Amélie Châtel
email: amelie.chatel@uco.fr

Melanie Auffan

Hanane Perrein-Ettajani

Lenka Brousset

Isabelle Métais

Perrine Chaurand

Mohammed Mouloud

Simon Clavaguera

Yohann Gandolfo

Mélanie Bruneau

Mélanie Auffan

Armand Masion

Alain Thiéry

Jérôme Rose

Catherine Mouneyrac

The necessity of

Keywords: Mesocosm, TiO 2 MNMs, Scrobicularia plana, Planorbarius corneus

come   L'archive ouverte pluridisciplinaire

INTRODUCTION

Releases of Manufactured Nanomaterial (MNMs) can occur during any stage of the MNM life cycle i.e. production stage of nanoproduct, the use/application stage of these nanoproducts and their ultimate end-of-life management/disposal. A comprehensive understanding of the potential for such releases along the whole life cycle and their possible effects is crucial to ensure the safe and sustainable use of these new materials (Salieri et al., 2018). Among all MNMs, TiO 2 MNMs are introduced into many products such as paints, plastics, food additives, sunscreens and other care products (Yin 2012). The use of TiO 2 MNMs into cement is a recent application in building material industry. Thanks to its photocatalytic properties, it confers to the building material air decontamination, selfsterilizing, self-cleaning and anti-fogging abilities (Jimenez et al., 2016). For those reasons, photocatalytic cement appears to be an appealing market for industry that represents from 0.1 to 1% of the total European production of TiO 2 and hence about 10.2t to 102t of TiO 2 MNMs released each year (Nanotechproject.org). TiO 2 MNMs incorporated in the cement matrix are usually non-coated anatase with a mass concentration ranging from 0.3 to 10 wt% (Ruot et al., 2009). Degradation of TiO 2 MNM-based cement is likely to happen at each stage of the cement life cycle (production, manufacturing, use disposal and recycling) (Bossa et al., 2017).

The main causes of release of TiO 2 MNMsfrom photocatalytic coatings is the stripping of the TiO 2 from the coatings because of the water flow, the dispersion of agglomerate under NaCl and UV light condition and finally its discharge from loosening caused by mechanical damage (Olabarietta et al., 2012). A recent study showed that TiO 2 MNMs were released (18.7 ± 2.1 to 33.5 ± 5.1 mg of Ti/m 2 of cement after 168 h) from photocatalytic cement pastes that were leached at a lab-scale to produce a range of degradation rates, meaning that in the worst-case scenario of weathering a negligible mass of TiO 2 (0.04w.%) was released from the photocatalytic cement (Bossa et al., 2017). TiO 2 MNMs release comes from a very thin active surface layer where both the cement surface chemistry and its pore network morphology control the TiO 2 MNMs diffusion (Bossa, 2019).

Laboratory studies have extensively demonstrated the adverse effects of TiO 2 MNMs on many aquatic organisms (Ramsden et al., 2009;Binh et al., 2016;Hall et al., 2009;Kulacki et al., 2012). Nevertheless, those studies have been conducted in simple systems (microcosm) and they did not reflect the MNMs fate and behavior in the environment due to processes such as sorption and aggregation of MNMs [START_REF] Auffan | An adaptable mesocosm platform for performing integrated assessments of nanomaterial risk in complex environmental systems[END_REF]. As a consequence, for a strongly characterization of risk, the combination of the organism, its environment and MNMs needs to be taken into account and requires interdisciplinary expertise in physical-chemistry, biology and ecotoxicology [START_REF] Auffan | An adaptable mesocosm platform for performing integrated assessments of nanomaterial risk in complex environmental systems[END_REF]. In that context, mesocosms represent relevant experimental systems for investigating the complex issue of exposure that enable to get quantitative time-and spatial data on the distribution of MNMs within a simulated ecosystem. A mesocosm refers to "an experimental system that simulates real-life conditions as closely as possible, while allowing the manipulation of environmental factors" (FAO, 2009). As stated during the H2020 European commission funded NANoREG project (Project #646221), mesocosms have been shown to provide a reliable methodology to obtain quantitative time-and spatially regarding exposure-driven environmental risk assessment.

In this context, two indoor mesocosm platforms (one marine and one freshwater) were conceived with small size tanks (60 L) for investigating MNM exposure and impacts on aquatic species that allows to recreate freshwater and estuarine conditions (sediment, tide cycles, controlled temperature, salinity and redox potential) [START_REF] Auffan | Contribution of mesocosm testing to a single-step and exposure-driven environmental risk assessment of engineered nanomaterials[END_REF]. TiO 2 MNMs and TiO 2 MNM-based cement fate, behavior, bioaccumulation and toxicity were evaluated after a 28 day exposure in two mollusks representative of the estuarine and freshwater ecosystems : the bivalve Scrobicularia plana and the gastropod Planorbarius corneus. Scrobicularia plana is an endobenthic bivalve involved in the functioning and the structure of estuarine ecosystems and has also been largely demonstrated to represent a relevant model for biomonitoring (Mouneyrac et al., 2014). Planorbarius corneus is a hermaphroditic snail that inhabits small temporary ponds. This species belongs to the Planorbidae, the largest family of aquatic pulmonate gastropods distributed all over the world (Jopp, 2006). Planorbarius corneus play an important role in trophic chains as grazer and as prey (Wojdak and Trexler, 2010) and have already been used as model organisms for exposure and toxicity studies in mesocosms [START_REF] Tella | Transfer, Transformation and Impacts of Ceria Nanomaterials in Aquatic Mesocosms Simulating a Pond Ecosystem[END_REF], 2015[START_REF] Auffan | Environmental Exposure of a Simulated Pond Ecosystem to Cuo Nanoparticle Based-Wood Stain Throughout Its Life Cycle[END_REF].

The originality of the project was to compare the fate and behavior of a nano-enable product (TiO 2 MNM-based cement) in these two freshwater and marine ecosystems. Two stages of the MNM lifecycle were considered : the formulation stage using bare TiO 2 MNMs and end of life stage of the cement containing TiO 2 MNMs using cement leachate. Freshwater and marine mesocosms were used to obtain resolved data on the distribution, transformation and impact towards these mimicked ecosystems depending on the physical-chemical properties of the environment (salinity, pH, conductivity, tide cycle or not…) and the physical-chemical properties of the contaminant at two stages of the lifecycle. One of the major drawbacks in assessing environmental impact of MNMs is that the environmental concentrations are not yet known. Herein, we used between 1and 1.2 mg.L -1 of TiO 2 MNMs which belong to the threshold values estimated in highly exposed areas [START_REF] Bourgeault | The challenge of studying TiO2 nanoparticle bioaccumulation at environmental concentrations:crucial use of a stable isotope tracer[END_REF].

MATERIAL AND METHODS

TiO 2 NPs

Primary size and shape of TiO 2 MNMs (NM212, JRC repository) were determined by an ultra-high resolution scanning electron microscopy SEM LEO 1530 (LEO Electron Microscopy Ltd, Cambridge, England) and Transmission Electron Microscopy (analytical TEM Field Emission Gun (FEG) 200 KV Osiris from Tecnai, FEI, Japan). The SEM and TEM images corroborate the nanometric size of the particles (see SI, figure S1). X-ray diffraction (XRD) patterns of the samples were obtained using a Bruker D8 X-ray diffraction (XRD) system in a θ-2θ mode and Cu Kα X-ray source. The TiO 2 MNMs have a bodycentered tetragonal anatase crystal structure (see SI). The width of the XRD peaks were used to calculate a crystallite size about 9 nm. A specific surface area of 223 m 2 /g was determined by the Brunauer-Emmett-Teller (BET) adsorption method using the N 2 adsorption isotherm measured at 77K (BELSORP-max, BEL Japan Inc.).

TiO 2 MNMs-based cement

Photocatalytic white Portland cement incorporating TiO 2 MNMs was provided by a European cement manufacturer (Calcia, France) through the French Technical Association of Industries of Hydraulic Binders (ATILH, France). This cement is mainly composed of Ca and Si (≈66wt % CaO and ≈23 wt% SiO 2 ) and contains 2.85 wt% of TiO 2 (anatase) (Bossa et al., 2017).

Cylindersof hardened cement (4 cm diameter, 8 cm high) were obtained after 28 days of hydration at 20°C with a water/cement ratio of 0.5. Hardened cement pastes exhibit a complex mineralogy, i.e. a mixture of hydrated minerals (portlandite, calcium silicate hydrates, ettringite) and residual anhydrous minerals (di and tricalcium silicates). TiO 2 MNMs are homogeneously dispersed in the hydrated paste, with the exception of few high spotsof50 µm (Bossa et al., 2017).

Cement degradation residue generation was simulated using accelerated lab-scale approach to conduct a so-called « worst-case scenario » and to generate a quantity of cement degradation residues for mesocosms dosing. Finely crushed cement pastes were leached in batch using ultra-pure water (UPW) with an elevated liquid-to-solid ratio (L/S) of 100. After pH stabilization (pH > 12.5), the suspension of cement degradation residues was neutralized with slow addition of nitric acid (22.37 mol.L -1 ) reach a pH of 7.8 and a conductivity of 13 mS.cm - 1 . The solution is composed of a dissolved fraction (mainly Ca and Si, 203 and 3.96 mg.L -1 respectively) and a particulate fraction with a TiO 2 concentration of 143.7±2.6 mg.L -1 . In accordance with the very low TiO 2 MNM solubility, no TiO 2 MNM dissolution was observed (Table S1). The concentrations of Ca and Si in the dissolved fraction reveal the high degradability of the cement matrix in natural media (pH 7.8). Presence of free TiO 2 MNMs, i.e. not embedded in cement matrix, in the solution of cement degradation residues is then suspected. In neutralized cement degradation residues, TiO 2 MNMs were observed mainly associated with aggregates larger than 0.45 µm and with SiAl intermix chains. SiAl chains are supposed to be geopolymers stable at pH 7 and resulting from secondary precipitation/ polymerization during the pH neutralization process (Bossa et al., 2017).

Animals

Individuals of Scrobicularia plana (15-20 mm length) were hand-collected in November 2015 in the intertidal mudflat on the French Atlantic coast (Bay of Bourgneuf: N 47°01'50.35", W 1°59'04'80'') and transported in cool boxes to the laboratory. Then, bivalves were immediately placed into aerated artificial water (Tropic marin ® ) at 30 practical salinity units (psu) during 5 days in a temperature controlled room at 15°C (temperature experienced in the field at the collection time). A natural inoculum containing picoplankton as primary producer (bacteria, algae, protozoa, etc.) was also collected in the intertidal mudflat. Physico-chemical parameters of seawater from the collection site were : pH= 7.7; salinity 28 psu; conductivity 40 mS.cm -1 . Individuals of Planorbarius corneus (L., 1758) (Great Ram's Horm snail, benthic grazer) were hand-collected in October 2015 in a non-contaminated temporary pond part of the Natura 2000 reserve network in south of France (Bonne Cougnes: N 43°20'47.04", E 6°15'34.786'', 246 m a.s.l.) and transported in pond water to the laboratory. A natural inoculum containing picobenthosas primary producer (bacteria, algae, protozoa, etc.) was also sampled in the pond. Physico-chemical parameters of the pond water from the collection site were: water temperature 14.9°C; conductivity 819 mS.cm -1 ; concentration of dissolved oxygen 0.72 mg.L -1 (6.6%).

Mesocosm setup

Freshwater mesocosms. The mesocosm experiments were already described by [START_REF] Auffan | An adaptable mesocosm platform for performing integrated assessments of nanomaterial risk in complex environmental systems[END_REF], [START_REF] Tella | Transfer, Transformation and Impacts of Ceria Nanomaterials in Aquatic Mesocosms Simulating a Pond Ecosystem[END_REF], [START_REF] Tella | Chronic Dosing of a Simulated Pond Ecosystem in Indoor Aquatic Mesocosms: Fate and Transport of Ceo 2 Nanoparticles[END_REF], [START_REF] Auffan | Environmental Exposure of a Simulated Pond Ecosystem to Cuo Nanoparticle Based-Wood Stain Throughout Its Life Cycle[END_REF](figure 1). Tanks (750 x 200

x 600 mm) were filled with 6-8 cm artificial sediments containing 89% SiO 2 , 10% kaolinite and 1% of CaCO 3 w/w adapted from OECD guideline (OECD, 2004). Primary producers were brought by ~300 g of water-saturated natural sediment (sieved at 200 µm) laid at the surface. The mesocosms were then gently filled with 50 L of Volvic water with pH and conductivity close to the natural pond water (pH 7, 11.5 mg.L -1 Ca 2+ , 13.5 mg.L -1 Cl -, 71 mg.L -1 HCO 3 2-, 8 mg.L -1 Mg 2+ , 6.3 mg.L -1 NO 3 -, 6.2 mg.L -1 K + , 11.6 mg.L -1 Na + ).

After 2 days, the physical-chemical parameters of the mesocosms were stabilized (turbidity, pH, dissolved O2, redox). Then, 19 adult P. corneus were added per mesocosm and acclimatized for one week. Organisms were exposed for 28 days in a temperature controlled room (18°C) and under controlled light (photoperiod day/night 10:14). Physico-chemical parameters including temperature (°C), pH, redox potential in the water column and the sediment (mV), and dissolved oxygen (mg O2.L-1) were monitored every 2 min during the whole duration of the experiment. Among the 6 freshwater mesocosms, 2 were kept as negative control (without contamination), 2 were exposed to TiO2 MNMs (considered as positive control), and 2 were exposed to cement leachate. While the first control (negative control) condition allows to follow animal behavior (mortality) during the experiment, the second one serve as a positive control experiment to follow TiO2 bioaccumulation by the organisms in order to compare with animals treated with cement for both freshwater and marine systems.

. Marine mesocosms. Each experimental unit was composed with two tanks (mesocosm and reserve tank), two pumps (Eheim compact 300L.h -1 ) and a mechanical timer (IDK PMTF 16A) allowing to mimicking the tidal cycle (figure 1). The mesocosm tank (750 x 200 x 600 mm) was filled with 14 kg synthetic sediment (90% SiO 2 , 9% kaolinite, 1% CaCO 3 w/w) adapted from OECD guideline (OECD, 2004). Three hundred g of water-saturated natural inoculums was laid at the surface to bring primary producers. Then, each mesocosm tank was flooded with 35 L of the artificial seawater Tropic Marin™ (Tropicarium Buchshlag Dreieich, Germany) at 30psu. The reserve tank (700 x 500 x 37 mm) was placed under the first one (mesocosm tank) to collect removed water from the mesocosm tank during low tide.

Reservoir tank was always filled with a minimum of 25 L of artificial seawater at 30 psu to constantly maintain the measuring probe immersed.

After one week, the physical-chemical parameters of the mesocosms were stabilized (turbidity, pH, dissolved O 2 , redox). Then, 55 S. plana were added per mesocosm and acclimatized for 5 days. Organisms were exposed for 28 days in a temperature controlled room (15°C), under controlled light (photoperiod 16:8) and at a tidal cycle (6h of low tide, 6h of high tide; two tides /day). Physical-chemical parameters including temperature (°C), salinity (psu), pH, redox potential (mV), dissolved oxygen (mg O 2 .L -1 ) were monitored every 15 min into the water column from the reserve tank during the whole duration of the experiment. Among the 9 marine mesocosms, 3 were kept as negative control (without contamination), 3 were exposed to TiO 2 MNMs (positive control) and 3 were exposed to cement leachate.

Figure1. Scheme of the freshwater (left) and marine (right) mesocosms.

Mesocosm dosing

Aqueous suspensions of TiO 2 MNMs and TiO 2 MNM-based cement degradation residues (with a stabilized pH of 7.8) were prepared prior injections in the mesocosms. Aliquots of these suspensions were digested using an Ultra WAVE microwave digestion system with 1 mL HNO 3 67% (NORMATOM) and 1 mL HF 47%-51% (PlasmaPure) and analysed by ICP-MS (Perkin Elmer © Nexion 300 ICP-MS) for their total Ti contents. A concentration of 4.86±0.13 g.L -1 TiO 2 (n=3) was found for the TiO 2 MNM suspension (2.91±0.08 g.L -1 Ti). The TiO 2 concentration measured in the solutions of cement degradation residues (n=6) was 143.7±2.6 mg.L -1 (86±1.6 mg.L -1 Ti). Both suspensions were close to the targeted concentrations and showed excellent recovery yields after digestion (> 95%).

A multiple dosing experiment was performed on a 4 week-period. A total of 12 dosings were achieved (3 times per week), corresponding to 0.09 mg.L -1 of TiO 2 per injection in order to reach a final nominal concentration of 1mg.L -1 TiO 2 per mesocosm. As the suspension of cement degradation residues is not stable over time, a new neutralized batch was prepared every two injections and stored at 4°C in dark between the two injections.

Ti quantification in the different compartment of the mesocosms

The concentration of Ti in the mesocosms following TiO 2 MNMs or cement leachate contamination was measured in the water column, in the surficial sediments and in the organisms sampled at 0, 7, 14, 21 and 28 days. Water was sampled at ~10cm from the air/water interface. Surficial sediments (between 500 µm to 1000 µm depth) were sampled at three different locations and then pooled before being dried. Samples were digested using microwaves at 180°C before analysis by ICP-MS.

For the marine mesocosms, Ti quantifications were performed by Micropolluants Technologie S.A. (Metz, France) using an Agilent 7700 ICP-MS (Agilent Technologies France). 10 mL of water or 2 mL of surficial sediments were mixed with 1mL 32-35% HCl, 1mL 67-69% HNO 3 , 100 µL 94-98% H 2 SO 4 , and 1 mL 47-51% HF prior ICP-MS measurements. For S. plana, whole soft tissues were mixed with 1 mL 67-69% HNO 3 , 100 µL 94-98% H 2 SO 4 , and 1 mL 47-51% HF. For the freshwater mesocosms, water samples (2 mL) were digested with 1 mL HNO 3 67-69% and 0.5 mL HF 47%-51%. For the surficial sediments (50 mg), a mixture of 3 acids (1 mL HCl 34%, 2 mL HNO 3 67%, 0.5 mL HF 47%-51%) was used. For P. corneus, the digestive glands were dissected, before being digesting using 1 mL HNO 3 67%, 0.5 mL H 2 O 2 30%-32% and 1 mL HF 47%-51%. Samples were digested using the microwave Ultra WAVE and the analysis were performed using the Perkin Elmer Nexion 300 ICP-MS. Using sediments and freshwater organisms spiked with TiO 2 nanoparticles, a recovery yield of >95% after microwave digestion and ICP-MS analysis was obtained.

Evaluation of immunotoxic effects in S. plana: pp38 level measurement by Western blot

Total whole soft tissues of S. plana exposed for 28 days (n=7 for each condition) were homogenized with lysis-buffer (NaCl 0.2M, DTT 1mM, protease inhibitor cocktail 0.1%) in a mortar at 4°C. The clear supernatant was then obtained by centrifugation (13,000xg, 10 min, 4°C) and stored at -20°C until analysis. Protein concentrations were determined according to Bradford (1976) using bovine serum albumin as a standard. Protein extracts were mixed with sample buffer (0.5 M Tris-HCl, pH 6.8, 2% SDS, 10% glycerol, 4% 2-mercaptoethanol, 0.05% bromophenol blue) 1:3 and boiled for 5 min at 95°C. Proteins (40 µg per lane) were separated using a 12% polyacrylamide gel. Western blot analysis was performed as previously described (Châtel et al., 2011b). After transfer, membranes were incubated with a mouse monoclonal antibody anti-Phospho-p38 MAPK (Thr 180 /Tyr 182 ) (9216-Cell signaling Biotechnology) diluted in 1/1000 in TBS/BSA 5% or with a mouse monoclonal antibody antiβ-Actin (A5441 -SIGMA) diluted in 1/2000 in TBS/BSA 5%. After washing (3 times for 5 min), membranes were incubated with a goat anti-Mouse IgG antibody coupled with alkaline phosphatase (A3562, Sigma Aldrich) diluted 1:2000 in TBS/BSA 5%. Detection of immune complexes was carried out by colorimetric reaction using a solution of 5-bromo-4-chloro-3indolyl phosphatase (BCIP) and nitroblue tetrazolium (NBT). After visualization, membranes were scanned and band intensity, which is the relative amount of protein expression, was quantified as Relative Optical Densities (ROD; pixels/mm 2 ). Results of pp38 were normalized according to actin expression.

Statistical analysis

The measured values were compared among different groups using the non-parametric test Mann-Whitney (XL-Stat software) and the Student's t-test. Statistical significance was accepted at p<0.05.

RESULTS and DISCUSSION

Favorable physical-chemical conditions in freshwater and estuarine mesocosms

During the 28 days of contamination several physical-chemical parameters were monitored to assess the global response of the mesocosms to the presence of TiO 2 MNMs and cement leachate. In marine as well as in freshwater mesocosms, the average temperature, dissolved O 2, conductivity, and pH were not significantly different between negative controls and contaminated mesocosms(see SI, Figures S2 andS3).

Oxido-reductive probes indicated that freshwater was oxidative (310±20 mV), while reductive conditions prevailed in the sediments (ca -370 mV). Regarding the conductivity, a step by step increase from day 0 to day 28 (200 ± 1 µS.cm -1 to 288 ± 0.4 µS.cm -1 respectively) was observed. Conductivity drops were recorded during the weekly refills with ultrapure water to compensate the evaporation. On the whole, no significant differences were observed between controls and contaminated mesocosms.

Consequently, during the exposure to TiO 2 MNMs and cement leachate, the physico-chemical conditions of the 15 mesocosms remained favorable with the oxygenation, pH, temperature, redox potential in the range of natural conditions.

Homo-aggregationof TiO 2 MNMs and accumulation in the surficial sediments

Bossa et al. (2017) estimated using an accelerated aging protocol that a negligible mass of TiO 2 (0.04w.%) was released from the photocatalytic cement (Bossa et al., 2017). Herein, we used an accelerated lab-scale approach to conduct a so-called « worst-case scenario » assuming that 100% of the Ti contained in the cement would have been released. Figure 3 and 4 show the Ti concentrations measured in the water column and sediments of both freshwater and marine mesocosms as a function of time. Ti was detected in both waters and sediments sampled in control mesocosms proving that a high geochemical background of this element existed in the mimicked ecosystems. Average background Ti concentrations in freshwater mesocosms were 19.2±17.2 µg.L -1 in the water column and 2230±928 mg.kg -1 in surficial sediments. Average background Ti concentrations in marine control mesocosms were 567±273mg.kg -1 in surficial sediments and below the quantification limit (<2.5 µg.L -1 ) in the water column. Ti is a naturally occurring element in mineral and amorphous phases occurring in freshwater and marine environments. Ti can be found in titanium-iron oxide minerals (as ilmenite), TiO 2 minerals as rutile, anatase, and brookite. Herein, the TiO 2 MNMs used were engineered nanosized anatase minerals. Consequently even if the Ti background concentration was elevated, it is noteworthy that the speciation and reactivity of the naturally occurring Tibearing phases might be different from the MNM injected.

In the surficial sediments of marine mesocosms, high concentrations of Ti were detected after 7 days (control, TiO 2 MNMs, and cement leachate) and progressively decreased until 28 days (Figure 4, right). However, because of the elevated geochemical background of Ti, no statistical difference was observed between controls and contaminated mesocosms. Similarly, no increase in Ti concentration could be evidenced in the surficial sediments of contaminated freshwater mesocosms compared to controls. Besides, the fluctuations of Ti concentration measured over time were likely related to the heterogeneity of the Ti distribution and the difficulty of sampling the surficial sediments(Figure 4). These results highlighted the challenge of a reliable quantification of Ti in that compartment.

Total Ti concentrations in the water column of marine mesocosms (control, TiO 2 MNMs and cement leachate) were always below the quantification limit estimated at 2.5 µg.L -1 whatever the duration of exposure. On the opposite, total Ti concentrations in the water column were always above 10 µg.L -1 in freshwater mesocosms. The only condition for which a statistically significant difference was observed between the water column of controls and contaminated freshwater mesocosms was after 7 days of exposure to TiO 2 MNMs. At this time point, the difference between TiO 2 MNMs contaminated mesocosms and geochemical Ti background were 2.2±1.2 µg.L -1 Ti for a total Ti concentration injected of 180 µg.L -1 Ti (300 µg.L -1 of TiO 2 ). Based on these values, we estimated that 98-99 % of the Ti injected was removed from the water column after 7 days. Although no increase in Ti concentration could be evidenced in the surficial sediment of freshwater mesocosms, we hypothesize that both cement leachate and TiO 2 MNMs settled at more than 98% at the surface of sediments. Based on the 31.0±0.6 mg and 35.0±0.9 mg Ti introduced respectively after 28 days in mesocosms contaminated with cement leachate and TiO 2 MNMs, the remaining of 2% of Ti particles in the water column should entail a theoretical increase in the surficial sediment of176 mg.kg -1 , which is far below the standard deviation determined for Ti background in that compartment. This explains why Ti accumulation at sediment surface remained undetected by chemical analysis.

In addition, in marine mesocosms, due to the tidal system, part of the sediment were removed along with the water in the lower tank and sedimentation of TiO 2 occurred as well in this compartment favoring decrease in its concentration as compared to freshwater mesocoms. Figure 3. Total Ti concentration in the water column after 7, 14, 21 and 28 days of exposure in freshwater mesocosms. Ti concentration in the water column in marine mesocosms is not represented as values were always below the quantification limit estimatedat 2.5 µg.L -1 . Statistical significance was determined by the Student's t-test (*: p<0.05). Figure 4. Total Ti concentration in surficial sediment after 7, 14, 21 and 28 days of exposure in freshwater (left) and marine (right) mesocosms.

In freshwater mesocosms, the size distribution of the suspended matter in the 0.1 µm -1000 µm size range and the total number of suspended particles in the 0.4 µm -0.9 µm size range were not different between control and contaminated mesocosms (Figure 5). This highlighted that the main mechanism of aggregation and settling down expected in the water column was the homo-aggregation of the TiO 2 MNMs either pristine or brought via cement leachate. In marine mesocosms, MNM homo-aggregation was expected to be even faster due to higher alkalinity and ionic strength as compared to freshwater environments [START_REF] Peralta-Videa | Nanomaterials and the environment: a review for the biennium 2008-2010[END_REF][START_REF] Rocha | Gold-supported magnetically recyclable nanocatalysts: a sustainable solution for the reduction of 4-nitrophenol in water[END_REF][START_REF] Vale | Manufactured nanoparticles in the aquatic environment-biochemical responses on freshwater organisms: A critical overview[END_REF]. It is noteworthy that the aggregation of MNMs allows their deposition onto the surficial sediment [START_REF] Peralta-Videa | Nanomaterials and the environment: a review for the biennium 2008-2010[END_REF], resulting in high exposure of benthic organisms compared to planktonic organisms [START_REF] Mohd Omar | Aggregation and disaggregation of ZnO nanoparticles: Influence of pH and adsorption of Suwannee River humic acid[END_REF]Mouneyrac et al., 2014).

* Figure 5. (left) Size distribution of colloidal particles in the water column of freshwater control mesocosms at day 0. The dotted lines mark out the 0.4 µm -0.9 µm fraction. (right) Evolution of the number of colloidal particles in the 0.4µm -0.9 µm range from day 0 to 28, under the three conditions tested (control, cement leachate and TiO 2 MNMs) in freshwater mesocosms.

Bioaccumulation and effects on benthic organisms

P. corneus and S. plana are two benthic grazer species. While P. corneus eat algae and biofilms at the sediment/water interface [START_REF] Jones | Aspects of Respiration in Planorbis Corneus L. And Lymnaea Stagnalis L. (Gastropoda: Pulmonata)[END_REF], S. plana can either feed suspended particles from the water column but also ingest sedimentary particles [START_REF] Hughes | A study of feeding in Scrobicularia plana[END_REF]. For S. plana exposed in marine mesocosms, elevated background of Ti concentrations were measured in the control group (84.8±42.3 mg.kg -1 dry weight) which did not allow to discriminating any bioaccumulation process in organisms exposed to TiO 2 MNMs and cement leachate (97.1±43.9 and 107.5±48.2 mg.kg -1 dry weight, respectively) (figure 6).

Background concentrations of Ti measured in the digestive glands of unexposed P. corneus were one order of magnitude lower. Following exposure to cement leachate, no difference in Ti concentration in the digestive glands were measured with respect to control P. corneus.

However, statistically different concentrations of Ti were measured in the digestive glands compared to controls following exposure to TiO 2 MNMs i.e.1.5 ± 0.2 mg Ti.kg -1 (dry weight) and 2.5 ± 0.1 mg Ti.kg -1 (dry weight) after 21 and 28 days of exposure respectively (figure 6). This suggests that an ingestion of Ti by P. corneus occurred likely resulting from the accumulation of TiO 2 MNMs on the surficial sediments. Some authors have shown abilities to discriminate natural Ti from TiO 2 NMs. For example, [START_REF] Bourgeault | The challenge of studying TiO2 nanoparticle bioaccumulation at environmental concentrations:crucial use of a stable isotope tracer[END_REF] resolved this lack of sensitivity using isotopically modified TiO 2 nanoparticles ( 47 Ti) to characterize the processes governing Ti bioaccumulation in a freshwater environment. Thanks to the 47 Ti labeling, they detected bioaccumulation of NPs in Dreissena polymorpha exposed for 1 h at environmental concentrations via water (7-120 μg/L of 47 TiO 2 NPs) and via their food (4-830 μg/L of 47 TiO 2 NPs mixed with 1 × 10 6 cells/mL of cyanobacteria) despite the high natural Ti background, which varied in individual mussels. Such a methodology would be particularly relevant in mesocosms experiment mimicking real environments with high Ti background. Figure 6. Total Ti concentration in the digestive gland of P. corneus (left) and total soft tissues of S. plana (right) after 7, 14, 21 and 28 days of exposure in mesocosms. The statistical significant was determined by the Student's t-test (*: p<0.05; ** : p<0.01).

During the 28 days of exposure in mesocosms, the survival rates of P. corneus and S. plana (<2% of mortality, data not shown), picoplankton and picobenthos (see SI, Figure S4) were not affected by the presence of TiO 2 MNMs and cement leachate. Hence, no acute toxicity was observed towards these two trophic levels. Nevertheless, a thorough characterization of the biological responses (at the individual, sub-individual, and community levels) is still needed to better understand the biological mechanisms of interactions.

One of the main effect associated with TiO 2 toxicity was the induction of immune responses.

The MAPKs represent a superfamily of protein Ser/Thr-kinases, highly conserved through evolution [START_REF] Kyriakis | Mammalian mitogen-activated protein kinase signal transduction pathways activated by stress and inflammation[END_REF][START_REF] Roux | ERK and p38 MAPK-activated protein kinases: a family of protein kinases with diverse biological functions[END_REF], that can transduce stress signals into cellular responses [START_REF] Kultz | Mitogen-activated protein kinases are in vivo transducers of osmosensory signals in fish gill cells[END_REF][START_REF] Kyriakis | Mammalian mitogen-activated protein kinase signal transduction pathways activated by stress and inflammation[END_REF]. Three subfamilies of the MAPKs have been well described in mammals: the extracellular regulated protein kinase (ERK), the c-Jun NH 2 -terminal kinases (JNK) and the p38-MAPK. ERKs have been more associated to cell division, growth and differentiation whereas JNKs and p38-MAPKs are activated in various types of stress going from osmotic stress to chemical stress and can trigger cell survival or death (apoptosis), depending on their isoform and/or cell type [START_REF] Canesi | Insulin-like effect of zinc in Mytilus digestive gland cells: modulation of tyrosine kinase-mediated cell signaling[END_REF][START_REF] Canesi | Signaling pathways involved in the physiological response of mussel hemocytes to bacterial challenge: the role of stress-activated p38 MAP kinases[END_REF][START_REF] Canesi | Immunomodulation by 17 beta-estradiol in bivalve hemocytes[END_REF][START_REF] Châtel | Activation of MAP kinase signaling pathway in the mussel Mytilus galloprovincialis as biomarker of environmental pollution[END_REF]Châtel et al., , 2011a,b),b). They have been demonstrated to play a key role in immune responses in mammals [START_REF] Caffrey | The evolution of the MAP kinase pathways: coduplication of interacting proteins leads to new signaling cascades[END_REF] but also in invertebrates and more particular in bivalves [START_REF] Canesi | Insulin-like effect of zinc in Mytilus digestive gland cells: modulation of tyrosine kinase-mediated cell signaling[END_REF][START_REF] Canesi | Signaling pathways involved in the physiological response of mussel hemocytes to bacterial challenge: the role of stress-activated p38 MAP kinases[END_REF][START_REF] Canesi | Immunomodulation by 17 beta-estradiol in bivalve hemocytes[END_REF]. Moreover p38 MAPK have been shown to be induced by TiO2 exposure in bivalves [START_REF] Couleau | Hemocyte responses of Dreissena polymorpha following a shortterm in vivo exposure to titanium dioxide nanoparticles: preliminary investigations[END_REF].

P38 MAPK in S. plana have been studied in the laboratory and antibody matching has already been verified on this specie as opposed to P.corneus. Since no ingestion of Ti by S. plana was identified by ICP-MS, western blot analysis of S. plana using specific antibodies directed against the phosphorylated form of p38 MAPK were used (Figure 7).

In the present study, membrane revelation showed that the molecular weight of pp38 in S. plana is around 38 KDa. After normalization of the different bands representing pp38 expression with actin, results revealed that there was no significant modification in pp38 expression level for any of the conditions tested (TiO 2 MNMs or cement leachate), as compared to control group (figure 7). This suggested no stimulation of immune response of S. plana following 28 days of exposure. [START_REF] Couleau | Hemocyte responses of Dreissena polymorpha following a shortterm in vivo exposure to titanium dioxide nanoparticles: preliminary investigations[END_REF] observed in the freshwater mussel D. polymorpha exposed to TiO 2 (0.1 to 25 mg.L -1 during 24 h), that ERK ½ was activated for all concentrations tested in this study whereas p38 activation was only observed when bivalves were exposed to 5 and 25 mg.L -1 ) indicating that p38 phosphorylation was less sensitive than ERK ½ to this contaminant. This could be the case in the present study.

Moreover, an in vitro M. galloprovincialis hemocyte exposure to TiO 2 (10 µg.ml -1 ) for 5 to 60 min showed that pp38 activation was transient, with an increase in phosphorylated form of p38 after 5 and 15 min, followed by a dephosphorylation at 30 and 60 min [START_REF] Canesi | In vitro effects of suspensions of selected nanoparticles (C60 fullerene, TiO2, SiO2) on Mytilus hemocytes[END_REF]. Even though p38 is implicated in immune responses, absence of p38 activation does not mean that immune response is not present. However, in the present study, the long duration of exposure (28 days) could explain the absence of pp38 response depicted in S. plana and investigation of its response at shorter time points would have been interesting to perfom. Figure 7. Expression of pp38 in S. plana control, TiO 2 MNMs or cement leachate, analyzed by Western blot. Results have been normalized to actin expression levels.

Conclusion

In the present study, impact of TiO 2 MNMs and TiO 2 MNM-based cement leachate was investigated in marine and freshwater mesocosms, that allows to reproduce realistic environmental exposure (mid-term duration, low doses, chronic contamination,…) and in particular, a tidal system in the marine mesocosm. Such tools have been demonstrated as being relevant since they take into account both hazard and exposure and hence the synergetic and/or antagonistic effects of different physico-chemical parameters (temperature, pH, redox potential, conductivity), that is of great interest for the regulation of the use of NMs [START_REF] Auffan | Contribution of mesocosm testing to a single-step and exposure-driven environmental risk assessment of engineered nanomaterials[END_REF].The originality of the project was also to compare the exposure and potential impact of TiO 2 and cement containing TiO 2 MNMs on two species, representative of the estuarine/freshwater continuum(with a salinity gradient),that are particular targets towards nanomaterials at the water/sediment interface. The use of similar design for both freshwater and marine systems showed challenging points and limitations, that enable consistent comparison of fate and behavior of NMs in different species. However, even with same procedures, characterization of TiO 2 in different abiotic compartments was difficult, as stated in this study, and made challenging investigations of differences in bioaccumulation and effects in these benthic species. The standardization of stable test suspensions for nanomaterials is an ongoing challenge as it is well documented that the preparation method influences the interpretation of toxicity according to the exposure. In the context of developing a regulatory framework this is a challenge as it necessary that all nanomaterials have equivalent preparation techniques in order to have a better standardization of experiments and hence a more comparable set of data generated for nanomaterial-related data categorization.

Finally, studying the impact of TiO 2 at different stages of the TiO2 MNMs life cycle allows identifying critical stages at which Safe by design (SbD) concepts can be implemented to reduce adverse impacts or decrease exposure to MNMs. Five mL of water and 15 mL of sediment were sampled, treated with formaldehyde (3.7%), and stored at 4°C before counting. Before picoplankton counting, 1 mL of each water column sample was centrifuged (5.9 × g at 4°C for 15 min), and 200 μL of each sediment sample was treated with 800 μL of 0.1 mM sterile tetrasodium pyrophosphate and vortexed with a steel ball for 30 seconds. For the counting, 10 μL of each sample was mixed with 5μL of 3μM SYTO® 9 Green Fluorescent Nucleic Acid Stain and dropped on a glass slide. Concentration of picoplankton was the mean ± standard deviation of five counts.

  Figure 2. For each injection, a low and realistic concentration of 0.1 mg.L -1 of injected TiO 2was targeted in the mesocosm (0.06 mg.L -1 Ti). After 30 days (12 injections), the cumulated concentration of TiO 2 injected reached 1-1.2 mg.L -1 in the mesocosms.

Figure S2 .

 S2 Figure S2. Evolution of the physical-chemical parameters in the water column of the marine mesocosms. Temperature, Redox potential, dissolved oxygen, pH were measured during phases I (stabilization) and II (contamination). Day 0 corresponds to the first dosing of NPs. The grey surface is defined by the maximum and minimum values of each parameter, and the dark line corresponds to the average values of the 9 mesocosms. One measurement was performed every 5 min.

Figure S4 .

 S4 Figure S4. Concentration of picoplankton in water column at 10 cm below water surface (Top) and in surficial sediments(depth: 0.5 to 1 mm) (B)on a weekly basis. Five mL of water and 15 mL of sediment were sampled, treated with formaldehyde (3.7%), and stored at 4°C before counting. Before picoplankton counting, 1 mL of each water column sample was centrifuged (5.9 × g at 4°C for 15 min), and 200 μL of each sediment sample was treated with 800 μL of 0.1 mM sterile tetrasodium pyrophosphate and vortexed with a steel ball for 30 seconds. For the counting, 10 μL of each sample was mixed with 5μL of 3μM SYTO® 9 Green Fluorescent Nucleic Acid Stain and dropped on a glass slide. Concentration of picoplankton was the mean ± standard deviation of five counts.

Table 1 .

 1 Concentrations of Ti, Ca, Al, Fe, Ca and Si after cement degradation in the total (dissolved + particulate fractions) and soluble fraction solution

		Ti	Na	Al	Fe	Ca	Si
	Total (mg.L -1 )	89.91 1.89	54.06 12.10	2216.00	2407.80
	Soluble fraction (<3 kDa) (µg/l)	3.22 182.00	1.00	1.00	2.03E+05	3960.00

ACKNOWLEDGEMENTS

The research leading to these results has received funding from the European Research Council under the European Union's FP7 Grant Agreement n.310584 (NANoREG project).

The authors wish to thank L. Izoret (ATILH, Paris, France) for providing cements, as well as A. Guiot, S. Artous, S. Jacquinot and O. Sicardy (CEA, Grenoble, France) for their participation to the characterization of the raw materials. The TEM used in this study was part of Nano-ID platform which was funded by the EQUIPEX project ANR-10-EQPX-39-01. Part of this study was also funded via the French ANR through the ANR-3-CESA-0014/ NANOSALT program, and the Excellence Initiative of Aix-Marseille University -A*MIDEX, a French "Investissementsd'Avenir" program through its associated Labex SERENADE project. This work was also a contribution to the OSU-InstitutPythéas. Finally, the authors acknowledge the CNRS funding for the international research project IRP iNOVE.


Keywords: Pyramid wavefront sensor, Extremely large telescopes, Modal control, Wavefront reconstruction

The pyramid wavefront sensor (PWFS), due to its extremely high sensitivity in comparison to the Shack-Hartmann WFS, is the design choice of most single-conjugate adaptive optics (AO) instruments currently being developed for extremely large telescopes (ELTs). This sensitivity benefit is served, however, with several technical drawbacks to overcome, one of which is the intrinsic non-linearity of the sensor. Even in modulated operation, the gradient measurement saturation non-linearity is strongly exacerbated by in-loop phase residuals for typical on-sky regimes, with high spatial frequencies inducing a dramatic sensitivity reduction for the controlled modes. This phenomenon has been dubbed "optical gain", and it was demonstrated that a modal gain compensation on an appropriate control basis provides an adequate mitigation of the sensitivity reduction, and improves the end-to-end performance on ELT SCAO systems across all relevant guide star magnitudes and seeing conditions.

Several techniques have been proposed to achieve this nominal performance recovery, however most require offline computation of interaction matrices; or some alterations to the usual AO loop operation. In this paper, we present the CLOSE (Correlation-Locked Optimization StratEgy) algorithm, which achieves determination of the modal gains, in a real-time fashion, through the sole use of the modal decomposition of the WFS measurements. Real-time estimators are implemented to implicitly measure resonance levels of the integrator transfer function, which is used as a proxy to control the modal gains through a second-layer servo loop. Using this method, we achieve compensation of the optical gain in the command law, and a fully automatic optimization of the modal integrator depending on the signal-to-noise level. Simulated end-to-end results are presented, for stationary or quickly varying seeing conditions, all at the scale of the MICADO SCAO design on the ELT. We also discuss the applicability of the CLOSE scheme on other known AO problems.

INTRODUCTION

Probing the distant universe with always finer resolution and precision requires to increase the diameter of the next generation of ground-based telescopes 1-3 so as to improve light collection and resolving power. The latter is limited by atmospheric turbulence, making extremely large telescopes (ELTs) a waste if not for the use of adaptive optics (AO). The pyramid WFS [START_REF] Ragazzoni | Pupil plane wavefront sensing with an oscillating prism[END_REF] (PWFS) in particular is the preferred sensor for ELTs, a choice motivated by its increased sensitivity at low flux regimes, and also by technical advantages such as the reduced number of required pixels. Unfortunately, the PWFS also comes with a list of technical and theoretical difficulties and challenges; one such drawback is the variation of the sensor sensitivity with wavefront conditions, [START_REF] Costa | Modulation effect of the atmosphere in a pyramid wave-front sensor[END_REF][START_REF] Korkiakoski | Applying sensitivity compensation for pyramid wavefront sensor in different conditions[END_REF] called optical gain; sensitivity depends upon the magnitude and structure of the residual phase measured, and is thus influenced by the seeing, the wind speed or any other parameter that has an impact on the loop residuals.

Moreover, this optical gain intertwines with the integrator loop gain, i.e. the value used by the AO real-time computer (RTC) to scale the sensor feedback. Indeed, most AO systems use an integral controller, as such a law is conceptually simple and uses moderate computing power. Tuning the loop gain is a way to increase the loop performance, as gain impacts in opposite ways the temporal error and the noise propagation. A fine-tuned modal integrator thus makes it possible to optimally balance those error terms towards residual variance minimization. [START_REF] Gendron | Astronomical adaptive optics. 1: Modal control optimization[END_REF] Previously existing approaches [START_REF] Gendron | Astronomical adaptive optics. 1: Modal control optimization[END_REF][START_REF] Dessenne | Optimization of a predictive controller for closed-loop adaptive optics[END_REF] are made complex by the sensitivity variation of the PWFS: the optical and loop gains multiply and bias the outcome: the sensitivity must be known to optimize the integrator.

We started to tackle this problem in the context of the SCAO module of the MICADO 9 instrument, a firstlight, near-infrared imaging camera for the European ELT. The built-in SCAO 10 uses a PWFS working at optical wavelengths. We previously presented a method for estimating on-sky the optical gain, [START_REF] Deo | A telescope-ready approach for modal compensation of pyramid wavefront sensor optical gain[END_REF] and demonstrated that a modal compensation [START_REF] Korkiakoski | Improving the performance of a pyramid wavefront sensor with modal sensitivity compensation[END_REF] applied on a well-suited basis allows for significant performance improvements, in particular for poor seeing conditions. Yet, we did not address the optimization of the integrator against the signal-to-noise ratio (SNR) and speed of turbulence, which is what we now propose in the present paper. CLOSE (Correlation-Locking Optimization StratEgy) is a self-regulating method that permanently maintains the equilibrium between small temporal residuals and a reasonable noise amplification, while coping with an arbitrary hidden, variable WFS sensitivity, such as PWFS optical gain. Without assumptions, CLOSE applies beyond the sole case of the PWFS: it also naturally applies to any other AO system, whether the sensor gain varies or not (Shack-Hartmann systems, using or not quad-cells, elongated laser guide stars, etc). CLOSEoriginally inspired by a proposition (Montera et al. [START_REF] Montera | Adaptive gain in closed-loop tilt control and adaptive optics[END_REF] ) to apply single-layer neural networks to AO RTCs-is a second-level servo-loop, which drives modal gains through real-time multiplicative updates computed from the temporal correlations of the modal decomposition of WFS measurements. The steady-state condition reached for this top-level loop closely matches the variance optimization criterion for the residuals, regardless of the currently-ongoing optical gain alteration of the WFS response. Altogether, CLOSE is a fully automatic, without intrusive signals, real-time pipeline optimizing integrator-based AOs with unknown sensitivity variations.

In section 2, we introduce our model of the PWFS and describe our dealing with nonlinearity. Section 3 explains how CLOSE operates, and section 4 will describe its possible implementations. Finally, section 5 shows some simulation results for the MICADO SCAO for stationary and varying seeing conditions, and discusses CLOSE capabilities beyond the originally envisioned PWFS modal gain compensation.

A QUASI-LINEAR MODEL OF THE NONLINEAR PWFS

We show on fig. 1 the schematic of the SCAO that is considered throughout this paper. The various wavefronts φ • represented on fig. 1 are meant as their vectorized decomposition on the control basis of the deformable mirror (DM): (φ 1 , ..., φ N ), plus some additional component orthogonal to the DM space. The wavefront sensor is represented by its modal interaction matrix dPyr, which is the differential of the WFS response, i.e. computed using infinitesimal push-pulls around a flat wavefront. We introduce before this interaction matrix a square, modal confusion matrix M, which is a random variable dependent on the residual wavefront φ Res shown to the PWFS. This random matrix M is the mathematical representation we choose of the optical gain effect.

The confusion matrix M has some reasonable properties when described on an appropriate modal basis, which are the foundation of optical gain modal compensation for the PWFS. [START_REF] Korkiakoski | Applying sensitivity compensation for pyramid wavefront sensor in different conditions[END_REF][START_REF] Korkiakoski | Improving the performance of a pyramid wavefront sensor with modal sensitivity compensation[END_REF] In previous work, [START_REF] Deo | A telescope-ready approach for modal compensation of pyramid wavefront sensor optical gain[END_REF][START_REF] Deo | A modal approach to optical gain compensation for the pyramid wavefront sensor[END_REF][START_REF] Deo | Analysis and implementation of the pyramid wavefront sensor for high-order adaptive optics on ELTs[END_REF] we performed a thorough numerical assessment of the fluctuations of M when the power spectrum density (PSD) of φ Res is stationary, and validated the key properties described thereafter; these analyses were performed using a Karhunen-Loève (KL) basis orthonormalized on the DM, [START_REF] Ferreira | Numerical estimation of wavefront error breakdown in adaptive optics[END_REF] built with modes φ i containing a mix of spatial frequencies of a single given norm, and ordered by spatial frequency. The last few hundred modes (at the ELT scale) contain a variety of waffles, until the cutoff is reached. We use this basis for all purposes in this paper.

We have demonstrated that: (1) M is essentially diagonal for low-order modes, which bear most of the power of the atmospheric turbulence; (2) that the diagonal coefficients vary by no more than a few percent for a given set of wavefronts φ Res of identical PSD, a property in accordance with theoretical derivations through convolutional PWFS descriptions; [START_REF] Fauvarque | Kernel formalism applied to Fourier-based wave front sensing in presence of residual phases[END_REF][START_REF] Chambouleyron | Modal gain optimization of the pyramid wave-front sensor using a convolutive model: from theory to experimental validation[END_REF] and (3) that the off-diagonal portion of M, while non-negligible for high-order φ i , is of a negligible average value across wavefronts of identical PSD.

These properties enable the modal gain compensation strategy. It is shown in the "Reconstruction" block of fig. 1: first, a modal space description is obtained through the reference command matrix Rec = dPyr † ; then, an array of multipliers G i,1≤i≤N is applied to modal commands, with such multipliers ideally selected to encompass (1) compensation of the M nonlinear effect for ongoing turbulent conditions and (2) the gain factor such that the modal integrators show appropriate transfer functions and ideal rejection levels. The stability property of M against the spectrum of φ Res ensures that G i values can be kept constant as long as the descriptive statistical parameters (r 0 , L 0 , C 2 n (h), ...) of the turbulence remain constant. While we have well assessed that M is not, in general, a diagonal matrix, its average for a given φ Res PSD is, and it remains quite interesting for design purposes to pursue this hypothesis in the general case. Assuming the diagonality, fig. 1 can then be simplified to the flowchart shown on fig. 2, which applies as one of N decoupled servo-loops for each of the controlled modes. The reference interaction and command matrices dPyr and Rec simplify to give scalar, decoupled diagrams, with M reduced to its i-th diagonal coefficient α i . As α i is always smaller than 1, it has often been called modal sensitivity reduction.

Under the diagonal hypothesis leading up to fig. 2, we can also factor in that α i varies only with the statistical properties of the turbulence, and hence changes slowly relative to the rate the AO loop is executed at. Considering timescales over which all α i are static, it follows that we simplified the problem of the nonlinear PWFS to N superimposed linear modal servo-loops, although each with an unknown sensitivity parameter. The performances of these loops are entirely defined by a small number of parameters: the temporal spectra of the turbulence and noise for the i-th mode, and the α i and G i scalars. The temporal spectrum for a single mode is well described in the literature [START_REF] Conan | Wave-front temporal spectra in high-resolution imaging through turbulence[END_REF][START_REF] Gendron | Optimisation de la commande modale en optique adaptative: applications à l'astronomie[END_REF] for Kolmogorov or Von-Kármán turbulence; we shall assume that the noise is white. The temporal dynamics of the loop are described by the sole "true gain" α i G i , which effectively defines what the closedloop transfer function will be. However, except for in-situ calibrations used by other optical gain compensation methods, [START_REF] Deo | A telescope-ready approach for modal compensation of pyramid wavefront sensor optical gain[END_REF][START_REF] Korkiakoski | Improving the performance of a pyramid wavefront sensor with modal sensitivity compensation[END_REF][START_REF] Esposito | Non common path aberration correction with non linear WFSs[END_REF] this overall loop gain is in general unknown to the operator and/or the RTC.

CLOSE Autocorrelation estimators Controller

THE CLOSE SOLUTION TO MODAL GAIN

The diagram shown on fig. 2 introduces the principle of the CLOSE servo-loop; its objective is to provide a unified technique to optimize the rejection, defined by the hidden value α i G i , based on the modal SNR, and operating only on the known modal multiplier G i . It is introduced as a second-layer supervisory loop, which takes as inputs the modal decomposition of the PWFS measurements. From there, a frame-by-frame estimation of modal temporal autocorrelation (AC) is performed, and an update of the modal gain G i is computed and applied at every time step based on these estimates. With all the priors on the temporal spectra of the modal components of the turbulence and noise, estimating the normalized AC for a single temporal shift enables the estimation of the actual loop gain α i G i , and through this to automatically drive the value of G i so that the transfer function given by α i G i is ideal for the control of the AO.

For each mode, the loop described in section 2 is a classical feedback loop with a delayed integrator of gain α i G i . The rejection of such loops are a high-pass transfer function, and they become unstable when the gain reaches a value g crit , which only depends on the loop latency (expressed in frame units). As the loop gain increases towards g crit , the closed loop transfer function exhibits a typical resonance peak, with a central frequency converging towards a value ν crit defined only by the system latency (expressed in frame units) as well. An example of modal measurements power spectra | mi (ν)| 2 , where ν is the temporal frequency and • denotes a temporal Fourier transform, is shown on fig. 3. The left "peak" on fig. 3 is the remainder of the turbulence spectrum cutoff after application of the high-pass rejection transfer function. The right peak (converging to ν crit -83.3 Hz in this example with a sampling frequency ν S of 500 Hz ) is the result of the amplification of the noise floor as the AO loop, with an effective gain α i G i closing on g crit , exhibits as strong resonant effect. The latency considered in the example shown on fig. 3 is 1.0 frame, resulting in g crit = 1; in this paper, we define latency values as not including WFS integration and DM zero-order hold effects. Values of ν crit and g crit with latency are summarized in table 1.

Table 1. Parameters related to transfer function divergence of the AO loop depending on the latency of the system.

Latency

ν crit g crit ∆t (frames) (frames) 0 ν S / 2 2.0 1 1 ν S / 6 1.0 3 2 ν S / 10 ≈ 0.618 5
The rationale of CLOSE is to leverage this typical structure of the modal measurement spectrum to implement a servo-loop supervising α i G i . The amplitude of the resonant peak is used as a monotonically varying indicator to provide control on the value of the true gain α i G i . The AO modal gain G i is then adjusted to converge on the desired α i G i value. In order to estimate the amplitude of the resonant peak, CLOSE uses the anti-correlation of the measurements for a time-shift ∆t that is half the period corresponding to ν crit . Values for ∆t are also given in table 1. With m * i [∆t] being the AC of the time series of modal measurements m i [k] for a time-shift of ∆t frames, the normalized

m * i [∆t] m * i [0] = k m i [k]m i [k + ∆t] k m i [k] 2 , (1)
is a monotonic proxy for the true gain α i G i . From there, one can act on G i in order to lock the correlation value onto a steady-state solution verifying

m * i [∆t] m * i [0] = r ∈ [-1, 1], (2)
where r is the smartly chosen, supervisory loop setpoint. The value of r shall be adjusted (or defined per-mode) as to fit a performance-maximizing criterion in all useful situations the AO would face, and across the complete range of the effective modal SNR. A higher value for r will work towards a more cautious and robust solution with a lower loop gain. A smaller value will lead to more aggressive loop behavior, possibly reaching nearly-divergent transfer functions, but with a maximized rejection of the low frequency components.

With the condition of eq. 2 reached, CLOSE enforces a transfer function constraint that is independent of the sensitivity reduction of the WFS. Therefore, it provides a go-around strategy regarding the impossibility to apply to the PWFS (or other systems compatible with the description discussed in section 2) some methods [START_REF] Gendron | Astronomical adaptive optics. 1: Modal control optimization[END_REF][START_REF] Dessenne | Optimization of a predictive controller for closed-loop adaptive optics[END_REF] based on numerical estimations of transfer functions that are restricted to linear systems without unknowns.

Choosing the r setpoint

In order to assess what values of r shall be chosen, we performed semi-analytical computations of the steadystate solution of CLOSE, and compared to the optimal solution for modal integrators minimizing the residual variance of Gendron & Léna (1994). [START_REF] Gendron | Astronomical adaptive optics. 1: Modal control optimization[END_REF] As we use near-KL modes, the variance minimization is similarly obtained by optimizing each of the N modal loops separately. These computations showed that for latencies of 0, 1 and 2 frames, and across orders of magnitude of the range of modal SNR (i.e. for any mode and any SNR), the CLOSE steady-state solution never diverges from the optimal one by more than 20%, when keeping a constant setpoint value of r = 0. Certainly a smart fine tuning of the value of r could lead to some slight, marginal improvement of the performance. But we claim that choosing r = 0 is so close to the optimum over such a huge range of situations that it can be set as the baseline value with confidence. The retained value is not critical for the performance, provided it is not too close to -1 or +1. As said before, playing with values in r ∈ [-0.2, 0.2] makes it possible to explore different compromises of performance versus robustness. These results show that CLOSE can, on top of making the loop independent from arbitrary hidden modal factors, enforce a near-optimization of the modal integrator with a very simple control law.

PRACTICAL IMPLEMENTATION

Having studied the steady-state solutions of the CLOSE servo-loop, we now propose our real-time implementation to achieve convergence to such states. From the time series m i [k] of modal measurements, two AC estimators are built using discrete integrators:

N 0 i [k] = p m i [k] 2 + (1 -p)N 0 i [k -1] N ∆t i [k] = p m i [k]m i [k -∆t] + (1 -p)N ∆t i [k -1], (3)
where k is the time step index, and p ∈ [0, 1] a smoothing parameter. N 0 i and N ∆t i contain time-windowed estimates of m * i [0] and m * i [∆t]; after an empirical optimization of the parameter p, we opted for fast integrators with p = 0.3 for all simulations presented in section 5.

After the AC estimation, the G i are updated using multiplicative increments as follows:

G i [k] = G i [k -1] × 1 + q ± N ∆t i [k] N 0 i [k] -r . (4)
The r parameter is the same loop setpoint as defined in section 3. While the theoretical derivations were most accurate using r = 0, it is to be noted that for numerical simulations we maximized the long exposure Strehl ratio (SR) empirically, which in the end lead us to always using r = -0.1.

The q ± learning factor encompasses two different values, with either q + and q -used depending on the sign of

N ∆t i [k]/N 0 i [k] -r.
This asymmetry is introduced as to make the algorithm more reactive to overshooting transients (with q -), as compared to tracking gain increases due to a transfer function deemed too slow (using q + ). As such we will be using q -= 5q + ; the numerical values of q ± used in the numerical simulations in section. 5 are q + = 10 -2 and q -= 5.10 -2 . These q ± learning factors are the determining parameter of the time constants associated with the convergence and tracking ability of the CLOSE loop. Simulations here use what is near the maximum acceptable value to limit computation time while maintaining AO stability. We however infer that for a real AO system, q + values in the range of 10 -3 -10 -4 should be used assuming 500 Hz frequency, hence providing typical time constants in the 2-20 seconds range. The ideal choice of q ± will probably remain dependent on the system, and will probably require some adjustments accounting for robustness and responsiveness to variations of turbulence conditions or other transient events.

Expected additional strain on the RTC

Implementing CLOSE in a real-time fashion is of course expected to add some additional RTC strain. While the AC estimations and gain updates themselves (eqs. 3 and 4) are negligible compared to the required matrix-vector multiplication (MVM), having the m i [k] available in real-time requires to do the reconstruction in two successive MVM steps. The first MVM converts WFS measurements to modal values, with a computational burden nearly identical to the usual measurements-to-DM-commands MVM. The second step computes DM increments from modal values, with a nearly square matrix of size the number of actuators.

For a typical PWFS AO system, the number of pixels read out is typically 5 to 6 times the number of actuators. If performing the measurement in a slopes-maps fashion, the RTC strain increase is of about 33 -40%; if using a full-pixel measurement technique, it is an additional 16 -20% increase only.

Block-wise, zero-strain alternative

If the RTC software cannot be altered on an existing system, or if the additional strain is not acceptable within the RTC specifications, CLOSE can be implemented in a block-wise flavor. In such case, all estimators, gain updates, and command matrix updates are performed in offline time, certainly in another process and preferably on another machine. This buffered strategy enables to deploy CLOSE on nearly any existing AO system.

A time-continuous buffer of K WFS measurements is forwarded to the CLOSE process, which turns them into modal measurements m i [0]...m i [K -1] using the modal reconstructor Rec. For each mode, the AC estimators of eq. 3 are replaced by the direct computation of the normalized ∆t-shifted AC term over the telemetry buffer:

N block i = 1 K -∆t K-∆t-1 k=0 m i [k]m i [k + ∆t] 1 K K-1 k=0 m i [k] 2 (5)
The gain update equation can then be performed:

G i [new] = G i [old] × 1 + q ± N block i -r , (6)
using q ± factors adjusted for the longer integration time and the increased SNR on AC estimation; typically q ± ought to be larger by a factor √ K for a dynamical effect comparable to the real-time implementation. The new command matrix can then be computed accounting for the new G i values, and when all side-tracked computations are finished, can be set into the RTC.

NUMERICAL SIMULATION RESULTS

This section covers some end-to-end numerical simulations demonstrating the performance achieved with CLOSE when applied to the MICADO SCAO design [START_REF] Clénet | The MICADO first-light imager for the ELT: towards the preliminary design review of the MICADO-MAORY SCAO[END_REF][START_REF] Vidal | Analysis of the MICADO-MAORY SCAO performance[END_REF] (see table 2). All simulations were performed using the COM-PASS [START_REF] Gratadour | COMPASS: status update and long term development plan[END_REF] platform. In the following sections, we present studies on the convergence of modal gains when bootstrapping the AO loop, and the end-to-end performance for stationary and varying seeing conditions. In addition, videos showing the dynamical behavior of some CLOSE simulations are available online. 24

Gain convergence at loop closing

We can take a first look at the behavior of CLOSE when the AO loop is closed. Without any priors given, we choose an initialization condition G i [0] = 0.5. With the 2 frames of latency considered, the critical gain value is g crit ≈ 0.61; given that the sensitivity reduction α i is always smaller than 1, this ensures that the loop is initially closed with stable transfer functions. From these initial 0.5 values, the G i are driven by CLOSE to their steady-state values, which account both for non-linearity compensation and the temporal variance minimization.

We show on fig. 4 the values of the 4 309 modal gains G i , averaged on certain subsets of frames within the first two seconds after the AO loop is closed. These simulations are performed for four different cases, with r 0 of 14.5 and 9.0 cm, and guide stars of brightnesses M R = 0 and M R = 16. For the bright cases, steady state is reached by frame k ≈ 500, i.e. within one second. The process is slightly slower for the M R = 16 cases, with a continued convergence of the G i between frames k = 500 and k = 1000.

Simulations at M R = 0 are essentially performed with an infinite SNR. As such, the loop true gain which minimizes the output variance is close to the maximum stability value g crit , and the G i coefficients reached in steady-state are essentially reflecting the inverse α -1 i of the PWFS sensitivity reduction. These curves reached after k = 1000 frames in M R = 0 cases are compliant with the abacuses we presented in previous work, [START_REF] Deo | A telescope-ready approach for modal compensation of pyramid wavefront sensor optical gain[END_REF][START_REF] Deo | A modal approach to optical gain compensation for the pyramid wavefront sensor[END_REF] with α i decreasing up to mode 30, which contains spatial frequencies corresponding to the modulation radius, then increasing again roughly as a power law up to the highest order modes. q + = 10 -2 , q -= 5.10 -2 Modal integrator with double MVM: When comparing the G i values reached between M R = 0 and M R = 16 cases, one can observe the effect of the SNR-dependent optimization of the transfer function, with steady-state gain values dampened by typically 20-50% depending on the mode number and the r 0 . Altogether, results presented on fig. 4 tend to validate that -without any priors and regardless of the PWFS sensitivity reduction -CLOSE is able to make the modal integrator adaptively converge to the adequate solutions, across a 1 to 2 second period.

r = -0.1 Pixels -→ [m i ] × [G i ] -→ actuators

Results with stationary turbulence

Besides the adaptive capability, it is most important to look at the AO performance achieved once CLOSE reaches its steady-state behavior. In order to perform this analysis, we generalize the simulations to a larger range of r 0 values and guide star magnitudes.

Measured performances are shown on figure 5, with the long exposure H-band SR plotted against the star magnitude and computed for 5 different seeing conditions. For all the results the SR is averaged over 2-second exposures, starting 2 seconds after the AO loop is closed, and with initial modal gains G i = 0.5 as previously.

We report the performance achieved for r 0 values from 8.9 to 21.5 cm, and for guides stars from M R = 10 to 17.5 with CLOSE (solid lines). Circles overlaid at M R = 10 and 16 are performance without using modal gain compensation, but after an optimization of a global scalar loop gain. Square markers are when using the dithering-based determination of modal gains as reported in previous work, [START_REF] Deo | A telescope-ready approach for modal compensation of pyramid wavefront sensor optical gain[END_REF] and after an optimization of the scalar loop gain. The latter dithering-based performance is also identical to what can be obtained using the sensitivity normalization, the original method proposed by Korkiakoski et al . [START_REF] Korkiakoski | Applying sensitivity compensation for pyramid wavefront sensor in different conditions[END_REF][START_REF] Korkiakoski | Improving the performance of a pyramid wavefront sensor with modal sensitivity compensation[END_REF] From the performances reported, it follows that CLOSE compares to other modal non-linearity compensation techniques crafted for high-order PWFS, with added benefits: a single, real-time technique factors in both the non-linearity component and the transfer function optimization, with a far greater responsiveness to transient events; and as compared to either of the aforementioned modal compensation techniques, offline computation of modal gain abacuses or in-situ control matrices is no longer required.

Continuously varying turbulence

When mentioning the robustness of CLOSE regarding optimizing the modal integrator through transient events, it is interesting to evaluate how the performance evolves for continuously varying seeing conditions.

We report on fig. 6 the results of a simulation in which the r 0 value changes from 22 cm to 7.0 cm then back to 22 cm over the course of 100 seconds of operation, without ever opening the AO loop or performing any external action on the AO parameters. A similar simulation was performed in previous work [START_REF] Deo | A telescope-ready approach for modal compensation of pyramid wavefront sensor optical gain[END_REF] for several gain compensation strategies. The performance is measured in terms of SR over successive 0.1 sec (solid lines) and 2 sec exposures (circles), starting 2 sec. after the loop is closed. An identical experiment is ran for guide stars of M R = 5 and M R = 16.

In practice, the COMPASS-generated numeric turbulence screen is continuously extruded from one edge of the pupil, then translated with the simulated wind. The r 0 given on fig. 6 is the one of the wavefront pixels being extruded at a given time; yet it takes 4 seconds for those turbulent features to entirely cross the pupil. This induces a delay of about 2 seconds between the time a given r 0 is reported, and when the associated performance is expected on the imager.

The SR complies with the values found for stationary r 0 cases for the bright and the M R = 16 case, demonstrating that although the seeing conditions vary very quickly, the responsiveness of the modal gain curve can easily adjust the integrator regime for such variations, maintaining the maximum possible SR for a given r 0 /M R combination. The symmetry of the two r 0 decreasing and r 0 increasing phases is also to be noted: CLOSE enables the integrator to accommodate both cases with similar flexibility. Cases with the seeing improving were noticeably less robust with previous modal compensation methods, as the increased sensitivity of the PWFS can lead to a diverging integrator if the modal gains are not adjusted in a timely manner. The symmetry, in particular at M R = 16, also underlines that the integrator is adequately maintained in a robust regime, without accumulation of waffle or divergence of single actuators, after more than 20 seconds spent with a residual wavefront error of about 1 λ RMS on the PWFS.

M R =5, SR 0.1 s M R =5, SR 2.0 s M R =16, SR 0.1 s M R =16,

Additional capabilities

Not only CLOSE is able to track gains through varying observing conditions 24a , but it can also adapt the system to some other situations. We have simulated CLOSE when sensing on double stars 24b , and tested the results against different separations, different orientations with respect to the pyramid edges, and different flux ratios of the guiding binary. The detailed results have not been reported in this paper, but we were able to verify that the functioning point reproduced the same performance that could be obtained using standard methods. This also demonstrates that an interaction matrix for a single star can be converted to another adequate to binary sources using a modal rescaling only on our DM KL basis.

The test has also been done using uniform disk-like objects of various diameters from 10 to 800 mas (a simulation of Titan as guide object 24c ). Not surprisingly, each of them exhibits a similar behavior where the gains stabilize rapidly to the optimum value, with a performance level consistent with that found using classical methods. The case of more peculiar objects (triple or multiple stars, galactic nuclei exhibiting a plateau around a central peak, small globular clusters, etc.) has not been studied but we are confident that CLOSE would also converge smoothly on those cases.

Also not tested yet when writing the present article, we think that CLOSE can also cope with variations of the modulation radius (without a substitution of the command matrix), as this impacts the WFS sensitivity -at first order-as a modification of the modal gains. Whether that interesting property can be leveraged is another, wider topic to be discussed in the perspective of optimizing the overall pyramid sensor behavior even better.

We also need to mention that CLOSE can be applied to systems using other wavefront sensors than pyramids. In particular, CLOSE could certainly help in the case of the centroid gain induced by quad-cells in a Shack-Hartmann sensor, which acts as a global unknown multiplicative factor. We think it could also be of some help in the case of significantly elongated laser guide stars (LGS), possibly truncated, which induce some unknown fluctuations of the sensitivity in the measurements with the thickness changes of the sodium layer. However, we think this would possibly have to be coupled with a smart choice of the modal basis to act on. We envision a scheme where one CLOSE loop is run in the slope space to compensate centroid gain effects, and another in the modal space for integrator optimization, held together with adequate normalization conditions. We think that CLOSE could be of help any time a modal gain optimization on an integrator law is to be done in a situation where sensitivity fluctuations (either of the sensor, or the adaptive mirrors) are to be expected.

CONCLUSION AND PERSPECTIVES

We have presented a self-regulating method that allows us to track, either in hard or soft real-time, the modal gains of the integrator controller in an AO system, in order to maintain the maximum performance against variable conditions (seeing, wind speed, SNR) and variable sensitivity of the WFS. Our method differs from previous works as it doesn't require any knowledge about the sensitivity of the sensor, but permits to counteract its variations. This property makes the method particularly suitable whenever sensitivity fluctuations of the feedback loop (either of the sensor, or the adaptive mirrors) are to be expected, like in the case of high-order PWFS designs on ELTs.

The method is based on the value of the temporal auto-correlation of the modal phase residuals computed at a single given time-shift ∆t, followed by the appropriate counter-reaction on the modal gain in order to lock the previously mentioned ∆t-correlation value to some chosen setpoint. We have demonstrated first that, for some given conditions, there is an unequivocal relation between the gain and the value of that ∆t-correlation, and second that locking the ∆t-correlation at a fixed well-chosen value through multiplicative adjustments of the integrator gain will keep the phase residuals near their achievable minimum. The method has been called CLOSE, for Correlation-Locked Optimization StratEgy.

We were able to experience through end-to-end AO simulations the remarkable behavior of the CLOSE algorithm: extremely promising, it appears to be self-regulating, and seems to adapts naturally to any new case whether we deal with any combination of good or low SNR, good or bad seeings, extended objects or else. 24 However, our simulations at the time of writing are restricted to a PWFS (that of the SCAO module of MICADO ELT instrument, which was the primary target for our study). We are confident that CLOSE also applies to others AO systems equipped with non-pyramid sensors: future numerical simulations should be able to confirm this, and there is certainly a wealth of potential applications to follow. Today, CLOSE is our baseline algorithm for optimizing the end-to-end simulations running with a pyramid sensor.

Coming now to limitations, we shall warn potential users that the update equation (eq. 4) contains an integrator, which definitely requires a proper feedback to avoid any fatal divergence. Blocking of the feedback on the correlation value may be triggered by unexpected effects, such as actuator saturation on the deformable mirror, or by the absence of feedback from the main AO loop -which happens when the loop "crashes" or when the flux disappears. Other cases may exist, but those are sufficient to draw our attention to the fact that eq. 4 needs to be completed with some monitoring and safeguarding system in order to be fully applicable to a real system. We shall also investigate the impact of non-Kolmogorov input perturbations such as telescope windshake, or vibrations. While telescope wind-shake is generally a low-frequency perturbation that should not harm too much the algorithm, the way CLOSE will interact with high-frequencies vibrations potentially amplified by the rejection overshoot remains to be looked in detail. Whether CLOSE reacts in a right or wrong way depending on the frequency of the perturbation is not obvious at first sight.

Finally, it should be raised that CLOSE does not say anything about the WFS sensitivity value, which knowledge is of importance for a correct compensation of non-common path aberrations. As a consequence, our present algorithmic design for the SCAO sensor of MICADO includes both CLOSE and a standard algorithm for measuring the WFS optical gain, which seems to be a waste. The possibility of deriving simultaneously an optimum modal gain with the WFS optical gain is currently envisioned, based on the measurements of the correlation for different ∆t, possibly leading to an all-in-one algorithm.

Figure 1 .

 1 Figure 1. General modelization of the AO loop with the WFS, RTC and DM, in the nonlinear confusion matrix model presented. The confusion matrix M (slowly) depends on the structure of the residual φRes.

Figure 2 .Figure 3 .

 23 Figure 2. Reduction of the PWFS AO loop model (fig. 1) to a single mode. The matrix M is reduced to its i-th diagonal term αi; residual off-diagonal terms are to be included in the modal noise bi.

M R = 16 ,

 16 r 0 = 9.0 cm G i averaged over frames k: k=0 k [50,60] k [100, 150] k [500,600] k [900,1000]

Figure 4 .

 4 Figure 4. Convergence of CLOSE gains on the 2.0 sec following loop closing, for guide stars of MR = 0 and 16 and atmospheric r0 of 14.5 and 9.0 cm. All Gi are set to 0.5 at loop closing (blue line). Gi values are shown as averaged over the frame intervals given in the legend. Curves are smoothed along the i index for clarity. Final SRs are given in H-band and computed from the cumulative exposure between frame 900 and 1000 (200 msec).

Figure 5 .

 5 Figure 5. Plain lines: Long-exposure SR in H-band obtained with CLOSE for guide star magnitudes MR=10 -17.5 and r0=8.9 -21.5 cm. Circles: Best performance obtained without using modal gains. Squares: Best performance with modal gains optimized through a dithering measurement technique, recalled from previous work.[START_REF] Deo | A telescope-ready approach for modal compensation of pyramid wavefront sensor optical gain[END_REF]

Figure 6 .

 6 Figure 6. SR in H-band obtained for 0 th and 16 th guide star magnitudes, as the seeing conditions cycles from r0 = 22 cm to 7 cm and back across 100 sec of simulated AO time. Lines: 100 msec SR; markers: 2.0 sec SR.

Table 2 .

 2 AO parameters used for end-to-end numerical simulations

		Simulation parameters
	Telescope	D = 39 m	Turbulence von Kármán -single ground layer
		ELT pupil model		r 0 (500 nm) from 7.0 to 22.0 cm
		Spiders are omitted		L 0 = 25 m, || -→ v || = 10 m.s -1
	Guide star On-axis natural star	PWFS	92 × 92 subapertures (42 cm pitch)
		zero point 2.6 × 10 10 ph.s -1 .m -2		24 080 pixel values read-out
	DMs	Tip-tilt		"Full pixels" measurement space 25-27
		ELT M4 model		Monochromatic at 658 nm
		pitch 54 cm, coupling 0.24		0.28 throughput (quantum efficiency inc.)
		4310 actuators driven		Circular modulation, r Mod = 4 λ D
	RTC	Frequency 500 Hz		Read-out noise 0.3 e -
		Latency 2 frames	CLOSE	Real-time implementation
		(exposure/hold excluded)		p = 0.3
		Controlled on KL basis 16

ACKNOWLEDGMENTS

The authors express their wishful thanks to D. Montera, whose adaptive control algorithm gave us the push towards designing CLOSE. This research is performed in the frame of the development of MICADO, first light instrument of the ELT (ESO), with the support of ESO, INSU/CNRS and Observatoire de Paris.