Marc Despinoy

Pierre Audisio

Franck Nivole

Iksandar Leite Costa

Lea Moyon

Lea Moyon Raise

Raise public awareness on the importance of mangroves

POSSIBLE CONSERVATION MEASURES

Raise public awareness on the importance of mangroves.

Implement conservation strategies to ensure sustainable protection .

Promote sustainable practices that depend on the mangroves.

Identify the needs of mangrove stakeholders and guide them towards these needs.

Input data (Multispectral images)

Image processing

PLATEFORM PRODUCTS

Protect Educate

Apprehend

CONSERVATION

Mangrove conservation is a major environmental protection issue (e.g. combating coastal erosion, protecting coral reefs, etc.). It is therefore crucial that the various stakeholders become agents of change.

SATELLITE MONITORING OF MANGROVES :

A MANAGEMENT TOOL

MANGROVES, A RICH ECOSYSTEM

In New Caledonia, the mangrove is a coastal ecosystem of salt marshes that develops in the intertidal zones along the coast of the "Grande Terre" and the Loyalty Islands.

Covering a total area of 160 km2, it's the second largest mangrove area in France's overseas territories. It's home to a high level of biodiversity, including endemic species, and provides important ecosystem services.

The multispectral images received as input are subjected to a series of processing operations in order to isolate only areas where mangroves are present and to analyse their evolution.

Products images

Choice of calculation period and frequency : Average Minimum / Maximum Quartiles Standard deviation

Conservations Pillars

Decision-makers

To implement a policy of conservation, compensation and/or controlled exploitation.

Associations

To carry out restoration and monitoring campaigns.

Scientists

To provide tools and expertise on environment.

FOR WHOM? MONITORING A FRAGILE ECOSYSTEM

This collaborative project, co-funded by a number of partners, aims to set up a near-real-time monitoring platform of mangroves, a vital ecosystem both for coastal protection and for the populations who live with it on a daily basis.

Using open-access satellite imaging technology, enables the monitoring of environmental changes resulting from human activities and meteorological phenomena that threaten the mangrove.

AUDISIO PIERRE, COSTA IKSANDAR, DESPINOY MARC, MOYON LÉA, NIVOLE FRANCK AUDISIO PIERRE, COSTA IKSANDAR, DESPINOY MARC, MOYON LÉA, NIVOLE FRANCK

Satellite constellation composed of two satellites, Sentinel-2A and Sentinel 2-B, for Earth observation.

Dedicated to Earth observation, the Sentinel-2 satellite constellation acquires multi-spectral images of the entire territory every 5 days. These data are freely accessible.

"Presence of mangrove" maps, vegetation indices, state of health, etc. All these elements will enable the platform to provide precise information on mangrove areas.

A Mangrove map is produced using a model based on raw channels (visible, PIR and SWIR) as well as NDVI (Nomarlized Difference Vegetation Index) and NDWI2 (Normalized Difference Water Index 2) indices.

This monitoring work will serve as a mapping and a reference base. It could enable stakeholders to work together to develop various conservation strategies (identification of priority areas for protection). For more information regarding the platform, please contact:

  ), no change (grey) and gain (green) of mangroves in the area of interest under consideration "Mangrove" product, showing the extent of mangrove in the area under consideration These products enable the monitoring of mangrove area change over time Statsitical productsIMPLEMENTATION OF THE FRENCH PROJECT "SESAME" IN NEW-CALEDONIAThese actions are part of the project, "Monitoring the state of mangrove health in the pacific", financed by the Pacific Fund, in French the SESAME project. SESAME stands for " Surveillance de l'Etat de Santé des Mangroves dans le pacifiquE"


Yi Zhang

A Mesaros

K Fujita

S D Edkins

M H Hamidian

K Ch'ng

H Eisaki

S Uchida

J C Séamus

Ehsan Khatami

Eun-Ah Kim

Machine learning in electronic-quantum-matter imaging experiments

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

defied microscopic identification for decades 20 , recently it has been reported that rotational and translational symmetry are spontaneously broken in this phase. Rotational symmetry breaking is referred to as a nematic (NE) state 18,19,23,24 ; it occurs at wavevector 𝑸=0 as the breaking of 90 o -rotational (C4) symmetry at 𝑇 < 𝑇 * (𝑝) (Fig. 1a). This presents a conundrum because, in theory, ordering at 𝑸=0 cannot open an energy gap in the electronic spectrum. The translational symmetry breaking or density wave (DW) state, which should open such an energy gap, is detected using SISTM visualization 17 and X-ray scattering 22 . It consists of periodic spatial modulations of electronic structure with finite wavevector 𝑸 and thus with periodicity 𝜆 = 2𝜋/|𝑸|, that occur within the pseudogap phase (Fig. 1a). A key challenge for this field is to identify the correct microscopic theory for the DW state (Methods Section 1), and to find the relationship (if any) between it and both the NE state and the pseudogap.

3

A DW state with wavevector Q is described by a spatially modulating function 𝐴 𝒓 = 𝐷 𝒓 𝐶𝑜𝑠 𝑸 • 𝒓 + 𝜙 ! 𝐫 : 𝐴 𝒓 represents the density amplitude, 𝜙 ! (𝒓)

represents effects of disorder and topological defects, 𝜆 = 2𝜋/|𝑸| is the periodicity, 𝑸/|𝑸| is the direction of the modulation, while 𝐷 𝒓 is the DW form factor symmetry. For a tetragonal crystal, an s-symmetry form factor remains unchanged under 90 o rotations, while a d-symmetry form factor changes sign as observed in cuprates 25 . One theoretical approach to understanding a DW state is based on conventional electrons with welldefined wave momentum 𝒑 𝐸 = ℏ𝒌 𝐸 . DW states can then appear at a wavevector 𝑸 = (𝒌 ! 𝐸 = 0 -𝒌 ! 𝐸 = 0 ) if many pairs of (𝒌 ! 0 , 𝒌 ! 0 ) are connected by the same wavevector 𝑸, i.e., nested (red arrow Fig. 1b). Under these circumstances, Q should usually be incommensurate (Fig. 1b). Alternatively, strongly interacting particle-like electrons may have well-defined position in 𝒓-space, being fully localized in the MI phase or selforganized into electronic liquid crystal states 18,19,24 . For cuprates, such states are often predicted 18,19,24 to exhibit periodic charge density modulations that are unidirectional, crystal-lattice-commensurate, with wavelength 𝜆 = 4𝑎 ! or wavevector 𝑸 = 2𝜋 𝑎 ! 0.25,0 oriented along the Cu-O-Cu axis (Fig. 1c and Methods Section 1). Such latticecommensurate charge modulations in position-based theories (Fig. 1c) are expected to be robust against changes with electron-density p and electron-energy, while those associated with the geometry of Fermi surface in momentum-based theories (Fig. 1b) are expected to evolve continuously with p.

4

A central challenge has therefore been to determine if the electronic structure modulations in hole-doped CuO2 (e.g. Fig. 1d,e) are lattice-commensurate, unidirectional, with specific periodicity, or if they evolve continuously with electron-density and electronenergy. But, because of their inherent limitations, it has not been possible to discriminate between these position-based or momentum-based theoretic perspectives by using traditional analysis techniques. First, due to the extreme disorder observed in cuprate EQM images 17 (Fig. 1d) or concomitantly the broad line-widths detected in reciprocal space 22 , theory demonstrates that conventional Fourier analysis is fundamentally limited 26,27 in determining the exact symmetries of the EQM state. Second, when such complicated electronic-structure motifs exist at atomic-scale in r-space 17 , Fourier analysis spreads all that information throughout reciprocal space. Consequently, the customary Fourier analysis of SISTM and X-ray data focusing on a single intensity peak, which has long reported incommensurate modulations that evolve continuously with p in the range . 17,22), disregards much information. Specifically, the key insights contained in atomic-scale electronic-structure motifs (Fig. 1d), discommensurations 28 and topological defects (Methods Section 2) are all discarded. By contrast, ML analysis of EQM images holds great promise because it avoids this information loss and analyzes the complete image array objectively.

0.22 ≲ 𝑄(2𝜋/𝑎 ! ) ≲ 0.3 (Ref

5

High-data-volume imaging studies of EQM (e.g. Fig. 1e) use SISTM, a technique for visualizing 𝑁(𝒓, 𝐸) with sub-atomic resolution and crystal-lattice register 17 . The resulting image-array for a given sample is built up from measurements of STM-tip-sample differential electron tunneling conductance 𝑑𝐼/𝑑𝑉(𝒓, 𝑉) ≡ 𝑔 𝒓, 𝑉 at a square array of locations r and at a range of tip-sample voltage differences V. For technical reasons, images 𝑍 𝒓, 𝑉 ≡ 𝑔 𝒓, +𝑉 /𝑔 𝒓, -𝑉 , which accurately represent the spatial symmetry of electronic structure but avoid systemic errors 17 , are most frequently used. While Fourier analysis of 𝑍 𝒓, 𝑉 to yield 𝑍 𝒒, 𝑉 is an obvious approach to studying the EQM modulation wavevectors 17,22 , it faces severe limitations as discussed above. To identify the fundamental broken-symmetry EQM state from an array of such 𝑍(𝒓, 𝐸 = 𝑒𝑉) images (e.g. Fig. 1e) therefore poses an iconic challenge for ML techniques.

6

Here we introduce a specific ML approach using ANN's to achieve hypothesis testing with EQM image-arrays. It is based upon supervised ML within an ANN-human coalition. Its goals are to automatically search experimental EQM image-arrays (e.g. generally has an accuracy >99% when tested on validation images (Fig. 2d and Methods Section 4). The ANN design is a fully connected feed forward network with a single hidden layer (Fig. 3 with the highest recognition probability to again be C=2, meaning that the predominant modulations have period 4𝑎 ! for all energies exceeding 66meV (Fig. 5b-d). Again, despite intense masking by QPI phenomena, the ANN's recognize commensurate, 4a0 periodic, DW modulations and reveal that it occurs predominantly near the pseudogap energy scale 𝐸 = Δ ! .

9

A third ANN discovery in Fig. 5i-l is that the commensurate, 4a0 periodic modulations exhibit a strong preference for breaking symmetry under 90 o rotations (C4).

This is revealed because the ANN array yields up to 3 times higher probability in the specific category (C=2) when the data is presented in the X orientation (red) compared to when the identical data is presented to it in the Y orientation (yellow) (Fig. 5j-l). Although the extreme nanoscale disorder masks it in the images Fig. 5a-d, the DW modulations are therefore occurring primarily along the x-axis of the CuO2 plane. ANN analysis of the energy dependence of this complete 𝑍(𝒓, 𝐸) image array in Extended Data Fig. 1 further confirms that the appearance of this nematicity (Fig. 5i-l) occurs approaching the pseudogap energy scale which is Δ ! ≈ 80𝑚𝑒𝑉. Thus, the ANNs find that a nematic state emerges at the pseudogap energy specifically due to highly disordered yet unidirectional 4a0 periodic modulations. This discovery strongly implies that the nematic electronic structure of CuO2 is a vestigial nematic state 32 whose characteristic energy gap is the pseudogap. Advanced theory predicts that a unidirectional DW that is reduced by disorder to extremely short spatial coherent lengths, should generate a nematic state dubbed a vestigial nematic state 32 . Although experimental validation for this hypothesis is formally impossible using conventional FT techniques 26,27 , here it is demonstrably achievable by an ANN array (Fig. 5, Extended Data Fig. 1). Existence of a vestigial nematic state in carrier-doped CuO2 would provide a direct, internally consistent link between a nematic state and the unidirectional 4𝑎 ! periodic DW modulations, whose energy gap is the pseudogap (Fig. 4).

The evidence for a vestigial nematic emerged unexpectedly from ANN analysis of experimental image arrays not optimized for such studies; for the ANN suite to determine a complete p dependence will require new measurements of appropriately optimized image arrays.

10

To summarize: we have developed and demonstrated a new general protocol for ML-based identification of the symmetry-breaking ordered states in electronic structure image-arrays from EQM visualization experiments. Our ANNs are trained to learn the defining motifs of each category including its topological defects, and to recognize those motifs in real EQM image arrays (Fig. 1e). Despite the complexity of the hole-doped Mott insulator state, instrument distortion and noise, and the intense electronic disorder of the EQM image arrays studied (Figs.1d,3a,b;4,5), the ANNs repeatedly and reliably discover predominant features of a specific ordered state. Its signature, for 0.06 ≤ 𝑝 ≤ 0.14, is a lattice-commensurate, unidirectional, d-symmetry form factor, 𝜆 = 4𝑎 ! periodic electronic structure modulation (Fig. 4). As an advance in CM physics, the predominance of this phenomenology (Fig. 4) implies that a strong coupling position-based theory is central to these broken-symmetry states of carrier-doped CuO2. The ANN array also reveals evidence that it is the 𝜆 = 4𝑎 ! DW modulations at the pseudogap energy that break the global rotational symmetry to generate a nematic state (Fig. 5, Extended Data Fig. 1). This implies that the PG region of the CuO2 phase diagram (Fig. 1a) contains a vestigial nematic state.

Concurrently, a milestone for general scientific technique is achieved with the demonstration that ANN's can process and identify specific broken symmetries of highly complex image-arrays from non-synthetic experimental EQM data. Overall, these combined advances open the immediate prospect of additional ML-driven scientific discovery in EQM studies.

Fourier Transform Analysis of EQM Images: Disorder and Information Loss. A

Fourier transform of two-dimensional image data is a linear transformation of that data. All the information that was in the original image appears in the full, complex Fourier transform throughout reciprocal space. Importantly, when there are complicated local patterns or motifs of short-range order at atomic-scale in real space, that information gets spread over all of reciprocal space. This is because what is extremely local in real space becomes completely delocalized in reciprocal space. But, in the traditional mode of FT analysis, one typically picks a compact region in the reciprocal space to be of importance, because the intensity is peaked at that point. Crucially in this approach there is abundant information throughout reciprocal space away from the peak-intensity wavevector that has been discarded. For hole-doped CuO2 the real-space electronic structure at atomic scale is uniquely complex (Fig. 1). For instance, one always finds that the STM image whose FT peak-intensity occurs away from Q=0.25 (see Extended Data Fig. 3a), hosts vivid local motifs that are commensurate with the lattice (see Extended Data Fig. 3b). Since any information local in position space gets spread over all reciprocal space, when one discards much of the data throughout reciprocal space crucial insights contained in atomic scale electronic-structure motifs, discommensurations and topological defects are all lost. On the other hand, because of the versatility of ANN to capture any function whatsoever, 33 the new ML approach allows one to impartially inspect the entirety of the data in each STM image with no loss of information. This is a key distinction between the traditional FT approach and the ML approach which impartially analyzes all the data throughout real space. the DFF (𝐼 !,!,! !"" ) and SFF (𝐼 ! !"" )form factor modulations with noise models were i=1…nd, with windings wi=±2π and total winding 0. The total dislocation-contributed fields are:

𝐼 !,!,! !"" 𝑥, 𝑦 = 𝐴 !"" 1 + 𝜀 ! 𝐴 ! 𝑥, 𝑦 𝐴 ! 𝑥, 𝑦 𝐶𝑜𝑠 2𝜋𝑥/𝜆 ! + 𝜀 ! 𝜑 ! 𝑥, 𝑦 + 𝜑 ! 𝑥, 𝑦 + 𝜑 !"" , 𝐼 ! !"" 𝑥, 𝑦 = 𝐴 !"" 1 + 𝜀 ! 𝐴 ! 𝑥, 𝑦 𝐶𝑜𝑠 𝜀 ! 𝜑 ! (𝑥, 𝑦) + 𝜑 !"" , (
𝐴 ! 𝒙 = (1 -𝑒𝑥𝑝 -|𝒙 -𝒙 ! |/𝜉 ! ) ! ! !!! 𝜑 ! 𝑥, 𝑦 = 𝐴𝑟𝑔 𝑠𝑔𝑛(𝑤 ! ) 𝑥 -𝑥 ! + 𝑖 𝑦 -𝑦 ! ! ! !!!
, where the amplitude recovery length is ξd=a, motivated by 𝑍 𝒓, 𝐸 .

Then the training set for each category C combines the different form factor components into image intensity at pixel position (x,y) in units of a through 𝐼 ! 𝑥, 𝑦 = 𝐼 !,!"" 𝑥, 𝑦 * 𝐷 𝑥, 𝑦 + 𝐼 !"" 𝑥, 𝑦 * 𝑆 𝑥, 𝑦 , using atomic masks: the SFF mask 𝑆 𝑥, 𝑦 is a sum of two-dimensional Gaussians with maxima equal to one and spatial widths equal to 0.35a, each located at a Cu atom position (x,y integer), while the DFF mask 𝐷 𝑥, 𝑦 is a sum of positive Gaussians at locations of Ox and negative ones at Oy's. The total intensity 𝐼 ! 𝑥, 𝑦 of all simulated images is normalized to take values between 0 and 1. All simulated images have 6 pixels per nearest Cu-Cu distance a, and contain 2x86x86 unit-cells, for the total size of 516x516pixels.

4

Configuration of Artificial Neural Network (ANN).

In a feed-forward fullyconnected artificial neural network, the neurons form a layered structure and the output of each neuron is sent to all the neurons in the subsequent layer. Each neuron assesses all the inputs with a series of weights w, and an additive constant b known as the bias, and For supervised machine learning, we divide the data set into a training set containing 90% of the images and the rest 10% for unbiased validation, speed control, and overfitting detection during the training. The weights and biases of the ANN are optimized using stochastic gradient descent to minimize the cross-entropy cost function:

𝐶 = 1 𝑁 𝑦 ! 𝑙𝑛(𝜎 ! ) + (1 -𝑦 ! )𝑙𝑛(1 -𝜎 ! ) ! !!! 𝒙 ,
where yi and 𝜎 ! are, respectively, the desired output consistent with the label and the actual ANN output for each of the input image data x. We use a batch size of 50, and L2 regularization to avoid overfitting. We include 50 neurons in the hidden layer and choose the sigmoid function as the neuron activation function unless stated otherwise. In Extended Data Fig. 5a we show examples of the cost function as well as the accuracy on the validation data set for both choices of the sigmoid and the ReLU activation functions during the training. Extended Data Fig. 5b shows the achieved accuracy and cross-entropy cost after 25 epochs as a function of the number of neurons in the single hidden layer. We have trained 81 ANNs with random initial conditions by using a stochastic training process. The outputs of the finalized ANNs are robust and quantitatively consistent with each other. Our results in the main text show the average and standard deviations from all 81 ANNs.

To verify that our results are robust against changes to the architecture of the ANN, we have trained 6 ANNs with 100 neurons in the single hidden layer, and 6 ANNs with two hidden layers, and we found that the results agree with each other within error bars.

Because they are drawn from a historic image-array archive not designed for ML based studies, the SI-STM image-arrays 𝑍 𝒓, 𝐸 vary in spatial resolution from sample to sample from 1.7 to 11.5 pixels per a, the average Cu-Cu distance. The number of CuO2 unitcells in experimental images also varies from 2x55x55 to 2x175x175. The Cu and Ox,y atom positions, registered from the topograph, show random distortions of the lattice due to the STM tip drift effect (Extended Data Fig. 6a).

To correct for the drift and standardize all the 𝑍 𝒓, 𝐸 , we prepare each 𝑍 𝒓, 𝐸 : (1) using interpolation we map the 𝑍 𝒓, 𝐸 to the resulting input image, in a way that each topographic atom position maps onto a position in a perfect atomic lattice with Cu-Cu distance of a=6pixels (see Extended data Fig. 6b,c), which corrects both the drift effect and standardizes the spatial resolution; (2) we crop or tile the image to size 516x516pixels; (3) to study the degree of unidirectionality, for each input image we create a copy rotated by 90 o , since the training images have modulations only along X direction for simplicity and clarity. An example Mathematica notebook file for data preparation is available. Extended Data Fig. 7 shows the 𝑍 𝒓, 𝐸 and prepared input data at different dopings of Bi2Sr2CaCu2O8.

It should be noted that the results are reliable only if the test data lie reasonably consistently within the input space given by the synthetic training sets.

5

Validation and Benchmarking. To assess the discriminatory power of ANNs' categorization, we study obvious modulations in two experimental images (Extended Data We also checked the robustness of our approach against existence of Bi2Sr2CaCu2O8 superlattice modulations. The assessment of the ANN's were independent of existence or absence (data with superlattice modulation removed from the FT) of the superlattice modulations.

We and complete confusion over different candidate categories for p=0.2 (Extended Data Fig. 9e and j). The energy dependence comparison between the ANN's assessments in the main text (Extended Data Fig. 1a or Extended Data Fig. 9e) and the assessments of the ANN trained with the altered disorder model (Extended Data Fig. 9j) shows that the tie between the onset of preference for the commensurate period 4a0 and the nematicity at the pseudogap energy scale is equally robust against variations in the disorder model used to train ANN's.

6

Discommensurations and Maximum Intensity Wavevector. The Fourier transform(FT) based linear analysis of equivalent data in Ref.28 was carried out using the fact that the power spectral density is not smoothly distributed (Extended Data Fig. 10a,b, reproduced from the SI of Ref.28.). We had introduced the concept of demodulation residue (DR), using

𝑹 𝒒 ! 𝜓 ≡ 𝑑 ! 𝒙 𝐿 ! 𝑅𝑒 𝛹 𝒒 * 𝒙 -𝑖𝜕 ! 𝛹 𝒒 𝒙 , 𝛼 =
𝑥, 𝑦, which measures the phase fitness of the q-modulation in spatial pattern ψ(r) through filtered FT:

𝛹 𝒒 𝒌 = 𝑒𝑥𝑝 - 𝒌!𝒒 ! !! ! 𝑒𝑥𝑝 -𝑖 𝒒 • 𝒙 𝜓(𝒒 + 𝒌), (S2)
where 𝜓(𝒌) is the FT of the data. By minimizing the DR, 𝑅 𝒒 [𝜓] ≡ 𝑹 𝒒 ! 𝜓 ! + 𝑹 𝒒 ! 𝜓 ! , for a given modulation while considering different q-modulations, we showed that one can obtain the phase averaged wave vector 𝑸 of DW modulations. Within the limits of Fourier transform, which is a linear basis transform, this approach was an advancement in dealing with situations when the amplitude does not show well defined peaks, due to severe disorder.

However, there are limitations in this approach because FT is a linear transformation of basis and is useful when the desired phenomenon has sharp features in the new basis: the wavevector basis. However, when there are randomly placed, highly disordered, patches of a real-space DW pattern with sprinkles of topological defects, Fourier transform based methods perform very poorly. Obviously, one would not attempt a

Fourier transform in trying to recognize human faces in an image for precisely this reason.

The limitation of the FT-based methods is evident in that, even when a modulation pattern consists of commensurate period 4a0 modulation (Q0=2π/4a0) everywhere except for a sequence of discommensurations (phase slips in commensurate modulation pattern), the Furthermore, the DR based approach therein averaged over topological defects (dislocations) ignoring their role. Finally, the DR based approach required manual choice of Fourier cutoff (𝛬 in Eq.S2) again based on human visual inspection of the data. Hence the entire process is time consuming and high-level human labor intensive and fraught with human perceptual bias. It is therefore not possible to study the largest SISTM image-arrays with this FT approach in any consistent way, rendering it impossible to inspect the complete electron-density and electron-energy dependence of the largest EQM image-array archives.

The ANN-based approach we introduce in the main text is far more powerful, selection of Fourier regions of interest, and is not tied to any basis. The ANN is inherently non-linear and an ANN with sufficient number of neurons can express/detect any function. 33 Due to the versatility of ANN's, our ANN-based approach allows us to rapidly analyze a complete image-array data set in its entirety, without any ad-hoc Fourier filtering or selection. Hence the ANN approach is quite unbiased. Moreover, once the ANN's are trained, the automatic assessment of new data set takes minutes, allowing for a highthroughput analysis. It is this efficiency that allowed discovery of the connection between nematic state and commensurate density wave state, both setting in at the pseudogap energy scale (Extended Data Fig. 1).

Methods References

33 Cybenko, G. Approximation by superposition of a sigmoidal function. Math. Control Signals Systems 2, 303-314 (1989).

Extended Data

  Fig. 1e), to recognize spatial modulations in a variety of distinct categories, to identify their fundamental periodicity and lattice register throughout an image, and to distinguish if the modulations are unidirectional or bidirectional. The first stage is generation of sets of ANN training images, each labeled by a hypothesis: the different DW modulations to be discerned. Here, we test four hypotheses associated with four distinct types of ideal periodic modulations, all with a d-symmetry form factor, and with fundamental wavelengths λ=4.348a0, 4.000a0, 3.704a0, 3.448a0 respectively. Notice that only category 2 represents a commensurate pattern with 𝜆 = 4𝑎 ! . Four training sets for categories C=1,2,3,4 are then generated using identical procedures, in which we introduce specific forms of heterogeneity designed to mimic the noise, intrinsic disorder and topological defects of experimental data (Fig. 2a and Methods Section 3). Throughout these simulated training-image-sets, the heterogeneity disrupts the long-range ordered patterns in r-space, as shown for a typical training image in Fig. 2b. It also scrambles the peaks in the d-symmetry Fourier transforms 17 of the training images, rendering them broad and chaotic (Fig. 2c). In the second stage, we establish an ANN architecture that trains well with these training-image-sets. During training, the parameters of the ANN are adjusted iteratively to minimize a cross-entropy cost function 29 . Stochastic gradient descent along with backpropagation 30 is used for lowering the cost function. The training is complete and all parameters of each ANN are set when the cross-entropy 31 saturates. Each finalized ANN

Figure 1 .(

 1 Figure 1. Electronic quantum matter imaging in hole-doped CuO2. a, Schematic phase diagram of hole-doped CuO2. At p=0 a single electron is localized at each Cu site in a Mott insulator (MI) state. As holes are introduced (electrons removed) the MI disappears quickly. The high temperature superconductivity (SC) emerges at slightly higher p, reaching its maximum critical temperature Tc near p~0.16. However, in the range p<0.19 and up to temperatures T * an enigmatic phase of EQM, dubbed the pseudogap (PG) phase, is known to contain periodic charge density modulations of imprecise wavevector Q. b, In the CuO2 Brillouin zone, the Fermi surface is defined as the 𝒌-space contour 𝒌 𝐸 = 0 that separates the occupied from unoccupied electronic states, and its locus changes rapidly with changing carrier density p. Density wave (DW) states may then appear at a wavevector 𝑸(𝒌 ! 𝐸 = 0 -𝒌 ! 𝐸 = 0 ) if the electron states 𝒌 ! 𝐸 and 𝒌 ! 𝐸 are "nested" (red and yellow arrows). c, Strongly correlated electrons may be fully localized in the Mott insulator phase, or self-organized into electronic liquid crystal states in 𝒓 -space. Schematically shown here is a simple example of a state with unidirectional charge density modulations in the CuO2 plane, having wavelength 𝜆 = 4𝑎 ! or wavevector 𝑸 = !! ! ! 0.25,0

Figure 2 .

 2 Figure 2. Training ANN to identify broken-symmetry states in SISTM data. a, The ANN array is trained to recognize a DW in electronic structure images (e.g. 𝑍 𝒓, 𝐸 ) representing different EQM states. A synthesized training-image set for the ANNs is obtained by appropriately diversifying pristine images of 4 distinct electronic ordered states. Each translational symmetry-breaking ordered state is labeled by a category 𝐶 = 1,2,3,4 associated with its wavelength: 𝜆 ! = 4.348𝑎 ! , 4𝑎 ! , 3.704𝑎 ! , 3.448𝑎 ! respectively. The training-images in each category are diversified by appropriate addition of noise, short correlation-length fluctuations in amplitude and phase, and topological defects. b, Example of a training-image in category C=2 which is a d-symmetry form factor (dFF) DW along xaxis with 𝜆 = 4𝑎 ! within which smooth amplitude and phase fluctuations and randomized positions of topological defects (dislocations) have been added to simulate typical phenomena encountered in experimental EQM visualization (e.g. 1D). The full 516x516 pixel image contains 2x86x86 entire CuO2 unit-cells with Cu-Cu distance of 6 pixels diagonally. c, The d-symmetry Fourier transform of b. Absence of a well-defined modulation wavevector 𝑸 within the modulations in b has been successfully simulated in the training-image as seen by the region of 𝒒-space (grey dashed circle) within which strong variation in the amplitudes at different wavevectors occur. Grey dots are at 𝒒 = !! ! ! ±0.5,0 ; 0, ±0.5 . d, Each ANN is trained by minimizing the cross-entropy cost

Figure 3 .

 3 Figure 3. ANN analysis of experimental EQM visualization data. a, Typical measured 16nmX16nm 𝑍 𝒓, 𝐸 = 84𝑚𝑒𝑉 image of Bi2Sr2CaCu2O8 with p=0.08 (Tc=45K). The disorder and complexity of cuprate EQM are manifest. b, Typical measured 𝑍 𝒒, 𝐸 = 84𝑚𝑒𝑉 image of Bi2Sr2CaCu2O8 with p=0.08 (Tc=45K) being the d-symmetry Fourier transform of a. The disorder and complexity of EQM are equally vivid here in the broad and fluctuating peaks around 𝑄 ! ± 𝛿𝑄 ! , 𝛿𝑄 ! 2𝜋/𝑎 ! and (𝛿𝑄 ! , 𝑄 ! ± 𝛿𝑄 ! )2𝜋/𝑎 ! with 𝛿𝑄 ! = 𝛿𝑄 ! ≈ 0.2. Grey dots are at the 0.4,0 ; 0,0.4 2𝜋/𝑎 ! points. c, Schematic of ANN analysis procedure for experimental 𝑍 𝒓, 𝐸 images: the successfully trained neural network with fixed parameters (weights W (1) and W (2) of the hidden layer and the output layer respectively and biases) is a classifier: It classifies each experimental image as belonging into one of the four categories. Neuron activation functions in our ANNs are taken to be the sigmoid function.

Figure 4 .

 4 Figure 4. ANN detection of broken-symmetry evolution with electron-density. a-e, Measured 16nmX16nm 𝑍 𝒓, 𝐸 images of Bi2Sr2CaCu2O8 in the range p=0.06,0.08,0.085,0.14,0.20 (Tc(K)=20,45,50,74,82). Each image is measured at 𝐸 = Δ ! (𝑝) the pseudogap energy at that electron-density. Obviously disorder and complexity of cuprate EQM abound throughout this whole electron-density range (black double headed arrow in Fig. 1A). f-j, The d-symmetry Fourier transforms 𝑍 𝒒, 𝐸 from a-e. The disorder and complexity of EQM are equally vivid as broad fluctuating peaks around 𝑄 ! ± 𝛿𝑄 ! , 𝛿𝑄 ! 2𝜋/𝑎 ! and (𝛿𝑄 ! , 𝑄 ! ± 𝛿𝑄 ! )2𝜋/𝑎 ! . Grey dots are at the 0.4,0 ; 0,0.4 2𝜋/𝑎 ! points. k-o, Output categorization by 81 ANNs of the input data from a-e. Top row numbers: the category's fundamental wavelength, in units of 𝑎 ! . We take statistics of independent assessment on the given experimental image by 81 ANN's that are independently trained to arrive at the probabilities P(C) of the image belonging to category C. The error bars mark the statistical spread (one standard deviation) of P(C) among 81 independently trained ANN's (see Methods). Since the training-images for ANNs are unidirectional, i.e., their pristine orders are along x-axis, categorization results for two modulation orientations X,Y (red and yellow bars) are obtained by inputting to ANNs the 𝑍 𝒓, 𝐸 images and their 90-degree rotated versions, respectively.

Figure 5 .

 5 Figure 5. ANN detection of broken-symmetry at different electron-energies. a-d, Measured 16nmX16nm 𝑍 𝒓, 𝐸 images of Bi2Sr2CaCu2O8 in a range of electron-energy 𝐸=66,96,126,150 (meV) for p=0.08 (Tc(K)=45K). EQM complexity in the identical field of view, now evolves rapidly with electron-energy, a purely quantum mechanical effect. e-h, The d-symmetry Fourier transforms 𝑍 𝒒, 𝐸 from a-d. The disorder and complexity of EQM are strong as seen in the broad fluctuating peaks around 𝑄 ! ± 𝛿𝑄 ! , 𝛿𝑄 ! 2𝜋/𝑎 ! and (𝛿𝑄 ! , 𝑄 ! ± 𝛿𝑄 ! )2𝜋/𝑎 ! but now 𝛿𝑄 ! , 𝛿𝑄 ! evolve rapidly with electron-energy (another quantum mechanical effect). Grey dots occur at 0.4,0 ; 0,0.4 2𝜋/𝑎 ! points. i-l, Output categorization by 81 ANNs of the input data from a-d. Top row numbers: the category's fundamental wavelength, in units of 𝑎 ! . We take statistics of independent assessment on the given experimental image by 81 ANN's that are independently trained to arrive at the probabilities P(C) of the image belonging to category C. The error bars mark the statistical spread (one standard deviation) of P(C) among 81 independently trained ANN's (see Methods). Categorization results for two modulation orientations X,Y (red and yellow bars) are obtained by inputting to ANNs the 𝑍 𝒓, 𝐸 image-array and its 90-degree rotated version, respectively.

3

  Training image set generation. The diversification of synthetic images of a unidirectional DW to create a training image set (see Extended Data Fig.4) starts from dwave and s-wave form factor (DFF and SFF) components, and includes (1) heterogeneity through independent amplitude and phase fluctuations and (2) topological defects or dislocations in DFF. For any of the C=1,2,3,4 categories with representative wavelength λ ! ,

  S1)with overall constants ADFF=1, ASFF=0.5 and phase offsets 𝜑 !"" = 𝜋/4, 𝜑 !"" = 0. Here the amplitude field 𝐴 ! (𝑥, 𝑦) and the phase field 𝜑 ! (𝑥, 𝑦) capture smooth fluctuations (different random realizations in 𝐼 !,!,! !"" 𝑥, 𝑦 and 𝐼 ! !"" 𝑥, 𝑦 ), and 𝐴 ! (𝑥, 𝑦), 𝜑 ! (𝑥, 𝑦) capture dislocation defects. For each category, we generate different realizations labeled by f and d. For each realization f the 𝐴 ! (𝑥, 𝑦) field is two-dimensional Gaussian fluctuation field with spatial length scale ξA=8a, normalized between (-1) and 1, while 𝜑 ! (𝑥, 𝑦) is two-dimensional Gaussian fluctuation field with the same spatial lengthscale ξφ=8a, normalized between -π and π. The values of correlation lengthscales ξA, ξφ are motivated by a simple analysis of an SI-STM 𝑍 𝒒, 𝐸 Fourier transform (Fig.3). The strengths of amplitude and phase fluctuations εA=0.8, εφ=0.5 are also chosen to produce images in rough consistency with a typical 𝑍 𝒓, 𝐸 . In each image, there are nd=2 dislocations at random positions xi=(xi,yi),

  determines the output through a non-linear transformation 𝑓(𝒘 • 𝒙 + 𝑏) , called the activation function. The bias b and the weights 𝒘, are the parameters of the ANN and adjusted during the training. The activation function usually takes the form of the sigmoid function or the rectified linear unit, see the inset of Extended Data Fig.5a. We also use a softmax function 𝜎(𝒙) ! = 𝑒 ! ! / 𝑒 ! ! ! for the output layer to normalize the output and allow a probabilistic interpretation for the different categories.

Fig. 8 )

 8 Fig.8): (1) Topograph of Bi2Sr2CaCu2O8, which has no human-discernible modulation except for the Cu atomic lattice (an SFF at Q=0); (2) 𝑍 𝒓, 𝐸 of NCCOC, with obvious commensurate period 4a0 modulations, apparent in a DFF Fourier transform. The ANNs' categorization is in full accord.

  further tested the robustness of the ANN decisions against change in the disorder model. For this we trained a new ANN with the training set generated with different disorder parameters. Specifically, we decreased the amplitude fluctuation intensity εA by 13%, and phase fluctuation intensity εφ by 20%, while making the disorder profiles vary more rapidly in space by decreasing the correlation lengths ξA, ξφ by 6%.Repeating the assessment of experimental data shown in Fig.4k,l,m,o and Extended Data Fig.1awith the new ANN, we find the results remain unchanged. This is shown through the comparison between the reprint of Fig.4k,l,m,o and Extended Data Fig.1ahere as Extended Data Fig.9a-e respectively and the output from the ANN trained with the new disorder model as Extended Data Fig.9f-j. Robust observations are 1) preference for the commensurate period 4a0 for systems with 0.06<p<0.14 (Extended Data Fig.9a-d, and f-i)

  Rq[ψ] minimization (as well as the FT amplitude maximization) incorrectly identifies an apparent period of 𝑄=0.3*2π/a0 (Extended Data Fig.10e). Although in Ref.28 the DR minimization yielded 𝑄 = 2𝜋/4a0 for pseudogap energy data (single data set for each doping) for various dopings, this depended critically on human visual inspection to identify commensurate patches in Fig.S6Bof Ref.28 (see also Extended Data Fig.3here).

  Fig. 1 ANN detection of unidirectionality at different electronenergies. a, b, Output categorization by 81 ANNs of the 16nmX16nm 𝑍 𝒓, 𝐸 images of Bi2Sr2CaCu2O8 in a range of electron-energy 𝐸=30...150 (meV) in steps of 6 meV for p=0.08 (Tc(K)=45K). Plot symbols are larger than the statistical spread (one standard deviation) of the ANN outputs, as estimated from our ensemble of 81 ANN realizations (see Methods). a, Output for modulation orientation X is obtained by inputting to ANNs the 𝑍 𝒓, 𝐸 imagearray. b, Output for modulation orientation Y is obtained by inputting to ANNs the 90degree rotated versions of the 𝑍 𝒓, 𝐸 used for a. Extended Data Fig. 3 Local commensurate motifs in STM images. a, Large field of view, high precision, STM image of electronic structure integrated to E=100meV in Bi2Sr2CaCu2O8 with p~0.08. Inset shows the power spectral density FT while lower-right inset shows that data plotted along a line from 0.1 to 0.5 in units of 2π/a0. Clearly, the maximum intensity peak occurs at <Q>=0.28. b, Within each of the eight 6.5nm-square regions taken from a there are many commensurate, unidirectional 4a0 electronic-structure motifs (inside white rectangles). The Cu sites, independently determined from topographic imaging, are shown as fine dots. 44 Extended Data Fig. 10 Weakness of Fourier Transform analysis of EQM. a, b, The DFF Fourier amplitude, |Ψ 𝒒 |, with wavevector 𝒒 restricted to a square area with corner at the Fourier space origin (black square) and center at 𝑸 ! = ! ! 𝑮 ! (in a) or 𝑸 ! = ! ! 𝑮 ! (in b), where 𝑮 ! and 𝑮 ! are the Bragg peaks. Data from Bi2Sr2CaCu2O8 sample at doping level p=0.10 (Tc(K)=65K). c, Modulation is the real part of complex wave 𝜓 𝑥 = 𝐴(𝑥)𝑒 !(! ! !!!(!)) having commensurate domains with local wavevector 𝑄 ! = ). The amplitude 𝐴 𝑥 ≥ 0 varies smoothly around value 1. Phase slips are incorporated in 𝜑(𝑥) (see d). The average wavevector is 𝑄 = 0.3× !! ! . d, The local phase 𝜑(𝑥) of 𝜓 𝑥 in c, constructed as a discommensuration (DC) array in the phase argument Φ 𝑥 = 𝑄 ! 𝑥 + 𝜑(𝑥) . Phase slips of all DC's are set to +𝜋 . The distances between neighboring DC's vary randomly around average distance set by value of incommensurability 𝛿 = 𝑄 -𝑄 ! = 0.05× !! ! . e, Fourier amplitudes |𝜓 𝑞 | of the modulation 𝜓 𝑥 in c (blue line) show narrow peak at 𝑄 = 0residue |𝑅 ! | (red dashed line) has the minimum exactly at the average 𝑄.

  𝛿𝑄 ! , 𝛿𝑄 ! 2𝜋/𝑎 ! and (𝛿𝑄 ! , 𝑄 ! ± 𝛿𝑄 ! )2𝜋/𝑎 ! in Here the ANNs reveal that, on the average, the phenomenology of the C=2, 𝜆 = 4𝑎 ! training-images has the highest probability of being recognized within the 𝑍 𝒓, Δ ! image array, but only for electron-densities 0.06 ≤ 𝑝 ≤ 0.14. 𝐸 into 𝒌 ! 𝐸 , resulting in quantum inference at wavevectors 𝑸 !" 𝐸 = 𝒌 ! 𝐸 -𝒌 ! 𝐸 , and generating modulations of 𝑁 𝒓, 𝐸 or its Fourier transform 𝑁 𝑸 !" , 𝐸 .

	o we show the response of the ANNs as the probability P(C) that the presented EQM image
	is identified in the category C. Thus, the ANNs identify a predominant translational symmetry breaking, occurring
	commensurately with the specific wavelength 𝜆 = 4𝑎 ! (Fig. 4a-d). Overall, the ANNs
	conclude that the identical, commensurate, 4𝑎 ! periodic, electronic structure modulations
	were hidden throughout the 𝐸 ≈ Δ ! EQM images from the 0.06 ≤ 𝑝 ≤ 0.14 area of the CuO2
	and Methods Section 4). Statistical reliability of this ML system against phase diagram.
	different network architectures and different initial conditions is achieved by training 81
	distinct ANNs in parallel with the same training image-set (Methods Section 4). 8 A second key physics issue is the energy dependence within an 𝑍 𝒓, 𝐸 image-array.
	Quasiparticle scattering interference 17 (QPI) occurs when an impurity atom scatters wave-
	7 arrays versus changing electron-density. The measured 𝑍 𝒓, 𝐸 electronic-structure images Our ANN ensemble is first used to hypothesis test the experimental EQM image-are from samples of the hole-doped cuprate Bi2Sr2CaCu2O8 that span the range 0.06 ≤ 𝑝 ≤ like states 𝒌 ! QPI is a distinct physical phenomenon from a DW state because, while the modulation
	0.20. Obviously disorder and complexity of EQM abound in 𝑍 𝒓, Δ ! throughout this whole wavevectors of the former evolve rapidly with 𝐸, for latter they do not. Therefore, the
	electron-density range (black double headed arrow in Fig. 1a) and are equally apparent in ANNs explore a Bi2Sr2CaCu2O8 𝑍 𝒓, 𝐸 array of 16nmX16nm EQM images, that are
	the broad fluctuating peaks around 𝑄 ! ± 𝑍 𝒒, Δ ! (see Figs. 3a,b). Definite fundamental periodicities seem undetectable in these
	Z 𝒓, Δ ! data. The set of experimental Z 𝒓, 𝐸 image-arrays have FOV 16nmX16nm, but are
	measured in a sequence of independent experiments on distinct crystals with p≈0.06, 0.08,
	0.085, 0.14, 0.20 (Tc(K)=20, 45, 50, 74, 82). The ANNs analyze these 𝑍 𝒓, Δ ! images as a
	function of p, focusing on the pseudogap energy 𝐸 = Δ ! 𝑝 because cuprate EQM
	symmetry-breaking emerges at this energy 17,25 . Figures 4a-e show the actual 𝑍 𝒓, Δ !
	images presented to the trained ANN system while Figs. 4f-j show their d-symmetry
	Fourier transforms. The ANN's succeed with high reliability in discriminating and
	identifying the periodic motifs throughout these images (Methods Section 5). In Figures 4k-

measured in a sequence of independent experiments at distinct electron-energy

𝐸=66, 96, 126, 150(meV)

on the same crystal with p=0.08. Figures

5a-d

show this 𝑍 𝒓, 𝐸 image set that is presented to the same ANN system. EQM complexity in the identical field of view now evolves rapidly with electron-energy because they are dominated by QPI. Similarly, Figures 5e-h are the d-symmetry Fourier transforms Z 𝒒, 𝐸 from Figures 5a-d, showing broad fluctuating peaks that evolve rapidly with electron-energy as expected in QPI. Welldefined fundamental periodicities appear indiscernible in these Z 𝒓, 𝐸 (A-D); Z 𝒒, 𝐸 (E-H) data. However, Figures 5j-l demonstrate that the ANN suite finds the hypothesis category

Acknowledgements

We thank Paul Ginsparg, Jenny Hoffman, Steve Kivelson, Roger Melko, Andy Millis, Miles Stoudenmire, Kilian Weinberger and Jan Zaanen for helpful discussions and communications; A.M., and Y.Z. acknowledge support from DOE DE-SC0010313; Y.Z. acknowledge support from DOE DE-SC0018946; E.-A.K. and J.C.S.D. acknowledge support by the Cornell Center for Materials Research with funding from the NSF MRSEC program (DMR-1719875); E.K. and K.C. acknowledge support from the NSF Grant No. DMR-1609560. E.-A.K. and E.K. acknowledge support from the Kavli Institute for Theoretical Physics, supported in part by the NSF under Grant No. PHY-1748958, where initial discussions about the project took place. S.U. and H.E. acknowledge support from a Grantin-aid for Scientific Research from the Ministry of Science and Education (Japan) and the Global Centers of Excellence Program for Japan Society for the Promotion of Science. K.F. and J.C.S.D. acknowledge support from the U.S. Department of Energy, Office of Basic Energy Sciences, under contract number DEAC02-98CH10886; S.D.E, M.H.H and J.C.S.D. acknowledge support from the Moore Foundation's EPiQS Initiative through Grant GBMF4544; J.C.S.D. acknowledges salary support from the European Research Council (ERC) under Award # DLV-788932.

Extended Data Fig. 2 Schematic image of density waves arising from strong coupling position-based theories in CuO2 plane. a, The d-symmetry 4a0 charge density wave. The charge density at Ox site is modulating with four-unit-cell periodicity along horizontal direction, and similarly for that at Oy but out of phase by π (d-symmetry). Cu locations are marked by small dots. b, The 8a0 pair density wave state. The d-wave Cooper pair density is modulated with eight-unit-cell periodicity along horizontal direction. Such modulation in Cooper pair density can cause 4a0-period modulation in the local density of states N(r). Extended Data Fig. 6 Experimental SI-STM images. a, Example 𝑍 𝒓, 𝐸 of underdoped Bi2Sr2CaCu2O8 with hole density p=0.06 (Tc(K)=20). The inset is a zoom-in with marked atom positions determined from topograph (Cu: red/light, O: purple/dark). b. A small region of a. c, The standardized version of b (see Methods). Extended Data Fig. 8 Benchmarking categorization using experimental images. a, Input data for the topograph of overdoped Bi2Sr2CaCu2O8 with p=0.22 (Tc(K)=70). b, Output categorization by 81 ANNs of a, showing absence of translation-breaking signal. Results for two modulation orientations X,Y are obtained by inputting to ANNs the image in a and its 90-degree rotated version, respectively (see Methods). c, The input data for 𝑍 𝒓, 𝐸 of NCCOC at doping p=0.12 at E=150meV. d, Output categorization by 81 ANNs of c, showing commensurate modulations (category 2).


Remote Sensing K L Mitchell
email: karl.l.mitchell@jpl.nasa.gov

R Hodyss

M Choukroun

J Molaro

A Le Gall

ENCELADUS' BRILLIANT SURFACE 2: RATIONALIZING CASSINI RADAR AND OPTICAL

Introduction:

The fresh, clean ice that dominates Enceladus surface makes it the most reflective surface of any Solar System body across a broad range of wavelengths, from visible to microwave. Fine-grained micron to 10s of micron particles resulting from plume or E-ring particle deposition dominate optical wavelengths, enabling enhanced geometric albedo due to coherent backscatter. However, high albedo at centimetric radar wavelengths suggests scattering from characteristic spatial scales of millimetric or greater. To date, no single model of surface material structure has been proposed that can explain all the observed phenomena. We propose that sintering of fine particles during past periods of low or zero cryovolcanic activity may create subsurface layers that enhance radar backscatter sufficiently to explain the observations. The thickness of the upper, unsintered layer is likely at least 1-2 cm, and probably well under a meter. More modeling and laboratory work is required to test the validity of our assertion that sintering during quiescent periods of plume activity is responsible for the enhanced radar backscatter.

Remote sensing constraints: Cassini carried a diverse suite of instruments which supplement terrestrial telescopic observations.

Visible imaging: Enceladus' visual geometric albedo is 1.38 [1]. A geometric albedo of >>1 means that, in addition to being remarkably bright, a target exhibits an considerable degree of retro-reflection. In Enceladus' case, this is best explained using a model that combines both moderate shadow-hiding and coherent backscattering components [2], the latter of which are common for surfaces that exhibit roughness at nearwavelength scales. Enceladus' nearest neighbours are nearly as bright (fig. 1), with geometric albedos following a trend best explained either as a function of Ering density or distance from Enceladus; These factors are of course related, as the E-ring is supplied from Enceladus' plumes. Over a global scale, variations in color/scattering remain diffuse, rather than defined by geological units [3]. Like other icy worlds within the E-ring, Enceladus exhibits a leading-trailing dichotomy, albeit slight. This implies a direct control of scattering properties from plume and E-ring particle fallout, rather than something affected by surface age or maturity. Only on Dione and Rhea, where fallout rates are significantly lower, does surface age, specifically tectonized terrains, cause variations in brightness along boundaries.

IR spectroscopy:

The VIMS instrument on Cassini enabled hyperspectral near IR imaging of Enceladus' surface at spatial resolution of up to few km/pixel, resulting in a clearer understanding of the composition of the surface. Brown et al. [4] analyzed the terrain of the south polar region in some detail based on the first three Enceladus flybys. The spectra are compositionally consistent with ground based observations, dominated by water ice, but with the additional detections of carbon dioxide and organic features. Grain sizes were estimated to be 50 to 100 µm globally, increasing to 100 to 300 µm near the tiger stripes. The degree of crystallinity of the ice was also shown to be greater in the region around the tiger stripes. Later analyses of additional VIMS spectra acquired as the mission progressed generally agree with Brown's initial findings. Smaller particles (~10-50 µm) are found away from the tiger stripes, while large particles (up to 200 µm) are concentrated in the tiger stripes [5]. This is consistent with ballistic deposition.

Cassini CIRS data analyzed by Howett et al. [6] show that the surface of Enceladus has an average thermal inertia of ~ 15 J m -2 K -1 s -0.5 . Such low values imply a highly porous material. The diurnal skin depth for the derived thermal properties is of 0.5 cm, consistent with a 1-2 cm cover of very loose materials.

Radar remote sensing: As discussed previously [7], Cassini RADAR observations at ~2.2-cm also show unusually bright surfaces in backscatter. This is inconsistent with a global layer of fine particles as discussed above, which would tend to absorb (loss tangents of 10 -2 to 10 -3 for snow reported by [8]) if sufficiently thick (at least centimeters thickness) and/or forward scatter if sufficiently smooth (at millimetric scales at beyond), and create relatively radar-dark surfaces. Three key observations may give hints as to the reason for the high backscatter: (1) Globally averaged backscatter from icy worlds in the Saturn system follows trends much like for optical albedo ([9]; fig. 1) implying a link to fine particle fallout; (2) Brightness varies discretely on Enceladus' surface, delimited by tectonically-resurfaced margins (as seen in E16 SAR imagery) rather than diffusively, suggesting that surface maturity/age plays a role; (3) The magnitude of the backscatter to radar is extreme, with units in the E16 SAR swath exhibiting s 0 <= 3.9 (5.9 dB), where s 0 is a single fixed polarization normalized radar cross section. Taken together, we infer that particle fallout is partly responsible, but that something else is going on causing enhanced backscatter.

Discussion: Microwave energy will tend to scatter preferentially from ice volumetrically, as the vacuumice interface only results in partial reflection of incoming energy. This means that any structural components responsible for high backscatter are likely to be in the subsurface, potentially at considerable depth (potentially thousands of wavelengths).

The only other known location in the solar system with comparable radar backscatters are in or near Xanadu on Titan [10], especially in sinuous channels on Titan [10] with s 0 ~ 3.2 (5 dB). This is larger than easily explained by coherent backscatter effects, and is best explained by (near) spherical structures of corner reflectors (such as cubes), which seems reasonable for Titan's channels, as river/stream beds often include rubble or pebbles. On Enceladus, however, no plausible geological justification has been given for such structures, and indeed, given the rates of fine particle fallout (~1 um/yr), one might expect them to be buried over geological timescales.

In our previous work, we concluded that surface roughness was insufficient to produce the observed backscatter, and instead proposed that either organized or random subsurface structures at millimetric scales or greater might be sufficient to produce enhanced backscatter of the magnitudes observed [7].

One possible explanation is structural changes in fallout products resulting from sintering at cm-scale depth. Terrestrial research has shown that density is the dominant factor controlling the dielectric properties of dry snow (e.g. [11]), and thus sintering timescales can be used to constrain the time and spatial scales over which surface layering may develop at Enceladus. Following [12], we estimate sintering timescales of spherical ice grains in the near surface of Enceladus based on a mean surface temperature of 80 K and a grain size of 1 µm. We assume an aggregate density equal to the typical, random packing density of spheres (~64%). Significant sintering can occur over much shorter timescales (10000 years for ice, 100 years for salty ice), but densification effects would be negligible, and so it's unclear if there would be a difference in radar properties. An increase in 1-10% of the aggregate density is required to achieve a significant change in the dielectric properties of the ice, which we estimate occurs after 100 -1000 Ma in pure water ice, and 10 -100 Ma for ice containing 2.5% sodium chloride by mass. Compared with global resurfacing rates (~1 µm/yr), these timescales are long, but not ludicrous. Assuming a deposition rate of 1 µm/yr, fresh plume material would form a 10 cm layer over the surface after 0.1 Ma, effectively halting the densification in the subsur-face. If activity ceases for these times periods, then sintering may well result in layering that would likely result in enhanced backscatter.

References et al., 2010). SL-2 is radar equivalent to optical geometric albedo, and a summation of two orthogonal polarizations. Note that the radar SL-2 albedos reported here are a factor of 2 less than reality, due to a mistake in analysis (R. West, pers. comm.). Optical albedos for Mimas, Enceladus, Tethys, Dione, and Rhea are from Verbiscer et al. (2007). A trend in brightness for both optical and radar can be interpreted as relating either to E-ring density or to distance from Enceladus. Leading = L, trailing = T.

2924.pdf 49th

  : [1] Verbiscer, A., et al. (2007) Science 315, 815; [2] Verbiscer, A. J. et al., (2005) Icarus 173, 66-83; [3] Schenk, P., et al., (2011) Icarus, 211, 740; [4] Brown, R. H. et al. (2006) Science 311, 1425-1428; [5] Jaumann, R. et al. (2008) Icarus 193, 407-419; Taffin, C. et al. (2012) Planet. Space Sci. 61, 124-134; Fillacchione, G. et al. (2012) Icarus 220, 1064-1096; [6] Howett, C. J. A. et al. (2010) Icarus 206.2, 573-593; [7] Mitchell, K. L. et al. (2013) LPS XLIV, #2902; Khankhoje, U. K.. et al. (2013) LPS XLIV, #2531; [8] Stiles, W. H. and Ulaby, F. T. (1981) RSL Tech. Rep. 527-1; [9] Ostro, S. J. et al. (2010) Icarus 206, 498-506; [10] Le Gall, A. et al. (2010) Icarus 207, 948-958; [11] Glen, J.W. and J.G. Paren (1975) J. of Glaciology, 15(73), pp.15-38; [12] Molaro, J. L., et al. (2017) DPS 49, #203.08. Additional Information: This research was carried out at the California Institute of Technology Jet Propulsion Laboratory under a contract from NASA. It was supported by internal JPL Advanced Concepts funds.

Figure 1 :

 1 Figure1: Cassini measurements of SL-2 (squares) and average optical geometric albedos (circles), plotted for satellites vs. distance from Saturn(Ostro et al., 2010). SL-2 is radar equivalent to optical geometric albedo, and a summation of two orthogonal polarizations. Note that the radar SL-2 albedos reported here are a factor of 2 less than reality, due to a mistake in analysis (R. West, pers. comm.). Optical albedos for Mimas, Enceladus, Tethys, Dione, and Rhea are fromVerbiscer et al. (2007). A trend in brightness for both optical and radar can be interpreted as relating either to E-ring density or to distance from Enceladus. Leading = L, trailing = T.

  Lunar and Planetary Science Conference 2018 (LPI Contrib. No. 2083)


domain: phys spi

text:
Meriem Tamart

Elodie Richalot #

Julien De Rosny

Passive characterization of the couplings within a multi-antenna system through noise correlation

Keywords: Multi-antenna system, reverberation chamber, measurements, antenna coupling, noise-correlation

This communication deals with a technique to passively retrieve the couplings between several antennas. The mutual-impedance of coupled antennas are deduced from field correlations in a reverberation chamber (RC). It is experimentally shown that the impedance matrix between 2 slot antennas or 3 horn antennas are reconstructed with good accuracy whatever the antenna properties. The accuracy is quantified with respect to the distance between the antennas.

I. INTRODUCTION

The increasing demand for higher transmission rates and quality of service in existing and emerging wireless communication systems requires solutions to improve their performance. One solution is the use Multiple Input Multiple Output (MIMO) methods [START_REF] Gesbert | From theory to practice: An overview of MIMO space-time coded wireless systems[END_REF], [START_REF] Martin | MIMO radio channel measurements: Performance comparison of antenna configurations[END_REF]. This last uses multiple transmit and receive antennas to ensure reliable connections and good network coverage without increasing the transmit power or spectral bandwidth. However, the improvements of multi-antenna systems are accompanied by significant technical challenges. These multiple antennas suffer from high correlation and mutual coupling [START_REF] Foschini | On Limits of Wireless Communicatiosn in a Fading Environment when Using Multiple Antennas[END_REF]. As it has been demonstrated that mutual coupling can have a positive or negative effect, its evaluation remains an essential tool for estimating the performances of the MIMO system [START_REF] Svantesson | The Effects of Mutual Coupling Using a Linear Array of Thin Dipoles of Finite Length[END_REF]. Hence, taking mutual coupling into account in multi-antenna systems, either in their design or in antenna processing algorithms, allows improve the actual radiation efficiency of each element.

In this context, this article aims at validating a novel technique to passively characterize the coupling between the elements of a multi-antenna system by diffuse field correlation in a reverberation cavity.

Based on an analogy with results obtained in acoustics and seismology [START_REF] Lobkis | On the emergence of the Green's function in the correlations of a diffuse field[END_REF], [START_REF] Campillo | Seismic imaging and monitoring with ambient noise correlations[END_REF], we showed experimentally that the cross-spectral density between mutual-impedances is linearly related to the radiation impedance between two receiving antennas [START_REF] Tamart | Diffuse field cross-correlation in a reverberantion chamber[END_REF]. Very recently, the underlying theory was derived [START_REF] Tamart | Passive antenna characterization through impedance correlations in a diffuse field[END_REF] and it provides the expression of the cross-spectral density with respect to the real part of the impedance between two antennas in a reverberation chamber. This expression takes into account both the cavity losses and the antenna efficiency, which were not considered in previous works on correlation of S-parameters that only focused on lossless antennas [START_REF] Davy | Diffuse field cross-correlations: Scattering theory and electromagnetic experiments[END_REF].

This paper presents a validation and an extension of the aforementioned passive method. In Section II, we extend the theoretical developments between the Power Spectral Density (PSD)/the Cross Spectral Density (CSD) and the real part of the self/mutual-impedance to N coupled antennas. These theoretical formulas are validated in Section III using two facing slot antennas as receiving antennas. In Section IV, we test the robustness of our method by varying the distance between the antennas under test (AUT) and evaluate the convergence of the passive reconstruction to the active reference measurement by computing the Pearson similarity coefficient. Section V is dedicated to the application of the impedance correlation technique to estimate the coupling between each pair of antennas in a system consisting of three elements. After discussing the measurement results, we conclude this paper.

II. THEORY

We consider a Tx-antenna of self-impedance Z T xT x and of radiation efficiency η T x . A set of N coupled Rx-antennas is characterized by its impedance matrix. One element of this matrix Z ij is the mutual-impedance between antenna i and j when i ̸ = j and the self-impedance of antenna i when i = j. An example of 2 antennas A 1 and A 2 placed in a reverberation chamber (RC) of volume V is illustrated in Fig. 1. We assume that the load impedance of each Rx-antenna is sufficiently high such that the voltage induced on Rx-antenna i by the Tx-antenna is directly proportional to the mutual-impedance Z iT x . The auto and cross-correlations, i.e., the cross and power spectral densities between Z iT x and Z jT x are defined as

C ij = Z iT x Z * jT x . (1)
Symbol ⟨•⟩ indicates an averaging over all measurement configurations in the RC.

Based on the theory developed in [START_REF] Tamart | Passive antenna characterization through impedance correlations in a diffuse field[END_REF], the impedance correlation can be expressed in terms of the average energy density W as follows:

C ij = c ⟨W ⟩ λ 2 2π|I T x | 2 ℜ(Z ij ). (2)
If a source antenna transmits a power P T x expressed by Eq.3 , all of this power is absorbed through dissipation processes in the RC.

P T x = η T x ℜ(Z T x ) |I T x | 2 . (3)
The transmitted power in this case is given by :

⟨P T x ⟩ = ⟨W ⟩ V α (4)
From equations 3 and 4, we can extract the expression of W, which will be substituted into the impedance correlation expression, resulting in the following expression of impedance cross-correlation

C Zi̸ =j = Z iT x Z * jT x , C Zi̸ =j = λ 2 cη Tx ℜ(Z TxTx ) 2παV ℜ(Z ij ) (5)
as well as the autocorrelation expression

C Zii = ⟨Z iT x Z * iT x ⟩, C Zii = λ 2 cη Tx η i ℜ(Z TxTx ) 2παV ℜ(Z ii ), ( 6
)
where λ is the wavelength, α the RC energy decay rate, and

η i = R i /ℜ(Z ii ) is the radiation efficiency of antenna i (R i is the radiation impedance).

III. EXPERIMENTAL RESULTS

A. Measurement Setup

All experiments are performed within the ESYCOM RC of dimensions 2.95 × 2.75 × 2.35 m 3 whose lowest usable frequency is estimated to be 400 MHz. It is equipped with a Z-fold mechanical stirrer (60 equally-spaced positions are considered over a full rotation). The source antenna, labelled "T x ", is a horn antenna oriented towards the mechanical stirrer and positioned on a vertically-rotating structure in order to perform source stirring over N src = 11 positions.

a-Experiment with 2 receiving antennas

For the first experiment, two antennas under test (AUTs), labelled "A 1 " and "A 2 " are facing each other, separated by distance d = 30 cm. A 1 and A 2 are slot antennas, based on a half-disc slot excited by a microstrip with a frequency bandwidth from 1.7 to 2.8 GHz (Fig. 2). Scattering parameter measurements are carried out at 9001 frequency samples uniformly spaced on the frequency band of [1.4 -3.2] GHz with a Rohde & Schwarz ZNB20 Vector Network Analyser (VNA).

To investigate the convergence of the estimated impedances to the measured ones, we analyze the impact of the distance between the AUTs. Specifically, we keep antenna A 1 fixed and move antenna A 2 to vary the distance between the two antennas from 30 cm to 50 cm, with a step of 10 cm. The second experiment consists of an extension of the proposed method to the case of 3 antennas in reception. For this purpose, we examine a reception system of three directional horn antennas. Two of the antennas, A 1 and A 2 , are SH800 model horn antennas. The third antenna, A 3 , is a Schwarzbeck horn antenna. These antennas are arranged facing each other and are separated by distances of d 12 = 36 cm, d 13 = 35 cm and d 23 = 28 cm and the measurement is performed in the frequency range [START_REF] Gesbert | From theory to practice: An overview of MIMO space-time coded wireless systems[END_REF][START_REF] Martin | MIMO radio channel measurements: Performance comparison of antenna configurations[END_REF][START_REF] Foschini | On Limits of Wireless Communicatiosn in a Fading Environment when Using Multiple Antennas[END_REF][START_REF] Svantesson | The Effects of Mutual Coupling Using a Linear Array of Thin Dipoles of Finite Length[END_REF][START_REF] Lobkis | On the emergence of the Green's function in the correlations of a diffuse field[END_REF] GHz.

We perform the mutual-impedance reconstruction for each pair of receivers using the impedance correlation between the source antenna and each receiving antenna individually.

B. Data Processing

As we are only interested in the Z-parameters, the measurements of the scattering parameters between the source antenna and each AUT are carried out using the same loading conditions as if the impedance were directly measured, i.e. by loading the other two AUTs by an open circuit. The obtained S-sub-matrix permits to extract the Z-matrix between the T x antenna and the AUT. This operation is repeated for each AUT. A further reference measurement was conducted by utilizing all the ports of the VNA. This enabled a comparison between the results obtained through correlation method and those acquired from a direct measurement for both mutual and self-impedances.

C. Results a-Results with 2 AUTs

Figs. 3, 4 and5 show the results of the real parts of the mutual-impedance Z 12 as well as the self-impedances Z 11 and Z 22 reconstructed passively by the impedance correlation method compared to those obtained by active measurements, for the first experiment, in both the frequency domain and the time domain through inverse Fourier transform. A good agreement is observed between the impedance values obtained from the correlation method proposed and the ones measured directly between AUTs.

In Fig. 6a, the time of arrival of the main peak is plotted as a function of the spacing between the AUTs, resulting in a straight line with a constant slope. As expected, the displacement of the peak position between two consecutive measurements corresponds to a distance variation of 10 cm. We observe in Fig. 6b that the amplitude of the peak decreases as the distance between the antenna increases. Fig. 3. The real part of Z 12 obtained by a direct measurement between 2 slot antennas or through cross-correlation between impedances Z 1T x and Z 2T x for a distance of 30 cm between AUTs, as a function of time (above) and frequency (below). The results of the reconstruction of the self-impedances Z 11 and Z 22 for the three different spacings between the AUTs are depicted in Fig. 7. It can be observed that the self-impedances of the AUTs are not affected by the spacing between them. To evaluate how closely the impedances estimated from the theoretical model match up with those obtained through an active measurement between antennas, we compute the Pearson similarity coefficient and the obtained results are indicated the table below. Based on the information presented in Tab. 1, it can be concluded that the self-impedances are not significantly affected by the spacing between AUTs. However, the reconstruction of mutual-impedance becomes less precise as the distance between AUTs increases. Actually, the observed reduction in amplitude, depicted in Fig. 6b decreases the signal-to-noise ratio and therefore the Pearson correlation coefficient.

b-Results with 3 AUTs

The real parts of the mutual-impedances Z 12 , Z 13 and Z 23 for the three antenna system were measured passively using the correlation method. These measurements are then compared to the results obtained by directly measuring the mutual-impedance. Figs. 8,9, and 10 present the results in both frequency and time domains.

To assess the similarity of mutual-impedances obtained through passive measurements using impedance correlation method with those obtained through active measurements for each pair of receiving antennas, we computed the three Pearson coefficients. Tab. 2 displays the results, which yields an average Pearson coefficient of 0.75. This value is deemed acceptable as the antennas are not oriented facing to each other, leading to a weak coupling between them (and thus a reduced signal-to-noise ratio).

It is important to note that the distance between antennas is a crucial factor in achieving convergence. This is because the degree of coupling between antennas rises as their distance decreases. This phenomenon is demonstrated by the highest similarity value of Z 23 , which corresponds to the lowest spacing (28 cm) between antennas A 2 and A 3 .

IV. CONCLUSION

In this paper, a method for characterizing the coupling between antennas using correlation of the diffuse field generated in a reverberation chamber is presented. Through experimental validation, it has been shown that the mutual impedance between two slot antennas can be accurately obtained at three different distances between the AUTs. Furthermore, the method has been validated with a system comprising three AUTs, successfully retrieving the coupling between each antenna pair. This technique is not limited to a specific number of elements and can be expanded to larger arrays, allowing for faster characterization of antenna arrays.

The notable advantage of this method is that it does not require multiple measurements in both transmit and receive modes to characterize the mutual coupling between antenna pairs. Instead, antennas in the system can remain in mode while a single transmit antenna is introduced to measure the entire system in a instance. The precision of this method depends on the measurement environment, specifically the reverberation chamber used in this study. limitations encountered in measuring within a reverberation chamber are influenced by various factors, including the number of uncorrelated configurations. However, these limitations are not inherent to the method itself but rather stem from the characteristics of the measurement environment. By ensuring improved conditions of diffuse fields, optimal precision can be achieved.

Fig. 1 .

 1 Fig. 1. Measurement configuration in a reverberation chamber with a source antenna Tx and two antennas under test A1 and A2.

Fig. 2 .

 2 Fig. 2. (a) Photo of the slot antenna; (b) reflection coefficient

-

Fig. 4 .

 4 Fig.4. The real part of Z 11 obtained by a direct measurement between 2 slot antennas or through auto-correlation of impedance Z 1T x , for a distance of 30 cm between AUTs, as a function of time (above) and frequency (below).

Fig. 5 .

 5 Fig.5. The real part of Z 22 obtained by a direct measurement between 2 slot antennas or through auto-correlation of impedance Z 2T x , for a distance of 30 cm between AUTs,as a function of time (above) and frequency (below).

Fig. 6 .

 6 Fig. 6. (a) The variation of the arrival time of the pulse related to the direct path as a function of the spacing between AUTs; (b) The variation of the amplitude of the pulse related to the direct path as a function of the spacing between AUTs

Fig. 7 .

 7 Fig. 7. The inverse Fourier transform of the real part of self-impedances obtained by the correlation method between 2 slot antennas for three different spacings between them.

Fig. 8 .

 8 Fig.8. Real part of Z 12 obtained by a direct measurement between A 1 and A 2 or through cross-correlation between impedances Z 1T x and Z 2T x for a distance of 36 cm between AUTs, as a function of time (above) and frequency (below).

Fig. 9 .

 9 Fig.9. Real part of Z 13 obtained by a direct measurement between A 1 and A 3 or through cross-correlation between impedances Z 1T x and Z 3T x for a distance of 35 cm between AUTs, as a function of time (above) and frequency (below).

Fig. 10 .

 10 Fig.10. Real part of Z 23 obtained by a direct measurement between A 2 and A 3 or through cross-correlation between impedances Z 2T x and Z 3T x for a distance of 28 cm between AUTs, as a function of time (above) and frequency (below).

Table 1 .

 1 Pearson correlation coefficient calculated for impedances obtained by direct measurement or by the correlation method in the cases of 2 AUTs and for three different spacings.

		30 cm	40 cm 50 cm
	ℜ(Z 11 )	0.9972	0.9971	0.9971
	ℜ(Z 22 )	0.9968	0.9971	0.9968
	ℜ(Z 12 )	0.9065	0.8728	0.8538

Table 2 .

 2 Pearson correlation coefficient calculated for the real part of the mutual-impedance, between each antenna pair, in the case of 3 AUTs, obtained by direct measurement or by the correlation method.

	ℜ(Z 12 )	ℜ(Z 13 )	ℜ(Z 23 )
	0.6822	0.6864	0.8979


Josephine Pichereau
email: josephine.pichereau@univ-eiffel.fr

Zied Fritiss
email: zied.fritiss@segula.fr

Hakim Takhedmit
email: hakim.takhedmit@univ-eiffel.fr

Patrick Poulichet
email: patrick.poulichet@esiee.fr

Laurent Lanquetin
email: laurent.lanquetin@segula.fr

Olivier Français
email: olivier.francais@esiee.fr

Elodie Richalot
email: elodie.richalot-taisne@univ-eiffel.fr

Sensing biological materials with differential RF broadband and resonating microsensors

Keywords: complex permittivity extraction, biological tissues, non-invasive diagnostic

This paper presents two dielectric sensors dedicated to biological sample diagnostic. The first one is a resonating sensor for the characterization of small liquid sample. The second one is a broadband non-invasive sensor submm spatial resolution for melanoma detection. In both cases, a differential approach is adopted in order to enhance the sensor sensitivity by limiting the impact of ambient factors (skin thickness, temperature, humidity…).

I. INTRODUCTION

Due to the permittivity variation of the biological samples versus their state, dedicated sensors can be of help in the diagnostic step. One encountered difficulty is however the influence of other factors related to the measurement environment of the patient state. Therefore, the use of a reference sample in the same conditions than the sample under test is of a great interest in order to increase the sensor accuracy and fiability.

The first sensor presented concerns applications for the analysis of small liquid samples and uses interaction of the matter with RF waves. To enhance the sensor sensitivity, a resonating structure (resonance around 1.35 GHz) has been selected. Its design is based on the symmetrical excitation of two Split Ring Resonators (SRR) loaded by the sample under test [START_REF] Bahar | Dielectric properties measurement based on split ring resonator for microfluidic characterization[END_REF]. The use of two resonators permits to consider a reference liquid and to detect small permittivity variations in regard to this reference.

The second sensor uses permittivity variation between healthy skin and melanoma, to analyze a suspicious area [START_REF] Mirbeik-Sabzevari | Ultra-wideband millimeter-wave dielectric characteristics of freshly excised normal and malignant human skin tissues[END_REF]. A small sensing area (in the millimeter range) is necessary to detect tumors at its beginning of their development [START_REF] Mohammed | Changes in epidermal dielectric properties due to skin cancer across the band 1-50 GHz[END_REF] and a good sensitivity is required to distinguish several types of lesions due to characteristics in permittivity dependence [START_REF] Naqvi | Benign and malignant skin lesions: dielectric characterization, modelling and analysis in frequency band 1-14 GHz[END_REF]. As the skin properties vary versus the body parts, individuals or the physiological conditions, in that applications, a broadband device (form 1 to 6 GHz) has been chosen and differential approach has been adopted to differentiate tumors from healthy skin in order to reduce influence of measurement environment.

II. RESONATING STRUCTURE IN TRANSMISSION FOR SMALL

SAMPLE ANALYSIS

A. Sensor design a) Presentation

The proposed sensors operates in transmission mode and contains a micro-strip line symmetrically loaded by two rectangular split ring resonators (rectangular-SRR) made of copper and printed on a substrate Arlon 25N with dielectric constant and loss tangent of 3.32 and 0.0025, respectively at 1.35 GHz. The copper thickness is of 35 µm and the substrate height given by the manufacturer of 1.6 mm. From these data, the width of the micro-strip line has been chosen to ensure impedance matching to 50 Ω. The prototypes of the two considered sensor versions, for respectively liquid and solid samples, are shown in Fig. 1. The dimensions of the sensor are presented in Table I.

The rectangular Split Ring Resonator (SRR) can be modeled as the association of an inductance and a capacitor, the later principally depending on the gap (g = 3 mm) within the resonator. When the material under test is placed in the gap of the SRR, the gap equivalent capacitance is modified that subsequently leads to a modification of the resonant frequency [START_REF] Withayachumnankul | Metamaterial-based microfluidic sensor for dielectric characterization[END_REF]. Two sensor design have been developed in order to measure liquid or solid samples. For the structure on a left in Fig 1, at the gaps of both resonators, the substrate was dug and the liquids under test have been placed within these cavities to benefit from the strongest electric field amplitudes within the substrate [START_REF] Mirbeik-Sabzevari | Ultra-wideband millimeter-wave dielectric characteristics of freshly excised normal and malignant human skin tissues[END_REF]. Thus, the liquid samples under test are introduced directly inside the fabricated holes for a volume of 23 µL per hole. For the sensor on the middle of Fig 1, the sizes are the same as the previous one however the substrate was not dug to simplify the measurement for a solid sample. Using two SRRs permits to realize two different types of measurements instead of just one when using only one SRR. Two SRRs are used in order to obtain a strong coupling and to measure the lowest possible S21 at the resonance [START_REF] Galindo-Romera | Submersible Printed Split-Ring Resonator-Based Sensor for Thin-Film Detection and Permittivity Characterization[END_REF]. When the two SRRs are loaded symmetrically (with the same sample in each gap) the filtering obtained is better than with one single SRR. When the two SRRs are loaded asymmetrically, one SRR can be used as a reference which reduces the impact of the environment on the measurement results [START_REF] Mohammadi | A Label-Free, Non-Intrusive, and Rapid Monitoring of Bacterial Growth on Solid Medium Using Microwave Biosensor[END_REF][START_REF] Ebrahimi | Differential Sensors Using Microstrip Lines Loaded With Two Split-Ring Resonators[END_REF].

b) Analysis of gap dimensions

To improve the performance of the sensor, various parametric studies were carried out, in particular at the level of the detection zone of the sensor. Simulations are performed using Ansys HFSS software. The sensor is simulated with its 3.5 mm SMA connectors, and radiation conditions have been applied at the boundaries. The S-parameters have been simulated over the frequency band from 1 GHz to 1.5 GHz.

Fig. 2. shows the simulation results of a parametric study of the gap, named as g, in the case of an empty sensor or when both holes are symmetrically totally filled with deionized water. Table II indicates in each case, the volume of sample, the minimal value of the transmission coefficient and the resonance frequency without sample as a function of g. According to this figure, the minimal transmission is easy to detect in all cases. In Table III, the frequency difference Sfr between both loading conditions is higher with the biggest volume which is the highest value of g. A trade-off has been made to analyze small liquid samples and to respect constraints of fabrication and measurement. In this end, the dimension g = 3 mm has been chosen.

B. Simulation

To study the response of the sensor for different materials, a total of 5 materials have been chosen: air, acetone, ethanol, methanol and deionized water. Their complex relative permittivity is calculated using the Debye formula:

ɛ * ɛ ɛ ɛ (1)
Where ɛ , ɛ and respectively correspond to the permittivity at high frequency, the permittivity at low frequency and the relaxation frequency with respect to frequencies f. These parameters at 25°C for those liquids are available in [START_REF] Mariam | Dielectric Spectroscopy Characterization within a Microfluidic Device based on Open-Ended Coplanar Waveguide[END_REF] and listed in Table III, along with the real part of the relative permittivity of these liquids at 1.35 GHz (resonant frequency of the unloaded sensor).

a)

Symmetrical configuration: two holes filled in Fig. 3 shows the simulated transmission coefficients obtained in case of unloaded sensor ("Air") and for the four liquid samples. The resonant frequency obtained varies as a function of the dielectric properties (complex permittivity) of the material under test. The frequency shift in regard to the unloaded case is called Sfr in the following. As expected, the higher is the permittivity of a material, the lower is the resonant frequency and thus the higher the frequency shift Sfr between the loaded and unloaded cases.

b)

Asymmetrical configuration: one single loaded hole Fig. 4 represents the simulated transmission coefficients obtained with one hole empty and one hole filled in with the four different liquid samples. Due to the dissymmetry of the sensor, two resonances appear; the highest one, related to the unloaded resonator, remains stable when the liquid changes whereas the position of the lowest one depends on the liquid under test and decreases as the permittivity increases. Thus, this configuration offers a second fixed resonance peak that serves as a reference. This structure is designed to operate as a differential sensor and the chosen metric or indicator is the frequency difference between both resonance frequencies Δfr.

C. Measurement

In order to validate the simulated prototype, it has been fabricated using LPKF Protomat S100 micro-etching machine with a substrate Arlon 25N. The measurements of the transmission coefficient S21 have been made using a Vector Network Analyzer ZNB8 from Rohde & Schwarz. Both configurations have been considered with one or two sides loaded by the liquids under test.

In Fig 5, the measured and simulated transmission coefficient have been compared for unloaded sensors ("Air"). As shown in Table IV, the minimum transmission and the resonance frequency for both measurement and simulation are very close. Fig. 6 shows the measured transmission coefficient obtained in the symmetrical configuration. A shift of the resonant frequency versus the liquid under test is clearly observed. Even if there are some differences between simulated and measured curves, the shape of the curves remains similar. The resonant peaks appear along the frequency axis according to the same order in simulation and measurement with, from right to left, air, ethanol, acetone, methanol and deionized-water corresponding to the order of the real parts of their permittivity from the lowest one to the highest one.

For a more precise comparison of simulation and measurement results, Table V indicates the frequency shift Sfr in regard to the empty sensor along with the minimal value of the transmission coefficient in the case of the symmetrically filled sensor. According to Table V, measurement and simulation results are coherent in all cases. The simulated and measured frequency shifts are in the same ascending order. The difference can be explained by slight manufacturing defects of the sensor but also by difficulties to introduce the same volume of sample in each hole in measurement. In particular, some materials as acetone present a high evaporation rate that complicates the measurement procedure.

b) Measurement results in the asymmetrical configuration and comparison with simulation.

Fig. 7 shows the measured transmission coefficient obtained in the asymmetrical configuration. It can be seen that, as in simulation, there is a fixed peak that can serve as a reference and a peak moving as the liquid under test changes.

Table VI presents the difference Δfr between both resonance frequencies along with the minimal transmission coefficient value at the lowest resonance frequency when one hole is empty. The frequency differences between both resonances obtained through simulation and measurement are in the same ascending order. Frequency differences obtained through measurement are however lower than those obtained by simulation. As with the previous configuration, the repeatability of measurements is difficult to get due to the effective filling of the holes with the same volume of sample as in simulation. The comparison of the results obtained in both configurations shows that the symmetrical case achieves a deeper transmission minimum than the asymmetrical case, as might be expected. Furthermore, in the asymmetrical case, the frequency differences are of the same order of magnitude in measurement and simulation. The second sensor is a broadband skin sensor operating between 1 and 6 GHz and it has been designed in order to detect cutaneous permittivity variations indicating the development of a tumor. It consists of an open-ended probe whose sensing area mimics a coaxial probe [START_REF] La Gioia | Open-ended coaxial probe technique for dielectric measurement of biological tissues: Challenges and common practices[END_REF] and is connected to a SMA connector through a stripline in Fig. 7. The sensitive part is printed on a 1.52 mm thick Rogers 3003 substrate (εr = 3.00 and tanδ = 0.0010 at 10 GHz) whereas two 1.524 mm thick Arlon 25N substrates (εr = 3.32 and tanδ = 0.0025 at 10 GHz) are used to form the stripline access. To obtain a coaxial-like sensitive area, the metallization is removed on a 2.3 mm diameter circular area in purple in Fig. 8, a 0.5 mm diameter metallized vias is inserted as a central conductor, and eight 0.5 mm metallized vias are added to mimic the outer conductor and improve the sensor resolution. The small diameter of the sensing area enables the examination of small surfaces consistent with skin heterogeneity imaging; indeed, the diameter of the circular area where the metallization is removed (of 2.3 mm) is smaller than the average size of a melanoma lesion (around 6 mm).

A permittivity extraction method suited for openended sensors [START_REF] Wagner | Numerical 3D FEM and experimental analysis of the open-ended coaxial line technique for microwave dielectric spectroscopy on soil[END_REF] permits to extract the permittivity of the material under test after a calibration step implying the measurement of three samples of known permittivity. The capability of this sensor to retrieve with a good accuracy the permittivity of the material under test over the whole 1 GHz-6 GHz frequency band has been shown [START_REF] Fritiss | Design and characterization of a broadband PCB-based coaxial sensor for permittivity screening in skin cancer detection applications[END_REF]. Following the process proposed in [START_REF] Aminzadeh | Characterization of low-cost tissue mimicking materials at millimeter-wave frequencies[END_REF], skin phantom tissues of different properties have been fabricated and the ability of the sensor to distinguish different tissues has been tested [START_REF] Fritiss | Design and characterization of a broadband PCB-based coaxial sensor for permittivity screening in skin cancer detection applications[END_REF].

To simplify the use of this sensor by medical practitioners, an alternative approach avoiding the calibration step has been proposed. This differential approach consists of a comparison of the complex reflection coefficients measured on a patient at two close locations respectively corresponding to safe skin (considered as a reference) and a suspicious lesion. The used indicator is calculated as ΔS11 = |S11MUT -S11ref| while comparing the reflection coefficient obtained for the material under test (MUT) and for the reference material (ref). Measurements performed on different phantom tissues show the sensitivity of the proposed indicator in Fig. 9.

IV. MEASUREMENT ON TUMOR PHANTOM TISSUES USING BOTH SENSORS

Using the process presented in [START_REF] Fritiss | Design and characterization of a broadband PCB-based coaxial sensor for permittivity screening in skin cancer detection applications[END_REF], samples reproducing the dielectric properties of melanoma has been fabricated. Measurements have been simultaneously performed using the coaxial sensor and the resonating sensor for solid samples. The real and imaginary parts of the relative permittivity extracted from the measurements using the coaxial sensor are presented in Fig. 10.

These extracted values at 1.35 GHz have been used to simulate the resonator sensor loaded by the same material. V. CONCLUSION This paper presents two sensors dedicated to biological diagnostic applications.

The first one concerns a resonant design operating in mode around 1.35 GHz and dedicated to characterize the dielectric properties of small volumes of liquids and solid biological samples. Both in simulation and in measurement, a shift of the resonance frequencies linked to the permittivity of the samples under test is observed with a good concordance. Whereas an asymmetry in the sensor loading leads to the appearing of two resonance peaks, it could permit to determine small composition variations between a reference liquid and a liquid under test; this property could be of interest for disease diagnostic.

The second one has been designed in order to probe, in the [1 GHz ; 6GHz] frequency band, small skin surfaces in regard to melanoma lesion size and permits to distinguish safe skin from tumor with a good accuracy. The fabrication of tumor phantom samples has permitted to verify the coherence of the results obtained using both sensors.

Fig. 1 .

 1 Fig. 1. Fabricated and measured sensors: microstrip structure with two ring resonators for small liquid sample (left) and for solid sample (middle). Geometrical parameters of the sensor are given in the right drawing.

Fig. 2 .

 2 Fig. 2. Parametric study of the variation of the transmission parameter versus g value, in the case of an empty sensor or when loaded by deionized water (simulation results).

Fig. 3 .

 3 Fig. 3. Simulated transmission coefficient S21 versus frequency when both holes are filled in for each liquid sample.

Fig. 5 .

 5 Fig. 5. Measured and simulated transmission coefficient S21 versus frequency when unloaded sensorTABLE IV. COMPARAISON BETWEEN MEASUREMENT AND SIMULATION FOR FREQUENCY SHIFT AND TRANSMISSION COEFFICIENT MINIMUM IN THE SYMETRICAL CONFIGURATION Sfr (MHz) Sim Meas

Fig. 6 .

 6 Fig. 6. Measured transmission coefficient S21 versus frequency when both holes are filled in for each liquid sample.

Fig. 4 .

 4 Fig. 4. Simulated transmission coefficient S21 versus frequency when one hole is filled in and the other one is empty, for each liquid sample.

Fig. 7 .

 7 Fig. 7. Measured transmission coefficient S21 versus frequency when one hole is filled in and the other one is empty, for each liquid sample.

Fig. 9 .

 9 Fig. 9. Measurement results of the difference between the complex reflection coefficients with several PE powder-based phantoms, for areference material obtained using 10g of PE powder.

Fig. 8 .

 8 Fig. 8. Sensor prototype (left) and 3D-view (right) with (a) the openended sensitive area, (b) the SMA connector to stripline transition.

Fig. 11

 11 Fig.11shows a comparison of the simulated and measured transmission parameters when the resonating sensor is symmetrically or asymmetrically loaded by this phantom tissue. The similar frequency shift obtained in simulation and measurement indicates coherent responses of both sensors.

Fig. 11 .

 11 Fig. 11. Simulated and measured transmission coefficient S21 versus frequency with tumor sample on the resonating sensor.

TABLE I .

 I DIMENSIONS OF THE SENSOR

		L_srr	W_srr	d	c	g	W
	Size in mm	20	22	1	2	3	3.6

TABLE II .

 II STUDY OF PARAMETERS AS A FUNCTION OF THE GAP

	g (mm)	2	3	4	5	6
	Volume (mm 3 )	12	23	37	55	75
	(MHz)	158	160	188	186	196
	S21 Air (dB)	-16.2	-17	-17.1	-17.3	17.2
	S21
	Water
	(dB)

-5.67 -5.45 -5.3 -5.27 -5.15

TABLE III .

 III PARAMETERS OF DEBYE FOR DIFFERENT LIQUIDS AT 25°C AND REAL PART OF THE RELATIVE PERMITTIVITY AT 1.35 GHZ

		ɛ	ɛ	(GHz)	ɛ at 1.35GHz
	Deionized	78.36	5.20	19.24	78.03
	Water
	Methanol	32.66	5.56	3.14	28.74
	Acetone	20.59	4.21	27.44	20.55
	Ethanol	24.43	4.5	0.964	11.52

TABLE V .

 V COMPARAISON BETWEEN MEASUREMENT AND SIMULATION FOR FREQUENCY SHIFT AND TRANSMISSION COEFFICIENT MINIMUM IN THE SYMMETRICAL CONFIGURATION

		Sfr (MHz)	S21 (dB)
		Sim	Meas	Sim	Meas
	Water	235	230	-3.83	-3.09
	Methanol	105	102	-2.15	-2.12
	Acetone	78.4	76.6	-8.54	-7.69
	Ethanol	49	49	-2.06	-2.22

TABLE VII .

 VII SIMULATED AND MEASURED RESULTS WITH THE PHANTOM TISSUE ON THE RESONATING SENSOR IN BOTH CONFIGURATIONS

		Tumor
	Symmetrical configuration	Sim	Meas
	Δfr (MHz)	165	181
	S21 (dB)	-4.41	-2.7469
	Asymmetrical configuration	Sim	Meas
	Sfr (MHz)	164	180.5
	S21 (dB)	-2.72	-1.7521

ACKNOWLEDGMENT

The authors thank Stéphane Protat from ESYCOM/UGE for the fabrication of coaxial sensors and his involvement in these two different projects and Jimmy Leszczynski from ESYCOM/UGE for the fabrication of microstrip sensors.