Eduard Muslimov
email: eduard.muslinov@lam.fr

David Valls-Gabaud

Gérard Lemaître

Emmanuel Hugot

Wilfred Jahn

Simona Lombardo

Xin Wang

Pascal Vola

Marc Ferrari

A fast, wide-field and distortion-free telescope with curved detectors for surveys at ultra-low surface brightness

We present the design of an all-reflective, bi-folded Schmidt telescope aimed at surveys of extended astronomical objects with extremely-low surface brightness. The design leads to a high image quality without any diffracting spider, a large aperture and field of view, and a small central obstruction which barely alters the PSF. As an example, we design a high-quality, 36 cm diameter, fast ( f /2.5) telescope working in the visible with a large field of view (1. • 6 × 2. • 6). The telescope can operate with a curved detector (or with a flat detector with a field flattener) and a set of filters. The entrance mirror is anamorphic and replaces the classical Schmidt entrance corrector plate. We show that this anamorphic primary mirror can be manufactured through stress polishing, avoiding high spatial frequency errors, and tested with a simple interferometer scheme. This prototype is intended to serve as a fast-track scientific and technological pathfinder for the future space-based MESSIER mission.

INTRODUCTION A. Scientific rationale

The current ΛCDM paradigm of structure formation has been well tested on linear scales (e.g., the fluctuations of the Cosmic Microwave Background), and leads to a very successful theory of galaxy formation and evolution, although serious problems arise on mildly non-linear scales (e.g., the putative cosmic web of filaments) and highly non-linear scales (e.g., number of satellite galaxies, see [START_REF] Bullock | Small-Scale Challenges to the LambdaCDM Paradigm[END_REF]). In spite of their widely different scales and densities, they share the common property of having extremely low surface brightness (LSB), well below the ground-based sky background. While some instruments are able to uncover new galaxies and LSB features (e.g., [START_REF] Martínez-Delgado | Stellar Tidal Streams in Spiral Galaxies of the Local Volume: A Pilot Survey with Modest Aperture Telescopes[END_REF][START_REF] Van Dokkum | Forty-seven Milky Way-sized, Extremely Diffuse Galaxies in the Coma Cluster[END_REF][START_REF] Knapen | Ultra-deep Imaging: Structure of Disks and Haloes[END_REF][START_REF] Mihos | The Burrell Schmidt deep Virgo survey: tidal debris, galaxy halos, and diffuse intracluster light in the Virgo cluster[END_REF][START_REF] Abraham | Ultra-Low Surface Brightness Imaging with the Dragonfly Telephoto Array[END_REF]), a systematic study of the ultra-low surface brightness universe requires large surveys from space. The reasons are obvious: (1) a specially-designed instrumentation will maximise the signal-to-noise ratio (SNR) of their detection, (2) exploiting the much lower sky brightness in space, (3) compact PSFs (the scattering produced by atmospheric molecules yields very extended PSF wings), (4) systematics and accurate flat-fielding can be measured accurately. All these factors are required for a proper photometry of LSB objects. This is the basic concept behind MESSIER, a space mission optimised to measure the ultra-low surface brightness universe [START_REF] Valls-Gabaud | The MESSIER surveyor: Unveiling the ultra-low surface brightness universe[END_REF]. The mission has a number of tight constraints for its design in order to achieve its aims of measuring surface brightness levels as low as 35 mag arcsec -2 in the optical (350-1000 nm) and 38 mag arcsec -2 in the UV (200 nm). First, the accuracy of the flat fielding should reach the 0.0025% level, which is only achievable through time-delay integration or drift scanning (see, e.g. [START_REF] Zaritsky | The Great-Circle Camera: A New Drift-Scanning Instrument[END_REF]). Second, the optical system cannot include lenses, as they will produce a massive Cherenkov emission by the abundant relativistic particles. Third, the PSF must be as compact as possible and no high spatial frequency errors are acceptable on the optical surfaces. This implies that support structures such as spiders cannot be placed in the optical train, while the drift-scan mode requires the optical design to be distortion-free at least in one direction.

The goals of the MESSIER mission are achievable with a highquality, 50 cm diameter, fast ( f /2) UV-visible telescope with a huge field of view (> 2 • × 4 • ). In this paper, we consider a reduced version of the telescope, intended to serve as a pathfinder for the main mission. The manufacturing of the pathfinder represents a fast-track project, aimed at testing and improving a few key technologies required for the full-scale project implementation, hence some mitigation of the main requirements is allowed. Taking into account the currently available technologies and components, the telescope target specifications are defined as follows (see Table 1). The resolution requirement is defined by the useable pixel size and approximately corresponds to 2. 5 per pixel. Using the rms spot radius is a simplified but convenient way to estimate the optical quality during design and optimisation, while controlling the spot size makes the PSF core to match the size of the pixel. To achieve the most compact shape of the PSF we should minimize the obscuration and exclude spiders at the design stage. In this context, many different options for the optical design of such survey telescopes have been considered (see e.g. [START_REF] Buffington | Very-wide-angle optical systems suitable for spaceborne photometric measurements[END_REF][START_REF] Yu | New designs of survey telescope[END_REF][START_REF] Yu | On the capabilities of survey telescopes of moderate size[END_REF]). In particular, off-axis optical designs such as the Three Mirror Anastigmat (TMA) with aspherical [START_REF] Singaravelu | Obstructed Telescopes Versus Unobstructed Telescopes for Wide Field Survey-A Quantitative Analysis[END_REF][START_REF] Chang | Off-axis reflecting telescope with axially-symmetric optical property and its applications[END_REF][START_REF] Chang | Elimination of linear astigmatism in off-axis three-mirror telescope and its applications[END_REF], or freeform mirrors surfaces [START_REF] Challita | Design and development of a freeform active mirror for an astronomy application[END_REF][START_REF] Agócs | Freeform mirror based optical systems for FAME[END_REF] yield a very high performance over an extended field of view (FoV). These designs were analysed in detail and compared with other schemes such as the Schmidt and SEAL telescopes [START_REF] Hugot | A freeform-based, fast, wide-field, and distortionfree camera for ultra-low surface brightness surveys[END_REF][START_REF] Lemaître | Reflective Schmidt Designs for Extended Object Detection in Space Astronomy -Active Optics Methods[END_REF], and led to the conclusion that the modified reflective Schmidt design fulfils all the requirements in terms of optical performance and, in addition, is made up of easily manufacturable optical components. Further, the simple optical scheme eases the telescope assembling and alignment.

In this paper we therefore study the properties, limitations and manufacturability of this reflective Schmidt optical design. We first present the basic bi-folded Schmidt design, and consider and quantify the advantages and shortcomings inherent to this type of telescopes. We then describe a design to reach to the specifications given above for a MESSIER pathfinder telescope, and study the anamorphic aspherical mirror used in this scheme, providing details on its manufacturability by active optics methods and its optical quality testing.

BI-FOLDED SCHMIDT DESIGN

A. The design concept

The basic principle of the wide field telescope invented by B. Schmidt is a single concave spherical mirror, used with an entrance pupil stop at its centre of curvature [START_REF] Schmidt | Ein lichtstarkes komafreies speigelsysten[END_REF] (though a similar principle was considered by a few authors before him). This combination is corrected of each aberration, over the FoV, except for spherical aberration. To compensate, an entrance refractive corrector plate is placed at the entrance pupil that provides corrected images over all the field of view (Fig. 1a). By balancing the slopes of the aspherical plate, i.e., the 1st-order derivative of the aspherical plate, the chromatic variation of spherical aberration (sphero-chromatism) remains the dominating aberration residual. Another basic feature of the Schmidt design is the advantage of a curved focal surface on which the celestial sphere is naturally projected, resulting in a projection that is entirely free from distortion aberration, and making it ideally-suited for wide-field telescopes aimed at sky surveys. Similarly, the proposed all-reflective design shown in Fig. 1b uses an off-axis reflective aspheric corrector, so that sphero-chromatic blur aberrations disappear. In his analyses of reflective Schmidt designs for telescopes and spectrographs, Lemaître (1979,[20]) showed that in all-reflective designs the best angular resolution over the field of view is achieved by balancing the meridian curvatures, i.e. the 2nd-order derivatives, of the aspherical mirror or diffraction grating [START_REF] Lemaître | Sur la résolution des télescopes de Schmidt catoptrique[END_REF][START_REF] Lemaître | Astronomical Optics and Elasticity Theory -Active Optics Methods[END_REF]. If, as we do in this paper, one assumes an incident beam with a circular cross section at the entrance pupil aspheric mirror (primary mirror M1) of clear aperture 2R m , the curvature balance rule states that any parallel ray within a cylindrical tube of aperture 2R 0 will reach an elliptical null-power zone in M1 such that the relationship between the R 0 and R m radii is given by the simple ratio

R 0 R m = 3 2 ≈ 1.224 . (1)
This leads to an elliptical null-power zone outside the clear aperture. Incidentally, this result is very different from the case of a refractor plate where the null-power zone is such that R 0 /R m = √ 3/2 ≈ 0.866, i.e., inside the clear aperture of the beam. Hence the optical surface of the M1 mirror is generated by homothetic ellipses having principal axis lengths in the ratio cos i. The principal axis lengths of the elliptical clear aperture entrance pupil M1 are 2R 0 and 2R 0 / cos i. Such reflective Schmidt design geometries have been adopted for broad-band faint object spectrographs with aspherised gratings [START_REF] Lemaître | Astronomical Optics and Elasticity Theory -Active Optics Methods[END_REF] and also for the giant Chinese segmented telescope LAMOST [START_REF] Wang | Special configuration of a very large Schmidt telescope for extensive astronomical spectroscopic observation[END_REF][START_REF] Cui | The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST)[END_REF]. However, in these cases, the focal surface in the middle of the beam creates a central obscuration and additional diffraction spikes are caused by the holding spider.c Therefore, in our proposed design, both the spiders and the corresponding diffractive deformation of the PSF are eliminated by adding a folding flat mirror. This also allows a much better access to the focal surface, which is placed outside the optical train (see Fig. 1b).

In the case of a purely reflective Schmidt, except for particular cases such as aspherised grating cameras working in reflected normal-diffraction [START_REF] Lemaître | Astronomical Optics and Elasticity Theory -Active Optics Methods[END_REF], a rotational symmetric corrector does not reach the optimal resolution. Indeed, a 5th-order astigmatism aberration (Astm 5 ) residual remains all over the field of view and thus is not corrected at the centre. A much higher angular resolution can be achieved through a non-axisymmetric corrector where the M1 surface has homothetic elliptic level lines. When the extreme curvatures along meridian sections of the aspheric are balanced (Eq. 1) -algebraically opposite at centre and edge-the resolving power d NC is given by [START_REF] Lemaître | Sur la résolution des télescopes de Schmidt catoptrique[END_REF][START_REF] Lemaître | Astronomical Optics and Elasticity Theory -Active Optics Methods[END_REF]

d NC = 3 256 Ω 3 ϕ 2 m + 3 2 i ϕ m , ( 2
)
where Ω is the focal ratio, i the folding angle and ϕ m the maximal semi-field angle (Fig. 1b). Hence the resolution degrades not only with increasing the aperture and/or the field of view, but also with the folding angle. Note that all the angles and distances in the optical scheme should provide gaps between components accounting for their real thickness, mechanical holders and other parts. For a convenient angular resolution, Eq. 2 implies exploring designs with f -ratios Ω = 2 -2.5, field angles in perpendicular direction to the telescope symmetry plane 2ϕ m = 2.

• 5 -5 • , and folding angles i = 10 • -13 • . In the next section we consider a number of possible designs and investigate the factors limiting their performance.

B. Exploration of parameter space

To quantify the above-mentioned limiting factors a few similar bi-folded Schmidt schemes were designed, all of them with square fields of view. Each time the general configuration was changed, the angle of rotation of the 1st and 2nd mirrors were modified as well to avoid ray obscuration by the back side of any of the mirrors. When necessary, the distances between the mirrors were also adjusted. Each system was numerically optimised to provide high optical quality on a curved surface. In total, some 15 different configurations varying the FoV and f -ratio were considered. We found that the optical quality at the field centre is relatively stable and never overcomes the limit of 12µm set by the requirements (Table 1), while the spot radius at the edge of the field of view breaks this limit at some point. The distortion never exceeds the limit if it is measured along one axis of the square field of view. Other design parameters such as the asphericity of the primary mirror and the size of the telescope detector curvature do not change significantly and never reach critical values. The resulting numerical data were fitted with simple polynomial approximations to derive the dependencies of the resolution and central obscuration on the field of view and f -ratio values (see Fig. 2a andb, respectively). The hatched areas correspond to spot RMS radii smaller than 12µm (Fig. 2a) and central obscurations smaller than 15% (Fig. 2b). This critical value is rather arbitrary as there is no obscuration requirement which follows directly from the scientific and engineering goals.

Figure 2 shows that the central obscuration grows rapidly when the FoV and aperture are increased, while the resolution remains acceptable over a large area in parameters space. The central obscuration is therefore the main limiting factor for this type of optical designs, and it can be loosened to some extent using decentered and/or elliptical openings in the secondary mirror, but it cannot be completely eliminated. Another undesired effect observed when the FoV and f -ratio are increased is the decrease of the distance from the back side of the secondary mirror to the detector. This effect is not taken into account yet, as some critical values and limits -not yet defined-strongly depend upon the type of detector and on the conditions of its use. The behaviour of these quantities in parameter space were used when designing the MESSIER pathfinder optical scheme, and they can also be very useful for any future developments exploiting the same concept.

TELESCOPE DESIGN A. Optical scheme

In contrast with the full-scale space-based MESSIER telescope, the ground-based pathfinder must be delivered in a relatively short time. Under these conditions, two versions of the optical scheme can be considered:

Configuration I: The focal surface is covered with a curved detector, and no auxiliary optics is used. This version corresponds to the instrument for the future MESSIER mission, but has higher technological risks.

Configuration II:

The telescope uses a conventional ordinary flat detector and a refractive field flattener. This version has the highest tecnological readiness level, but cannot used for space applications. In this case a filter wheel must be added to enhance the contrast and reduce the field-flattener chromatism.

Figure 3 shows the general view of the telescope scheme in Configuration I. The folding angle in this case is i = 11 • , the rest of the main design parameters correspond to those in Table 1.

The geometry of Configuration II is almost the same but a symmetrical bi-convex field-flattener lens (R=635.75 mm, d=4 mm in fused silica) and a filter wheel are introduced directly in front of the detector. We adopt the SDSS filter set [START_REF] Fukugita | The Sloan Digital Sky Survey Photometric System[END_REF] in the u, g, r, i and z passbands. A central opening in the secondary mirror is implemented in the form of a decentred trapezoid to decrease the obscuration losses. This configuration change requires a shift of both the spherical mirror and the detector unit. The change from Configuration I to Configuration II implies that the secondary-to-tertiary distance should be decreased by 31.78 mm, while the distance from the tertiary to the detector increases by 2.96 mm. These modifications are relatively small and can easily be implemented in the same optomechanical design.

B. Image quality

The image quality of the telescope is measured through spot size diagrams. The diagrams for Configuration I (Fig. 4a) show that the image quality is close to the diffraction limit. In Figure 4b, the energy concentration plots demonstrate that the contribution of the residual aberrations observed on the spot diagrams is negligible. The spots radii for both configurations are given in Table 2. Note the high uniformity of the image quality across the FoV. The image quality in Configuration II remains almost unchanged and matches the requirements.

Finally, one of the key requirements for the instrument is the absence of distortion. We illustrate the implementation of this requirement in Fig. 5. The correction of distortion over an extended FoV is inherent to Schmidt-type designs, so the distortion along both axes is insignificant and well below the requirements. We note here that the current design is relatively sensitive to the components misalignments and manufacturing errors. It is an unavoidable property of off-axial optical systems using aspheres. However, preliminary tolerances estimations performed by standard Monte-Carlo techniques show that all the values are technologically realistic. For instance, the typical limit for mirrors longitudinal shift of the mirrors is 0.1 mm, and for the detector it ranges from 0.02 to 0.1 mm depending upon the assumptions made on the focusing mechanism. The typical limits to the decentering of the components are 0.05-0.1 mm. The corresponding values for the tilts are 0. • 003-0. • 1 with the highest sensitivity for the spherical mirror. The tolerances on surface shapes depend strongly on the initial assumptions and calculation techniques. Approximate limits are 500, 100 and 50 µm for the primary, secondary and tertiary mirrors, respectively. It is premature at this stage to provide here a more detailed tolerance analysis, which will be carried out in a forthcoming study.

In addition to the usual ordinary image quality estimates, the shape of the PSF is an essential factor, and particularly its wings, for the proper photometry of ultra-low surface brightness objects. We sampled two points in the FoV: the center at (0 • , 0 • ) and one corner at (1. • 3, 0 • 8). The Huygens formalism is used to compute the PSF, so the results are normalized to the diffraction limit. Fig. 6 shows the results, converted to logarithmic scales in both cases (with and without central obscuration taken into account in the computations). One can see from the diagrams that the perturbations on the PSF wings are very small. We also note that the central obscuration and deviation from the axial symmetry affect the PSFs, but their influence is insignificant outside of the core.

Figure 7 shows that, after averaging over circular annuli, the PSF for our design of the bi-folded reflective Schmidt telescope approaches the diffraction limit (the diffraction limit curve is re-sampled to facilitate comparison), and at this scale the effects of aberrations and central obscuration are almost negligible. Compared with the optical scheme of, for example, the Antarctic Survey Telescope -an axial Schmidt-type design with refractive correctors [START_REF] Yuan | Optical system of the Three Antarctic Survey Telescopes[END_REF]-, the PSF of our design is about one order of magnitude better at 22 arcsec, and at larger angular distances the difference is even more important. In addition, it has also a larger Strehl ratio. Therefore our design leads to a notable improvement for observations of extremely faint extended objects in comparison with the existing telescopes of the same class.

C. Notes on the primary mirror feasibility

The most complex component in the telescope design is the primary mirror. As mentioned above, when the mirror inclination angle exceeds a certain value it becomes impossible to use an axisymmetric shape of the surface. Its surface should be anamorphic. There are different ways to describe such a surface, and in practice it is more efficient to use Zernike polynomials when optimising the optical design. However, at the manufacturing and optical testing phases, it is more convenient to use an anamorphic asphere equation (a standard option in the ZEMAX optical design software)

Z = C x x 2 + C y y 2 1 + 1 -(1 + K x )C 2 x x 2 -(1 + K y )C 2 y y 2 (3)
+ AR (1 -AP)x 2 + (1 -AP)y 2 2
where (y, z) is the symmetry plane of the telescope. Assuming K x = K y = -1, the denominator can be excluded, and in this case the primary mirror shape for the design under consideration is described by just four coefficients: C x = -3.622 10 -6 , C y = -3.490 10 -6 , AR = 2.203 10 -11 , AP = -0.01854.

It is a flat asphere with a RMS deviation of only 11.9 µm and a maximum deviation of 19.7 µm in comparison with the best-fit sphere (BFS) of radius 2.56 10 7 mm. Figure 8a and8b show the surface sag and its deviation from the BFS, respectively.

The mirror is of the freeform class [START_REF] Forbes | Characterizing the shape of freeform optics[END_REF][START_REF] Hugot | FAME: Freeform Active Mirrors Experiment[END_REF], as its surface has no axial symmetry and cannot be simply described by conicoids extensions or off-axis conicoids. This surface can easily be manufactured through active optics methods [START_REF] Lemaître | Astronomical Optics and Elasticity Theory -Active Optics Methods[END_REF][START_REF] Lemaître | Aphérisation par relaxation élastique de miroirs dont le contour circulaire ou elliptique est encastré ou semi-encastré[END_REF]. We assume that the mirror is the surface of twin vase-form elliptic blanks, made of Zerodur [START_REF] Pepi | Strength Properties of Glass and Ceramics[END_REF], Young modulus 90.2 GPa and Poisson ratio 0.243. These vase forms are glued by a DP490 epoxy resin of 100 µm, Young modulus 659 MPa and Poisson ratio 0.380. In this particular geometry, called closed vase or closed biplate form, the radial thickness of assembled outer rings (t r =18 mm with homothetic ratio variation) provides a semi-built-in effect in order to achieve the required aspheric profile over the whole optical clear aperture of the inner constant thickness plate. The outer rings have an axial thickness of 38 mm and their inner surfaces are built-in to the plate at the elliptical contour 356×362.7 mm which defines the clear aperture. A round inner corner R=5 mm avoids stress concentration at the link. Next we analyse how to generate the freeform surface with both basic analytic calculations and by finite-element analysis (FEA). The FEA model takes into account the bi-symmetry of the mirror: only a quarter of the mirror is meshed. A fixed node on the central axis and radially sliding plane degrees of freedom define the kinetic boundary conditions. When a constant pressure is applied to the close vase form, the inner plate surface is bent accordingly, following a bi-quadratic law, i.e. co-adding the curvature and 4th degree modes. The correct shape is achieved after an elastic relaxation phase which takes place once the load is removed after polishing.

Additional optimisations using the elasticity code and the optical design code showed that the entire surface of the inner plate can be used as the clear aperture entrance pupil of the telescope. In doing so, the ratio between the null power zone R 0 radius and the clear aperture R m radius (i.e. R 0 /R m = 1.224 in Eq.1), is slightly modified and becomes

R 0 R m = 1.118 . (4)
In spite of this decrease, the angular resolution remains close to the original value, as the resolution increases very slowly for smaller values of this ratio [START_REF] Lemaître | Sur la résolution des télescopes de Schmidt catoptrique[END_REF]. The entire surface of inner plate can then be used as clear aperture. The FEA analysis further shows that a constant pressure q=0.687×105 Pa must be applied in the close vase form, with inner plates of 18 mm constant thickness during the stress figuring and polishing. The general view of the FEA model (Fig. 9a) illustrates the close vase form required to achieve the theoretical shape (defined by Eq. 4) where the maximum flexural sag from the center to the elliptical clear aperture is 34.8 µm with the above parameters. The surface to be polished reaches the outer contour at 376×383.3 mm, including a part of the outer elliptical ring ending with a round corner of radius R=8mm. Fig. 9b shows the difference, over the entire surface, between the flexural sag predicted by the FEA and the one predicted by the simple theoretical analysis. By removing the ring zone that does not belong to clear aperture, residual errors become negligible. Further details on elasticity analysis for these configurations can be found in [START_REF] Lemaître | Aphérisation par relaxation élastique de miroirs dont le contour circulaire ou elliptique est encastré ou semi-encastré[END_REF][START_REF] Hugot | Active optics: single actuator principle and angular thickness distribution for astigmatism compensation by elasticity[END_REF][START_REF] Lemaître | Multi Object Spectrograph of the Fireball-II Balloon Experiment [with plane-aspherized grating[END_REF].

The RMS value of the sag residual shown on Fig. 9a is 0.13 µm, while its PTV value is 0.4 µm. These values are computed for the entire surface, including the outer annulus. For the clear aperture the deviation is even smaller.

D. Notes on the optical testing of the primary mirror

We now turn to the optical testing of the freeform mirror. The precise measurement of a large freeform mirror, with a complex anamorphic shape and almost zero optical power, could be difficult. Several options for the testing scheme included the use of lens compensators [START_REF] Malacara | Optical shop testing[END_REF], computer-generated holograms [START_REF] Larionov | Holographic monitoring of off-axis aspheric mirrors[END_REF] and their combinations, but all of them imply the use of large-format customised optical components. This would not only increase the cost of the mirror, but also would require more time and expertise in performing the optical testing. We adopted the alternative of using a single optical element, an existing lab testplate, for the testing scheme. The scheme (see Fig. 10a) operates in autocollimation, when a laser beam emitted by a point source is shaped by the testplate and reflected back by the mirror. The beam path backwards is almost identical to that in the forward direction. Some residual aberrations remain, due to the surface asphericity. However, the simulated interferogram indicates that these residuals correspond to only 7 interference fringes (see Fig. 10b). Such an interference pattern can be easily measured and then compared with the calculated one to control the surface shape with a high precision. Among other features, the interferogram clearly demonstrates anamorphic shape of the surface.

CURVED DETECTOR OPTIONS

The image quality analysis shows that the best performance of this design is achieved using a curved detector. The Configuration I described above requires a curvature radius of 887.1 mm and an active area of 40×25 mm, which can be achieved within current technologies. Indeed, over the past few years, there have been several developments in curved detectors carried out by Sarnoff [START_REF] Swain | Curved ccds and their application with astronomical telescopes and stereo panoramic cameras[END_REF], Stanford [START_REF] Rim | The optical advantages of curved focal plane arrays[END_REF][START_REF] Dinyari | Curving monolithic silicon for nonplanar focal plane array applications[END_REF], University of Arizona [START_REF] Lesser | Focal Plane Technologies for LSST[END_REF] and JPL [START_REF] Nikzad | Solid-state curved focal plane arrays[END_REF]. The different techniques proposed for the bending of CCD and CMOS have yielded prototypes with a very low performance loss in terms of dark current, noise, and a filling factor above 80%. In astronomy, R&D activities have been undertaken by ESO for the development of large-format, highlycurved detectors for the VIS range [START_REF] Iwert | First results from a novel curving process for large area scientific imagers[END_REF]. The manufacturing process has been fully developed and has delivered a working component suitable for astronomical applications. Likewise, the Laboratoire d'Astrophysique de Marseille (LAM) and the LETI (CEA) recently proposed to combine active mirrors technology with flexible dies to generate deformable detectors [START_REF] Ferrari | Development of a variable curvature mirror for the delay lines of the VLT interferometer[END_REF]. This active mirror technology has achieved variable curvature detectors, variable astigmatic detectors and also multi-mode detectors. The variable curvature mirror (VCM) technology consists of a cir- cular membrane with a variable thickness distribution. A force F, applied at the centre of the structure and perpendicularly to the membrane surface, results in an accurate spherical bending of the top surface of the membrane with a radius of curvature which depends on the applied force F. The thinned CMOS sensor attached on top of the VCM surface follows this curvature variation (convex to concave) [START_REF] Chambion | Tunable curvature of large visible CMOS image sensors: Towards new optical functions and system miniaturization[END_REF]. Another promising technology uses a tunable active mirror technology to bend the support to which the thinned CMOS sensor is attached (see [START_REF] Laslandes | Mirror actively deformed and regulated for applications in space: design and performance[END_REF], developed for space missions). This technology is able to generate many different shapes. The prospects for using a curved detector for the MESSIER pathfinder telescope are therefore more than promising.

CONCLUSIONS

In this paper we propose and analyse in detail a new optical design for a fast wide-field telescope based on the bi-folded reflective Schmidt scheme. This design provides high image quality over a large field of view, with minute distortion. The use of a flat folding mirror makes the design compact and eliminates spiders with their associated diffraction spikes and ghosts. The main factor which drives the optical design is the central obscuration. Applied to the optical scheme of the MESSIER pathfinder telescope, it has a f -ratio of 2.5 and provides nearly diffractionlimited image quality over an extended FoV of 1. • 6 × 2. • 6, with compact PSF wings which are almost indistinguishable from the PSF of an unobstructed design. With minor modifications the telescope is able to operate either with a curved detector or with a standard ordinary flat detector mounted in a cryostat and equipped with a set of standard photometric filters. While the optical scheme consists of rather simple components, the most complex part is the freeform primary mirror. However, this mirror can be manufactured through existing active optics techniques and tested in a relatively simple setup using standard auxiliary optics. This scheme will be used for the manufacturing of a reduced prototype for the MESSIER telescope, and eventually for the full-scale instrument.

This space mission will bring definitive answers to several key questions which have been recognised by various international panels (ESA's Cosmic Vision [START_REF]Cosmic Vision, Space science for Europe[END_REF], Europe's ASTRONET [START_REF] Robson | ASTRONET Space science update[END_REF] and USA's Decadal Survey [START_REF]New Worlds, New Horizons in Astronomy and Astrophysics[END_REF]) to be critical for our understanding of galaxy formation through the detection and characterisation of ultra-faint dwarf galaxies (which are predicted to be extremely abundant around normal galaxies, but which remain unobserved), and tracing the cosmic web (which feeds dark matter and baryons into galactic haloes) and which may contain the reservoir of missing baryons at low redshifts.

Funding Information. ERC (European Research Council) (ERC-STG-2015-678777), LIA-ORIGINS (CNRS-CAS).

Fig. 1 .

 1 Fig. 1. The main optical schemes of Schmidt telescopes. a Refractive design: the basic telescope layout with a refractive corrector plate and a curved focal plane. b Bi-reflective Schmidt configuration with the definition of its basic parameters.

Fig. 2 .

 2 Fig. 2. Dependence of the basic parameters of a purely reflective Schmidt telescope as a function of f -ratio and field of view (in degrees): a RMS spot radius (in microns) at the edge of the FoV, b Central obscuration (in percentage).

Fig. 3 .

 3 Fig. 3. Optical scheme of the bi-folded reflective Schmidt telescope.

Fig. 4 .

 4 Fig. 4. Telescope image quality in Configuration I: a Spot diagrams (the solid circle corresponds to the Airy disk at λ=350 nm, r=1.1 µm ), the dashed circle is that at λ=1000 nm, r=3.1 µm), b Diffraction encircled energy.

Fig. 5 .

 5 Fig. 5. Telescope distortion: a along the X axis, and b along the Y axis.

Fig. 6 .

 6 Fig. 6. Telescope PSFs in Configuration I: a at the centre (0 • , 0 • ) of the FoV with obscuration, b at a corner (1. • 3, 0. • 8) of the FoV with obscuration, c FoV centre without obscuration, d FoV corner without obscuration.

Fig. 7 .

 7 Fig. 7. Circularised PSF of the MESSIER pathfinder telescope in comparison with (1) the diffraction limit, and (2) the PSF for the Antarctic Survey Telescope design [25].

Fig. 8 .

 8 Fig. 8. Surface shape of the freeform primary mirror. a Surface sag (in millimeters), b asphericity (in microns).

Fig. 9 .

 9 Fig. 9. Analysis of the freeform surface as shaped through active optics methods: a finite-element model of the deformed mirror, b residual of the surface sag.

Fig. 10 .

 10 Fig. 10. Optical testing of the freeform primary: a measurement mounting scheme, b simulated interferogram at 632 nm.

Table 1 .

 1 Main parameters for the MESSIER pathfinder telescope.

	Parameter Symbol Value	Value
			(pathfinder)	(space telescope)
	Field of	FoV	1.
	view

• 6 × 2. • 6 2 • ×

Table 2 .

 2 Image quality of the optical design with filters.

	Waveband limits	Spot rms radius	Spot rms radius
	[nm]	at FoV center [µm] at FoV edge [µm]
		Configuration I
	350 -1000	2.1	3.1
		Configuration II
	350 -410	1.8	3.7
	400 -560	2.3	3.8
	550 -700	1.7	3.4
	680 -860	1.7	3.3
	860 -980	1.7	3.3

Acknowledgments. The authors acknowledge the support of the European Research council through the H2020-ERC-STG-2015-678777 ICARUS program, and the LIA-ORIGINS programme. DVG was supported as an Overseas Fellow of Churchill College, University of Cambridge, and an as International Senior Visiting Professor (Chinese Academy of Sciences). The authors thank Prof. Christopher Mihos for useful discussions on the PSF of the Burrell Schmidt telescope.


Le Stradic Soizig

Elise Buisson
email: elise.buisson@univ-avignon.fr

Fernandes G Wilson
email: gw.fernandes@gmail.com

Vegetation Composition and Structure of Some Neotropical Mountain Grasslands in Brazil

Keywords: Biodiversity, campos rupestres, herbaceous communities, Rupestrian grasslands, Serra do Cipó

The description and understanding of plant communities is fundamental for the implementation of conservation or restoration programs, especially when these communities are highly threatened and need to be restored. Campos rupestres, some Neotropical mountain grasslands located in central Brazil and part of the Cerrado biome (covering 2 million km²) host unique plant communities, currently threatened by quarrying and mining. The grassy matrix of campos rupestres, has long been considered a rich mosaic under the control of local topography and the nature of substrate, but this affirmation has not been well studied. We analyzed whether plant communities varied in relation to edaphic factors within the stony substrate and the sandy substrate of this grassy matrix. We selected 5 sites where occur both grasslands on stony substrate and on sandy substrate, and we carried out vegetation surveys and soil analyses. We counted 222 plant species within our communities, among which 38.6% are exclusively found on campos rupestres. Our results show that both soil-types are strongly acidic, nutrient poor and exhibit a seasonal variation. Phosphorus increases and pH and organic carbon decrease during the dry season. Stony soils are slightly richer in nutrients than sandy soils and differences in soil granulometry and composition have led to the formation of distinct plant communities. Some species are confined to either one or the other grassland-type, which makes the plant composition of each community unique. Variations in edaphic factors generate heterogeneous grasslands favorable to a high plant diversity. Conservation programs and restoration actions have to maintain or recreate this heterogeneity. The presence of distinct plant communities implies that different strategies might be adopted to improve the restoration of these ecosystems.

Introduction

In 2004, the Parties of the Convention on Biological Diversity (CBD) adopted a work program on mountain biological diversity in order to improve knowledge on the functioning and composition of mountain ecosystems (CBD 2004), a fundamental tool to implement any conservation network. Indeed, the CBD recognized the fragility of mountain ecosystems and species and their vulnerability to anthropogenic and natural disturbances, particularly in the current context of land-use and climate changes. Mountain ecosystem conservation is essential for many reasons: they host a great biodiversity, they act as refuges for species, they are important for water resources since mountains play a critical role in the water cycle (FAO 1998[START_REF] Price | Mountains: globally important ecosystems[END_REF]. Excluding the Andean vegetation, there are three main highland vegetation formations in South America, the Tepuis on the Guayana shield, campos de altitude (i.e. Brazilian páramos) and campos rupestres, both in Brazil.

Campos rupestres (which means rupestrian grasslands) are species-rich tropical ecosystems occurring at altitudes ranging from 800 m to 2000 m along the Espinhaço range mountain in south-eastern Brazil and often included in the Cerrado domain (Brazilian savanna, the richest tropical savannah in the world, covering 22% of the country). Campos rupestres is described primarily as a more or less continuous herbaceous stratum with scattered rocky outcrops that harbour small sclerophyllous evergreen shrubs and sub-shrubs [START_REF] Giulietti | Espinhaço range region: eastern Brazil[END_REF]). However [START_REF] Giulietti | Espinhaço range region: eastern Brazil[END_REF] noted that rather than a homogeneous vegetation type, these campos rupestres are an assemblage of communities forming a rich mosaic under the control of local topography and the nature of substrate, with rocky outcrops, grasslands and some bogs situated along streams. Campos rupestres are constrained ecosystems, their soils are shallow, acidic and coarsely textured, with high aluminum and low nutrient content [START_REF] Benites | Solos e vegetação nos complexos rupestres de altitude da Mantiqueira e do Espinhaço [Soils and vegetation of the altitudinal rupestrian complexes of Mantiqueira and Espinhaço[END_REF][START_REF] Benites | Soils associated with rock outcrops in the Brazilian mountain ranges Mantiqueira and Espinhaço[END_REF]. Despite these harsh conditions, these grasslands are important centers of biodiversity [START_REF] Giulietti | Flora da Serra do Cipó: caracterização e lista das espécies [Serra do Cipó flora: characteristics and species list[END_REF][START_REF] Giulietti | Biodiversity and Conservation of Plants in Brazil[END_REF][START_REF] Lara | The highest diversity of galling insects: Serra do Cipó, Brazil[END_REF]FAO 1998;[START_REF] Carvalho | The mosaic of habitats in the high-altitude Brazilian rupestrian fields is a hotspot for arbuscular mycorrhizal fungi[END_REF]) and represent one of the highest levels of endemism in the Cerrado biome [START_REF] Alves | Plant species endemism in savanna vegetation on table mountains (Campo Rupestre) in Brazil[END_REF][START_REF] Giulietti | Espinhaço range region: eastern Brazil[END_REF][START_REF] Silva | Biogeographic Patterns and Conservation in the South American Cerrado : A Tropical Savanna Hotspot[END_REF][START_REF] Echternacht | Areas of endemism in the Espinhaço Range in Minas Gerais[END_REF].

Human disturbances of campos rupestres began in the 18 th century, and were mainly associated with mining activities (i.e. gold, precious stones, iron, manganese) in the region. Nowadays degradations are also associated to an increase in uncontrolled anthropogenic burnings and in fire frequency (while natural fires are a rare event, farmers burn grasslands annually to stimulate grass regrowth in order to support cattle breeding), wood extraction, eucalyptus plantation, harvesting of ornamental plants (orchids, bromeliads, Eriocaulaceae) [START_REF] Giulietti | Espinhaço range region: eastern Brazil[END_REF], and road construction [START_REF] Barbosa | Distribution of non-native invasive species and soil properties in proximity to paved roads and unpaved roads in a quartzitic mountainous grassland of southeastern Brazil (campos rupestres)[END_REF]. While threats increase, limited data on conservation targets, such as plant communities [START_REF] Heywood | Plant conservation: old problems, new perspectives[END_REF], hamper the conservation and the restoration of these campos rupestres. Indeed, to implement a conservation network, lists of habitats (described by their environmental characteristics and their plant communities) and species that are recognized as being of interest are necessary. A conservation network such as NATURA 2000 in Europe, for example, is a network of areas designed to protect the most seriously threatened habitats and species across Europe (European Commission 2000). Thereby, the recognition, precise description, and understanding of plant communities are fundamental tools to implement conservation networks and restoration projects [START_REF] Soulé | Research Priorities for Conservation Biology[END_REF][START_REF] Alves | Can campo rupestre vegetation be floristically delimited based on vascular plant genera?[END_REF].

So far, most of the studies carried out on campos rupestres dealt with the shrubby physiognomy occurring on rocky outcrops [START_REF] Meguro | Phytophysiognomy & composition of the vegetation of Serra do Ambrósio, Minas Gerais, Brazil[END_REF][START_REF] Conceição | Delimitação de habitats em campos rupestres na Chapada Diamantina, Bahia: substratos, composição floristica e aspectos estruturais [Habitat delimitation in campos rupestres of the Chapada Diamantina, Bahia: substrate, floristic composition and structure[END_REF][START_REF] Conceição | Floristics, structure and soil of insular vegetation in four quartzite-sandstone outcrops of " Chapada Diamantina ", Northeast Brazil[END_REF][START_REF] Jacobi | Plant communities on ironstone outcrops: a diverse and endangered Brazilian ecosystem[END_REF][START_REF] Scarano | Rock outcrop vegetation in Brazil: a brief overview[END_REF], but very few studies addressed the variation of plant communities in the herbaceous layer [START_REF] Conceição | Delimitação de habitats em campos rupestres na Chapada Diamantina, Bahia: substratos, composição floristica e aspectos estruturais [Habitat delimitation in campos rupestres of the Chapada Diamantina, Bahia: substrate, floristic composition and structure[END_REF][START_REF] Viana | Floristica e caracterização dos campos rupestres sobre canga na Serra da Calçada, Minas Gerais, Brasil [Floristic and characterization of canga campos rupestres in the Serra da Calçada, Minas Gerais, Brazil[END_REF][START_REF] Borges | Altitudinal distribution and species richness of herbaceous plants in campo rupestres of the Southern Espinhaço range, Minas Gerais, Brazil[END_REF], whereas it represent the matrix and thus the quintessence of these grasslands. In this grass layer, a mosaic of different pedoenvironments, which sustain abrupt changes, have already been highlighted [START_REF] Benites | Solos e vegetação nos complexos rupestres de altitude da Mantiqueira e do Espinhaço [Soils and vegetation of the altitudinal rupestrian complexes of Mantiqueira and Espinhaço[END_REF][START_REF] Alves | Can campo rupestre vegetation be floristically delimited based on vascular plant genera?[END_REF][START_REF] Carvalho | The mosaic of habitats in the high-altitude Brazilian rupestrian fields is a hotspot for arbuscular mycorrhizal fungi[END_REF]; Figure 1a), and should lead to the variation of plant communities. However this assumption has not been experimentally tested within the grassy matrix of campos rupestres, while these community variations may explain the extremely rich biodiversity of these tropical grasslands.

Within this framework we analyzed the soils, the composition and structure of two grassland-type communities, one located on stony substrate and the other one located on sandy substrate, but both located within the grass matrix of campos rupestres and we assessed whether plant communities varied in relation to edaphic factors.

Material and Methods

Study area and sites

Our study took place in Brazil, in the southern portion of the Espinhaço Range, one of the largest mountain range in Brazil recognized as Biosphere Reserve by UNESCO in 2005 and representing over 30 000 km² (UNESCO 2005). Study areas were located in the Environmental Protected Area Morro da Pedreira, in the buffer zone of the Serra do Cipó National Park (state of Minas Gerais). Campos rupestres are the main vegetation formation in the Serra do Cipó region, totalling more than 1600 plant species [START_REF] Giulietti | Flora da Serra do Cipó: caracterização e lista das espécies [Serra do Cipó flora: characteristics and species list[END_REF]). The regional climate is classified as Cwb with a warm temperature, a dry winter and a warm summer, according to the Köppen's system [START_REF] Köppen | Versuch einer Klassifikation der Klimate, vorzugsweise nach ihren Beziehungen zur Pflanzenwelt [Climate classification attempt, mainly according to its relationship with plant world[END_REF]. It is markedly seasonal, with two distinguishable seasons, a rainy season from November to April and a dry one from May to October. The mean annual precipitation and temperature are respectively 1622 mm and 21.2°C [START_REF] Madeira | Reproductive phenology of sympatric taxa of Chamaecrista (Leguminosae) in Serra do Cipó[END_REF].

We selected 5 sites, where occur both herbaceous communities, growing on either a sandy substrate that we called sandy grasslands hereafter (Figure 1b) or on a stony substrate that we called stony grasslands hereafter (Figure 1c). Within a site, the selected sandy grassland and stony grassland were close together, separated from each other by a minimum of 10 m and a maximum of 500 m. Sites are between 1ha and 5ha. These substrates are the two main in campos rupestres. All sites were located between 1100 m and 1300 m.

Plant survey

We surveyed fifteen 1 m² quadrats at each sandy grassland site (n=5) and twenty 1 m² quadrats at each stony grassland site (n=5) according to the minimal area which was previously assessed in December 2008 for each grassland type (species/area curves -Mueller-Dombois and Ellenberg 1974). Contrary to soil samples taken both at the dry and wet season, the vegetation was surveyed only once. Because a large majority of the species are perennial, community composition is not expected to change much during the year. At each quadrat the following information was collected: (1) percent cover of bare ground, litter, moss and lichen (hereafter "cryptogams"), forbs, ligneous species, Velloziaceae (a shrubby-looking characteristic family of campos rupestres), and graminoids; (2) a list of the species, (3) the abundance of each species (number of individuals or clumps per m 2 ), (4) the percent cover of each species visually estimated, based on the vertical projection of all aerial plant parts (Mueller-Dombois and Ellenberg 1974), (5) the frequency of each species, based on the number of subquadrats (25 20 cm ×20 cm subquadrats / m 2 ) in which each species was found. Plants were identified by experts and by using specific literature [START_REF] Giulietti | Flora da Serra do Cipó: caracterização e lista das espécies [Serra do Cipó flora: characteristics and species list[END_REF]Forzza et al. 2010) and the Herbarium BHCB at the Universidade Federal de Minas Gerais in Belo Horizonte, Brazil. Voucher specimens were conserved at the LEEB laboratory at the Universidade Federal de Minas Gerais in Belo Horizonte.

In order to find out whether the two grassland types had different plant communities, the Importance Value Index (IVI -Mueller-Dombois and Ellenberg 1974) and Relative Dominance were calculated for each species and at each site. The IVI is the sum of the Relative Density (Dr), the Relative Dominance (Dor) and the Relative Frequency (Fr) and allows a species with high frequency but low cover to be considered as important. IVI was used to compare the importance of each species (maximum value = 300): the higher is the IVI, the higher is the importance of the species (Muller-Dombois and Ellenberg 1974). As Dr, Dor and Fr are proportions, they range from 0 to 100.

1) The Relative Density (Dr) is Dr=100×Da/Dt, where Da (Absolute Density) is the number of individuals / m 2 and Dt (Total Density) is the sum of the all the Da. The Absolute Density is Da=Σni×S/A with ni = number of individuals of species i, S= quadrat area, A= total area of sampling at the site.

2) The Relative Dominance (Dor) is Dor=100×Doa/Dot, where Doa (Absolute Dominance) is the area in cm 2 occupied by the species / m 2 and Dot (Total Dominance) is the sum of the all the Doa. The Absolute Dominance (cm 2 /m 2 ) is Doa=100×ΣRi×Si/A with Ri= area covered by species i (percent cover), Si= plot area, A= total area of sampling at the site.

3) The Relative Frequency (Fr) is Fr=100×Fa/Ft, where Fa (Absolute Frequency) is the percent of subquadrats occupied by the species at a site and Ft (Total Frequency) the sum of the all the Fa. The Absolute Frequency is Fa=100 *ΣSqi/Sqt with Sqi = number of subquadrats occupied by species i and Sqt = total number of subquadrats / site.

In order to analyze the characteristics (i.e. geographic distribution, endemism and IUCN threatening status) of the species, all species were classified according to (1) life-form according to Raunkiaer's life form modified by [START_REF] Mueller-Dombois | Aims and methoods in vegetation ecology[END_REF], (2) their plant forms, (3) habitats, (4) distribution ranges, (5) IUCN status and (6) life cycle. (1) The life-forms were assessed according to Raunkiaer (1904) modified by [START_REF] Mueller-Dombois | Aims and methoods in vegetation ecology[END_REF]. While the life-form system was elaborated to characterize plant strategies during the cold season, it can still be of some use in tropical systems with regular disturbances because position of buds is not solely a consequence of climatic conditions, but also a consequence of regular disturbances. (2) The considered plant forms were: forbs, graminoids, sub-shrub, shrub, liana, fern. (3) Habitats in Brasil were determined based on literature: campos rupestres, altitude grassland, cerrado (sensu-lato including rupestrian grasslands), caatinga, Atlantic rainforest, Amazon rainforest, wet grassland [START_REF] Giulietti | Flora da Serra do Cipó: caracterização e lista das espécies [Serra do Cipó flora: characteristics and species list[END_REF]; Lista de Espécies da Flora do Brasil 2013). ( 4) The distribution ranges, also based on the literature and a database, comprised: (a) endemic from the Serra do Cipó, (b) endemic from the Espinhaço Range in the state of Minas Gerais, (c) endemic from the Espinhaço Range (states of Minas Gerais and Bahia), (d) distributed in the state of Minas Gerais, (e) distributed in Brazil, (f) wide distribution [START_REF] Giulietti | Flora da Serra do Cipó: caracterização e lista das espécies [Serra do Cipó flora: characteristics and species list[END_REF]; Lista de Espécies da Flora do Brasil 2013; database SpeciesLink). (5) The IUCN status was defined according to [START_REF] Mendonça | Lista Vermelha das Espécies Ameaçadas de Extinção da Flora de Minas Gerais [Red list of threatened plant species of Minas Gerais[END_REF]: vulnerable, critical, and endangered. ( 6) We also included the life cycle: perennial or annual.

Soil analyses

Soil analyses were carried out on 60 soil samples, 6 taken at each of the 10 grassland sites. At each grassland site, 3 soil samples were taken during the rainy season (February) and 3 during the dry season (July). For each sample, three subsamples of soil were randomly gathered in the 10 first centimetres in the vicinity of a randomly selected vegetation quadrat before being pooled. To assess the granulometry of the coarse fraction of the soil, each sample was sieved through 1cm and 2mm mesh sieves. The fine fraction (<2mm) was used for physical (granulometry) and chemical (pH, MO, total N, P, K, Mg 2+ , Ca 2+ , Al 3+ ) soil analyses: P and K in mg/dm 3 , N and C in dag/kg, Mg 2+ , Al 3+ , Ca 2+ in cmolc/dm 3 , Organic Carbon (Corg) in dag/kg. P, N and K were analysed with the Mehlich 1 extraction method; Ca 2+ , Mg 2+ , Al 3+ with 1 mol/L KCl extraction; COrg following the Walkley-Black method. Analyses were conducted at the soil laboratory of Viçosa Federal University, Viçosa, Minas Gerais, Brazil. Soil analysis followed the recommendations of EMBRAPA (1997).

Statistical analyses

To compare vegetation composition and structure of the two grasslands, different tests were carried out. To assess plant similarity between stony and sandy grasslands, the Steinhaus similarity index, based on species abundance, was calculated (Steinhaus = 1-Bray-Curtis index, values range between 1 and 0, the higher the Steinhaus value, the more similar plant compositions, [START_REF] Legendre | Numerical Ecology[END_REF]. To assess the differences of the Steinhaus index when comparing sites belonging to the same or to different types of grasslands, we performed a Generalized Linear Model (GLM) procedure using a Gaussian distribution and identity link function, with similarity index as the response variable, the modality (comparison between stony and sandy grasslands, within stony grasslands and within sandy grasslands) as explicative variables, by setting the site effect as an offset component of the GLM. An offset specifies an a priori known component to be included in the linear predictor during fitting.

To identify groups, a ward clustering of a matrix of chord distances among sites was performed using species percent cover data. Then, to corroborate classifications and find out if the cluster overlapped or not, we plotted the cluster membership using a correspondence analysis (CA) on plant percent cover matrix (222 species × 175 quadrats). We therefore identified which species discriminated each groups to establish the community type. To test the difference between the two grassland types in the number of species per site and per m 2 , paired t-tests were performed.

To compare soil composition and structure of the two grasslands, different tests were performed. To compare the fine fraction granulometry between campo rupestre types, paired t-tests were performed after checking the data for normality and homogeneity of variance. To compare the coarse fraction granulometry between grassland types, the paired t-test with estimated separate variance was performed as the variances were not homogeneous. To compare chemical soil composition between grassland types and seasons we used a nested two-way ANOVA for each chemical element. Log-transformations were applied before comparing P, K, Ca 2+ , Mg 2+ and Organic Carbon [START_REF] Sokal | Biometry: The Principles and Practice of Statistics in Biological Research[END_REF].

To analyse the relationship between soil and plant composition, a co-inertia analysis was run between plant and soil data. This type of analysis is used to determine if there is a co-structure between two data tables by performing simultaneous analysis of the two tables. The optimizing criterion in co-inertia analysis is that the resulting sample scores (environmental scores and floristic scores) are the most covariant (Doledec and Chessel 1994). The co-inertia analysis was based on one correspondence analysis (222 species) and one Principal Component Analysis PCA (11 physico-chemical variables) at the 10 sites (10 points); a test based on permutations was performed to find out about the co-inertia significance. All analyses were carried out in R version 2.9.1 (R Core Development Team 2010) using ADE-4 and stats packages.

Results

Plant community comparison

The similarity between sites from different grassland types was significantly lower than the similarity within sites from the same grassland type (mean Steinhaus similarity index of 0.25 ± 0.07 between sites from different grasslands, 0.46 ± 0.04 within sites of sandy grassland and 0.40 ± 0.06 within sites of stony grassland, GLM procedure P<0.001). Furthermore, differences in similarity were significant between and within both grasslands (R between stony and sandy grasslands= 0.49, R within stony grasslands= 0.45 and R within sandy grasslands= 0.29, P<0.001), highlighting also the presence of a higher heterogeneity within stony grassland communities compared to sandy grassland communities.

A Ward clustering analysis allowed the discrimination of two distinct floristic groups based on floristic composition and structure, the sandy grasslands on one side and the stony grasslands on the other side (Figure 2). Correspondence analysis allowed to visualize this distinction. Axes 1 and 2 of the CA performed on plant percent cover explained 47% of the total inertia. Axis 1 (29%) separated sandy from stony grasslands while axis 2 (18%) showed an inter-site variability in plant composition, particularly in the stony grasslands (Figure 3). Some species, such as Vellozia albiflora, V. resinosa, V. caruncularis, Bulbostylis lombardii, B. paradoxa, Diplusodon orbicularis, Xyris minarum, X. melanopoda, Paepalanthus geniculatus, Sebastiana ditassoides and Vochysia pygmaea were typical of the stony grasslands, while Xyris asperula, X. insignis, X. nubigena, Syngonanthus cipoensis, Panicum cyanescens, Vellozia epidendroides and Rhynchospora ciliolata were strongly associated with sandy grasslands (Figure 3). The main Poaceae species, such as Tatianyx arnacites, Mesosetum exaratum and Homolepis longispicula, can be found in both grassland types, but with different importance indices and dominance values. According to the IVI and dominance values, the sandy grasslands were characterized by Tatianyx arnacites, Homolepis longispicula, Paspalum erianthum, Lagenocarpus tenuifolius and Mesosetum exaratum. These five dominant species represented 56.4% of the vegetation cover while the first 16 dominant species accounted for 80.0% of the vegetation cover (Supplementary online material, Appendix 1). In the stony grasslands, Mesosetum exaratum, Tatianyx arnacites, Lagenocarpus tenuifolius, Homolepis longisticula and Xyris minarum can be considered the main species based on their IVI values, while Vellozia resinosa and V. caruncularis can be characterized as important, having important dominance values (Appendix 1). The top five most dominant species represented 51.3% of the vegetation cover while the top 19 dominant species accounted for 80%.

Soil analyses

As expected, grasslands with a stony substrate (stony grasslands) presented a significantly greater proportion of gravel (gravel > 1cm represented 28%) compared to grasslands with a sandy substrate (sandy grasslands) (Table 1) and sandy grasslands had a significantly higher proportion of fine sand (< 2mm) than stony grasslands (t= 4.65, P<0.001) (Table 1). In stony grasslands, N, P, K, Ca 2+ , Mg 2+ concentrations and Corg content were significantly higher and the soil was more acidic than in sandy grasslands (Table 2, Figure 4). Both grasslands presented seasonal variation for P and Corg content and pH. During the dry season, P concentrations were significantly higher while Corg contents and pH were significantly lower (Table 2, Figure 4). The aluminum concentration did not vary between grasslands or between seasons (Table 2, Figure 4).

Relationships between vegetation and soil

A strong co-structure between soil and vegetation data was observed (RV= 0.70, P<0.001), revealing a significant relationship between the soil composition and the species composition of the different communities (Figure 5). Axis 1 (79.4%) showed the distinction between the stony and sandy grasslands (Figure 5a). Stony grasslands are characterized by higher concentrations of nutrient such as N, K, Ca 2+ , Mg 2+ concentrations and Corg content while the sandy grasslands are characterized by finer soil and a less acidic pH (Figure 5b). Axis 2 (10.5%) showed the heterogeneity within each grassland-type, mainly characterized by variation in Al 3+ (Figure 5b), heterogeneity which is higher within stony grasslands compared to sandy grasslands (Figure 5).

Conservation value of campos rupestres

In the 10 sandy and stony grasslands that were investigated, we found one species of pteridophytes and 221 species of angiosperms, 120 monocotyledons and 101 dicotyledons, distributed into 34 plant families (Appendix 1). We recorded 158 species in the sandy grasslands and 170 species in the stony grasslands of which 13.9% and 17.1% were endemic species, respectively (Table 3).

Around one third of the species are restricted to one or the other grasslands, 32.9% of species (52 species) are exclusively found in sandy grasslands while 37.6% of species (64 species) are restricted to stony grasslands, which confirms the significant heterogeneity of the grass layer of campos rupestres. The mean number of species/m 2 (t=2.93, P<0.01) as well as the mean number of shrubs (W=1, P<0.05) were higher in the stony grasslands (Table 3, Appendix 1).

These ecosystems can be defined as graminoid lands rather than common tropical grasslands (Figure 6) because, besides the importance of Poaceae species (26 and 28 species in sandy and stony grasslands, respectively), other graminoid families were very well represented such as Cyperaceae (23 and 25 species), Xyridaceae (20 and 14 species), Eriocaulaceae (9 and 14 species). Among the most characteristic families of such ecosystems we can also cited Velloziaceae (5 and 7 species) for the Monocotyledons and Asteraceae (14 and 13 species), Melastomataceae (6 and 8 species), Polygalaceae (7 and 1 species) and Apocynaceae (4 and 5 species) for the Dicotyledons (Figure 6). This original family composition confers to these graminoid lands a high interest value for conservation.

Graminoids (representing 45% and 51% of species in sandy and stony grasslands, respectively) were clearly the dominant plant form in both communities. Forbs (25% and 26% of species in sandy and stony grasslands, respectively) and sub-shrubs (17% and 21%) were also well represented. Shrubs, lianas and ferns represent 7% of the species in sandy grasslands and 8% in stony grasslands. In both sandy and stony grasslands, a large majority of species are hemicryptophytes (i.e. 82% of species in sandy grasslands and 81% of species in stony grasslands). Chamaephytes represent 8% of species in sandy grasslands and 11% of species in stony grasslands while geophytes represent 3% and 4% of the species in sandy and stony grasslands respectively. Other life forms (hemicryptophytes lianas, nano-phanerophytes and therophytes) represent around 5% of the species in both grasslands. A large part of the species is perennial in both communities and monocotyledons represent 56.9% in sandy grasslands and 55.9% in stony grasslands (Table 3). Only 5.3% of all species (12 species) were found in all sites while 39% of species (87 species) were encountered at only one site (singletons).

The distribution pattern of 174 species showed that 12.6% of the total number of species (i.e. 28 species) are endemic to the Serra do Cipó, while 21.6% of species (48 species) are restricted to the Espinhaço range whether in the state of Minas Gerais or in the states of Bahia and Minas Gerais (Figure 7). Among the 160 species for which bibliographical data were available, 38.6% of species (86 species) are restricted to the campos rupestres and 13.9% of species (31 species) are cerrado species (Figure 7). 10.7% of species (i.e. 24 species) are classified as either endangered, critical, or vulnerable according to the IUCN criteria (Table 3, Appendix 1).

Discussion

Plant communities linked to soil composition and structure

One of the main findings of this study was the stark heterogeneity of the grassy matrix of campos rupestres, with at least two distinct plant communities occurring: one on the sandy substrate and one on the stony substrate. Some species are restricted to one or another grassland, such as Paspalum hyalinum, Xyris asperula and X. insignis in sandy grasslands and Paepalanthus nigrescens, Prestelia eriopus, Marcetia acerosa and Vellozia albiflora in stony grasslands. This composition heterogeneity leads to an overall high plant diversity and an exceptional intrinsic value to each grassland type.. The co-inertia analysis showed that each plant community is closely related to a specific soil composition. The stony grasslands are characterized by a coarse granulometry, particularly quartzic stones, which is the result of greater water erosion. In the same way, stony grasslands are rarely flooded while sandy grasslands can experience temporary flooding during the rainy season [START_REF] Vitta | Composição florística e ecologia de comunidades campestres na Serra do Cipó, Minas Gerais [Floristic composition and ecology of grassland communities in the Serra do Cipó[END_REF], we then expect stony grasslands to be drier than sandy grasslands. This is illustrated by the important presence in stony grasslands of Vellozia spp., which are strongly associated with such dry environments [START_REF] Porembski | Granitic and gneissic outcrops (inselbergs) as centers of diversity for desiccation-tolerant vascular plants[END_REF]. In dry systems, water availability is a source of heterogeneity (Jobbagy et al. 1996), and local drainage further diversifies the environment by creating relatively humid or arid sites. This might explain why higher heterogeneity is observed within the stony grasslands compared to the sandy grasslands. Nonetheless heterogeneity within each grassland-type is low compared to the heterogeneity between grassland-types.

The nature of the substrate and its heterogeneity, even at a scale of a few centimeters, separate the grassland types from one another. Our data indicate that the soil of stony grasslands is more acidic and richer in nutrients (N, P, K, Ca 2+ , Mg 2+ ) and carbon content than sandy grassland soil, which explain in part the discrimination of the two plant communities. As sandy grasslands are less subject to water erosion during the rainy season, they accumulate water, which slowly percolates, and this might facilitate the eluviation of the soluble organic compounds that are associated with iron and aluminum and can leach through and into deeper soil. This translocation is favored by humic acid, which is common in these soils (Schaeffer and Ker 2003). Normally, at lower pH, phosphorus (a critical element in the development of the vegetation [START_REF] Sarmiento | The ecology of Neotropical Savannas[END_REF])) precipitates, for example, with aluminum, and becomes less available to plants. However, in the stony grasslands we studied, it was found that during the dry season, soil pH decreased while phosphorus concentrations increased in what may be related to a reduction in the loss of mineral nutrients due to the absence of rainfall [START_REF] Sarmiento | The ecology of Neotropical Savannas[END_REF]. The extreme abiotic conditions of the campos rupestres have strong consequences in terms of plant adaptation to constrained environmental conditions. However, as each campo rupestre physiognomy is characterized by its own constraints (e.g. type of substrate), different adaptations can be observed between both grassland types (see [START_REF] Carvalho | The mosaic of habitats in the high-altitude Brazilian rupestrian fields is a hotspot for arbuscular mycorrhizal fungi[END_REF][START_REF] Negreiros | CSR analysis of plant functional types in highly diverse tropical grasslands of harsh environments[END_REF].

Main characteristics of campos rupestres flora

Both sandy and stony grasslands are species-rich plant communities highlighting the relevance of campos rupestres for the maintenance of an important biodiversity. On the contrary to other tropical grasslands or savannas dominated by grasses (Poaceae), both studied grassland-types of campo rupestre are dominated first by a graminoid strata with Poaceae (Paspalum, Andropogon) and Cyperaceae (Lagenocarpus, Rhynchospora, Bulbostylis), combined with Xyridaceae (Xyris), Eriocaulaceae (Paepalanthus, Leiothrix, Syngonanthus), Velloziaceae (Vellozia, Barbacenia) and Iridaceae (Trimezia, Pseudotrimezia). The predominance of monocotyledons, which has already been noted in earlier botanical surveys of campos rupestres [START_REF] Meguro | Phytophysiognomy & composition of the vegetation of Serra do Ambrósio, Minas Gerais, Brazil[END_REF][START_REF] Conceição | Delimitação de habitats em campos rupestres na Chapada Diamantina, Bahia: substratos, composição floristica e aspectos estruturais [Habitat delimitation in campos rupestres of the Chapada Diamantina, Bahia: substrate, floristic composition and structure[END_REF][START_REF] Viana | Floristica e caracterização dos campos rupestres sobre canga na Serra da Calçada, Minas Gerais, Brasil [Floristic and characterization of canga campos rupestres in the Serra da Calçada, Minas Gerais, Brazil[END_REF][START_REF] Borges | Altitudinal distribution and species richness of herbaceous plants in campo rupestres of the Southern Espinhaço range, Minas Gerais, Brazil[END_REF], indicates the presence of limiting ecological factors according to [START_REF] Granville | Monocotyledons and pteridophytes indicators of environmental constraints in the tropical vegetation[END_REF]. Globally the soils of campos rupestres are poor in nutrients. Clays, which are usually associated with a higher capacity of nutrient retention, are almost entirely absent. This pattern might have been exacerbated by periods of intense leaching followed by long-term podzolization, an important process that occurs in these highaltitude ecosystems [START_REF] Turenne | Influence de la saison des pluies sur la dynamique des acides humiques dans les profils ferrallitiques et podzoliques sous savanes de Guyane française [Wet season influence on humic acid dynamics in the ferrallitic and podzolic layers of savannas in French Guyana[END_REF][START_REF] Benites | Soils associated with rock outcrops in the Brazilian mountain ranges Mantiqueira and Espinhaço[END_REF]). The marked dominance of hemicryptophytes is characteristic of savannas and tropical grasslands and particularly in Cerrado and campos sulinos [START_REF] Overbeck | Adaptive strategies in burned subtropical grassland in southern Brazil[END_REF] and underline the high capacity of campos rupestres species to resprout after fire. However, we suggest that it could be interesting to adopt a new life-form classification in order to take into account the large variety of underground storage organs found in tropical ecosystems [START_REF] Stanton | The underground in grasslands[END_REF]) and illustrate the diversity of life forms in such ecosystems.

Conservation value of campos rupestres

Heterogeneity within the grassy matrix of campos rupestres favored an important biodiversity with high level of endemism in both studied grassland-types. Seventy percent of Vellozia species are restricted to the Espinhaço Range [START_REF] Mello-Silva | Aspectos taxonômicos, biogeográficos, morfológicos e biológicos das Velloziaceae de Grão-Mogol, Minas Gerais, Brasil. [Taxonomic, biogeographic, morphologic and biological aspects of Velloziaceae of Grão-Mogol, Minas Gerais, Brazil[END_REF]. In addition [START_REF] Giulietti | Flora da Serra do Cipó: caracterização e lista das espécies [Serra do Cipó flora: characteristics and species list[END_REF] noted that a large number of Eriocaulaceae species are endemic to the Espinhaço Range. For Xyridaceae, Wanderley (2011) recorded 14 endemic taxa in the Serra do Cipó and attributed the recent origin of Xyris species to explain their restricted distribution. Despite the lack of geographically broader studies, many campo rupestre species have been said to be endangered because of their restricted distribution [START_REF] Ribeiro | Impactos potenciais das alterações no Código Florestal sobre a vegetação de campos rupestres e campos de altitude [Potential impacts of environmental code alteration on campo rupestre and campo de altitude vegetation[END_REF]. Numerous species (38.6%) are found exclusively on campos rupestres, suggesting a uniqueness to this ecosystem, though vicarious species can contribute to a high floristic variation among them [START_REF] Giulietti | Espinhaço range region: eastern Brazil[END_REF][START_REF] Alves | Can campo rupestre vegetation be floristically delimited based on vascular plant genera?[END_REF]. [START_REF] Alves | Can campo rupestre vegetation be floristically delimited based on vascular plant genera?[END_REF] have already noted that genera alone are not sufficient to separate campos rupestres from other vegetation formations, such as highland grasslands (campos de altitude), and that floristic studies at the species-level must be combined with environmental variables to help design general functioning patterns for the campos rupestres.

Both grasslands are threatened by increasing mining, quarrying and eucalyptus plantations, which is why designing conservation areas and elaborating restoration protocols are urgent matters. However variations in edaphic factors which generate heterogeneous grasslands have to be taking into account when conservation and restoration programs are implemented to maintain or recreate this heterogeneity favorable to the high plant diversity. More specific measures should be taken to conserve endemic species. The potential changes in Brazilian environmental legislation may weaken the already modest conservation requirements for the region, thereby increasing the threat to campo rupestre biodiversity and the ecosystem services they provide. The conservation of pristine areas and the restoration of already degraded ones are more than urgent and necessary.

Conclusions

Campos rupestres are species-rich Neotropical mountain grasslands, occurring on harsh abiotic conditions with nutrient poor soils. We demonstrated that plant communities varied in relation to edaphic factors within the grassy matrix. Some species are confined to one or the other grassland type, highlighting finely tuned adaptations to environmental conditions. This heterogeneous matrix is favorable to a rich biodiversity with high level of endemism. Our study also brings to light the lack of information on numerous species, underscoring the need for research on their biology, distribution and ecology. These findings have important implications for the conservation and restoration of these grasslands. [START_REF] Giulietti | Flora da Serra do Cipó: caracterização e lista das espécies [Serra do Cipó flora: characteristics and species list[END_REF], Forzza et al. 2010): CR: Campos Rupestres, AG: altitude grassland, Ce: cerrado, Ca: Caatinga, AtR: Atlantic rainforest, AmR: Amazon rainforest, WG: wet grassland. Distribution range [START_REF] Giulietti | Flora da Serra do Cipó: caracterização e lista das espécies [Serra do Cipó flora: characteristics and species list[END_REF], Forzza et al. 2010

  Figure1a) The herbaceous layer of campos rupestres are generally confounded and defined as a more or less continuous herbaceous layer. However some herbaceous communities seems to exist, separated by few centimeters, the stony grasslands on the left side of the picture and the sandy grassland on the right side; b) Picture of a sandy grassland; c) Picture of a stony grassland. Photo credit: Soizig Le Stradic.

Figure 2

 2 Figure 2 Ward clustering of a matrix of chord distances among sites (species data). Sa-= sandy campo rupestre grasslands and St-= stony sandy campo rupestre grasslands.

Figure 3

 3 Figure 3 Correspondence analysis run on the matrix of plant percent cover in 1m² quadrats in the 5 sandy (Sa) and 5 stony (St) grasslands [175 points × 222 species]. Projection of the two first axes, axis 1 (29%) and axis 2 (18%). Inertia= 0.19, P<0.001, Monte-Carlo permutations.

Figure 4 Figure 5

 45 Figure 4 Mean and standard error values of chemical soil parameters, from soils collected in sandy and stony grasslands (3 samples / 5+5 sites / 2 seasons, n=60). Open circles represent dry season and full circles rainy season. See Table2for two-way ANOVA results.

Figure 6

 6 Figure 6 Number of species from the most-represented families in sandy grasslands (black columns) and stony grasslands (grey columns) (5 sites of each physiognomy, 15 x 1 m 2 quadrats in sandy grasslands and 20 x 1m 2 in stony grasslands).

Figure 7

 7 Figure 7 Pie charts representing the percentage of species according to a) their distribution range (N=174 species) and b) their habitat in Brazil (N=160 species).

  , database SpeciesLink: http://splink.cria.org.br/): (a) Serra do Cipó, (b) Espinhço range in the state of Minas Gerais, (c) Espinhaço Range, (d) State of Minas Gerais, (e) Brasil, (f) Wide distribution. IUCN status (Fundação Biodiversitas para o Estado de Minas Gerais (Mendonça and Lins 2000)): VU: Vulnerable, CR: Critical, EN: Endangered. Life cycle: A: annuals and P: perennials. R: species observed resprouting after fire, empty cells mean no observation of the species in the burnt area.

  Wanderley MG (2011) Flora da Serra do Cipó, Minas Gerais: Xyridaceae [Serra do Cipó flora, Minas Gerais: Xyridaceae]. Boletim de Botânica da Universidade de São Paulo 29:69-134. (In portuguese). DOI: 10.11606/issn.2316-9052.v29i1p69-134. White PS, Jentsch A (2001) The search for generality in studies of disturbance and ecosystem dynamics. Progress in Botany 62: 399-450. Zappi DC, Lucas E, Stannard B, et al. (2003) Lista das plantas vasculares de Catolés, Chapada Diamantina, Bahia, Brasil [Vascular plant list of Catolés, Chapada Diamantina, Bahia, Brazil]. Boletim de Botânica da Universidade de São Paulo 21: 345-398. (In portuguese) Table 1 Mean and standard error values of granulometric soil parameters, from soils collected in 5 sandy and 5 stony grasslands (3 samples / site , n=30).

			Sandy grasslands Stony grasslands t value
	Coarse fraction	soil >1 cm (%)	1.79 ± 0.71	27.63 ± 1.18	18.81***
	of soil	soil >2 mm (%)	12.98 ± 2.42	60.04 ± 1.89	16.26***
	Fine fraction of	Coarse sand (dag/kg)	19.66 ± 2.48	25.80 ± 2.42	1.63 ns
	soil < 2 mm	Fine sand (dag/kg)	46.87 ± 2.04	37.33 ± 1.41	4.65***
		Silt (dag/kg)	29.27 ± 1.94	31.53 ± 1.49	0.85 ns
		Clay (dag/kg)	4.20 ± 0.43	5.33 ± 0.47	1.54 ns
	Notes: T-tests were run using separate variance estimates for the coarse fraction. ns: non-significant difference, *** :
	significant difference with P<0.001.

Table 2

 2 Results of the two-way ANOVAs performed for chemical soil parameters, from soils collected in 5 sandy and 5 stony grasslands (3 samples / site / season, n=60) (Units for Ca 2+ , Mg 2+ , Al 3+ : cmolc/dm 3 ; Unit for N, Organic carbon : dag/kg ; Units for P, k : mg/dm 3 ).

		Two-way ANOVAs: F
		Season	G-type	Interaction
	N	1.09 ns	8.69 *	1.93 ns
	pH (H2O)	41.99 ***	9.26 *	0.17 ns
	P	188.26 ***	6.34 *	3.49 ns
	K	2.63 ns	15.04 **	1.68 ns
	Ca 2+	3.09 ns	18.53 **	0.63 ns
	Mg 2+	0.23 ns	19.37 **	0.79 ns
	Al 3+	0.94 ns	0.14 ns	0.82 ns
	Organic carbon	6.83 *	23.18 **	4.73 *
	Notes: G-type: Grassland type; ns: non-significant difference, *: significant difference with P<0.05, ***: significant
	difference with P<0.001.

Table 3

 3 Family and species distribution between sandy (5 sites, 15 quadrats / site, n=75) and stony grasslands (5 sites, 20 quadrats / site, n=100). Sandy-gl: Sandy grassland; Stony-gl: Stony grasslands; ns: non significant difference, *: significant difference with P<0.05.

	Sandy-gl	Stony-gl	t-test

Acknowledgements

We are grateful to Shishir Paudel, Thierry Dutoit, Yumi Oki, Frederico de Siqueira Neves, José Eugênio Côrtes Figueira, and anonymous reviewers for their suggestions on the text, to Benoit Loeuille (Asteraceae), Pedro Lage Viana (Poaceae), Renato de Mello-Silva (Velloziaceae), Livia Echternacht (Eriocaulaceae), Nara de O. Mota Furtado (Xyridaceae), Fernando A. O. Silveira (Melastomataceae) for their assistance in the botanical identifications. We would like to thank Kolo D. Wamba from PROEDITING (San Diego, CA) for review the English of the manuscript. This work was carried out with grants from the Conselho Nacional de Pesquisa (CNPq 561883/2010-6), Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG: APQ-04105-10), RTP CNRS-CEMAGREF "Ingénierie Ecologique" [Ecological Engineering] SAVER -SAVanna Ecological Restoration, Natural Reserva Vellozia and the Ministère Français des affaires étrangères et européennes (EGIDE).

Electronic Supplementary Material: Supplementary material (Appendix 1) is available in the online version of this article at http://dx.doi.org./10.1007/s11629-013-2866-3.


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