Bastian Joachim-Mrosko

Tatsuhiko Kawamoto
email: kawamoto.tatsuhiko@shizuoka.ac.jp

Hélène Bureau
email: helene.bureau@upmc.fr

Experimental and Observational Constraints on Halogen Behavior at Depth

Keywords: element partitioning, volatiles, degassing, subduction, fluid inclusions

Halogens are volatile elements present in trace amounts in the Earth's crust, mantle, and core. Except for fluorine, they show volatile and incompatible behavior, which makes them key tracers of fluidmediated and/or melt-mediated chemical transport processes. Even small quantities of halogens can profoundly affect many physicochemical processes such as melt viscosity, the temperature stability of mineral phases, the behavior of trace elements in aqueous fluids, or the composition of the atmosphere through magma degassing. Experiments allow us to simulate deep-Earth conditions. A comparison of experimental results with natural rocks helps us to unravel the role and behavior of halogens in the Earth's interior.

INTRODUCTION

Halogens are present in the deep Earth as volatile trace elements. Whereas fluorine is relatively abundant in crustal rocks (~550 ppm), as is chlorine (~240 ppm), bromine and iodine are more than three orders of magnitude lower (<1 ppm). In the Earth's primitive mantle, the halogens are present in low concentrations, ranging from 7 ppb for iodine to 25 ppm for fluorine, with even lower concentrations in the depleted mantle. In contrast, the halogens are relatively enriched in the outer reservoirs of the Earth, e.g., ~2 wt% Cl in seawater and ~28 ppm iodine in marine sediments (Pyle and Mather 2009 and references therein).

The heavy halogens (chlorine, bromine, and iodine) behave incompatibly in most minerals due to their large ionic radius, and they partition preferentially into melts or fluids. Their distribution is influenced by fluid mobility, crystal fractionation, degassing, and partial melting, which makes them excellent tracers for volatile transport processes in the deep Earth. Fluorine, the lightest halogen, shows a more compatible and rather lithophile behavior due to its smaller ionic radius, which is comparable to that of an OH group. As a consequence, F and the heavy halogens decouple during fluid-mediated metamorphic reactions and magmatic differentiation. Knowledge of the behavior, abundance, and distribution of F and the heavy halogens can help us to better understand the mechanisms that control the origin, distribution, and transport of volatiles in the deep Earth and the complex processes during subduction and recycling of oceanic lithosphere.

Here, we discuss the importance of the halogens by examining experimental challenges and by reviewing pioneering studies on the halogen abundance, distribution, and behavior. This review will focus on the application of experimental studies to four topics corresponding to different halogen-bearing reservoirs in the deep Earth: [START_REF]Experimental partitioning of F and Cl between olivine, orthopyroxene and silicate melt at Earth's mantle conditions[END_REF] the behavior of halogens in magmas; (2) the constraints on halogen transport and storage in silicate minerals; (3) halogens in fluids, with implications for their recycling in subduction zone settings; (4) halogens in metallic phases, including the first constraints on their abundance in the Earth's core.

EXPERIMENTAL CHALLENGES

Microthermometry uses a heating and cooling stage under an optical microscope. This method can characterize fluid inclusions, under the assumption that there is a constant volume that will reestablish itself to the original pressure during experimental heating. High-temperature furnaces at atmospheric pressure are used to study silicate melts, the assumption being that the effect of pressure on the studied process (e.g., melt viscosity) may be negligible [START_REF] Dingwell | Melt viscosities in the system Na-Fe-Si-O-F-Cl: contrasting effects of F and Cl in alkaline melts[END_REF].

In contrast, the study of magmatic processes requires reproducing the pressure (P) and temperature (T) conditions relevant to those of magma chambers and conduits. Most of the experiments that study halogen partitioning between fluids, melts, and minerals, and their solubility in these magmatic phases, are performed in a large variety of high-P-high T apparatuses, such as rapid quench cold-seal pressure vessels (up to a few GPa and up to 1,200 °C; i.e., [START_REF] Bureau | Volcanic degassing of bromine and iodine: experimental fluid/melt partitioning data and applications to stratospheric chemistry[END_REF] or piston cylinders (0.5-5 GPa, up to 1,600 °C).

These experimental setups come with two major limitations. First, they usually last only hours or days, which is orders of magnitude shorter than natural processes. Second, experiments have to be quenched (cooled down) as fast as possible in order to preserve the volatiles (i.e., the halogens and water) and the silicates that were dissolved in the fluid phases during the experiment. It is often assumed that the halogen concentrations in a glass, which represents a quenched melt, reflects the respective equilibrium concentrations at a designated P and T. Today, we know that this approach is not accurate for the investigation of fluid properties, which requires that volatile species are monitored in situ at high-P and high-T. A new generation of experiments has been proposed that can associate specific high-P tools, such as diamond anvil cells (up to a few GPa and up to 1000 °C) and combine these with in situ characterizations (e.g., Bureau et al. 2016).

Another challenge is the analysis of heavy halogens in small experimental samples. Conventional analytical methods require crystal sizes with a diameter of at least several tenths of micrometers.

This can be achieved with the addition of small crystal nuclei to the starting material [START_REF] Dalou | Experimental determination of F and Cl partitioning between lherzolite and basaltic melt[END_REF], slow cooling [START_REF] Beyer | Fluorine in nominally fluorine-free mantle minerals: experimental partitioning of F between olivine, orthopyroxene and silicate melts with implications for magmatic processes[END_REF], or deliberate temperature-cycling around the target temperature. Potential methods to assess, if these crystals were in equilibrium with the surrounding melt are (1) euhedral, monocrystalline, and inclusion-free crystal shapes; (2) a homogeneous majorelement distribution between crystals and melts; (3) partition coefficients that are identical at varying crystal growth rates [START_REF]Experimental partitioning of F and Cl between olivine, orthopyroxene and silicate melt at Earth's mantle conditions[END_REF].

HALOGENS IN MAGMAS

The Role of Halogens in Crustal Magmatic Systems

Fluorine and chlorine were the first halogens to be analyzed in volcanic glasses and rocks because of their relatively high abundances. They have been the subject of numerous studies since the 1980s.

During the last two decades, the role of bromine and iodine in magmatic processes has also been studied thanks to methodological advances, including in situ chemical analyses and satellite monitoring. Over the last few decades, databases that can correlate halogen concentration and distribution with depth in the Earth have been established (see [START_REF] Pyle | Halogens in igneous processes and their fluxes to the atmosphere and oceans from volcanic activity: a review[END_REF]. Experimental studies of the role of the halogens in magmatic processes include determining their solubilities in melts; their partitioning behavior between fluids, silicate melt, and mineral phases; chemical differentiation during mineralization; and their effects on the physical properties of magmas.

Experimental constraints on halogen properties in silicate melts

The term solubility refers to the maximum amount of halogens that can be dissolved in a silicate melt that is saturated with an immiscible aqueous fluid + brine assemblage at a given set of conditions [START_REF] Carroll | Chlorine solubility in evolved alkaline magmas[END_REF]) (FIG 1A). Partitioning is defined by the Nernst-type partition coefficient D between two phases, for example between an aqueous fluid (f) and a melt (m) (Dhalogen f/m ). Halogens also fractionate into minerals from melt during crystallization. Vapor-liquid immiscibility processes have been observed at magmatic conditions, mostly for Cl (FIG. 1B). Indeed, depending upon the bulk halogen concentration, a silicate melt can coexist with variable phases: a low-density aqueous phase (vapor); a vapor-liquid mixture; solid salts; and a liquid, also called a high-density hydrous phase or a hydro-saline liquid.

Many studies have measured the solubility of chlorine in hydrous felsic melts at pressures and temperatures relevant for crustal conditions (e.g., [START_REF] Webster | Chloride solubility in felsic melts and the role of chloride in magmatic degassing[END_REF][START_REF] Carroll | Chlorine solubility in evolved alkaline magmas[END_REF] and references therein). Both, Cl and F solubilities in magmatic melts depend on the Al content, Na/Si ratio, and on network-modifier alkalis (FIG. 1A). Whereas chlorine is mainly associated with the networkmodifying cations Al, Na, and K, fluorine forms complexes with Al and Na. Dissolved water has a strong effect on the silicate melt structure. The solubility of F increases with increasing water content, while the solubility of Cl decreases (FIG. 1B) [START_REF] Dalou | The effect of H2O on F and Cl solubility and solution mechanisms of in aluminosilicate melts at high pressure and high temperature[END_REF].

Solution mechanisms established for Cl are also found for Br [START_REF] Bureau | An experimental study of bromine behaviour in water-saturated silicic melts[END_REF], and their solubilities are comparable in felsic melt compositions (FIG. 1A). Iodine shows a similar solubility despite its larger ionic size [START_REF] Leroy | Xenon and iodine behaviour in magmas[END_REF], which opposes the expectation that the four halogens exhibit a systematic change in solubility in chemically identical melts depending on their ionic radii.

In fact, the three heavy halogens have the capacity to be incorporated at similar concentrations in hydrous silicate melts (FIG. 1A). Fluorine, the smallest halogen, is the most compatible in silicate melts and has the highest solubility (e.g., Dalou and Mysen 2015 and references therein).

Several experimental observations illustrate that the effect of F and Cl in petrogenesis. For example, the presence of ≥1 wt% F in a diopside melt causes a depression of the liquidus temperature that is of similar magnitude to that of dissolved water, and the addition of F to depolymerized liquids increases that liquid's viscosity [START_REF] Dingwell | Melt viscosities in the system Na-Fe-Si-O-F-Cl: contrasting effects of F and Cl in alkaline melts[END_REF]. In polymerized peraluminous or peralkaline melts, the extent to which dissolved water decreases viscosity is suppressed due to the presence of dissolved F and Cl (Baasner et al. 2013 and references therein). Small amounts of dissolved chlorine can lower the liquidus temperature of basaltic melts. Chlorine also forms complexes with Fe, and perhaps Mg and Ca, in basaltic melts, which increases silica activity and stabilizes pyroxene against olivine (Filiberto and Treiman 2008).

Experiments also reveal the strong affinity of Cl to form complexes with ore metals and trace elements that preferentially partition into hydrothermal fluids and are responsible for mineralization. Halogen behavior during magma degassing can be controlled either by partitioning into vapor/aqueous fluid phases or by saturation of a halogen-bearing mineral phase. Halogen behavior in immiscible brine is probably controlled by saturation processes alone (see Shinohara 2009 for Cl).

Experimental Constraints on Volcanic Degassing of Halogens

The exsolution of magmatic volatiles is a key process in volcanic systems, because it drives magma differentiation, crystallization, ascent, and eruption. Locally, it also drives hydrothermal alteration and mineralization. Because halogens are lost from magmatic melts through degassing, the best constraints on their initial melt concentrations are through the analyses of melt inclusions trapped in crystals.

The impact of volcanic degassing of halogens on atmospheric chemistry is one important justification for experimental research on halogen behavior in magmas. For example, estimates of halogen fluxes into the oceans and atmosphere are based on measurements from fumaroles and plumes, and mass-balance calculations between melt inclusions and volcanic glasses. However, these calculations require knowledge of the partitioning behavior of halogens between silicate melts and fluids at magmatic conditions. Early experimental studies have shown that Cl partitions strongly into fluids (i.e., large DCl f/m ) [START_REF] Webster | Experimental constraints on the partitioning of Cl between topaz rhyolite melt and H2O and H2O + CO2 fluids: new implications for granitic differentiation and ore deposition[END_REF]. For example, in the topaz-rhyolite-H2O ± CO2 ± F system at 0.5-5 kbar and 725-950 °C, the DCl f/m ranges from 2 to 130. The Dhalogen f/m may approach unity as the miscibility gap is closed between melt and an aqueous fluid (Bureau et al. 2016).

Although F, the most compatible halogen in silicate melts, exhibits late degassing at shallow depths, the heavier halogens experience early degassing, which is enhanced by the presence of water [START_REF] Bureau | Volcanic degassing of bromine and iodine: experimental fluid/melt partitioning data and applications to stratospheric chemistry[END_REF](Bureau et al. , 2016)). In felsic melts (e.g., albitic melts), Dhalogen f/m increases with increasing ionic radius at 0.2 GPa and 900 °C: 8.1 ± 0.2 for Cl, 17.5 ± 0.6 for Br, and 107 ± 7 for I [START_REF] Bureau | Volcanic degassing of bromine and iodine: experimental fluid/melt partitioning data and applications to stratospheric chemistry[END_REF] (FIG. 1C). Despite their low concentrations in silicate melts, Br and I can, nevertheless, be released into the atmosphere, as confirmed by measurements from volcanic plumes.

Combining natural halogen abundances with experimentally derived partition coefficients enables the calculation of volcanic halogen input to the atmosphere. Experimentally combining fluid-meltmineral phase equilibria at magmatic pressure-temperature conditions with in situ characterization (i.e., by synchrotron radiation X-ray fluorescence, and/or by Raman and infrared spectroscopy) is a powerful tool to understand halogen behavior in magma chambers and volcanic conduits because it avoids quench modifications (FIG. 2). This experimental approach established the extreme efficiency of water to wash out Br and I from hydrous silicate melts and their significant input to the atmosphere during magma ascent (e.g., Bureau et al. 2016 and references therein), and also applies to the study of recycling processes of volatiles in subduction zones (i.e., slab burial).

HALOGENS IN SILICATE MINERALS

Mid-ocean-ridge basalt (MORB) and ocean island basalt (OIB) can provide sources of information for the abundance and distribution of halogens in the Earth's mantle, because they represent partial melts that originate from different mantle sources and depths. Elemental ratios (e.g., Cl/K or F/P) have long been used to determine respective halogen concentrations in different source regions and still offer a reliable and important database (Pyle and Mathers 2009 and references therein). Here, the focus is on recent experimental and analytical developments that allow the investigation of fluorine and chlorine partitioning behavior between silicate melt and residual minerals at the P-T conditions where the mantle partially melts. These provide an independent approach to estimate halogen concentrations in these mantle source regions.

The major residual minerals that remain in the mantle after partial melting are olivine and pyroxene.

Temperature strongly affects the partitioning behavior of halogens between olivine (ol) and a silicate melt (Dhalogen ol/m ). As an example, DF ol/m increases by about two orders of magnitude from ~0.003 at 1,350 °C [START_REF] Beyer | Fluorine in nominally fluorine-free mantle minerals: experimental partitioning of F between olivine, orthopyroxene and silicate melts with implications for magmatic processes[END_REF]) to ~0.3 at 1,600 °C [START_REF]Experimental partitioning of F and Cl between olivine, orthopyroxene and silicate melt at Earth's mantle conditions[END_REF]. The DF ol/m also increases linearly with increasing dissolved water in the silicate melt [START_REF]Effect of water on the fluorine and chlorine partitioning behavior between olivine and silicate melt[END_REF], which is not the case for DCl ol/m . The effect of pressure on fluorine and chlorine partitioning behavior seems to be negligible in the upper mantle. Halogen partition coefficients between the pyroxenes and silicate melt are usually greater than those between olivine and a melt. Fluorine partitioning between orthopyroxene and melt seems to be largely independent of the crystal chemistry and correlates positively with increasing melt polymerization, whereas initial results suggest that the increase of a jadeite component (NaAlSi2O6) in orthopyroxene and the increase of a calcium tschermakite (CaAlAlSiO6) component in clinopyroxene can promote Cl incorporation [START_REF] Dalou | Experimental determination of F and Cl partitioning between lherzolite and basaltic melt[END_REF]). These experimentally derived halogen-partitioning data allow the concentrations of halogens in MORB and OIB mantle source regions to be calculated based on a simple batch melting model, which neglects degassing of halogens during ascent and eruption of the basalts because of the relatively low volatile concentrations in MORBs and OIBs [START_REF] Beyer | Fluorine in nominally fluorine-free mantle minerals: experimental partitioning of F between olivine, orthopyroxene and silicate melts with implications for magmatic processes[END_REF][START_REF]Experimental partitioning of F and Cl between olivine, orthopyroxene and silicate melt at Earth's mantle conditions[END_REF][START_REF]Effect of water on the fluorine and chlorine partitioning behavior between olivine and silicate melt[END_REF].

A comparison of the halogen concentrations in the MORB source region with primitive mantle estimates indicates that the upper mantle is degassed and relatively homogeneous with respect to fluorine and chlorine. In contrast, the fluorine and chlorine concentrations in the OIB source region are heterogeneous and show a significant enrichment in fluorine relative to the primitive mantle, which indicates substantial fluorine recycling and partial separation between fluorine and the heavy halogens during the subduction of oceanic lithosphere into deeper mantle regions.

Serpentinization and deserpentinization of peridotite play a crucial role for volatile transport of the heavy halogens in subduction zones. After deserpentinization, most of the heavy halogens are likely to be transported via fluids (and through melts if supersolidus temperatures are reached) to the overriding mantle wedge due to their hydrophilic nature. Fluorine will more likely be transported in mineral phases because of its lithophile behavior. An important fluorine-and water-bearing mineral in subducting oceanic crust is amphibole, which can retain significant quantities of fluorine in the solid residue, so leading to substantial F/Cl fractionation during partial melting (Van den Bleeken and Koga 2014). Other minerals that may lead to halogen recycling into the mantle through subduction and a partial fluorine-heavy halogen separation in the subducting slab are olivine, humite group minerals, garnet, apatite, lawsonite, phlogopite, and phengite.

In the Earth's mantle, potentially important hosts for the halogens are the hydrous minerals apatite and humite, although their abundance can be limited by available concentrations of phosphorus and titanium, respectively. Nominally anhydrous minerals (NAMs) are another potentially important host due to their large modal abundance. An example is olivine, which is the most abundant mineral in the upper mantle. Experimental results show that olivine may contain hundreds of ppm of Cl (170 ppm) [START_REF] Dalou | Experimental determination of F and Cl partitioning between lherzolite and basaltic melt[END_REF]. A combination of high P-high T experiments and first-principle calculations shows that fluorine and water are clumped and associated with Si vacancies in the crystal structure of forsterite, resulting in fluorine solubilities of up to ~1,715 ppm at 2 GPa and 1,250 °C (Crépisson et al. 2014). This implies that significant amounts of associated F and OH have the potential to be stored in the upper mantle and can be recycled into deeper mantle regions in the peridotite layer at the bottom of subducting plates. At depths of the transition zone (410-670 km), which represents the zone between the upper and lower mantle, olivine becomes unstable and is transformed into wadsleyite (Wd) and ringwoodite (Rw), whose fluorine solubilities decrease with increasing water concentrations. These minerals may not only store significant amounts of fluorine but also up to 200 ppm (Wd) and 113 ppm (Rw) chlorine in hydrous systems [START_REF] Roberge | Chlorine in wadsleyite and ringwoodite: an experimental study[END_REF]. This implies that the transition zone can be a significant repository for fluorine and the heavy halogens in the Earth's mantle. Bridgmanite (Brg) is another potential host for fluorine in the deep Earth, having a solubility of >8,000 ppm in aluminous and water-bearing systems at 1,800 °C and 25 GPa. However, in Al-free and water-free systems, Brg exhibits fluorine contents below 50 ppm at identical P-T conditions [START_REF] Yoshino | Fluorine solubility in bridgmanite: a potential fluorine reservoir in the Earth's mantle[END_REF].

If substantial amounts of halogens are recycled from the surface and stored in the Earth's upper mantle, the transition zone, and perhaps the lower mantle, these may have an effect on physicochemical properties. For example, the presence of fluorine has the potential to increase the stability of mineral phases, such as clinohumite, to higher temperatures [START_REF] Grützner | The role of F-clinohumite in volatile recycling processes in subduction zones[END_REF].

Fluorine-rich phlogopite may produce electrical anomalies in the upper mantle, thus challenging the assumption that high electrical conductivity zones are always related to the presence of partial melts, aqueous fluids, saline fluids, graphite, or sulfides [START_REF] Li | Unusually high electrical conductivity of phlogopite: the possible role of fluorine and geophysical implications[END_REF].

HALOGENS IN MANTLE FLUIDS

Chlorine is observed in arc volcanic gasses as a form of hydrochloric acid, with an abundance that follows water, carbon dioxide, and sulfur dioxide/hydrogen sulfide. The enrichment of alkaline, alkaline earth elements, and Pb is characteristic for subduction-zone basalts compared to MORB and has been attributed to "slab-derived components". Chlorine, present in aqueous fluids in the form of (Na, K)Cl, has a strong effect on the partition coefficient of these enriched elements between aqueous fluid and andesitic melt. This was first shown by quench experiments [START_REF] Keppler | Constraints from partitioning experiments on the composition of subductionzone fluids[END_REF] and later verified in situ using an externally heated diamond-anvil cell combined with synchrotron radiation X-ray fluorescence (FIG. 2) [START_REF] Kawamoto | Large-ion lithophile elements delivered by saline fluids to the sub-arc mantle[END_REF]. The partition coefficient of Pb between saline fluid and melt increases by more than one order of magnitude compared to that between pure H2O fluid and melt (FIG. 3A). A similar effect is observed for alkaline elements (Rb) and the alkaline earth elements (Sr), which show enhanced partitioning into saline fluids. Geochemical systematics suggest that the ingredients of arc magmas are a mantle peridotite component, a slab-derived aqueous fluid component, and a slab-derived melt component (FIG. 3B). FIGURE 3A and 3B indicate that slab-derived fluids are saline fluids that contain Pb, alkaline, and alkaline earth elements, whereas slab-derived melts contain the fluid-insoluble elements Th, Ta, P, Zr, Hf, Y, and the rare earth elements.

Fluid inclusions are locally observed in mantle peridotite xenoliths and high-pressure metamorphic rocks [START_REF] Kawamoto | Mantle wedge infiltrated with saline fluids from dehydration and decarbonation of subducting slab[END_REF][START_REF] Kawamoto | Fluid inclusions in jadeitite and jadeiterich rock from serpentinite mélanges in northern Hispaniola: trapped ambient fluids in a cold subduction channel[END_REF]. Raman microscopy shows that the fluid inclusions are composed of aqueous solutions and vapor bubbles. Findings of magnesite-bearing saline fluid inclusions in tremolite-bearing harzburgite xenoliths from Mount Pinatubo Volcano (Philippines) suggest the presence of H2O-CO2-NaCl fluids at high-pressure and high-temperature conditions. This discovery led to the hypothesis that seawater-like saline fluids are present in the mantle wedge beneath the Philippine volcanic arc (FIG. 3C) [START_REF] Kawamoto | Mantle wedge infiltrated with saline fluids from dehydration and decarbonation of subducting slab[END_REF]. The presence of tremolite indicates P-T conditions of <830 °C at 0.9 GPa, which is above the temperature stability of serpentine minerals and talc and below the solidus temperature of H2O-saturated mantle peridotite.

Thus, the P-T conditions that stabilize tremolite allow excess H2O to exist as aqueous fluids in the mantle wedge.

Microthermometry on fluid inclusions in mantle xenoliths and metamorphic rocks from various arcs allows an estimate of the NaCl equivalent concentrations in the entrained rock: 5.1 ± 1 wt% in the harzburgite beneath Mount Pinatubo Volcano; 3.7 ± 1 wt% in lherzolite beneath Ichinomegata Volcano; 4.5 ± 1 wt% in jadeitite and jadeite-bearing rocks in the suprasubduction zone of the Dominican Republic; and 3-7 wt% in the high-pressure metamorphic rocks of the southwest Japan arc (e.g., [START_REF] Kawamoto | Mantle wedge infiltrated with saline fluids from dehydration and decarbonation of subducting slab[END_REF]Kawamoto et al. 2018) (FIG. 4). This suggests that subduction-zone fluids are slightly more saline than present seawater (3.5 wt% NaCl). Rare-gas and heavy-halogen systematics show that the fluid inclusions in mantle xenoliths from Mount Pinatubo have chemical features similar to sedimentary pore-fluids and to serpentinite, both of which are enriched in iodine through the decomposition of subducted organic materials [START_REF] Kobayashi | Slab-derived halogens and noble gases illuminate closed system processes controlling volatile element transport into the mantle wedge[END_REF]. This implies that subduction-zone fluids are probably produced through hydration and dehydration processes during seawater-oceanic plate interactions and inherit their sedimentary signature possibly through the dehydration of serpentinites.

Experimental studies suggest that saline (i.e., halogen-bearing) fluids not only enhance the dissolution of metals but also that of carbonate [START_REF] Newton | Experimental determination of calcite solubility in H2O-NaCl solutions at deep crust/upper mantle pressures and temperatures: implications for metasomatic processes in shear zones[END_REF]. For example, 10 wt% NaCl-bearing fluids can dissolve more than double the amount of carbonate at 800 °C and 1 GPa. This shows the importance of being salty in subduction zone fluids for the enhancement of elemental transfer. Experiments and natural observations indicate the presence of H2O-CO2-NaCl fluids in the mantle wedge (e.g., [START_REF] Kawamoto | Mantle wedge infiltrated with saline fluids from dehydration and decarbonation of subducting slab[END_REF], although CO2 is less common in fluid inclusions in the high-pressure metamorphic rocks that originate from subduction channels, the interplate boundary layers composed of oceanic crust and serpentinites at the base of the mantle wedge (e.g., [START_REF] Kawamoto | Fluid inclusions in jadeitite and jadeiterich rock from serpentinite mélanges in northern Hispaniola: trapped ambient fluids in a cold subduction channel[END_REF]. Isotopic investigation of the carbon in magnesite found in fluid inclusions within mantle xenoliths may be useful for understanding the transfer of carbon in subduction channels and the mantle wedge.

HALOGENS IN METALLIC PHASES

During core formation, which occurred early in Earth's history during the ~100 My interval after the initial solar nebula processes, the partitioning behavior between Earth's silicate mantle and crust and the metal core controlled the elemental distribution between these reservoirs. Whereas chlorine seems to be largely lithophile and remains in the silicate melt, iodine exhibits mildly siderophile behavior, indicating that the core could be a significant iodine reservoir containing up to 82% of the bulk Earth's budget (Armytage et al. 2013 and references therein).

FUTURE PERSPECTIVES

To date, available studies strongly indicate that the transport of water and halogens into the deep Earth are closely linked, either through halogen-bearing aqueous and/or fluids or through the combined incorporation of OH groups and halogens in hydrous or nominally anhydrous minerals. This implies that a better understanding of the halogen behavior and distribution in the solid Earth is of fundamental importance for understanding the deep volatile cycle and its effects on physicochemical processes. This, in turn, will give a deeper insight into the role of halogens during the origin and evolution of our planet.

Carefully designed experiments to identify the key halogen-carrier phases in the crust, subducting slab, and mantle, are needed to better understand the halogen-incorporation mechanisms in minerals and melts, halogen speciation in fluids and melts, and to quantify their distribution, mobility, and release through partitioning or degassing at depth. The unquenchable properties of deep fluids/melts will require the novel use of in situ characterization techniques (i.e., infrared spectroscopies, X-ray characterization) combined with either laser-heated diamond anvil cells or any optical or X-ray-transparent high-pressure devices. These experimental strategies must be associated with new analytical tools, such as synchrotron X-ray fluorescence using nanoscale beams.

Conventional setups will remain relevant to investigate processes and properties in the Earth's mantle, such as the solubilities of halogens in mineral phases, and mineral-melt partitioning of the heavy halogens. These will require the development of analytical techniques that allow for the precise analysis of Cl, Br and I down to the parts-per-billion level with high spatial resolution to analyze them in individual phases.

FIGURE CAPTIONS

FIGURE 1 (

 1 FIGURE 1 (A) Representative solubility data for Cl, Br, and I versus (A/CNK)/Si [molar (Al2O3/(CaO + Na2O + K2O)/SiO2] determined using similar experimental protocols at water saturation (except for I): 0.1-0.4 GPa and 900-1,400 °C for felsic (open symbols) and mafic (closed symbols) melts. Blue triangles = Cl; red squares = Br; orange circles = I. Data for Br and I are limited; nevertheless, the diagram illustrates that Cl, Br, and I a similar solubility mechanism in felsic melts at a comparable range of pressures and temperatures. In mafic melts (i.e., basalts), Cl (closed blue triangles) may have a higher solubility compared to I. (B) Phase relations in the silicate melt-water-Cl system between 800 °C (low temperature, LT) and 1,700 °C (high temperature, HT). The curves delimit isobaric solubilities of saturated magmatic volatile phases and silicate melts. They show that small quantities of Cl have a dramatic effect on volatile phase exsolution. The curves designate the H2O and Cl solubilities and delimit the stability of silicate melt, melt-plus-vapor (or low-density gas), melt-plus-liquid (or brine), and melt-plus-vapor-plus-liquid. The light curves express the volatile solubilities and phase relations at comparatively lower temperatures. The H2O solubility varies only minimally as the melt composition changes from felsic to mafic at constant pressure. The Cl solubility in H2O-poor melts increases by an order of magnitude. The strong relationship between melt composition and Cl solubility implies that the chemical evolution of magma from mafic to more felsic composition enhances the role of Cl in driving volatile phase exsolution. The dotted red curve represents the Cl in a haplogranite (HGR solubility curve at 0.05 GPa, illustrating the strong pressure effect on Cl solubility. (C) Fluid/melt partition coefficients (D f/m , where D = partition [i.e., distribution] coefficient, f = fluid, m = melt) of halogens versus their ionic radius in the albite-water system at 900 °C and 0.2 GPa. REFERENCES FOR DATA IN ONLINE SUPPLEMENT.

FIGURE 2

 2 FIGURE 2 (A) Experimental setup of Synchrotron Soleil's DIFFABS ('diffraction/absorption') beamline (France). The hydrothermal diamond anvil cell (DAC) is aligned to the high energy (17 keV) X-ray beam. Synchrotron radiation X-ray fluorescence (XRF) is detected with a Si-drift detector. The experiment is monitored through an optical microscope. (B) Diagrammatic section through the DAC during an experiment at high pressure and temperature. Globules of silicate melt are in equilibrium with an aqueous fluid in the sample chamber. Because the X-ray beam can cross the DAC, the halogen content in the melt and fluid phases can be quantified simultaneously. (C) Scanning electron microscope (SEM) image of the sample chamber after quenching.

FIGURE 3

 3 FIGURE 3 (A) Partition (distribution) coefficients (D fluid/melt ) of Pb, Rb, and Sr between aqueous fluids and coexisting haplogranite (HGR) or jadeite (Jd) melts as a function of pressure. Open symbols denote a Cl-free system; filled symbols denote systems with 5 mole (Na, K)Cl/kg. (B) Schematic diagram of trace element concentrations in arc basalts normalized to mid-ocean-ridge basalt (MORB). Aqueous fluid-and melt-like components are attributed to aqueous fluids and sedimentderived melts or supercritical fluids from subducted oceanic plate, respectively. (C) Fluid inclusion composed of saline solution (H2O L ), vapor (H2O V ), and magnesite (Mgs) in an olivine from a tremolitebearing harzburgite xenolith collected from a pyroclastic flow from the Mount Pinatubo (Philippines) eruption of 1991. REFERENCES FOR DATA IN ONLINE SUPPLEMENT.

FIGURE 4

 4 FIGURE 4 Salinity map of subduction-zone fluids. Symbol: % NaCl = wt% NaCl-equivalent. Arima-Takarazuka (Japan) is a hot spring in the forearc region and is characterized by high 3 He/ 4 He ratios suggesting its deep mantle origin. Aqueous fluids with 4.5 % NaCl and 3-7 % NaCl are observed in jadeite-rich rocks formed in subduction channels of Dominican Republic and Southwest Japan arc, respectively. REFERENCES FOR DATA IN ONLINE SUPPLEMENT.

Figure 1 Figure 2 Figure 3 Figure 4

 1234 Figure 1

Acknowledgements

We thank D. Baker and K. Koga, who provided valuable reviews that significantly improved the quality of this article. We also thank P. Clay, H. Sumino, R. Lange and J. Rosso for careful editorial handling.


Marine Vernet
email: marine.vernet@espci.org

Qing Yang

Marie Gruselle

Mareike Trams

Zoï Kapoula
email: zoi.kapoula@egp.aphp.fr

Switching between gap and overlap pro-saccades: cost or benefit?

Triggering of saccades depends on the task: in the gap task, fixation point switches off and target appears after a gap period; in the overlap task, target appears while fixation point is still on. Saccade latencies are shorter in the gap task, due to fixation disengagement and advanced movement preparation during the gap. The two modes of initiation are also hypothesized to be subtended by different cortical-subcortical circuits. This study tested whether interleaving the two tasks modifies latencies, due to switching between different modes of triggering. Two groups of healthy participants (21-29 vs. 39-55 years) made horizontal and vertical saccades in gap, overlap, and mixed tasks; saccades were recorded with the Eyelink. Both groups showed shorter latencies in the gap task, i.e. a robust gap effect and systematic differences between directions. For young adults, interleaving tasks made the latencies shorter or longer depending on direction, while for middle-age adults, latencies became longer for all directions. Our observations can be explained in the context of models such as that of Brown et al. (Neural Netw 17:471-510, 2004), which proposed that different combinations of frontal eye field (FEF) layers, interacting with cortico-subcortical areas, control saccade triggering in gap and overlap trials. Moreover, we suggest that in early adulthood, the FEF is functioning optimally; frequent changes of activity in the FEF can be beneficial, leading to shorter latencies, at least for some directions. However, for middle-age adults, frequent changes of activity of a less optimally functioning FEF can be time consuming. Studying the alternation of gap and overlap tasks provides a fine tool to explore development, aging and disease.

Introduction

Eye movement is a window to study brain function [START_REF] Zee | Neuro-ophthalmology and neuro-otology[END_REF]. In 1967, Saslow first showed different saccade latencies between two different paradigms. In the gap paradigm, the fixation point switched off and target appeared after a gap period; in the overlap task, the target appeared while the fixation point was still on; saccade latencies were found to be shorter in the gap paradigm than in the overlap paradigm. Another important phenomenon could be seen in a gap paradigm: the proportion of very-short latency (80-120 ms) saccades, called express saccades, increased (to 20-30%) [START_REF] Fischer | Separate populations of visually guided saccades in humans: reaction times and amplitudes[END_REF][START_REF] Takagi | Gap-overlap effects on latencies of saccades, vergence and combined vergence-saccades in humans[END_REF][START_REF] Goldring | Reaction times of vertical prosaccades and antisaccades in gap and overlap tasks[END_REF].

In neuropsychology, several original cognitive tasks have been introduced to evaluate the switching capacity in relation to normal behavior, cognitive aging and pathology. The switching design consists mainly in alternating between two different tasks in the same block of trials (mixed block) versus performing each task in separate blocks of trials (pure block). Commonly, a cue indicates shortly before the presentation of the stimulus which type of task the participant has to perform on the stimulus. For example the different tasks can consist in alternating between adding two digits and subtracting two digits (see for instance [START_REF] Belleville | Task switching capacities in persons with Alzheimer's disease and mild cognitive impairment[END_REF].

In almost all neuropsychological studies, switch costs were obtained: the reaction time and the percentage of error were higher (a) in mixed blocks compared to pure blocks (global switch cost) and/or (b) inside the mixed block, for switch trials (e.g. task B following task A) compared to non-switch trials (e.g. task B following task B, local switch cost). These costs reflect: (1) maintaining a set of two potentially relevant tasks in working memory; indeed, an "overhead", i.e. a global controller, is needed to maintain and implement the intention to alternate [START_REF] Pashler | Task switching and multitask performance[END_REF]; (2) the online reconfiguration, also called "task set reconfiguration" [START_REF] Pashler | Task switching and multitask performance[END_REF][START_REF] Belleville | Task switching capacities in persons with Alzheimer's disease and mild cognitive impairment[END_REF], i.e. blocking the set of responses associated with the first task and preparing the set of responses associated with the second task. This reconfiguration is particularly impaired in patients with Alzheimer Disease [START_REF] Belleville | Task switching capacities in persons with Alzheimer's disease and mild cognitive impairment[END_REF]).

In the field of eye movements, the switching capacity has also been studied, mainly using the pro-saccade and the anti-saccade tasks [START_REF] Slovin | Frontal cognitive impairments and saccadic deficits in low-dose MPTP-treated monkeys[END_REF][START_REF] Zhang | Neuronal switching of sensorimotor transformations for antisaccades[END_REF][START_REF] Barton | Antisaccades and task switching: studies of control processes in saccadic function in normal subjects and schizophrenic patients[END_REF][START_REF] Cherkasova | Antisaccades and task-switching: interactions in controlled processing[END_REF][START_REF] Hunt | Eliminating the cost of task set reconfiguration[END_REF][START_REF] Manoach | Schizophrenic subjects show deficient inhibition but intact task switching on saccadic tasks[END_REF][START_REF] Bojko | Age equivalence in switch costs for prosaccade and antisaccade tasks[END_REF][START_REF] Hodgson | Reflexive, symbolic, and affective contributions to eye movements during task switching: response selection[END_REF][START_REF] Barton | Switching, plasticity, and prediction in a saccadic task-switch paradigm[END_REF][START_REF] Cameron | Contrasting instruction change with response change in task switching[END_REF][START_REF] Hikosaka | Brain mechanisms for switching from automatic to controlled eye movements[END_REF]. In the pro-saccade task, the participant has to saccade reflexively to the target; while in the anti-saccade task, he or she is asked to direct his/her eyes opposite to the target location. In these studies, a switch cost was found for pro-saccades but for anti-saccades a switch benefit was found most of the time. The two types of eye movements are believed to involve different cortical-subcortical circuits that have been investigated extensively by brain imaging and electrophysiology (for a review, see [START_REF] Leigh | The neurology of eye movements[END_REF][START_REF] Johnston | Neurophysiology and neuroanatomy of reflexive and voluntary saccades in non-human primates[END_REF].

The purpose of this study is to examine the existence of a switch cost within the class of pro-saccades, using both the gap and the overlap tasks. To our knowledge, such switching effect was never reported. Most of the time, naive participants are not aware of performing distinct tasks. Our driving-hypothesis is that even though in both tasks the participant has to make a saccade quasi reflexively to the target, the mechanisms of saccade preparation and triggering in the two paradigms may be different. We consequently expect a switch effect to be found when alternating between gap and overlap trials.

This hypothesis is compatible with physiological and behavioral studies providing evidence for earlier fixation disengagement and advanced movement preparation in the gap task relative to the overlap task (e.g. [START_REF] Dorris | Neuronal activity in monkey superior colliculus related to the initiation of saccadic eye movements[END_REF][START_REF] Rolfs | On the limited role of target onset in the gap task: support for the motor-preparation hypothesis[END_REF][START_REF] Rolfs | On the limited role of target onset in the gap task: support for the motor-preparation hypothesis[END_REF][START_REF] Rolfs | On the limited role of target onset in the gap task: support for the motor-preparation hypothesis[END_REF] reported that the advanced movement preparation in gap trials occurs mainly when the uncertainty of target position was low. The hypothesis of different mechanisms is also compatible with several models assuming the existence of different cortico-subcortical circuits subtending triggering for gap and overlap trials (see for instance [START_REF] Isa | Switching between cortical and subcortical sensorimotor pathways[END_REF][START_REF] Schiller | Neural mechanisms underlying target selection with saccadic eye movements[END_REF]. A model of particular interest is the one proposed by [START_REF] Brown | How laminar frontal cortex and basal ganglia circuits interact to control planned and reactive saccades[END_REF]. In this model the frontal eye field (FEF) plays an instrumental role for all types of eye movements: different combinations of layers in the FEF, interacting with other cortical and subcortical areas, control different types of saccades such as in gap and overlap trials. Thus, FEF is involved differently for the generation of saccades in gap and overlap trials. We suggest that switching between gap and overlap trials would result in changes in the activity in FEF, leading to a switch effect. Moreover, we suggest that, depending on the age, different functioning of FEF could result in switch cost or benefit.

Another motivation of the present study is methodogical, concerning the use of "mixed" versus "pure" experimental design in the investigation of saccades. This study investigates the switching effect between gap and overlap tasks on saccade latencies for all directions of saccades (leftward, rightward, upward and downward) and for two different age groups: young adults (21-29 years) and middle-age adults (39-55 years). We found that for young adults, interleaving tasks shortened or lengthened latencies depending on direction, while for middle-age adults, latencies became longer for all directions. These results are compatible with the idea that the FEF controls differently the preparation and the triggering of the saccades in gap and overlap trials and with the additional assumption of a positive or negative switch effect across lifespan.

Materials and methods

Participants

Ten young adults from 21 to 29years old (mean 23.7 § 2.5 years) and ten middle-age adults from 39 to 55 years old (mean 45.0 § 5.9 years) were tested. The participants were recruited among laboratory collaborators and their family. Two young adults and three middle-aged adults had already participated in eye movements experiments; all other participants were not familiar with saccade tasks. All participants were healthy without any neurological, neuro-otological or ophtalmological symptoms. They had normal or corrected-to-normal vision. Binocular vision was assessed with the TITMUS test of stereoacuity; all individual scores were normal (40 of arc or better). Each participant gave informed consent to participate in the experiment. This investigation was approved by the local ethics committee and consistent with the Declaration of Helsinki.

Stimuli/visual display

The participant was comfortably seated in an adapted chair with chin rest to stabilize the head. The participant viewed binocularly the visual display, composed of five white luminous dots (angular size .2°), presented on a black computer screen placed 57 cm away from the participant. One of these five dots was at the center of the screen, two were at an eccentricity of § 7.5° horizontally and two were at an eccentricity of § 7.5° vertically.

Oculomotor task

Two paradigms were used: a gap paradigm and an overlap paradigm (Fig. 1). The gap paradigm started by lighting the central dot during approximately 1,500 ms (standard deviation = 100 ms, in order to avoid predictability of the exact moment of the target onset). After this fixation period, the fixation dot was turned off. Following a gap of 200 ms, a target, i.e. one of the horizontally or vertically eccentric dots, appeared for 1,500 ms. The overlap paradigm started by lighting the central dot during approximately 1,700 ms (standard deviation = 100 ms). Then, a peripheral target appeared; both dots were lighted on together during a 200 ms period. Following this overlap period, the central dot disappeared and the peripheral dot remained for another 1,300 ms. Consecutive trials were separated by a period of 1,000 ms with no dot lighted on. The instruction given to the participant was to look at the light dot as accurately and as rapidly as possible.

During each session, the participant performed four blocks. The "pure gap" block contained 60 trials (15 upward saccades, 15 downward saccades, 15 leftward saccades and 15 rightward saccades) of gap paradigm. The "pure overlap" block contained 60 trials (15 toward each direction) of overlap paradigm. The "mixed" block contained 64 trials of either gap or overlap paradigm, with eight trials for each direction and each paradigm. This block was run twice during a session. In each block, the four directions were randomized; in the "mixed" blocks, the two paradigms were also randomized. The order of the blocks was counter-balanced.

Before each block of the oculomotor task, the participant made a sequence of saccades between the white dots, in the four directions; each dot was turned on during 1,000 ms (which is long enough to allow accurate and stable fixation). From these recordings were extracted the calibration factors for each eye.

Eye movement recording

Horizontal and vertical eye movements were recorded binocularly with the EyeLink II device; each channel was sampled at 250 Hz. The system has an accuracy of .5° (absolute position error <.5°) and a resolution of .025° (smallest variation of position detectable <.025°).

Data analysis

Calibration factors for each eye were extracted from the saccades recorded in the calibration task. A calibration was run on the vertical and horizontal signals with a linear function to fit the calibration data. From the two independently calibrated eye position signals, we derived the horizontal or vertical conjugate signal (mean of the two eye positions). The onset (respectively, the offset) of horizontal or vertical saccades was defined as the time when the eye velocity of the conjugate signal exceeded (respectively, dropped below) 10% of the maximum velocity. Similar criteria have been used in several other studies [START_REF] Goldring | Reaction times of vertical prosaccades and antisaccades in gap and overlap tasks[END_REF][START_REF] Yang | The latency of saccades, vergence, and combined eye movements in children and in adults[END_REF]. The automatic placement of the markers by the computer was checked by visual inspection of the individual eye movement traces. From these markers, we measured the amplitude and the latency of saccades.

Altogether, the 20 participants contributed to a total of 4,960 saccade trials; 142 saccades (2.9%) were discarded because they were contaminated by blinks. Among the 4,818 collected saccades, 75 (1.6%) were anticipatory saccades (latency <80 ms), 3 were slow saccades (latency >600 ms) and 3 saccades only (with latency slightly higher than 80 ms) were oriented toward the wrong direction and should rather be classified as anticipatory: thus they were removed from quantitative analysis. The scarcity of anticipation was probably related to the mixing of four directions of saccades within the same block. As all other saccades were toward the correct direction, we can be confident that they were predominantly visually driven saccades.

We calculated the mean latency for each participant in each condition. Four-way ANOVA was applied on latencies to test the effect of the paradigm (gap/overlap), the direction (left/right/up/down), the switching (pure blocks/ mixed blocks) and the age (young adults/middle aged adults). Paradigm, direction and switching were the independent variables and age group was the between-group variable. The LSD test of Fisher was then used for post hoc two-by-two comparisons. Finally, an additional analysis was performed to differentiate between global switching effect (difference between trials in pure blocks and non-switch trials in mixed blocks) and local switching effect (difference, inside the mixed blocks, between switch trials and nonswitch trials). For instance, a non-switch gap trial is a gap trial following another gap trial; a switch gap trial is a gap trial following an overlap trial. A four-way ANOV A was applied; the factors were paradigm (gap/overlap), direction (left/right/up/down), switching (pure blocks/ non-switch trials in mixed blocks/switch trials in mixed blocks) and age (young adults/middle aged adults).

Results

Paradigm, direction, switching and age effects on latencies

Table 1 shows the saccade amplitude for all conditions (the required amplitude was always 7.5°). As saccade latency and saccade accuracy can be interdependent, e.g. the longer the latency, the more accurate the saccade (see [START_REF] Van Donkelaar | Multiple saccades are more automatic than single saccades[END_REF], we first checked the effect of age, paradigm, switching and direction on the amplitude of saccades with a four-way ANOVA. None of these parameters had an effect on saccade amplitude: no main effect and no significant interaction were found (P < .05).

Figure 2 shows the mean latencies for each direction in the gap and overlap paradigms and in the pure and mixed conditions for the young adults and for the middle-age adults. The ANOVA (see Fig. 3) showed (a) a significant effect of the paradigm (F(1, 18) = 96.55; P < .001); (b) a significant effect of the direction (F(3, 54) = 12.72, P < .001); (c) a significant interaction between direction and paradigm (F(3, 54) = 3.13; P < .05); (d) a significant interaction between switching and age (F(1, 18) = 4.88, P < .05); (e) a significant interaction between direction, switching and age (F(3, 54) = 3.56; P < .05); and (f) a significant interaction between direction, switching and paradigm (F(3, 54) = 3.52; P < .05).

The post hoc tests showed the following results: (a) The significant effect of the paradigm was the gap effect: the latencies were 61 ms shorter in the gap than in the overlap paradigm (P < .001). (b) The latencies of downward saccades were 22 ms longer than the latencies of upward saccades and 40 ms longer than the latencies of horizontal saccades; latencies of upward saccades were on average 18 ms longer than the latencies of horizontal saccades (P < .05). (c) The post hoc analysis for the interaction between direction and paradigm showed that all two-by-two comparisons were statistically significant (P < .05) except for the leftward and rightward saccades in the gap trials and for the leftward and rightward saccades in the overlap trials (P > .05). (d) The switching had no effect on the latency in young adults when all directions were considered (P > .05), but influenced the latency in middle-aged adults (11 ms longer in mixed blocks; P < .05). In pure blocks, latencies were similar for both groups (P > .05) but in mixed blocks, latencies were 23 ms shorter for young adults (P < .001). (e) For young adults, leftward saccades latencies were 14 ms shorter in mixed blocks (switch benefit, P < .01) and rightward saccades latencies were 11 ms longer (switch cost, P < .05); for middle-aged adults, upward latencies were 15ms longer in mixed blocks (switch cost, P < .01) and downward latencies were 13 ms longer (switch cost, P < .01). (f) Rightward saccades latencies in the overlap paradigm were 12 ms longer in mixed blocks (P < .01) and downward saccades latencies in the overlap paradigm were 15 ms longer (P < .001).

In summary, both groups of participants showed a clear gap effect: latencies were shorter in the gap trials than in the overlap trials (Fig. 3a). The effect was similar for middle-age adults (67 ms) and for young adults (57 ms). Secondly, a direction effect existed for both groups: the latencies of downward saccades were longer than the latencies of the saccades in the three other directions and the latencies of upward saccades were longer than the latencies of the horizontal saccades (Fig. 3b). Finally, switching influenced saccade latency differently depending on age, target direction and/or paradigm (interaction switching-age, interaction switching-direction-age and interaction switching-paradigm-direction). These interactions with the switching factor are complex; we will only discuss the most relevant results. Although simplified, in young adults, switch benefit and cost might exist, whereas in middle-aged adults, only costs were observed (Fig. 3d,e). Moreover, for some directions, switching had different effects on gap and overlap trials (Fig. 3f).

Local and global switching effect

The switching effect may occur at two levels: a local switching effect (difference between switch trials and non-switch trials inside the mixed block) and a global switching effect (difference between non-switch trials inside the mixed block and trials in pure blocks). For instance, a non-switch gap trial is a gap trial following another gap trial; a switch gap trial is a gap trial following an overlap trial. To differentiate the local and global effects, the four-way ANOVA was applied again but with three modalities for the switching factor: trials in pure block, non-switch trials in mixed blocks and switch trials in mixed blocks. This analysis confirmed the paradigm main effect (gap effect), the direction main effect and the interaction between paradigm and direction reported in the main analysis. It also showed an interaction between switching and direction (F(6, 108) = 2.51, P < .05) and an interaction between switching and age (F(2, 36) = 5.48, P < .01). The post hoc test for the interaction between switching and direction showed that a global switch cost and a local switch benefit were found for upward saccades only (P < .05). Figure 4 shows the result of the post hoc test for the interaction between switching and age. For young adults there was no evidence for significant switching effect, neither global nor local. In contrast for middle-aged, there was a 15 ms global switching effect (P < .01) and no local switching effect.

Discussion

Summary of the results

The main results are the following. (a) A robust gap effect (shorter latencies for saccades in gap than in overlap trials) was present in all conditions. (b) Spatial anisotropies (shorter latencies for horizontal than for vertical saccades, and for upward than for downward saccades) also appeared in all conditions. (c) Switching influenced latencies differently depending on age (young/middle-age), saccade direction (left/right/up/down) and paradigm (gap/overlap). [START_REF] Saslow | Effects of components of displacement-step stimuli upon latency for saccadic eye movement[END_REF] was the first to describe the gap effect: shorter latencies in the gap paradigm than in the overlap paradigm. In the present study, a strong gap effect was found for both young adults and middle-age adults: on average, latency was 61 ms shorter. The gap effect was comparable to that found in elderly (e.g. [START_REF] Yang | Prolongation of latency of horizontal saccades in elderly is distance and task specific[END_REF]). Thus, once established during childhood (see [START_REF] Munoz | Age-related performance of human subjects on saccadic eye movement tasks[END_REF], the gap effect is stable throughout life. This stability reveals specific robust neurophysiological mechanisms.

Robustness of the gap effect

Different interpretations have been proposed to explain the reduction of mean latency. The theory involving a disengagement of attention during the gap [START_REF] Fischer | Separate populations of visually guided saccades in humans: reaction times and amplitudes[END_REF][START_REF] Tam | Viewing behavior: ocular and attentional disengagement[END_REF] was rejected [START_REF] Kingstone | Visual offsets facilitate saccadic latency: does predisengagement of visuospatial attention mediate this gap effect?[END_REF]. Instead, a disengagement of the fixation, decreasing the competition between the tendency to fixate new items and the tendency to remain fixated on the current, may occur [START_REF] Saslow | Effects of components of displacement-step stimuli upon latency for saccadic eye movement[END_REF][START_REF] Kingstone | Visual offsets facilitate saccadic latency: does predisengagement of visuospatial attention mediate this gap effect?[END_REF][START_REF] Tam | Viewing behavior: ocular and attentional disengagement[END_REF][START_REF] Tam | Fixation disengagement and eye-movement latency[END_REF][START_REF] Klein | Against a role for attentional disengagement in the gap effect: a friendly amendment to Tam and Stelmach (1993)[END_REF] and an advanced movement preparation may take place [START_REF] Fischer | Separate populations of visually guided saccades in humans: reaction times and amplitudes[END_REF][START_REF] Klein | Against a role for attentional disengagement in the gap effect: a friendly amendment to Tam and Stelmach (1993)[END_REF]. Recordings in monkey superior colliculus (SC) showed that fixation-related neurons reduce their activity during the gap period, providing evidence for release of ocular fixation; moreover saccaderelated neurons display phasic target-related responses, providing evidence for advanced motor preparation [START_REF] Dorris | Neuronal activity in monkey superior colliculus related to the initiation of saccadic eye movements[END_REF]. The advanced movement preparation could be a temporal preparation, a state of readiness induced by a warning signal provided by the extinction of the fixation point [START_REF] Ross | Saccade latency and warning signals: stimulus onset, offset, and change as warning events[END_REF][START_REF] Ross | Saccade latency and warning signals: effects of auditory and visual stimulus onset and offset[END_REF][START_REF] Kingstone | Visual offsets facilitate saccadic latency: does predisengagement of visuospatial attention mediate this gap effect?[END_REF][START_REF] Findlay | A model of saccade generation based on parallel processing and competitive inhibition[END_REF]. [START_REF] Rolfs | On the limited role of target onset in the gap task: support for the motor-preparation hypothesis[END_REF] showed that spatial motor preparation contributes to the effect; spatial components are already taken into account during the gap.

Theoretical models suggest that saccades triggered in the overlap task and saccades triggered in the gap task, in particular the express saccades, are produced by different cerebral subcortical circuits. A short circuit, SC-brainstem [START_REF] Isa | Switching between cortical and subcortical sensorimotor pathways[END_REF] or occipital cortex-SC-brainstem (the posterior system, Schiller and Tehovnik 2005) plays an important role in the generation of rapid, shortlatency saccades in a gap paradigm. The generation of long latency saccades in an overlap paradigm would be controlled by a larger circuit also involving the anterior system (parietal cortex, temporal cortex, FEF) [START_REF] Isa | Switching between cortical and subcortical sensorimotor pathways[END_REF][START_REF] Schiller | Neural mechanisms underlying target selection with saccadic eye movements[END_REF].

Spatial anisotropies

In the present study, latencies were shorter for the horizontal directions than for the vertical directions; secondly, latencies were shorter for upward saccades than for downward saccades. These results extend prior studies using only horizontal or vertical saccades (e.g. [START_REF] Honda | Saccades to targets in three-dimensional space: dependence of saccadic latency on target location[END_REF][START_REF] Goldring | Reaction times of vertical prosaccades and antisaccades in gap and overlap tasks[END_REF][START_REF] Tzelepi | The effect of transcranial magnetic stimulation on the latencies of vertical saccades[END_REF]: anisotropies are still present when all four directions are interleaved. [START_REF] Goldring | Reaction times of vertical prosaccades and antisaccades in gap and overlap tasks[END_REF] hypothesized that saccade generation is prepared by fixation disengagement (non-directional mechanism) and a spatially selective mechanism which is more or less effective across the visual field. To explain that the horizontal saccades show the shortest latencies, we suggest that reading activity leads to an optimization of the horizontal saccadic system. Tests of populations with different reading systems would be of interest. To explain the up/down asymmetry, [START_REF] Honda | Saccades to targets in three-dimensional space: dependence of saccadic latency on target location[END_REF] suggested a possible association between downward movements and convergence; the preparation of a convergent command may delay the triggering of downward saccades. [START_REF] Tzelepi | The effect of transcranial magnetic stimulation on the latencies of vertical saccades[END_REF] explained the asymmetry by a less eYcient disengagement of the fixation before a downward saccade and the possible role of the posterior parietal cortex in this fixation disengagement. The less eYcient disengagement of fixation for downward saccades could be related to increased capacity of peripheral visual analysis in the lower hemifield, thereby diminishing the necessity for fast triggering of saccades. It has also been speculated that upward saccades could be of shorter latency than downward saccades because of the overall motion of the visual field corresponding to the ground during the walk of a foveated, front-eyed animal. Indeed, such motion causes a downward following eye movement which is then reset by an upward quick-phase eye movement. Such specialization could subserve the advantage of upward saccades [START_REF] Previc | Functional specialization in the lower and upper visual fields in humans: Its ecological origins and neurophysiological implications[END_REF]).

In summary, there are spatial anisotropies on saccade latencies in both groups of participants. The exact mechanisms are still unknown; several complementary hypotheses exist but further experiments are needed to test the hypothetical mechanisms.

Switch cost or benefit

The present study shows switch costs and benefits when gap trials and overlap trials are mixed in the same block. To our knowledge, only [START_REF] Coubard | Gap effects on saccade and vergence latency[END_REF] examined the effect of mixing different types of pro-saccades: gap trials were mixed with simultaneous trials (the fixation disappears and the target appears simultaneously, sometimes referred as "0-gap trials") in the same blocks. [START_REF] Coubard | Gap effects on saccade and vergence latency[END_REF] failed to report a mixing effect on the latencies of saccades. However, in their study, gap trials were interleaved with simultaneous trials and not with overlap trials, probably leading to weaker effect, failing to achieve statistical significance. More importantly, the absence of mixing effect was probably due to the fact that they examined a group of adults heterogeneous in age (18-47 years). Indeed, the most unexpected result in the present study is that in young adults, mixing could speed up initiation of eye movements at least for some directions whereas mixing always slowed down initiation in middle-age adults.

Only a few studies in the literature on task switching reported switch benefit. [START_REF] Jersild | Mental set and shift[END_REF], cited by [START_REF] Pashler | Task switching and multitask performance[END_REF], reported some switch benefit when using univalent lists. In univalent lists, there are two different types of stimuli, each of them being associated with its own task; in bivalent lists, a same stimulus is associated with different tasks to be accomplished. The existence of switch benefit with univalent lists remains unclear. In the studies of switching between pro-saccades and antisaccades, a switch cost was found for pro-saccade, but strikingly, a switch benefit was most of the time found for anti-saccade [START_REF] Barton | Antisaccades and task switching: studies of control processes in saccadic function in normal subjects and schizophrenic patients[END_REF][START_REF] Cherkasova | Antisaccades and task-switching: interactions in controlled processing[END_REF][START_REF] Bojko | Age equivalence in switch costs for prosaccade and antisaccade tasks[END_REF][START_REF] Barton | Switching, plasticity, and prediction in a saccadic task-switch paradigm[END_REF]. The cost and the benefit varied as a function of cue-to-target interval [START_REF] Barton | Switching, plasticity, and prediction in a saccadic task-switch paradigm[END_REF]), but were not affected by aging [START_REF] Bojko | Age equivalence in switch costs for prosaccade and antisaccade tasks[END_REF]). Paradoxical cost versus benefit is attributed to inhibition of the saccadic response system by the anti-saccade task; such inhibition would lead to a cost for pro-saccades and a benefit for anti-saccades [START_REF] Barton | Antisaccades and task switching: studies of control processes in saccadic function in normal subjects and schizophrenic patients[END_REF][START_REF] Barton | Switching, plasticity, and prediction in a saccadic task-switch paradigm[END_REF]). Another explanation suggests that operation of a second cognitive function requiring attention (task switching) facilitates the execution of nondominant responses (anti-saccades) and delays usual response (pro-saccades). In the present study, the switch benefit and costs were in the range of 11-15 ms (see Fig. 3e), similar to the range of switch cost and benefit found in other studies with pro and anti-saccades (e.g. [START_REF] Cherkasova | Antisaccades and task-switching: interactions in controlled processing[END_REF]. However, none of these two explanations is applicable to the gap and overlap trials used here, both involving pro-saccades.

Many interpretations can be considered for the existence of a switching cost when gap and overlap trials are interleaved. For instance, fixation activity threshold could be overall increased in mixed blocks to avoid anticipatory saccades for overlap trials. Another explanation is that alternating between different triggering mechanisms or distinct subcircuits has a cost, similarly to what is observed in neuropsychological studies, where participants alternate between different cognitive tasks. Note that in the present study, switching effects could be different for gap and overlap trials, at least for some directions (see Fig. 3f); this also supports the existence of different triggering mechanisms for gap and overlap trials. Yet, such interpretations cannot explain both benefit and cost.

Our observations can be explained in the context of models such as those of [START_REF] Isa | Switching between cortical and subcortical sensorimotor pathways[END_REF] and [START_REF] Brown | How laminar frontal cortex and basal ganglia circuits interact to control planned and reactive saccades[END_REF]. [START_REF] Isa | Switching between cortical and subcortical sensorimotor pathways[END_REF] suggest that different context-dependant collicular activations, in interaction with cortical areas and basal ganglia (BG), play a role in gating cortico-subcortical subcircuits for saccades triggered in gap (in particular short-latency saccades) and in overlap trials. In the TELOS model (Telencephalic Laminar Objective Selector), [START_REF] Brown | How laminar frontal cortex and basal ganglia circuits interact to control planned and reactive saccades[END_REF] proposed a similar idea, more focused on the role of the FEF. In this model, different combinations of layers in the FEF, interacting with the SC, BG, thalamus, and other cortical areas, would control different types of saccades; for instance, saccades triggered in gap trials and saccades triggered in overlap trials. Thus, according to [START_REF] Brown | How laminar frontal cortex and basal ganglia circuits interact to control planned and reactive saccades[END_REF] the FEF is implicated, even for saccades triggered in gap paradigm.

We suggest that switching between gap and overlap trials would correspond to changes in the activity of different layers within the FEF. The level of activity in the monkey FEF was shown to be related to saccade latency [START_REF] Hanes | Relationship of presaccadic activity in frontal eye Weld and supplementary eye Weld to saccade initiation in macaque: Poisson spike train analysis[END_REF][START_REF] Hanes | Neural control of voluntary movement initiation[END_REF]. In humans, functional MRI during anti-saccade preparation indicated an increase in brain activation from childhood to adulthood in frontal, parietal, striatal and thalamic regions [START_REF] Luna | Maturation of widely distributed brain function subserves cognitive development[END_REF]). Thus, brain activity depends on age and within adulthood, period of optimal functioning might exist in early adulthood, but this remains to be explored. Relative to the existence of both cost and benefit, one possibility is that in early adulthood, as the FEF is functioning optimally, frequent changes of activity in the FEF can be beneficial, leading to shorter latency (switch benefit). Later in adulthood however, frequent changes of activity in a less optimally functioning FEF can be time consuming (switch cost). Our speculation for benefit in young adults related to frequent switching and optimal function of FEF needs to be further tested.

The finding of a global switch cost for middle aged adults (see Fig. 4) is compatible with the idea of a common structure for controlling saccades in gap and overlap trials. In neuropsychology, a global switch cost is believed to reflect the activation of an "overhead", i.e. a global controller (see Introduction). Thus a cortico-subcortical network involving the FEF could be the neural equivalent of the concept of a global controller. Rivaud-Pechoux etal. (2007) examined mixing cost in patients with parkinsonian syndromes (Parkinson's disease, corticobasal degeneration and progressive supranuclear palsy). They compared latency and error rates in pure blocks of pro-saccades or anti-saccades to non-switch trials in mixed blocks (the equivalent of the global switching cost in the present study). They suggest that parietal and frontal cortices and the BG may participate in mixing behavior, particularly impaired in patients with corticobasal degeneration.

In conclusion, switching between gap and overlap trials may delay or speed up latency depending on age and direction. In line with models, we suggest that the activity of a common cortical structure (the FEF, in connection with other cortical and subcortical structures) regulates saccade preparation and triggering differently for gap and overlap trials. From a methodological point of view, it is important to consider the interaction between switching and age. Comparison of latencies between studies should take into account the design of each experiment and the age of the participants. In addition to theoretical and methodological interests, this study has clinical perspective. Correlations between switch cost or benefit of saccades and neuropsychological tests evaluating mental flexibility are of interest. Indeed, mixing of saccades in gap and overlap trials can be a tool to test switching capacity in various population, e.g. in children or in patients with neurodegenerative disorders. A switching effect between two different types of pro-saccades is interesting, because pro-saccades can be done in almost any population with no particular effort, unlike anti-saccades that require a higher level of cognitive function and cooperation.

Fig. 1

 1 Fig. 1 Experimental paradigms. a Gap paradigm, the central fixation point disappeared 200 ms before the appearance of the eccentric tar-get. b Overlap paradigm, the central fixation point remained illuminated for 200 ms after the appearance of the eccentric target. In both cases, the latency was the period between the onset of the target and the beginning of the saccade

Fig. 2 Fig. 3

 23 Fig. 2 Group means and standard errors of the latencies for each direction (left, right, up, down), paradigm (gap, overlap) and block (pure, mixed) for the young adults (a) and for the middle-age adults (b)

Table 1

 1 Group means and standard errors of the saccade amplitude for each direction (left, right, up, down), paradigm (gap, overlap), block (pure, mixed) and age group (young adults, middle-age adults)

Acknowledgments

The authors thank the reviewers for their comments, Antoine VERNET and Lea-Laetitia PONTANI for improving English in this article.


Some basic chemistry

• Secondary aroma compounds: Those formed after cell damage (chopping, peeling, squeezing, etc.).

Biosynthesis. Primary aroma compounds. Esters

• Primary aroma compounds: Those formed via the plant's metabolism (growth, maturation, ripening).

Terpenes

• Biosynthesised from isoprene (5 carbons)

• Usually have 10 carbons (terpenes) or 15 carbons (sesquiterpenes)

• Called terpenoids when contain a heteroatom (other than C and H)

• Provide characteristic aroma to herbs, spices, fruits (specially citrus).

Some terpenes and terpenoids found in citrus fruits

Formation of terpenes in citrus fruits

• Isoprene units (5 carbons) are present as isopentyl pyrophosphate

• Two isopentyl units can bind to form a longer 10-carbon chain

Biosynthesis. Secondary aroma compounds

• Secondary aroma compounds: Those formed after cell damage.

• When cells are broken, enzymes get in touch with substrates and initiate the enzymatic reaction.

• Before cell disruption, enzymes and substrates were physically separated.

• Two examples: formation of aroma in Allium and formation of "green" odour aldehydes.

Allium cepa onion

Allium sativum garlic

Allium cepa var. aggregatum shallots

Allium schoenoprasum chives

Allium ampeloprasum leek

Sulfur compounds in Allium

• Formed from alkyl or alkenyl (double bound) sulfoxide derivatives of the amino acid cysteine

• Enzyme: alliinase. Physically separated from the substrates; they get in contact after cell breakage.

• Alliin dominates in garlic (2 g/kg); isoalliin in onion (2.4 g/kg).

Sulphide bonds (-S-) can break and rearrange easily, giving a large variety of compounds. Also form di-(-S-S-), tri-(-S-S-S-) and tetrasulphides (-S-S-S-S-). The longer, the more unstable.

Sulphur aroma compounds

• Very potent aroma compounds. We can perceived them even at extremely low concentrations.

• They have a very characteristic aroma: garlic, onion, but also faecal.

• Unstable compounds. They decompose easily.

• Can form sulphides, disulphide, trisulphides…

Formation of "green" aromas. Enzymatic lipid oxidation

• Formed by the oxidation of lipids caused by lipoxygenase activity. It requires the presence of oxygen!

• The result is linear aldehydes and alcohols with usually 6 or 9 carbons, with very potent "green" or "fresh cut grass" aroma.

• Very potent; they can be perceived even in foods with very low fat content.

• Key aroma compounds in legumes (green peas, soya, etc.), cucumber, herbs, vegetables in general, oils (in excess, they are perceived as rancid*).

*Rancidification of oils can occur by other chemical processes, not only lipoxygenase activity, although the aroma compounds formed are similar.

20

FERMENTATION

• Fermentative processes not only help degrade proteins, carbohydrates and other macromolecules to make them more easily digestible.

• Lots of aroma compounds are formed in enzymatic reactions.

• From amino acids, we obtain mostly alcohols, esters and organic acids (Similar to the aroma compounds found in fruits by biosynthesis).

Esters and alcohols in beer

• Beer fermentation by yeast produces a huge variety of fruity alcohols and esters that give their characteristic aroma.

• Esters are predominant in beer and are responsible for the fruity flavour.

• These compounds are also present in other fermented beverages, such as rum, whiskey, wine, sake, etc.

• Also present in other fermented foods like cheese and bread. What aroma compounds can we get from phenylalanine and leucine (together in the same system) by fermentation? Take into account the presence of ethanol and acetyl-SCoA

THERMAL PROCESSING

Formation of a huge variety of aroma, taste and colour compounds.

• Caramelisation

• Maillard reaction

Caramelisation

• Occurs in food products with a high sugar content.

• Requires high temperature, above 120 °C.

• It involves the thermal degradation of sugars, usually mono-but also di-and trisaccharides.

• Since sugars contain only C, H and O, the compounds formed thereafter will only contain these atoms.

• Linear but also cyclic compounds are formed.

Lactose Some sugar molecules: Some cyclic aroma compounds:

• It is a very complex network of parallel and consecutive reactions.

• The final product, melanoidins, are a pool of heterogenous compounds with yellow or brown colour (Maillard reaction  Nonenzymatic browning)

• The amino compound is released and a very reactive dicarbonyl is formed. • This dicarbonyls reacts further with other compounds like amino compounds or it breaks down into other products.

• When the dicarbonyls reacts with an acid, an aldehyde is formed via the Strecker degradation. • This aldehyde will have one carbon less than the amino acid of origin.

Sulphur compounds from cysteine

• Formation of character impact meaty compounds

•

Ribose is a monosaccharide present in meat. Cysteine is an amino acid containing sulphur.

• These compounds are also key in coffee aroma.

• Vegetables and fruits do not contain cysteine and ribose, that is why they do not produce meaty aromas.

35

furfurylthiol another important aroma compound in meat and coffee 2-methyl-3-furanthiol

• Although the Maillard reaction is usually associated with thermal processes, it is a spontaneous reaction.

• It can happen very slowly at room temperature.

Higher temperatures increase the reaction rate.

• Ripened cheeses, aged Port wine

• Biosynthesis

• Primary: Esters, terpenes, terpenoids

• Secondary: Linear aldehydes (saturated and unsaturated, usually C6 and C9), sulphides in Allium

• Fermentation

• Alcohols, organic acids, esters from amino acids

• Thermal processing 4-hydroxy-2,5-dimethyl-3(2H)-furanone 28.

3-hydroxy-4,5-dimethyl-2(5H)-furanone

•

  Foods consumed raw: fruits, vegetables, salads, spices • What is flavour for us are attractants or repellents for other animals • Primary aroma compounds: Those formed via the plant's metabolism (growth, maturation, ripening).

25

  Pires et al. 2014 DOI: 10.1007/s00253-013-5470-0 Exercise 1.

banana aroma) Ethyl hexanoate (pineapple, apple) Ethyl butanoate (strawberry, orange)

			SCoa
			Acetyl CoA
	3-methylbutanal (malt, cocoa)	3-methyl-1-butanol (mango, fruity)	3-methylbutyl acetate (banana)
	leucine (2-amino-	SCoa	ethanol
	4-methylpentanoic acid)
			ethyl 3-methylbutanoate
	3-methylbutyl CoA	(apple, pineapple)
	smells/

• Mostly esters and terpenes. Very important in fruit aroma 6 3-methylbutyl acetate ester (https://jameskennedymo nash.wordpress.com/201 3/12/13/infographictable-of-esters-and-their-

12 lemon p-menthene-8-thiol

	1,8-cineol (eucaliptol) eucaliptus	Cuminaldehyde (p-isopropylbenzaldehyde) cumin		α-caryophyllene (humulene)
	grapefruit	pine	grapefruit	hops
	Two stereoisomers, two different aroma qualities:
	R-(-)-carvone spearmint
	S-(+)-carvone caraway
	lemon	citrus, geranium

Exercise 2. Origin of these aroma compounds?

	Alcohols
	1.	methylpropanol
	3.	3-methylbutanol
	15.	3-(methylthio)-propanol
	22.	2-phenylethanol
	Aldehydes 9. 13.	3-(methylthio)-propanal phenylacetaldehyde	Esters 2. 4.	3-methylbutyl acetate ethyl hexanoate
	Organic acids		7.	ethyl octanoate
	8.	acetic acid	18a.	2-phenylethyl acetate
	11.	methylpropanoic acid
	12.	butanoic acid	Terpenes
	14a.	2-methylbutanoic acid	10.	linalool
	14b. 19. 26. 33.	3-methylbutanoic acid hexanoic acid octanoic acid phenylacetic acid	Cyclic compounds 6. 2-acetylpyrroline 25b.

• Caramelisation: a variety of linear, branched and cyclic compounds (C,H,O)

• Maillard reaction: Aldehydes from amino acids, heterocyclic compounds (C,H,O,N,S), ketones, sulphur compounds…

an example:

https://link.springer.com/chapter/10.1007/978-3-319-56526-2_5 cysteine

(transaminases) (decarboxylases)(alcohol dehydrogenase)

REDUCING SUGAR + AMINO COMPOUND

How can we guess the origin of an aroma compound?

• Ingredients

• Composition. Sugar? Fats? Proteins?

• Processing

• Is there a thermal process involved?

• Is the product fermented?

• Both?

• Nature of the aroma molecule 3-methylbutanol 15.

3-(methylthio)-propanol 22.

2-phenylethanol Aldehydes THERMAL (Maillard) 9.

3-(methylthio)-propanal 13.

phenylacetaldehyde

3-methylbutyl acetate 4.

ethyl hexanoate 7.

ethyl octanoate 18a.

2-phenylethyl acetate

Origin of these aroma compounds?


domain: phys spi

text:
Viala Erwan
email: erwan.viala@onera.fr

Rivière Nicolas

Risser Laurent

Dupouy Paul-Édouard

INCREASING SPATIAL RESOLUTION OF 3D LIDAR BY COMPRESSIVE SENSING

Keywords: LiDAR, GmAPD, Compressive Sensing, 3D focal plane array, long-range imagery

ONERA -The French Aerospace Labdevelops new concepts of LiDAR imaging systems including new sensor technologies and data processing. The rising complexities and costs of high performance systems, and the shrinking time to design drove the ONERA approach. The home-grown MATLIS software has been evolving for the past decade. It allows both linear mode LiDAR and single photon electro-optical systems simulation (both GmAPD and SPL) embedded on dynamic platforms (eg. UAVs, Aircrafts).

In this paper, we present an algorithm for 3D scene reconstruction with unprecedented lateral resolution. This method is suitable for Geiger mode Avalanche Photodiode (GmAPD) 3D focal plane arrays. The main idea behind of this work is reconstruction of higher resolution 3D images by sub-pixel spatial modulation.

We manage to reconstruct sub-pixel information by using Compressive Sensing (CS) algorithms, such as Orthogonal Matching Pursuit (OMP). Then we have verified our theoretical approach using simulated 3D images generated using the MATLIS software from a facetted three-dimensional scene.

INTRODUCTION

Context and motivation

Long-range observation typically above 10 kilometers, is necessary to anticipate potential threats for site surveillance (eg. drone detection) or aerial / maritime protection (eg. identification of floating debris, ship self-protection). The operational needs of these tasks require a persistence of the detection and identification function under any weather and illuminance conditions (eg. day, night, sun glare). In this context, one can notice that passive imagery techniques (visible or infrared) answer partially to the identification function. Operational deployment especially in weak visibility or strong solar illuminance variation in time as proven to be challenging. Active imaging as illustrated in Fig. 1 is less sensitive to it by the use and control of its own illumination source. Moreover, the identification function needs a good lateral and telemetric resolution and the image telemetry bring additional dimension which eases the identification. Active imaging is governed by the capacity to capture laser-light backscattered by a target. The combined need for range, resolution and reduced SWaP (Size, Weight and Power) mandates the use of a specific sensor to image the scene. In this case, we focus on systems using GmAPD sensor, capable of statistically detecting fractional photons return levels. These sensors have some drawbacks.

GmAPDs are limited to a few large pixels (up to 128x32 pixels), which gives an insufficient resolution for the identification function. In section 2, we will show how this can be alleviated by using CS to increase the resolution at the cost of a spatial modulator and a fast algorithm.

Moreover, those sensors, in gated mode, are only capable of capturing the first triggering event. The low dynamic range and temporal correlation complicate the application of CS to such a 3D imagery. In section 3, we will explain these difficulties in more detail and our approach to solve OPTRO2022 -paper 50 them. Then in section 4 we illustrate, our approach by reconstruct with increased resolution an image at a range of 10 km on simulated data. Let 𝛷 follow the 2𝑘-Restricted Isometry Property if for 𝑘 < 𝑁, ∃𝛿 2𝑘 ∈, such that :

COMPRESSIVE SENSING

(1 -𝛿 2𝑘 )‖𝑋‖ 2 ≤ ‖𝛷 2𝑘 𝑋‖² ≤ (1 + 𝛿 2𝑘 )‖𝑋‖ 2 (1)
For all 𝛷 2𝑘 composed of 2𝑘 columns extracted from 𝛷.

Thus, from the 2K-RIP (Eq. 1), we have two resulting restrictions: the signal must be sparse in a basis 𝛹 which may be unknown, and the measurement matrix 𝛷 must be sufficiently inconsistent with the basis 𝛹.

Theorem (Noisy recovery with bounded noise):

[3] If 𝛿 2𝑘 ≤ √2 -1, then ‖𝑥 0 -𝑥 ⋆ ‖ ≤ 𝐶 0 √𝑘 ‖𝑥 0 -𝑥 𝑘 ‖ 1 + 𝐶 1 𝜀 (2)
where 𝑥 𝑘 is the best 𝑘-term approximation of 𝑥 0 , 𝑥 ⋆ is the reconstructed signal and 𝐶 0 , 𝐶 1 are related to 𝛿 2𝑘 and are rather small.

According to Eq. 2, this property is sufficient to guarantee a limited error on the reconstruction.

In our case, we choose the two most commonly used bases in LiDAR application (especially in single pixel imaging), which are the random basis composed of multiple Bernoulli, and the Hadamard basis, which is determinist. The Random basis or Hadamard basis (Fig. 2), which are respectively incoherent with all basis with high probability and with basis like Haar or Daubechies in which the natural scene is generally sparse.

[5]

3D LiDAR Application

We use DMD (Digital Micro-mirror Device) to compress backscattered signal in 3D LiDAR application as illustrated in Fig. 3.

Figure 3 -Optical scheme

A DMD is an array of mirrors which are orientable (Fig. 4 and Fig. 5), so we can structure the detection by directing the light to the sensor or not. Then we can easily compress the signal with basis composed of zero and one, like the example in Fig. 2.

Figure 4 -Left: two mirrors from a Texas Instrument DMD. Right: DMD with ant-leg for scale

Thus, we compress our signal with a DMD. One need to make additional assumptions to process a suitable signal for CS. Each pixel is supposed to be spatially and temporally independent of its neighbors. This assumption is needed to reconstruct independently three-dimensional objects in each temporal bin of each pixel. We also assume that the signal is time-dependent but not pattern-dependent, which is not the case, in section 3.2 we developed a way to solve this issue.

Then, we acquire the 3D-LiDAR data with measurement basis according to CS theory, adjust the data and finally reconstruct the image by solving the CS optimization problem with classical algorithm like Orthogonal Matching Pursuit (OMP) [6].

PRECOMPUTATION STAGE

When we deal with CS in LiDAR GmAPD imaging, we encounter at least two major problems as already mentioned in sections 1 and 2:

-Low dynamics -Time-dependency

In this section we will briefly aboard a way to deal with them.

Low dynamics

The first problem is the lack of dynamics of the sensor. Because of high dead-time and the high sensitivity of the sensor, the output from the sensor is limited to the information that an event (backscattered photon or noise) is detected at a time, only for the first trigger (for each pixel) and without information about the number of photons.

Therefore, a classical way to deal with this problem is to use a histogram of return time to infer the quantity of photon which could be counted at each bin of each pixel.

The error can be bounded by using the Hoeffding inequality [7], as follow (Eq. 3):

|𝐻 -𝑌| ≤ √ 𝑙𝑛 ( 2 𝛼 ) 2𝑁 (3)
Where 𝐻 is the normalized histogram, 𝑌 is the measure expected, -𝛼 is the level of trust and 𝑁 is the number of acquisition.

Once this method is applied, we get an error-bound approximation of the signal waveform for each pixel.

Time-dependency

The time-dependency is a more involved problem.

It is linked with the pattern-dependency. Of course the signal depends on time since it decreases quadratically with time, but it's also pattern dependent which is the real problem. This effect is illustrated in fig. 6.

Figure 6 -Illustration of time-dependency error

For a given pattern the more of an object is exposed the more signal we should have. It's not always the case because it depends on the quantity of object seen before the bin of interest. This error will lead to a mismatch between the weight applied on the pattern and the quantity of the shape exposed. Thus, when an object is detected in a bin, all the following bins could have wrong weight which could be a problem when solving the CS optimization problem.

To overcome this problem, we just reweighed each bin with a coefficient, which depends of the previous bins. This coefficient is obtained by making some assumption about the probability of return in each point. This observation is experimentally validated by [8], on the same kind of sensor.

Another problem which comes with this method is the presence of noise. When we apply the weigh to reweigh all bins, noise is highly amplified. In order to avoid a too noisy reconstruction, we must use a denoiser.

SIMULATED RESULTS

In order to test our algorithm, we have used simulated 3D LiDAR acquisitions by MATLIS software [9].

Input parameters for MATLIS software

The simulation parameters used are chosen to be as realistic as possible. The laser energy is around 10 -5 Jand the total noise (solar + dark count rate) around 10 6 Hz as in daylight conditions. The sensor is placed at a range of 10km of the scene with a field of view around 10 -4 rad which is equivalent at a 5m by 5m square at 10km. The Geiger focal plane is composed by 32 × 32 pixels and the DMD by 256 × 256 mirrors. The frame rate and DMD pattern update-rate correspond to realistic parameters.

Figure 1 -

 1 Figure 1 -Concept of 3D LiDAR acquisition based on focal plane array.

2. 1 .

 1 General concept CS can be considered as an acquisition technique that compresses the signal during the acquisition process in order to acquire already compressed information and then uses of a L 1 optimization algorithm to reconstruct the acquired information. The main concepts of CS were developed between 2005 and 2009 by three mathematicians (Candès, Tao and Romberg) [1-3] and in parallel by Donoho since 2006 [4]. CS uses the sparsity of the scene on a certain basis (which may be unknown) and the inconsistency between this basis and a specific measurement basis to enable the correct reconstruction of the image. Theorem (2K-RIP): [1,2]

Figure 2 -

 2 Figure 2 -Bases examples

Results

The 3D scene was designed to illustrate the improvement brought by the method (Fig. 7a). In Fig. 7b and Fig. 7c, colors represent the normalized intensities, after the histogram of time return (Fig. 7b) and reconstruction with CS (Fig. 7c). Considering the biggest and less detailed objects, the improvement for recognition is not high ('ONERA' letters), even though borders are slightly better defined. The French motto is unreadable in Fig. 7b but it's pretty clear in Fig. 7c. The bust of the French Marianne is also better defined.

CONCLUSION

In this paper we describe a new theoretical 3D LiDAR process based on compressive sensing. We use simultaneously a focal plane array in Geiger mode and a CS approach based on DMD. We have highlighted the fact that this application is not trivial. We also developed an algorithm using signal processing and then CS with OMP to achieve a 3D reconstruction. The resolution of the final image is increased at long range (<10 km) under realistic daylight conditions.

ACKNOWLEDGMENTS

The authors would like to thank the Région Occitanie for funding this research through a doctoral fellowship.