Jacques Gustin
email: gustin@astro.ulg.ac.

Ian Stewart
email: ian.stewart@lasp.colorado.edu

Jean-Claude Gérard
email: jc.gerard@ulg.ac.be

Larry Esposito
email: larry.esposito@lasp.colorado.edu

Characteristics of Saturn's FUV airglow from limb viewing spectra obtained with Cassini-UVIS

Keywords: airglow, Saturn, spectroscopy, ultraviolet observations

This study reports the analysis of far ultraviolet (FUV) limb spectra of the airglow of Saturn in the 1150-1850 Å spectral window, obtained with the Ultraviolet Imaging Spectrograph (UVIS) onboard Cassini, spanning altitudes from -1200 to 4000 km. The FUV limb emission consists of three main contributions: 1) H Ly-peaking at 1100 km with a brightness of 0.8 kilo-Rayleights (kR), 2) reflected sunlight longward of 1550 Å which maximizes at -950 km with 16.5 kR and 3) H 2 bands in the 1150-1650 Å bandwidth, peaking at 1050 km reaching a maximum of 3.9 kR.

A vertical profile of the local H 2 volume emission rate has been derived using the hydrocarbon density profiles from a model of the Saturn equatorial atmosphere. It is well matched by a Chapman function, characterized by a maximum value of 3.5 photons cm -3 s -1 in the 800-1650 Å UV bandwidth, peaking at 1020 km.

Comparisons between the observed spectra and a first order synthetic airglow H 2 model in the 1150-1650 Å bandwidth show that the spectral shape of the H 2 bands is accounted for by solar fluorescence and photoelectron excitation. The best fits are obtained with a combination of H 2 fluorescence lines and 20 eV electron impact spectra, the latter contributing ~68% of the total H 2 airglow emission.

Introduction

The first observations of Saturn's ultraviolet (UV) emissions were obtained by the Voyager encounters in the early eighties. Comparisons between the emissions at Jupiter and Saturn showed that they are qualitatively similar [START_REF] Broadfoot | Extreme ultraviolet observations from Voyager 1 encounter with Saturn[END_REF]. The most intense emission at Saturn detected by the ultraviolet spectrometer (UVS) onboard Voyager 1 (V1)

was the aurora, with ~10 kilo Rayleighs (kR) for both the Hydrogen Lyman (Ly-) and the H 2 bands, followed by dayside Ly-with ~ 1.5 kR and H 2 dayglow with ~0.7 kR in the Lyman and Werner bands [START_REF] Broadfoot | Extreme ultraviolet observations from Voyager 1 encounter with Saturn[END_REF]. The latter value is four times lower than the Jupiter value, consistent with the factor of ~3 reduction in the solar flux from Jupiter to Saturn. This fact, among others, pleaded for a dayglow stimulated by the solar flux. Several UVS spectra were examined by [START_REF] Shemansky | The Saturn spectrum in the EUV: Electron excited hydrogen[END_REF]. They compared the observed dayside H 2 bands with electron-excited synthetic spectra that includes the

+ Σ u B 1 , + Σ g F E 1 , , u C Π 1 , + Σ u B 1 ' , u D Π 1 , + Σ u B 1 "
, and

u D Π 1 ' to + Σ g X 1
vibronic transitions and confirmed that, as for Jupiter, H 2 emission from electronic collisions makes a significant contribution to the observed UV intensity. They also pointed out that the emission longward of 1500 Å is dominated by reflection of solar radiation. Although the electron impact excitation and the solar flux control suggest that the H 2 dayglow is produced by photoelectrons, this idea has been, at first, partially rejected for energy budget considerations [START_REF] Broadfoot | Extreme ultraviolet observations from Voyager 1 encounter with Saturn[END_REF]. Precipitation of magnetospheric electrons has been proposed several times [START_REF] Strobel | The ionospheres of the major planets[END_REF], Chen, 1981), but never been considered as an appropriate mechanism to account for the various features of the dayglow phenomenon.

As for Jupiter and Saturn, the dayglow observed after the Voyager Uranus encounter was found to exceed the available photoelectron energy, assuming that 15% of the total solar EUV energy goes into photoelectron excitation of FUV emission [START_REF] Cravens | The absorption of energetic electrons by molecular hydrogen gas[END_REF]. A process called "electroglow" was proposed by [START_REF] Broadfoot | Ultraviolet Spectrometer Observations of Uranus[END_REF]. As many UVS dayglow spectra were well fit by electron excitation models, it was considered that electroglow consisted of soft (~50 eV) charged particle excitation in the presence of sunlight.

Since the dayglow demonstrated correlation with solar zenith angle and the heliocentric scaling, it was supposed that electroglow was completely controlled by the incident solar flux [START_REF] Yelle | The dependence of electroglow on the solar flux[END_REF]. Several mechanisms were considered. For example, [START_REF] Yelle | The dependence of electroglow on the solar flux[END_REF] proposed that electroglow was produced by fluorescence or H -photolysis. Since electroglow was created to explain the emission in excess of available solar energy, [START_REF] Clarke | The excitation of the far ultraviolet electroglow emissions on Uranus, Saturn, and Jupiter[END_REF] objected that electroglow was not a direct consequence of solar input, but produced by in-situ electric field acceleration of photoelectrons and ions through an atmospheric dynamo. This mechanism was neither satisfactory, as it should have a strong dependence of magnetic coordinates, which was not observed. [START_REF] Yelle | H 2 emissions from the outer planets[END_REF] suggested that solar fluorescence could significantly contribute to the observed outer planet dayglows. He built two independent models of H 2 emission, excited by photoelectrons and solar fluorescence, and first pointed out significant differences between the emission due to the two excitation sources: the electronexcited spectrum consists of a large number of vibronic transitions distributed relatively smoothly with wavelength, while the solar fluorescence H 2 spectrum mainly consists of a series of bright emission lines produced by the absorption and reradiation of solar lines into H 2 bands. Using a combination of photoelectron-excited and solar fluorescence-excited spectra, he was able to obtain a good fit to a Jovian Voyager UVS spectrum without the need for additional sources. As the Saturn UVS spectra appear very similar to that of Jupiter, he also predicted that Saturn's dayglow emission could be accounted for by a combination of fluorescence and photoelectron excitations. He however indicated that his simple model suffered from substantial uncertainty. Combined with the uncertainties in the solar flux he used, UVS calibrations, and low UVS spectral resolution (~30Å), he was not able to determine the respective contribution of fluorescence and photoelectron and univocally state that fluorescence and photoelectron excitations can account for the total observed brightness.

This controversy was finally cleared out by [START_REF] Liu | The ultraviolet spectrum of the Jovian dayglow[END_REF] and HD, producing an energy spectrum of photoelectron flux, exciting UV H 2 bands by collision, as described in [START_REF] Shemansky | The Saturn spectrum in the EUV: Electron excited hydrogen[END_REF]. The fluorescence part of the UV emission is produced by the strong wavelength coincidences between solar emission lines and absorption lines of H 2 in the 900-1100 Å bandwidth. They found that the UV spectrum of the Jovian dayglow can be accounted for in both brightness and spectral shape by solar fluorescence and photoelectron excitation, without other energy source. In particular, Fig. 3 of [START_REF] Liu | The ultraviolet spectrum of the Jovian dayglow[END_REF] shows that the majority of photoelectrons producing the UV photons are confined below 60 eV, with a maximum flux at 25 eV and an average energy of 33 eV.

These values lie near the maximum of the excitation cross-section of the EF cascade (~20 eV) and B, C (~40 eV) [START_REF] Ajello | Laboratory studies of UV emissions of H 2 by electron impact -The Werner-and Lyman-band systems[END_REF]. With a maximum flux at 25 eV, it is likely that the cascade process which populates the

+ Σ u B 1 electronic state through + Σ g F E 1
, , has a important contribution in the photoelectron-excited spectrum. This point was raised by [START_REF] Prangé | New evidence for the role of photoelectrons in the H 2 -dayglow of the giant planets[END_REF], who observed a small peak near 1300 Å in a low resolution V1 UVS Saturn's disk spectrum, which may indicate a enhancement of EF cascade in the dayglow emission compared to the aurora. [START_REF] Liu | The ultraviolet spectrum of the Jovian dayglow[END_REF] estimated solar fluorescence to contribute 57% to the total 2.3 kR of the Jovian dayglow HUT spectrum. Since the airglow brightness depends on solar conditions and gas temperature, these values may not be readily applied to our Saturn observations. Yet, the work by [START_REF] Liu | The ultraviolet spectrum of the Jovian dayglow[END_REF] gives a good overview of the processes responsible to the observed dayglow UV emissions.

The Saturn limb profiles from V1 and Voyager 2 (V2) have been re-analyzed by [START_REF] Yelle | Altitude variation of EUV emissions and evidence for proton precipitation at low latitudes in the Saturnian atmosphere[END_REF]. At that time, the source of the UV dayglow emission was still controversial, but some interesting conclusions should be emphasized. First, they noticed that the limb profile of Ly-and H 2 band peaked at about the same altitude, near the homopause, at ~60000 km minimum ray height (MRH) for the V2 limb drift. As they assigned the 1 bar level at ~59000 km, it situates the H 2 emission near 1000 km above the 1 bar level. The uncertainty is determined by the slit width, which was ~400 km. The line of sight (LOS) measurements must be inverted to yield the emission rate variation with altitude. [START_REF] Yelle | Altitude variation of EUV emissions and evidence for proton precipitation at low latitudes in the Saturnian atmosphere[END_REF] used a forward technique, consisting of modeling the volume emission rate (VER) and adjusting the model to get the best fit to the observed limb profile. Using the CH 4 densities from [START_REF] Smith | Saturn' s upper atmosphere from the Voyager 2 EUV solar and stellar occultations[END_REF] to take into account the extinction due to methane, their best VER was a combination of two exponentials. A first one with a scale height of 1500 km, which best fit the observed brightness above 60500 km and a second one with a scale height of 200 km, best fitting the observed brightness below 60500 km. This vertical VER produced ~ 2 photons cm - 3 s -1 at the merging 60500 km. As the scale heights they used is from five to ten times the ambient gas value from [START_REF] Smith | Saturn' s upper atmosphere from the Voyager 2 EUV solar and stellar occultations[END_REF], [START_REF] Yelle | Altitude variation of EUV emissions and evidence for proton precipitation at low latitudes in the Saturnian atmosphere[END_REF] concluded that the airglow emission was present throughout the entire thermosphere. They also mentioned that similar results had been achieved with an inversion technique calculations.

In terms of composition, a first model of Saturn's upper atmosphere has been derived

by [START_REF] Smith | Saturn' s upper atmosphere from the Voyager 2 EUV solar and stellar occultations[END_REF] the signal along the LOS, 2) provide a spectral analysis of the FUV airglow limb spectra and 3) establish limb profiles of the sources of the observed emissions.

Observations and data reduction

The data examined here consist of six sets of observations listed in Table 1. The first two sets were collected on 29 October 2005 and the other four ones on 27 November 2005, i.e. near solar minimum. Fig. 1a shows the projection of the UVIS FUV slit near Saturn's disk for the first set and Fig. 1b gives a general outlook of the viewing geometry. The UVIS instrument has been thoroughly described by [START_REF] Esposito | The Cassini Ultraviolet Imaging Spectrograph investigation[END_REF]. In brief, UVIS includes a two-channel imaging spectrograph, from 1115 to 1912 Å in the FUV, and from 563 to 1182 Å in the EUV. Three slits are available: a high resolution slit (75 and 100 m slit width for the FUV and EUV channel, respectively), a low resolution slit (150 and 200 m slit width for the FUV and EUV respectively), and an occultation slit of 800 m width, identical for both channels. The data discussed here were obtained with the low resolution slit and FUV channels, providing spectra at ~5.5 Å spectral resolution. The detector is a Codacon (CODed Anode array CONverter), consisting of 1024 pixels in the spectral direction and 64 pixels in the spatial direction. The spectral dimension was compressed by two pixels throughout the observation sequences to reduce data volume. The distance between Cassini and Saturn at the tangent point varied from 2.7 x 10 5 to 3.0 x 10 5 km, leading to a spatial resolution of about 300 km per pixel, assuming a spatial pixel field of view of 1.0 mrad. The average phase and incidence angles of all spatial pixels at the tangent point along the LOS are 96.0 and 24.7

degrees respectively, with a constant emission angle of 90 degrees.

Taking into account the illuminated spatial pixels only (56 pixels for all observations except observation number two which has 57), the dataset consists of 14133 spectra. The first step of the reduction process is to sort all the spectra by MRH and add them up into bins of 50 km, in order to examine the dayglow variations with altitude. This procedure has been applied

by [START_REF] Stevens | The Production of Titan's Far Ultraviolet Nitrogen Airglow[END_REF] in the analysis of Titan's UVIS limb spectra. Assigning the central altitude value for each 50 km bin, we obtain a total of 109 spectra, spanning a continuous altitude range from -1325 to 4125 km MRH. Negative values of the MRH correspond to altitudes where the tangent point of the line of sight is situated below the 1 bar level. The spectra are then calibrated, using a procedure already applied to other UVIS analysis [START_REF] Ajello | Titan airglow spectra from the Cassini Ultraviolet Imaging Spectrograph: FUV disk analysis[END_REF][START_REF] Gustin | Characteristics of Saturn' s polar atmosphere and auroral electrons derived from HST/STIS[END_REF][START_REF] Stevens | The Production of Titan's Far Ultraviolet Nitrogen Airglow[END_REF]. It consists in a subtraction of the background noise due to the radioisotope thermoelectric generator onboard Cassini, a flatfield correction, and conversion from counts to Rayleigh Å -1 using the time-dependent sensitivity curve prescribed by the UVIS team. The last three high-altitude spectra at 4025,

FUV solar reflectivity

The main goal of the study is to describe the characteristics of the H 2 dayglow.

Between -1325 and 775 km, the spectra in the 1500-1650 Å bandwidth are a combination of the H 2 bands and reflected sunlight. The first natural step is to model the reflected sunlight emission in order to separate the two contributions. The reflected emission is the result of the solar radiation scattering by atmospheric H 2 and He and absorption by the hydrocarbons along the photon trajectory. First, we calculate Saturn's FUV reflectivity in the 1500-1880 Å window using a procedure previously applied by [START_REF] Ajello | Titan airglow spectra from the Cassini Ultraviolet Imaging Spectrograph: FUV disk analysis[END_REF], based on a multiple scattering formalism designed for limb-viewing geometry [START_REF] Wallach | Light scattering in a spherical, exponential atmosphere, with applications to Venus[END_REF]. Each Because of the limb-viewing geometry, the path crossed by the light is much larger than for disk observations. Therefore we chose to include in the modeled reflectivity, in addition to C 2 H 2 and C 2 H 6 , nine minor hydrocarbons which may have an effect on the total attenuation: The average abundance ratios between the "free" and "tied" hydrocarbons along the vertical profile are used to relate the tied hydrocarbons to the free ones. After multiple tests, we added C 6 H 6 in the model, whose important absorption cross-section near 1780 Å improved the fit.

C 2 H 4 , C 3 H 6 ,
Since the H 2 emission significantly contributes in the 1500-1650 Å bandwidth, we also included in the regression a synthetic H 2 airglow spectrum in that spectral region as a free parameter. This synthetic H 2 spectrum, provided by J. Two examples of fits are shown in Fig. 3, illustrating the strong variation of the H 2 contributions compared to reflected sunlight in the 1500-1700 Å spectral region. Figure 4 shows the C 2 H 2 and C 2 H 6 mixing ratios of the best fits for the low altitude spectra up to the The VER and hydrocarbon density profiles are unknown a-priori. Since they both significantly influence the emergent signal and are independent unknowns, we chose to fix the vertical hydrocarbon density profiles by using the values from the [START_REF] Moses | Photochemistry of Saturn's atmosphere I. Hydrocarbon chemistry and comparisons with ISO observations[END_REF] model.

To determine the VER, we evaluate equations ( 1) and (2) using the [START_REF] Moses | Photochemistry of Saturn's atmosphere I. Hydrocarbon chemistry and comparisons with ISO observations[END_REF] atmospheric model, with a Chapman-type function to model the vertical VER:

)} e 1 ( f exp{ m α - - α - ν = ν (3) where - H / ) Z Z ( m - = α
is the reduced height, m is the maximum of at the altitude Z m , -f is the shape factor, defining a -Chapman when f=0.5 and a -Chapman when f=1.

-H determines the thickness of the emission profile. In the case of a -Chapman profile, H is the scale height of the emission, i.e. the height range in which the topside VER changes by a factor of e (~2.718). The -Chapman is chosen a-priori in our study.

We adopt the following steps in the spectral analysis: 2 of [START_REF] Liu | The ultraviolet spectrum of the Jovian dayglow[END_REF]. The best fit between the observed and modeled emergent spectra provides a first estimate of the contribution of each excitation process.

Volume emission rate

Applying the procedure described in 4.1., the first synthetic CR profile we derived was too high and did not match the observed one at all (see the orange curve with diamonds in Fig. 7). A natural way to decrease the CR is to reduce the amount of CH 4 in the model. A (2007) showed that an altitude offset corresponding to a spacecraft altitude-control pointing uncertainty of ~2 mrad [START_REF] Flasar | Exploring the Saturn system in the thermal infrared: The composite infrared spectrometer[END_REF]) was also required to fit their observations. The 125 km offset we need, which corresponds to 0.4 mrad, is therefore well within Cassini pointing uncertainties. Figure 5a shows the shifted UVIS brightness profile in the integrated 1550-1620 Å bandwidth with the best fit in red. The model, calculated every 50 km MRH, has been smoothed over 7 pixels to account for the slit spatial resolution (300 km). The blue points show the 1550-1620 Å brightness before subtraction of the reflected sunlight component and illustrate well the requirement to separate the H 2 from the reflected sunlight components to study the airglow. The effect of the hydrocarbon absorption is illustrated in Fig. 5b, which

shows the unsmoothed synthetic brightness, with and without the effect of the hydrocarbon absorption. It is seen that the attenuation is effective below 900 km, with a 50% reduction of the signal at 50 km MRH. The brightness peaks near the homopause level, as already noted by [START_REF] Yelle | Altitude variation of EUV emissions and evidence for proton precipitation at low latitudes in the Saturnian atmosphere[END_REF]. The best vertical VER displayed in Fig. 5c is a -Chapman profile, characterized by a maximum value of 0.67 photons cm -3 s -1 at 1020 km and a scale height of 284 km. This solution is not unique, as a range of shape factors can be attributed to the Chapman function. Comparable fits to the 1550-1620 Å brightness have been experimented

with a shape factor fixed to 0.5 or varying freely in the regression. In the case of shape factor fixed to 0.5, the best VER is characterized by a maximum of 0.71 photons cm -3 s -1 at 1000 km. When left free, the best shape factor is 2.1, with a maximum of 0.65 photons cm -3 s -1 at 1038 km. Compared to the best -Chapman, this gives m and Z m variations of 6% and 2%, respectively. The 1550-1620 Å VER can be extended to the entire H 2 UV bands in 800-1650

Å by multiplying m by 5.27, which is the factor between the integrated intensities in these two bandwidths in the synthetic H 2 airglow spectrum.

As mentioned previously, two factors affect the emergent spectra. The first one is the absorption by hydrocarbons which partly attenuates the emission between the emitter and the observer. The second one is the shape of the VER, which puts more or less weight on some portion of the LOS, as illustrated in Fig. 6. Figure 6a shows the average optical depth (S) in the 1150-1650 Å bandwidth for Z 0 =50 km, while Fig. 6b shows the corresponding VER intercepted by the LOS. It is seen that the unabsorbed emission (black curve) has two separate components. The one with S<0 is completely absorbed and does not contribute to the observed emission. As the MRH increases, the two portions of the intercepted VER come near each other and start to merge at ~ 450 km to form a one-block bulk of emission. Figure 6c and 6d demonstrate this merging in the case of Z 0 = 700 km. The hydrocarbon attenuation is weaker and a substantial portion of the emission at S<0 starts to contribute to the total signal. At Z 0 = 900 km, the average optical depth is less than unity all along the LOS and the emission in each point contributes to the observed signal. This figure demonstrates that a large increase/decrease of the hydrocarbon number densities may not have a noticeable effect on the emergent brightness. At 50 km MRH for example, a large increase of the hydrocarbon densities will not influence the emission at S<0, as the optical depth is already much larger than unity. This increase would only affect the region where (s) is near unity, i.e around S=7000 km. As the intercepted VER has a minor contribution in this portion of the LOS, the emergent signal would not be significantly modified.

Taking into account the 125 km shift, the lowest probed altitude is -1200 km MRH. As the hydrocarbon density profiles start at -115 km in the [START_REF] Moses | Photochemistry of Saturn's atmosphere I. Hydrocarbon chemistry and comparisons with ISO observations[END_REF] model, we need to extend these profiles to lower altitude to examine the full dataset. The Moses hydrocarbon density profiles have been extended to -1200 km by keeping their first value at -115 km constant throughout the lower altitudes until -1200 km. Figure 7 shows a comparison between the observed CR (black curve) and the CR deduced from the best synthetic emergent spectra (red curve). The CR for the unabsorbed synthetic airglow spectrum is 1.5, higher than the 1.1 value pointed out for an auroral (i.e. electron impact) H 2 spectrum [START_REF] Gustin | Characteristics of Jovian morning bright FUV aurora from Hubble Space Telescope/Space Telescope Imaging Spectrograph imaging and spectral observations[END_REF].

Starting from the top, it is seen that the synthetic CR is constant at 1.5 between 4000 and 950 km, as all spectra are unaffected by hydrocarbons. At 950 km, the modeled CR starts to increase as the hydrocarbon layer is reached. The CR maximizes at 850 km and then decreases at lower altitudes. This effect is due to the intercepted VER, which starts to separate into two components. The emission with S<0 starts to be completely absorbed for all wavelength, while the emission for S>0 is less and less affected by hydrocarbons, because 1) the path from S to infinity is too short to create a significant optical depth 2) the VER shifts towards the right, i.e. towards lower values of (s), leaving the low altitude emergent spectra practically unabsorbed. In other words, the absorption at low altitude does not affect much the spectral shape of the emergent emission but essentially attenuates the overall integrated brightness by a factor of ~2. Between 4000 and 2500 km MRH, the observed CR are scattered around the theoretical value because of the low S/N ratio. Between 2500 and 1100 km, the observed CR is significantly lower than the theoretical value. This is due to an unidentified feature at 1255 Å peaking in this portion of the atmosphere, which gives more weight to the denominator of the observed CR. Below 1100 km, the synthetic and observed CR fit well down to -500 km, where the observed CR are lower than expected, likely because the lowaltitude spectra longward of 1500 Å is strongly influenced by the reflected sunlight emission.

This component has been removed from the data, but the residual of the subtraction may lead to a significant uncertainty on the remaining H 2 signal.

We experimented other methods to extend the hydrocarbon density profiles to the lower altitudes, basically in lowering the density profiles. As expected, these attempts did not notably change the resulting synthetic CR profiles because of the position of the intercepted VER along the LOS, as discussed before. At this point, a visual comparison between the observed and best synthetic emergent spectra has been performed for all altitude bins. The fits were found very satisfactory in terms of general shape, overall intensity and hydrocarbons absorptions. However, a few individual lines in some best fits were found too intense or too weak depending on the altitude bin examined. This is illustrated in Fig. 8a for the emergent spectrum at 300 km, which shows that the overall fit to the data is good, but presents a few over-bright lines at specific wavelengths. Figure 8b shows a comparison between the Hallet et al. (2005) airglow spectrum used in this study and a laboratory H 2 spectrum obtained from impact of 20 eV electrons [START_REF] Dziczek | Cascade contribution to the H 2 Lyman band system from electron impact[END_REF]. It is seen that the main differences between the two spectra are due to several individual lines, and correspond to the discrepant peaks observed in Fig. 8a, as indicated by the arrowed lines. They correspond to H 2 transitions excited by fluorescence and are identified by using Table 2 of [START_REF] Liu | The ultraviolet spectrum of the Jovian dayglow[END_REF], which lists the principal fluorescence H 2 lines resulting from the absorption of EUV solar radiation obtained from the study of the Jovian airglow. The transitions determined in Fig. 8 generally correspond to the most intense fluorescence lines of this table. from solar EUV pumping. Two e-impact laboratory spectra at 300 K have been tested. The first one has been obtained from impact of 100 eV electrons [START_REF] Liu | Electron-impact excitation and emission cross sections of the H 2 Lyman and Werner systems[END_REF]) and the second one from 20 eV electrons [START_REF] Dziczek | Cascade contribution to the H 2 Lyman band system from electron impact[END_REF]. The main differences between the 100 eV and 20 eV spectra are due to the EF cascade, which populates the B electronic state through

+ + Σ → Σ u 1 g 1 B F , E
transitions. The cascade is enhanced for low energy excitation and maximizes for 20 eV electrons (see Fig. 10 of [START_REF] Ajello | The Cassini Campaign observations of the Jupiter aurora by the Ultraviolet Imaging Spectrograph and the Space Telescope Imaging Spectrograph[END_REF]. This enhancement can be detailed by the examination of a spectrum resulting from the EF cascade process only (without direct excitation), obtained with a time-resolved electron-impact technique [START_REF] Dziczek | Cascade contribution to the H 2 Lyman band system from electron impact[END_REF]. The EF spectrum shows that cascade has emission bands all over the EUV and FUV bandwidth. The cascade process most strongly populates the v=0 vibrational state of B, whereas direct excitation mainly populates v=6, 7 of B. The EF spectrum is more intense in the FUV, with a maximum contribution of the L(0,3) band at 1276Å, L(0,4) at 1335 Å and L(0,5) and 1395 Å, followed by well-defined peaks near 1436,1458,1488,1518,1546,1578 and 1608 Å.

For both e-impact spectrum, an emergent spectrum is calculated for each 50 km altitude bin following equations ( 1), ( 2) and ( 3), with the hydrocarbons from the [START_REF] Moses | Photochemistry of Saturn's atmosphere I. Hydrocarbon chemistry and comparisons with ISO observations[END_REF] model and the best VER obtained in the previous paragraph. We add to this spectrum the strongest solar fluorescence lines reported in Table 2 of [START_REF] Liu | The ultraviolet spectrum of the Jovian dayglow[END_REF]. Each line is convolved to the UVIS spectral resolution and is allowed to vary freely in the fitting procedure. Five additional lines have been included in the procedure to improve the fit: Ly- 2. It is seen that the Ly-line maximizes at 1100 km with 802 R, which corresponds to the altitude of the airglow peak within 50 km (i.e. below the spatial resolution of one UVIS pixel), as already noticed for V1 and V2 limb scans [START_REF] Yelle | Altitude variation of EUV emissions and evidence for proton precipitation at low latitudes in the Saturnian atmosphere[END_REF]. The total emission due to fluorescence peaks at 900 km with 1445 R and the emission due to electron impact peaks at 1150 km with 2743 R, for a total airglow emission of 3943 R peaking at 1050 km. Taking into account the 11 years solar cycle, these numbers can be readily compared to the limb values obtained from the two Voyager encounters with Saturn. The Ly-line is about two to three times weaker for UVIS compared to Voyager, while the total H 2 emission compares well. The much higher Lybrightness observed during the Voyager observations is attributed to the tilted Saturn's rings reflecting a significant amount of emission into the detector, while the rings appeared horizontal during the UVIS observations. Table 2 also gives the intensity of the pumped line used in the analysis of a HUT disk spectrum of the Jovian dayglow [START_REF] Liu | The ultraviolet spectrum of the Jovian dayglow[END_REF], converted to our observation conditions. The Liu and Dalgarno figures have been derived from a disk spectrum and thus cannot be readily compared to ours, which have been obtained from limb-viewing observations. Yet, comparisons between the Liu and Dalgarno values and the UVIS pumped lines brightness averaged from -1200 to 2500 km show that the main contributor to fluorescence for both planets is Ly-, followed by solar OVI, CII, and NII in that order. The main lines contributing to fluorescence are the L(6,13) P(1) and L(5,12) R(1) transitions at 1607.50 Å and 1607.90 Å respectively. This contribution is clearly seen in the fits presented in Fig. 9. The fits require the addition of the OI triplet at 1304 Å for the lowaltitude spectra, and a mystery feature at 1255 Å which peaks at 1200 km. The altitude profile of the 1255 Å line displayed in Fig. 10 looks triangular, quite different from the fluorescence lines. It should be stressed out that the fluorescence lines from Table 2 of [START_REF] Liu | The ultraviolet spectrum of the Jovian dayglow[END_REF] used in our regression correspond to the main features of the pure fluorescence spectrum. However, they only represent 28% of the total integrated fluorescence spectrum presented in [START_REF] Liu | The ultraviolet spectrum of the Jovian dayglow[END_REF], as the fluorescence emission exhibits a continuous emission in the UV. If we then multiply the intensity of the pumped lines used in our regression by 3.57 and remove this total fluorescence contribution from the best fits, we find that the electron impact excitation process dominates the emission, with a maximum contribution of 80% at 1400 km and an average contribution of 68% in the -1200 to 2500 km range. The technique we use to evaluate the fluorescence and electron impact contributions to the total airglow should be considered as a first order survey, as it bears two main weaknesses. First, the contribution of the main fluorescence lines listed in Table 2 of [START_REF] Liu | The ultraviolet spectrum of the Jovian dayglow[END_REF] somewhat depends on the gas temperature and second, we scaled the electron impact spectrum component to the calculated VER and added the fluorescence lines afterwards in the regression, which may lead to an overestimate of the electron impact contribution. On the other hand, the comparison between the e-impact laboratory spectra and the airglow synthetic spectrum from Hallet et al. (2005) in Fig. 8 shows that the airglow spectrum can be very well reproduced by combining the e-impact spectra with the fluorescence pumped solar lines. We thus find this method appropriate in our airglow simulations.

Conclusions

A total of 109 UVIS limb spectra at ~5.5 Å resolution of the Kronian airglow, spanning the altitude range -1200 to 4000 km at the tangent point have been analyzed. The volume emission rate has been derived from fits between the observed and modeled H 2 limb brightness in the 1550-1620 Å bandwidth. We find that the best agreement is obtained by shifting the data upward by 125 km, within the pointing uncertainty related to our observations. Our best representation of the vertical volume emission rate is a -Chapman function which peaks at 1020 km and emits 3.5 photons cm 3 s -1 in the 800-1650 Å bandwidth.

The scale height of the Chapman function is 284 km, which is five times the scale height of the neutral atmosphere (H=~53 km assuming a temperature of 130 K). This result, already pointed out by [START_REF] Yelle | Altitude variation of EUV emissions and evidence for proton precipitation at low latitudes in the Saturnian atmosphere[END_REF], shows that the source of excitation extends throughout the entire upper atmosphere of the planet.

A comparison between the observed and synthetic spectra has been carried out using a first-order hybrid model of airglow, consisting of a free combination between an electron impact H 2 spectrum and intense fluorescence H 2 lines reported by [START_REF] Liu | The ultraviolet spectrum of the Jovian dayglow[END_REF].

Laboratory spectra excited by 20 eV and 100 eV electrons have been tested. The main differences between these two spectra are due to the EF cascade process, which increases the population of the v=0 vibrational level of B and enhances specific H 2 emitted lines. This effect is maximum for 20 eV electrons and is used to discriminate between 20 eV and 100 eV spectra. However, the spectral lines enhanced by cascade coincide with fluorescence lines, which makes it difficult to choose between the modeled emergent spectra obtained with the 20eV and 100 eV spectra. Nevertheless, the emergent synthetic airglow spectra built with the 20 eV spectrum provided overall better fits to the observations. This suggests that the airglow is principally due to low-energy photoelectrons, as was already suggested by the study of the Jovian UV airglow by [START_REF] Liu | The ultraviolet spectrum of the Jovian dayglow[END_REF]. The photoelectron flux spectrum they derived from XUV solar excitation had energies mostly lower than 60 eV, with an average of 33 eV and a peak at 25 eV. We find that electron impact process dominates Saturn's airglow emission, with an average contribution of ~ 68% in the -1200 to 2500 km MRH range.

This study provides the first study of recent UV spectra of the Kronian airglow, which is scarcely described in the literature. A next step in the study of airglow would be to use a self-consistent spectral model of H 2 , based on the incident XUV and EUV solar flux. This would help to univocally determine 1) the mean energy of the photoelectrons responsible of the airglow, 2) the relative contribution of photoelectron and fluorescence excitation to the total emission and 3) that the airglow at Saturn, as for Jupiter, can be solely attributed to solar fluorescence and photoelectron excitation without the need of an additional energy source. 3,5,[START_REF]Values from fluorescence lines listed in Table 2 of Liu and Dalgarno[END_REF][START_REF] Liu | the solar fluorescence on Jupiter contributes 57% of the total observed dayglow emission[END_REF]11,12,13,14. L stands for Lyman and W for Werner bands. 2. x = 5, 7, 9, 10, 14 3. x = 1, 2, 5, 8, 9, 10 4. x = 4, 5 5. x = 3, 5, 6, 8, 10, 12

Tables

Figure captions

  4075 and 4125 km have been used as background reference and have been subtracted from all spectra. Another source of background signal that affects the recorded spectra is scattering of the H Ly-α line on the detector. This wavelength-dependent background, directly proportional to the Ly-α intensity, has been modeled, scaled to the observed Ly-α and subtracted from the data. Fig 2a shows the variations of the spectral contents and intensity for several altitude bins. It is seen that a strong solar reflectance structure longward of 1500 Å dominates the overall intensity for lower altitude spectra (~-1325 to ~425 km) and spectra above ~ 425 km contain strong H 2 Lyman and Werner bands. Limb spectra above 2700 km start to be very noisy and structureless. Fig. 2b shows the brightness variations of the reflected sunlight emission in 1700-1880 Å, plus the 1250-1300 and 1550-1620 Å spectral windows, used to define the H 2 color ratio (CR), which is a measure of the absorption by methane (Gustin et al. 2004). The limb reflected solar profile has a maximum of 16.5 kR, peaking at ~-1075 km. The 1230-1300 and 1550-1620 Å profiles exhibit the same trend at high altitude up to 1100 km, where the 1250-1300 Å brightness starts to reveal the effect of methane absorption, active shortward of 1400 Å. The integrated limb brightness in 1550-1620 Å peaks near ~825 km and 1230-1300 Å one peaks near ~975 km. The altitudes scale used in Fig. 2a and 2b is provided by the nominal pointing in the NAIF SPICE C kernel toolkit. It will be demonstrated later that

  spectrum we analyze is the sum of all spatial pixels into 50 km MRH bins. Since the solar incidence and phase angles can be very different for each pixel into a 50 km bin, we calculated the reflectivity for each individual pixel and then computed a weighted averaged reflectivity, based on each pixel intensity between 1700 and 1880 Å. The modeled reflectivity so calculated is then multiplied by a solar spectrum which accounts for the angle between Saturn, the Sun and the Earth to correct for the solar rotation and the resulting delay between the solar photon flux reaching the Earth and Saturn. The solar flux is then corrected for the distance between the Sun and Saturn. Since the datasets have been obtained 29 days apart, two solar spectra should be considered. We retrieved solar spectra obtained from the TIMED/SEE database[START_REF] Woods | Solar EUV Experiment (SEE): Mission overview and first results[END_REF], measured on 21 October 2005 and 22 November 2005, related to the 29 Oct. 2005 and 27 Nov. 2005 limb observations respectively. As both spectra were found identical, we chose the 21 Oct. 2005 spectrum in our calculations.

  T. Hallet (personal communication, from Hallet et al., 2005), is described in more details in section 4.1.a. It is used in the present paragraph as an all-around airglow spectrum simulating the influence of H 2 within the reflected sunlight signal. It will be the base of our VER determination presented in section 4.1 and 4.2. A least-square fit between the observed and modeled spectra in 1500-1880 Å minimizing chi squares ( 2 ) is then applied, yielding the best parameters, which are the mixing ratios of the absorbing components and the scale factor of the synthetic H 2 spectrum.

  1x10 4 mbar level (~800km) along with the Moses et al. (2000) values and other published measurements. The Moses et al. (2000) profiles show the mixing ratios averaged along the LOS. Data points from disk viewing observations obtained by other studies are also shown. The UVIS C 2 H 2 profiles below ~1 mbar and C 2 H 6 below ~1x10 -2 mbar do not exhibit a strong The emergent brightness B at Z 0 MRH is the sum of the H 2 emission on each point S along the LOS, attenuated by hydrocarbons (Fig. 1b): VER of the H 2 airglow intercepted at distance S along the LOS -) S ( τ is the optical depth due to absorption by hydrocarbon HC, of density n HC at S' and absorption cross-section HC σ .

  photoelectron and solar photon of the X ground electronic state to B, C, B', D, B", D' states,

  lowering of CH 4 by a factor of 100 (compared to the Moses model) was needed to match the synthetic and observed CR, which does not seem realistic. An other way to adjust the CR is to modify the VER altitude profile. This can be achieved by modifying the hydrocarbon profiles in 4.1.a or by using another profile than the Chapman function defined in equation (3). Many combinations have been tried (lowering or increasing the hydrocarbon density profiles, using Gaussian, generalized Gaussian, asymmetric Gaussian or Epstein profiles), which did not provide a satisfactory result. Finally, we obtained a very good fit of the CR profile by shifting the UVIS observations upward by 125 km, using a Chapman function and the[START_REF] Moses | Photochemistry of Saturn's atmosphere I. Hydrocarbon chemistry and comparisons with ISO observations[END_REF] density profiles, without additional modification. In a study of Titan's limb spectra obtained by the Composite InfraRed Spectrometer (CIRS) onboard Cassini,Vinatier et al.

4. 3 .

 3 Electron-impact and fluorescence contributions. The H 2 spectrum from Hallet et al. (2005) used in the previous sections represents an average airglow emission and is composed of a fixed combination of electron impact and solar fluorescence excitations. The ratio between the contribution of electron impact and fluorescence on the emergent emission may vary with altitude. In order to evaluate the magnitude of both contribution with MRH, the spectral analysis in the 1150-1650 Å bandpass is performed again here, with the Hallet et al. (2005) spectrum replaced by the blending of an e-impact H 2 spectrum obtained in the laboratory and individual fluorescence H 2 lines arising

  at 1215.7 Å, the OI triplet at 1302.2, 1304.09 and 1306.0 Å and the mystery feature at 1255 Å. The combination of these contributions forms a new synthetic airglow spectrum that is compared to the observed spectra at each MRH. The least-squares regressions have been performed for altitudes from -1200 to 3000 km MRH. The results reveal that the best fits with 100 eV and 20 eV spectra are very similar, with a slight preference for the 20 eV spectra. It is however difficult to point out a particular spectral region with systematic improvement, because of all the individual lines varying freely included in the regression. In fact, because of the medium resolution of the data (~5.5 Å), some intense pumped H 2 lines included in the regression coincide with lines enhanced by the EF cascade: the 1276 Å line coincides with the pumped lines at 1272.81 Å and 1279.10 Å [L(11,7) R(1)+P(3) from CII and OVI], the 1335 Å line coincide with the 1334.28 Å pumped line [L(5,6) R(1) from CII and OVI] and the 1395 Å line coincide with the pumped 1394.25 Å line [L(11,10) R(1) from Ly-]. This means that a specific observed peak enhanced by the EF cascade can be fitted as well with the 20 eV spectrum alone or a combination of the 100 eV spectrum with solar pumped lines. Still, the overall fit with the 20 eV spectrum are found slightly better when compared to the data. Examples of best fits at -700, 50 and 1050 km MRH are shown in Fig. 9. For all spectra, the 20 eV electron impact component dominates the total emission, along with a few fluorescence lines. The most intense fluorescence H 2 lines, clearly apparent in Fig. 9, are found at 1265.68 Å [L(6,5) P(1)], 1362.04 and 1365.66 Å [L(11,9) P(3) and [L(6,7) P(1)], 1369.0 Å [L(2,5) P(6)], 1461.97 Å [L(6,9) P(1)], 1546.72 Å [L(6,13) P(1)], 1607.50 and 1607.90 Å [L(6,11) P(1)] and [L(5,12) R(1)]. The contribution of the 1255 Å mystery feature is weak for the spectra at -700 and 50 km MRH in Fig. 9 but clearly visible for the 1150 km spectrum. In order to determine the contribution of the different EUV solar lines in the pumping process, the individual H 2 lines due to the same solar source have been added up for each best synthetic spectrum and plotted versus MRH in Fig. 10. This figure also shows the Ly-line limb profile and presents the contributions of e-impact and fluorescence to the total airglow emission. Some relevant number from the plots in Fig. 10 are tabulated in Table

  limb brightness in the 1150-1850 Å range is dominated by Ly-, peaking at 1100 km MRH with 802 R, reflected sunlight maximizing at -950 km MRH with 16.5 kR and H 2 Lyman and Werner bands which peak at 1050 km MRH with a maximum of 3.9 kR. The UVIS integrated H 2 brightness at the altitude peak compares well with the values obtained with the UVS V1 and V2 spectrometers, taking into account the EUV solar flux ratio at the time of the observations. The Ly-brightness peaks at the same altitude as the H 2 bands, near the homopause level, but our value is significantly lower than the V1 and V2 observations[START_REF] Yelle | Altitude variation of EUV emissions and evidence for proton precipitation at low latitudes in the Saturnian atmosphere[END_REF], probably because of the reflection of interplanetary Ly-by Saturn's rings, more inclined towards the instrument during the Voyager observations. A model of the airglow emission taking into account hydrocarbon absorption along the LOS has been developed, based on a H 2 synthetic airglow spectrum (Hallet et al. 2005) and the Moses et al. (2000) model of the Saturn equatorial atmosphere. A vertical profile of the H 2

Figure 1 :

 1 Figure 1: a) Projection of the UVIS slit for the limb viewing observation obtained on 29October 2005 (case 1 in Table1), showing the four records of the sequence. The long side of

Figure 2 :

 2 Figure 2: a) All the raw UVIS spectra have been summed into 50 km altitude bins. The few examples shown here indicate that the emission longward of 1550 Å is dominated by

Figure 3 :

 3 Figure 3: Comparison between the UVIS spectra at -1025 and 525 km MRH and a model that includes H 2 and solar reflected emissions. The best synthetic solar reflected

Figure 4 :

 4 Figure 4:Mixing ratio profiles of the two main absorbing species obtained from the best fits to the reflected sunlight component between 1500 Å and 1880 Å (solid lines). The

Figure 5 :

 5 Figure 5: a) Best fit to the observed integrated brightness in the 1550-1620 Å range with a Chapman function, following equations (1), (2) and (3) listed in paragraph 4.1. The modeled

Figure 6 :

 6 Figure 6:Examples of the VER intercepted along the LOS and mean optical depth in the 1150-1650 Å bandwidth for two impact parameters. At low altitude, the emission consists of

Figure 7 :

 7 Figure 7:Color ratio between the integrated brightness in the 1550-1620 Å and 1230-1300 Å bandwidths, illustrating the effect of the CH 4 absorption. The light orange curve

Figure 8 :

 8 Figure 8: a) Example of fit of the airglow emission with the model described in section 4.2. which includes the modeled airglow spectrum of H 2 (fluorescence and electron impact) as

Figure 9 :

 9 Figure 9:Examples of best fit to the H 2 airglow emission, for three altitude bins, obtained from the combinations of a 20 eV electron impact spectrum and individual H 2

  Figure 7

  CH 2 CCH 2 , C 4 H 2 , C 4 H 8 , CH 3 C 2 H, C 3 H 8 , C 4 H 8 and C 4 H 10 . Since this high number of parameter may lead to unstable results, we chose to tie some hydrocarbon mixing ratios to others. We first choose the hydrocarbons whose number density altitude profiles follow the same trend in the Moses et al. (2000) model and tied them to the most abundant one, which can vary freely. In our selection of hydrocarbons, C 2 H 2 and C 2 H 4 vary freely, C 3 H 6 , CH 2 CCH 2 , C 4 H 2 and C 4 H 8 are tied to CH 3 C 2 H, and C 3 H 8 and C 4 H 10 are tied to C 2 H 6 .

Table 1 :

 1 overview of the UVIS limb scan dataset

	Start time	Number of records	Integration per record (s)	Mean latitude, longitude (deg)	Mean incidence angle (deg)	Mean phase angle (deg)
	1 Oct. 29 2005 19:27:45	4	120	-17, 26.5	23	68
	2 Oct. 29 2005 19:35:33	77	30	3-16.5, 35	17	73
	3 Nov. 27 2005 08:57:53	7	75	-17.5, 133.5	9	79
	4 Nov. 27 2005 09:07:07	68	18	-18, 140	7	81
	5 Nov. 27 2005 13:17:55	7	75	-17.5, 227.5	40	125
	6 Nov. 27 2005 13:27:07	88	18	-18, 238	44	128

Table 2 :

 2 Characteristics of the main contributions to the airglow emission.

	Emission	Peak limb brightness from UVIS (R) 6	Peak altitude (Km)	Main H 2 line contributing	Average brightness from -1200 to 2500 km MRH (R)	Disk values from Liu and Dalgarno, 1996 (R) 7	Peak limb values from V1 and V2 (R) 8
	H Ly-	802	1100	-	441		V1: 1936, 2543, V2: 1845
	L(6,x) 1 P(1) from H Ly-	120	1000	L(6,11) P(1) at 1546 Å	42	9.2
	L(11,x) 2 R(1) + P(3) from H Ly-	13	750	L(11,7) P(3) at 1279 Å	6	2.8
	L(2,x) 3 R(4) + P(6) from NII	35	900	L(2,10) R(4) at 1623 Å	15	3.1
	W(1,x) 4 Q(3) from NII & OVI	26	1250	W(1,5) Q(3) at 1208 Å	10	2.2
	L(5,x) 5 R(1) + P(3) CII & OVI	60	900	L(5,11) P(3) at 1613 Å	18	7.1
	1607 Å from H Ly-, CII & OVI	137	950	L(6,13) P(1) and L(5,12) R(1)	33	8.1
	1255 Å mystery feature	18	1200	-	7
	OI triplet	6	-1000	-	4
	Total H 2 bands from e -impact Total H 2 bands from fluorescence	2743 1445	1150 900	--	1054 460	131 9 173 9
	Total H 2	3943	1050	-	1514	304 9	V1: 5386, 4787; V2: 3075
	1. x =

agreement between the data and model.

altitude dependence. This is an effect of the limb-viewing geometry, which averages the hydrocarbon local density profiles along the LOS and smoothes their variations with the MRH. It should be noted that the UVIS values reflect, for a given MRH, the product of the local solar illumination by the optical depth, summed on each point along the LOS. Therefore, they cannot be readily compared with other published values, since the unattenuated vertical profile of the solar flux is not known, which make it unfeasible to simulate the average mixing ratios that would be obtained in limb-viewing geometry. This is not essential to our analysis, since our goal is to subtract the modeled reflected sunlight component from the observed spectra in order to get the H 2 emission free of solar contamination. Once a best synthetic spectrum is obtained for each MRH, the solar reflected component is then removed from the observations to retain the airglow H 2 emission only.

Fig. 2

Figure 6

Acknowledgements

The PRODEX program of ESA provided financial support for this research. J.-C.G. acknowledge support from the Belgian Fund for Scientific Research (contract NAS5-32985). This work is supported by the Cassini Project.

transitions at 1607.50 Å and 1607.90 Å respectively. A mystery line is added to the regression at 1255 Å. Its effect on the best fit is clearly seen in the 1150 km spectrum.


Pieternella C Luttikhuizen
email: pieternella.luttikhuizen@nioz.nl

Anneke Bol

Harry Witte

Judith Van Bleijswijk

Oliver Haddrath

Allan J Baker

Theunis Piersma

Jeroen Reneerkens

Novel and cross-species microsatellite markers for parentage analysis in sanderling Calidris alba

Keywords: microsatellite markers, parentage analysis, breeding system, population genetics Zusammenfassung Neue, Art-übergreifende Mikrosatellitenmarker für Herkunftsanalysen beim Sanderling Wir isolierten und testeten sechs neue Mikrosatelliten-Loci auf Eignung polymorph, aber fünf der artübergreifenden loci konnten wegen ungenügender Vervielfältigungsmuster nicht ausgewertet werden von Familien enthielt, wurden für einen Teil des Sets mit Daten von fünf adulten, im gleichen und alle loci waren ungekoppelt. Aufgrund der weiblichen Heterozygoten wurde angenommen, dass alle loci autosomal waren

We isolated and tested six novel microsatellite loci in sanderling (Calidris alba) from Greenland for paternity analyses. In addition, we tested 11 already published microsatellite markers which were originally developed for the congeneric species Calidris melanotos, the pectoral sandpiper. All loci were polymorphic, but five of the cross-species loci were not scorable due to suboptimal amplification patterns. The 12 successful loci were tested on 87 individuals, yielding an average of 9.0 (range 4-19) alleles per locus and mean expected heterozygosity of 0.70. Because this data set contained families, tests for Hardy-Weinberg equilibrium, linkage disequilibrium and probability of identity were done on a subset of the data containing 25 adults caught in the same year. The overall probability of identity was 1.0•10 -13 . Only one locus displayed significant homozygote excess and all loci were unlinked.

On the basis of female heterozygotes, all loci are assumed to be autosomal.

Introduction

Sanderlings Calidris alba are small sandpipers that migrate annually between their High Arctic breeding grounds and the non-breeding grounds along temperate and tropical shorelines (Reneerkens et al. 2009). Based on 24 h nest observations in the Canadian Arctic and on the dissection of two incubating females with scars in their oviducts that suggested the laying of two complete clutches, [START_REF] Parmelee | Breeding behavior of the sanderling in the Canadian High Arctic[END_REF] and [START_REF] Parmelee | On multiple broods and the breeding strategy of arctic sanderlings[END_REF] concluded that sanderling females lay two clutches in rapid succession. The first clutch was suggested to be incubated by the male and the second by the female. As a result of this breeding system, called 'double-clutching', uniparental males and females would take care of incubation and the subsequent young. Double-clutching has been suggested to also occur in a few other sandpiper species [START_REF] Breiehagen | Nesting biology and mating system in an alpine population of Temminck's Stint Calidris temminckii[END_REF][START_REF] Hildén | Breeding system of Temminck's Stint Calidris temminckii[END_REF][START_REF] Hildén | Zur Brutbiologie des Zwergstrandlaufers, Calidris minuta, in Finnmark[END_REF].

In contrast to the findings of [START_REF] Parmelee | On multiple broods and the breeding strategy of arctic sanderlings[END_REF], seven clutches in northeast Greenland were incubated by both a male and a female [START_REF] Pienkowski | Breeding biology of Sanderlings in north-east Greenland[END_REF]. The existence of both uniparental and biparental clutches next to each other was confirmed in another area in northeast Greenland based on behavioural observations and data of nest attendance of individually recognised birds (Reneerkens et al. 2009;Reneerkens et al. submitted MS) as well as in northern Taimyr, Siberia [START_REF] Tomkovich | Social organisation of sanderlings breeding at northern Taimyr, Siberia[END_REF]. These more recent data demonstrate that 'double-clutching' certainly is not the norm, although it may indeed occur in sanderling. Yet, the existence of clutches incubated by a single parent is not necessarily the result of double-clutching. Clearly, we need more work to unravel the breeding system in sanderling.

Here, we report the development of seven novel microsatelite markers and the crossamplification of seven already existing, microsatelite loci to allow parentage analyses to test for paternity to verify earlier suggestions based on behavioural observations on 'doubleclutching'. Furthermore, it will shed light on poorly understood aspects of the breeding biology of the sanderling, such as the occurrence of extra-pair fertilisations, and possible geographical variations herein.

Methods

Genomic DNA was extracted from tissue of sanderling 2SAN7b (Southhampton Island, Nunavut, Canada) using a standard phenol extraction. A DNA library was constructed following [START_REF] Hamilton | Universal linker and ligation procedures for construction of genomic DNA libraries enriched for microsatellites[END_REF]. DNA was digested using three blunt-end restriction enzymes (NheI, RsaI, HaeIII; New England Biolabs), and ligated to SNX linkers to enable PCR amplification of inserts. Amplification was followed by hybridization to biotinylated (GT) 15 and (CT) 15 di-repeats. Biotinylated DNA fragments were captured using Dynabeads (Dynal). Di-repeat enriched DNA was recovered using PCR. Amplified enriched DNA was ligated into a PCR 2.1 cloning vector, and plasmids were transformed to competent cells using TA Cloning kit (Invitrogen). A total of 490 clones with inserts were isolated on Hybond Nylon membranes (Amersham) and a second hybridization with biotinylated oligonucleotides using NRET Phototope Star Detection (New England Biolabs) detected 81 clones with direpeats.

Positive clones were sequenced with forward and reverse M13 primers using BigDye Terminator version 3.1 (Applied Biosystems) and an ABI 3100 automated capillary sequencer (Applied Biosystems). Sequences were assembled and edited using Chromas-Pro 1.33 and MEGA 3.1 [START_REF] Kumar | MEGA3: Integrated software for molecular evolutionary genetics analysis and sequence alignment[END_REF]). Nineteen sequenced clones had motif repeats with unique flanking sequences, for which primers were designed using OLIGO and Jellyfish software. Primers were tested on DNA extracts of blood samples of 26 sanderlings from geographically distinct locations. Products were analysed to screen for polymorphic loci.

PCR was carried out on a Mastercycler epgradient S (Eppendorf). The volume of PCR reaction mixture was 12.5 µL, which contained 1X PCR buffer (10 mM Tris-HCl pH 8.3, 50 mM KCl, 2.5 mM MgCl 2 , 0.01% gelatin), 200 µM dNTP (Invitrogen), 0.2 µM forward primer (Invitrogen), 0.2 µM reverse primer (Invitrogen), and 0.20 µM universal dye-labelled M13 (TGTAAAACGACGGCCAGT) tail (6-FAM, HEX; Thermo Scientific), 0.25 U Taq (Invitrogen) and 1 µL DNA template. PCR conditions included an initial denaturation step at 94 °C for 4 min, 36 cycles of denaturation at 94 °C for 30 s, primer annealing for 30 s at respectively 50 °C for primer pair gt22; 55 °C for gt24, an3 and m11; 58 °C for m18; 59 °C for m14; followed by primer extension at 72 °C for 30 s. A final step at 72 °C for 5 min was used to complete primer extension. Fragment analysis was run on an ABI 310. Alleles were sized using ROX size standard (GENEMARK350; Northern Biotech); allele sizes were assigned with GelCompar II software (Applied Maths). Cross-species amplifications were done with eleven primer pairs (Cme1 through Cme10 and Cme12) developed for the pectoral sandpiper Calidris melanotos [START_REF] Carter | Eleven polymorphic microsatellite markers for paternity analysis in the pectoral sandpiper, Calidris melanotos[END_REF].

Blood samples (10-50 microliters) of adults, chicks and near-fledged juveniles were collected during the breeding season near our study site at Zackenberg, northeast Greenland (74º30'N 21º00'W). Adults and near-fledglings were bled from the brachial vein, and chicks from the leg vein. Samples were stored in 96% ethanol at -80°C. DNA was extracted using the Sigma mammalian DNA kit.

We analysed the 12 loci for a total of 87 sanderlings caught at Zackenberg which were also molecularly sexed following [START_REF] Fridolfsson | A simple and universal method for molecular sexing of non-ratite birds[END_REF] with primers 2602F and 2718R adjusted for calidrid waders (OH, unpublished data). This data set was expected to show linkage disequilibrium (LD) and deviations from Hardy Weinberg equilibrium (HWE) because it contains numerous parent-offspring and sibling relationships. Analyses were therefore also done on a subset of the data, consisting of the adults only (N=25).

The number of alleles and observed and expected heterozygosities were assessed using Arlequin, version 3.11 [START_REF] Excoffier | Arlequin ver. 3.0: An integrated software package for population genetics data analysis[END_REF]. Conformity to HWE and LD were evaluated using Genepop, version 4.0 [START_REF] Rousset | Genepop'007: a complete re-implementation of the genepop software for Windows and Linux[END_REF]. Micro-checker, version 2.2.3 (Van Oosterhout et al. 2004) was used to test for the presence of null alleles. The probability of observing identical multilocus genotypes between two individuals sampled from the same population ('probabiilty of identity', P ID ) was estimated from the data set containing the adults only, following [START_REF] Waits | Estimating the probability of identity among genotypes in natural populations: cautions and guidelines[END_REF] and using the program GIMLET [START_REF] Valière | GIMLET: a computer program for analysing genetic individual identification data[END_REF]. Exclusion probabilities (P E1 and P E2 ) were calculated using CERVUS 3.0 [START_REF] Kalinowski | Revising how the computer program CERVUS accommodates genotyping error increases success in paternity assignment[END_REF].

Results and Discussion

The six newly developed microsatellite markers (Genbank accession numbers HQ259972-HQ259977) could be amplified consistently (i.e., produced PCR product in all individuals). They were all polymorphic. Of 11 cross-species loci, six gave consistent PCR results. All these 12 loci (six new plus six cross-species) were highly polymorphic (average number of alleles per locus N A =9.0 and 7.8; average expected heterozygosity H E =0.699 and 0.708; for full data set and adults only, respectively). On the basis of female heterozygotes, all loci are assumed to be autosomal.

In the full dataset, as expected, excess homozygosity and linkage disequilibrium were observed. Three loci displayed significant deviations from Hardy-Weinberg equilibrium (after Bonferroni correction, an3: P<0.0001; m18: P<0.0001; Cme9: P=0.0023; Table 1) and linkage disequilibrium was significant for 17 out of 66 pairwise comparisons (at Bonferroni corrected P-level of 0.0008). In the partial data set, there was no evidence for linkage between any locus pair and only one locus had an excess of homozygotes (m18: P=0.0022;

Bonferroni corrected P-level of 0.0042; Table 1). Micro-checker detected evidence for possible null alleles in the loci an3, m18 (both data sets) and Cme9 (only the partial data set).

The probabilities of identity per locus are shown in Table 1. For all loci together, P ID was estimated to be 1.0•10 -13 (Table 1). The average probability that the loci will exclude a random unrelated candidate parent from parentage of an arbitrary offspring when the genotype of the other parent is unknown (P E1 ) is 0.9969; when one of the parents is known, the exclusion probability (P E2 ) increases to 0.9999.

Homozygote excess and linkage disequilibrium in the full data set can be attributed to the relatedness among the birds sampled. While pairwise difference (in number of alleles) among the 87 adult and juvenile birds averaged 15.06, the difference between one particular male (z013) and his four presumed offspring (z123-z126), as an example, averaged 9.25.

We suspect that the remaining locus (m18) not in Hardy-Weinberg equilibrium among the 25 adults in the partial data set may be attributable to further relatedness, rather than to null alleles. This is because sanderlings, and males in particular, are faithful to their breeding sites and will return to the same breeding grounds in subsequent years (Reneerkens and Grond 2009). The most extreme known example consists of a brother and sister that both nested during at least two successive breeding seasons less than 500 m from the nest location where they were born; the likelihood of capturing brothers or fathers and sons may be substantial. We conclude that this set of 12 microsatellite markers will be a valuable tool for assessing parentage in sanderling.

  ; B ) bold values indicate significant homozygote excess (Bonferroni corrected). F = forward primer; R = reverse primer; bp = basepairs; HO = observed heterozygosity; HE = expected 233 heterozygosity; NA = number of alleles; NT = total number of alleles observed; PID = probability of identity.

Acknowledgements

The Netherlands Arctic Programme, administered by the Netherlands Organisation for Scientific Research (NWO) supported our work financially in Greenland. We are grateful to the Danish Polar Center for providing logistics at the research station at Zackenberg and to Petra de Goeij, Joop Jukema and Welmoed Ekster for assisting in the field work in Zackenberg.


Alain Blouin
email: alain.blouin@nrc.ca

Philippe Delaye
email: philippe.delaye@iota.u-psud.fr

Jean-Pierre Monchalin
email: jean-pierremonchalin@nrc.ca

Gérald Roosen
email: gerald.roosen@iota.u-psud.fr

Détection d'ultrasons par interférométrie adaptative dans des cristaux photoréfractifs

Keywords: ultrasons-laser, dispositif photoréfractif, interferomètre adaptatif Laser-ultrasonics, photorefractive device, adaptive interferometry

Les ultrasons sont à la base d'une technique non destructive puissante couramment utilisée dans l'industrie pour mesurer des épaisseurs, détecter des défauts et caractériser des matériaux. Ils nécessitent cependant un contact ou un couplage par fluide et des géométries bien définies. Quand ceci n'est pas le cas (hautes températures, géométries complexes ou mal définies), la technique des ultrasons générés et détectés par laser offre une solution pratique intéressante et souvent unique. Les difficultés rencontrées par la détection et causées en particulier par la rugosité des surfaces industrielles a traditionnellement été un obstacle à l'utilisation de cette technique. Bien que des solutions de type passif aient été apportées (interféromètre de Fabry-Perot confocal), l'interférométrie adaptative basée sur le mélange deux-ondes dans des cristaux photoréfractifs offre une solution des plus puissantes. Nous décrivons dans cet article le système développé, ses avantages par rapport au Fabry-Perot confocal et les approches utilisées pour optimiser sa sensibilité et son usage pratique, lesquelles ont permis sa commercialisation.

ABSTRACT.Ultrasonic-based nondestructive techniques are powerful industrial tools for thickness measurements, detection of defects and materials characterization. However, ultrasonic techniques require either a contact with the material or a liquid couplant to transmit ultrasound in the material. This drawback forbids the applications of ultrasonics to materials at high temperature or materials with a complex geometry. Laser-ultrasonics is a non-contact technique that uses lasers for generation and detection of ultrasound. The surface roughness of the industrial surfaces represents a challenge for the detection of ultrasound by interferometric methods. Although passive solutions based on a confocal Fabry-Perot already exist, adaptive interferometry based on two-wave mixing in photorefractive crystals is a new and simple emerging powerful technique. We described in this paper the advantages of this new technique compared to the confocal Fabry-Perot-based techniques. We present also the different approaches devised for maximizing the sensitivity and the practical use of the two-wave mixing-based adaptive interferometer for ultrasound detection, which have led to its commercialization.

Introduction

On assiste actuellement à un développement important de nouveaux moyens optiques pour l'industrie. L'optique a l'avantage d'opérer à distance, sans contact avec les produits ou matériaux sous évaluation, mais ne peut cependant pas sonder directement l'intérieur de matériaux opaques à la lumière, lesquels représentent en fait la plupart des matériaux industriels. Les ultrasons au contraire permettent l'inspection sous la surface des matériaux et conduisent ainsi à la mesure des propriétés élastiques et à la microstructure des matériaux, lesquelles conditionnent leurs propriétés de déformation et de rupture.

Le principe du laser-ultrason (aussi appelé ultrason-laser) consiste à utiliser un laser impulsionnel pour générer les ultrasons et un second laser couplé à un interféromètre pour les détecter [SCR 90]. La génération d'ultrasons peut d'abord se faire par un mécanisme thermoélastique qui n'affecte pas le matériau. Ce mécanisme consiste en l'échauffement d'une couche superficielle, plus ou moins épaisse selon la pénétration lumineuse, suivie de la dilatation de cette couche et de la création, au voisinage de la surface, de déformations et de forces qui sont à la source des ondes ultrasonores. Des ondes longitudinales, de cisaillement ou de surface (ou de plaque) sont en général générées [SCR 90, HUT 88]. Un cas particulièrement important se produit dans les polymères et matériaux à matrice polymère avec l'utilisation d'un laser infrarouge (tel que le laser CO 2 TEA). Dans ce cas, on a une absorption distribuée et l'émission forte d'une onde longitudinale normale à la surface (pour une tache sur la surface non ponctuelle). Lorsque la densité d'énergie à la surface excède le seuil d'ablation, il y a un effet de recul de la matière éjectée, qui conduit aussi à l'émission d'une onde longitudinale forte normale à la surface. Ce régime est utilisé quand l'état de surface du matériau n'est pas critique ou bien à haute température, l'ablation ne produisant dans ce cas que l'arrachement de l'oxyde superficiel, lequel est souvent régénéré rapidement. Quand le laser vaporise une faible couche de contaminant à la surface du matériau (par exemple, de l'huile) sans affecter le substrat lui-même, il y a aussi une émission importante normale à la surface.

La détection optique des ultrasons s'effectue à l'aide d'un second laser, très stable (i.e. généralement monomode longitudinal), qui est modulé en phase ou en fréquence par le mouvement de la surface produit par les ondes ultrasonores. La lumière diffusée par la surface est par la suite collectée et transmise à un dispositif visant à démoduler la phase. Les déplacements ultrasonores de surface à détecter sont très petits (de l'ordre du nanomètre ou de l'angström), ce qui nécessite une technique très sensible basée sur l'interférométrie. Ces déplacements sont cependant à des fréquences bien supérieures à celles des vibrations mécaniques ambiantes, ce qui permet de les détecter pour autant que l'interféromètre n'est pas sensible ou s'adapte à ces perturbations ambiantes. La plupart des matériaux rencontrés en industrie ont des surfaces optiquement rugueuses et la lumière diffusée par ces surfaces présente des tavelures. Un interféromètre insensible aux tavelures est donc préférable pour la détection des ultrasons, bien que des systèmes sensibles aux tavelures, basés en particulier sur l'interférométrie hétérodyne soient appropriés à des travaux menés en laboratoire

Caractéristiques requises d'un capteur optique d'ultrasons

La détectivité est le plus petit déplacement de surface ultrasonore pouvant être mesuré par le capteur par unité de bande passante. Ce plus petit déplacement est obtenu pour un rapport signal-à-bruit de 1. Pour les capteurs optiques d'ultrasons, cette détectivité dépend aussi de la quantité de lumière collectée de la cible. Pour des puissances collectées raisonnables, les capteurs optiques d'ultrasons sont beaucoup moins sensibles que les transducteurs piézo-électriques [BOL 95]. La sensibilité ultime d'un capteur optique d'ultrasons est obtenue pour une configuration homodyne simple, telle que décrite à la figure 1. On suppose ici que les faisceaux ont des fronts d'onde plan et que le bruit de photon est la source de bruit dominante.

En supposant une bande passante électronique de 1 Hz et une puissance laser collectée de la cible de 1 W afin de comparer différents systèmes, le plus petit déplacement de surface pouvant être mesuré s'écrit :

! lim = " 4# h$ 2% [1]
où λ est la longueur d'onde optique, h la constante de Planck, ν la fréquence optique de l'onde de détection et η l'efficacité quantique du photodétecteur.

Detecteur Oscillateur local

Faisceau signal

Mélangeur

Figure 1. Schéma de la configuration homodyne.

Cette limite de détection est la valeur ultime prévue par la théorie classique i.e. pour des états cohérents de la lumière livrés par les lasers. On peut espérer, en principe, dépasser cette limite en utilisant des états comprimés ou d'autres états nonclassiques de la lumière [CAV 81]. Un capteur optique d'ultrasons se doit évidemment d'avoir une détectivité la plus proche possible de la limite ultime.

La deuxième caractéristique importante du capteur est sa capacité à s'adapter aux fluctuations spatiales et temporelles de la lumière diffusée par les surfaces des matériaux inspectés. Ces surfaces sont en général optiquement rugueuses et diffusent une lumière ayant un front d'onde formé de plusieurs tavelures auquel le capteur doit s'adapter. Cette capacité d'adaptation est caractérisée par l'étendue du capteur, définie par le produit de la surface illuminée de l'objet inspecté et de l'angle solide sous-tendu par le système optique de collection de la lumière. La plupart des systèmes existant, de type homodyne ou hétérodyne, fonctionne avec des ondes planes ou en ne collectant qu'une seule tavelure [MON 86]. Leur étendue est donc limitée à environ λ 2 , conformément au théorème de l'antenne, ce qui correspond à 10 -6 mm 2 •sr pour une longueur d'onde de 1 µm. Pour l'inspection de surfaces rugueuses, on peut utiliser ces dispositifs de faible étendue en limitant l'ouverture de la pupille de collection entraînant ainsi une très faible quantité de lumière collectée et un capteur de faible sensibilité. Une seconde approche consiste à focaliser le faisceau laser sur la surface à inspecter de manière à augmenter la taille des tavelures et à ne collecter qu'une seule de ces tavelures. Cette seconde solution, habituellement préférée en pratique, souffre d'une petite profondeur de champ et d'une quantité de lumière variant fortement d'un point à l'autre de la surface suite à la brillance aléatoire des tavelures.

Des modifications pour accroître l'étendue d'interféromètres de type Michelson ou Mach-Zehnder ont été proposées pour la détection d'ultrasons [MON 86

]. Toutefois, en pratique, l'utilisation d'un interféromètre Fabry-Pérot confocal, multi-passages et de large étendue, s'avère beaucoup plus profitable, ce qui fait que ce type d'interféromètre est maintenant implanté dans l'industrie. L'étendue requise pour un capteur optique d'ultrasons doit typiquement correspondre à celle d'une fibre optique multimode à large coeur utilisé pour transmettre simplement et avec flexibilité la lumière de la surface à inspecter au capteur. Par exemple, une fibre de 1 mm de coeur et d'une ouverture numérique de 0.39 a une étendue de 0.4 mm 2 •sr, ce qui est supérieur de cinq ordres de grandeur à l'étendue des capteurs limitée par le théorème de l'antenne. L'utilisation d'un dispositif à large étendue permet de travailler avec de l'optique de faible qualité et à bas coût puisque le système n'est pas sensible aux aberrations et aux distorsions de phase du front d'onde.

L'adaptabilité aux fluctuations temporelles signifie que le capteur s'adapte ou compense les vibrations mécaniques ambiantes. Le spectre de fréquences de ces vibrations est habituellement inférieur à 10 kHz. Le capteur devrait donc avoir un temps de réponse aux changements de l'ordre de 10 µs afin de ne pas être sensible à ces basses fréquences. De plus, compte tenu des épaisseurs des matériaux inspectés, la mesure des échos ultrasonores dure typiquement quelques dizaines de µs. Il est donc avantageux de faire cette mesure à l'aide d'un laser générant des impulsions de quelques dizaines de µs, plus puissant qu'un laser continu, afin de récolter une plus grande puissance lumineuse de la surface et ainsi accroître la sensibilité. L'utilisation d'un tel laser requiert aussi un temps de réponse du capteur inférieur à la durée de l'impulsion de détection i.e. à nouveau de quelques µs. Finalement, l'utilisation de ce capteur pour l'inspection de surfaces en mouvement, selon l'axe optique ou perpendiculaire à cet axe, ou pour l'inspection avec un laser qui balaie la surface, peut demander un temps de réponse plus court que la dizaine de µs, typiquement de quelques centaines de ns. Ces courts temps de réponse sont aisément obtenus avec un interféromètre de Fabry-Perot confocal. En contrepartie, le capteur est d'autant moins sensible aux basses fréquences ultrasonores de l'ordre du MHz qu'il est rapide. En résumé, en fonction de l'application visée, un capteur devrait avoir une fréquence de coupure d'environ 10 kHz à 1 MHz i.e. un temps de réponse de 100 ns à 10 µs. Idéalement, un temps de réponse ajustable en fonction de l'application serait un atout.

Une autre caractéristiques requise pour le capteur est une large bande passante, s'étendant jusqu'à la centaine de MHz ou plus. Il est à noter que cette large bande de mesure est un avantage de la détection optique d'ultrasons par rapport aux capteurs piézo-électriques. Il serait aussi préférable que le dispositif ait une réponse en fréquence plate, ce qui permet d'obtenir un signal dénué de distorsions et reflétant le mouvement ultrasonore de la surface.

Nous avons présenté les principales caractéristiques attendues d'un capteur optique d'ultrasons. Nous utiliserons ces caractéristiques pour comparer divers capteurs. D'une moindre importance, ajoutons la robustesse, la facilité d'utilisation et une taille et un poids raisonnable. Un capteur munis d'un système de détection différentielle serait aussi avantageux pour éliminer les fluctuations d'amplitude du laser ou l'enveloppe du laser impulsionnel.

Interféromètre adaptatif par mélange à deux ondes

L'interféromètre adaptatif basé sur le mélange à deux ondes a été initialement proposé et testé dans un cristal photoréfractif de BaTiO 3 [ING 91]. Le temps d'écriture de l'hologramme dans ce cristal, typiquement de l'ordre de la seconde, ne permet pas au dispositif de s'adapter aux vibrations ambiantes, même dans un environnement de laboratoire. La sensibilité de l'interféromètre s'en trouve réduite et fluctuante. L'interféromètre a par la suite été testé et analysé, dans les configurations isotropes et anisotropes, avec un cristal de GaAs semi-conducteur [BLO 94]. Les temps d'écriture obtenus sont de l'ordre de quelques dizaines de µs, ce qui est suffisant pour permettre à l'interféromètre de s'adapter aux vibrations ambiantes. Le dispositif a par la suite été développé dans des cristaux semiconducteurs d'InP:Fe mis sous haute tension, afin d'obtenir une sensibilité égale ou supérieure au Fabry-Perot et un temps de réponse suffisamment court pour être utilisable avec un laser de détection impulsionnel (durée typique de l'impulsion 50µs), lequel permet grâce à sa puissance une sensibilité accrue de la technique [DEL 97, BLO 98]. Ces cristaux photoréfractifs semi-conducteurs peuvent être opérés à la longueur d'onde proche infra-rouge de 1.064 µm, bénéficiant ainsi des sources lasers puissantes et très stables, disponibles commercialement à base de Nd:YAG. D'autres gammes de longueur d'onde depuis le visible jusqu'à la longueur d'onde de sécurité oculaire de 1.5µm sont aussi accessibles, avec les mêmes cristaux semi-conducteurs ou des cristaux de la famille des sillénites pour le visible, avec les mêmes propriétés et des performances similaires.

Ces interféromètres adaptatifs sont particulièrement intéressants pour détecter les basses fréquences ultrasonores (en deçà de 2 MHz), seules à être transmises dans les pièces épaisses ou les matériaux très atténuants. Ils sont de plus compacts et peuvent être munis d'un détecteur différentiel qui permet d'éliminer les fluctuations d'intensité du laser et l'enveloppe du laser impulsionnel.

Principe de fonctionnement

Une lame séparatrice à la sortie du laser est utilisée pour créer une onde signal et une onde pompe. L'onde signal est projetée sur la surface à inspecter où elle acquiert une modulation de sa phase à la fréquence des vibrations ultrasonores ainsi qu'une distorsion spatiale de son front d'onde suite à la rugosité de surface. La lumière diffusée par la surface est par la suite collectée par un système optique et mélangée au faisceau pompe à l'intérieur du cristal photoréfractif. Le schéma de principe de ce capteur est présenté à la figure 2. Les deux faisceaux interfèrent et écrivent un hologramme dynamique dans le cristal. A la sortie du cristal, on retrouve l'onde signal transmise par le cristal ainsi que l'onde pompe diffractée par l'hologramme. De par les propriétés de l'holographie, l'onde pompe diffractée a un front d'onde qui est la réplique exacte du front d'onde de l'onde signal. De plus, le temps d'écriture du réseau étant long devant la période des ondes ultrasonores, l'onde pompe est diffractée par un réseau fixe et est dénuée de la modulation de phase associée à l'onde ultrasonore. L'onde pompe diffractée agit donc comme l'onde de référence ou l'oscillateur local de l'interféromètre homodyne ainsi formé. Les deux ondes interfèrent par la suite sur un photodétecteur afin de transformer la modulation de phase en modulation d'un signal électrique.

Figure 2. Principe de fonctionnement du capteur optique d'ultrasons par mélange à deux ondes dans un cristal photoréfractif.

Puisque les deux faisceaux ont des fronts d'onde adaptés, l'interféromètre est doté d'une grande étendue. De plus, le capteur ne requiert pas de stabilisation externe puisque l'hologramme est constamment réécrit et s'adapte aux changements basses fréquences de l'onde signal. Plus précisément, le capteur agit comme un filtre passe-haut, coupant les vibrations de basses fréquences et détectant les vibrations aux fréquences ultrasonores. La fréquence de coupure est donnée par le temps de réponse du milieu holographique, qui dans le cas des matériaux photoréfractifs est inversement proportionnel à la densité de puissance incidente (avec aussi une dépendance mineure avec le champ électrique appliquée au cristal).

Modèle théorique

Le dispositif peut être décrit par un modèle simple. Soit deux ondes de même polarisation, une onde pompe et une onde signal de beaucoup plus faible amplitude, qui écrivent un réseau ou un hologramme dans un cristal photoréfractif. Cet hologramme est un réseau d'indice caractérisé par un gain photoréfractif complexe γ = γ' + i γ", dont les parties réelles et imaginaires représentent les composantes du réseau d'indice respectivement en quadrature et en phase avec la structure d'illumination qui a créé l'hologramme. Supposons une modulation de phase dont la fréquence est grande devant la fréquence de coupure basse du capteur et qui possède une faible amplitude de modulation (ϕ(t)<<π/2), le champ à la sortie d'un cristal d'épaisseur d et d'absorption α s'écrit : [DEL 95]

E d d, t ( ) = e ! "d 2 E d 0,0 ( ) e #d ! 1 ( ) + e i$ t ( ) [ ] [2]
Le premier terme représente l'amplitude de l'onde diffractée i.e l'oscillateur local, et le second terme est associé à l'onde transmise. De cette expression, nous obtenons l'intensité incidente sur le détecteur :

I d d,t ( ) = e !"d I d0 e 2 # $ d + 2e # $ d sin # # $ d ( )% t ( ) [ ] [3]
où I d0 est l'intensité incidente sur le capteur. Cette expression indique tout d'abord que la détection d'une modulation de phase nécessite que la partie imaginaire du gain photoréfractif soit non nulle i.e. que la composante de l'hologramme en phase avec la figure d'illumination soit non nulle, ce qui est l'équivalent de la mise en quadrature du signal et de l'oscillateur local dans une détection homodyne classique. Deuxièmement, nous déduisons de cette expression que l'efficacité de démodulation ne dépend pas du rapport des intensités pompe et signal. En conséquence, le temps de réponse du capteur peut être contrôlé en variant l'intensité pompe, sans incidence sur la détectivité du capteur.

De l'équation 3, on obtient que la limite de détection du capteur s'écrit :

! = ! lim ! rel = " 4# h$ 2% e &d 2 sin ' ' ( d [4]
Dans la limite d'une absorption nulle et d'un gain optimum (γ''d= π/2), on obtient une limite de détection relative δ rel de 1, telle qu'attendue d'un système de détection idéal. En pratique, l'écriture de réseaux photoréfractifs nécessite l'absorption de photons afin de créer les porteurs libres qui sont repiègés ailleurs dans le cristal. On peut toutefois s'approcher de la détection idéale en utilisant un cristal ayant une absorption faible et satisfaisant la condition de gain optimum. Il est aussi à noter que le temps d'écriture du réseau est proportionnel à l'absorption du cristal et avec un temps de réponse trop long, le réseau ne peut s'adapter aux vibrations ambiantes. Ainsi la valeur de l'absorption optimum résulte d'un compromis entre la détectivité et le temps de réponse.

Nous avons décrit la configuration la plus simple du capteur d'ultrasons par mélange à deux ondes mais plusieurs autres configurations sont possibles [DEL 97]. Une configuration opérant avec des faisceaux dépolarisés a aussi été proposée [DEL 99].

Performances du capteur

Nous avons effectué des études avec des cristaux semi-conducteurs de GaAs, d'InP:Fe et de CdTe:V à des longueurs d'onde du proche infrarouge de 1 à 1.55 µm. Les meilleurs résultats ont été obtenus avec des cristaux de CdTe:V sous tension [DEM 97]. La figure 3 présente les résultats théoriques et expérimentaux obtenus.

L'étendue du dispositif est déterminée par l'angle entre les faisceaux signal et pompe et par la taille du cristal. Pour les valeurs de cet angle permettant d'optimiser la détectivité du capteur et pour un cristal de quelques millimètres de côtés, l'étendue obtenue est typiquement de l'ordre de 1 mm 2 sr. Cela permet d'utiliser une fibre multimode de large coeur et de grande étendue pour amener la lumière collectée de la cible au capteur (Fig. 4). En ce qui a trait au temps de réponse, des temps de réponse de l'ordre de la centaine de µs sont possibles avec des lasers continus, ce qui est satisfaisant pour certaines applications. En utilisant un laser impulsionnel des temps de réponse de l'ordre de 1µs avec tension appliquée et 100 ns sans tension ont été obtenus, ce qui permet au capteur de s'adapter aux vibrations rencontrées en industrie. Notons qu'un temps de réponse de 1 µs correspond à une fréquence de coupure d'environ 100 kHz. Néanmoins, ces temps de réponse ne sont pas suffisants pour s'adapter aux

Figure 3 .

 3 Figure 3. Courbe théorique et points expérimentaux indiquant la détectivité du capteur en fonction du rapport du gain photoréfractif sur l'absorption. La limite de détection idéale ainsi que la limite de détection d'un Fabry-Perot confocal (CFPIR) utilisé en mode réflexion sont indiquées sur la figure.

  variations d'une cible que se déplace rapidement et limite la vitesse possible de balayage d'une pièce. Le Fabry-Perot confocal est par contre beaucoup plus rapide, le temps d'adaptation du Fabry-Perot étant à peu près égal au produit de la finesse par le temps d'aller-retour dans le Fabry-Perot. Par exemple, pour un Fabry-Perot confocal de 1 m ayant une finesse de 10 i.e. des miroirs de 85 % de réflectivité, le temps de réponse est d'environ 70 ns.

Figure 4 .

 4 Figure 4. Réponses en fréquence du capteur photoréfractif et du Fabry-Perot obtenus pour des faisceaux tavelés. La limite de détection relative obtenue est proche de celle obtenue avec des ondes planes (Fig. 3).

Figure 5 .Figure 6 .

 56 Figure 5. Schéma de la pièce de graphite-epoxy. Les nombres indiquent la distance entre la surface plate de la pièce et le fond du trou à fond plat.

Figure 7 .

 7 Figure 7. Signal ultrasonore engendré dans une plaque de silice par un laser eximère. A : forme temporelle du signal, B : zoom de A.où l'on voit l'impulsion optique UV et le premier écho ultrasonore.

  [MON 86]. Pour qu'un interféromètre soit insensible aux tavelures, il doit avoir une grande étendue. L'interféromètre de Fabry-Perot confocal, utilisé en transmission ou réflexion, proposé il y a plusieurs années est désormais un moyen bien accepté [MON 86a, MON 89]. L'interféromètre fonctionne comme un filtre optique qui démodule la modulation de fréquence ou de phase présente dans la lumière diffusée.Une autre approche permettant l'insensibilité aux tavelures est basée sur l'holographie en temps réel dans des cristaux photoréfractifs. Plusieurs approches ont été proposées dont le mélange à deux ondes [ING 91, BLO 94], la double conjugaison de phase [DEL 95a], l'auto-modulation de la polarisation [KAM 00] ou utilisant la force photo-électro-motrice transitoire [PET 90]. On réalise ainsi un interféromètre adaptatif qui s'adapte aux tavelures et aux perturbations ambiantes.

	Nous décrivons dans cet article, les caractéristiques d'un interféromètre adaptatif
	pour la mesure des ultrasons basé sur le mélange à deux ondes dans un cristal
	photoréfractif et donnerons quelques exemples d'applications de ce capteur. Nous
	comparons aussi ses performances à celles du Fabry-Perot confocal.