R Siano

A Chapelle

V Antoine

Elisabeth Guillou

F Rigaut-Jalabert

Citizen participation in monitoring phytoplankton seawater discolorations

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

1. Introduction

Phytoplankton blooms in marine ecosystems correspond to high concentrations of eukaryotic singlecelled (protist) photosynthetic organisms. Single species of typical bloom-forming microalgal groups such as dinoflagellates or diatoms, react relatively rapidly to environmental changes (variation of nutrient concentration ratios, water mixing, etc.) due to their high duplication rates, physiological plasticity and life strategy adaptations [START_REF] Smetacek | Microbial food webs: The ocean's veil[END_REF]. Under favorable environmental conditions which allow cellular duplication, blooms can be observed, generally with high biomass production [START_REF] Cloern | Phytoplankton bloom dynamics in coastal ecosystems: A review with some general lessons from sustained investigation of San Francisco Bay, California[END_REF]. The remineralization of this high biomass by bacteria can cause anoxia/hypoxia phenomena, leading to mass mortality of the marine fauna inhabiting the zone where the bloom occurred. Mass mortality of marine fauna can hit wild populations or farmed stocks [START_REF] Hallegraeff | Recent range expansion of the red-tide dinoflagellate Noctiluca scintillans in Australian coastal waters[END_REF]. If anoxia induced by high biomass-production blooms occurs in aquaculture exploitations, the linked economic activities are strongly affected, with large-scale losses of live fish or shellfish destined for human commercialization and consumption (Zingone and Enevoldsen 2000). Massive biomass accumulation can also cause surface seawater discoloration (i.e. green, red, brownish or whitish colors) or foam production, thus altering the appearance and aesthetics of coastal waters. These impressive and sometimes eye-catching natural events can hinder tourism activities (i.e. water sports, leisure, beaches, hotels, restaurants) whose economic benefits depend on the good aesthetics of the water in the coastal area (Zingone and Enevoldsen 2000). Tourists are reluctant to visit areas where discolorations are more frequent and intense, hence affecting the local economy. Some blooming species can also metabolize toxins which are directly harmful when released outside the cell (hemolytic, ichtyotoxic, cytotoxic effects) to marine fauna or indirectly for humans who can suffer from Diarrheic (DSP), Paralytic (PSP), Neurotoxic (NSP), Amnesic (ASP), and Azaspiracid (AZP) Shellfish Poisoning as well and Ciguatera Fish Poisoning (CFP) through the consumption of seafood that has bioaccumulated toxic substances. Finally, skin irritations and respiratory problems have been reported in humans who have gotten into contact with aerosols developed after blooms of toxigenic species. All phenomena connected to phytoplankton developments that are detrimental to the ecosystem and/or human health and/or economic activities are classified and known as Harmful Algal Blooms (HABs) (Hallegraeff 2000, Zingone andEnevoldsen 2000).

Countries in possession of fishery and aquaculture sectors are particularly aware of HABs, and in particular of the toxigenic potential of some phytoplankton species. They therefore implement monitoring activities for toxic phytoplankton species in zones inhabited by natural and cultivated shellfish populations.

Despite the problems that phytoplankton discolorations may cause to tourism and wildlife, phytoplankton monitoring systems are not designed for this kind of HAB phenomenon. This is for example the case in France of the REPHY (REseau de surveillance et d'observation du PHYtoplankton et des PHYcotoxines) (http://envlit.ifremer.fr/surveillance/phytoplancton_phycotoxines/presentation) which, since its launch in 1984, is designed to monitor toxic species and not water discolorations. Seawater discolorations can affect relatively small and patchy areas, or can extend across very large (hundreds of kilometers) areas, rendering them visible by satellite [START_REF] Cloern | Phytoplankton bloom dynamics in coastal ecosystems: A review with some general lessons from sustained investigation of San Francisco Bay, California[END_REF]. These phenomena occur in different regions of the World Ocean, both in offshore areas (i.e. coccolithophore blooms), and, more frequently, in coastal areas, mainly in semi-confined zones (harbours, estuaries (Hallegraeff 2000, Zingone andEnevoldsen 2000). They can develop rapidly, locally and die out relatively quickly (within a few days) [START_REF] Cloern | Phytoplankton bloom dynamics in coastal ecosystems: A review with some general lessons from sustained investigation of San Francisco Bay, California[END_REF]. The ephemeral nature of seawater discoloration phenomena hinders the experimental design of their monitoring. Local phytoplankton monitoring systems are based on fixed sampling stations, with surveys scheduled at regular intervals. This static organization of monitoring systems (with stations often located near shellfish farms to monitor toxic species for sanitary reasons) can cause seawater discolorations to be overlooked. These can occur either between scheduled sample collections (which generally take place every fortnight) or in sites or during periods not usually sampled. Seawater discolorations are often reported in a sporadic and random way, based on personal observations of individuals (scientists or otherwise) aware of the environmental issues associated to such an event.

Citizen observations can potentially provide complementary information to ongoing sanitary monitoring programs of phytoplankton or field campaigns [START_REF] Castilla | Quantification of phytoplankton bloom dynamics by citizen scientists in urban and peri-urban environments[END_REF]. They contribute towards a better grasp of both the spatial and temporal scales at which water discolorations occur in coastal waters, particularly during the summer. This is the time of year when these phenomena are most likely to develop, which corresponds to the period when there are more people present on the coast. Citizen science is a nexus between science and society, being both a new opportunity for scientists to acquire new data and for the public to interact with science [START_REF] Jarvis | Citizen science and the power of public participation in marine spatial planning[END_REF][START_REF] Martin | Understanding drivers, barriers and information sources for public participation in marine citizen science[END_REF]. Although the citizen science movement is well-established, [START_REF] Miller-Rushing | The history of public participation in ecological research[END_REF], particularly in terrestrial monitoring programs, the engagement of non-professional actors in scientific investigations has dramatically increased in recent years, especially in environmental sciences (ornithology, paleontology, marine and terrestrial biodiversity) (e.g. [START_REF] Bodilis | Can citizen science survey non-indigenous fish species in the eastern Mediterranean Sea?[END_REF]) that all require large amounts of data from heterogenic sources [START_REF] Kelling | Data-Intensive Science: A New Paradigm for Biodiversity Studies[END_REF]). Citizen science have been lauded for: i) the education of voluntary participants to environmental issues, ii) providing low-cost data useful for sustainable management decisions [START_REF] Jarvis | Citizen science and the power of public participation in marine spatial planning[END_REF], iii) empowering citizens to participate more actively in local conservation and management decisions [START_REF] Martin | Understanding drivers, barriers and information sources for public participation in marine citizen science[END_REF], and iv) engaging stakeholders in conservation planning [START_REF] Jansujwicz | The Maine Vernal Pool Mapping and Assessment Program: Engaging Municipal Officials and Private Landowners in Community-Based Citizen Science[END_REF].

Marine citizen science monitoring programs are increasingly common, with the public now being able to get involved in the detection and identification of: a) marine macrofauna easily observed from the sea surface (i.e. marine mammals, sharks, jellyfish) or b) marine organisms, which can be observed by 'citizen' SCUBA divers (i.e. [START_REF] Goffredo | Unite research with what citizens do for fun: "recreational monitoring" of marine biodiversity[END_REF][START_REF] Holt | Comparing diversity data collected using a protocol designed for volunteers with results from a professional alternative[END_REF]. However, the use of a citizen science approach for studying plankton is not frequently chosen as a tool, compared to the number of classical sanitary monitoring programs for plankton existing worldwide. Nevertheless some examples of the use of a citizen science approach to study phytoplankton exist. Volunteer HAB monitoring programs were launched along the west coast of United States in the early 1990's [START_REF] Anderson | Monitoring and Management Strategies for Harmful Algal Blooms in Coastal Waters[END_REF]) and more recently along Canada's west coast [START_REF] Mcintyre | Formation of a Volunteer Harmful Algal Bloom Network in British Columbia, Canada, Following an Outbreak of Diarrhetic Shellfish Poisoning[END_REF] Algal Bloom (HAB) surveillance program. The scientific objectives of all these programs concern the distribution, phenology and managing of toxigenic species. As for water discolorations, structured management systems implementing a citizen science approach are not common. An example exists in northern Europe, but it is mainly focused on the identification of marine cyanobacteria blooms (e.g. [START_REF] Kotovirta | Participatory surface algal bloom monitoring in Finland in 2011-2013[END_REF] and not on eukaryotic microalgae. Other citizen-monitoring programs, whose main goal is the detection of changes in sea colour, have been adopted (i.e. the Citclops project (http://www.citclops.eu), or Plymouth University's Secchi App -(ref http://www1.plymouth.ac.uk/marine/secchidisk/Pages/default.aspx). Indeed, people directly (beach activity owners, aquaculture fishermen, scientists) or indirectly (environmentally-aware citizens, non-profit organizations) concerned by water discoloration phenomena point out the absence of a clearly identified interlocutor (institutional or non-government organization) who could receive observations and process the biological and ecological information in order to better manage these phenomena. This shows the need for a structured management system for water discoloration events, coupled with better awareness-raising about the causes and the effects of water discolorations on humans and the environment.

In 2013, a citizen monitoring program focused on water discoloration observations was launched across Brittany (France) waters in parallel to the ongoing phytoplankton and biotoxin monitoring network REPHY. This project, named Phenomer (an acronym for 'visible phenomena at Sea', combined with 'Phenology', in French) (http://www.phenomer.org/) has been put into practice by both public scientific institutes and non-governmental organization partners [START_REF] Curd | PHENOMER: Better knowledge of HAB with the help of Citizen observations[END_REF]. Beyond communication and outreach objectives on phytoplankton and HABs, the overall aim of Phenomer was to introduce citizens to HAB management and scientific analysis. From a marine coastal management point of view, Phenomer creates a working relationship between volunteers and researchers, with the aim of improving and structuring the observations of water discolorations. Indeed, the major objective of Phenomer was to establish if a citizen science approach aimed at the detection of water discolorations may complement sanitary monitoring systems (such as the REPHY in France) which were not specifically conceived for the analysis of such a phenomena (http://www.phenomer.org/). Information gained through Phenomer could also contribute to the economic development (shell farms, tourisms) in coastal areas where water discolorations are less frequent or absent. From a scientific point of view, Phenomer aims to explore the possibility to acquire scientifically valuable data on water discoloration and HABS in general, in particular by means of citizen alerts and with both ecological and sociological scientific purposes. Through the help of volunteer participation, Phenomer aims to i) extend the monitoring survey area for coastal water discolorations and structure their observations, ii) identify general trends where HABs and water discolorations in particular are more likely to occur, thus providing scientific data for current and future research, iii) promote an increased awareness and education of the public on HABs, and iv) analyze the perception of visible phytoplankton blooms by inquiring in what way contributors perceive the harm (i.e. environmental, human health, personal) provoked by these phenomena. This study reports the results from the first three years (2013)(2014)(2015) of this project.

Materials and Methods

Communication and outreach on the project

The understanding of a project subject and the acquisition of scientifically valid data through citizen participation are directly dependent on communication actions through appropriate media [START_REF] Wehner | Citizen Science, Communication, and Expertise: An Examination of the Port Townsend[END_REF]. In order to recruit a broad spectrum of participants to the Phenomer project, a number of procedures were developed. A project coordinator together with a scientific communication officer were assigned the development and distribution along Brittany's coastline of 30 000, 32 000 and 38 000 leaflets and 1000, 800 and 700 posters presenting the Phenomer project in 2013, 2014 and 2015 respectively. The communication on the project objectives was stepped up prior to the summer period of each year, when water discolorations were presumed to occur more frequently. Stickers, postcards (1000 prints of each per year) and a board game for children in 2013 were also developed to ensure the best possible attentiveness to the project. Lectures, interviews on radio shows, articles in the regional press as well as meetings with volunteers at a number of marine events across Brittany over the course of the summer months were organised. A website (http://www.phenomer.org/), and social media page were also developed and regularly updated. Finally, in 2015, a smartphone application (Phenomer©) (Supp. Fig. 1) was developed to facilitate the sending of water discoloration photographs taken by citizens thanks to immediate geolocalisation. The geolocalised picture is sent to the scientific team of the consortium via the application, which improves the rapidity of the intervention in the field.

Warning protocol of water discoloration detections by volunteers

Citizens were invited to report and take pictures of all HAB events they may have observed (water discolorations, foam production or fauna mortalities) across Brittany's coastal waters, either by calling a landline, using the smartphone application, or via an on-line form present on the website (Fig. 1). A group of scientists from the three research institutes in the partnership filled out a duty roster on a weekly basis, during which time they committed to responding to all Phenomer alerts as quickly as possible. Observations made by the general public were analyzed by the on-duty scientist in order to filter out false alerts, such as macroalgae accumulations, river runoff, etc. (Fig. 1). It was part of the scientists' responsibilities to respond to any email or phone correspondence related to the project he or she received during the week they were on-duty. Some valuable information could be obtained over the phone, for example establishing whether the observed phenomenon was provoked by macroscopic organisms (visible to the naked eye, e.g. small jellyfish, other gelatinous zooplankton, macroalgae) or by inorganic particles (e.g. sand). On the occasions where the information provided made it plausible that the water discoloration was caused by phytoplankton, either the research team of the project network located closest to the bloom promptly reached the area and took a sample, or the volunteers were asked to follow a sampling and storage protocol (Fig. 1). In 2013, few samples of water discoloration were collected (Table 1), either because water discolorations occurred in areas far away geographically from phytoplankton research laboratories, which limited the rapidity of the intervention of scientists, or because citizens were not able within a short time-frame to transport samples themselves to the nearest research station. In order to overcome this problem, as of 2014 a network of nearly 60 relay structures was created to make it easier for observers to deposit samples somewhere in the vicinity of the observed discoloration. These relay structures are environmental organizations, port and town authorities, water sport clubs, lifeguarding stations or natural protected areas that formally accepted to take part in the project. They were trained by the Phenomer scientific consortium (scientists and Non-Governmental organisations) to the steps to take in the event of receiving a water sample taken by an observer (i.e. seawater fixation, preservation and expedition to a scientific laboratory). Once a sample arrived in a relay structure, it was then picked up and analyzed by the nearest laboratory to the water discoloration event (there are 6 dotted around Brittany's 2730 km of coastline). The species responsible for the bloom was identified through light microscopy by a taxonomist of the Phenomer consortium. When samples were not collected, the species responsible for the water discoloration was inferred either from data of the REPHY monitoring program or from data of ongoing scientific research projects in areas near the water discoloration event. Feedback was both spread to the scientific community for further research and to the general public on the website, via social media and newsletters (Fig. 1). When a toxic species was identified as being responsible for the bloom, the REPHY, the French phytoplankton monitoring program, was informed and precautionary actions were initiated. Citizens were privately thanked by personal direct communication and, with their consent, when using their photographs in Phenomer communication medium (Fig. 1).

Fig. 1 here

Analysis of water discoloration perception by citizens

During 2013-2014, a series of 13 preliminary semi-structured phone interviews were carried out with those observers having accepted to be interviewed. The preliminary results from these interviews made it possible to outline a typical profile of the people taking part in Phenomer and to construct an ad-hoc questionnaire adapted to this population (Supp. Materiel 1). Composed of a dozen questions, the questionnaire cross-examines the context in which the observation is made, what observers feel in relation to these phenomena and whether, according to them, HABs are likely to impact human health and/or the environment in either a good or a bad way. This questionnaire was then taken by water discoloration observers in 2015. All participants were informed of the data protection legislation protecting their personal data rights, in compliance with the CNIL (Commission Nationale de l'Informatique et des Libertés) (CNIL 2016), the French committee responsible for ensuring that information technology complies with national data protection legislation. Participants submitting a phytoplankton bloom observation via the online form or Smartphone application are asked to tick a box certifying they have read and understood the "charte d'utilisation" (terms of use), which serves as a statement of informed consent, explaining their rights regarding personal data. When participants reported their bloom observations over the phone, they were informed of their personal data rights over the phone, and a log was kept of the conversation. All participant consent is recorded in the back office of the Phenomer website (ww.phenomer.org) where a database kept track of every phone call and completed form. The CNIL approved the type of data collected on participants, and manner in which collecting participant consent is recorded (ref.

number 1684966 v0).

Results

Citizen observations of water discoloration phenomena

During the spring-summertime periods (March-August) of 2013, 2014, and 2015, the means of contact most used for Phenomer was the internet site, with an increasing number of visitors over time (2621 in 2013, 6987 in 2014, and 11044 in 2015). During the three years of project implementation citizens made 69, 74 and 88 mostly one-off alerts either by phone, smartphone application or via the website form (Table 1). Out of these alerts, 40, 40 and 47 observations reported by citizens were phenomena potentially linked to plankton. The other contacts were mostly general enquiries about various marine phenomena observed in the intertidal zone (macroalgae, bioluminescence, even nudibranch [Aplysia spp.] egg-ribbons). These general inquiries are a normal part of any citizen science program. After discussions by phone with the observers, sample collections and/or data comparison with the REPHY network or other research programs, respectively 24, 40 and 30 observations were considered to be valid scientific observations and potential phytoplankton water discolorations (Table 1). The discarded observations were put aside either after viewing the photos provided and/or talking with the observer. Some were observations of macroalgae. Others either had inconclusive pictures, descriptions more closely resembling zooplankton aggregations, concerned brackish lagoons or were located outside of Brittany in areas not covered by the Phenomer network. Many of the observations made by citizens were reported in areas outside the routine phytoplankton monitoring perimeter. In 2013 (10 observations), 2014 (31 observations), and 2015 (15 observations), respectively 42%, 77%, and 50% of potential discolorations phenomena occurring in Brittany were not reported in the frame of the routine phytoplankton monitoring system (Table 1). Out of these potential water discoloration phenomena, 14, 32 and 28 could be sampled and definitively proved to be water discolorations caused by massive phytoplankton development (Table 1). The remaining 10, 8 and 2 observations could not be sampled either because citizens contacted the Phenomer program too late or the blooms disappeared, or because the phenomena occurred in remote areas, far from research centers where samples could be quickly deposited. This second bias occurred especially in 2013 (10 water discolorations not sampled) before the setup of relay structures. The confirmed phytoplankton blooms corresponded to red, green, and dark brown discolorations; most of which were observed during July-August. In 2013, 2014 and 2015 respectively, 7, 24 and 14 phenomena were observed outside of routine monitoring points (Table 1).

Table 1 here

Citizen perception of water discolorations resulting from semi-structured phone interviews

During the 2015 season a total of 25 questionnaires were completed. About 80% of Phenomer observers were already informed about the HAB phenomena taking part in the program, and out of these 60% had already observed phytoplankton under the microscope. Observers were then asked to give their opinion about their perception of how frequently water discolorations occur. The majority (52%) of observers considered water discoloration events to occur sporadically, 32% considered them to occur regularly, 12% considered these events to occur frequently, 0% felt them to occur more rarely and 20% felt unable to answer the question because of insufficient knowledge. The vast majority (83%) believed water discolorations to have an environmental impact, in both a harmful and a useful way (Fig. 2A). To a lesser extent (25%), interviewees felt that seawater discolorations have economic impacts and impacts on human health. Few people considered water discoloration harmful from a personal or aesthetic point of view. Observers were driven to report water discolorations events out of environmental awareness (Fig. 2B), to help the program, or to understand the origin and effects of bloom phenomena. People wanted to understand more about water discoloration whether in relation to its effect on mankind, the environment, or in general, in near-equal proportions. No observers wished to complain about the presence of water discolorations.

Observed water discolorations in relation with monitoring activities

Red discolorations were regularly observed during the three years of project implementation from May to August from at different locations in southern Brittany's coastal waters, across an area of about 150 km in 2013 and 130km in 2015 (Fig. 3, Fig. 4A,C). Red discoloration phenomena were mostly restricted to the shoreline or to the first hundreds meters of the coastal waters (Fig. 4A). Across the three years, 14 over the 28 observations (50%) occurred in areas not monitored by the sanitary monitoring system (Table 1). Given their small surface area, they were mostly observed by tourists on the shore or people working in coastal waters. They were always linked to massive development and dominance in the phytoplankton samples of the protist Noctiluca scintillans (200-1200 µm in size, Fig. 4B). In 2013, red discolorations were observed mostly in July-August. In less than a 3B). Fig. 3 here, Fig. 4 here Green seawater discolorations were the most frequent phenomena detected over the three years (Table 1, Fig. 3, Fig. 4D,F). All warnings corresponded to massive development in phytoplankton samples of the dinoflagellate Lepidodinium chlorophorum (Fig. 4E). Green blooms of L. chlorophorum were observed in coastal and off shore areas, with some localized and some very widespread discolorations. Across the three years, 25 over the 36 green bloom observations (69%) occurred in areas not monitored by the sanitary monitoring system (Table 1). In 2013 green discolorations were detected four times in a relatively restricted area (between the Bay of Vilaine and the Loire River outlet), in a time window (from the 19 th to the 30 th of August) not sampled by the REPHY monitoring (Fig. 3A). In nearby REPHY zones, on the 26-28 th August, cell counts of L. chlorophorum, during the green discoloration phenomena varied between 14 800 cells.L -1 and 2.90 X 10 6 cells.L - 1 (Le Croisic, Coupelasse large). In 2014, 24 observations of green water discolorations were reported almost daily over a period of about one about month (from the 3 rd to the 8 th of August) across a wider area than in 2013, throughout southern Brittany's coastal waters, remaining however more frequent in the Bay of Vilaine zone (Fig 3B). Discolorations were either limited to the shoreline and reported by beachgoers or largely extended off-shore waters and were observed by amateur yachtsmen and light aircraft pilots. Off-shore phenomena were particularly impressive due to their spatial extension (Fig. 5A). Discolorations occurred generally in surface waters, but a green bloom was also reported by a scuba diver at 23m depth on the 26 th July. When heavy water discolorations occurred in coastal waters, 9 citizens out of the 24 observing green water discolorations, reported slimy, dense waters, which emitted a pungent, unpleasant odor. From the 16 th to the 19 th of July, citizens reported fish (soles, sand eels, weevers), jellyfish, mollusks and crab mortalities both in the water (Fig. 5B) and washed up on the beach (Fig 5C). On five occasions (16 th , 17th 19 th , 21 st , 22 nd of July) multiple warnings were received from different locations, demonstrating both the amplitude of the phenomena and the concern of the citizens (Fig. 3B).

The highest cell concentration of the species, 7.5 X 10 6 cells.L -1 was reported on the 22 nd of July (Port Manez), but it is likely that cell maxima during the episode largely exceeded this value. Due to this phenomenon, the 2014 season of the project has the highest number of warnings (Table 1). As in 2013, in 2015, green discolorations were less frequent, less extended, and located mainly outside of the REPHY (Table 1). No event was observed in August (Fig. 3C). Three observations were performed south of the Phenomer project's perimeter, demonstrating that these phenomena also occur at lower latitudes. Fig. 5 here Other phenomena were observed beyond N. scintillans and L. cholorophorum water discolorations. On August 12 th 2013, two separate citizen observations of dark-brown discolorations were reported from separate shallow locations in the Bay of Vilaine in zones not monitored by the REPHY network (Fig. 3A, Table 1). In phytoplankton samples collected in both areas on the same day following citizen warnings, co-occurring blooms of the marine-fauna toxic raphidophyte Heterosigma akashiwo (max 3.00 X 10 6 cells.L -1 ) and the dictyochophyte Pseudochattonella verruculosa (max 1.90 X 10 6 cells.L -1 ) were observed. Seawater dissolved oxygen concentrations at the sea floor in both locations were very low (4.9 and 5.5 mg L -1 ), and at one site a mass mortality of bivalves and small crustaceans was observed. Other brown discolorations were attributed to diatom proliferations. On the 20 th July 2014 a red discoloration observed in the Bay of Brest, in an area not routinely monitored by the REPHY, was attributed to the massive presence (3.6 cells.L -1 on the 21 st of July, Penfoul) of the toxic dinoflagellate Alexandrium minutum (PSP causative species) (Fig. 3B, Table 1). A pinkish/brownish discoloration was observed by citizens on the 14 th June 2014 in the Iroise Sea (Douarnenez Bay). Microscopic analyses made it possible to attribute the discoloration to the massive presence of the dinoflagellate Ceratium kofoidii (1.85 X 10 5 cells•L -1 , June 14 th ), associated to the presence of other species such as Ceratium fusus (1.26 X 10 4 cells•L -1 ) and Leptocylindrus danicus (3.00 X 10 4 cells•L -1 ) (Fig. 3B). Two brown discolorations in 2014 from both the English Channel and the Atlantic waters corresponded to a mixture of diatom species with higher concentrations of the species Leptocylindrus danicus (4.4 X 10 6 cells.L -1 , 16 th May) and Guinardia delicatula (9,8 X 10 5 cells.L -1 , 16 th May) among other diatoms (Fig. 2B). One event in 2015 was attributed to the bloom of Brockmanniella brockmannii (Fig. 3C). On 9 March 2015 foams due the proliferation of Phaeocystis were observed in the north-eastern part of Brittany, facing the English Channel (Fig. 3C).

Discussion

The citizen science program Phenomer deployed in Brittany from 2013 to 2015 represents the first structured monitoring program of water discoloration phenomena in the area. It gives a good example of the validity of this new approach for studying and managing HAB phenomena. The project was an opportunity for a first sociological analysis of the audience and their motivation for reporting these phenomena. In addition, it provides new information useful to analyse HAB species phenology and distribution. Phenomer has revealed itself to be very complimentary to the ongoing French phytosanitary monitoring which was not designed for the detection of water discolorations, and has more generally helped to clarify the possible contribution and limits of the citizen science approach for plankton studies.

Citizen feedback

Citizens who took part in Phenomer had heard about project mostly through articles in the regional press and through the internet website. The target audience of Phenomer was composed entirely of people frequenting the Brittany coastline. Our questionnaire shows that people who took part in Phenomer were relatively well informed and interested about the aims of the project. Most of the people who took part in the project had heard about water discolorations caused by microalgae before the implementation of Phenomer. The majority (60%) of the observations whilst the participants carried out their professional activities (i.e. fishing, performing environmental analyses within Marine Protected Areas,etc.). However, during telephone discussions between scientists and observers some clarifications were given, especially concerning health risks connected to water discoloration phenomena. Often the difference between green macroalgal proliferations (i.e. Ulva spp.) and phytoplankton blooms was explained. Massive proliferations of green macroalgae that recurrently wash up on Brittany's beaches are a highly mediatized topic, and the difference between the two phenomena had to be carefully explained in the Phenomer communication materials and during phone conversations.

The questionnaire submitted to the water discoloration observers in 2015 helped to better identify the sociological profile of people participating to the project, as already discussed in other citizen science approaches [START_REF] Martin | Understanding drivers, barriers and information sources for public participation in marine citizen science[END_REF]. These first results show that the audience most receptive to Phenomer was a limited proportion of the total population frequenting the marine coastal zone. It was composed of people already informed about the water discoloration phenomena and their development. Their knowledge of this natural phenomenon drove them to call. They participated in the project because they wanted to know more about what they observed and the effects, if any, on humans and the environment. Their wish to help scientists in understanding triggering factors of water discolorations was particularly noticed. Water discolorations were not perceived as harmful phenomena, and the people taking part in the project were not protesting about these phenomena, but instead were people sensitive to and concerned by environmental issues. However, the profile of people participating to Phenomer in 2015 has to be considered in the light of the absence of major, impressive phenomena, and therefore as a typical Phenomer participant profile. In 2014, pre-analyses of people driven to signal water discoloration phenomena included not only typical profiles of well informed and environmentally concerned people, but also that of people alarmed by the repetitive and impressive green discoloration as well as the fauna mortalities recorded in July. Hence, the intrinsic natural variability of the water discolorations and their effects on the environment may trigger changes first and foremost in the people affected by, and aware ofthese phenomena. From a broader perspective, the nexus between a scientific and sociological analysis of HABs remains inadequate, and prevents the assessment of HAB real impact on human well-being (Wells et al., 2016).

Ecological analysis of the water discolorations observed

Despite only having been collected over a relatively short time period, and with an innovative approach for phytoplankton bloom studies, our data sheds new light on the frequency and spatial and temporal extension of water discoloration phenomena along Brittany's coastline. The first three years of the project running demonstrate variability in the number, frequency and month of summer in which alerts are reported. If most of water discolorations were signaled during the end of July and August, in 2015 red discolorations of N. scintillans were observed mostly in June and the last observation was performed on the 16 th of July. The reasons for this variability are not found in a difference in the project implementation (i.e. communication efforts, scientific engagement) but rather in meteorological conditions which affected both phytoplankton proliferations and the tourist season. The end of summer 2015 was particularly cool and unsettled, with heavy rain at times, hampering phytoplankton development as well as tourism along the north Atlantic and English Channel ("Met Office UK Climate Summary -Summer 2015," n.d.). Water discoloration alerts can therefore vary from one year to the next not because of bias in our citizen science project construction, but because of the intrinsic biological variability of phytoplankton bloom phenology.

Most of the red discolorations observed during the three years of the project implementation are linked to the massive presence of the protist Noctiluca scintillans. This species is generally considered as an aberrant heterotrophic dinoflagellate, having significant morphological and biological differences with typical dinoflagellates (diploidy, presence of tentacle, absence of condensed chromosomes) (Gomez et al. 2010).

Noctiluca scintillans can feed upon a large variety of preys (diatoms, dinoflagellates, copepod eggs and small ciliates), but diatoms seem to be its preferred food source for proliferation (Gomez et al. 2010). Cells start feeding and growing in the water column, then move to the surface, where the bloom is visible as a thin red layer. Therefore the red visible discolorations caused by N. scintillans actually correspond to the end of the species bloom [START_REF] Harrison | Geographical distribution of red and green Noctiluca scintillans[END_REF]. Red discolorations are typical coastal phenomena as abundance of N. scintillans decreases offshore. High concentrations occur along water fronts [START_REF] Hesse | A winter study of plankton distribution across a coastal salinity front in the German Bight[END_REF]) and wind direction plays a role in concentrating the bloom at the shoreline [START_REF] Harrison | Geographical distribution of red and green Noctiluca scintillans[END_REF]. Blooms of red N. scintillans are common and well-known phenomena across all French coastlines, as they have been observed in the English Channel (Boalch 1987), western Brittany (Le Fèvre & Grall 1970), the southern part of the Bay of Biscay [START_REF] Quevedo | Evidence of heavy predation by Noctiluca scintillans on Acartia clausi (Copepoda) eggs off the central Cantabrian coast (NW Spain)[END_REF][START_REF] Cabal | Mesozooplankton species distribution in the NW and N Iberian shelf during spring 2004: Relationship with frontal structures[END_REF]) and the Mediterranean Sea [START_REF] Métivier | Organisation of cytoskeleton during the tentacle contraction and cytostome movement in the dinoflagellate Noctiluca scintillans (McCartney)[END_REF]. Red discolorations are observed annually across Brittany waters, always through sporadic, ad hoc observations. Despite being visible from an aircraft, studies at large spatial scales are still missing. Le Fèvre and Grall (1970) studied a large bloom (20 nautical miles) which occurred on July 20 th , 1967 off the western coast of Brittany (Iroise Sea) and concluded that a surface convergence area due to an outflow of coastal water produced a large bloom of N. scintillans. Observations reported by citizens during the summer 2013 within the framework of Phenomer project provide a first structured assessment of N. scintillans discolorations across southern Brittany waters and an estimate of their spatial extension. It is not possible to infer that all 2013 observations belonged to a unique bloom and population. Single, separate blooms could have occurred locally and/or at different times.

Water horizontal transport coupled with wind direction (all 2013 events observed occurred with westerly winds) have certainly contributed to accumulate N. scintillans cells, spotlighting red discolorations, either in correspondence with frontal water masses, or in nearshore local embayment. Relatively low (max 3200 cell.L -1 ) cell concentration counts for a phytoplankton bloom event in areas near observed phenomena argue in favor of a local, patchy accumulation of N. scintillans water discolorations across Brittany waters.

Green water discolorations caused by dinoflagellates are poorly scientifically documented [START_REF] Honsell | Interesting ultrastructural features of a green dinoflagellate[END_REF][START_REF] Jimenez | Green mass aggregations of Gyrodinium cf. aureolum Hulburt in the Ria of Pontevedra (North-West Spain)[END_REF][START_REF] Sournia | The repetitive and expanding occurrence of a green, bloom-forming dinoflagellate (Dinophyceae) on the coasts of France[END_REF][START_REF] Paulmier | Gyrodinium corsicum nov. sp. (Gymnodiniales, Dinophycees), organisme responsable d'une « eau Verte » dans l'Etang marin de Diana (Corse), en Avril[END_REF][START_REF] Elbrachter | Gymnodinium chlorophorum, a new, green, bloom-forming dinoflagellate (Gymnodiniales, Dinophyceae) with a vestigial prasinophyte endosymbiont[END_REF]. The dinoflagellate Lepidodinium chlorophorum has been recognized as one potential cause of these discolorations. It is a naked dinoflagellate of the 'green lineage' of the dinoflagellate evolution characterized by the presence of chlorophyll b as the principal pigment, which gives the green color to the dinoflagellate [START_REF] Hansen | Ultrastructure and large subunit rDNA sequences of Lepidodinium viride reveal a close relationship to Lepidodinium chlorophorum comb. nov. (=Gymnodinium chlorophorum)[END_REF][START_REF] Siano | Unarmoured and thin-walled dinoflagellates from the Gulf of Naples, with the description of Woloszynskia cincta sp. nov. (Dinophyceae, Suessiales)[END_REF]. Green water discolorations caused by Lepidodinium spp. can be extensive and spectacular phenomena reported from Italy (Adriatic Sea) [START_REF] Honsell | Interesting ultrastructural features of a green dinoflagellate[END_REF]), the North-West of Spain [START_REF] Jimenez | Green mass aggregations of Gyrodinium cf. aureolum Hulburt in the Ria of Pontevedra (North-West Spain)[END_REF]) and the North Sea [START_REF] Elbrachter | Gymnodinium chlorophorum, a new, green, bloom-forming dinoflagellate (Gymnodiniales, Dinophyceae) with a vestigial prasinophyte endosymbiont[END_REF]. In France, the species was reported along the West Atlantic coast for the first time in 1982 [START_REF] Lassus | Plancton toxique et plancton d'eaux rouges sur les côtes européennes[END_REF]. Since then, the abundance, extent, duration and intensity of the blooms have seemingly increased, with large water discolorations being observed in the Bay of Vilaine (southern Brittany) and in the Bay of Seine (English Channel, Normandy) until 1991 [START_REF] Sournia | The repetitive and expanding occurrence of a green, bloom-forming dinoflagellate (Dinophyceae) on the coasts of France[END_REF]).

As reported by [START_REF] Sournia | The repetitive and expanding occurrence of a green, bloom-forming dinoflagellate (Dinophyceae) on the coasts of France[END_REF], discolorations caused by L. chlorophorum were reported via Phenomer as being gelatinous, mucous or slimy. Tourists and swimmers complained about the appearance and consistency of seawater. Depending on the episodes and their locations, mortality of mussels, oysters, smaller mollusks, shrimps, crabs, and smaller crustaceans, werelinked to a decrease of the oxygen availability due to the decomposition of the phytoplankton biomass. Between 1982[START_REF] Thompson | Ecocentric and anthropocentric attitudes toward the environment[END_REF][START_REF] Sournia | The repetitive and expanding occurrence of a green, bloom-forming dinoflagellate (Dinophyceae) on the coasts of France[END_REF] correlated water discolorations with riverine freshwater inputs. Cysts of the species were observed in water samples and daily vertical migration of the species was observed with peaks in concentration varying throughout the water column [START_REF] Sournia | The repetitive and expanding occurrence of a green, bloom-forming dinoflagellate (Dinophyceae) on the coasts of France[END_REF]. Discolorations during 1982-1991 were reported in the summer time, except for two episodes which occurred in autumn (October and December) [START_REF] Sournia | The repetitive and expanding occurrence of a green, bloom-forming dinoflagellate (Dinophyceae) on the coasts of France[END_REF]. It is acknowledged that L. chlorophorum can be an important component of the late summer-autumn phytoplankton community, as reported in the English Channel [START_REF] Napoléon | Dynamics of phytoplankton diversity structure and primary productivity in the English Channel[END_REF]. Episodes reported by citizens in 2013 and 2014 in the frame of the Phenomer project confirmed that the Vilaine Bay and the Loire River output in southern Brittany are high risk areas for L. chlorophorum blooms. 2014 observations yielded new information on the areas which could be potentially affected by these phenomena, both to the north and to the south of the Loire River output and the Vilaine Bay (Fig. 3B). Data collected in the frame of Phenomer suggest L. chlorophorum blooms can be long lasting across southern Brittany waters. Continuous data (almost daily citizen alerts, 24 observations in total) over a period of almost one month suggest that blooms of this species can last at least one month and that a higher intensity of L. chlorophorum blooms can coincide with a fish mortality presumably caused by anoxic conditions. Interestingly, L. chlorophorum was considered as not being ingested by the oyster Magallana gigas, ,after in-situ observations carried out in the Bay of Vilaine, which suggest a potential negative effect on oyster growth during bloom concentrations (Alunno-Bruscia et al. 2011).

Dark brown discolorations caused by diatoms, as those observed in the frame of the Phenomer projet, are frequent phenomena reported worldwide. Other microalgae of the phylum Ochrophyta (Heterokontophyta) are responsible for dark brown discolorations, including members of the class Raphidophyta and Dictyochophyta to which Heterosigma akashiwo and Pseudochattonella verruculosa (ex. Chattonella verruculosa, Hosoi-Tanabe S. 2007) belong respectively. Both species have been traditionally associated to fish mortalities (Hara andChihara, 1987, Yamamoto &[START_REF] Yamamoto | Two species of harmful red tide plankton increased in Fukuoka Bay[END_REF][START_REF] Hallegraeff | Taxonomy of harmful marine raphidophytes[END_REF], but their toxic effect can potentially extend to other marine organisms. Indeed in vitro experiments demonstrated that H. akashiwo may have lethal and sublethal impacts on shellfish (Hégaret et al. 2011) and that rotifers died when fed upon P. verruculosa [START_REF] Chang | Molecular phylogeny, pigment composition, toxicology and life history of Pseudochattonella cf. verruculosa (Class Dictyochophyceae) from Wellington Harbour, New Zealand[END_REF]. It is hard to discern if the episode of massive mortality of bivalves and small crustaceans observed in 2013 is related to the high concentration of one or both toxic species, or to the anoxic conditions which developed during the bloom.

Citizen science as a complementary approach to phytoplankton studies and monitoring programs: advantages and limits

Citizen sciences offer the possibility to increase the frequency of observations/samples of a research program providing relatively low cost-data [START_REF] Jarvis | Citizen science and the power of public participation in marine spatial planning[END_REF]. The example of Phenomer showed that the citizen science approach may be applied to plankton data collection and analyses and that the information gained through this method allows the acquisition of information that can be overtaken by routine plankton monitoring. The 61% of water discolorations observed by citizens were sampled outside of areas covered by the REPHY French monitoring system (Table 1). This monitoring network, as with all those classically used for sanitary purposes, was not conceived for surveying and studying water discoloration. Hence, Phenomer demonstrated therefore that a citizen science network can complete routine monitoring systems for structuring the detection and analysis of water discoloration phenomena. In addition, Phenomer provided new scientific information and pointers for studying the phenology of water discoloration causing species, as well as new information on the biogeography of species capable of HAB events.

Our example of a citizen approach for getting information on plankton, allowed us to better discern identification of the constraints and limits of such an application. Obtaining data on species responsible for seawater discolorations, is dependent on: i) the frequency at which coastal zones are observed and subsequently sampled with respect to other areas (see [START_REF] Jarvis | Citizen science and the power of public participation in marine spatial planning[END_REF] for the analysis of the importance of citizen science in the marine spatial planning of coastal ecosystems), ii) the perception and identification of an 'anomalous' phenomenon (an unusual color of the sea) by the general public, iii) the awareness, responsiveness and sense of civil responsibility of the citizens towards the marine environment and potential ecological risks, and iv) the rapidity and the quantity of the analysis of bloom samples.

Despite communication efforts about water discolorations remaining constant throughout the three years of project deployment and across the geographic Brittany territory, we cannot ensure that the Phenomer program accounts for all discoloration phenomena occurring in Brittany. In the English Channel sector only a few discolorations caused by diatoms were reported in 2014 and 2015. It is possible that other unreported visible blooms may have occurred in this area. Indeed blooms of phytoplankton taxa exceeding for example from 1 to 7 million cells.L -1 (Chaetoceros spp., Dactyliosolen fragilissimus, Pseudo-nitzschia spp., cryptophytes, Thalassionema spp.) were detected in the northern as well as in southern stations of the REPHY network (REPHY data). Yet, such high cell concentrations do not automatically correspond to water discolorations.

Conversely, seawater discolorations do not always correspond to phytoplankton high abundances. Seawater can be colored for instance by pollutants (i.e. oils, petrol), sediment suspension, and other physico-chemical properties. This aspect has been taken into account in the formulation of the protocol and always analyzed during the interview made by scientists to the water discoloration observers. In some ecosystems, natural phenomena (storms, rains, winds, currents, and river plumes) can contribute to re-suspend bottom sediments and increase water turbidity, thus giving the sea a more or less dark/light brown color for example. The color of the sea that a common citizen can perceive as 'normal' is a relative concept, strictly dependent on the ecosystems. People living along stretches of coastline with clear waters can relatively easily identify a drastic change in the color of the sea and react to this phenomenon. However, people living on coastlines with turbid coastal waters are used to a light/dark brown appearance of the seawater. They may therefore have difficulties, first in perceiving 'anomalous' dark brown discolorations and second in attributing them to phytoplankton bloom events. Only a multiannual evaluation of the number and frequency of the alerts collected by Phenomer, coupled with an interview analysis of the observers with respect to their ecosystems will smooth the bias linked to coast frequentation and citizen reactivity, eventually allowing a complete census of all discoloration phenomena potentially occurring across Brittany coastal waters.

The rapid analysis of a water discoloration sample and the correct taxonomic identification of responsible species are needed for biodiversity and ecological studies on microalgae. Dark brown discolorations may be caused by different algal species and even classes. Equally, different shades of red discolorations may be provoked not only by N. scintillans but also by other dinoflagellates (e.g. Alexandrium. spp., Prorocentrum spp., Ceratium spp.), ciliates (e.g. Mesodinium rubrum) and cryptophytes. Whilst it is true that few dinoflagellates may cause green discolorations, other green-pigmented microalgal classes (Prasinophyta and Cyanophyta) are known to frequently provoke green blooms. It is therefore incorrect and a potential risk to associate univocally a color of the water to a single microalga. The collection of water samples and their analysis is of course time consuming and may be discouraging, but it is a key component in the longevity and scientific validity of a citizen science project addressing ecological and biodiversity questions on plankton In the frame of Phenomer, if the reactivity and the participation of people after a water discoloration observation was successful, the logistics for ensuring a rapid and efficient sample collection were heavy. In 2013, 10 observed phenomena could not be sampled. In the following years the set-up of the relay structure network revealed to be a good strategy to overcome the problem and fewer phenomena (7 in 2014 and 2 in 2015) were overlooked. The down-sizing of the study area, or a citizen science strategy based on a specific community of people (shellfish farmers, environmental associations) rather than a very broad target audience such as that in Phenomer, could probably help in the building trust and loyalty between researchers and citizens, which are the very foundations of a citizen science approach.

Conclusions

Results obtained on the Brittany coast of France in the first three years (2013-2015) of deployment of the Phenomer project show that our citizen science approach was very helpful for: 1) signaling water discoloration phenomena not observed by the routine, national monitoring, thus showing the complementarity of these two networks; 2) assessing a potential spatial extension of water discolorations, and particularly of those caused by N. scintillans across southern Brittany; 3) giving a time frame to the duration of discoloration phenomena, in particular of green ones caused by L. chlorophorum in the Vilaine Bay-Loire estuary area. As well as being of regional interest, these data contribute to the study of global biogeography of harmful species and HAB events.

In addition, a first sociological profile of people concerned by water discolorations was elaborated.

People concerned by water discoloration phenomena were well-informed citizens, aware of and concerned by environmental issues. Water discolorations are mostly perceived as an anomalous, alarming status of the environment. However the sociological profile of people participating in such a citizen science project can vary accordingly to the gravity of water discolorations occurrences and effects.

Phenomer has shown the potential of citizen science in research on phytoplankton ecology, biodiversity and visible HAB detections and allows the identification of some recommendations. Future application of the citizen science approach to plankton should: i) carefully evaluate, at the time of designing the study, how citizens can help to attain scientific research objectives (information to be collected, sampling frequency, relay points to deposit samples); ii) develop clear and simple communication medium presenting the research objectives and sampling protocol; iii) target the community of people that could be more concerned by the problematic of the project as a guarantee of citizen investment in the project activities. Beyond scientific objectives, the application of a citizen science approach in the frame of a research project has the great unquantifiable value of disseminating knowledge on microscopic organisms, and educating voluntary participants to environmental issues connected to phytoplankton such as HABs. Citizen science could be a new method to helping HABs be recognized as one facet of complex ecosystem interactions with human society. This approach, coupled with research, monitoring, and management of HAB phenomena, could help to find local solutions to a global issue.

1

Table and Figure Captions

  in response to the onset of human poisoning syndrome (ASP and DSP) events. In 2001, the Phytoplankton Monitoring Network (PMN) was established by the National Oceanographic and Atmospheric Administration of the United States department of Commerce (NOAA), initially as part of South Carolina's Pfiesteria Harmful

Fig

  Fig. 2 here

  week's time (21 st -26 th July 2013), citizen observations were made almost simultaneously across an area of more than 150km, between the Yeu (21 st July) and Groix (22 nd July) islands in areas not monitored by the REPHY system (Fig. 3A) In 2014 and 2015 red discolorations attributable to N. scintillans discolorations were reported in southern Brittany earlier in the summer, in June-July. No observations were made in August in 2014 and 2015 (Figs 3A,

Fig. 1 .Fig. 2 .

 12 Fig. 1. Phenomer water discoloration reporting process flowchart (single column fitting)

Fig. 3 .

 3 Fig. 3. Water discoloration phenomena reported by citizens in 2013, 2014 and 2015 and dominant taxa identified by the phytoplankton taxonomists of the Phenomer consortium in water samples. Sampling stations of the National Phytoplankton Monitoring System REPHY of Ifremer are also indicated. (two column fitting).

Fig. 4 .

 4 Fig. 4. Red discoloration pictures (A, C), caused by Noctiluca scintillans (B, scale bar: 50 µm). Green discoloration pictures (D, F) caused by Lepidodinium chlorophorum (E, scale bar: 20µm). Pictures A, C, D and F are taken either by citizens from the coast and or from aircrafts (C). (1.5 column fitting).

Fig. 5 . 1 .

 51 Fig. 5. Green discolorations and fish mortality in the Bay of Vilaine (South of Brittany) in 2014. (1.5 column fitting).

Zingone, A., Oksfeldt Enevoldsen, H., 2000. The diversity of harmful algal blooms: a challenge for science and management. Ocean & Coastal Management 43 : 725-748. doi:10.1016/S0964-5691(00)00056-9

30 15 15 28 9-7 2-6 3-1

Acknowledgments

The authors gratefully acknowledge all Phenomer participants (citizens and scientists) who shared discoloration observations and provided data and pictures of the phytoplankton blooms. The communication service of Ifremer/Nantes, and in particular Sophie Pilven, is greatly acknowledged for its support for all communication actions and information dissemination of the project. The authors kindly thank Elisabeth Nézan and Nicolas Chomérat (Ifremer LER/BO Concarneau) for their help in the identification of the species toxic for marine fauna in occasion of the brown discolorations and for providing pictures of N. scintillans and L. chlorophorum (Fig. 3).

The authors also thank Beatriz Beker, Charlotte Soler (LEMAR) and Pascale Malestroit (Ifremer) for their identification of microalgal species. Pierre Bodénès is acknowledged for his help in figure designing. Support for Phenomer was provided by the "Quels littoraux pour demain?" grant of the Fondation de France (grant n°:00038383), the Loire-Brittany Water Agency, the French Ministry of Environment and Ifremer for supporting

all scientific and communication action strategies of the project. The objectives of Phenomer tie in to the scope of the French GDR (Groupement de Recherche) on harmful microalgae Phycotox (http://www.phycotox/fr). The anonymous referees are acknowledged for providing major improvements to the manuscript.


Alberto Aguilar

Jorge García-Márquez

J E A Landgrave

Super-resolution with a complex-amplitude pupil mask encoded in the first diffraction order of a phase grating

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

INTRODUCTION

Diffraction imposes a barrier that prevents an optical system from resolving two points closer than half the wavelength used to illuminate them [START_REF] Landgrave | Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung[END_REF]. Later, it was demonstrated that the minimum separation between two points to be resolved is in fact nearly a quarter of a wavelength [START_REF] Sales | Smallest Focal Spot[END_REF]. Several efforts have been made to surpass this limitation, either in microscopy or in astronomical instrumentation. Optical super-resolving systems are conceived to cope with fundamental challenges proper to the targeted application. For instance, in microscopy, fluorescence is extensively used nowadays, and different techniques have been proposed to obtain super-resolved images with fluorescence microscopy. Examples of these techniques are Structured Illumination Microscopy (SIM) [START_REF] Gustafsson | Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy[END_REF], deterministic functional techniques such as 2 STimulated Emission Depletion (STED) [START_REF] Hell | Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy[END_REF], and stochastic techniques like STochastic Optical Reconstruction Microscopy (STORM) [START_REF] Rust | Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM)[END_REF]. Dyba and Hell used a Phase Mask (PhM) in a STED-4Pi microscope [START_REF] Dyba | Focal spots of size λ/23 open up far-field florescence microscopy at 33 nm axial resolution[END_REF]. Since then, PhMs have been incorporated in microscopy. LCoS-SLMs have been proposed for phase measurements below the wavelength by using optical vortices [START_REF] Aguilar | Multi-step vortex filtering for phase extraction[END_REF]. More recently, spatial light modulators (SLMs) have also been incorporated in microscopy with the intention of surpassing the diffraction limit barrier [START_REF] Tzang | Two-photon PSF-engineered image scanning microscopy[END_REF][START_REF] Huang | Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy[END_REF][START_REF] Gustavsson | 3D single-molecule super-resolution microscopy with a tilted light sheet[END_REF]. In the case of astronomical telescopes, it has been suggested that the deformable mirrors that are used to compensate atmospheric turbulence can also be used to implement phase-only, continuous PhMs to achieve a moderate amount of super-resolution [START_REF] Cagigal | Design of Continuous Superresolving Masks for Groundbased Telescopes[END_REF].

Super-resolving PhMs, also known as pupil filters or pupil masks, were originally proposed by Toraldo di Francia [START_REF] Di Francia | Super-Gain Antennas and Optical Resolving Power[END_REF]. They were obtained in practice with two transmitting SLMs, used to synthesize a complex-amplitude (CA) PhM with two superimposed fields [START_REF] Gundu | High efficient superresolution combination filter with twin LCD spatial light modulators[END_REF][START_REF] Kowalczyk | Collective matrix of spatial light modulators for increased resolution in holographic image projection[END_REF] (A CA-PhM modifies both, the amplitude and the phase of an incoming beam). The new generation of SLMs, however, can exhibit phase fluctuations, a phenomenon known as flicker, preventing thus the realization of CA-PhMs with this method. This flicker depends on the electronic addressing of the signal to be displayed by the pixelated liquid crystal (LC). Then, the superposition of the fields from the two SLMs is neutralized by a biting phenomenon produced by the field fluctuations. In other words, given two SLMs acting as mirrors, each reflecting a portion of a common beam, the superposition of the two wavefronts reflected by the SLMs will be affected by non-synchronous fluctuations in phase resulting in a nullified interference pattern [START_REF] García-Márquez | Flicker minimization in an LCoS spatial light modulator[END_REF][START_REF] Márquez | Blazed grating theory to minimize the non-idealities in LCoS devices[END_REF]. Efforts have been made to reduce these fluctuations with polarized light [START_REF] Márquez | Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization[END_REF], by cooling the LC molecules [START_REF] García-Márquez | Flicker minimization in an LCoS spatial light modulator[END_REF][START_REF] Calderón-Hermosillo | Flicker in a twisted nematic spatial light modulator[END_REF], or by changing the period of the pulsed width modulation (PWM) of the SLMs [START_REF] Yang | Phase flicker optimisation in digital liquid crystal on silicon devices[END_REF].

In addition to the limitation that represents this phase fluctuation, to achieve super-resolution with SLMs the panel should be flat with an optical quality better than that imposed by Maréchal's condition [START_REF] Born | Principles of Optics[END_REF], which is approximately of 1 4 λ . In [START_REF] García-Márquez | Recursive wavefront aberration correction method for LCoS spatial light modulators[END_REF], a method to compensate the SLM panel deformations with residual errors below 3 0 λ was shown. This correction could not be improved further due to irregularities in the LC thickness, as described in [START_REF] López | Non-uniform spatial response of the LCoS spatial light modulator[END_REF]. Therefore, it is essential to calibrate the panel with a reference flat, since in this form it would be metrologically linked to a physical standard [START_REF] García-Márquez | Calibración de un interferómetro fizeau: cálculo de incertidumbres[END_REF]; after doing this, all subsequent panel modifications could be readily detected. As explained in [START_REF] García-Márquez | Recursive wavefront aberration correction method for LCoS spatial light modulators[END_REF], a recursive wavefront aberration-compensation procedure with a Liquid Crystal on Silicon (LCoS) SLM can attain a high degree of correction for the +1 diffraction order of a sinusoidal phase grating recorded on it.

To avoid the effects of the phase fluctuations in SLMs, and other polarization effects [START_REF] Lizana | Influence of the temporal fluctuations phenomena on the ECB LCoS performance[END_REF][START_REF] Márquez | Static and dynamic effects of flicker in phase multilevel elements on LCoS devices[END_REF], it is desirable to attain super-resolution using only one SLM, which would have the further benefit of simplifying the setup that is used for this purpose. Despite the flicker, the polarization effects, the surface aberrations, and the spatial distribution of LC molecules, we show here that a single SLM can be used to produce a dynamic, easy-to-use, super-resolving PhM. In section 2 we describe the modulation technique that we employ for this aim, in section 3 we validate this technique with a numerical simulation, and in section 4 we describe our experimental setup and present our best results. Section 5 includes some concluding remarks.

COMPLEX-AMPLITUDE PUPIL MASK ENCODING

Coding a phase and amplitude mask in a spatial light modulator is done by using two SLMs, one in phase and the other in amplitude. However, some SLMs such as LCoS are dependent on the polarization of the incident beam [START_REF] Lizana | Influence of the temporal fluctuations phenomena on the ECB LCoS performance[END_REF][START_REF] Márquez | Static and dynamic effects of flicker in phase multilevel elements on LCoS devices[END_REF]. Usually, for the optimal setup using two SLMs, two different incident polarizations must be created, one for the phase and one for the amplitude and then recombine them together. However, this procedure causes unwanted depolarizing effects in the output beam. By using only one SLM working in the first diffraction order instead of two different workings in the order zero, polarization effects can be neglected, as there is no interference of two different beams with different polarizations.

One of the main advantages of using phase gratings to encode CA-PhMs is that they allow changing the diffraction efficiency at any point of its surface. As we mentioned above, one SLM was used before to generate an amplitude transmittance PhM, while a second one was used to make a phase-only PhM. As shown in [START_REF] Gundu | High efficient superresolution combination filter with twin LCD spatial light modulators[END_REF], by superposing the outcome of both SLMs we obtain a CA-PhM. Aberrations introduced by the optical elements of a super-resolving system, however, is an important concern when making super-resolving PhMs. In optical engineering, we always look for reducing the number of elements because of several reasons: lower production costs, less raw materials, less space (compactness), to facilitate alignment, among others. This experiment was designed considering all these design parameters. Polarization, flicker, and LC-SLM intrinsic aberrations could be avoided with a CA-PhM embedded in a single SLM. Taking advantage of this, we decided to encode the CA-PhM in the field produced by the phase gratings in their +1 diffraction order.

Let us suppose that a modulated phase grating is displayed on an LCoS SLM. At normal incidence, the CA of the field reflected by the LCoS of a plane wave of amplitude A will be

[ ] { } [ ] 0 ( , ) exp ( , ) cos 2 ( , ) exp ( , ) , U x y A i x y u x x y A i x y β π φ α = + = ( 1
)
where A is a real constant, 0 u is the spatial frequency of the grating, and 2β(x,y) and φ(x,y) are, respectively, the phase modulation depth and the phase modulation function of the grating. Equation (1) resemblances the Jacobi-Anger expansion [START_REF] Weisstein | Jacobi-Anger Expansion[END_REF],

exp cos exp , (2)
where n J is the Bessel function of the first kind and th n order, thus Eq. ( 1) can be rewritten as

, = β , exp φ , exp 2π (3)
so that, except for the constant factor i n , the CA of the beam diffracted into the order +1 is

[ ] [ ] 1 1 ( , ) ( , ) exp ( , ) . U x y AJ x y i x y β φ + = ⋅ (4)
If we wish to use 1 ( , )

U x y + to design a PhM with an equivalent CA transmittance [ ] ( , ) ( , )exp ( , ) , 0 ( , ) 1, t x y a x y i x y a x y φ = ≤ ≤ (5)
from Eqs. ( 4) and ( 5) follows that we must have

[ ] 1 ( , ) ( , ). A J x y a x y β = (6)
By construction, ( , ) a x y is a bounded function; if we restrict the values of the phase ( , )

x y β to those within the first half-lobe of J1[β(x,y)], 0≤β(x,y)≤1.8412, so 0≤J1[β(x,y)]≤0.5819, then necessarily A=1/J1(βmax), where βmax≤1.8412 is the maximum value that can assume β(x,y). With this in mind, Eq. ( 6) can be rewritten as [ ] ( )

1 1 max max max ( , ) ( , ) 0, 0 ( , ) , 1.8412. J x y J a x y x y β β β β β - ⋅ = ≤ ≤ ≤ (7)
For this work we chose βmax(x,y)=1.8412, so that J1(βmax)=0.5819.

If we add the phase , required to compensate the aberrations of the super-resolving system, including those introduced by the LCoS panel, from Eq. ( 1) follows that the phase we need to encode in the LCoS is:

[ ] 0 ( , ) ( , )cos 2 ( , ) ( , ) c x y x y u x x y x y α β π φ φ = + + , (8)
where ( , )

x y β is obtained from Eq. ( 7), and ( , ) and ( , ) a x y x y φ are given functions [Eq. ( 5)].

Apart from the case of a phase-only PhM [ ( , ) 1 ] a x y = , where max ( , )

x y

β β =
, the values of ( , )

x y β must be obtained from Eq. ( 7) through a root-finding algorithm. Eq. ( 7) can in principle have multiple solutions, depending on the value of ( , ) a x y . For our purposes, however, those outside the first half-lobe of ( ) 1 J β would be irrelevant. The excursion of the phase ( , )

x y α , then, will be at most ± βmax = ± 1.8412 ∼ ± 0.59π [Eq. ( 8)], or, equivalently, [0, 1.18 ] π . This phase interval was reachable with classic SLMs, which allowed a phase range 0

( , ) 2 x y α π ≤ ≤
, approximately. In short, with this encoding technique we only required about 59 % of the maximum phase shift provided by our LCoS.

To encode the phase α(x,y) in an LCoS, we display first in a personal computer monitor a 255 grayscale image I(x,y) of the function α(x,y). In our case this had 1016×720 pixels -the number of pixels in our LCoS. Assuming for simplicity that φ(x,y) = 0 and φc(x,y) = 0, from Eq. ( 8) we would have ( )

( ) 0 0 0 0 max 0 ( , ) ( , ) ( , ) cos 2
( , ) cos 2 ,

I x y I x y I x y u x I V x y u x α β π β π = + = + = + (9)
where 0 I is a constant and max ( , ) ( , ) , 0 ( , ) 1

x y V x y V x y β β = ≤ ≤ . ( 10
)
Evidently ( , ) V x y is related to the visibility, or contrast, of the fringes in the pattern ( , ) .

I x y

Notice that max 0 max

min 0 max ( , ) 255, ( , ) 0.

I x y I I x y I

β β = + ≤ = - ≥ (11)
and thus

m ax m in m ax ( , ) ( , ) 2 . I x y I x y β - = (12)
Therefore, the number of gray levels, or phase steps, assigned to ( , ) I x y is proportional to m ax β . If m ax 0 . 7) and [START_REF] Gustavsson | 3D single-molecule super-resolution microscopy with a tilted light sheet[END_REF]. It is clear that the last yields a better mapping, but the price we pay for this is less light in the +1 diffraction order of the phase grating, and a coarser sinusoidal profile, which will produce stronger diffracted fields of high spatial frequencies (noise).

Fig. 1. Visibility V (contrast) in the hologram to be displayed in the LCoS vs the amplitude a of the PhM. When a ∼1, the curve corresponding to βmax = 0.59π (solid line) becomes very steep. This undesirable behavior can be avoided if we choose βmax = 0.35π (dashed line), but the light in the +1 diffraction order would be less [Eq. ( 4)], and the sinusoidal phase grating profile in this case would be coarser.

Since ( , ) a x y is variable, ( , )

x y β , and thus ( , ) V x y , would also be variables [Eqs. ( 7) and [START_REF] Gustavsson | 3D single-molecule super-resolution microscopy with a tilted light sheet[END_REF]]. When at some point of the LCoS ( , )

V x y decreases, the amplitude ( , ) a x y of the CA-PhM also decreases (Fig. 1). If ( , ) 0

V x y = , there is no diffraction at that point and therefore the amplitude of the CA-PhM would be zero there. If in other point we shift the local fringes (phase modulation), the phase ( , )

x y φ of the PhM will change according to Eqs. ( 8) and ( 5). The idea behind the coding procedure can be presented as follows. We start with an ordinary phase grating, i.e., with a sinusoidal phase grating of constant phase depth and constant period. Let us vary the phase depth of every single pixel with respect to the original grating. The actual amplitude of the wave diffracted by every single pixel, ( , ) a x y , would depend on its new phase depth, 2 ( , )

x y β

[Eq. ( 7)] keeping the same orientation of the grooves. The new pixel's phase, relative to the phase of the wave diffracted ( , )

x y φ [Eq. ( 8)] by the original grating (order +1) [Ec. [START_REF] Hell | Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy[END_REF]], depend on the shift that we gave to the modified grating.

Thus, the amplitude ( , ) a x y of the PhM is encoded as the visibility V(x,y) of the fringes of the pattern I(x,y) [START_REF] García-Márquez | Instrumentations optiques inférieures à la limite de diffraction[END_REF]. Next, this pattern is relayed to the LCoS to obtain a digitized, modulated phase grating with a CA reflectance

[ ] [ ] { } 0 0 max 0 ( , ) exp ( , ) exp ( , ) cos 2 ( , ) ( , ) c r x y r i x y r i V x y u x x y x y α β π φ φ = = ⋅ + + , ( 13
)
where 0 r is a constant. For simplicity, we shall refer to ( , ) I x y , the grayscale image of the phase ( , )

x y α , as the hologram [Eq. ( 9)].

NUMERICAL VALIDATION

Complex amplitude phase mask

A numerical simulation was carried out to validate the complex-amplitude encoding method described above. A super-resolving, axially symmetric, CA-PhM, proposed by V. F. Canales and M. P. Cagigal [START_REF] Canales | Pupil filter design by using a Bessel functions basis at the image plane[END_REF], was encoded in a phase grating. The mask consisted of 5 annuli, delimited by the normalized radial coordinates n ρ = ( 0.098, 0.222, 0.238, 0.472, 1 ), n = 1, 2, … ,5. The amplitude transmittances of these annuli were n a = ( 0.598, 0.712, 0.824, 0.955, 1 ); beyond the last annulus, the LCoS was diaphragmed, and thus we had ( ) 0 a ρ = for 1 ρ > . The phases were alternatively π and 0: n φ = ( π, 0, π, 0, π ) (see Fig. 2). The corresponding values of ( )

V ρ were obtained from Eqs. ( 7) and ( 10), with m a x 1 .8 4 1 2 .

β =

These were n V = ( 0.4056, 0.5017, 0.6137, 0.8061, 1 ). We used 33 fringes within a circle of 14 mm diameter, so that the value of the spatial frequency of the hologram was 0 2 . To check that the previous CA-PhM acts indeed as a super-resolving pupil, we computed the corresponding point spread function (PSF):

{ } 2 2 ( , ) ( , ) h u v t x y = F , ( 14
)
where ( , ) t x y is given by Eq. ( 5), and F stands for Fourier transformation. The spatial frequencies ( , ) u v are related to the coordinates ( )

Influence of flicker in the PSF when using two SLMs

In this paper, we have shown that a complex filter can be implemented using only one phase spatial filter by encoding the amplitude into the visibility of a hologram. This complex filter can also be implemented using two different SLM, one acting as the phase component and the second one as an amplitude component. By superposing both components, the complex filter is achieved. However, these devices are well known to have an intrinsic flicker in the phase and or amplitude due to the move of the liquid crystal molecules.

It has been shown that the flicker can be modelled in a simplified version with a triangular function

Γ " = # $ % & ' % ( 2 )* + ,/) " 0 / " 0 , ) $ % ( 3' % & 2 )* + ,/) " , ) / " 0 2 , ( 16
)
where $ % is the retardance of the flicker fluctuation independent to each SLM panel. ' % corresponds to the fluctuation level. Polarimetric or physical methods can reduce the intrinsic flicker's level as already shown [START_REF] García-Márquez | Flicker minimization in an LCoS spatial light modulator[END_REF][START_REF] Yang | Phase flicker in liquid crystal on silicon devices[END_REF]. We point out that in such a case, the flicker level is controlled, its retardance is exceptionally complicated to control. Let us model two different LCoS; each one has an amount of flicker and own transmittance.

" 3 , , " = ' 3 , ( Γ 3 " " ) , , " = exp4 5$ , ( Γ ) " 67

, ( 17
)
The transmittance of the panels is configured so that one SLM behaves as only-phase and the second one as an amplitude modulator. Moreover, it has to be noticed that the flicker function of each transmittance is different, and there is no way to synchronize the respective SLM's panel retardance $ % 3 and $ % 8 . For simplicity, we are assuming that both SLMs have the same level of fluctuation ' % . Thus, after superposing both transmittances, the resulting field can be expressed as % , , " = ' 3 , ( Γ 3 " exp4 5$ , ( Γ ) " 67.

A simulation using Eq. 18 has been done using the same values of the complex filter as in section 3.1, ' % was set as a constant; nevertheless, it depends on the grey-level used by the spatial light modulator. Here, an amplitude of 0.001 volt/grey-level was chosen. The difference between the retardance of flicker in both SLMs was varied to look for effects in super-resolution.

Here we express this difference as

Δ$ % = |$ %) & $ %3 |.
A temporal average in over one period was obtained in equation 18, and the resulting PSF computed.

; % , < = 〈| % , , " | ) 〉 , (19)
Where 〈 . 〉 corresponds to the average through the whole period of the flicker function. In Fig. 5, the effect over the PSF when two different SLM are not synchronized is shown. The PSF shows a degradation in amplitude and resolution, as the Strehl ratio of the function is reduced. In Figure 5b, it can be seen that, when the respective SLM flicker is not in phase super-resolution is not achieved, or in the best case, flicker could provoke a certain error.

EXPERIMENTAL SETUP AND RESULTS

Fig. 6 shows the experimental setup that was used to record super-resolving PSFs. The beam of a He-Ne laser (L), 633 nm λ =

, was expanded by a 25× microscope objective (MO), a spatial filter (SF) and a 250 mm focal length collimating lens (L0). The SLM was a twisted nematic LCoS from Holoeye, model LC-R 2500. To bound the pupil area, a 14 mm diameter diaphragm (D) was placed in front of the LCoS. This diameter was equal to the height of the LCoS rectangular aperture of 2 [START_REF] Calderón-Hermosillo | Flicker in a twisted nematic spatial light modulator[END_REF]

mm ×

, and corresponded thus to the largest circle that could be inscribed on it. To observe a super-resolving PSF, we had to focus on a charge-coupled device (CCD) the beam diffracted by the LCoS and reflected by the beam splitter (BS), using a 1,000 mm focal length lens (L1). When doing this, it was essential that the focused beam was free from off-axis aberrations, basically coma and astigmatism, as well as spherical aberration. If the aberrations of the LCoS are compensated, the first could be averted if the ray through the center of the diaphragm D, after being diffracted by the LCoS into the +1 diffraction order, and reflected by the BS, coincides with the optical axis of the lens L1. Spherical aberration would be negligible if the focal ratio of the focusing beam were very large; it was for this reason that we chose L1 with a large focal length. In the present case, this focal ratio was ∼F/70. Additionally, this arrangement magnifies sufficiently the PSFs to be resolved by the CCD, which was from a Lumenera M-LU175 camera and had a pixel size of The radius of the first zero of the Airy pattern in the focal plane of L1 is ( )

1 1.22 1.22 # . r f F D λ λ = = (20)
In the present case, λ = 0.633 ×10 -3 mm, D = 14 mm and f = 1000 mm. Therefore, the diameter of the central lobe of the pattern was 2r1 ∼ 110 μm. Summarizing, to observe a super-resolving PSF, it is crucial to form a relatively large, virtually aberration-free PSF. Otherwise, its potential super-resolving features would be lost.

A. Spatial Light Modulator calibration

Since the LCoS panel is thin, it is inevitable that it will have slight deformations that will spoil a potential super-resolving PSF, even if these deformations are small. At the top of Fig. 7 is shown an interferogram of our LCoS panel, obtained with a WYKO 6000 digital Fizeau interferometer. The deformation of the panel is evident. Using the raw data files from the interferometer, we can map this deformation in m, µ change their sign, and inject them back into the LCoS, following the procedure described in [START_REF] García-Márquez | Recursive wavefront aberration correction method for LCoS spatial light modulators[END_REF]. This is a recursive procedure, in which we consecutively test the wavefront emerging from the +1 diffraction order of a phase grating displayed in the LCoS, something that is physically attained by the proper (small) tilt of the LCoS. We will end up with a phase-modulated phase grating [Eq. ( 13)], like those shown in Fig. 8. In the second row of Fig. 7 we can see the initial phase map obtained from the LCoS, and the subsequent maps with phase corrections obtained from the +1 diffraction order of the phase grating displayed by this. The third row shows the PSFs corresponding to these maps. Since an LCoS panel is rectangular, the appearance of the PSFs approaches that of ( )

2 sinc ,
x y l u l v , where u and v are spatial frequencies [Eq. ( 15)], and x l and y l are the length and the height of the LCoS panel [START_REF] Goodman | Introduction to Fourier Optics[END_REF]. The fourth row of Fig. 7 shows the phase maps for the circular aperture in successive iterations. Limiting the LCoS aperture to a circular aperture will, of course, improve the correction achieved in each cycle, because we will remove the largest residual deformations, which are in the panel edges. Finally, in the fifth row of Fig. 7 we show the peak-to-valley (P-V) deformations and Strehl ratios for the successive rectangular (in red) and circular (in blue) phase maps, with the P-V deformations given as fractions of the wavelength, 633 nm λ =

. Notice that these values are well below 14 λ , Marechal's condition for a well corrected optical system [START_REF] Born | Principles of Optics[END_REF].

B. Observed super-resolving PSFs

Fig. 9a andb show two experimental PSFs recorded with a CCD; the first one has been obtained with a clear pupil and the second one with the super-resolving pupil. The clear pupil is aberration-corrected by the LCoS . Its output beam travels the same optical path and has the same numerical aperture as the complex PhM so that it can be appropriately compared.

Their central horizontal section of these PSFs are shown in Fig. 10a and b, the first with a gray line, and the second with a black one. As expected, the lobe of the second PSF is narrower than the first, and the first PSF is brighter than the second.

CONCLUSIONS

We described a method to design super-resolving PhMs that requires only one, phase-only, SLM. This method allows the generation of CA-PhMs by means of a phase grating displayed in an LCoS SLM. We showed that the aberrations introduced by this device can be successfully compensated in this grating, with residual aberrations bellow λ/14, the condition that must satisfy a well corrected optical system according to Maréchal [START_REF] Born | Principles of Optics[END_REF]. However, this can only be achieved after an interferometric calibration of the panel flatness of the LCoS, which we did with a digital Fizeau interferometer.

There are improvements, of course, that can be made to this technique of producing superresolving masks. Their phase encoding is simple, not so much the amplitude encoding. In the case presented here, βmax≤1.8412. When a(x,y)∼1, the mapping of the PhM amplitude to the visibility (contrast) of the fringes in the grayscale image I(x,y) that is relayed to the LCoS is highly non-linear [Fig. 1]. This drawback can be surmounted if we reduce the maximum phase depth of the grating, 2βmax, in the LCoS [Eq. ( 13)], although this would reduce as well the amount of light intended for the super-resolving image.

The phase flicker of LCoS SLM devices that appeared as a biting phenomenon when superposing two different pupils has been overcome by generating a complex-amplitude phase mask in a single phase-only SLM.

  of phase steps at our disposal would be reduced from (1.18π/2π)×255 ∼ 150 (∼59%) to (0.70π/2π)×255 ∼ 89 (∼35%). In Fig.1are shown the graphs of ( , )V x y vs ( , ) a x y for m ax 0 ) obtained from Eqs. (

  Fig. 3 shows this hologram. Notice that phase variations are encoded as fringe dislocations, and amplitude changes as fringes of increasing contrast from the first to the last annulus.

Fig. 2 .

 2 Fig.2. Maps of Canales and Cagigal's complex-amplitude pupil mask: a) amplitude, b) phase[START_REF] Canales | Pupil filter design by using a Bessel functions basis at the image plane[END_REF].

Fig. 3 .

 3 Fig.3. Hologram of Canales and Cagigal's complex-amplitude pupil mask. Phase variations appear as fringe dislocations and amplitude changes as fringes of distinctive contrasts (visibilities)[START_REF] Canales | Pupil filter design by using a Bessel functions basis at the image plane[END_REF].

Fig. 4 shows with a solid line the section 2 ( 1 r

 21 Fig.4shows with a solid line the section

Fig. 4 .

 4 Fig. 4. Computed PSF for the CA-PhM encoded in the +1 diffractive order of the phase grating recorded with the hologram of Fig. 3 (solid line). The normalized PSF of a diffraction-limited system, the so-called Airy pattern, is shown for comparison with a dashed line. The values of the abscissas are of 1 f x r , where 1 r is the radius of the

Fig. 5 .

 5 Fig. 5. Effect of the flicker when two unsynchronized LCoS are used in super-resolution complex filters. a) deterioration of the PSF, b) Deterioration of the resolution gain (normalized with the Airy pattern).

Fig. 6 .

 6 Fig. 6. Schematic diagram of the experimental setup. L is a He-Ne laser λ = 633 nm ; MO a 25× microscope objective; L0 and L1 are lenses of 250 and 1,000 mm focal length, respectively; BS is a beam splitter; D a 14 mm diameter diaphragm; LCoS a 1016×720 pixels liquid crystal on silicon SLM; and CCD a charge-coupled device with pixels of 5.2×5.2 μm 2 .

Fig. 7 .

 7 Fig. 7. The LCoS panel aberrations were corrected in three measurement iterations, as shown in the second row. Their PSFs appear below, in the third row. A circular pupil contained in the LCoS rectangular aperture is shown in the fourth row. The correction within the rectangular aperture of the LCoS reached λ/15, and within the circular aperture λ/33, as shown in row 5. Notice that in both apertures the final Strehl ratio is virtually 1.

Fig. 8

 8 Fig.8shows our hologram (Fig.3) after compensation of the panel aberrations. As we mentioned above, this was achieved by adding the correction phase ( , ) c x y φ

Fig. 8 .

 8 Fig. 8. The hologram of Fig. 3 after including the phase correction term c φ to compensate the aberrations

Fig. 9 .

 9 Fig. 9. Experimental point spread functions and computed modulation transfer function. a) Airy distribution, b) super-resolving PSF obtained with the +1-diffraction order, c) MTF of the Airy distribution, d) MTF with the hybrid phase maskThe Fourier transform of the Figures9a and bcan be seen in Figures9c-d. The Fourier transformation of the PSF corresponds to the modulation transfer function (MTF). MTF lets us determine the cutoff frequency of the system @ A . The radial average of the MTF is displayed in

Fig. 10 .

 10 Fig. 10. Horizontal central sections in Fig. 9 a) Experimental PSF, b) Radial average of the MTF.

AKNOWLEDGEMENTS

J. E. A. Landgrave is indebted to Abundio Dávila, from Centro de Investigaciones en Óptica, for discussions on the technicalities of the LCoS SLM.