝑚/𝑝𝑥) which yields a uncertainty of 1.1%. The reference for the defocusing distance measure is taken when hand positioned item of interest appears sharp at maximum diaphragm opening. By this mean, uncertainty on the defocusing distance is estimated to be ~1𝑚𝑚, which yields ~1.3%. These two terms are constant over the field therefore only induce a bias on the results. Based on measurement done on relevant reference cases, one could properly adjust the amplification factor 𝐴 thus removing the error made on geometrical measurement.

The last term 𝐽 in Eq. 10 is the error ratio which may be considered as an estimation of the overall uncertainty of cross-correlation on the signal on the integrated displacement. This term holds both the uncertainty of the cross-correlation algorithm, and the acquisition white noise component. As seen on Fig. 6a, maximum dispersion is held at the center of the reconstruction. On one diameter after the nozzle, reconstructed value in the jet center is supposed to be equal to the CO2 density, therefore we may consider giving an estimation of 𝐽 based on the stochastic oscillations observed on Fig. 6b. Working in steady conditions, a first temporal averaging is done on 𝛿 & (i.e. averaging

Application on an electric discharge in air

The electric discharge study is done with a top plug automobile inductive coil (BERU ZSE 041).

The electrodes made of tungsten alloy E3® are of 2mm diameter with conic tip of 11.25° half angle and disposed axe aligned, with a gap of 2mm. During the discharge, voltage is recorded with a Tektronix P6015A and intensity with a LeCroy CP031 probe (Fig. 9). Delay is ensured by a pulse and delay generator (DG535, Stanford Research Systems) which synchronizes the camera, the oscilloscope and the coil. For the discharge images are recorded with a defocusing distance of 𝑙 = -36𝑚𝑚 which yields a higher spatial limitation of 𝑑 2E = 0.39𝑚𝑚. Because the overall acquisition time is shorter, the laser power is set to maximum (3W) and the intensifier gain is lower to 200 (out of 255). Images are taken 2.5𝑚𝑠 after the breakdown, at the end of the glow phase. The heated gas is supposed to be air at ambient composition and pressure for which we apply a semi-perfect behavior. It means that perfect gas law apply and calorific capacity is temperature dependent which is taken as standard Gordon-McBride polynomial form. Furthermore, electrons contribution to refractive index is 20.5 times more than the one of ions [START_REF] Meidanshahi | Measurement of temperature and electrons density distribution of atmospheric arc plasma by moiré deflectometry technique[END_REF]. Therefore the refractive index is only supposed to depend on the neutral gas species temperature.

The temperature is directly calculated from density. For enthalpy calculation, one should remember that post-tomography inversion, the field is given in cylindrical coordinates.

Calculation is based on the heated mass contained in a cylindrical control volume 𝒱 of 4mm of radius by 4mm wide which includes the phenomena and some non-disturbed area, then with 𝐶 " being the massic calorific capacity at constant pressure,

𝐻 = (𝐶 " 𝑇 𝑇 -𝐶 " 𝑇 pOE• 𝑇 pOE• )𝜌𝑑𝑉 𝒱 ( 14
)
With 𝜌 being the heated gas density. Even if tip-tip electrodes configuration is used, the discharge does not appear to be repetable enough for consistent displacement temporal averaging. Each couple of images will then be processed without averaging which may result in a lower SNR ratio thus in a higher value of 𝐽 as of Eq. 12. The calculation of the displacement is made without any mask, therefore the integration is performed on the electrode's orthogonal displacement component to avoid false vector induced by their shades. However, they are materialized in order to give a spatial reference. On Fig. 8a, one verifies that the displacements are of the same order as the one of the CO2 jet. Based on 9 images, enthalpy calculation yields 𝐻 = 10.22 ± 0.47𝑚𝐽 which corresponds to a 4.6% deviation.

Although no temporal averaging is done, deviation on the energy calculation is quite low. It seems to confirm the white nature of the noise, despite a 𝐽 OE ~19.1% for single shot acquisition on the CO2 jet, double integration seems to have considerably lowered the dispersion.

Fig. 10d shows that at the end of the process, local enthalpy is not mainly depending on temperature close to the discharge center (i.e. axis). At this time (2.5ms), the kernel temperature is found to be quite low (Fig. 10b) which is a consequence of diffusion and expansion effect of the initial streamer. Considering the rather low temperature (Fig. 10b), volumic enthalpy and massic enthalpy are quite similar (Fig. 10c), enthalpy is only depending on temperature and therefore present the same uncertainty as the jet (Eq. ( 10)). Local enthalpy is heavily weighted at core by the volume term (which results in a 1/𝑟 convolution factor). Therefore enthalpy appears, as presented on Fig. 10d, concentrated in the gradient area, where as showed by Fig. 6a the noise influence is the lowest.

For the calculation of the discharge global efficiency, the electrical energy is calculated at a time 𝑡

Conclusion

In this paper we presented an experimental method for measurement of axisymmetric field of density based on BOS. The method uses recent BOS development [START_REF] Meier | Improved Background oriented schlieren imaging using laser spckle illumination[END_REF] with speckle as background (SBOS). We validated the SBOS measurement first on a CO2 laminar and steady jet with a ±6.7% estimated maximum uncertainty, close to the ±2-3% of Elsinga [START_REF] Elsinga | Assessment and application of quantitative schlieren methods: Calibrated Color Schlieren and Background Oriented Schlieren[END_REF]) and Hargather [START_REF] Hargather | A comparison of three quantitative schlieren techniques[END_REF] and furthermore, corroborated by low experimental dispersion of ±3.5%. Then the method is extended to enthalpy variation measurement induced by axisymmetric electric discharges. The enthalpy measurement gives satisfying results, with a rather low deviation (4.6%), and are consistent with the ones found in literature [START_REF] Saggau | Kalorimetrie der drei Entladungsformen des elektrischen Ztindfunkens[END_REF]) [START_REF] Teets | Calorimetry of Ignition Sparks[END_REF]) [START_REF] Verhoeven | Interferometric spark calorimetry[END_REF]. This successful application of speckle-based BOS for microcalorimetry highlights the quantitative potential and resolution issues of BOS methods applied to highly instationary millimetric-dimension systems. Further work should investigates other discharge instants and configurations.

Fig. 1 :

 1 Fig. 1: Geometry of BOS configuration with negative focus to subject field distance Simple geometrical considerations based on Fig. 1, assuming optical Gaussian conditions and near axes ray light yields expression of the integrated displacement field 𝛿 as

18th

  International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 -7, 2016 schlieren plane objects often look blurry because of defocusing. Although most works emphasize on keeping the schlieren object as close as possible to the depth of field, it is often not a possibility. Blurring results in an averaging of the measured physical refractive index gradient. The work of Gojani and al. (Gojani, Kamishi and Obayashi 2013) gives an estimation of the consequences of the intrinsic blur on spatial resolution in BOS configuration. Blur seemingly adds to the signal a sliding averaging window convolution which width should be at least of 𝑑 2E dimensions (Fig 2).

Fig. 2 :

 2 Fig. 2: Schema of defocusing effect calculation with negative focus to subject field distance From geometric consideration one can easily establish (Gojani, Kamishi and Obayashi 2013) a rather simple expression for 𝑑 2E ,

  backgrounds have been used to obtain quantitative measurement on density, such as dot printed black and white ones[START_REF] Elsinga | Assessment and application of quantitative schlieren methods: Calibrated Color Schlieren and Background Oriented Schlieren[END_REF]), printed black and white wavelet noise[START_REF] Iffa | Gas Flame Temperature Measurement Using background Oriented Schlieren[END_REF] or regular colored grid (CGBOS[START_REF] Ota | Quantitative 3D density measurement of supersonic flow by colored grid background oriented schlieren (CGBOS) technique[END_REF]). More recently the work of Meier[START_REF] Meier | Improved Background oriented schlieren imaging using laser spckle illumination[END_REF] introduces the speckle of a laser as a background choice.

Fig. 3 :

 3 Fig. 3: Schema of flow configurationThe gas is supplied by a 4bar, 10L CO2 pressure tank (gas impurities <50ppm), the nozzle inside diameter is of 4mm and consist of a machined 6x4mm tube at a 11.5° angle. To ensure ideal steady flow conditions, the 4mm diameter is reamed on 60mm long. Estimations based on upstream pressure yields a Reynolds number, calculated with nozzle diameter, low enough (estimated to be around 40) to ensures laminar flow in steady conditions. Pressure expansion is low enough to suppose that CO2 temperature variation is negligible. As BOS measurement only gives a differential density measurement, ambient temperature is measured in the room, 𝑇 0 = 20.0 ± 0.5°𝐶 and pressure is supposed to be 𝑝 0 = 1.00 ± 0.01bar which yields 𝜌 ]^_ = 1.806𝑘𝑔/𝑚 n and 𝜌 2op = 1.190𝑘𝑔/𝑚 n .

Fig. 4 :Fig. 5 :

 45 Fig. 4: Schema of optical configuration Our optical collection system consists of two lenses, of focal length and center respectively 𝑂 and 𝑓 ) = 500𝑚𝑚 and 𝑂 s and 𝑓 _ = 300𝑚𝑚, and of a diaphragm, focus the speckle light on the naked camera sensor plan. The camera used is a PiMax 1k GenII RB-SG, CCD intensified camera with a 1Hz acquisition which suits the need for the short exposure time required. Intensification is channeled using fiber optic coupling which greatly reduces loss of resolution and distortion.Under laminar conditions, close to the nozzle, flow is supposed to be axisymmetric enough to consider a single view for tomography. Pixel size is 𝑐 = 13𝜇𝑚. Optimum quality/exposure time ratio has been found using a 250 (on a maximum of 255) intensifier gain value, and 65% of the maximum laser power (as to avoid photocathode damaging during long acquisition). Although the whole discharge process takes about 2.5ms, rapid advection movement occurs therefore the exposure time is chosen as short as possible. The best trade-off, imaging-wise, is found for 1𝜇𝑠 exposure time which is thus also used for the CO2 jet. The lenses positioning was 𝐴𝑂 = 170𝑚𝑚, 𝑂𝑂′ = 492𝑚𝑚 and 𝑂𝐴′ = 500𝑚𝑚 which ensures a global magnification ratio of 𝑀 = -1.0. The diaphragm positioned at C, is closed at 5mm in diameter which, at a distance 𝐶𝑂 s = 45𝑚𝑚, yields an effective exit pupil diameter of 𝐷~5,32𝑚𝑚. This configuration yields a speckle size of 61.6𝜇𝑚 which is about 4.7px which fits PIV software requirements. The defocusing distance is 𝑙 = -80𝑚𝑚

  on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 -7, 2016

Fig. 6 :

 6 Fig. 6: Density distribution shape taken on 4mm above nozzle exit (a) and density in the jet core (r=0) (b) Averaging lowers to negligible value any MatPIV induced peak-locking (as noted in (Atcheson, Heidrich and Ihrke 2009)). Fig. 7 shows displacement profiles along a radius at 𝑦 = 1.34𝑚𝑚 and 𝑦 = 2.84𝑚𝑚 which are the position of the two extremes value of Fig. 6b, which look almost identical. Those profiles present the same medium-high frequency oscillations as observed on the Fig. 6b.

Fig. 7 :

 7 Fig. 7: Displacement profiles at extreme Fig. density fluctuation values In SBOS as in BOS, noises origin from both step of the density field measurement, the acquisition and the reconstruction. During the acquisition, typical BOS noise sources are mainly camera sensor intrinsic noise (i.e. CCD dark current), vibration of the pattern generator (e.g. the ground glass in SBOS or the screen in BOS), local room temperature gradient and intensification noise in our case.Fig. 8 shows the typical remnant noise in reference images cross-correlations which consists in high frequencies (superior to 4𝜇𝑚) background displacement fluctuation for which part of it can actually be considered as speckle luminous intensity locally waves during acquisition. Reconstruction first step, cross-correlation presents an intrinsic uncertainty which may be considered as a white noise during the reconstruction and may largely account for what is seen on Fig. 8. Vibration effects may introduce a displacement bias which may be compensated.Considering the refractive object axisymmetric, the overall average of the displacement field

Fig. 8 :

 8 Fig. 8: Mean horizontal displacement (a) and displacement RMS (b) in pixels between 10 references images

Fig. 1 :

 1 Fig. 1: Electric signal of an electric discharge Working with ionized gas and considering the Gladstone-Dale constant calculation, one should first estimate electron contribution (Fomin 1998). The work of Maly (Maly 1984) estimates the glow discharge electron density to be of 𝑁 OE ~2.10 )[ 𝑐𝑚 Zn . The contribution to refractive index (Meidanshahi, Madanipour and Shokri 2013) on electron is given by

Fig. 10 :

 10 Fig. 10: Results in cylindrical referential (attached to the left electrode center) of one images couple through different step of the process of vertical displacement on the electric discharge, from the displacement field (a), to the temperature (iso-100K lines) (b), to the local volumic enthalpy (iso-0.05mJ/mm3 lines) (c), then to the local difference of enthalpy field (iso-2.10 Z-𝑚𝐽 lines) (d)

  𝑡 0 is the breakdown starting time, V and I the electrical tension and intensity. Measurements for the 9 acquisition at 2.5𝑚𝑠, right before the discharge stop, yields 𝐸 = 38.36 ± 1.46𝑚𝐽. This lead to a global efficiency, which can be defined as 𝜂 = 𝐻/𝐸, of 𝜂 = 26.67 ± 1.59%. The results are consistent with the orders and values found in the literature[START_REF] Saggau | Kalorimetrie der drei Entladungsformen des elektrischen Ztindfunkens[END_REF])[START_REF] Teets | Calorimetry of Ignition Sparks[END_REF] [START_REF] Verhoeven | Interferometric spark calorimetry[END_REF]. Teets[START_REF] Teets | Calorimetry of Ignition Sparks[END_REF] with 0.5mm titanium wire in air gives a transfer efficiency of 𝜂 = 23 ± 1%.18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 -7, 2016

One can estimate the expected maximum intensity of 𝜀 based on the deviation that would occurred at the extremity of a gas sphere of refractive index 𝑛 placed in a fluid of refractive index 𝑛 0 based on

	18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 -7, 2016
		Keagy's (Keagy,
	Ellis and Reid 1949) calculations. It roughly gives
	𝜀 12& ~2 𝑛 𝑛 0 -1 (3)
	Usually refractive index is not the measure of interest. In fluids, the Lorentz-Lorenz equation states
	a relation between refractive index 𝑛 and density 𝜌 which can be simplified as the known
	Gladstone-Dale equation
	𝑛 -1 = 𝜌𝐺	(4)

Doing so, one should keep in mind that because 𝜀 results from integrating a gradient, the local measurement obtained at the end should only be a refractive index variation.

Acknowledgements

This work is part of the CAPA research program on Alternative Combustion Mode for airbreathing Propulsion supported by SAFRAN Tech, MBDA France and ANR (National Research Agency).

between the acquisition fields the same way as in Fig. 6 results processing), then the statistics is made along y. This way one can give a majorant value of 𝐽 by a 𝐽 ? as follow

Where < > ? is the temporal averaging operator and L is the field radial dimension. With 𝜎 + being the standard deviation operator in the direction and < > + being the spatial averaging operator in the vertical direction y.

In case of unsteady condition when temporal averaging is not possible, a higher majorant, 𝐽 ‹ may be computed. In this case, the statistic should be formed on the ensemble of profiles of each acquisition which yields

Where A is the ensemble of a 100 acquisitions. Calculations yields 𝐽 ? ~3.1% and 𝐽 ‹ =19.1%. This should be compared with the order of the cross-correlation uncertainty which is about 0.1px.

Considering that a value of the integration of 𝛿 & along x is ~300px, it yields 16.7% of possible PIV uncertainty. Given that PIV intrinsic noise manifests as a white noise, integration and temporal averaging should reduce considerably these value which explains the rather low 𝐽 ? value. The total uncertainty on 𝐼, the line of sight integrated density difference, adds up to 5.5%. Doing so, uncertainty is only evaluated before tomography. Tomography adds its own uncertainty in the reconstruction which is quite complex to evaluate. Comparing the oscillations amplitude value (3.5%) with 𝐽 ? shows quite values which may indicate that the addition of tomography should be quite low, seemingly in the order of 1%.

Final result uncertainty must take in account the reference temperature and pressure measurement which are used to calculate the ambient gas density and add up a low 1.2%. Uncertainty on measured density is thus estimated to be of 6.7% which is consistent with the 3.5% deviation measured and the 2.3% lower difference of density.


A Seydou

A Claverie

J Sotton

M Bellenoue

Experimental investigation of the effects of nanosecond repetitive pulsed (NRP) discharges on ignition of methane-air mixtures

Keywords: NRP discharges, Particle Image Velocimetry, planar laser induced fluorescence, chemiluminescence, ignition, combustion

We performed simultaneous planar laser-induced fluorescence (PLIF) and chemiluminescence on OH radical during methane-air mixture ignition and combustion initiated by nanosecond repetitive pulsed (NRP) discharges in a cubic chamber. Single PLIF images are taken at different time delays after the occurrence of the repetitive discharges while chemiluminescence images are synchronized to the discharge and record early stages of the ignition kernel as well as flame propagation. An analysis based on apparent flame velocity of the reactive front is used to understand the ignition process and the observed ignition delay reduction and flame front wrinkling as the number of discharge pulses is increased. In addition, particle image velocimetry (PIV) in an inert airflow was developed in order to characterize the hydrodynamic effects of NRP discharges, namely shock wave and hot kernel relevant to the observed flame properties enhancement. The main objective of this study is to understand the effects of NRP discharges in plasma-flame interactions for a better comprehension of the main physical processes involved in plasma assisted ignition and combustion of hydrocarbon flames.

Introduction

One of the most important aspects of thermal engines efficiency enhancement and pollutant reduction lies in the optimization of combustion processes. In this context, low temperature nonequilibrium plasmas have been efficiently used for the last decades to promote ignition and combustion of fuel-containing mixtures. The efficiency is considered in terms of ignition delay reduction [START_REF] Aleksandrov | Electron Distribution Function in 4:1 N2-O2 Mixture[END_REF]], production of active radicals [START_REF] Yin | OH Radical and Temperature Measurements during Ignition of H2-Air Mixtures Excited by a Repetitively Pulsed Nanosecond Discharge[END_REF]], flame stabilization [START_REF] Pilla | Etude Expérimentale de la Stabilisation de Flammes Propane-Air de Prémélange par Décharges Nanosecondes Impulsionnelles Répétitives[END_REF]] and pollutant formation reduction . Although different phenomena are involved in plasma-assisted ignition/combustion, [Jiguang Ju & Wenting sun (2015)] have identified four different pathways of combustion enhancement by plasma discharges: thermal, chemical, fuel decomposition and hydrodynamic [START_REF] Bellenoue | Spark Plug and Corona Abilities to ignite Stoichionetric and Lean Methane-Air Mixtures[END_REF]] pathways. The influence of each effect is to date not quantified and the complex plasma-flame interaction still remains unresolved. Previous studies [START_REF] Pilla | Etude Expérimentale de la Stabilisation de Flammes Propane-Air de Prémélange par Décharges Nanosecondes Impulsionnelles Répétitives[END_REF]], [START_REF] Tholin | Simulation of the Hydrodynamic Expansion Following a Nanosecond Pulsed Spark Discharge in Air at Atmospheric Pressure[END_REF]] supported that the mechanisms of interaction are mainly chemical and thermal effects. Thermal effect consists in a rapid heating of the mixture through translational energy transfert between electrons and molecules, resulting in acceleration of reaction rates as described by the Arrhenius law. Chemical effect corresponds to reactive species and radicals production by highly energetic excited electrons, ions and molecules. This will accelerate chemical reaction rates and can potentially promote the production of new combustion initiation and development pathways. Recently, experimental [START_REF] Borghese | Development of Nitrogen Kernel Produced by a Very Fast Spark Discharge[END_REF], [START_REF] Da | Experimental Study of the Hydrodynamic Expansion following a Nanosecond Repetitively Pulsed Discharge in Air[END_REF], [START_REF] Xu | Thermal and Hydrodynamic Effects of Nanosecond Discharges in Air and Application to Plasma-Assisted Combustion[END_REF]] and numerical studies [START_REF] Tholin | Simulation of the Hydrodynamic Expansion Following a Nanosecond Pulsed Spark Discharge in Air at Atmospheric Pressure[END_REF]] have shown interesting results on the hydrodynamic effects of the NRP discharges, namely shock waves in the earlier stages followed by a hot kernel in later stages. These aerodynamic effects potentially play relevant role in plasma-flame interactions [Da Xu (2013)], but their influence is being neglected.

Nevertheless, the physico-chemical processes responsible for this optimization remain not well understood. The objective of this experimental work is to highlight the hydrodynamic effects of NRP discharges on ignition of stoechiometric methane-air-N2 flames for a better comprehension of the main physical processes involted in plasma-flame interaction.

Experimental setups and diagnostics

Cubic combustion chamber

The experimental setup for plasma-assisted combustion used in the current study consists in a stainless steel cubic combustion chamber. It is composed of 3 square faces of 66 mm height each and offers a total volume of about 198 mm 3 . In order to perform simultaneously OH radical PLIF and chemiluminescence, 2 fused silica windows are mounted on two opposite faces and allow a maximum pressure in the chamber of 4 MPa. The methane-air-N2 mixture is manually introduced into the combustion chamber through the valve from vacuum to the desired pressure.

The pressure inside the combustion chamber was monitored with a Kistler 601 A piezoelectric pressure sensor. The combustion chamber allows single shot experiments and the pressure evolution is only dependent on heat release and thermal loses.

Two cylindrical tungsten electrodes with 1 mm gap distance are mounted onto a micrometric displacement device and placed into the combustion chamber in vertical pin-to-pin configuration, so that the middle of gap is located at the center of the chamber. An adjustment shim is used to control and settle the gap at 1 mm before each experiment to ensure the same experimental conditions. The nanosecond repetitive (NRP) discharges are delivered by a FID GMBF pulse generator (FGP 10-30NM10) of 10 ns duration and maximum voltage amplitude In order to perform planar laser-induced fluorescence (PLIF), the OH radical excitation is achieved using a doubled dye laser Continuum ND6000 (with Rhodamine 590) pumped by the second harmonic of a pulsed Nd-YAG Continuum Surelite III laser. The later laser is run at 10 Hz by a Stanford DG645 pulse and delay generator. The tunable dye-laser beam enables to get a wavelength corresponding to the Q1 (6) absorption band of OH around 282.9 nm with precision on the order of 1 picometer. The laser provides pulses of about 6 ns duration and reaches a maximum energy and frequency of around 15 mJ and 10 Hz respectively. A cylindrical lens was placed at the exit of laser in order to generate a 30 mm height, 500 µm width and 10 mJ energy laser sheet that illuminate a region located at around 1 mm behind the electrode gap position. The energy level and laser characteristics obtained in this study follow the linear regime of OH radical fluorescence [START_REF] Bresson | Techniques d'Imagerie Quantitatives: Fluorescence Induite par Laser Appliquées aux Ecoulements et aux Combustion[END_REF]. An intensified Princeton PI-Max 4 CCD camera with maximum frequency of 5 Hz when using 1024*1024 pixels 2 resolution is placed at the opposite side to record the OH radical 2D fluorescence signal. The coupled intensifier allows nearly 100% amplification gain of the initial signal and acquisition duration as short as 100 ns. This short duration of the amplification avoids collecting OH* chemiluminescence and phosphorescence signals Due to different characteristics times of the devices, a precise synchronization scheme was set up in order to perform simultaneous chemiluminescence and PLIF on the OH radical and guaranty the reliability of the results. A single shot PLIF image is coupled to the time-resolved chemiluminescence film. We use the delay generator 1 as master clock of the 10 Hz PLIF laser that delivers a trigger signal to Photron SAZ rapid camera operating at 30 kHz with 25 µs gate time (see figure 2). The output signal of this camera controls and triggers NRP discharges that operate with the same frequency, thus chemiluminescence images are systematically recorded during and after the discharge pulses. A 23 µs gate time intensifier was used to lower the integration time and avoid glare light on the camera sensor especially during the first moments after the pulses. The chemiluminescence images correspond then to the time interval between the pulses. The 100 ns gate time intensified camera (PI-Max 4) is delayed with the desired delay time after the discharges initiation at which a PLIF image is taken. This way, we record single shot image of PLIF at a specific delay time after the ignition and the entire high speed video of chemiluminescence within the region of interest recording the discharge application as well as resulting flame propagation. In order to synchronize the different elements of the PIV system, a reference trigger signal from the control unit, is simultaneously sent to the 10 Hz laser and the delay generator (DG) 1.

Firstly, the synchronized camera and laser device takes a couple of frames of the ''undisturbed'' medium. The signal is then delayed by a delay time Δt and sent to the delay generator 2 that launches the discharge pulses. The basic idea is to set a delay time Δt, so that the discharge pulse(s) end(s) at an instant ''Dly'' before the second couple of frames (located 100 ms after the first one).

The value of Dly was varied from 1 "s to 10 "s for the shock wave propagation and from 33 "s to 100 "s for the hot kernel development. The maximum jitter between the delay generator 2 and the discharge was found to be around 500 ns. By this method, hydrodynamic effects of the train of the NRP discharges are highlighted. The resulting chronogram of the synchronization methodology is displayed below.

Results and discussion

Stoichiometric quiescent methane-air-N2 mixture diluted with 20% mass of N2 is ignited using a burst of 4, 23 and 40 NRP pulses corresponding respectively to 3.9 mJ, 18.31 and 32.07 mJ electrical energy. The initial pressure and temperature are set to P0 = 1 bar and T0 = 300 K respectively. The different experiments were carried out in identical conditions. For this mixture, the minimum number of pulses that lead to successful ignition was found to be about 4 pulses.

The mean electrical energy was equal to 1.5 mJ for the first pulse and about 0.8 mJ for the subsequent pulses. This can be explained as follows: the first pulse is applied in a fresh medium, so it requires high voltage to overcome the electrical resistance of the gap and produce the spark.

The subsequent pulses take place in a medium which could contain intermediate species and residual heat from the previous pulse(s). After the ignition, the flame develops outwardly within the region of interest. For each discharge burst, single shot PLIF images on the OH radical taken respectively at 1ms, 2 ms and 3 ms after the discharge pulses and their corresponding OH* chemiluminescence images are displayed in figure 5. Each couple of images corresponds to a single experiment so that the two simultaneous diagnostics provide complementary information about geometrical aspects of flame front structure. At 1 ms after the ignition, the small flame kernel is not enough developed to reach the acquisition area where the laser sheet is located. This explains why PLIF OH signal intensity is low at 1 ms for 4 pulses. The produced PLIF OH signal then slowly increases until 3 ms. When we increase the number of pulses up to 23 and 40 pulses, the OH signal intensity dramatically increases and the flame already spreads out of the gap in comparison to the same instants as for 4 pulses. Furthermore, the flame front is more distorted as the number of pulses is increased. This is clearly visible on PLIF images. We did not take a PLIF image at 1 ms under 40 pulses simply because at this instant, the discharge pulses are not finished yet. Qualitative chemiluminescence allows 3 dimensional integration of the OH* spontaneous emission along the depth of field. Nevertheless, the wrinkled flame front shape can easily be distinguished as the number of pulses increases and it corresponds approximately to that of PLIF for each experiment.

Quantitative analysis:

From chemiluminescence images, we can extract the temporal contour of the flame front within the region of interest as the flame propagates outwardly after ignition. Otsu's algorithm is used for the binarization of chemiluminescence images in order to detect time evolution of flame contour. We define an equivalent flame radius (Req) based on the surface. The apparent velocity is obtained by calculating the ratio of the average distance between two consecutive flame contours and the corresponding time step. A centered finite differencing scheme with second order accuracy is used to calculate an average of the apparent flame velocity in the frame laboratory's reference:

𝑆 " = 2 𝐴 &'( + 𝐴 &+( (𝐿 &'( + 𝐿 &+( )(𝑡 &'( -𝑡 &+( )
Where An is the area inside the contour and Ln is the contour length at the time step tn. Color range goes from red for the earlier stages to blue as the flame propagates. This can be explained by a more pronounced hydrodynamic effects that enhance mixing and reaction rate as the number of pulses (energy) increases.

Hydrodynamic effects of NRP discharges

When a discharge is applied in a gas or a combustible mixture, the instantaneous intense energy release produces a spherical shock wave that propagates outwards from the gap center.

This phenomenon takes place few microseconds after the discharge and is followed by a hot plasma kernel from residual heat at time scales of tens of microseconds. Initially, the shock wave is cylindrical supersonic and progressively becomes spherical sonic wave due to electrodes configuration as it can be seen in figure 9.a. The ensuing competition between spherical and cylindrical expansion in the spark gap and the boundary layer on the electrode surface both generate vorticity, resulting in the toroidal shape of the hot gas kernel and enhanced mixing [Bane et al. (2014)]. The repetition of discharge pulses at a high frequency produces subsequent shock waves and increases the hot kernel size, thus amplifying density gradient and momentum transfer around the electrodes (see figure 8). This results in larger instabilities that modify local aerodynamic conditions of the media by heat transfer to electrodes and specific small scale flow prior to ignition. Particle image velocimetry (PIV) images displayed in figure 8 are respectively taken 9 "s and 33 "s after 1 pulse of 1.5 mJ and 10 pulses of 8.7 mJ electrical energy show a spherical shock wave and hot kernel mentioned above. discharges increases. This observation can be explained as follows: when the deposited energy (number of pulses) increases, a hot plasma kernel and a recirculation zone are formed prior to ignition, that lead to earlier formation of ignition kernel. Initially, the toroidal hot kernel largely influences the ignition. Additional pulses tend to increase the size of the hot kernel and enhance mixing around the electrodes as showed in figure 8. As 4 pulses are sufficient to ignite the mixture, the hot kernel obtained from the repetition of pulses influences the ignition to a certain extent, typically the hot kernel area. When the flame develops sufficiently away from this area, spherical shock waves that pass through the flame front are dominant on propagation and acceleration as we observed by simultaneous chemiluminescence and PLIF. Indeed, the ignition kernel is an interface of strong density gradients while successive spherical shock waves generate pressure gradients (see figure 9.b) along the interface. The simultaneous presence of misaligned density and pressure gradients at the interface produces vorticity that enhances mixing and disturbs the flame front. Because of these baroclinic effects, the flame front is more and more wrinkled and additional instabilities are generated. Thus, local reaction rate increases [Oran and Gardner (1985)] and favors ignition and flame velocity increase. Similar results on flame speed enhancement of lean propane air flames under NRP discharges were obtained by [START_REF] Xu | Thermal and Hydrodynamic Effects of Nanosecond Discharges in Air and Application to Plasma-Assisted Combustion[END_REF]].

Conclusion

The current study gives insight on aerodynamic effects of NRP discharges on methaneair mixtures ignition as well as significant information about morphological aspects of flames.

These effects modify local aerodynamic conditions prior, during and after ignition and combustion. PIV results are used to describe aerodynamic effects of NRP discharges and interpret flame kernel development observed by simultaneous OH chemiluminescence and PLIF imaging.

Thus, aerodynamic effects of NRP must be considered along with thermal and chemical effects for validating numerical codes for future design of reliable, energy-efficient, low cost and environmentally friendly automotive and aerospace engines. These original and interesting results contribute to a better understanding of the main physical processes involved in plasma assisted ignition and combustion.

(

  Umax) and pulse repetition frequency (PRF) of 10 kV and 30 kHz respectively. A high voltage charge resistance Kanthal of R = 50 ! ±5% is connected to the high voltage part of the electrical 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 -7, 2016 circuit for impedance matching and current signal noise reduction. The discharge voltage and current intensity are measured by means of a high voltage Lecroy PPE20kV probe and pearson coil 6585 sensor respectively, thus the electrical energy of the discharge can then be deduced. Due to different time scales between the NRP discharges and the combustion, the electrical signals (voltage, current) and pressure signal are recorded on a separate oscilloscopes.

Fig. 1

 1 Fig. 1 Cubic constant volume combustion chamber for plasma-assisted combustion

(

  characteristic time of about 1 ms). A Nikon lens of 105 focal length and f/2.8 maximum aperture is placed on the camera and supports a set of bandpass filters Scott WG280 and UG11 centered around 310 mm to select OH fluorescence wavelength only and avoid background scattering. The acquisition region obtained in this case is a 27*27 mm 2 size square for a resolution of around 26.4 µm/pixel.

Fig. 2

 2 Fig. 2 Experimental setup of simultaneous PLIF and chemiluminescence of OH radical in methane-air-N2 flames.

Fig. 3

 3 Fig. 3 Experimental setup of particle image velocimetry in quiescent air.

Fig. 4

 4 Fig. 4 Chronogram of synchronization methodology for PIV measurements

Fig. 5

 5 Fig. 5 Simultaneous OH radical PLIF and OH chemiluminescence images at different instants of methane-air-N2 mixture ignition by 4, 23 and 40 NRP pulses. P0 = 1 bar, T0 = 300 K.

Fig. 6

 6 Fig. 6 Time evolution of flame front contours for a) 4 pulses, b) 23 pulses and c) 40 pulses. Time step = 400 µs

  on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 -7, 2016 Time evolution of flame equivalent radius is shown in figure 7.a and follows monotonic linear evolution with increasing values from 4 to 40 pulses. Fig. 7.b displays apparent velocity as function of flame radius for 4, 23 and 40 pulses. It can be noticed that for the same equivalentradius the apparent velocity of the flame increases as the number of pulses increases. Before 6 ms, the apparent velocities in case of 23 and 40 pulses are higher than that of 4 pulses, thus confirming the observation of simultaneous PLIF and chemiluminescence images. The apparent flame velocity reaches a steady-state value around 3.7 m/s irrespectively of the number of pulses, suggesting that the enhancement effect occurs at early stages of discharge application and ignition.

Fig. 7

 7 Fig. 7 a) Time evolution of equivalence radius and a) and b) apparent flame velocity function of equivalent radius for atmospheric pressure methane-air-N2 mixtures ignited with 4, 23 and 40 NRP pulses.

  on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 -7, 2016

Fig. 8

 8 Fig. 8 PIV images of induced shock waves and recirculation by a) 1 pulse (E1p1.5 mJ) and b) 10 pulses (E10p=8.7 mJ) in air at ∆t=9 "s and ∆t=33 "s. Vai r=0.2 m/s, P=1 atm, Tai r=300 K.

  on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 -7, 2016

Acknowledgements:

This work is supported by ANR-PLASMAFLAME-2011BS0902501 project.


Marc Gesnik

Kevin Blaize

Thomas Deffieux

Jean-Luc Gennisson

José-Alain Sahel

Mathias Fink

Serge Picaud

Mickaël Tanter

3D Functional Ultrasound Imaging of the cerebral visual system in rodents

de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The ability to process visual information surrounding each individual is one of the most astonishing and complex task each vertebrate can perform. This ability relies on the cerebral visual system. Its complex chain of information processing begins with the gathering of photons on the retina. Visual information travels along the optic nerves, is pre-processed in sub-cortical relays such as the left and right Lateral Geniculate Nuclei (LGN) or the Superior Colliculus (SC) and is finally processed in the Visual Cortex. The so-processed information is then sent to other cerebral areas that will for instance trigger an action or a memorization [START_REF] Nolte | The Human Brain: An Introduction to Its Functional Anatomy[END_REF]. This complex and multi-component system has been widely studied using electrophysiology [START_REF] Adams | the Projection of the Rat'S Visual Field on the Cerebral Cortex[END_REF][START_REF] Espinoza | Retinotopic organization of striate and extrastriate visual cortex in the hooded rat[END_REF][START_REF] Hubel | AND FUNCTIONAL ARCHITECTURE IN THE CAT †TM S VISUAL CORTEX From the Neurophysiolojy Laboratory , Department of Pharmacology central nervous system is the great diversity of its cell types and inter-receptive fields of a more complex type ( Part I ) and to[END_REF]. Nevertheless, due to its three dimensional spatial complexity at varying depths in the brain, to its interactions with other functional regions of the brain and to a variety of dynamic tasks performed along the chain, the full understanding of the visual system remains a challenge.

Although electrophysiology benefits from an excellent sensitivity and gives fundamental information from the direct measurement of the neurons activity, it is mainly restricted to local measurements. Mapping the full visual system activity, is therefore a time-consuming task and remains constrained by a limited number of implantable electrodes per subject. Furthermore, this approach is very invasive when considering deep brain areas like thalamic relays.

Additionally functional Magnetic Resonance Imaging (fMRI), has extensively contributed to understand the visual system through its ability to map the brain activity in 3D (Op de [START_REF] Op De Beeck | Perceived shape similarity among unfamiliar objects and the organization of the human object vision pathway[END_REF]. Its non-invasiveness and ability to map the brain in 3D makes it a highly suited method for the study of vision in human [START_REF] Denison | fMRI of the magnocellular and parvocellular subdivisions of human LGN[END_REF][START_REF] Reitsma | Atypical Retinotopic Organization of Visual Cortex in Patients with Central Brain Damage: Congenital and Adult Onset[END_REF][START_REF] Warnking | fMRI retinotopic mapping--step by step[END_REF]. However, its spatial and temporal resolution can become a struggle when scaling down the technique to rodents, since it requires always higher magnetic fields, averaging functional maps over several animals [START_REF] Niranjan | fMRI mapping of the visual system in the mouse brain with interleaved snapshot GE-EPI[END_REF]Pawela et al., 2008aPawela et al., , 2008b;;[START_REF] Zhou | Balanced steady-state free precession fMRI with intravascular susceptibility contrast agent[END_REF] or contrast agent [START_REF] Chan | In vivo visuotopic brain mapping with manganese-enhanced MRI and resting-state functional connectivity MRI[END_REF] to resolve smaller structures, especially for the study of small sub-cortical structures such as the LGN (Lau et al., 2011a(Lau et al., , 2011b) ) and SC [START_REF] Chan | Functional MRI of postnatal visual development in normal and hypoxic-ischemic-injured superior colliculi[END_REF] or for retinotopic map reconstruction in the rodent visual cortex (Bissig andBerkowitz, 2011, 2009). Moreover, the limited temporal resolution of fMRI makes it difficult to estimate response delays between different brain regions. To answer this drawback in rodents, optical intrinsic imaging becomes a competitive imaging modality and allows to realize accurate measurements at the surface of the cortex [START_REF] Gias | Retinotopy within rat primary visual cortex using optical imaging[END_REF][START_REF] Kalatsky | New paradigm for optical imaging: Temporally encoded maps of intrinsic signal[END_REF][START_REF] Schuett | Mapping retinotopic structure in mouse visual cortex with optical imaging[END_REF]. However, optical imaging is limited by the strong multiple scattering of the optical waves in biological tissues and is restricted to measurements at the superficial layers of the cortex, down to a few micro-meters [START_REF] Gias | Retinotopy within rat primary visual cortex using optical imaging[END_REF]. Neither the function of deep layers of the visual cortex nor of the thalamic relays can be imaged this way with a wide field of view.

In the present study, a new technique so-called functional ultrasound (fUS) imaging [START_REF] Macé | Functional ultrasound imaging of the brain[END_REF] is presented. fUS is a recently developed functional neuroimaging technique based on ultrafast ultrasound imaging [START_REF] Tanter | Ultrafast imaging in biomedical ultrasound[END_REF] which has already offered new insights in diagnostic imaging [START_REF] Tanter | Quantitative Assessment of Breast Lesion Viscoelasticity: Initial Clinical Results Using Supersonic Shear Imaging[END_REF] and blood flow imaging [START_REF] Bercoff | Ultrafast compound doppler imaging: Providing full blood flow characterization[END_REF][START_REF] Osmanski | Ultrafast Doppler imaging of blood flow dynamics in the myocardium[END_REF][START_REF] Udesen | High frame-rate blood vector velocity imaging using plane waves: Simulations and preliminary experiments[END_REF]. Ultrafast ultrasound imaging can capture more than 20,000 frames per second, compared to the usual 50 frames per second in conventional ultrasound scanners. This increase in temporal resolution allows to revisit Power Doppler imaging [START_REF] Rubin | Power Doppler US: a potentially useful alternative to mean frequency-based color Doppler US[END_REF] and results in a high boost (up to 50) of sensitivity to blood flow. Contrary to the Doppler frequency which is dependent on the angle between the ultrasonic beam and the vessel, the integral of the Doppler spectrum (known as Power Doppler) in a pixel is proportional to the number of moving red blood cells within the ultrasonic sample volume [START_REF] Rubin | Fractional moving blood volume: estimation with power Doppler us[END_REF][START_REF] Rubin | Normalizing fractional moving blood volume estimates with power Doppler US: defining a stable intravascular point with the cumulative power distribution function[END_REF][START_REF] Shung | Scattering of Ultrasound by Blood[END_REF]. This proportionality is valid only if backscattering properties do no vary versus time. As long as the haematocrit and shear rate remain time-invariant during the acquisition time, this assumption was proven to be valid [START_REF] Cloutier | Ultrasound backscattering from non-aggregating and aggregating erythrocytes--a review[END_REF]. Note that the CBV measurement from Power Doppler is independent of the direction of the flow except when the flow direction becomes almost perpendicular to the ultrasonic beam (between 80° and 90°) as shown in [START_REF] Mace | Functional ultrasound imaging of the brain: theory and basic principles[END_REF]. Thus measuring CBV with ultrafast ultrasound allows a detection of subtle hemodynamic changes in much smaller vessels compared to conventional Doppler ultrasound.

Similar to other neuroimaging techniques based on the neurovascular coupling such as fMRI [START_REF] Ogawa | Brain magnetic resonance imaging with contrast dependent on blood oxygenation[END_REF] with Blood-Oxygen-Level-Dependant (BOLD) and optical intrinsic imaging [START_REF] Frostig | Cortical functional architecture and local coupling between neuronal activity and the microcirculation revealed by in vivo high-resolution optical imaging of intrinsic signals[END_REF][START_REF] Grinvald | Functional architecture of cortex revealed by optical imaging of intrinsic signals[END_REF], fUS relies on activity-dependant CBV changes in small blood vessels to detect active neuronal assemblies in vivo [START_REF] Mace | Functional ultrasound imaging of the brain: theory and basic principles[END_REF][START_REF] Shung | Scattering of Ultrasound by Blood[END_REF]. Though CBV convey distinct information from BOLD, they both are a manifestation of the neurovascular coupling [START_REF] Martindale | The hemodynamic impulse response to a single neural event[END_REF] and their measurements yield indirect information on brain neuronal activity. CBV gives access to the number of red blood cells within the pixel whereas BOLD signal depends on Blood Oxygenation. Similarly to BOLD fMRI fUS was shown to map the brain activity in response to sensory-motors stimuli [START_REF] Macé | Functional ultrasound imaging of the brain[END_REF] and to odor-evoked stimuli deep in the brain [START_REF] Osmanski | Functional ultrasound imaging reveals different odor-evoked patterns of vascular activity in the main olfactory bulb and the anterior piriform cortex[END_REF] with an excellent spatiotemporal resolution (100µm in plane and 100ms for a single trial acquisition).

By using fUS imaging and a simple visual stimulation setup we investigated the feasibility of mapping the visual system in the rat brain. Using a motorized translation of the ultrasonic probe to overcome the two dimensional limitation of our field of view and extend it to 3D, we were able to map the activation of the visual cortex and of the SC and LGN along the visual pathway. We leveraged simple changes in the visual stimuli to assess changes in the response intensity or localization in these visual areas. We also measured CBV response delays between the different vision-involved areas.

Materials and methods

Animals, surgical procedures

Adult male Long-Evans rats (Janvier Labs; France) weighting 250 g to 350 g, and aged 7 to 9 weeks were included in this study. They were housed two by cage with free access to food and water and maintained under standard conditions (12/12 h light-darkness cycle, 22 °C). All experiments were conducted in accordance with the European Council Directive (2010/63/EU) and the study was approved by the institutional and regional committees for animal care (Committee Charles Darwin n°5, registration number 5486).

All rats underwent surgical craniotomy before the imaging session. Anaesthesia was induced with 5% isoflurane and followed by intraperitoneal (i.p.) injection of a mixture of ketamine (60 mg/kg, Imalgene 1000®, Merial; France) and medetomidine (0.4 mg/kg, Domitor®, Pfizer, Santé Animal; France). Anaesthesia was maintained by a periodic i.p. dosage using 1/3 of the initial dose every 45 minutes. Buprenorphine was injected subcutaneously (0.05 mg/kg, Buprecare®). Body Temperature was maintained at 37 °C using a heating blanket throughout the experiment. Animals were placed in a stereotaxic apparatus during surgery and imaging. A sagittal skin incision was performed across the posterior part of the head to expose the skull. Parietal bone were removed by drilling rectangular flaps and gently moving the bone away from the dura mater. Thus exposing the cortex over the visual cortex from Bregma -4 to Bregma -7 mm, with a maximal width of 14 mm. For 3D scans more of the bone was removed so that the cortex exposure spans from Bregma +2 to Bregma -8 mm. The animals were kept under dark conditions from the beginning of the surgery to the stimuli trials. The surgery lasting about an hour, animals can be considered to be dark-adapted.

Stimuli delivery

Visual stimuli were delivered using a 51 x 29 cm², 1920 x 1080 pixels screen (P2314H 23", Dell), in front of the rat at 8 cm, therefore covering 145° of the visual field in the horizontal dimension and about 122° in the vertical dimension. At 8 cm, we measured a maximum luminance of 8 cd/m² (full white screen) and a minimum luminance of 0.04 cd/m² (full black screen). Stimulation runs consist in episodic presentations of black and white flickering on the screen interleaved with black screen period for rest: A run consisted in 30 s of rest followed by 30 s of flicker repeated 5 times and ended with 30 s of rest for a total duration of 330 s (Figure 1A andB). The stimuli were designed and displayed using Matlab (Psychtoolbox-3, Mathworks, Natick, Massachusetts, USA), which allows a great flexibility in the change of the stimuli parameters. Between stimuli presentation sessions, the rats were kept in a dark environment.

2D fUS acquisition sequence and data analysis fUS imaging was performed using a linear ultrasound probe (128 elements, 15 MHz, 110 µm pitch and 8 mm elevation focus, Vermon; Tours, France) driven by an ultrafast ultrasound scanner (Aixplorer, Supersonic Imagine; Aix-en-Provence, France). The biophysics, technical procedure and statistical analysis for fUS were fully explained in our previous publications [START_REF] Mace | Functional ultrasound imaging of the brain: theory and basic principles[END_REF][START_REF] Macé | Functional ultrasound imaging of the brain[END_REF][START_REF] Osmanski | Functional ultrasound imaging reveals different odor-evoked patterns of vascular activity in the main olfactory bulb and the anterior piriform cortex[END_REF].

In summary, the ultrasound sequence works as follow: First, the brain is insonified by using ultrasonic plane wave with a high Pulse Repetition Frequency (PRF) (25 kHz). Second, the backscattered echoes coming from a wide-field view on the transducer array are recorded. Finally, the raw data are beamformed to produce an image in few hundreds of milliseconds.

In order to ensure a high-quality ultrasound image while preserving an ultrafast framerate, we added several plane wave images coherently (with amplitude and phase) from successive transmissions of tilted plane waves [START_REF] Montaldo | Coherent plane-wave compounding for very high frame rate ultrasonography and transient elastography[END_REF]. In this study, the plane wave compounding consisted of coherently adding the images of the brain tissue from 11 different tilted plane waves, with angles varying from -10° to 10° and at 2° step in order to compute one high-quality ultrasound image. To sample blood flow changes, we repeated this sequence 200 times with a 500 Hz frame rate (corresponding to a 400 ms acquisition time). To discriminate the blood motion from tissue motion artefacts in these sets of data, we used a recently developed Singular Value Decomposition (SVD) based spatiotemporal clutter filter technique (Demene et al., 2015). Finally one image of Power Doppler intensity is obtained by the incoherent temporal averaging of the blood signal in each pixel. Our ultrafast scanner (6 CPU core unit, 24 GB RAM) requires 0.6 s to beamform the 200 echo-based images, resulting in a final temporal sampling rate of 1 s per power Doppler image. After 5 minutes and 30 seconds of a 5-trials session, we thus obtain 330 images with a dimension of 14.08 mm along the direction (x) and 8 mm in depth (z), with 128 x 78 pixels of 110 x 100 µm² resolution.

As well as in [START_REF] Macé | Functional ultrasound imaging of the brain[END_REF][START_REF] Osmanski | Functional ultrasound imaging reveals different odor-evoked patterns of vascular activity in the main olfactory bulb and the anterior piriform cortex[END_REF], for each session, a map of activated pixels was reconstructed by computing the normalized correlation coefficient (r) between the local power Doppler signal obtained from fUS and the temporal pattern of the visual stimulus. Activation was considered significant for a correlation r > 3σ, where σ is the spatial standard deviation of at least 400 correlation values from non-active areas of the correlation map, in agreement with the Paxinos rat brain atlas. . The time course for a given region was calculated by averaging the Power Doppler signal over time for all responding pixels in the activated region (r > 3σ). The intensity of the Power Doppler was represented as the percentage of change relative to the baseline calculated during the 30 s of rest before each 5-trials session.

3D acquisition protocol

For 3D fUS acquisition sequences, we used a 4 axis motorized stage (three VT-80 Pollux and one DT-80 Pollux, PI Micos; Germany): 3 translations along x, y and z axis and one rotation around z (Figure 1A) that has been previously described in [START_REF] Demené | 4D microvascular imaging based on ultrafast Doppler tomography[END_REF]. The 3D fUS sequence consists in the repetition of the 2D stimulating (Figure 1B) imaging sequence we previously described in each coronal plan spanning from Bregma -3 mm to Bregma -8 mm, with a 0.5 mm step. The thickness of the imaging plane, shaped by the elevation lens of our ultrasonic probe being approximately 500 µm, this is the biggest step we can achieve without missing a potentially activated structure in the brain. Our voxel size is therefore 110 x 500 x 100 µm 3 . Since we repeat 2D fUS acquisitions in different planes that last 330 s each, with no supplementary time for rest, the overall time of acquisition of a whole volume is about an hour (11 plans from B-3 to B-8 mm times 5 minutes and 30 seconds). We therefore spaced the i.p. injections of anaesthetic from 1 hour instead of 45 minutes.

Delays measurement

For delay measurement between two signals, the parabolic interpolation of the maximum of correlation of those two signals has been used. This consists in the construction of the unique parabola that passes through the three points around the maximum of correlation to locate its summit. This constitutes an unbiased estimator of the delay between two correlated band-limited signals. Previous reports have shown a typical precision below 5% of the sampling time which is ultimately limited by the SNR of the signals [START_REF] Carter | Coherence and time delay estimation[END_REF][START_REF] Dejong | Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fUltrasound sensitivity[END_REF][START_REF] Sandrin | Time-Resolved Pulsed Elastography with Ultrafast Ultrasonic Imaging[END_REF][START_REF] Walker | A fundamental limit on the accuracy of speckle signal alignment[END_REF].

Results

2D fUS imaging of the CBV response to a simple visual stimulus

The ultrasonic probe was positioned over a coronal plane at Bregma -4.5 mm. That plane presents several known vision-involved structures [START_REF] Paxinos | The Rat Brain in stereostaxic coordinates[END_REF]. Those structures are, the visual cortex (V1/V2), the Lateral Geniculate Nucleus (LGN) and the Superior Colliculus (SC) (Figure 2A). While imaging with fUS ultrasonic sequence, we episodically stimulated the full visual receptive field by 3 Hz full screen flickering during stimulation periods. Figure 2B-C present the results of that 330 s 5-trials single imaging session.

After correlation with the stimulus pattern and noise σ-thresholding, we obtained a functional activation map (Figure 2B) that matches very nicely the expected areas. Making the assumption that each cluster of correlated pixels constitutes one of these areas, we extracted and plotted the mean CBV signal over the responding pixels in the visual cortex area (Figure 2C). We can clearly see an increase in CBV correlated to the stimulation periods. A similar increase in CBV during stimulation periods can also be observed in the other vision-involved areas, the LGN and SC (Figure 2C).

Figure 2 : Result of a single 5-trials 330 seconds fUS imaging session of the visual areas in the rat. A. Coronal schematic view of the rat brain at Bregma -4.5 mm with the delimitations of Visual Cortex (V1/V2), Lateral Geniculate Nucleus (LGN) and Superior Colliculus (SC). B. fUS imaging of the visioninduced activity at Bregma -4.5 mm, with superimposition of the correlated pixels (hot scale) over the brain vasculature (grey scale). The precision of the map allows to retrieve the shape of the 3 vision related structures present in that coronal slice. Scale bar = 2 mm. C. Mean CBV signal over responding pixels in the visual cortices (blue, up), SC (red, middle) and LGN (green, bottom) during that single imaging session composed of 5 flickering screen stimulation trials.

Influence of stimulus parameters

After demonstrating the feasibility of using fUS to image vision-involved structures, we tackled the task of finding optimal stimulation parameters in terms of frequency and contrast. The whole screen was used to stimulate the full receptive field and investigate two parameters. First the Flickering frequency: is simply defined by the frequency of the black/white alternation of the screen during the 30 s stimulation periods. A flickering frequency of 0 Hz corresponds to a steady white screen for 30 s. Second the Flickering contrast: is defined by the luminance ratio between the white screen and the black screen during the stimulation period. A flickering contrast of 1 corresponds to the most brilliant white and the darkest black we can get with our set-up. While a contrast of 0 correspond to a constant 50 % grey screen. Only these two parameters of the protocol were modified during the experiment.

For the optimization part, we first evaluated the effect of these parameters on two rats (one for frequency, one for contrast) over the Bregma -5 mm coronal plane. The 5-trials imaging session protocol described above was used. Each session was dedicated to test one different value (e.g. 5 times 30 s of flickering at 5 Hz with a contrast of 1 interleaved with 30 s of black for rest) in a randomized order. Each imaging session was repeated five times. In post-processing, for each session, fUS activation maps were computed and the maximum value of correlation was recovered. To get a good compromise for the whole brain, we choose to recover the maximum of correlation in two different vision-involved areas: the SC region and the visual cortex (both hemispheres). A contrast of 1 is expected to produce the best response. Therefore we first performed the frequency study with a contrast of 1. Figures 3A to C illustrate the evolution of response in the rat brain to a flickering frequency of 0 Hz, 3 Hz and 10 Hz and Figure 3D summarizes this evolution for the different tested frequencies. In the visual cortex, it appeared that the best response is obtained at a 3 Hz flickering frequency with a contrast of 1 while the higher 10 Hz frequency was eliciting a lower response. In SC, the maximum was reached earlier at a 1 Hz frequency and the responses remained stable for higher frequencies up to 10 Hz. The 3 Hz frequency, which represents the peak sensitivity for the cortex, was therefore selected to perform the contrast frequency analysis. In the contrast sensitivity, the maximum was reached at a contrast of 0.5 and remained stable for the subsequent contrast values up to 1 in the two structures, the SC and the cortex (Figure 3E). The flickering frequency investigation protocol was repeated on two other rats and similar curves were obtained (see Supplementary figure 1). Thus, despite individual variations, the flickering frequency seems rather robust and was kept at the value eliciting the maximum responses in the following of the study (3 Hz).The contrast was also kept at 1. ) and the flickering contrast on rat #2 (E.) on the response amplitude in the SC (dashed red line) and in the visual cortex (solid blue line). The quality of the response is measured via the maximum of correlation on the fUS data map. Each curve is normalized with the maximum value of correlation coefficient obtained in the corresponding brain area. Error bars: standard deviation of the normalized maximum of correlation in the considered area over the 5 trials of each parameter. See Supplementary Figure 1 for the influence of the flickering frequency on rat #3 and #4.

Lateralization of the visual response to simple stimuli

The visual cortex treats information coming from the contralateral visual field, for instance, the left hemisphere treats visual information from the right visual field [START_REF] Nolte | The Human Brain: An Introduction to Its Functional Anatomy[END_REF]. This lateralized response can thus serve as an additional confirmation that fUS imaging observations are not mere artefacts but true measurements of visual circuit activities. To address this question the ultrasonic probe was positioned over a coronal slice containing the visual cortex in both hemispheres. The stimulus parameters were fixed at 3 Hz flickering frequency and a contrast of 1. However, instead of stimulating the complete visual field using the whole screen, the screen was divided in 5 column sectors of identical width. In a first 5-trials imaging session, only the extreme-right sector was flickering, whereas in the second session, we shifted the illumination to the extreme-left sector. 3D fUS imaging of the visual system fUS imaging provides a 2D information coming from the imaging plane of the ultrasonic probe. However, the visual cortex and the sub-cortical visual areas are 3D structures that cannot be imaged entirely using a single imaging session. To generate 3D fUS imaging of these structures, several linear scans were performed while moving the probe to successive planes to perform a fUS acquisition at each position.

Following this strategy, we scanned the rat brain from Bregma -8 mm to Bregma -3 mm by 0.5 mm steps. Figure 5 and supplementary video 1 show the functional 3D volumes that can be reconstructed by this imaging strategy. The 3D structures of the visual function are well recovered and the shape of the visual cortex atop the LGN and the SC can easily be identified. Scale bars = 2 mm. Brain mini-maps made using [START_REF] Bakker | The Scalable Brain Atlas: Instant Web-Based Access to Public Brain Atlases and Related Content[END_REF][START_REF] Kjonigsen | Waxholm Space atlas of the rat brain hippocampal region: Three-dimensional delineations based on magnetic resonance and diffusion tensor imaging[END_REF][START_REF] Papp | Waxholm Space atlas of the Sprague Dawley rat brain[END_REF][START_REF] Sergejeva | Anatomical landmarks for registration of experimental image data to volumetric rodent brain atlasing templates[END_REF] brain atlas.

Measuring CBV response delays

As three areas of the brain are mainly involved here, CBV response delays between those zones were investigated. First, plotting the mean CBV response to N = 30 stimuli in responding pixels in the SC and in the visual cortex (Figure 6A) reveals a difference of shape of the CBV response curve for this two areas. We can, for instance, observe the "on" and "off" peaks in the SC response (Fukuda and Activity, 1978;[START_REF] Van Camp | Light stimulus frequency dependence of activity in the rat visual system as studied with high-resolution BOLD fMRI[END_REF][START_REF] Wang | Visual receptive field properties of neurons in the superficial superior colliculus of the mouse[END_REF]. Furthermore, the response in the visual cortex seems to be slower.

To go further, on N = 8 rats, we performed the fUS imaging over a plane containing the visual cortex and the SC (Bregma -5.5 mm) and on N = 5 rats we performed the imaging over a plane that contains also the LGN (Bregma -4.5 mm). Stimuli consisted in 3 Hz full field flickering. Then the temporal CBV response was recovered over responding pixels in the visual cortex, SC and LGN. Within cortices and

LGNs the CBV response was averaged over both hemispheres. The CBV in the SC was taken as a reference. Delays between the SC and cortex and between the SC and LGN were measured using a parabolic interpolation of the maximum of cross-correlation between both signals (see example, Figure 6B). However, the "off" peaks in the SC response might lengthen the CBV response with respect to the other areas and therefore distort the delay measurement. Thus the falling edge of all CBV responses were cut beforehand and replaced by the mean CBV value over the following period of rest. On Figure 6C are presented CBV response delays for both couple of regions. It appears that the CBV response happens about 0.35 s earlier in the SC than in the visual cortex (two-tailed t-test, p<0.001). It also seems that the CBV response happens earlier in the SC than in the LGN. The CBV response seems to happen significantly earlier in V1/V2 than in the LGN (two-tailed t-test, p<0.002).

Discussion

In the present study, fUS imaging was used on anesthetized rats to perform several basic functional imaging studies related to vision. The high resolution mapping of visual patterns in the whole brain such as lateralized stimuli and flickering stimuli was presented. The best stimulation parameters for imaging of the visual cortex were investigated. A flickering frequency of 3 Hz was found to elicit the highest CBV response in accordance with previous BOLD studies [START_REF] Bailey | Analysis of Time and Space Invariance of BOLD Responses in the Rat Visual System[END_REF][START_REF] Pawela | A protocol for use of medetomidine anesthesia in rats for extended studies using task-induced BOLD contrast and resting-state functional connectivity[END_REF]. We also showed a contrast saturation effect after a 0.5 contrast value also in accordance with the literature [START_REF] Albrecht | Striate cortex of monkey and cat: contrast response function[END_REF][START_REF] Lund | Receptive field properties of single neurons in rat primary visual cortex[END_REF].

A 3D protocol was developed and tested and has allowed the reconstruction of the main visual structures of the brain in 3D. The anaesthesia was performed in i.p. just before the beginning of the scan. It is then to be expected that the last planes to be acquired may have a different response than the first ones. Therefore an intravenous drip anaesthetic might benefit the measurement of the functional volume. Furthermore, the development of full 3D ultrafast scanners [START_REF] Provost | 3D ultrafast ultrasound imaging in vivo[END_REF] will allow instantaneous acquisitions of the whole brain and remove the need for successive planes acquisitions.

Compared to BOLD fMRI, the fUS technique benefits from a high spatial and temporal resolution at low cost with a portable device. When fMRI needs to average over several animals or to inject contrast agents, fUS allowed us a quicker and simpler retrieval of the visual areas. The main inconvenience of fUS lays in the necessity of a craniotomy to overcome the distortion of the ultrasound waves through the skull and the limitation of the measure in a 2D plane. However it has been shown that fUS can be perform through the skull using microbubbles [START_REF] Errico | Transcranial functional ultrasound imaging of the brain using microbubble-enhanced ultrasensitive Doppler[END_REF].

Compared to optical imaging techniques which provides high resolution functional imaging are limited to the superficial cortical areas, fUS can be used to image the full depth of the brain, including the LGN or the SC in our case.

It has been widely demonstrated through different functional imaging methods [START_REF] Engel | Retinotopic organization in human visual cortex and the spatial precision of functional MRI[END_REF][START_REF] Espinoza | Retinotopic organization of striate and extrastriate visual cortex in the golden hamster (Mesocricetus auratus)[END_REF] that the treatment of the visual information is spatialized in the rodent brain. By stimulating the left visual field and the right visual field, we showed that it is possible to study visual spatialization in the brain with fUS. As in [START_REF] Gias | Retinotopy within rat primary visual cortex using optical imaging[END_REF][START_REF] Schuett | Mapping retinotopic structure in mouse visual cortex with optical imaging[END_REF], the screen was divided in different sectors and successively used to stimulate the rat visual field by using those different sectors to infer the corresponding activated regions in the brain. Furthermore, the high inplane resolution of fUS could be leveraged to more finely segregate areas of the brain according to their function. For instance reducing the width of the stimulation sectors on the screen, would yield the detection limit of fUS in term of spatial extend of the responding cerebral areas.

The ability of fUS to measure delays in the CBV response between regions consistent with previous BOLD measurement [START_REF] Yen | BOLD responses to different temporal frequency stimuli in the lateral geniculate nucleus and visual cortex: Insights into the neural basis of fMRI[END_REF] was highlighted, therefore demonstrating its high temporal resolution. However those hemodynamic delays are far larger than the neural delays directly measured in electrophysiology, which are in the [10;100 ms] range [START_REF] Saul | Development of Response Timing and Direction Selectivity in Cat Visual Thalamus and Cortex[END_REF]. Thus, the hemodynamic delays we measured here could as well be due to effective delays in the neural response than to different vascular, or neurovascular coupling dynamics [START_REF] Li | High-Resolution Neurometabolic Coupling in the Lateral Geniculate Nucleus[END_REF][START_REF] Wibral | Timedependent effects of hyperoxia on the BOLD fMRI signal in primate visual cortex and LGN[END_REF]. Nonetheless, this could be combined with continuously moving bars stimuli that has been shown to produce retinotopic measurements in a much shorter time than by stimulating selectively and successively sectors of the visual field [START_REF] Kalatsky | New paradigm for optical imaging: Temporally encoded maps of intrinsic signal[END_REF]M. P. Vanni et al., 2010;Matthieu P. Vanni et al., 2010).

Finally, this study investigated rather simple stimuli and simple responses of the rat brain with simple analysis. However the functional imaging of vision is a very rich field of research. Many subtler stimuli have been designed to stimulate the visual field and investigate the richness of visual information processing in the brain. Furthermore, to date, no side by side comparison between the respective sensitivity of fUS imaging and fMRI was done, but previous fUS papers on whisker or olfactory stimuli have shown that fUS imaging is able to map functional activity for subtle stimuli difficult to assess in fMRI, such as single whisker stimulus. It gives hope that fUS will perform well for these other types of visual stimuli already investigated by fMRI.

The recent demonstration of fUS in awake and freely moving rodents [START_REF] Sieu | EEG and functional ultrasound imaging in mobile rats[END_REF] also opens exciting possibilities to study the visual response of the brain in more complex and natural environments and without influence of the anaesthesia.

The association of state of the art visual stimulation techniques with high resolution and sensitivity whole brain functional imaging paves the way to novel original experiments to push our understanding of the vision in the brain.

Conclusion

The fUS imaging technique coupled with a 4 axis motorized stage and a visual stimulation device was shown to accurately detect and 3D map the activation of visual functions in the rat brain. Responses to simple visual flickering were presented. The high sensitivity of fUS imaging enables to record unbiased and repeatable CBV responses even with a small number of stimuli repetition. These experiments emphasize the capability of fUS imaging to become a particularly suitable neuroimaging tool for the fundamental understanding of the cerebral visual system.

  Introduction 1 MG and KB and co-first authors 2 SG and MT are co-last authors

Figure 1 A

 1 Figure 1 A. Schematic view of the experimental setup. B. Stimulus pattern for episodic visual stimulation: 30 s of rest are followed with 30 s of flickering of the screen at a frequency in the [0; 10 Hz] range.

Figure 3 :

 3 Figure 3 : Evolution of the rat brain response to variation of flickering parameters. A to C: fUS imaging of a rat during a 0 Hz (A), 3 Hz (B) and 10 Hz (C) flickering stimulus. Each activation map is the average of 5 imaging sessions. Scale bar = 2 mm. E and D: Influence of flicker parameters for fUS imaging of vision. Influence of the flickering frequency on rat #1 (D.) and the flickering contrast on rat #2 (E.) on the response amplitude in the SC (dashed red line) and in the visual cortex (solid blue line). The quality of the response is measured via the maximum of correlation on the fUS data map. Each curve is normalized with the maximum value of correlation coefficient obtained in the corresponding brain area. Error bars: standard deviation of the normalized maximum of correlation in the considered area over the 5 trials of each parameter. See Supplementary Figure1for the influence of the flickering frequency on rat #3 and #4.

Figure 4

 4 Figure 4 illustrates the results of those 2 imaging sessions. Each stimulation sector elicits a fUS signal only in the respective contralateral visual cortex. These observations demonstrate the ability of the

Figure 4 :

 4 Figure 4 : Visualization by fUS of the lateralization of the visual response in the visual cortex: A. Activation map after a single 5-trial imaging session, while stimulating only with the extreme right sector of the screen. A CBV increase in the left visual cortex is observed. B Activation map after a single 5-trial imaging session, while stimulating only with the extreme left sector of the screen. A CBV increase in the right visual cortex is observed.. Scale bar = 2 mm.

Figure 5 :

 5 Figure 5 : 3D fUS imaging of brain structures responding to visual stimuli. A. General View of the activated areas, left and right visual cortices (V1/V2), Superior Colliculus (SC) and LGN, which were manually superimposed to a Calabrese rat brain model. B. Sagittal cut at Bregma showing the activated SC. C. Sagittal cut at Bregma +3.7 mm showing both LGN and V1/V2. D. Top view of the brain surface showing V1/V2 activation. E. Transversal cut at 3 mm depth showing the activated SC. F. Transversal cut at 5.4 mm depth showing the activated LGN. Scale bars = 2 mm. Brain mini-maps made using[START_REF] Bakker | The Scalable Brain Atlas: Instant Web-Based Access to Public Brain Atlases and Related Content[END_REF][START_REF] Kjonigsen | Waxholm Space atlas of the rat brain hippocampal region: Three-dimensional delineations based on magnetic resonance and diffusion tensor imaging[END_REF][START_REF] Papp | Waxholm Space atlas of the Sprague Dawley rat brain[END_REF][START_REF] Sergejeva | Anatomical landmarks for registration of experimental image data to volumetric rodent brain atlasing templates[END_REF] brain atlas.

Figure 6 :

 6 Figure 6 : CBV Response delays between visual areas. A. Average CBV response curves to the stimulus in the visual cortex (solid blue line) and in SC (dashed red line). Error: Standard Error of the Mean. Black rectangle = Stimulus. "On" and "Off" CBV peaks in SC (black arrows). B. Example of Cross-Correlation curves between CBV responses in SC and visual cortex (Solid blue line) and between SC and LGN (dashed green line), zoom around the maximum of cross-correlation. Crosses: experimental data points. Lines: interpolated curves between data points to visualize the delay at maximum of cross-correlation (black arrows) (not used for measurement). Mini-box in up-right corner: Full view of the cross-correlation curves. C. CBV response delays measured between SC and both visual cortices (V1/V2), N = 8 rats, and between SC and both LGNs, N = 5 rats. *p<0.002

Acknowledgements

This work was supported by the European Research Council SYNERGY Grant scheme (HELMHOLTZ, ERC Grant Agreement #610110), Europe and partly supported by the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC grand agreement no 339244-FUSIMAGINE.

Video legend "3D fUS imaging of the rat brain structures responding to visual stimuli. Responding areas, left and right visual cortices, Superior Colliculus and LGN, were manually superimposed to a Calabrese rat brain model. Thus allowing 3D visualization in depth in the brain or along different coronal crosssections."