A Le Febvrier

Stephanie Deputier
email: stephanie.deputier@univ-rennes1.fr

Valérie Demange
email: valerie.demange@univ-rennes1.fr

Valérie Bouquet
email: valerie.bouquet@univ-rennes1.fr

A C Galca
email: ac_galca@infim.ro

A Iuga
email: iuga@infim.ro

Lucian Pintilie
email: pintilie@infim.ro

Maryline Guilloux-Viry
email: maryline.guilloux-viry@univ-rennes1.fr

Stéphanie Députier

Arnaud Le Fevrier
email: arnaud.le.febvrier@liu.se

Maryline Guilloux

Effect of in-plane ordering on dielectric properties of highly 111-oriented bismuth-zinc-niobate thin films

Keywords: BZN, Bismuth based pyrochlore, thin films, dielectric properties

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

Introduction

Nowadays, the field of telecommunications arouses a strong interest in wireless technologies (e.g. Bluetooth, internet or Personal Navigation Device) which are added on the same equipment (e.g. mobile phone). All these technologies add value and/or space in the equipment, being detrimental to users' requirements in terms of size and cost. Therefore, reconfigurable devices that allow for example to change characteristics by a voltage application, have great potential. Among the studied materials to be used in such hardware, ferroelectrics in thin films form are widely investigated due to a high dielectric permittivity that can be driven by an external DC electric field. This property allows the elaboration of tunable and miniaturized microwave devices for various applications, such as planar capacitors, phase shifters, tunable filters or_ENREF_2 coplanar waveguides [START_REF] Kong | Electrically tunable dielectric materials and strategies to improve their performances[END_REF][START_REF] Gevorgian | Ferroelectrics in microwave devices, circuits and systems : physics, modelling, fabrication and measurements[END_REF][START_REF] Simon | Highly tunable microwave stub resonator on ferroelectric KTa 0.5 Nb 0.5 O 3 thin film[END_REF][START_REF] Kim | High-tunability and low-microwave-loss Ba 0.6 Sr 0.4 TiO 3 thin films grown on high-resistivity Si substrates using TiO 2 buffer layers[END_REF]. However, despite their high tunability, main ferroelectric materials present high dielectric losses in the microwave frequency range which presently restrain their use in such components. More recently, interest has been focused on other dielectric, but non-ferroelectric, materials such as the bismuth-zinc-niobate pyrochlore Bi 1.5-x Zn 0.92-y Nb 1.5 O 6.92-δ (BZN), which attracted a considerable attention for its integration in microwave devices [START_REF] Ren | Bismuth zinc niobate pyrochlore dielectric thin films for capacitive applications[END_REF][START_REF] Thayer | Medium permittivity bismuth zinc niobate thin film capacitors[END_REF]. Belonging to the dielectric relaxors family, the dielectric properties of this complex oxide depend on both temperature and frequency [START_REF] Nino | Dielectric relaxation in Bi 2 O 3 -ZnO--Nb 2 O 5 cubic pyrochlore[END_REF][START_REF] Zhang | Structures and dielectric properties of pyrochlore bismuth zinc niobate thin films with zinc compensation[END_REF]. BZN thin films have been deposited by various processes, such as rf-magnetron sputtering [START_REF] Hong | Voltage tunable dielectric properties of rf sputtered Bi 2 O 3 -ZnO-Nb 2 O 5 pyrochlore thin films[END_REF][START_REF] Lu | Low-loss, tunable bismuth zinc niobate films deposited by rf magnetron sputtering[END_REF], pulsed laser deposition (PLD) [START_REF] Cao | C -axial oriented (Bi 1.5 Zn 0.5 )(Zn 0.5 Nb 1.5 )O 7 thin film grown on Nb doped SrTiO 3 substrate by pulsed laser deposition[END_REF][START_REF] Febvrier | Structural, optical and dielectric properties of Bi 1.5-x Zn 0.92-y Nb 1.5 O 6.92-δ thin films grown by PLD on R-plane sapphire and LaAlO3 substrates[END_REF][START_REF] Zhang | Influence of substrate temperature on structures and dielectric properties of pyrochlore Bi 1.5 Zn 1.0 Nb 1.5 O 7 thin films prepared by pulsed laser deposition[END_REF][START_REF] Garni | Physical properties of the Bi 1.5 Zn 0.92-2x Hf x Nb 1.5 O 6.92 solid solutions[END_REF] or solution chemistry based on the Pechini method [START_REF] Michael | Cubic Pyrochlore Bismuth Zinc Niobate Thin Films for High-Temperature Dielectric Energy Storage[END_REF]. Such thin films exhibited a moderate permittivity (150-200), low dielectric losses (5.10 -4 < tan  < 5.10 -3 at 1 MHz) [START_REF] Ren | Bismuth zinc niobate pyrochlore dielectric thin films for capacitive applications[END_REF][START_REF] Thayer | Medium permittivity bismuth zinc niobate thin film capacitors[END_REF][START_REF] Zhang | Structures and dielectric properties of pyrochlore bismuth zinc niobate thin films with zinc compensation[END_REF][START_REF] Lee | Very high tunable inter-digital capacitor using bismuth zinc niobate thin-film dielectrics for microwave applications[END_REF][START_REF] Lee | Tunable coplanar waveguide (CPW line integrating bismuth zinc niobiate (BZN) thin films[END_REF] and a tunability up to 55 % (under high electric field of 2.4 MV/cm) [START_REF] Lu | Low-loss, tunable bismuth zinc niobate films deposited by rf magnetron sputtering[END_REF].

Few papers reported the impact of the epitaxial growth of BZN thin films on their dielectric properties. Cao et al. compared the dielectric properties of polycrystalline films deposited on Pt/TiO 2 /SiO 2 /Si and of (100) epitaxial thin film grown on Nb-doped (100)-SrTiO 3 ((100)Nb:STO) [START_REF] Cao | C -axial oriented (Bi 1.5 Zn 0.5 )(Zn 0.5 Nb 1.5 )O 7 thin film grown on Nb doped SrTiO 3 substrate by pulsed laser deposition[END_REF]; they reported that the polycrystalline thin films possess a higher permittivity (204) and a higher tunability (8 % at 750 kV/cm) with higher dielectric losses (0.008) than the (100) epitaxial films.

Same authors also reported a study on the influence of the out-of-plane orientation of epitaxial thin films deposited on (100) and (110) Nb:STO; it was found that {111}-oriented thin films exhibit higher permittivity (155), higher tunability (6.5 % at 750 kV/cm) and higher dielectric losses (0.02) than {100}-oriented films [START_REF] Cao | Effects of film thickness and preferred orientation on the dielectric properties of (Bi 1.5 Zn 0.5 )(Zn 0.5 Nb 1.5 )O 7 films[END_REF]_ENREF_14. Furthermore their investigation of the dependence of dielectric properties on the thickness in case of {100}-oriented films has shown that best results in terms of dielectric constant (122) and dielectric losses (0.004) are achieved for thick films (700nm), while the thinnest films (150nm) exhibit lower dielectric constant (70) and much higher dielectric losses (0.01).

The present study aims to investigate the impact on the dielectric properties of the in-plane ordering of BZN thin films grown on Pt, i.e. the in-plane structural orientation of the film in relation to that of the substrate and/or the bottom layer. The BZN thin films were deposited on two different electrodes: a textured {111}-oriented platinum electrode (Pt/Si) and a {111} epitaxial grown platinum electrode (Pt/R-sapphire). Both electrodes are expected to promote a highly {111} out-of-plane orientation of BZN, while an in-plane ordering of the crystallites might be achieved only on the epitaxial-like platinum electrode. The dielectric properties were investigated on metal/insulator/metal (MIM) Pt/BZN/Pt capacitor at 100 kHz and under a maximum electric field of 600 kV/cm. The influence of BZN epitaxial-like growth, related to the crystalline quality (i.e. textured or epitaxial growth) of the Pt bottom-electrode, on the dielectric properties of the thin films (permittivity and tunability) is discussed.

Experimental procedure

The BZN thin films were deposited on a commercial (Crystal GmbH) textured platinum layer grown on silicon with proper buffer layers {111}Pt/TiO 2 /SiO 2 /(100)Si (thin film thereafter named "A") and on a homemade 200 nm-thick {111} epitaxial platinum layer grown on R-plane sapphire (thin film thereafter named "B"). The 6 homemade Pt layer was prepared by dc-sputtering at 450°C, under an argon pressure of 10 Pa, at a voltage of -1.5 kV, the time of deposition being 20 min [START_REF] Duclère | ZnO thin films grown on platinum (111) buffer layers by pulsed laser deposition[END_REF]. The BZN films were grown by pulsed laser deposition using a KrF excimer laser (λ = 248 nm) and a stoichiometric Bi 1.5 Zn 0.92 Nb 1.5 O 6.92-δ target sintered by a conventional ceramic method following the conditions described elsewhere [START_REF] Febvrier | Structural, optical and dielectric properties of Bi 1.5-x Zn 0.92-y Nb 1.5 O 6.92-δ thin films grown by PLD on R-plane sapphire and LaAlO3 substrates[END_REF][START_REF] Valant | Synthesis and dielectric properties of pyrochlore solid solutions in the Bi 2 O 3 -ZnO-Nb 2 O 5 -TiO 2 system[END_REF]_ENREF_8. The BZN deposition parameters were as follows: fluence -2 J/cm 2 ; frequency -2 Hz; temperature -700°C; target-substrate distance -55 mm; deposition time -20 min; and oxygen pressure -30

Pa. These conditions were the proper ones to obtain highly {111} oriented thin films on both substrates. For the X-ray diffraction (XRD) analysis, two diffractometers were used: a D8 Advance Brüker AXS (θ-2θ configuration) equipped with a monochromatized Cu Kα 1 radiation source and a four-circle texture instrument (D8 Discover Brüker AXS) equipped with a parallel beam Cu Kα 1 radiation in θ-2θ, ω, and φ scan modes. The XRD peaks were fitted by using pseudo-Voigt functions (WinPLOTR software [START_REF] Roisnel | WinPLOTR: A Windows tool for powder diffraction pattern analysis[END_REF]) in order to determine peak positions and full-width-at-half-maxima (FWHM). The surface morphology and the thickness were determined via field-emission scanning electron microscopy (FE-SEM), using a JEOL JSM 6310F system working at a low accelerating voltage (7 kV). The composition of the films was analyzed by energy-dispersive X-ray spectroscopy (EDS), using a JEOL JSM 6400 scanning electron microscope equipped with an ISIS Oxford analyzer (10 kV was used as an accelerating voltage and 10 nA as a beam current). The dielectric properties were evaluated using Pt/BZN/Pt planar capacitor structures. The Pt top electrodes, with an area of 0.2 mm 2 , were deposited by radio frequency sputtering through a shadow mask onto the surface of the films. The dielectric constant and dielectric losses were measured with a LCR HITESTER 3532-50 instrument.

Results and discussion

Films composition and morphology

BZN/{111}Pt/TiO 2 /SiO 2 /(100)Si (film A) and BZN/{111}Pt/R-sapphire (film B), were deposited from a stoichiometric Bi 1.5 Zn 0.92 Nb 1.5 O 6.92-δ target. EDS measurements performed on the two samples led to an average composition of the BZN films corresponding to Bi 1.3 Zn 0.5 Nb 1.5 O 6.92- . Losses of bismuth and zinc from the target during deposition by PLD process have already been observed [START_REF] Febvrier | Structural, optical and dielectric properties of Bi 1.5-x Zn 0.92-y Nb 1.5 O 6.92-δ thin films grown by PLD on R-plane sapphire and LaAlO3 substrates[END_REF][START_REF] Febvrier | Ferroelectric and dielectric multilayer heterostructures based on[END_REF]; these losses are related to the high volatility of those two elements under the conditions of pressure and temperature used during the deposition. Whatever the characteristics of the Pt electrodes, the obtained BZN thin films, with a thickness of 160 nm, present a dense, homogeneous and crack free surface, as shown in figure 1.

Preferential orientations and epitaxial-like relationships

The θ-2θ XRD patterns of the two BZN thin films, presented in figure 2, evidenced the single {111} orientation of Pt (ICDD Powder Diffraction File (PDF) Card No. 04-0802; space group Fm3m (n°225); a = 3.9231 Å). In both cases, even with Bi and Zn deficiencies, the BZN cubic pyrochlore phase was obtained and no other phase was observed. The diffraction peaks were indexed considering the cubic pyrochlore structure with a unit-cell parameter equal to a = 10.566(4) Å for the film A and a = 10.585(4) Å for the film B, these parameters being close to the bulk value [START_REF] Wang | Structures, Phase Transformations, and Dielectric Properties of Pyrochlores Containing Bismuth[END_REF] (ICDD Powder Diffraction File (PDF) Card No. 052-1770; space group Fd-3m (n°227); a = 10.558 Å). The two thin films are preferentially oriented along the <111> directions with some secondary <100> orientation. The fraction of {hkl} oriented grains of BZN (X hkl ) was estimated by the following formula (1) [START_REF] Febvrier | Structural, optical and dielectric properties of Bi 1.5-x Zn 0.92-y Nb 1.5 O 6.92-δ thin films grown by PLD on R-plane sapphire and LaAlO3 substrates[END_REF]: The quality of the out-of-plane ordering (i.e. along the growth direction) was evaluated by performing ω-scans around the 222 reflection of BZN. The value of the FWMH () obtained from the -scan pattern is 5.3° for the film A and 0.3° for the film B, that highlights a significant difference of out-of-plane ordering between the two thin films (Table I). This difference is mainly related to the crystalline quality of the platinum underneath layers. On R-plane sapphire, the epitaxial homemade {111} Pt exhibits a  value of 0.3° (figure 3-inset), while the commercial textured one has a  value of 3.6°. In order to characterize the in-plane ordering, -scans were performed on both films. As expected, the thin film A did not show any in-plane ordering, due to the texture of the bottom Pt layer. The epitaxial growth of the preferential {111} orientation of the Pt layer of thin film B was evidenced (bottom-panel of figure 3; 2 = 46.24°;  = 54.74°)), in agreement with previous studies on Pt growth on R-plane sapphire [START_REF] Nefedov | High-resolution x-ray scattering study of platinum thin films on sapphire[END_REF][START_REF] Vargas | Epitaxial growth of iridium and platinum films on sapphire by metalorganic chemical vapor deposition[END_REF].

        bulk
Two sets of peaks shifted of 30° were observed, corresponding to two in-plane orientations, with FWHM  of 0.8° and 2.5°. These two in-plane orientations correspond to rotational twinning of Pt on sapphire that was fully described by Nefedov et al. [START_REF] Nefedov | High-resolution x-ray scattering study of platinum thin films on sapphire[END_REF]. II). The mismatch in the first case is equal to -8.64 %, and to 4.35 % in the second case. In the -scan, the intensity of the peaks of this second ordering are consequently higher due to this lower mismatch. The high values of mismatch are also in agreement with the assumption that only a part of the {100}-oriented crystallites is in-plane ordered. The {111}BZN growth on {111}Pt can be drawn as a hexagon-on-hexagon; in this case, three BZN hexagonal lattice units will correspond to four Pt hexagonal lattice units (Figure 4c) and the mismatch is very low (0.26 %) (Table II).

Fig. 4 Schemas of the coincidences between the {100}-oriented BZN cells on {111}Pt

having two in-plane ordering (a and b), and between {111}-oriented BZN cells on {111}Pt (c) (for simplification purpose, only one (111) layer of Pt is displayed).

Dielectric properties

The dielectric measurements under a bias voltage (at 100 kHz) were performed on the two thin films in MIM configuration after the deposition of a Pt-top electrode (figure 5). The thin film A presented a dielectric permittivity of 200 without applied electric field and a tunability of 6 % under 600 kV/cm. These values are close to those found in literature, for instance in reference [START_REF] Cao | C -axial oriented (Bi 1.5 Zn 0.5 )(Zn 0.5 Nb 1.5 )O 7 thin film grown on Nb doped SrTiO 3 substrate by pulsed laser deposition[END_REF] for a c-axis oriented BZN film. However, in the present study, the dielectric losses are high (0.05) compared to the best results reported in the literature; this could be linked to two main following factors: the thickness (160 nm) and the {111} preferential orientation of the BZN film. Indeed, several studies on dielectric thin films [START_REF] Cao | Effects of film thickness and preferred orientation on the dielectric properties of (Bi 1.5 Zn 0.5 )(Zn 0.5 Nb 1.5 )O 7 films[END_REF][START_REF] Li | Thickness dependence of dielectric loss in SrTiO 3 thin films[END_REF] have evidenced a thickness dependence of the dielectric losses: thinner films may induce higher dielectric losses correlated to the presence of higher leakage current and/or local strain with the in-plane ordering [START_REF] Cao | Effects of film thickness and preferred orientation on the dielectric properties of (Bi 1.5 Zn 0.5 )(Zn 0.5 Nb 1.5 )O 7 films[END_REF][START_REF] Oh | The dependence of dielectric properties on the thickness of (Ba,Sr)TiO 3 thin films[END_REF]. In the same way, in a comparative study of the dielectric properties of BZN films of different preferential orientations, {111} -oriented BZN films show higher loss tangent than {100} ones [START_REF] Cao | Effects of film thickness and preferred orientation on the dielectric properties of (Bi 1.5 Zn 0.5 )(Zn 0.5 Nb 1.5 )O 7 films[END_REF]. Moreover, the thin film A has a columnar structure as observed on the FE-SEM cross-section view (figure 1) which may contribute to the relatively high dielectric losses, especially when measured in planar metal/insulator/metal capacitor geometry. For the thin film B, measurements under the same electric field exhibited a higher value of permittivity of 245 with a better tunability (12 %) while preserving the value of the dielectric losses ( 0.05). The increase of dielectric permittivity and tunability could be related to the preferred {111} orientation as shown by Cao et al. [START_REF] Cao | Effects of film thickness and preferred orientation on the dielectric properties of (Bi 1.5 Zn 0.5 )(Zn 0.5 Nb 1.5 )O 7 films[END_REF] who have obtained better dielectric properties for {111} BZN thin films. In our study, by comparing films with the same thickness, we can state that the fraction of the {111} orientation that increases from 65 to 80 % between the film A and B influences the relative permittivity and the tunability. Epitaxial-like growth might have also its improving role, in agreement with a previous related study on Ba 0.6 Sr 0.4 TiO 3 thin films where the authors concluded that the epitaxial growth is a key factor to increase the permittivity and the tunability [START_REF] Yang | Microwave properties of epitaxial (111)-oriented Ba 0.6 Sr 0.4 TiO 3 thin films on Al 2 O 3 (0001) up to 40 GHz[END_REF].

The increase of the dielectric permittivity of preferentially oriented {111}BZN film may be correlated to the structure of the ideal A 2 B 2 O 6 O' pyrochlore which could be described using two networks, i.e. one consisting of octahedra BO 6 ((Nb,Zn)O 6 ) and another one consisting of tetrahedra O'A 2 (O'(Bi,Zn) 2 ). These latter, connected by their corners, create an alignment of reversed tetrahedra along the <111> directions (figure 6).

Conclusions

Highly oriented BZN thin films with both {111} and {100} out-of-plane orientations have been deposited by PLD on two different Pt covered substrates. As 20 expected, a textured {111} Pt/Si substrate leads to a textured BZN thin film whereas an epitaxial growth of Pt on R-sapphire induces an in-plane ordering of BZN. For the latter, the epitaxial-like growth of {111} BZN that is accompanied by the decrease of the {100} secondary orientation, promotes better dielectric properties: a doubled tunability (12%) and an increased dielectric permittivity (22%), compared to those of the textured thin film. However, the dielectric losses, characteristic for such thin films, do not significantly get changed and remain high, partly due to the {111} preferential orientation and the low thickness of the BZN film.

Fig 1

 1 Fig 1 FE-SEM views at 45° and cross-section views (insets) of BZN thin films grown on (a) a textured {111}Pt/TiO 2 /SiO 2 /(100)Si substrate (film A) and (b) on an epitaxial {111}Pt/R-plane sapphire substrate (film B)

Fig 2 θ

 2 Fig 2 θ-2θ XRD patterns of the BZN thin films A (a) and B (b)

  film is the normalized integral intensity of the {hkl} diffraction peak; this value is equal to the full-width-at-half-maximum (FWHM) of the {hkl} peak in the -2 pattern multiplied by the integral intensity of the peak of the corresponding rocking-curve (-scan). {I hkl } bulk is the intensity of the peak of bulk material after correction of the multiplicity. For the thin film A, 65 % of the grains are oriented out-of-plane along the <111> directions and 35 % along the <100> ones. For the thin film B, the fraction of the crystallites oriented along the <111> directions is higher and reaches 80 % while a fraction of around 20 % is calculated for the <100> oriented crystallites.

Fig 3

 3 Fig 3 XRD φ-scan patterns of film B. From bottom to top: -scan of R-plane sapphire performed on (0006) plane; -scan of {111}-oriented Pt electrode performed on the 200 reflection; -scan of {100}-oriented BZN performed on the 222 reflection; -scan of {111}-oriented BZN performed on the 400 reflection. The corresponding -scans are given in the inset for each XRD -scan pattern.

[ 10 - 1 ]

 101 BZN // [10-1] Pt 0.26 % In the case of {100} preferential orientation, one BZN unit-cell can match two hexagonal Pt cells (Figure 4a, Table II) ([010] BZN // [1-10] Pt ), while a second face to face matching can be possible by overlapping a BZN unit-cell on two hexagonal Pt cells oriented along the [34-1] direction (Figure 4b, Table

Fig. 5

 5 Fig. 5 DC bias field dependence of relative permittivity (ε r ) and dielectric losses (tan δ) measured at 100 kHz and 300 K of Bi 1.3 Zn 0.5 Nb 1.5 O 6.92- films: A (circle) and B (triangle)

Fig. 6

 6 Fig. 6 Ideal cubic pyrochlore structure A 2 B 2 O 6 O' described with two networks: a) corner-connected octahedra BO 6 and b) corner-connected tetrahedra O'A 2 ; c) representation of the tetrahedron sub-network along the [111] direction. Blue and red polyhedra: (Nb,Zn)O 6 and O'(Bi,Zn) 2 , respectively; Red and green spheres: oxygen and bismuth/zinc, respectively

Table I

 I

	Relative fractions of {hkl}-oriented crystallites and {100} out-of-plane and
	in-plane ordering quality (Δω and ) for thin films grown on a textured
	{111}Pt/SiO 2 /Ti/(100)Si substrate and on an epitaxial {111}Pt/R-plane sapphire
	substrate.
			Fraction of	Out-of-plane	In-plane
			{hkl}	ordering:	ordering:
	Name	Substrate	orientation	Δω of the	Δ of the
			{111} {100}	222 reflection	400 reflection
	Thin film A	Textured {111}Pt/SiO 2 /Ti/(100)Si	65 % 35 %	5.3°	-
	Thin film B	Epitaxial {111}Pt/R-plane sapphire	80 % 20 %	0.3°	0.9° and 2.5°

Acknowledgments

The authors acknowledge the Romanian Ministry of Research and Innovation (core program / project PN-III-16-48-02) for their financial support. I. Peron and F. Gouttefangeas are acknowledged for EDS analyses and J. Le Lannic for FE-SEM images performed at CMEBA (ScanMAT, UMS 2001 CNRS-University of Rennes 1) which received a financial support from the Région Bretagne and the European Union (CPER-FEDER 2007-2014, Présage n° 39126 and Présage n° 37339).


Gauvain Bourgne
email: bourgne@nii.ac.jp

Katsumi Inoue

Nicolas Maudet
email: nicolas.maudet@lip6.fr

Finding new consequences of an observation in a system of agents

Keywords: I.2.11 [Artificial Intelligence]: Distributed Artificial Intelligence -Multiagent systems Algorithms, Theory Distributed Consequence Finding, Incremental Consequence Finding, Abduction

When a new observation is added to an existing logical theory, it is often necessary to compute new consequences of this observation together with the theory. This paper investigates whether this reasoning task can be performed incrementally in a distributed setting involving first-order theories. We propose a complete asynchronous algorithm for this non-trivial task, and illustrate it with a small example. As some produced consequences may not be new, we also propose a post-processing technique.

INTRODUCTION

This paper deals with the problem of finding all interesting new consequences which can be derived from some observations, given a full clausal theory. A consequence is deemed interesting if it respects a given language bias, and new if it is a consequence of the observations taken together with the theory but was not a consequence of the theory alone. Consequence finding is a general reasoning problem which lies at the heart of many AI applications. By focusing on computation of new consequences, one can perform efficient online computation of interesting consequences, an essential feature in dynamic contexts. On top of it, some problems specifically require to compute only new consequences, such as abduction by the principle of inverse entailment. Indeed, the set of abductive hypotheses is exaclty the set of the negation of new consequences of the negated observation wrt the background theory. The computation of new interesting consequences is thus a very important challenge.

Appears in: Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems (AA-MAS 2012), Conitzer, Winikoff, Padgham, and van der Hoek (eds.), Of course, one can always compute new consequences by computing all consequences of the theory with and without the observations, and making the difference. But focusing only on new consequences is much more efficient, which can be especially interesting in context when information is accessed progressively. The research question we address in this paper is the following: does it still hold in a distributed setting? There exist methods for computing new consequences in a distributed setting [START_REF] Adjiman | Distributed reasoning in a peer-to-peer setting: Application to the semantic web[END_REF], but restricted to the propositional case. On the other hand, some recent work [START_REF] Bourgne | Partition-based consequence finding[END_REF] focus on computing interesting consequences of a firstorder theory, but not only the new ones. We propose here a method that can deal with first order clausal theories while focusing on interesting new consequences. We introduce, in Section 2, (distributed) new consequence finding, and then present our algorithm (Section 3). Section 4 then concludes.

FINDING NEW CONSEQUENCES

A clause is a disjunction of literals. A clause C subsumes another clause D if there is a substitution θ such that Cθ ⊆ D. A clausal theory is a set of clauses, interpreted as the conjunction of all clauses in it. A consequence of Σ is a clause entailed by Σ. A clause C belongs to a production field P = L , where L is a set of literals closed under instantiation, iff every literal in C belongs to L. The set of all subsumption-minimal consequences of a theory Σ that belongs to a production field P is called the characteristic clauses of Σ wrt P [START_REF] Inoue | Linear resolution for consequence finding[END_REF], and denoted by Carc(Σ, P). When some observations O are added to a clausal theory Σ, further consequences are derived due to this new information. Such new and interesting consequences are called new charactestic clauses. It is formally defined as the set of all subsumptionminimal consequences of Σ ∪ O belong to P that are not consequences of Σ, and denoted by N ewcarc(Σ, C, P).

We now consider a system of nA agents a0, . . . , an A -1, each having a clausal theory Σi. I = {0, . . . , nA -1} denotes the set of indexes of all agents in the system. These agents make some new observations (or acquire new information), represented as a set of clauses Oi, possibly empty. The objective is to determine all the new consequences of those new observations O = i∈I Oi wrt the whole theory Σ = i∈I Σi belonging to the shared target production field P = LP , that is, to compute N ewcarc( i∈I Σi, i∈I Oi, LP ). This specifies a distributed new consequence finding problem. We emphasize that agents do not share their theories, though for better efficiency, they share their respective languages.

Example 1. Consider a system of 4 agents, whose knowledge (theory and new observations) is defined as follows:

a0: Σ0 = {f ∨ g, a ∨ g}, O0 = {e}. a1: Σ1 = {¬a ∨ b, ¬g ∨ h}, O1 = ∅. a2: Σ2 = {¬b ∨ c ∨ d, ¬d ∨ ¬e}, O2 = ∅. a3: Σ3 = {¬c ∨ ¬f }, O3 = ∅.
The target production field is P = {h} (i.e. LP = {h}).

DISTRIBUTED ALGORITHM

The main principle of our algorithm is to compute locally all relevant new consequences (and only those ones) and forward them to agents that can resolve them. Relevant consequences either (i) are new characteristics clauses of the problem, or (ii) can be used by one or more other agents to build such a new characteristic clause. Those latter ones, called bridge consequences, necessarily contains literals that can be resolved by other agents. We thus define, for each agent ai the output language Li→ the set of all literals that (i) ai might produce 1 and (ii) can be resolved with a clause from another agent 2 and an input language L→i of an agent ai as the set of all literals that (i) might be produced by another agent and (ii) can be resolved by some clause in its knowledge. Agents do not know each other theories, but they know each other input languages. Agents can focus their computations by using L→i and LP . Though a bridge consequence C could have literals that are not in these production fields, such literals can only appear if they were in a received clause. We thus define the reduction of C wrt some language L (reduc(C, L)) as the set of all literals that appear in C, but do not appear in positive nor negative form in L.

To achieve better efficiency, we apply a prune function to the received clauses, which checks them against Σi ∪ listCsqi, removing any subsumed clause. Example 2. (ex. 1 ctd.) Figure 1 illustrates the unfolding of the asynchronous algorithm. Each box represents an agent (its index) applying the receive procedure. Arrows between two boxes correspond to the communication of some 1 meaning that it must appear in at least one clause of ai. 2 meaning that there is at least one clause in the theory of a different agent that contains the negation of this literal. clauses (given as label) by the first agent to the second one. The process is initiated by a0, who send e to a2 (as e is only in L→2). Then a2 computes the new consequences of e wrt to Σ2 with production field {h, ¬b, ¬e, c} getting ¬b ∨ c, which partially belongs to L all→1 (through ¬b) and L→3 (c). It is thus sent to these two agents. Then a1 computes N ewcarc(Σ1, ¬b ∨ c, {h, ¬a, b, ¬g, c} ), and gets ¬a ∨ ¬c, which is sent to a0 and a3, and so on, until h is sent as output and other branches are closed. ¬a ∨ c ¬b ∨ ¬f Termination is guaranteed for non-recursive theories. Otherwise, we need to enforce termination by fixing a limit to the number of resolve operations that can be applied to get a consequence.This algorithm is complete for multiagent new consequence finding, meaning that it outputs all new consequences of i∈I Oi wrt i∈I Σi and LP . It also ensures that each output is indeed a consequence of i∈I Oi ∪ i∈I Σi. However, it might also be a consequence of the theory alone (and thus not strictly a new consequence). If our purpose is to incrementally compute all characteristic clauses, this is not a problem at all, but in some other cases, such as the computation of abductive hypothesis, we should only output new characteristic clauses. This can be ensured as follows. We remove all new observations, and for each candidate consequence C , compute NC = N ewcarc( i∈I Σi, negC, ∅ ). If NC = {∅}, C is not new, otherwise, it can be kept as a solution.

Algorithm 1 Asynchronous algorithm

3 1 0 0 1 g ∨ c ¬a ∨ ¬f ¬a ∨ ¬f ¬b ∨ g 1 0 3 1 0 g ∨ ¬f h ∨ c g ¬a ∨ h 0 0 Output h ∨ ¬f h ∨ ¬f h

CONCLUSION

We proposed in this paper a complete asynchronous algorithm to compute the new interesting consequences of some observations with respect to a full clausal theory distributed among a set of agents. Termination is guaranteed in cases where the centralized case also terminates, and soundness is ensured for incremental computations of consequences. Moreover some post processing was proposed to ensure soundness for computation of new consequences.

Figure 1 :

 1 Figure 1: Asynchronous resolution of pb 1.


David Furió
email: david.furio@inria.fr

Stéphanie Fleck
email: stephanie.fleck@univ-lorraine.fr

Bruno Bousquet
email: bruno.bousquet@u-bordeaux.fr

Jean-Paul Guillet
email: jean-paul.guillet@u-bordeaux.fr

Lionel Canioni
email: lionel.canioni@u-bordeaux.fr

Martin Hachet
email: martin.hachet@inria.fr

HOBIT: Hybrid Optical Bench for Innovative Teaching

Keywords: ACM Classification H.5.2. Information Interfaces and Presentation (e.g., HCI): User Interfaces, K.3.1. Computers and Education: Computer Uses in Education Education and Training, Optics, Augmented Reality, Simulation, Michelson interferometer

Figure 1. Simulation and augmentation of a Michelson interferometer experiment. Physical and digital content are merged in a unique environment.

INTRODUCTION

In optics, many concepts and phenomena are difficult to perceive and understand. This is particularly true with wave optics where phenomena may appear as counterintuitive [START_REF] Liu | Combination of the Research-Based Learning Method with the Modern Physics Experiment Course Teaching[END_REF]. Hence, universities and schools generally reinforce theoretical courses with physical experiments where students manipulate the concepts to be learned. The integration of laboratory activities into the classroom is an essential part of science education [START_REF] Planinsic | Stimulating scientific reasoning through explorations of simple experiments[END_REF] since it allows students to observe, test hypotheses, and apply their understanding of the physical world [START_REF] Chiaverina | Learning Physics from the experiments[END_REF][START_REF] Millar | Towards a Role for Experiment in the Science Teaching Laboratory[END_REF]. Furthermore, the observation, testing and experimentation found in experimental physics have a positive impact on the students' motivation [START_REF] Trna | Motivation and Hands-on Experiments[END_REF][START_REF] Trna | Motivational Effectiveness of Experiments in Physics Education[END_REF].

However, current experimental setups suffer from several limitations, as reported by the optics teachers with whom we have worked (see Evaluation section). First, from a practical point of view, setting up and maintaining optics experiments may be time consuming (in particular in the case of wave optics). The required material is generally expensive and fragile. This limits the number of experiments that can be run. Experiments can be dangerous too, in particular as soon as laser sources are used. These observations were also reported in the literature [START_REF] Ma | The Design and Implementation of Middle School Physics Optical Simulation Experiment Platform[END_REF][START_REF] Sadowska | Problems in teaching physics in primary and secondary school, as seen by young Polish she-teachers[END_REF][START_REF] Debnath | Problems of Teaching Optics in Middle School: A Survey in Batadraba Education Block of Nagaon District, Assam, India[END_REF].

Second, from a pedagogical point of view, the teachers as well as other prior work [START_REF] Trna | Improvement of science and technology literacy by means of ICT-based collaborative action research including hands-on experiments[END_REF] reported that traditional experiments were not always sufficient for transmitting knowledge. Students often have difficulties to develop an understanding of the complexity and ambiguity of empirical work. They may also fail to acquire the skills needed to calibrate and troubleshoot 1 Authors' version setups used to make observations, whereas this learning is the main objective of practical works [START_REF] Millar | The role of practical work in the teaching and learning of science[END_REF].

All these issues prompt to upgrade traditional optics experiments by i) overcoming the practical limitations of the current experimental setups and ii) providing pedagogical supports aiming to help the understanding of the studied phenomena. To this end, we propose HOBIT, an interactive system which stands for Hybrid Optical Bench for Innovative Teaching. Our goal is to let students operate as if they were working with a real optics experiment, but where the observed phenomenon comes from a numerical simulation. Beyond the simulation, this system allows augmenting the experiment with co-located pedagogical supports (see Figure 1).

In a first step, we focused on the Michelson interferometer, which is used in numerous applications (e.g. Fourier Transform Spectroscopy, Laser Interferometer Gravitational-Wave Observatory, and so on). Consequently, the Michelson interferometer (Figure 2) is one of the most popular optics experiments. It is based upon the division of a light wave into two beams that reflects on two separate plane mirrors before merging back into a combined beam whose projection can be observed on a projection screen. By slightly modifying the axial position or the orientation of the mirrors, one can observe resulting interference patterns-fringes or rings-on the screen (See Figure 5(a)). Various experiments can be performed with a Michelson interferometer, such as the measurement of wavelengths (e.g. Helium-Neon Laser), precise distance, or refractive indexes of transparent materials. Therefore, it is fundamental that, during lab work sessions, students familiarize themselves with the setup adjustments. They also need to translate their theoretical background into practice and understand causal effects of their direct manipulations on optical interferences phenomena.

Our contributions for this work are

• the design of a new interactive system that simulates and augments a Michelson interferometer

• a study that assesses the pedagogical relevance of the proposed approach in an ecological situation.

RELATED WORK

Due to the abstract nature of the studied concepts, optics is one of the fields where many works were conducted to improve educational approaches and tools. Many authors emphasize the importance of Hands-on learning experience, as we do in our approach. This is notably the case of the workshop carried out by Takayama et al. [START_REF] Takayama | El Dia de la Luz (the Day of Light): two hours optics demonstration for secondary school students[END_REF]. During two hours, basic optics concepts (e.g. polarization and wavelength) were introduced to high school students who performed the experiments themselves, guided by two experts. Despite direct manipulations, such traditional experiments may suffer from a disconnection between the theoretical concepts to learn and the actual handling, since students can not observe the phenomena and the underlying theoretical concepts at the same time.

Beyond standard experiments, authors have explored alternative technologies to improve the teaching of physics (and optics) concepts. For example, Rodrigues and Carvalho [START_REF] Rodrigues | Teaching optical phenomena with Tracker[END_REF] developed video-based experimental activities. Real experiments were recorded and students had to answer questions by watching and analyzing the videos. Such multimedia systems have interesting advantages over traditional experiments.

Beyond cost and safety considerations, videos can be freely distributed on the web, making possible to spread them to a large number of students that can work with them at any time, and as many times they want. On the other hand, physical investigations are not possible with such intangible approaches. This can maintain misconceptions [START_REF] Vosniadou | Designing learning environments to promote conceptual change in science[END_REF]. To overcome this, our work supports physical interaction.

In past few years, new approaches based on Virtual Reality (VR) have emerged with the popularization of the related technologies. These approaches rely on the immersion of users in an interactive virtual environment. Related with optics education, Hayes et al. [START_REF] Hayes | Virtual-Reality-Based Educational Laboratories in Fiber Optic Engineering[END_REF] developed a VR educational module that implements a virtual laboratory with realistic models of optical devices. In this virtual lab, students can set up and perform an optical experiment, e.g. dealing with laser diode characteristics and fiber coupling. The module was composed of three levels with a short quiz at the end of each one to measure the student's understanding of the subject. Such VR environments are very flexible, and numerous experiments, which could be potentially dangerous or expensive in reality, can be built. On the other hand, pure VR approaches suffer from limitations. In particular, when equipped with a Head-Mounted-Display, the student is isolated in a virtual world, and the communication with other students and teachers is harder. This contradicts pedagogical principles that emphasis the importance of social interaction in learning [START_REF] Hutchins | Distributed cognition[END_REF][START_REF] Dillenbourg | The evolution of research on collaborative learning[END_REF]. Moreover, the way the student manipulates virtual optics components is very far from what she or he would do during a real experiment. Consequently, the transition from the virtual to the real environment might be a problem. At the opposite, with HOBIT, students and teachers interact around a tangible experiment that is very close to the true experiment.

Related to VR, Augmented Reality (AR) has grown in importance in the last years. By superimposing virtual elements to real ones, AR allows enriching the real world with additional information. In education, this can help students to understand abstract concepts that may not be visible in real life (e.g. [START_REF] Dünser | Creating interactive physics education books with augmented reality[END_REF][START_REF] Shelton | Exploring a Cognitive Basis for Learning Spatial Relationships with Augmented Reality[END_REF]). With regard to optics education, a few AR experiments have been carried out. Yamaguchi and Yoshikawa [START_REF] Yamaguchi | New education system for construction of optical holography setup Tangible learning with Augmented Reality[END_REF] developed a system for the construction of an optical holography setup. The virtual optics components (e.g. lenses, and mirrors) were displayed on a screen on top of filmed markers. The students had to build an optical holography experiment by manipulating the markers in front of a camera. Compared to this approach where the augmentation is observed through a screen, with HOBIT, virtual information is directly projected onto the physical environment, using Spatial Augmented Reality [START_REF] Bimber | Spatial Augmented Reality: Merging Real and Virtual Worlds[END_REF].

Some authors like Underkoffler and Ishii [START_REF] Underkoffler | Illuminating light: an optical design tool with a luminous-tangible interface[END_REF], or Falcão and Price [START_REF] Pontual | What Have You Done! The Role of 'Interference' in Tangible Environments for Supporting Collaborative Learning[END_REF] had followed an approach similar to ours where projection is used to combine real and virtual information within a same physical space. Underkoffler and Ishii system aimed at simulating the interaction of laser light with various optical components in holographic setups. A projector situated above a table allows displaying augmented information (light path) around physical objects that are tracked thanks to a video/markers system. Similarly, the system of Falcão and Price consisted in an interactive tabletop environment for simulating some basic optics phenomena and was targeted at children. A projector situated on top of the table displayed the augmented information and the different physical objects were tracked from below the table thanks to a video/markers system. Continuing with AR, Yoon and Wang [START_REF] Yoon | Making the Invisible Visible in Science Museums Through Augmented Reality Devices[END_REF] developed a system to observe and manipulate magnetic fileds in realtime. A camera placed above the working area tracked the magnets and the augmented information (magnetic fields) was displayed on a screen situated in front of the user. These systems reproduce conceptual and simplified optics or magnetics experiments. In our case, with HOBIT, our goal is to mimic as much as possible true experiments, and to augment them with pedagogical supports.

Another interesting project related to HOBIT is TinkerLamp, developed by Do-Lenh et al. [START_REF] Do-Lenh | TinkerLamp 2.0: Designing and Evaluating Orchestration Technologies for the Classroom[END_REF]. TinkerLamp tries to help logistics students learn the theoretical concepts through experimentation and AR in a scaled-down model of a warehouse. It is composed of an interactive tabletop, a projector and a camera placed above the tabletop, and a series of physical elements (sheets, models, cards, etc.) that can be tracked thanks to markers. HOBIT shares some of the ideas presented in TinkerLamp and some of the aforementioned projects. This notably includes tabletop configurations, top projectors, tangible interaction, and control cards.

Despite the effort that has been put to build these new educational tools, few studies have been conducted to assess the learning outcomes. Underkoffler and Ishii [START_REF] Underkoffler | Illuminating light: an optical design tool with a luminous-tangible interface[END_REF] performed a qualitative user study with 8 students. This study notably showed that the students were pleased with the fast prototyping capabilities provided by the system, but no learning outcomes were studied. In their study, Hayes et al. [START_REF] Hayes | Virtual-Reality-Based Educational Laboratories in Fiber Optic Engineering[END_REF] showed that the VR module they proposed improved significantly the initial knowledge of the targeted pedagogical content. On the other hand, no comparison with a baseline condition was performed.

The studies of Falcão and Price [START_REF] Pontual | What Have You Done! The Role of 'Interference' in Tangible Environments for Supporting Collaborative Learning[END_REF], and Yoon and Wang [START_REF] Yoon | Making the Invisible Visible in Science Museums Through Augmented Reality Devices[END_REF] were focused on children and the main goals focused on study-ing the collaboration between them. The results showed that AR and tangible interaction increased the teamwork of the children, but no learning outcomes were studied. Do-Lenh et al. [START_REF] Do-Lenh | TinkerLamp 2.0: Designing and Evaluating Orchestration Technologies for the Classroom[END_REF] carried out a study to evaluate the learning outcomes of TinkerLamp. The authors suggest that TinkerLamp improved the learning outcomes compared to the other conditions.

In this paper, beyond describing the HOBIT platform, we report an experiment whose goal is to explore how a hybrid system as the one we propose impacts the building of new knowledge and skills. To this end, we conducted a study with a large number of participants (N = 101), and we compared HOBIT to a standard Michelson interferometer (see section Evaluation).

TECHNICAL DESCRIPTION System Overview

HOBIT is an interactive platform dedicated to the simulation and the augmentation of optics experiments. The main components of the system are:

• A set of optical replicas whose goals is to mimic true optical elements (e.g. lenses and mirrors mounted on mechanical holders).

• A numerical simulation that computes in real-time interference patterns from a physical model, and for which the result is projected on a screen.

• An augmentation of the board by way of a second projector located on top of the experiment.

Users modify the parameters of the simulation by manipulating the optical replicas. As they would do with a real experiment, they can observe the result of their action on the projection screen. The augmentation aims at co-locating additional information within the physical experiment. HOBIT platform in a configuration that reproduces a Michelson interferometer.

The total cost of the components required to build the platform (laptop, videoprojectors, and sensors) is about four times cheaper than a standard Michelson interferometer, and several experiments can be built from the same platform. With HOBIT, the experiment is much faster to set up than with traditional optics experiments. Moreover, because the light sources are not real, HOBIT prevents from safety issues, in particular in the case of laser sources.

Optical replicas

Optical replicas are 3D printed objects equipped with electronic sensors. For the Michelson interferometer, we built the following components.

2 light sources (low-pressure sodium lamp and white LED) are plastic boxes with RFID tags. A stand equipped with a RFID reader allows detecting which light source is experimented.

2 mirror holders are equipped with knobs that mimic micrometric screws, which are used to control the position and orientation of mirrors in real experiments. One of them (mirror 1, see Figure 4) is equipped with one knob dedicated to control the axial translation of the (virtual) mirror. The other one (Mirror 2) is equipped with two knobs dedicated to the orientation of the mirror. It is worth noticing that translation and orientation changes on mirrors in reality are not perceptible. Hence, replicas appear as true mirror holders in the simulator. The resolution of the knobs is adjusted to mimic those installed in the real setup. In particular, for the axial translation, 1 full turn of the knob was set to induce a 500 µm translation. The same happens with the knobs of the Mirror 2 where one full turn of the knob is mapped to 1°.

1 movable lens mounted on a linear potentiometer allows simulating the modification of the lens-to-screen distance. One step of this sensor corresponds approximately to 0.29 cm.

2 passive elements mimic the role of the beam splitter and the compensator. The RFID reader as well as all the sensors are connected to an Arduino board located under the platform where the mirrors, beam splitter and compensator are fixed. This board detects all the changes in the sensors states and sends them to the computer via an USB connection. The data is transmitted every 50ms.

Numerical simulation

The numerical simulation computes the interference pattern from the characteristics of the light source and the position and orientation of the mirrors and lens. The intensity of a point on the screen is computed based on the theory of interference involving two waves. The detailed model that is used to compute the interference patterns is described in the accompanying complementary file for reproducibility purposes.

At the end, the obtained interference patterns are very close to the ones that are obtained from a true Michelson interferometer, as depicted in Figure 5.

Augmentation

The augmentation consists in projecting pedagogical information into the experiment. This information (e.g. texts, drawings, and animations) have been designed to support the students' needs. For example, with a standard Michelson, students may often be lost because they have no idea of what is happening when manipulating a mirror. Have they turned too much the screw? Or not enough? At the end, they may observe nothing without knowing why. With HOBIT, a schematic representation of the current state of the optical elements can be displayed next to them, as illustrated in Figure 6(a). This may help students to understand how their actions impact the observed phenomenon. Such an augmentation would not have been possible with a standard Michelson interferometer. Indeed, the precise state of the system needs to be known, which is not the case with a standard version.

Animations may also help students to understand how light propagates. To this end, we propose the option to launch an animation that highlights the light path, and that shows how the waves coming from the two mirrors superimpose together. This is illustrated in Figure 6 Similarly, advanced pedagogical supports can be displayed directly onto the experimental board. For example, Figure 7(a) and 7(b), illustrates two representations of the signal that could be measured at a specific point of the visualized interference pattern. This point can be selected by way of a mouse input. Such representations aims for helping students to understand how the two waves combine together and, consequently, why a resulting intensity is observed at the selected location. They also provide explanation on the changing contrast that is observed in the case of low-pressure sodium lamp, which spectrum is characterized by two wavelengths very close one to the other. Formulas related with these phenomena can be displayed, too (see Figure 6). The parameters of these formulas are updated in real-time according to the actions performed by the students. This may help the students to strengthen the link between the observed phenomena, various representations, and the underlying concepts, all of them in a unique environment.

(a) (b) It is worth noting that all the augmentations and visual feedback features can be activated on demand. They are toggled from a keypad that stands next to the experiment. This keypad is active only when the option card equipped with a RFID tag is in contact with a dedicated RFID reader. A start card can also be used to instantly put the system back to an initial state, which is not possible with a standard Michelson interferometer. These cards give the teacher control over the application and the different pedagogical supports. At any moment, the teacher can place one of the cards in the RFID reader to enable or disable the privileges the card gives. For example, students are not able to run the simulation until the teacher has given them permission to do it by using the start card. The option card lets the teacher enable or disable the keypad in order to display or hide the augmented feedback. This notably gives the professor the ability to support his or her explanation of the theoretical concepts during the experiment. It also enables the teacher to control the difficulty of the experiment. Of course, the teacher can also decide to let the students manipulate the keypad by themselves, so they can experience, test, and discuss about the experiment.

EXAMPLE OF PRACTICAL WORK WITH HOBIT

After having switched on the computer and the two videoprojectors, the teacher runs the application. It will remain in a "stand by" mode until the teacher uses the start card on the RFID. Then, she or he provides an exercise form to the group composed of, typically, two or three students. The students have to experiment with the system to answer this form.

For example, they have to find the right configuration of the setup for obtaining interference fringes with a sodium lamp. First, they place the (fake) sodium light on the dedicated stand. Then, they can manipulate the optical elements in order to find the concrete configurations that were theoretically presented during the lecture courses. If students encounter difficulties, the teacher can decide to display additional information like the current state of the mirror (see Figure 6(a)) and the place where the lens should be positioned to ensure adequate imaging conditions. To do so, the teacher just needs to activate the keypad with the option card, and toggle the corresponding option by pressing the associated key. Once the students have managed to obtain the expected interference pattern, they can physically measure the period of the fringes to determine the angle value of the mirror, directly on the projection screen (see Figure 8(a)), as they would do with a real Michelson interferometer. After the students have modified the system in order to observe rings on the screen, the teacher wants now to explain the modulation of contrast that can be observed on the pattern. The teacher decides to display a new visual feedback to support her or his explanation (see Figure 8

EVALUATION

We conducted a user study to evaluate HOBIT in a real experimental class similar to the one described in the previous section. Our main objective was to explore how this system impacts scientific and technical learning compared to a standard corresponding experiment. We also explored the user experience and attractiveness of the system.

Subjects and apparatus

A The study took place directly at the University of Bordeaux, during 3 months. Three conditions were tested:

• MI, a standard Michelson Interferometer

• SMI, a Simulator of a Michelson Interferometer, as described previously, but with no pedagogical augmentations. The SMI condition is thus a pure simulation of MI.

• ASMI, corresponding to the SMI condition, plus the pedagogical augmentations.

Our hypotheses were that H1: replacing a real experiment (MI) by a simulated one (SMI) does not decrease the learning performance H2: an augmented condition (ASMI) improves the learning compared to non-augmented ones (MI and SMI), H3: the students who have learned with HOBIT (SMI and ASMI conditions) are able to transfer their knowledge to a real condition (MI).

MI and [A]SMI were installed in two separate rooms of the training lab, with similar setups (comparable room size, similar tables and chairs, similar lighting conditions).

Experimental protocol

One month before the lab work sessions, all students answered a pre-test questionnaire PT0 (see description in the Results section). This allowed us to estimate their preliminary knowledge on Michelson interferometer after the lecture courses period. Then, the students were divided into four homogeneous groups (see Table 1). The training sessions were carried out in pairs and lasted four hours (two hours per condition). The members of group A1 and A2 used SMI (resp. ASMI) first, and then MI. The members of group B1 and B2 used first MI and then SMI (resp ASMI). Students from each group were assigned to each teacher in order to limit a "teacher effect" (see [START_REF] Nye | How Large Are Teacher Effects?[END_REF]).

During the first two-hours session, students had to solve a set of problems involving interferometry technical skills and knowledges. After the session, the students filled out a posttest learning assessment (PT1), and they swapped with the group having done the other condition. During the second two-hours session, students had to solve similar problems as in the first session. At the end of the second session, they answered a new post-test learning assessment (PT2), and they filled out a user experience questionnaire (UX) including the french translation of the simplified Attrakdiff survey [START_REF] Lallemand | Création et validation d'une version franc ¸aise du questionnaire AttrakDiff pour l'évaluation de l'expérience utilisateur des systèmes interactifs[END_REF]. The questions we asked in this UX questionnaire were oriented towards pedagogical needs, i.e. referring on usability, usefulness, and meaningfulness. Indeed, the personal perception of a pedagogical support could influence the learning quality, as it play a role in the extrinsic motivation of the user [START_REF] Ryan | Intrinsic and Extrinsic Motivations: Classic Definitions and New Directions[END_REF].

The pedagogical content, the training goals and the related exercises were prepared by the teachers team (see Table 2). A total of 95 students' forms were analyzed (4 students did not fill the forms, and 2 of them provided non-exploitable documents). Figure 9 summarizes the whole protocol. It is worth noting that in each session teachers explained how to use the system, either [A]SMI or MI. They were also available to clarify any doubts the students had, as done in ordinary lab work conditions. In order not to introduce possible inequity between the groups, no academic grade related to the Michelson interferometer was given.

Groups A1

A2

B1 B2

Global reliability and design relevance

Overall, the subjects found that HOBIT worked well (mean and SD score on a 7 points Likert scale: 5.73±1.57; 7 being "fully agree"). During their manipulations, the students declared that they were not disturbed by occlusion problems (1.74±1.14, 7 being "fully disturbed") nor by problems of delay between their actions and the resulting system reaction (2.05±1.31). They globally felt that the operating mode of HOBIT (SMI and ASMI conditions) was close to a standard Michelson interferometer (5.09±1.48, 7 being "fully agree"). These declarative results tend to show that the physical proximity of HOBIT with a standard Michelson experiment is meaningful.

Results on learning

In order to estimate the pedagogical relevance of HOBIT, we assessed its effectiveness in regard to the achievement of the learning goals described in Table 2. This assessment focused on the students capability to schematize and to explain scientifically an interferometer configuration and the related observable phenomena (e.g. Figure 2). In the pre-test (PT0), the students had to report how to obtain interference fringes with a monochromatic light source. In PT1, they had to explain how to obtain interference rings with a monochromatic light source. Finally, in PT2, we assessed their ability to explain how to obtain interference fringes, as in PT0, but with a polychromatic light source (see Figure 5(c)). Competency is effective for a learner when the integrated set of knowledges, skills and judgment enable her or him to effectively perform in various situations [START_REF] Curran | Research for Interprofessional Competency-Based Evaluation (RICE)[END_REF]. Slight variation between the tests ensures that the students have to think again about the correct answer. These tests allow us to estimate the impact of the condition (MI, SMI or ASMI) on the evolution of the learning and on its stabilization.

In addition to these tests, we also asked the students to answer a set of questions referring to general definitions and mathematical exercises about interferometry. These questions were asked after PT0, PT1, and PT2. They were related to previous courses (e.g. "definition of the parameters of an optics formula") and the corresponding skills were not targeted during the lab sessions (See Table 2). The assessment of these questions showed no differences between the groups, for each test. This allows us to verify that the observed learning evolutions were due to the learning condition only, and not to a group effect. Indeed, practical work may reactivate previous knowledge, and re-introduce non homogeneity concerning the initial knowledge of the groups.

The answers to the tests and the diagrams produced by the students were scored by a teacher and a researcher of the project team, using a scale from 0 to 5. The teacher and the researcher first scored 50 tests in a double-blind approach, with harmonization steps after 10, 30 and 50 assessments to validate the scoring scale. Then, i) the researcher assessed all the remaining tests and ii) the teacher checked the results in order to validate the scoring. Less than 10 equivocal tests were discussed. This analysis of the type of answers enabled us to estimate the learning level for each student after each session. The score of 5 was given to diagrams that were fully correct and adequately annotated. In this case, the learning is considered as acquired. The score of 4 corresponds to correct but partial answers with small omissions or broad wording.

The score of 3 corresponds to correct but partial answers with notable omissions (i.e., optical element, angle, etc.) and confused explanations (i.e., lack of scientific vocabulary). Both 4 and 3 scores were counted as an underway learning. Finally, the scores of 2, 1, and 0 were given in case of wrong answers (diagram without any of the expected elements and/or conflicting explanations), off-topics, or blank answers, respectively. This refers to not acquired knowledge. Figure 10 illustrates an example of diagram.

It is worth to mention that all the analyzes carried out for the learning data as well as the UX data use the Aligned Rank Transform for nonparametric factorial ANOVAs as described by Wobbrock et al. [START_REF] Wobbrock | The Aligned Rank Transform for Nonparametric Factorial Analyses Using Only Anova Procedures[END_REF]. After the Aligned Rank Transform processes the data, ANOVA tests can be performed. One advantage of using the Aligned Rank Transform with ANOVAs over common nonparametric tests is that we can analyze multiple factors and their interactions.

Pre-test PT0

The scoring of PT0 showed that 94% of the students were not proficient in schematization and explanation of interferometer configuration before starting the lab work training session (mean score of the whole cohort: 2.52±1.21, see Table 3 and Figure 11). Most of their mistakes were linked to inappropri- The screen has to be on the focal plane of the lens.

Monochromatic

Figure 10. Example of diagram produced by a student at PT1. She was asked to explain the configuration in which interference rings can be observed. This diagram has been marked as "under way". Indeed, the overall structure is correct, but important information is missing (e.g. lack of the shift distance d).

ate positioning or omissions of optical components, lack of relevant annotations, or confusions with other configurations or with other interferometer (e.g. Young's interferometer). It confirms previous studies indicating that university students do not easily understand the physical models and have many difficulties to construct mental images only with a theoretical approach (see e.g. [START_REF] Djanette | Determination of University Students' Misconceptions about Light Using Concept Maps[END_REF]). A one-way ANOVA revealed no significant differences between the four groups (F[3, 87]=1.33, p=0.27, h G 2 =0.04; see also PT0 in Table 3).

Post-test PT1

A two-factor mixed ANOVA showed that after the first two-hours training sessions, the overall knowledge about the interferometer configurations has improved significantly (F[1,86]=61.94, p<0.01, h G 2 =0.26 / PT0: 2.48±1.21; PT1: 3.88±1.17). The ratio of students with insufficient knowledge decreased in all groups, as illustrated in Figure 11.

The ANOVA also revealed that there is an effect of the learning condition on the scores obtained in PT1 (F[2,86]=3.51, p=0.03, h G 2 =0.04). A Tukey's pairwise test showed that the scores obtained in the ASMI condition (4.44±0.77) are significantly higher than the ones obtained in the other conditions (MI: 3.67±1.26 (p=0.02) -SMI: 3.63±1.16 (p=0.05)). This confirms that augmentations enhance the building of the targeted knowledge (H2). On the other hand, no significant differences were found between SMI and MI (p=0.99), which does not contradict H1. The ratio of students having acquired the knowledge is comparable in both conditions (Figure 11, second line). The typologies of errors were very similar (e.g. error of mirror angulation and error of distance between the beam splitter and the mirrors). This tends to show that the SMI condition reproduces closely the MI one.

Post-test PT2

We observed the evolution of the scores from PT1 to PT2 (see Table 3 and Figure 11). A two-factor mixed ANOVA showed that, for group A2, no significant differences were found (F [START_REF] Bimber | Spatial Augmented Reality: Merging Real and Virtual Worlds[END_REF][START_REF] Takayama | El Dia de la Luz (the Day of Light): two hours optics demonstration for secondary school students[END_REF]=0.88, p=0.36, h G 2 =0.04). This tends to indicate that the students who have learned with ASMI did not decrease their performance when moving to MI. Their scores remain higher than any other conditions. These students gained most of the understanding and skills required to calibrate and troubleshoot setups used to make interferometry observations. It seems to indicate a stabilization of their learning; the knowledge that has been built with ASMI could be reinvested effectively with a classical interferometer. This would go in the direction of H3.

On the other hand, for group A1, i.e. the students who experienced with MI after having learned with SMI, a two-factor mixed ANOVA highlighted an unexpected result. In this group, the learning achievement significantly decreased (F [START_REF] Bimber | Spatial Augmented Reality: Merging Real and Virtual Worlds[END_REF][START_REF] Nye | How Large Are Teacher Effects?[END_REF]=8.92, p=0.01, h G 2 =0.33, see Table 3). This partly refutes H3. The amount of students who were underway or without any clear acquisition was quite similar to those noticed in PT0. We observed that 20% of the A1 students did not answer to all the questions of PT2. They rushed their work or did a lot of basic mistakes. In comparison, this ratio was between 2 and 6% for all the other groups. A1 was the group that indicated the lowest motivational advantage to use a hybrid system compared to a standard Michelson interferometer in their UX results (see next section). Therefore, it appears as if they were demotivated. That leads us to the idea that these results could probably be linked to the hope the students put in simulator to support their learning. It might destabilize their first understanding noticed in PT1 and act as a disruption in the learning process by stating that they still had some difficulties to setup the classical Michelson interferometer even if they trained on a simulator just before. This needs to be confirmed by further analyzes and replications of the experiment. However, it opens the question of the students representation of the role of a simulator in educational context.

For the groups that have initially started with MI, no noticeable improvement can be observed after using SMI (B1) nor ASMI (B2). It tends to show that the augmentations that have shown undeniable benefits after PT1 (group A2), have little impact when activated in a second round of training session. Students may mainly built their knowledge during the first training session, where no augmentation were available. However, it worth noting that the typology of mistakes were different between the two groups. For instance, in the group using SMI at the second round (B1), 37% of the students forget to position the lens and the compensator. This indicates that they did not perceive the role of these components. At the opposite, with ASMI (B2), most of the mistakes were only due to incomplete annotations of the diagrams.

The results obtained for the questions that were not directly linked to the targeted knowledge and skills (i.e. general definition and mathematical exercises) for each step of the learning process (PT0/PT1/PT2) did not show any significant differences between the four groups. Additionally, all teachers confirmed the absence of notable modifications on their teaching practices induced by the study conditions (5.83±1.60; 7 being "fully similar"). Moreover, the participants declared that they were not stressed during the study (students: 1.21±0.63; teachers: 1.66±0.81, 7 being "fully stressed"). All these results allow us to exclude a group effect; the observed learning evolutions are due to the system only.

Understanding the role of the augmentations

To gain insight on the relevance of the augmentations, we have looked at the declared perceptions of the ASMI users (groups A2 and B2) and the declared perception of the SMI ones (groups A1 and B1). A one-way ANOVA was performed for each of the asked questions. The ASMI users perceived the tool as less complex to operate than the SMI users, in comparison with the MI condition (F[1, 92]=12.66, p<0.01, h G 2 =0.12 -see Figure 12). Similarly, the augmented version was perceived as more motivating (F[1, 91]=10.98, p<0.01, h G 2 =0.11), and more efficient (F[1, 74]=25.80, p<0.01, h G 2 =0.26) than a tool without augmentation (see Figure 12). Among the augmentations, the indications displaying the state of the manipulated components (Figure 6(a)) were the ones that the ASMI students cited first (69% of the them). 5 of the 6 teachers reported that they considered this augmentation as the most important. The students and the teachers also endorsed the schematic projections of the wave interferences (Figures 6(b A large majority of the ASMI users (91%) declared that the system they used have met or totally met their needs to their learning goals (5.95±1.15, 7 being "fully agree"). In comparison, the mean score for the SMI users is 4.19±1.54. About this question, the open-ended spontaneous answers (multiple answers were possible) of the ASMI users were that the system i) helped them to understand the theoretical aspect of the interferometry phenomena (49% of the answers), ii) supported or enhanced their cognitive conception (conceptualization) of the wave phenomena (32%), iii) highlighted the causal effect between their interferometer adjustments and the observed interference patterns (20%), and iv) supported or enhanced their understanding of technical adjustments of an interferometer (14%).

At the opposite, the answers of the SMI users were more neutral. They rarely declared pedagogical gains compared to the MI condition, except for the restart functionality.

Regarding the perceived attractiveness, the students of the ASMI condition found the system really appealing both for its pragmatic and hedonist attributes. Based on the Hassenzhal's model [START_REF] Hassenzahl | The Thing and I: Understanding the Relationship Between User and Product[END_REF] applied on the Attrakdif results, the augmented version of HOBIT appears as a desirable pedagogical tool (see Figure 13). In contrast, the students of groups A1 and B1 who did not experienced augmentations were a bit less enthusiastic.

The answers of the students are in line with the teachers comments. Teachers reported that the ASMI students were more motivated and engaged than the SMI ones. Three of them indicated that many of the SMI students did not perceived the added value of a simulated system without augmentations. All the teachers agree that the augmented version of HOBIT is much more interesting than a version without augmentations.

The pedagogical augmentation seems to be necessary to support students in their understanding of technical specificities of the interferometer configurations and on their adjustments. Each user constructs his or her personal representation of the system by defining (consciously or not) various attributes. The high perception of usefulness and attractiveness provided by the pedagogical augmentations, and the perception of the users that the system addresses their needs, could explain the fact that the ASMI group obtained the best learning results.

To strengthen these results, new experiments should be conducted to assess how the acquired knowledge stabilizes over long periods of time.

DISCUSSION AND CONCLUSION

To overcome the limitations of standard setups, we developed a hybrid platform, HOBIT, which allows us to mimick true optics experiments. This platform reduces the cost as well the setup and maintenance time as no real optical components are used. Beyond the simulation, we showed that HOBIT offers the opportunity to augment the experiment with pedagogical supports. A study conducted in an ecological situation allowed us to demonstrate that such an approach, which mixes simulation of the real phenomena and virtual augmentations, enhances the learning of students compared to traditional setups. HOBIT does not aim at fully replacing true optics experiments. Similarly to a flight simulator, this platform makes training sessions more convenient. Because we took care to mimic as much as possible the real condition, and because we embed relevant augmentations within the simulation, the good transfer to the real condition is favored.

In this work we focused on the Michelson interferometer experiment. HOBIT is not limited to this particular experiment. Numerous other augmented optics experiments can be designed from this platform. As an example, we are currently building new pedagogical activities for simulating and augmenting Young's interferometer and polarization experiments. Beyond optics, a similar approach could benefit other domains. This is notably the case of scientific fields were the visualization of abstract concepts is important. With augmented information it is possible to create new representations that can help students to observe those abstract concepts or invisible phenomena [START_REF] Wu | Current status, opportunities and challenges of augmented reality in education[END_REF]. For example, in the electronics field, an efficient learning and understanding of complex concepts remains a challenge.

We hope that our work will help practitioners to design new relevant learning environments in a variety of fields. To this end, we would like to remind the importance of taking into account the nature of the scientific knowledge and the pedagogical orchestration of practical works at the early stages of the technological design process. Co-design with experts and teachers of the targeted field is a key element for the design of meaningfulness systems that remain as close as possible to the real experiences. We also encourage evaluations in ecological situations, as we did with HOBIT. Both quantitative comparative studies and UX surveys help gaining insights about the factors that play significant roles in learning. Finally, we would like to remind that a technological enhanced tool in and of itself is not necessarily a golden bullet that enhances learning. Without proper pedagogical support, it can actually backfire, as we have shown in our study.

In this paper, we have focused on the evaluation of the learning efficacy by looking at the individual performances of the students. Beyond these performances, it would be interesting to explore how a system like HOBIT modifies the interactions between the students, and how it impacts teaching practices. Indeed, education has to be considered in a larger spectrum than learning performance only. This is one axis of development of our current work.

We hope that the approach we have described in this paper will open the way to a new generation of hybrid pedagogical systems used in real conditions at schools or at Universities.

Figure 2 .

 2 Figure 2. A picture of a standard Michelson interferometer where a user is moving the orientation of one of the mirrors. The interference pattern is projected on a screen located on the left of the interferometer (not visible in this image).

Figure 3 Figure 3 .

 33 Figure 3. The HOBIT platform reproducing a Michelson interferometer.

Figure 4 .

 4 Figure 4. The optical replicas in a Michelson interferometer setup. The Arduino board is embedded under the platform on which the mirrors, beam splitter and compensator are fixed.

Figure 4

 4 Figure4illustrates the optical replicas we build for the Michelson interferometer.

Figure 5 .

 5 Figure 5. Examples of ring interference patterns of the low pressure sodium lamp from (a) a standard Michelson interferometer and from (b) the numerical simulation of HOBIT. (c) White light fringes interference pattern obtained with HOBIT.

  (b).

Figure 6 .

 6 Figure 6. (a) Augmented information displayed next to the mirrors. The blue arrow indicates that Mirror 2 is being tilted forward, and the current angle is 0 0 22 00 . The drawing on the left gives an indication of the x orientation of Mirror 2, and the graduated linear scale on top magnifies the current position of Mirror 1. (b) Light path and waves combination.

Figure 7 .

 7 Figure 7. Intensity of the interference pattern at a given location (a) and modulation of contrast (b) can be displayed close to the observed phenomena.

Figure 8 .

 8 Figure 8. Example scenarios. (a) A student measures physically the period of the fringes on the projection screen. (b) Teacher explaining the modulation of contrast.

Figure 9 .

 9 Figure 9. Summary of the protocol. A1, A2, B1, and B2 are the groups of students, PT0 refers to the pre-test, PT1 and PT2 to the post-tests, and UX to the user experience questionnaire. MI refers to the real Michelson interferometer; SMI refers to the Michelson interferometer simulator; and ASMI refers to the interferometer simulator with augmentation.

d

  Mirror 1 and 2 have to be perpendicular and at different distances from the beam splitter. The observed interference rings patterns depend on distance d.

Figure 11 .

 11 Figure 11. Learning results as ratios of students being at different levels of knowledge and skills acquisition-before the experiment (first line), after the first training session (second line), and after the second training session (third line)

  ) and 7).

Figure 12 .

 12 Figure 12. Results of the UX questionnaire (selected questions). The symbol * indicates statistical significant differences between SMI and ASMI.

Figure 13 .

 13 Figure 13. Perceived attractiveness of SMI and ASMI from the Attrakdiff survey[START_REF] Hassenzahl | The Thing and I: Understanding the Relationship Between User and Product[END_REF].

  total of 101 students (82 males and 19 females; mean age: 19.16±0.82 years old) and 6 teachers (5 males and 1 female; mean seniority in teaching position: 18.2±6.2 years old) participated to the study. The students were second-year students of a University institute of technology in optics. The teachers (3 assistant professors, 2 associate professors and 1 university professor) were those in charge of the optics lab work training program. All the teachers were experienced with standard Michelson interferometer teaching. They were all motivated by teaching in practical sessions and confident in their professional skills. All of them declared a professional use of standard digital technologies (e.g. creation of their teaching contents or their presentation slides). On the other hand, they were novice with emerging technologies (e.

g. augmented reality and virtual reality). Before the experiment, the 6 teachers were invited to participate to a presentation and regulation session of the study methods. In order to get familiar with HOBIT, they first experimented with the system, guided by the research team, and they completed the problem-solving task corresponding to the upcoming students lab works. This took approximately 1 hour. After this training time, the mean perception of their a priori capability to use HOBIT during a lab work session was 5.1±2.2 on a Likert scale in 7 levels.

Table 1 .

 1 Distribution of the groups.

	Number of participants	19	27	22	27
	Mean±SD age	19.00±0.75	19.04±0.81	18.95±0.90	19.46±0.71
	Male/Female	13/6	21/6	20/2	22/5

Table 2 .

 2 Pedagogical objectives of the lab work training program

Table 3 .

 3 Knowledge scores for the pre-test (PT0), and the post-tests (PT1 and PT2).

	Groups A1	A2	B1	B2
	PT0 (Mean±SD score, max=5)
	Target knowledge	2.63±1.21	2.59±1.12	2.86±1.25	2.11±1.28
	General definitions	1.66±0.69	1.81±0.95	1.86±0.68	1.51±0.79
	PT1 (Mean±SD score, max=5)
	Target knowledge	3.63±1.16	4.44±0.77	3.72±0.89	3.63±1.47
	General definitions	3.18±0.68	3.28±0.68	3.39±0.46	2.92±0.71
	PT2 (Mean±SD score, max=5)
	Target knowledge	2.32±1.38	4.12±1.13	3.11±1.49	3.48±1.55
	General definitions	3.58±1.09	3.97±0.88	3.92±0.81	3.81±1.00

ACKNOWLEDGMENTS

The authors would like to thank the persons who participated to this project (Benoit Coulais, Jérémy Bergognat, Patrick Reuter, David Lacoste) as well as the teachers and students who participated to the study. This work was financially supported by Idex Bordeaux (CPU and LAPHIA) and Inria.