Lili Gao

Xiaotong Li

Boubacar Traoré

Yalan Zhang

Junjie Fang

Yu Han

Jacky Even

Claudine Katan

Kui Zhao

Frank Liu

Mercouri G Kanatzidis

m-Phenylenediammonium as a New Spacer for Dion-Jacobson 2D Perovskites

Two-dimensional (2D) halide perovskites come in several distinct structural classes and exhibit great tunability, stability and high potential for photovoltaic applications. Here, we report a new series of hybrid 2D perovskites in the Dion-Jacobson (DJ) class based on aromatic m-Phenylenediammonium (mPDA) dications. The crystal structures of the DJ perovskite materials (mPDA)MA n-1 Pb n I 3n+1 (n = 1, 2, 3) were solved and refined using single crystal X-ray crystallography. The results indicate a short I•••I interlayer distance of ~4.00 -4.04 Å for the (mPDA)MA n-1 Pb n I 3n+1 (n = 2 and 3) structures, which is the shortest among DJ perovskites. However, Pb-I-Pb angles are as small as ~158-160º reflecting large distortion of the inorganic framework that results in larger band gaps for these materials compared to other DJ analogues. Density functional theory calculations suggest appreciable dispersion in the stacking direction, unlike the band structures of the Ruddlesden-Popper (RP) phases which exhibit flat bands along the stacking direction. This is a consequence of a short interlayer I•••I distances that can lead to inter-layer electronic coupling across the layers. The solution deposited films (nominal (mPDA)MA n-1 Pb n I 3n+1 compositions of n = 1-6) reveal improved surface coverage with increasing nominal n value with the higher-n films being composed of a mixture of n=1 and bulk 3D MAPbI 3 perovskites. The films made from solutions of these materials behave differently from those of other 2D iodide perovskites and their solar cells have a mixture of n=1 DJ and MAPbI 3 as the light absorbing semiconductors.

Introduction

Halide perovskites are impacting several optoelectronic based technologies such as solar cells, [START_REF] Jung | Efficient, stable and scalable perovskite solar cells using poly(3-hexylthiophene)[END_REF][START_REF] Abdollahi Nejand | Vacuum-Assisted Growth of Low-Bandgap Thin Films (FA0.8MA0.2Sn0.5Pb0.5I3) for All-Perovskite Tandem Solar Cells[END_REF][START_REF] Ahlawat | Atomistic Mechanism of the Nucleation of Methylammonium Lead Iodide Perovskite from Solution[END_REF][START_REF] Alsalloum | Low-Temperature Crystallization Enables 21.9% Efficient Single-Crystal MAPbI3 Inverted Perovskite Solar Cells[END_REF][5] detectors, [START_REF] Liu | A 1300 mm(2) Ultrahigh-Performance Digital Imaging Assembly using High-Quality Perovskite Single Crystals[END_REF][START_REF] Wei | Sensitive X-ray detectors made of methylammonium lead tribromide perovskite single crystals[END_REF][START_REF] Shrestha | Highperformance direct conversion X-ray detectors based on sintered hybrid lead triiodide perovskite wafers[END_REF][START_REF] Stoumpos | Crystal Growth of the Perovskite Semiconductor CsPbBr 3 : A New Material for High-Energy Radiation Detection[END_REF][START_REF] He | High spectral resolution of gammarays at room temperature by perovskite CsPbBr3 single crystals[END_REF] light-emitting diodes, [START_REF] Han | Novel Lewis Base Cyclam Self-Passivation of Perovskites without an Anti-Solvent Process for Efficient Light-Emitting Diodes[END_REF][START_REF] Lee | Improving Performance of Perovskite Solar Cells Using [7]Helicenes with Stable Partial Biradical Characters as the Hole-Extraction Layers[END_REF][START_REF] Du | Highly oriented perovskites for efficient light-emitting diodes with balanced charge transport[END_REF][START_REF] Tsai | Critical Role of Organic Spacers for Bright 2D Layered Perovskites Light-Emitting Diodes[END_REF][START_REF] Zeng | Mixed-ligand engineering of quasi-2D perovskites for efficient sky-blue light-emitting diodes[END_REF] because of their outstanding properties, including high absorption coefficient, [START_REF] Mei | A holeconductor-free, fully printable mesoscopic perovskite solar cell with high stability[END_REF] tunable exciton binding energy (low exciton binding energy for 3D perovskites at RT or tunable exciton binding energies in low-dimensional perovskites), [START_REF] Blancon | Semiconductor physics of organic-inorganic 2D halide perovskites[END_REF] long-range charge transport, [START_REF] Stranks | Electron-Hole Diffusion Lengths Exceeding 1 Micrometer in an Organometal Trihalide Perovskite Absorber[END_REF] low trap density, [START_REF] Yang | Iodide management in formamidinium-lead-halide-based perovskite layers for efficient solar cells[END_REF] high defect tolerance [START_REF] Si | A-Site Management for Highly Crystalline Perovskites[END_REF] and low-cost solution processability. [START_REF] Wang | Accelerated degradation of methylammonium lead iodide perovskites induced by exposure to iodine vapour[END_REF] The record efficiency for the perovskite solar cells currently stands at > 25%. [START_REF] Yoo | Efficient perovskite solar cells via improved carrier management[END_REF] The most common three-dimensional (3D) perovskites adopt a general formula of AMX 3 (A = methylammonium (MA, CH 3 NH 3 + ), formamidinium (FA, CH 3 (NH 2 ) 2 + ), or Cs + ; M = Sn 2+ or Pb 2+ ; X = Cl -, Br -, or I -). The inorganic ions form the octahedral frame with [MX 6 ] 4-, and the small organic cations occupy cuboctahedral voids within the structure and counterbalance the charge of the [MX 6 ] 4-extended anion. [START_REF] Mao | Two-Dimensional Hybrid Halide Perovskites: Principles and Promises[END_REF] When large spacer cations are inserted into the 3D structure along different directions, such as (100), ( 110) and (111) planes, 2D perovskites can be obtained. [START_REF] Mao | Two-Dimensional Hybrid Halide Perovskites: Principles and Promises[END_REF][START_REF] Li | The 2D Halide Perovskite Rulebook: How the Spacer Influences Everything from the Structure to Optoelectronic Device Efficiency[END_REF] These perovskites have impressive structural diversity and great potential in optoelectronic applications. [START_REF] Li | Small Cyclic Diammonium Cation Templated (110)-Oriented 2D Halide (X = I, Br, Cl) Perovskites with White-Light Emission[END_REF][START_REF] Li | Two-Dimensional Dion-Jacobson Hybrid Lead Iodide Perovskites with Aromatic Diammonium Cations[END_REF][START_REF] Chen | 2D Ruddlesden-Popper Perovskites for Optoelectronics[END_REF] The (100)-oriented 2D perovskites are the most common ones, which can be further categorized into the Ruddlesden-Popper (RP) phases, [START_REF] Stoumpos | Ruddlesden-Popper Hybrid Lead Iodide Perovskite 2D Homologous Semiconductors[END_REF] the Dion-Jacobson (DJ) phases, [START_REF] Mao | Hybrid Dion-Jacobson 2D Lead Iodide Perovskites[END_REF] and the alternating cation in the interlayer space (ACI) phases, [START_REF] Soe | New Type of 2D Perovskites with Alternating Cations in the Interlayer Space, (C(NH2)(3))(CH3NH3)(n)PbnI3n+1: Structure, Properties, and Photovoltaic Performance[END_REF] with the general formulas of A′ 2 A n-1 M n X 3n+1 , A′′A n-1 M n X 3n+1 , and A ′

A n M n X 3n+1 , respectively. The A′is monovalent (+1) and A′′ is divalent (+2) large cations, which can intercalate into the anionic sheets of the 2D perovskites. The layer-number n not only enriches the structural complexity of the perovskite family but also allows for the fine-tuning of the optoelectronic properties as they offer tunable natural quantum wells. [START_REF] Blancon | Semiconductor physics of organic-inorganic 2D halide perovskites[END_REF][START_REF] Ke | Compositional and Solvent Engineering in Dion-Jacobson 2D Perovskites Boosts Solar Cell Efficiency and Stability[END_REF][START_REF] Jung | Self-Passivation of 2D Ruddlesden-Popper Perovskite by Polytypic Surface PbI2 Encapsulation[END_REF][START_REF] Jodlowski | Large guanidinium cation mixed with methylammonium in lead iodide perovskites for 19% efficient solar cells[END_REF][START_REF] Hoffman | From 2D to 1D Electronic Dimensionality in Halide Perovskites with Stepped and Flat Layers Using Propylammonium as a Spacer[END_REF][START_REF] Cho | Mixed 3D-2D Passivation Treatment for Mixed-Cation Lead Mixed-Halide Perovskite Solar Cells for Higher Efficiency and Better Stability[END_REF] The RP phases incorporate monovalent spacer cations interdigitating between the layers, and the inorganic layers are usually staggered. In contrast, the DJ phases incorporate short divalent cations and the inorganic layers have the tendency to stack exactly on top of each other. For linear diammonium cations NH 3 (CH 2 ) m NH 3 2+ , [START_REF] Li | Two-Dimensional Halide Perovskites Incorporating Straight Chain Symmetric Diammonium Ions, (NH3CmH2mNH3)(CH3NH3)(n-1)PbnI3n+1 (m=4-9; n=1-4)[END_REF][START_REF] Shen | Centimeter-Sized Single Crystal of Two-Dimensional Halide Perovskites Incorporating Straight-Chain Symmetric Diammonium Ion for X-Ray Detection[END_REF] even when the carbon-chain length is as short as m = 4, the adjacent inorganic layers are still slightly offset because of strong hydrogen-bonding of the cation. For shorter diammonium cation (CH 3 ) 3 NCH 2 CH 2 NH 3 2+ , it can form the DJ phase ((CH 3 ) 3 NCH 2 CH 2 NH 3 )SnI 4 even though it is asymmetric. [START_REF] Xu | CH3)3NCH2CH2NH3]SnI4: A Layered Perovskite with Quaternary/Primary Ammonium Dications and Short Interlayer Iodine-Iodine Contacts[END_REF] When more compact cyclic diammonium cations, such as x-(aminomethyl)piperidinium (AMP, x = 3 and 4), are incorporated, multilayer DJ phases can form with eclipsed octahedra. The aromatic analogues, x-(aminomethyl)pyridinium (AMPY, x = 3 and 4), can also template the DJ phases. [START_REF] Li | Two-Dimensional Dion-Jacobson Hybrid Lead Iodide Perovskites with Aromatic Diammonium Cations[END_REF] When both amino groups are primary amines, such as 1,4phenylenedimethanammonium, the DJ phase can also form in principle. [START_REF] Li | Bifunctional Organic Spacers for Formamidinium-Based Hybrid Dion-Jacobson Two-Dimensional Perovskite Solar Cells[END_REF] However, a conclusive structural determination is lacking partly because of the low solubility of the cation in HI. A similar cation with amino groups directly attached to the phenyl ring, p-phenylenediammonium, forms 1D structure with edge-sharing octahedra, [START_REF] Lemmerer | Two packing motifs based upon chains of edgesharing PbI6 octahedra[END_REF] which suggests symmetric diammonium cations cannot guarantee the formation of the DJ phase, while asymmetric cations may also be able to form the DJ phase. However, the meta analogue, mPDA, does form the n = 1 2D structure for chloride perovskite. [START_REF] Dobrzycki | Inorganic-organic hybrid salts of diaminobenzenes and related cations[END_REF] It offers the opportunity to further expand the family of DJ layered perovskites. The eclipsed stacking and short distance between the layers are also beneficial for the charge transport in photovoltaic devices. The field of the 2D perovskite solar cells with DJ phases has developed rapidly since we reported the first multilayer DJ structures, [START_REF] Mao | Hybrid Dion-Jacobson 2D Lead Iodide Perovskites[END_REF][START_REF] Zhang | Advances in two-dimensional organic-inorganic hybrid perovskites[END_REF][START_REF] Huang | Toward Phase Stability: Dion-Jacobson Layered Perovskite for Solar Cells[END_REF] however, the determination of the single-crystal structures is lagging behind, [START_REF] Ma | 2D Perovskites with Short Interlayer Distance for High-Performance Solar Cell Application[END_REF] therefore detailled crystallographic studies are nowadays priority to expand the DJ family and bring it on the same footing as the RP one. Here, we report a new series of DJ phases with mPDA, forming (mPDA)(MA) n-1 Pb n I 3n+1 (n = 1, 2, 3) 2D perovskites.

Detailed crystallographic investigations show that the inorganic layers stack exactly on top of each other. These materials exhibit smaller average Pb-I-Pb angles than other 2D perovskites using 3AMP, 4AMP and BA. The distorted inorganic framework in turn gives rise to a relatively larger band gap. DFT calculations suggest noticeable band dispersion in the stacking direction because of the small interlayer distance. The optical properties and morphology of (mPDA)(MA) n-1 Pb n I 3n+1 (n = 1-6, nominal composition) perovskite films are suitable for use in solar cell devices but the film formation behavior is different from that of currently known 2D perovskite iodides.

Results and Discussions

Single crystal growth

Single crystals of (mPDA)(MA) n-1 Pb n I 3n+1 (n = 1, 2, 3) were grown using a step-cooling method as reported previously to avoid the precipitation of non-perovskite light-yellow phase. [START_REF] Li | Two-Dimensional Halide Perovskites Incorporating Straight Chain Symmetric Diammonium Ions, (NH3CmH2mNH3)(CH3NH3)n-1PbnI3n+1 (m = 4-9; n = 1-4)[END_REF][START_REF] Li | Three-Dimensional Lead Iodide Perovskitoid Hybrids with High X-ray Photoresponse[END_REF][START_REF] Li | Negative Pressure Engineering with Large Cage Cations in 2D Halide Perovskites Causes Lattice Softening[END_REF] In this method, after everything is dissolved in the solution under heating to a boil, the solution temperature is first lowered to 120°C, which is right below the boiling point of HI (127°C), so that only the desired 2D perovskite phases can grow.

Suitable stoichiometric ratios of PbO and MACl, and sub-stoichiometric ratio of mPDA were dissolved in HI solution for the desired layer-number (n = 2 and 3). For n=1, it is difficult to obtain high quality single crystals directly from HI solution because of the low solubility. Instead, we found that n = 1 chloride perovskite can be easily grown from HCl as (mPDA)PbCl 4 and then be redissolved in HI [START_REF] Dobrzycki | Inorganic-organic hybrid salts of diaminobenzenes and related cations[END_REF] giving high quality (mPDA)PbI 4 crystals. The color of the crystals varies from orange (n = 1) to red (n = 2)

to dark red (n = 3), as shown in Figure S1.

The precise crystal structures of (mPDA)MA n-1 Pb n I 3n+1 (n = 1, 2, 3), shown in Figure 1, were determined using single-crystal X-ray diffraction. Selected crystallographic data and structural refinements for all compounds reported here are listed in Table 1, with more detailed crystallographic data provided in the Tables 23. The compounds were refined in the noncentrosymmetric monoclinic space group (Cc) for n=1 and 2, and noncentrosymmetric orthorhombic space group (Pmc2 1 ) for n = 3. The successful synthesis of the desired n member was further confirmed by powder X-ray diffraction (PXRD), as shown in Figure 2a, and the number of the low-angle peaks below 2θ = 14° is consistent with the expected layer-number. The characteristic diffraction peaks for n = 1, 2, and 3 crystals match well with calculated PXRD, as shown in Figure 2bd.

The n = 1 structure is highly distorted (Figure 1a) and the inorganic layers ar slightly offset, with a layer shift factor of (0.11, 0.12). In an ideal cubic structure, the four adjacent Pb atoms in a plane form a square. In lower symmetry (tetragonal or orthorhombic) structures, two opposite edges of the square are "pulled-in" and the other two are "pushed-out". From the top view, we can see rhombus-shaped voids, such as in the structures of n = 2 and 3 (Figure 1b,c). However, for the n = 1 structure, two adjacent edges are "pushed-out" and the other two are "pulled-in", so from the top view, trapezoid-shaped voids are observed. The Pb atoms are off-centered in the octahedra and the I-Pb-I angle deviate significantly from 90°. The deformation of octahedra can also be seen from the values of bond angle variance (𝜎) calculated by the expression,

σ # = (θ ( -90) # 11 .# (/.
, where 𝜃 1 is the individual I-Pb-I bond angle. The bond angle variance values for n = 1, 2 and 3 structures are 234.2, 1.1 and 3.0, respectively.

The large 𝜎 value for the n = 1 phase originates from the significant deviation of the Pb-I-Pb angles from 90°. This is probably because the aromatic dication spacer is very short and rigid, all the atoms must stay on the same plane except for the Hs on the amino groups that can rotate. It has been reported that some cations cannot form n = 1 perovskite by itself because the size is too small to template the 2D structure, but they can form more proper multilayer 2D perovskites with MA inside the cage. [START_REF] Hoffman | From 2D to 1D Electronic Dimensionality in Halide Perovskites with Stepped and Flat Layers Using Propylammonium as a Spacer[END_REF] We can calculate the lattice mismatch by the difference of the adjacent Pb-Pb distance of the 2D structures with that of the standard MAPbI 3 . [START_REF] Kepenekian | Concept of Lattice Mismatch and Emergence of Surface States in Two-dimensional Hybrid Perovskite Quantum Wells[END_REF] By comparison to other DJ and RP phases, mPDA (n=1) has both the largest mismatch with 3D MAPbI 3 and largest inplane anisotropy (Table 4), which caused large distortion and strain in the structure. By contrast, in the multilayer structures some of this strain can be relieved to an extent because of the templating effect of the A-site cation MA. The n = 1 phase has a much smaller adjacent Pb···Pb distance than the 3D MAPbI 3. When the MA cation is added to the cage to form the multilayer phases, it will expand the cage the adjacent Pb···Pb distance also increases, so the lattice mismatch between the inorganic and organic layers decreases, which helps to relieve the strain. But the trend remains that the mPDA compounds exhibit the largest lattice mismatch. The anisotropy of the structure,

calculated by [Pb 1 -Pb 3 -Pb 1 -Pb 5 ] /[(Pb 1 -Pb 3 + Pb 1 -Pb 5 )/2]
, is also shown in Table 4.

The mPDA compounds exhibit a larger anisotropy compared to the others, which originates from the irregular tilting of the Pb-I-Pb bonds (discussed above). All structures become more isotropic with increasing number of layers, as they become more like 3D MAPbI 3 . The adjacent organic spacer cations adopt a tilted conformation in the n = 1 structure (Figure 1a).

For n = 2 and 3, the inorganic layers with corner-sharing octahedra stack exactly on top of each other, with layer shift factor of (0, 0), [START_REF] Marchenko | Layer Shift Factor in Layered Hybrid Perovskites: Univocal Quantitative Descriptor of Composition-Structure-Property Relationships[END_REF] so they belong to the DJ structural class.

The octahedra are separated by the fully ordered mPDA cations. This is different from most aromatic spacer cations that are usually disordered, [START_REF] Du | Two-Dimensional Lead(II) Halide-Based Hybrid Perovskites Templated by Acene Alkylamines: Crystal Structures, Optical Properties, and Piezoelectricity[END_REF] and the cations need to be refined with restraints of bond lengths and bond angles. The mPDA rings are parallel to the stacking direction and adjacent cations adopt a face-to-edge configuration, which is also seen in the AMPY series. [START_REF] Li | Two-Dimensional Dion-Jacobson Hybrid Lead Iodide Perovskites with Aromatic Diammonium Cations[END_REF] As shown in Figure 1d, the amino groups are pointing to the right and front, leading to a net dipole moment in the structure that results in the noncentrosymmetric space groups.

For 2D perovskites, the interlayer space between inorganic slabs plays a crucial role for electronic band structure of 2D materials and in turn for the out-of-plane charge transport. It has been shown that small interlayer distance can lead to a weak but notable electronic interaction across the interlayer and give rise to a small band dispersion in the stacking direction. [START_REF] Mao | Hybrid Dion-Jacobson 2D Lead Iodide Perovskites[END_REF][START_REF] Li | Two-Dimensional Halide Perovskites Incorporating Straight Chain Symmetric Diammonium Ions, (NH3C mH2 mNH3)(CH3NH3) n-1Pb nI3 n+1 ( m = 4-9; n = 1-4)[END_REF][START_REF] Li | Two-Dimensional Dion-Jacobson Hybrid Lead Iodide Perovskites with Aromatic Diammonium Cations[END_REF][START_REF] Vasileiadou | Insight on the Stability of Thick Layers in 2D Ruddlesden-Popper and Dion-Jacobson Lead Iodide Perovskites[END_REF] The compact cation results in very short non-bonding I···I distance of 4.04 Å and 3.99 Å for n = 2 and 3 structures, respectively. This short I•••I distance between the inorganic layers is expected to be beneficial for carrier transport.

The penetration depth, defined by the distance between the amino group and the plane crossing the terminal iodine atoms, is 0.238 (0.349) Å, 0.404 (0.441) Å and 0.442 Å for the n = 1-3 phases, respectively, which is smaller compared to other DJ phases such as (xAMP)(MA) n-1 Pb n I 3n+1 and (xAMPY)(MA) n-1 Pb n I 3n+1 . This is because the primary amino group is connected to an alkyl linker and is free to rotate, but those of mPDA is rigid, which limits the penetration depth in the (mPDA)(MA) n-1 Pb n I 3n+1 series.

Even though the octahedra in n = 2 and 3 structures are not as distorted as n = 1, they are still highly tilted, especially in the in-plane direction, which can be seen from the small Pb-I-Pb angles. The Pb-I-Pb angle can be further categorized into the equatorial angle which is parallel to the layer and the axial angle which is perpendicular to the inorganic layer. For n = 2 and 3 structures, the axial angles are close to 180°, while the equatorial angles deviate strongly from 180°. So, the average Pb-I-Pb angle is one of the smallest among the reported structures of the same layer-number (Figure 3). It is an indication that the strain caused by lattice mismatch in the n=2 and 3 structures is not relaxed as efficiently as in other DJ phases (Table 4).

Optical Properties and Electronic Structure Calculations

The absorption spectra of the (mPDA)MA n-1 Pb n I 3n+1 (n = 1, 2, 3) exhibit high-energy absorption edges and low-energy exciton peaks (Figure 4a). In our previous works, we extracted the band gaps from the high-energy slope, which also matches the peak positions of the steady-state photoluminescence (PL) spectra. In the case of (mPDA)MA n-1 Pb n I 3n+1 (n = 1, 2, 3), however, since the slope is not very sharp, we estimate the band gaps (E g ) from the PL emission peaks (Figure 4b). The bandgaps decrease with increasing layer thickness, from 2.42 eV, and 2.16 eV to 2.00 eV for the n = 1, 2, and 3 perovskites, respectively. The PL spectra were measured in a single point from the crystal surfaces, as indicated in the photographs shown in Figure S2.

Comparing the band gap and PL trend of this series with those of other reported 2D perovskites of the same layer-number, we find that the (mPDA)(MA)Pb 2). For the n=3 compounds, the band gaps follow the trend mPDA = BA> 4AMP > 3AMP, while for both the equatorial and average Pb-I-Pb angles the trend is mPDA < 4AMP < BA < 3AMP, which suggests that the Pb-I-Pb bond angle is not the only determinant factor.

Previously, we suggested that close interlayer distances via I•••I interactions may result in slight widening of the bandwidth in the stacking direction, through a superlattice effect and concomitant small narrowing of band gap. [START_REF] Li | Two-Dimensional Dion-Jacobson Hybrid Lead Iodide Perovskites with Aromatic Diammonium Cations[END_REF][START_REF] Soe | New Type of 2D Perovskites with Alternating Cations in the Interlayer Space, (C(NH2)(3))(CH3NH3)(n)PbnI3n+1: Structure, Properties, and Photovoltaic Performance[END_REF][START_REF] Li | Two-Dimensional Halide Perovskites Incorporating Straight Chain Symmetric Diammonium Ions, (NH3CmH2mNH3)(CH3NH3)(n-1)PbnI3n+1 (m=4-9; n=1-4)[END_REF] Across the DJ phases with mPDA, 3AMP and 4AMP, the closest I•••I interlayer distance of ∼ 4 Å is found with mPDA compared to the longest of ∼ 7 Å for BA (see Figure 3c). The enhanced electronic interaction across the interlayer in DJ phases indeed counterbalances the effect of larger Pb-I-Pb angle distortions on the band gap. [START_REF] Mao | Hybrid Dion-Jacobson 2D Lead Iodide Perovskites[END_REF]

Electronic Structure Calculations

The band structures of the n = 2 and 3 compounds were obtained from density functional theory (DFT) calculations using the experimental crystallographic structures.

The Generalized Gradient Approximation (GGA) with revised-Perdew-Burke-Ernzerhof (revPBE) functional [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF][START_REF] Zhang | Generalized Gradient Approximation Made Simple[END_REF] was used to describe the exchange-correlation term.

Spin-orbit coupling (SOC) was included in its fully relativistic spin-DFT formalism. [START_REF] Cuadrado | Implementation of noncollinear spin-constrained DFT calculations in SIESTA with a fully relativistic Hamiltonian[END_REF] Additional corrections of the band gaps, using the revisited Slater half-occupation

Wavelength (nm)

technique in the so-called DFT-1/2 implementation [START_REF] Ferreira | Approximation to density functional theory for the calculation of band gaps of semiconductors[END_REF][START_REF] Tao | Accurate and efficient band gap predictions of metal halide perovskites using the DFT-1/2 method: GW accuracy with DFT expense[END_REF] , were performed and they generally exhibit a similar trend as with revPBE (Figure S3, Table S1). More computational details and results can be found in SI.

The band gaps of the DJ compounds are slightly indirect around the high-symmetry k points (Y, X or Z) due to slight Rashba spinor splitting as a result of the noncentrosymmetric nature of their space groups combined with the presence of giant spin-orbit coupling (Figure 5). The calculated band gaps for the mPDA n = 2 and n = 3 compounds are 0.92 eV and 0.86 eV, respectively, thus exhibiting a decreasing quantum confinement effect consistent with experimental results (Figure 4a,b). It is well known that DFT tends to underestimate the band gaps. Unlike the band structures of the Ruddlesden-Popper (RP) phases (Figure 5e), which exhibit flat bands in the stacking direction (Г-Y), the band structures of the DJ phases show clear band dispersions along those directions in the Brillouin zone (Table 5). For instance, this can be seen in the mPDA compounds along Y-M x and Г-X directions of the Brillouin zone for n = 2 and 3, respectively (Figure 5a,b). This is related to the short interlayer distance, especially when the closest I•••I distance is similar to the van der Waals radii, that can lead to interlayer electronic coupling across the layers, with anti-bonding character at the high symmetry k-point. [START_REF] Li | Two-Dimensional Dion-Jacobson Hybrid Lead Iodide Perovskites with Aromatic Diammonium Cations[END_REF][START_REF] Li | Two-Dimensional Halide Perovskites Incorporating Straight Chain Symmetric Diammonium Ions, (NH3CmH2mNH3)(CH3NH3)n-1PbnI3n+1 (m = 4-9; n = 1-4)[END_REF] This should be beneficial to the charge transport along the stacking direction even though the charge mobility is still expected to be much larger in the in-plane direction (Table 5). The valence band maximum (VBM) mainly consists of the hybridization between I 5p-orbitals and Pb 6s-orbitals , while the conduction band minimum (CBM) is dominated by the Pb 6p-orbitals with a little contribution of I 5p-orbitals (Figure S4), as expected from space group symmetries in 2D perovskites. [START_REF] Blancon | Semiconductor physics of organic-inorganic 2D halide perovskites[END_REF] Since the I orbitals mainly contribute to the VBM, the close I•••I distance leads to stronger band dispersion in the VBM than in the CBM. The band dispersion increases with increasing layer-number, as the materials becomes more 3D like. It is also worth noting that unlike other aromatic cations, the molecular orbitals of the organic spacer do not show up in the gap, which corresponds to a Type I quantum well structure in all cases. The calculated effective masses of the electrons and holes in the in-plane direction are shown in Table 5. The 3AMP compounds show the smallest effective masses, comparable to those of the BA compounds, which can be attributed to their large equatorial Pb-I-Pb angles close to 180°.

Comparing the band structures of (mPDA)(MA)Pb 2 I 7 with those of (3AMP)(MA)Pb 2 I 7 (4AMP)(MA)Pb 2 I 7 and (BA) 2 (MA)Pb 2 I 7 , we find that the DJ phases all show larger band dispersion than the RP phase in the stacking direction (Table 5). The calculated band gaps follow the experimental trend with E g (mPDA) > E g (4AMP) > E g (3AMP).

As discussed above, when the interlayer distances are similar, the Pb-I-Pb angle distortion is the main factor that can influence the band gap. Since the mPDA compound has the smallest Pb-I-Pb angle, followed by the 4AMP and then the 3AMP, the higher distortion level leads to less overlap between the Pb and I orbitals, thus higher band gap.

Film properties and solar cell devices

Although single phase sample of the higher members of the series (mPDA)MA n- 1 Pb n I 3n+1 (n=4-6) were not prepared in this work, thin films aiming at various 2D perovskite compositions corresponding (mPDA)MA n-1 Pb n I 3n+1 (n=1-6) were fabricated by dissolving stoichiometric ratios of the reactant precursors in N,N-Dimethylformamide (DMF). All the n values discussed in this part correspond to nominal or targeted values in thin films, but not necessarily to well defined layernumbers as in n=2,3 pure 2D perovskite single crystals. The optical absorption edges of the resulting films shift rather quickly to higher wavelengths (Figure 6a). However, the absorption peak characteristic of the n = 1 phase at 493 nm is also observed for films of different nominal n numbers but its intensity is gradually decreased. This

M Y Г A YM x Y 0 3 2 1 0 -1 Energy (eV) Z X U Y X X R S Г 3 2 1 0 -1 Energy (eV) (a) (b) (c) (d) (e)
indicates a co-existence of n=1 and 3D bulk phases in (mPDA)MA n-1 Pb n I 3n+1 (n = 2-6) films because of a fast dynamical crystallization process. Moreover, our crystallographic study of n=2 and n=3 crystals shows that strain accumulation is not completely released for intermediate n values, as indicated by sizeable octahedral tilting and lattice mismatch compared to other 2D phases (Table 4). It is therefore not totally surprising that pure multilayered 2D phases are not favored in thin films.

The photoluminescence (PL) spectra of the films illuminated from the front side exhibit two peaks, as shown in Figure 6b. The n = 1 emission located at 512 nm decreases its intensity with increasing targeted n number of (mPDA)MA n-1 Pb n I 3n+1 (n = 2-6) films, which is consistent with the decreased absorption intensity mentioned above and suggests decreased fraction of the n =1 phase. The second emission peak is around 773 nm, which is associated with the 3D bulk phase. These observations indicate that expected solution-casting of (mPDA)MA n-1 Pb n I 3n+1 (n = 2-6) films tend to yield mixed phases of n = 1 and 3D. The change in the precursor solution only tune the ratio between those phases, but since there is no intermediate multilayer phases formed on the fim, the absorption and PL spectra do not shift with the nominal "n" value. This is also verified from XRD (Figure 6c). The n = 1 phase can be observed for n ≤ 4 films.

While for n = 5 and 6 films, there is no distinct n = 1 diffraction peaks, which does not preclude the existence of n = 1 phase, instead it suggests sufficiently coherent crystallographic regions are not present in these films.

The SEM images of (mPDA)MA n-1 Pb n I 3n+1 films indicate that the n = 1 film exhibits poor coverage because of randomly stacked plate crystals of the n=1 phase with grain size of ~1-5 µm, Figure S5. Although the higher n films show improved surface coverage because the grain sizes of the n=1 phase which is present in them decrease to ~200-500-nm, we still observed severe phase separation with some long 2D plates randomly interspersed within small grains. The above results are consistent with the optical absorption spectroscopy observations that higher nominal n perovskite films tend to form a mixed phase of n = 1 2D and bulk 3D phases.

In addition, we investigated the light, heat, and humidity stability of (mPDA)MA n- 1 Pb n I 3n+1 (n = 1-6, nominal composition) films under the following conditions. The continuous light illumination test was conducted in air (temperature 22 ℃, humidity 35%) under standard 1 sun light intensity (AM 1.5G irradiation, 100 mW/cm 2 ). The long heating stability was conducted on a hot plate with temperature of 85 ℃, which placed in air (temperature 22 ℃, humidity 35%). The high humidity stability was conducted in a closed box with temperature of 22 ℃ and humidity of 85%. All stability tests were done with as-fabricated films without any encapsulation. The results are shown in Figure S6, S7 and S8. The mixed films (n ≥ 2) exhibit considerable heating stability lasting for over 30 hours before thorough decomposition (Figure S6). For the light stability, films with n ≥ 2 kept black color until continuous illumination over 20 hours, film with n = 1 decomposed after 10 hours illumination (Figure S7). It is worth noting that the higher nominal n members do not exhibit the best stability performance.

It is the middle members of n = 3 and 4 that exhibit the best stability. The films do not exhibit great stability under high humidity of 85% (Figure S8), and some new phases form after 1 h. It is possible that the perovskite phase on the film interacts with the H 2 O molecules and form a hydrate phase, since the 1,4PDA analogue is known to form the hydrates. This suggests a sealed in the device architecture or encapsulation, but a full undestaing and assessment of stability will requires considerably more optimization future exploration.

The PXRD and optical results discussed above (Figure 6a-c) suggest that dissolving the chemical precursors and then casting films of nominal n compositions does not give rise to the pure targeted 2D phases themselves but rather a combination of 2D n=1 phase and 3D MAPbI 3 in various fractions. Therefore, any solar cells prepared from the solutions will reflect this property. In this context, we also evaluated the preliminary photovoltaic performance of such films. Planar solar cells were fabricated with an architecture of FTO/TiO 2 /perovskite/ spiro-OMeTAD/Au for (mPDA)MA n-1 Pb n I 3n+1 (n = 1-6) perovskite films. The efficiencies (PCEs) gradually increase from 0.01% to 6.16% with increasing n number from 1 to 6 for (mPDA)MA n-1 Pb n I 3n+1 (n = 1-6) perovskite devices (Figure 6d, Table S2). The negligible photovoltaic outcome of devices with low n values can be attributed to poor surface coverage and the light absorption limitation of the wide band gap n = 1 phase. As the nominal n value increases, there is beneficial generation and dissociation of charges, giving significant increases in the short-circuit current density (J sc ) from 1.73 to 14.74 mA cm -2 , open-circuit voltage (V oc ) from 0.03 to 0.82 V and fill factor (FF) from 0.23 to 0.51. The stability of the unencapsulated devices examined under ambient conditions environment (20 ºC, humidity of 40 RH%) was improved compared to the unencapsulated films. Devices with nominal n = 6 showed better stability than lower n value, as shown in Figure S9.

This can be ascribed to poor film quality for the lower n film, where the large amount of grain boundaries accelerates moisture attack. of methylammonium chlorine (MACl) and 77.9 mg (0.6 mmol) of mPDA were added directly to the above solution under heating and stirring until dissolved totally. Then the temperature was cooled to 120 °C, and dark red crystals precipitated. The product was isolated by suction filtration followed by drying on the filtration funnel for 30 min.

Yield: 469 mg (36.1% based on total Pb content). Steady-state photoluminescence (PL) (excitation at 510 nm, front-side excitation) and time-resolved photoluminescence (TRPL) (excitation at 510 nm, front-side excitation)

Crystal Materials

were measured with a PicoQuant FT-300. Film XRD were carried out in a θ-2θ configuration with a scanning interval of 2θ between 3° and 60° on a Rigaku Smart Lab (X-ray Source: Cu Kα; λ = 1.54 Å). Film TG measurement was conducted by thermoanalyzer systems from 20-500 °C. The J-V cures were collected in air without any encapsulation using a Keithley 2400 source meter under simulated AM 1.5G irradiation (100 mW/cm 2 ) generated by a standard solar simulator. The light intensity

Figure 1 .

 1 Figure 1. Crystal structures of (mPDA)MA n-1 Pb n I 3n+1 , (a) n = 1, (b) n=2 and (c) n=3, (d) the zoom of the spacer part in (c).

Figure 2 .

 2 Figure 2. (a) Experimental PXRD patterns of (mPDA)MA n-1 Pb n I 3n+1 (n=1, 2, 3) crystals. Calculated and experimental PXRD for the (mPDA)MA n-1 Pb n I 3n+1 , (b) n = 1, (c) n = 2, (d) n = 3.

Figure 3 .

 3 Figure 3. Comparison for (mPDA)MA n-1 Pb n I 3n+1 , (3AMP)(MA) n-1 Pb n I 3n+1 , (4AMP)(MA) n-1 Pb n I 3n+1 , and (BA) 2 (MA) n-1 Pb n I 3n+1 , (n = 2 and 3), (a) average equatorial Pb-I-Pb angles, (b) average axial and equatorial Pb-I-Pb angles. (c) I···I interlayer distances.

  2 I 7 compound shows higher band gap than (BA) 2 (MA)Pb 2 I 7 (BA = butylammonium) and (xAMP)(MA)Pb 2 I 7 (x = 3 and 4), Figure 4c. For the n=3 set, the PL emission energy decreases as follows (mPDA)(MA) 2 Pb 3 I 10 ~ (BA) 2 (MA) 2 Pb 3 I 10 > (4AMP)(MA) 2 Pb 3 I 10 > (3AMP)(MA) 2 Pb 3 I 10 , Figure 4d. It is known that the Pb-I-Pb angles directly influence the band gap where smaller angles lead to less overlap of the Pb 6s and I 5p orbitals, resulting in higher bang gap. 56, 57 The average Pb-I-Pb angles for n = 2 and 3 phases follow the trend that mPDA < 4AMP < BA< 3AMP, as shown in Figure 3a, b. In the DJ phases, all the axial Pb-I-Pb angles are close to 180°, so the difference in the average Pb-I-Pb angles mainly comes from the equatorial ones (Table

  For the DJ phases, all axial Pb-I-Pb angles are close to 180° and the equatorial angles present main deviations from 180°. All DJ phases exhibit smaller equatorial Pb-I-Pb angles than the RP phases (BA compound), but the 3AMP compounds still show the lowest band gap for both n = 2 and 3 thanks to sizeable superlattice effects related to short I•••I interlayer distances.

Figure 4 .

 4 Figure 4. Optical properties of the (mPDA)MA n-1 Pb n I 3n+1 (n=1, 2, 3) perovskites crystals. (a) Optical absorption spectra. (b) Steady state photoluminescence (PL) spectra. Comparison of the PL spectra for the (c) n = 2 and (d) n = 3 2D perovskites (mPDA)MA n-1 Pb n I 3n+1 , (3AMP)(MA) n-1 Pb n I 3n+1 , (4AMP)(MA) n-1 Pb n I 3n+1 , and (BA) 2 (MA) n-1 Pb n I 3n+1 . (Note that the PL spectra of mPDA is bold so it can be seen when overlapping with BA)

Figure 5 .

 5 Figure 5. DFT calculations (with revPBE) of band structures for (mPDA)MA n-1 Pb n I 3n+1 with n number of (a) n = 2, (b) n = 3, compared with the band structures of (c) (3AMP)MAPb 2 I 7 , (d) (4AMP)MAPb 2 I 7 and (e) (BA) 2 MAPb 2 I 7 .

Figure 6 .

 6 Figure 6. Film properties of (mPDA)MA n-1 Pb n I 3n+1 (n = 1-6), (a) UV-Vis absorption

  Characterization. Single-crystal X-ray diffraction experiments were performed using a STOE IPDS II or IPDS 2T diffractometer with Mo Kα radiation (λ = 0.71073 Å) and operating at 50 kV and 40 mA. Integration and numerical absorption corrections were performed using the X-AREA, X-RED, and X-SHAPE programs. The structures were solved by charge flipping and refined by full-matrix least-squares on F2 using the Jana2006 package. The PLATON software46 was used to identify the twinning domains and validate the space groups of the compounds. Powder X-ray diffraction measurements were carried out on a Rigaku MiniFlex600 X-ray diffractometer (Cu Kα radiation, λ = 1.5406 Å) operating at 40 kV and 15 mA. Optical diffuse reflectance measurements were performed using a Shimadzu UV-3600 UV-vis-NIR spectrometer operating in the 200-1000 nm region using BaSO 4 as the reference of 100% reflectance. The band gap of the material was estimated by converting reflectance to absorption according to the Kubelka-Munk equation:α/S = (1-R) 2 (2R) -1 ,where R is the reflectance and α and S are the absorption and scattering coefficients, respectively. Steady-state PL spectra were tested by HORIBA LabRAM HR Evolution confocal RAMAN microscope with 473 nm laser.Solar Cell Device Fabrication. The FTO-coated glass substrates (Pilkington, 15 Ω sq -1 ) were cleaned by ultrasonic bath sequentially with acetone, ethyl alcohol, and deionized water for 15 min respectively, followed by a 15 min UV Ozone treatment. The electronic transport layer of TiO 2 was prepared by chemical bath deposition with the clean substrate immersed in a 0.2 M TiCl 4 aqueous solution with the at 70 °C for 1 h.Before the perovskite films preparation, the cleaned FTO/TiO 2 substrates were exposed to ultraviolet light and ozone for 10 min. Precursor solutions were made by mixing mPDAI 2 , MAI and PbI 2 in stoichiometric ratio with the formula of (mPDA)MA n- precursor solution was dropped on the TiO 2 surface and spin-casted at a low speed of 500 rpm for 3 s followed by a high speed of 4000 rpm for 60 s, and at ca. 45 s before the end of the last spin-coating step, 300 µL of chlorobenzene solvent was dropped onto the substrate. Then films were annealed at 100°C for 10 min. The spiro-MeOTAD solution was prepared by dissolving 72.3 mg of spiro-MeOTAD in 1 ml of chlorobenzene, to which 28.8 µl of 4-tert-butylpyridine and 17.5 µl of lithiumbis(trifluoromethanesulfonyl)imide(Li-TFSI) solution (520 mg LI-TSFI in 1 ml acetonitrile, Sigma-Aldrich, 99.8%) were added. The spiro-MeOTAD solution was spin coated on perovskite films with the speed of 5000 rpm for 30 s. At last, 80 nm Au was evaporated. The active area of the device was 0.09 cm 2 .Thin Film and Solar Cell Device Characterization. SEM images were characterized by SEM (FE-SEM; SU-8020, Hitachi) at an acceleration voltage of 3 kV. UV-visible absorption spectra were acquired on a PerkinElmer UV-Lambda 950 instrument.

  and -2.99 e•Å -3 0.85 and -0.77 e•Å-3

Table 1 .

 1 Crystal and Refinement Data for (mPDA)(MA) n-1 Pb n I 3n+1 (n = 1-3). (mPDA)PbI 4 (mPDA)(MA)Pb 2 I 7 (mPDA)(MA) 2 Pb 3 I 10

	Crystal system	monoclinic	monoclinic	orthorhombic
	Space group	Cc	Cc	Pmc2 1
	Unit cell dimensions	a = 21.727(3) Å b = 9.3607(8) Å c = 7.9858(11) Å β = 105.885(10)°	a = 34.682(3) Å b = 8.8518(9) Å c = 8.7227(7) Å β = 104.491(6)°	a = 23.118(5) Å b = 8.8462(18) Å c = 8.7530(18) Å
	Volume	1562.1(3) Å 3	2592.6(4) Å 3	1790.0(6) Å 3
	Z	4	4	2
	Density (calculated)	3.5078 g/cm 3	3.7018 g/cm 3	3.8273 g/cm 3
		-27<=h<=29	-47<=h<=47	-30<=h<=31
	Index ranges	-12<=k<=12	-12<=k<=12	-12<=k<=12
		-10<=l<=10	-11<=l<=10	-12<=l<=11
	Independent reflections 2948 [R int = 0.1]	4480 [R int = 0.0648] 3110 [R int = 0.0611]
	Completeness to θ = 25°	100%	99%	97%
	Data / restraints / parameters	2948 / 18 / 75	4480 / 15 / 115	3110 / 8 / 86
	Goodness-of-fit	3.81	4.12	1.53
	Final R indices
	[I>2σ(I)]

Table 2 .

 2 Summary of Pb-I-Pb Bond Angles.

	(mPDA)PbI 4		(mPDA)(MA)Pb 2 I 7		(mPDA)(MA) 2 Pb 3 I 10
	Label	Angles (°) Label	Angles (°)	Label	Angles (°)

Table 3 .

 3 Summary of Pb-I Bond Lengths.

		(mPDA)PbI 4	(mPDA)(MA)Pb 2 I 7	(mPDA)(MA) 2 Pb 3 I 10
	Label	Distances (Å) Label	Distances (Å) Label	Distances (Å)

Table 4

 4 Summary of the lattice mismatch.

			mPDA	3AMP 29	4AMP 29	BA 28, 63
		Pb 1 -63 Pb 3	9.361	9.213	9.170 / 8.881	8.863
	n=1	Pb 1 -Pb 5	7.986	8.673	8.559 / 8.858	8.682
		mismatch 50, 64	-2.5%	+0.5%	-0.3%	-1.3%
		anisotropy	14%	6%	7%	2%
		Pb 1 -Pb 3	8.852	8.861	8.844	8.947
	n=2	Pb 1 -Pb 5	8.723	8.858	8.841	8.859
		mismatch	-1.2%	-0.4%	-0.6%	+0.7%
		anisotropy	1.4%	0.0%	0.0%	1.0%
		Pb 1 -Pb 3	8.846	8.862	8.836	8.927
	n=3	Pb 1 -Pb 5	8.753	8.862	8.835	8.878
		mismatch	-1.1%	-0.4%	-0.7%	+0.1%
		anisotropy	1.1%	0.0%	0.0%	0.6%

Table 5 .

 5 Summary of the electronic band structure calculations with revPBE. a. Band dispersion in the stacking direction b. Average effective mass in the in-plane direction

			Band	Band dispersion a	Effective mass (m 0 ) b
	Cation		gap (eV)		(meV)
				VBM	CBM	m h	m e	µ
		n=2	0.92	63	27	0.26	0.20	0.11
	mPDA
		n=3	0.86	67	79	0.19	0.17	0.09
		n = 2	0.93	1	<1	0.21	0.14	0.085
	BA
		n = 3	0.70	1	1	0.14	0.12	0.066
	4AMP	n=2	0.66	53	25	0.22	0.18	0.10
		n=3	0.69	87	45	0.18	0.16	0.08
	3AMP	n=2	0.44	43	32	0.15	0.13	0.07
		n=3	0.35	70	46	0.18	0.14	0.08

Pb n I 3n+1 (n = 1-6). Then an appropriate amount of (mPDA)MA n-1 Pb n I 3n+1 (n = 3)

ACKNOWLEDGMENTS

This work was funded by the National Key Research and Development Program of China (2017YFA0204800), the National Natural Science Foundation of China (62004121), the DNL Cooperation Fund CAS (DNL180311), the 111 Project (B14041) and the Changjiang Scholars and Innovative Research Team (IRT_14R33). At Northwestern University work (synthesis, X-ray diffraction and solar cell fabrication) was supported by ONR grant N00014-20-1-2725. ISCR thanks Dr. S. Tao (Eindhoven University of Technology) for providing the source code of the DFT-1/2 program. B.T. and C.K. acknowledge funding from the European Union's Horizon 2020 program, through an Innovation Action under the grant agreement No. 861985 (PEROCUBE). J.E. acknowledges the financial support from the Institut Universitaire de France. The calculation work was granted access to the HPC resources of [TGCC/CINES/IDRIS] under the allocation 2020-A0080911434 made by GENCI.

was calibrated by using an NREL-certified monocrystalline Si reference cell to reduce the spectral mismatch.

ASSOCIATED CONTENT

Supporting Information

The materials characterization, crystallographic details of (mPDA)MA n-1 Pb n I 3n+1 (n = 1, 2, 3), computational details, projected density of states, additional results from DFT-1/2 calculations, SEM images and device stability.

X-ray crystallographic data for (mPDA)PbI 4 (CIF). X-ray crystallographic data for (mPDA)MAPb 2 I 7 (CIF). X-ray crystallographic data for (mPDA)MA 2 Pb 3 I 10 (CIF).

AUTHOR INFORMATION Corresponding Authors

m-kanatzidis@northwestern.edu szliu@dicp.ac.cn Author Contributions † These authors contributed equally to this work.

Notes

The authors declare no competing financial interest.


Gaëlle Fiard
email: gfiard@chu-grenoble.fr

Introduction:

Simulation-based training has proven to be a promising option allowing for initial and continuous training while limiting the impact of the learning curve on the patient.

The Biopsym simulator was developed as a complete teaching environment for the prostate biopsy procedure. This paper presents the results of an external validation of this simulator, involving urology residents recruited during a regional teaching seminar.

Methods:

Residents from 4 academic urology departments of the French Auvergne Rhône-Alpes region, who did not take part in the previous simulator validation studies, were enrolled.

After a short presentation and standardized initiation session, residents carried out a simulated systematic 12-core biopsy procedure and were asked to fill in a questionnaire collecting their expectations and evaluation of the Biopsym simulator. The number of biopsies reaching each targeted sector, the total score provided by the simulator and the duration of the procedure were recorded.

Results: Twenty-three residents were recruited. The overall added value (/100) for learning was rated at a median of 100 (interquartile range 83-100), overall realism of the biopsy procedure at 80 (65-89). The median percentage of biopsies reaching the targeted sector was n'était pas statistiquement significative. La durée médiane d'une procédure était de 4 :58 (minutes:secondes) (3 :49 -6:00). Les internes plus expérimentés étaient plus rapides que les internes non ou peu expérimentés 3 :53s (3 :39 -4 :56) vs 5 :10 (4 :59 -7 :10), p=0,01.

Conclusions : Cette étude de validation externe confirme une forte acceptation du simulateur par ses utilisateurs cibles. À notre connaissance, le simulateur Biopsym est le seul simulateur de biopsies prostatiques ayant fait la preuve de sa validité en dehors du centre à l'origine de son développement.

66.7% (62-75). The median score provided by the simulator was 50% (37-60). For both, the difference between residents with or without prior biopsy experience was not statistically significant. The median duration of the simulated biopsy procedure was 4:58 (minutes:seconds) (3:49 -6:00). Resident with prior experience required less time to complete the biopsy procedure 3:53 (3:39 -4:56) vs 5:10 (4:59 -7:10), p=0.01.

Conclusion:

This external validation study confirms a high acceptance of the simulator by the target audience. To our knowledge, the Biopsym simulator is the only prostate biopsy simulator that demonstrated such validity as evaluated by clinicians, outside the center involved in its early development.

Résumé

Introduction : La simulation chirurgicale s'impose progressivement comme une option intéressante permettant l'apprentissage initial et l'entraînement à une technique chirurgicale tout en diminuant l'impact de la courbe d'apprentissage sur le patient. Le simulateur Biopsym propose un environnement pédagogique complet pour l'apprentissage du geste de biopsies prostatiques. Nous présentons ici les résultats de la validation externe de ce simulateur, conduite auprès d'internes en urologie recrutés à l'occasion d'une journée de formation régionale.

Méthodes : Des internes de 4 services universitaires d'urologie de la région Auvergne-Rhône-Alpes, n'ayant pas pris part aux précédentes études de validation du simulateur, ont été inclus.

Après une courte présentation et une étape d'initiation standardisée, les internes réalisaient une procédure de 12 biopsies systématisées simulée, puis remplissaient un questionnaire recueillant leurs attentes et l'évaluation du simulateur Biopsym. Le nombre de biopsies atteignant chaque secteur prostatique, le score total donné par le simulateur et la durée de la procédure simulée étaient recueillis.

Résultats : Vingt-trois internes ont été inclus. L'apport global pour la formation (/100) était évalué à une médiane de 100 (écart interquartile 83-100), le réalisme global de la procédure à 80 (69-89). Le pourcentage médian de biopsies atteignant la zone visée était de 66,7% (62-75). Le score médian attribué par le simulateur était de 50% (37-60). La différence pour ces deux scores selon l'existence ou non d'une expérience préalable des biopsies prostatiques

Introduction

Systematic prostate biopsy is a key modality in the prostate cancer diagnostics pathway [START_REF] Rozet | French ccAFU guidelines -update 2020-2022: prostate cancer[END_REF]. This is supported by present evidence, which confirms improved detection of significant prostate cancer by a combination of both systematic and MRI-targeted biopsies if indicated [START_REF] Rouvière | Use of prostate systematic and targeted biopsy on the basis of multiparametric MRI in biopsy-naive patients (MRI-FIRST): a prospective, multicentre, paired diagnostic study[END_REF]. Thus, there is a persistent need for high-quality systematic biopsy and improved training programs.

The even distribution of systematic prostate biopsies is key to avoid missing or under sampling significant prostate cancer [START_REF] Mozer | Mapping of transrectal ultrasonographic prostate biopsies: quality control and learning curve assessment by image processing[END_REF]. So far, training offered to urology residents consist in the performance of several biopsy procedures under the supervision of a mentor. No feedback is provided on the actual distribution of the biopsies, and the pathology report only documents the presence or absence of cancer. A previous study aiming at defining the learning curve of the systematic biopsy procedure has suggested that 12 procedures were needed to reach a plateau, but this number should probably be interpreted with caution as the criterion used to define proficiency (total biopsy core length on pathological examination) does not necessarily imply improved biopsy distribution, as supported by a stable cancer detection rate throughout the study period [START_REF] El Fegoun | The learning curve of transrectal ultrasound-guided prostate biopsies: implications for training programs[END_REF].

Simulation-based training has proven to be a promising option allowing for initial and continuous training while limiting the impact of this learning curve on the patient. However, many commercialized simulation tools are lacking proper validation, and their added value both as a training and as an evaluation tool are yet to be demonstrated [START_REF] Fiard | Simulation-based training in urology: A systematic literature review[END_REF].

The Biopsym simulator was developed as a complete teaching environment for the prostate biopsy gesture, including several exercises designed to cover training needs [START_REF] Schout | Validation and implementation of surgical simulators: a critical review of present, past, and future[END_REF], and the possibility to virtually replicate the performance of a systematic, 12-core transrectal prostate biopsy procedure. Previous validation studies have shown that the simulator was capable of discriminating between experts and novices, and that skills acquired on the simulator could be reproduced in a real-life situation [START_REF] Fiard | Validating the Transfer of Skills Acquired on a Prostate Biopsy Simulator: A Prospective, Randomized, Controlled Study[END_REF]. Simulation-based training also proved to be superior to conventional training in this randomized study. However, all previous validation studies have been performed in the urology department involved in the simulator design.

We present here the results of an external validation of the Biopsym simulator, involving urology residents recruited during a regional teaching seminar and not involved in the previous simulator validation studies.

Methods

Participants

Participants were urology residents from the French Auvergne-Rhône-Alpes region, originating from 4 urology academic departments (Lyon, Saint Etienne, Clermont Ferrand, and Grenoble), recruited during a regional teaching seminar in October 2019. Residents from Grenoble could only be included if they had not already completed their rotation in the urology department involved in the previous simulator validation studies. Residents were prospectively enrolled, and stratified in two groups according to their prior biopsy experience based on their number of years of training: no or little experience (Post Graduate Year PGY 1-2) and significant prior experience (PGY 3-4-5).

Simulator

The current version of the Biopsym simulator is presented in Figure 1. Trainees can manipulate a mock transrectal ultrasound probe to navigate real prostate ultrasound volumes acquired during 14 transrectal biopsy procedures, representing a range of shapes, gland sizes and difficulties such as artefacts and calcifications. A dedicated software enables the user to simulate a complete biopsy procedure, using the keypad to retrieve samples, and obtain visual feedback and a score evaluating their performance.

Prostate biopsy procedure simulation

Residents were offered a short presentation and standardized initiation session, with the same supervisor, allowing them to familiarize themselves with the simulator features.

Once at ease with the use of the simulator, they were asked to autonomously perform a simulated 12-core systematic prostate biopsy procedure. The entire session for each resident lasted about 20 minutes.

Evaluation questionnaire

After completing the simulated systematic biopsy procedure, but before any performance feedback was given, residents were asked to complete an evaluation questionnaire divided into 3 parts (Appendix, in English and French).

The first part asked for information about the resident: name, age, dominant hand, sex, experience in prostate biopsy, targeted biopsy experience, video games proficiency.

The second part collected their opinions about the simulator in terms of added value for learning, simulator realism, interface realism, amplitude realism and force feedback realism.

The third part gathered the expectations of the residents regarding the usefulness of such simulation-based training for prostate biopsies in terms of initial teaching of the procedure, continuous training, performance feedback, performance improvement and graduation. For the second and the third parts of the questionnaire, visual scales were used and translated into 0 to 100 scores.

Training outcomes

At the end of the simulated procedure, but after filling in the evaluation questionnaire, residents were provided with feedback on their performance. This included visual feedback with a 3D representation of the prostate contour with their biopsy trajectories, and numerical feedback. The duration of the simulated procedure was also recorded.

Numerical feedback was given using two scores. A score in % was provided by the simulator software. This score takes into account the length of each simulated biopsy core correctly placed inside the considered sector (for example, the left lateral base sector). A score of 100% thus implies that all biopsies are entirely located within their targeted sector. Given the globally low level of experience of the trainees involved and their high likelihood of obtaining low scores, we added another score simply considering the rate of biopsies correctly reaching the targeted sector (i.e., the proportion of biopsies where at least the needle tip reached inside the targeted sector), in order to better analyze the differences between residents according to their previous biopsy experience and avoid the negative educational impact of receiving a low score. The way scores were calculated was not revealed to the residents during their session and did not bias the evaluation as the scores were communicated after the questionnaire was completed.

Statistical analyses

Results are presented as medians and interquartile ranges (IQR). A non-parametrical test (Wilcoxon-Mann-Whitney) was used to compare the scores obtained by residents according to their prior biopsy experience, and the Kruskall-Wallis test for the comparison of results between centers. Statistical analyses were conducted using R (version 4.0.3; The R Foundation for Statistical Computing, http://www.R-project.org), with statistical significance defined at p <0.05.

Results

Participants

Twenty-three residents were recruited, 11 having no or little prior biopsy experience and 12 with previous biopsy experience. The median age was 28 (28-30), and 6 participants were women (26%). Three residents (13%) were left-handed. A detailed description of the participants is provided in Table 1. Of interest, 52% of the residents had previously performed targeted biopsies using an MRI/ultrasound fusion device also providing feedback on the location of the biopsies during a biopsy procedure on a patient.

External validation of the Biopsym simulator

The results of the evaluation of the simulator by the 23 residents are provided in Figure 2. The usefulness of the simulator for initial training was rated at a median of 100 for an interquartile range (83-100), overall biopsy procedure realism at 80 (65-89), quality of the graphical user interface at 95 (87-100), realism of the ultrasound images at 87 (69-98), realism of the ultrasound probe range of motion at 87 (72-97) and force feedback realism at 72 (47-88). These scores did not statistically differ between residents with no/little experience and residents with significant prior experience (all p-values>0.05).

The expectations of the residents regarding the use of simulation for the initial teaching of the biopsy procedure are summarized in Figure 3.

The usefulness of such a tool for initial procedure teaching and performance improvement was rated at a median of 97 (87-100) and 96 (71-100), respectively. Use of the simulator for continuous training was also supported, with a median score of 88 (73-100) as well as performance feedback 90 (71-100), and potential use as an evaluation tool for graduation purposes, with a median score of 77 (51-87). The expectations did not statistically differ between the two groups « no or little experience » and « significant prior experience » (all p-values>0.05).

Training outcomes and scores

An example of the visual feedback obtained by 2 residents is provided in Figure 4.

The median duration of the simulated biopsy procedure was (minutes:seconds) 4:58 (3:49-6:0). The residents with prior experience required 3:53 (3:39-4:56), significantly less than the residents with no or little experience who required 5:10 (4:59-7:10), p=0.01 (Figure 5A).

The rate of biopsies reaching the targeted sector was 66.7% (62-75). The 12 residents with prior experience obtained a median score of 71% (66-77), and the 11 residents with no or little experience obtained 66.7% (50-75). This difference was not statistically significant (p=0.34) (Figure 5B).

The median score provided by the simulator software (taking into account the entire simulated core placement according to the sector targeted) was 50% (37-60). The 12 residents with prior experience had a median score of 55% (48-62), and the 11 residents with no or little experience was 52% (37-57), the difference was also not statistically significant (p=0.28) (Figure 5C).

The detail of scores obtained by residents from each center is provided in Table 2. No statistically significant difference between centers was noted for the 3 outcomes studied, procedure duration, rate of biopsies reaching the aimed sector and simulator score.

Discussion

This study allows for the external validation of the Biopsym prostate biopsy simulator, confirming a high acceptance among participants not involved in the previous simulator development steps.

These new users rated the added value and usefulness of the simulator for the simulator as very high, with a median score of 100 (83-100) and 97 (87-100), respectively. Both scores were high irrespective of the participant's previous biopsy experience.

These results are of particular importance for 2 reasons. Firstly, it is the first evaluation of the simulator performed outside the urology department involved in its development, mitigating a potential evaluation bias. Secondly, unlike previously conducted studies, all participants used the simulator for the considered procedure (12-core systematic prostate biopsy). In previous validation studies the participants were expert urologists and medical students [START_REF] Fiard | Validating the Transfer of Skills Acquired on a Prostate Biopsy Simulator: A Prospective, Randomized, Controlled Study[END_REF][START_REF] Fiard | Initial validation of a virtual-reality learning environment for prostate biopsies: realism matters![END_REF]. Their opinions, although of interest, did not necessarily reflect the needs of urologists-in-training. As the present study involved participants coming from 4 different academic centers, that were therefore exposed to a range of teaching methods, biopsy techniques and patient positioning, their feedback further confirms the place that such a simulator may have in the initial training of urology residents.

The validation of surgical simulation tools has been reported to be lacking for up to 93% of commercially available devices [START_REF] Stunt | How valid are commercially available medical simulators?[END_REF]. When initiated, advanced validation steps such as transfer validity demonstration (the ability of trainees to reproduce the skills acquired in reallife situations) and external validity were often overlooked.

In this external validation study, residents rated the overall realism of the biopsy procedure at 80, which compares favorably with the results obtained during previous validation studies conducted within the urology department involved in the simulator development, as detailed in Table 3. Interestingly, since improving the simulator's physical realism from the initial version of the simulator, median scores provided by the software have proven to be reasonably consistent to the training level of the involved participants.

Although it was not the primary objective of the study and this particular outcome has to be considered as exploratory, we did find some differences between residents with no or little prior experience in prostate biopsy and their more experienced counterparts. The difference was statistically significant for the duration of the procedure, but not for the rate of correctly placed simulated biopsies or global performance score attributed by the simulator software. This can probably be explained more by a lack of power of the study and the small sample size rather than by an absolute absence of difference. These results will have to be further explored and confirmed in a study with a higher number of participants, but this can be considered as an encouraging first step toward the use of the simulator as an evaluation tool.

Interestingly, and unlike previous survey results on the motivation of urology trainees to use simulation tools, residents taking part in this study displayed a high level of engagement and all wished they had had access to such a simulator before performing their first biopsy session [START_REF] Fiard | The role of simulation in the curriculum of French urologists-in-training: a study by the French Association of Urologists-in-Training (AFUF)[END_REF]. Previous experience (unpublished data) has shown that it was possible to fully train a resident with the simulator and have them perform their first biopsy on a patient with an excellent comprehension and mental representation of the prostate. Therefore, we believe that a virtual-reality simulator-based training should be introduced for every urology resident at the start of their residency. Some limitations of the study have to be acknowledged. The sample size was limited due to the duration of a simulation session for each resident and the short time frame, as well as the limited number of residents currently in training in the Auvergne-Rhône-Alpes region.

Conclusion

This external validation study confirms a high acceptance of the simulator among residents recruited from 4 different academic urology departments and not involved in the previous development or validation steps. High scores obtained in terms of overall procedure realism and usefulness of the simulator as an initial training tool also further support the validity of the Biopsym simulator and the place it could take in the training of urology residents. Although limited by the sample size, differences between the results obtained by residents with no or little prior experience and their more advanced colleagues suggest a potential usefulness of the simulator to be used as an evaluation tool.

  Although we only included residents with no prior training within the urology department involved in the simulator development, another limitation was that the urologist in charge of the study set up, supervision and simulator presentation was actively involved in previous validation studies. Additionally, it has not been demonstrated so far that the improvement in the initial training provided by the Biopsym simulator translated into increased prostate cancer detection. A multicentric, prospective randomized trial would be needed to compare cancer detection rates between residents trained using the simulator versus conventional training, in order to further support the clinical relevance of simulation-based training of prostate biopsies.

Figure 1 :

 1 Figure 1: Current version of the Biopsym simulator.

Figure 2 :

 2 Figure 2: Simulation realism and usefulness for initial training (scores from 0 to 100, 100=highest agreement).

Figure 3 :

 3 Figure 3: Expectations of the residents with regard to simulation for the use of prostate biopsy teaching and training (scores between 0-100, 100=highest agreement).

Figure 4 :

 4 Figure 4: Examples of visual feedback obtained by 2 residents (A-no prior biopsy experience; B-prior biopsy experience) at the end of the simulated procedure, showing the prostate contour, targeted sectors and simulated biopsy trajectories. (prostate sectors: blue = base, green = mid, pink = apex).

Figure 5 :

 5 Figure 5: Training outcomes and scores. A-Duration of the simulated 12-core systematic biopsy procedure; B-rate of biopsies reaching the aimed sector (where at least the tip of the simulated core was inside the sector -in %); C-score given by the simulator (taking into account the length of each simulated core inside the sector -in %). *statistically significant

Acknowledgment

This work was initially supported by French state funds managed by the ANR within the PROSBOT project under reference ANR-11-TECS-0017 and the Investissements d'Avenir programme (Labex CAMI) under reference ANR-11-LABX-0004, the Association Francaise d'Urologie -AstraZeneca (grant GF) and by INSERM CHRT (grant JT).


Lisa Poirier-Herbeck

Olivier Aubreton

David Fofi

Lisa Poirier--Herbeck

SURFACES BY SMART DEFLECTOMETRY, JUNE 2020 1 3D Reconstruction of mirror-like surfaces by smart deflectometry

Keywords: deflectometry, 3D reconstruction, specular, mirror-like

come

3D reconstruction of mirror-like surfaces by smart deflectometry

I. INTRODUCTION

The 3D reconstruction of the surface of specular objects is an important process and it is still a challenge for many application fields as the automobile industry, astronomy and advanced manufacturing to get a fast and accurate reconstruction of such objects. Deflectometry is a big set of techniques established to make the acquisition of specular surfaces. Among these techniques, shape-from-distortion is commonly used. It requires the reflection of a known pattern at the surface of the specular object. Another deflectometry technique, direct ray measurements, shows very accurate measurements which makes it promising. It is a geometric method which traces the light rays on the surface of the specular object. In other words, it employs the principle of light field applied to illuminations. The main drawback of these techniques of deflectometry in general is the light pose estimation. Indeed, as the pattern or the light source is generally displayed by LCD screens or by big plane objects, the estimation of the position of the light source remains a problem.

In this paper, we consider the problem of calibration encountered by the previous techniques. To solve it, it is necessary to reduce the size of the light source of the system in order to estimate it as a single point in space. As a solution, we propose a new deflectometry method based on a variation of the light field illumination principle. Indeed, our method is smart in a sense that it estimates the direction of the Fig. 1: Schema of the principle of our method: each ray emanating from the light source has its own properties of wavelength and direction.

reflected light ray thanks to its color properties to thus be able to get the perpendicular line to the mirror-like surface by triangulation. A reflective diffraction grating could represent such a light source, since its color varies depending on the view-point, meaning every light rays have their own properties of wavelength and direction. Plus, the optical formulas of the reflective diffraction grating are well-known and then usable.

The light source we propose to use has never been studied in the field of deflectometry. We prove that 3D reconstruction of mirror-like objects can be achieved using a light source that employs a new manner to use the light field illumination principle. Then, we propose an appropriate calibration process to estimate the position of the light source of our system. This paper provides in Section II a brief overview of related works concerning deflectometry and the light field principle. Then, in Section III we describe the proposed principle of our method and its calibration in details. Section IV presents our system simulated with the computer graphics software Blender, and experimental results proving the effectiveness of our approach.

II. RELATED WORKS

A. Deflectometry

Deflectometry is a set of techniques to make the 3D reconstruction of specular surfaces. Ihrke et al. [START_REF] Ihrke | Transparent and specular object reconstruction[END_REF] category Fig. 2: Coordinate systems of objects of the system. all acquisition approaches for reflective objects. Shape-fromdistortion [START_REF] Tarini | 3d acquisition of mirroring objects using striped patterns[END_REF] is a technique based on the principle of the phase measuring deflectometry [START_REF] Knauer | Phase measuring deflectometry: a new approach to measure specular free-form surfaces[END_REF]. The basic principle is to project two-dimensional sinusoidal fringe patterns onto a screen located remotely from the surface under test and to observe the fringe patterns reflected via the surface, then estimate the difference between the reflected and the real fringe pattern by applying the phase-shifting algorithm. This technique has established itself powerful and is used with great success in many industrial applications, even if it remains major challenges and deficiencies, especially for calibrating the screen [START_REF] Huang | Review of phase measuring deflectometry[END_REF]. Direct ray measurements is another technique used to avoid the depth-normal ambiguity, a main problem in deflectometry. As we can guess by the by the name of the technique, viewing rays reflected by the specular object can be measured. In general, a calibrated planar target is located at different positions and the distorted pattern is observed by a camera. The technique consists in measuring the reflected ray by decoding two world positions for every pixel. Approaches based on triangulation [START_REF] Bonfort | General specular surface triangulation[END_REF] , [START_REF] Kutulakos | A theory of refractive and specular 3d shape by light-path triangulation[END_REF] and polarization [START_REF] Tin | 3d reconstruction of mirror-type objects using efficient ray coding[END_REF] , [START_REF] Lu | Mirror surface reconstruction using polarization field[END_REF] have been demonstrated. By the computation of the direction of light rays, this technique employs the principle of light field. In deflectometry, the main problem which remains is the calibration of the light source. Indeed, the light is always a big plane object and is consequently difficult to calibrate.

B. Light Field

Light Field is a concept to describe the amount of light flowing in every direction through every points in space. The theoretical background for Light Field is the plenoptic function. [START_REF] Adelson | The plenoptic function and the elements of early vision[END_REF] , [START_REF] Levoy | Light field rendering[END_REF] Light Field principle has been first conceptualized for cameras. [START_REF] Lippmann | Epreuves reversibles donnant la sensation du relief[END_REF] , [START_REF] Lumsdaine | The focused plenoptic camera[END_REF] As said in Section II-A, some deflectometry techniques employ the principle of Light Field by the light source of their systems. The new formulation of this principle applied to light sources is called Light Field Illumination [START_REF] Wong | The plenoptic illumination function[END_REF]: the intensity of a light ray emanating from a light source depends on its own direction. The illumination component can be expressed as an directional light source [START_REF] Aoto | 4-d light field reconstruction by irradiance decomposition[END_REF] or a point light source [START_REF] Lin | Relighting with the reflected irradiance field: Representation, sampling and reconstruction[END_REF]. In the field of deflectometry, this conceptualization of illumination leads to the direct ray measurements technique: it generally uses two planes which are crossed by rays of a light source, and the reconstruction is parameterized by the direction and the intensity of the reflected ray. [START_REF] Lu | Mirror surface reconstruction using polarization field[END_REF] , [START_REF] Tin | 3d reconstruction of mirror-type objects using efficient ray coding[END_REF] Furthermore, on the basis of this plenoptic illumination model, Herschbach developed an optical system generating a structured light field from an array of light sources by means of refracting or reflecting light structuring element [START_REF] Herschbach | Optical system generating a structured light field from an array of light sources by means of a refracting or reflecting light structuring element[END_REF]. This optical system is interesting since the optical formulas are well-known making the spacing between light rays calculable. Besides, it is possible to associate the light field illumination principle to the optical phenomena of diffraction. Indeed, diffraction defines light rays by their wavelength and orientation. So, by knowing the color value of a ray, it is possible to get its direction in space. We propose to use this variation of the Light Field Illumination principle in deflectometry. This could be done using a diffraction grating by reflection. Since the grating is very small, we could consider its center as the point light source of the system. This could ease the calibration process of a deflectometry system.

III. METHODOLOGY

A. Geometric model of the system

We propose a new deflectometry method which uses an illumination based on the Light Field principle. Since each light ray emanating from a single light point has its own properties of wavelength and direction, we are able to determine the light ray reflected in the mirror and perceived by the camera. We calculate its direction in space by using triangulation and get the normal line at the reflection location in the mirror. We have conceived our method based on the behavior of the reflective diffraction grating : an incident white light ray is diffracted by the grating in multiple colors at calculable angles. Figures 1 and2 illustrate the principle of our method.

B. Triangulation

We base our calculations described in this Section, on the triangulation schema in Figure 3. Once the camera captures the reflected light source on the mirror, we binarize the image to extract pixels which reflect the light source in the mirror. We compute the part with reflection in HSV domain, in order to obtain the hue value of these pixels. Then, we have selected two methods to get the hue value of the perceived color:

• Associate each pixel to its own hue value and get several hue values with corresponding pixels in one image. • Compute the mean hue value of all colored pixels and the mean position of all these pixels. Once having the hue value, we recover the direction of the incident ray of the light source by computing the first angle of the triangulation α 1 pointing the light source (Figure 3). Since the light source provides information about wavelength and direction along a single axis, we only take into account the horizontal position of the reflected light source on the image sensor. Knowing this information and the configuration of the camera, we get the equation of the line Line 2 (Figure 3) passing through the focal point, image sensor and the mirror. Moreover, by computing the equation of Line 1 with the location of the light source and the one of the camera, we compute the angle α 2 at the intersection of these two lines Line 2 and Line 1 . Then the distance d 1 between the illumination and the camera is calculated. Hence, we have two angles and one side of the triangle and we can proceed to the triangulation calculations to get the last angle α 3 of the triangle and the distances d 2 and d 3 between the mirror and the camera and the light source (Figure 3):

α 3 = 180 • -α 1 -α 2 , d 2 = d 1 × sin(α 1 ) sin(α 3 ) , d 3 = d 1 × sin(α 2 ) sin(α 3 ) . (1)
Thus, we get the x m and y m coordinates of the third point of the triangulation, with a 2 the slope of Line 2 :

x m = d 2 2 a 2 2 + 1 , y m = d 2 2 1 + 1 a 2 2 . (2)
A first 2D bisector Line b is calculated with Line 2 and Line 3 .

For now, we consider the three points on a same plane. To get the 3D bisector and the third coordinate z m of the point at the mirror, we turn the light source to 90 • and we get the color value the same method as described previously. This new color gives a new angle of the ray emanating from the light source in the third axis (vertical). We add this new angle as a rotation of the bisector and the M point on their third axis (Figure 3). So the 2D bisector and the 2D M point becomes 3D elements, and the 3D bisector is in fact the normal line of the mirror at the observed reflection point M .

C. Calibration

Our proposed calibration method uses a pattern equipped with a mirror on its center. The well-known method of Zhang [START_REF] Zhang | A flexible new technique for camera calibration[END_REF] allows us to estimate the position and orientation of our Fig. 4: Calibration principle adapted for our system. The position of the light source, here the reflective diffraction grating, is estimated by calculating the normal line of the pattern on its center point.

pattern, and so, the position and orientation of the mirror at the center of the pattern. Depending on the position and the orientation of the mirror, the color of the light source perceived by reflection in the mirror varies. By capturing images of the pattern for different reflected colors, we are able to define the light ray descended from the light source for each image. This way of doing allows to configure the camera and the position and orientation of the light source in a same calibration process. We place a small mirror on the center of the pattern so that it is possible to see the reflection of the light source on its surface. Such an object is possible by cutting a hole in the center of the checkerboard and paste it on a plane mirror. We capture images for different pattern positions and when the light source is reflected in the mirror of the pattern. In this way, the camera observes different colors reflected in the mirror, as illustrated in Figure 4. Thanks to Zhang's method [START_REF] Zhang | A flexible new technique for camera calibration[END_REF], we are able to obtain the intrinsic and extrinsic parameters of the camera and then the positions of the checkerboard's corners in the world by projection. Once having 3D points of corners, by taking the first and the last corners of the pattern, we can estimate the 3D position of the mirror :

M = ( x C1 + x C2 2 , y C1 + y C2 2 , z C1 + z C2 2 ), (3)
with C 1 = (x C1 , y C1 , z C1 ) and C 2 = (x C2 , y C2 , z C2 ) the first and the last corners of the checkerboard and M the central point of the pattern, where the mirror is located. We need at least three positions of corners to compute the perpendicular line of the pattern. Mathematically speaking, the perpendicular line of the pattern is the perpendicular vector of two other vectors laying on the same plane, and can be calculated by the cross product of the two vectors. This line positioned in the middle of the pattern is in fact the normal line of the mirror. Afterwards, knowing the angle between this normal line and the perceived light ray, we estimate the vector of the reflected ray going from the mirror to the light source, using the rotation matrix described by the Euler-Rodrigues formula :

θ = acos V 1 × V 2 V 1 V 2 , ( 4
)
with θ the angle between the vector V 1 representing the line from the mirror to the camera, and the vector V 2 representing the normal line of the pattern, and :

U = V 1 × R(a, b, c, d), a = cos θ 2 , b = c = d = -V 2 √ V 2 × V 2 × sin θ 2 , (5)
with U the vector representing the line from the mirror to the light source calculated with V 1 and the rotation matrix R. Finally, we need at least two images to get two different line equations of the reflected ray, to calculate their intersection which is in fact the estimation of the position of the light source in the world.

IV. EXPERIMENTS A. Implementation

We simulate our system with the 3D computer graphics software Blender, and design the light source presented in Figure 6. This pinhole light source provides a color which varies depending on the point of view. We implement the method described in Section III-B and we base our simulation the most possible on a real system, in order to estimate some noises or errors that we could encounter in real world. The idea is to prove the feasibility and reliability of a deflectometry system which uses a new light source based on the light field principle. During the process, we move the object to be reconstructed along 2 axis since this is the most general motion established in deflectometry. Calibration images in Figure 5, made with Blender, show that it is possible to create such a pattern and visualize the reflection of the light source for different positions of the pattern.

B. Results and discussion

Reconstructed points Spherical object

Plane object method 1 method 2 method 1 method 2 mean (%) First, we consider the error due to calculation. Indeed, we use the equation based on the behaviour of the hue emitted by the light source according to the angle from the view point to the normal line of the light source. We separate this behaviour in multiple parts and compute a linear regression to every part in order to get the equation line with the smallest root-meansquare (RMSE) possible, varying between 0.7 • and 0.1 • . The more the behaviour is linear the smaller the RMSE is, and vice versa. It means that the value of this error really depends on the behavior of the direction and color properties of the rays of the light source. In a further work, the selection of another light source will have to take into account this problem of rays' behaviour in order to reduce or, if possible, remove this error by getting a light source with a linear behaviour of color versus viewpoint.

We evaluate two different object shapes: a plane and a sphere. Table I evaluates the errors for 126 reconstructed points and Figure 7 allows to get a first glance at the results obtained with point clouds and normal lines to the mirrors. The fact that the plane provides less errors than the sphere leads us to emit an hypothesis: it could be caused by a geometric distortion of the perceived color due to the curved surface of the sphere. Indeed, as we capture a beam of rays, the beam covers a larger part of the surface than just a single ray. So, for a sphere, this part of the surface is curved and not planar, and it means it has multiple normal lines which have different orientations, whereas this part for a plane has multiple normal lines which have the same orientation since they are parallel to each other. Having such a difference of orientations of normal lines in a small part of the surface of the mirror may lead to an unintended range or separation of colors. Then, the perceived color would be in fact a distorted image of the reflected color caused by spherical aberration, which we would not obtain with a plane mirror.

According to table I, the method n • 1 which computes the mean hue value of all the colored pixels and the mean position of all these pixels in the image, is way more better than the Fig. 7: Reconstructed point clouds (blue) and normal lines (green) for a planar and a spherical mirror. The planar mirror is represented in pink as the center of the sphere.

method n • 2, the pixel-by-pixel method (Section III-B). This shows it is preferable to apply a method based on the position and color average of pixels. Indeed, the theoretical ray-by-ray method is in practice a "beam-by-beam" method : the system captures a small beam of several light rays. Normal lines are directly linked to reconstructed points (Section III-B). Moreover, since we choose a spherical and a planar object to reconstruct, it is interesting to visualize their normal lines. Indeed, for the sphere, the normal lines should meet a the center point of the sphere. In spite of some errors due to the position of the reconstructed points, we can see in Figure 7 the normal lines are all directed in the area around the center of the sphere. In the case of the plane mirror, all the normal lines are supposed to be parallel to each other. We observe this situation in the images captured during the experiments in Figure 7. To conclude, the correct behaviours of normal lines among the tested objects are encouraging and validate our method.

V. CONCLUSION

We have proposed a simple yet efficient way to calibrate a deflectometry system following the widely know method of Zhang [START_REF] Zhang | A flexible new technique for camera calibration[END_REF]. We have integrated the light field as a solution in deflectometry, by studying RGB in a different manner than other RGB methods: compared to Tarini et al. [START_REF] Tarini | 3d acquisition of mirroring objects using striped patterns[END_REF] which uses color property of an RGB light source as patterns, we use color property of an RGB light source to recover the direction of the reflected light ray. This solution is an extension to the plenoptic illumination function, which is mainly used in deflectometry through direct ray measurements techniques. Indeed, whereas the common used plenoptic light sources are defined by the light intensity varying with the direction of their rays, our proposed plenoptic light source is defined by the color varying with the direction of its rays. So, the color value has a real importance in our system and this makes our deflectometry method unique.

Our experimental results are encouraging and validate our proposed approach. One limitation is clearly the behavior of direction and color properties of light rays which is not linear for the chosen light source. Besides, we have made the hypothesis that some of the obtain errors could be caused by a color distortion due to the curves of the mirror. One of the next steps is to elaborate a real system by leaning on the established simulated system. As we proved through simulation that a 3D reconstruction of specular surfaces is possible by using the proposed technique, we need to evaluate its limitations and capacities in real world.

Fig. 3 :

 3 Fig. 3: System's triangulation. The bisector Line b of the angle α 3 is in fact the normal line of the mirror at point M .

Fig. 5 :

 5 Fig. 5: Examples of images to simulate the calibration process. The light source is reflected in the center of the pattern.

Fig. 6 :

 6 Fig. 6: The pinhole light source. Depending on the viewpoint, the hole provides a different color.

TABLE I :

 I Experimental errors for the position of the reconstructed points. Sphere diameter is 12 meters.

ACKNOWLEDGMENTS

This work was carried out during the MSc thesis of Ms. Lisa Poirier--Herbeck, financed by the VIBOT programme of the University of Burgundy in Le Creusot.


Olivier Piller

Fereshte Sedehizade

Thomas Bernard

Mathias Braun

Nicolas Cheifetz

Jochen Deuerlein

Martin Wagner

Emmanuel Lapébie

Iris Trick

Jean-Marc M Weber

Aug- Mented

C Werey

Augmented Resilience of Water Distribution Systems following Severe Abnormal Events

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

Introduction

Toxicity sensors Hydraulic and water quality sensors Hydraulic stations (tanks, pumps, valves) Terrorist attack

OBJECTIVE Introduction

Prepare water utilities to crisis management by improving the system resilience with respect to 3 specific case studies: system failure, water quality deterioration and cascade effects between water, energy and IT infrastructures.

Better crisis management Case Studies Berlin:

Laboratories and Research Centers

1. Cut off of two waterworks by a regional power cut 2. Contamination (non-pathogen bacteria) 3. Cyber attack at control systems (stuxnet)

Case Studies Strasbourg:

1. Main production unit stopped by major flood event 2. Water quality degradation by intentional network contamination 3. IT attack: power plant stopped, event masked by false data

Case Studies VEDIF (Paris): Prepare water utilities to crisis management by improving the system resilience with respect to 3 specific case studies: system failure, water quality deterioration and cascade effects between water, energy and IT infrastructures. üAn assessment method is adopted for the vulnerability and resilience assessments of the three project end users. üThree use cases per water utility: Collapse of WDS, Water Quality Deterioration and Cascade Events are specified in details. üNew spectroscopic, biological sensors and a low-cost flow rate measurement system are under investigation in the project. They will be part of a broad and secure sensor network for monitoring the systems. üOther solutions were also studied in the project for the prevention and response of critical events.

OBJECTIVE AND METHOD

Conclusions

MAIN RESULTS

Conclusions

  Timeline for the three resilience phases in the ResiWater project VULNERABILITY and RESILIENCE signatures are assessed on a simple three-level scale:

  1. Fire Hydrants operation in "Street Pooling" situation; 2. Terrorist attack on network in the situation of a major International Event 3. Centennial Flood 4. Above Centennial Flood -Establishment of the major crisis emergency plan END USERS CASE STUDIES The resilience framework the german water center EMS (1): Main production unit stopped by major flood event Investigation and partly development of new sensors for online-Monitoring -Biological Sensor system « AquaBioTox » -Spectroscopic sensors -Low-Cost through-flow measurement system Development of a concept for integrated and secure sensor networks Self-learning Monitoring System § Plug-in software architecture for flexible data integration § Web-based frontend for multi-user access § Self-learning event detection algorithms Aim: Reliable and quick event detection in water distribution area with insufficient pressure after burst of trunk main

Ø

  Robust modelling for training in presence of large disconnected network parts, Ø Enhanced event detection by PCA and Gaussian mixture model (oscillating data and drifting sensor data) Ø Economic evaluation by cost benefit analysis.

-Prevention ?-Monitoring ? -Which responses?

Thank you for your attention! Any questions?

This work is part of the French-German collaborative research project ResiWater that is funded by the • French National Research Agency (ANR; project: ANR-14-PICS-0003)

• German Federal Ministry of Education and Research (BMBF; project: 13N13690).