Andra Anoaica
email: andra.anoaica@irt-systemx.fr

Hugo Levard
email: hugo.levard@exit.irt-systemx.fr

Quantitative Description of Internal Activity on the Ethereum Public Blockchain

Keywords: Blockchain, Ethereum, cryptocurrency, smart contract, graph analysis

One of the most popular platform based on blockchain technology is Ethereum. Internal activity on this public blockchain is analyzed both from a quantitative and qualitative point of view. In a first part, it is shown that the creation of the Ethereum Alliance consortium has been a game changer in the use of the technology. In a second part, the network robustness against attacks is investigated from a graph point of view, as well as the distribution of internal activity among users. Addresses of great influence were identified, and allowed to formulate conjectures on the current usage of this technology.

I. INTRODUCTION

A transaction between individuals, in the classical sense, requires either trust in each parties, or in a third party. Blockchain solves this problem of trust between the actors by using a consensus algorithm. Beyond the debate on whether or not this technology can be qualified as innovative or simply being an aggregation of already existing building blocks (peerto-peer protocols, multi-party validation algorithm etc.), it can be reasonably stated that its usage lies on a new paradigm of communication and value exchange . The number of scientific publications dedicated to the general concept of blockchain was multiplied by 15 between 2009 and 2016, which demonstrates both a growing interest for the technical development of blockchains compounds and for its applications in domains for which it has been thought to be potentially disruptive [START_REF] Ben-Hamida | Blockchain for Enterprise: Overview, Opportunities and Challenges[END_REF]- [START_REF] Tian | An agri-food supply chain traceability system for china based on rfid blockchain technology[END_REF].

Looming over the daily increasing number of available blockchain technologies, Bitcoin is by far the most popular and widely used blockchain. However, in February 2017, a consortium of major I.T. and banking actors announced the creation of the Ethereum Alliance, a large project aiming at developing a blockchain environment dedicated to the enterprise based on the Ethereum blockchain. This event suddenly promoted the latter to the level of world wide known and trustworthy blockchain technologies -that up to then only included Bitcoin -making it an essential element of the blockchain world.

Despite an increasing notoriety and a monthly growing fiat money equivalent volume, it remains difficult to find publications dedicated to the establishment of economical and behavioural models aiming at describing internal activity on Ethereum, similarly to the studies performed for the Bitcoin network [START_REF] Athey | Bitcoin pricing, adoption, and usage: Theory and evidence[END_REF]- [START_REF] Chiu | The Economics of Cryptocurrencies-Bitcoin and Beyond[END_REF]. Concomitantly, global, time-resolved or major actors-resolved statistical indicators on the past internal activity and on the blockchain network topology are not commonly found in the literature, while they exist for Bitcoin [START_REF] Kondor | Do the rich get richer? An empirical analysis of the Bitcoin transaction network[END_REF]- [START_REF] Lischke | Analyzing the bitcoin network: The first four years[END_REF].

This paper aims at providing basic quantitative insights related to the activity on the Ethereum public network, from the origin, on July 2015, to August 2017. In the first part, correlations in time between internal variables, and between internal variables and the USD/ETH exchange rate are computed. A strong sensitivity of the activity to external events is highlighted. In a second part, the network is analyzed from a graph point of view. Its topology and robustness against attacks is investigated, as well as the distribution of internal activity among users. This leads to the identification of major actors in the blockchain, and to a detailed insight into their influence on the Ethereum economy.

II. THE ETHEREUM TECHNOLOGY

Similarly to Bitcoin, Ethereum is a public distributed ledger of transactions [START_REF] Wood | Ethereum: A secure decentralised generalised transaction ledger[END_REF]. Yet, the latter differs from the former by major features, among which the existence of smart contracts. Smart contracts are pieces of code that execute on a blockchain. Users or other smart contracts can call its functions, in order to store or transfer tokens, perform simple calculations, dealing with multi-signature transactions etc.

The existence of smart contracts allows us to distinguish five different kinds of transactions:

• User-to-user: a simple transfer of tokens from one address to another -both addresses can belong to the same physical user. • User-to-smart contract: a signed call to one of the functions of a smart contract. • Smart contract deployment: a transaction that contains the binary code of a compiled smart contract and sent to a special deployment address. • Smart contract-to-smart contract and smart contract-touser: user calling a smart contract might call another function of the same smart contract, or of another smart contract, or again transfer tokens to a user. These are called internal transactions, and their study is beyond the scope of this paper.

A. Blocks and transactions

In order to collect data, a public Geth [14] node was connected to the Ethereum public network. Once synchronised, the blockchain was stored for further analysis. Within this paper, we only deal with validated transactions, i.e. inserted into a block that was mined and added to the main chain before August 31 st 2017.

B. Transactions features

Two main transactions features are retained for the analysis.

• address: A hexadecimal chain of characters pointing to an account, that can either be a user or a smart contract.

Even though there is no direct link between an address and its user identity, some of them are publicly known to belong to major actors such as exchange platforms or mining pools. The correspondence can be found on open access blockchain explorer websites, such as Etherscan 1 .

• value: the amount of tokens, expressed in wei, transferred through the transaction. The ether/wei conversion rate is a hard coded constant equal to 10 18 . The time-resolved exchange rate between ether (ETH) and USD is provided by the Poloniex website API. The notions of uncles, gas and gas price, inherent to block validation protocol on Ethereum, are not investigated in this paper. It is worth noting that although the user-to-user transactions gather almost two thirds of the total of all transactions, they carry almost 90% of the transferred amount of tokens. A detailed investigation of the use of smart contracts reveals that most of them have been called only once, but that a small fraction of them have been massively used; this explains the smallness of the number of smart contract deployments compared to the number of user-to-smart contract transactions.

Figure 1 displays the monthly total number of transactions and transferred value, respectively, for each of the three categories of transactions defined above. The first two, ranging within the same orders of magnitude, are plotted together for both kinds of plot ((a) and (c)).

1) Number of transactions:

A behavior common to the three categories when it comes to the variation of the number of transactions in time is a A very similar trend is observed on the same period concerning the USD/ETH exchange rate, leading to conjecture that these parameters are strongly correlated.

However, a careful examination of these variations reveals that two distinct time windows should be distinguished at this stage when investigating correlations between transactions internal features, and external features, on this network. Indeed, the activity on public blockchains such as Bitcoin or Ethereum, as they allow to invest traditional currencies through exchange platforms, may be subject to the same sudden fluctuations as those that can be observed on common market places after external events, such as marketing announcements or financial bankrupts. In the present case, we can reasonably conjecture that there is a causal relationship between the creation of the Ethereum Alliance on February 28 th 2017 and the sharp take-off of the above-mentioned features. Considering the renown of the initial partners, this announcement may have promoted Ethereum to a larger audience, even in the nonspecialist public, and may have brought a massive interest from individuals resulting in an exponential growth of the activity in terms of number of transactions of all kinds. Hence, the strong correlation that could be calculated between features on a global time range, because of scale effects, may be biased and not reflect a normal behaviour.

To test this hypothesis we computed the Pearson correlation coefficient [START_REF] Mckinney | pandas: a foundational Python library for data analysis and statistics[END_REF] between the USD/ETH exchange rate and the number of each of the three kinds of transactions defined above, for four different aggregation time periods, and for two subsets of data, that differ from their latest cut-off date: the first one includes all transactions from the creation date of the blockchain (July 31 st 2015) up to the announcement date of the Ethereum Alliance (February 28 th 2017), while the second one ends on August 31 st 2017. Results are displayed in table II.

When considering the entire blockchain lifetime (unbold figures), we observe a strong correlation coefficient between the exchange rate and both the user-to-user and the user-tosmart contract number of transactions for all aggregation time sizes (between 0.83 and 0.96), which is consistent with the visual impression discussed above. But when excluding the time range [March 2017-August 2017] (bold figures), such a strong correlation only remains for the user-to-user number of transactions, and for aggregation time sizes no shorter than a day (between 0.92 and 0.95). It turns out that this particular data set is the only one for which the exchange rate variation in time follows the bump observed between March and October 2016, which explains the low correlation coefficient for the two other kinds of transactions. As was conjecture, the Ethereum Alliance creation announcement seems to have been a game changer on the Ethereum internal activity.

2) Values: The total exchanged values by unit of time displayed on plots (c) and (d) of Figure 1 are shown on log scales for clarity. The peak of activity, in terms of number of transactions, in the period that follows the Ethereum Alliance creation translates here into an average multiplicative factor of 10 as for the total exchanged value through the user-to-user transactions (bottom left figure), compared to the period that precedes it. As for the range of value transferred through smart contract deployment, it spans two orders of magnitude on the whole blockchain lifetime time window, and shows no substantial correlation with any of the retained features within this study.

To emphasise the rise of interest Ethereum has benefitted between 2016 and 2017, we display in table III the equivalent in USD of the total value that circulated within the blockchain during the months of June of these two years. The fluctuation of the average amount of tokens transferred per transaction bears no relation to the sudden increase of both the USD/ETH exchange rate and the number of transactions after the Ethereum Alliance creation announcement. The tremendous rise of the total value exchanged is thus a direct consequence of the internal activity increase in terms of number of transaction, and not of a behavior change among the individual addresses in terms of amount of tokens transferred through transactions. The macro perspective presented can be The Ethereum blockchain graph is built by setting the addresses as nodes, the transactions as edges, and using a time window that includes all internal events from the first block on July 31 st 2015 to August 31 st 2017. The user-to-user and userto-smart-contract are different types of interaction. In this short paper, we thus limit to user-to-user transactions. The resulting graph contains 5,174,983 nodes (unique user addresses) and 33,811,702 edges (transactions).

1) Network scaling and robustness against attack: The topology is firstly analyzed. Random networks are modeled by connecting their nodes with randomly placed links, as opposed to scale-free networks [START_REF] Clauset | Power-law distributions in empirical data[END_REF], such as the Internet, where the presence of hubs is predominant. Following a scalefree architecture implies that the network is rather robust to isolated attacks, however, remaining vulnerable to coordinated efforts, that might shut down the important nodes. In order to understand potential vulnerabilities of the Ethereum Network, we will investigate the presence of central nodes.

In accordance with a previous study on the Bitcoin network in which it is shown to be scale-free [START_REF] Lischke | Analyzing the bitcoin network: The first four years[END_REF], and with what is commonly observed in real networks, a power law distribution of the nodes degree d of the form c • d -α is expected, with c a constant. Such a fit in the case of Ethereum gives α = 2.32, which lies in the observed range for most real networks [START_REF] Clauset | Power-law distributions in empirical data[END_REF].

2) Centrality on the Ethereum Network: In order to determine whether the activity is well spread among the users, or whether there exist major actors or activity monopoles, we make use of three different centrality indicators:

• In-Degree/Out-Degree: the number of incoming/outgoing edges a node is connected to; • Betweenness Centrality: an indicator that summaries how often a node is found on the shortest path between two other nodes and, when communities exist, how well it connects them; • Left Eigenvector Centrality: a measure of the influence of a node based on the node's neighbors centrality. Figure 2a depicts the network directed degree distribution discrete probability density p, i.e. the probability for a randomly picked node to show a certain in-(d i ) and out-(d o ) degree. The latter are plotted in logarithmic scale for clarity and, by convention, any initial in-(respectively out-) degree value of 0 is plotted with a -1 in-(respectively out-) degree coordinate, to preserve surface continuity. The probability associated with p is denoted P .

It appears that the great majority of users do a rather limited number of transactions, having an in-degree and an out-degree equal to 1 (30.0%), followed by users that just send transactions once, never receiving any (20.0%). Firstly, the radial anisotropy is seen subsequent to larger values on the d i = d o line, which implies that in-and out-degree distribution are not independent variables: with p(d i ) and p(d o ) following a power law distribution, it seems that p( . These results suggest that, regarding the description of degree distribution, more information on the blockchain network could be obtained using a more sophisticated model than a simple power-law [START_REF] Bollobas | Directed scale-free graphs[END_REF], contrarily to what was assumed above.

d i , d o ) = p(d i ) • p(d o ),
Following these results, the degree spread among addresses is being investigated. Figure 2b shows the cumulative in-and out-degree percentage that represent, over all users, the first 100 addresses in descending order according to their in-degree or out-degree. It reveals that, out of more than 1 million addresses, just 20 addresses account for more than 60% of the transactions sent and 20% of the transactions received. It is then of interest to look for the identity of these addresses and try to infer their public role on Ethereum.

Consequently, we identified the owner of each of the 20 first users in these two lists of addresses, and gather them under three labels, Mining pool, Exchange platform, Unknown, IV. Among the top 20 addresses that send transactions are found 12 mining pools (60%), 5 exchange platforms (25%) and 3 unknown addresses (15%). The top 20 addresses that receive transactions are 7 exchange platforms or addresses related to one of them. The rest of the addresses are unknown. Since the mining retribution is sent to the pool main address only, we can conjecture that around 40% of transactions consist in token redistribution to miners that contribute to a pool. Similarly, because of the lack of services proposing direct payment in ether, it is likely that miners transfer their earned tokens to exchange platforms to convert them into other numeric digital currencies, such as dollar or bitcoin.

The betweenness centrality of the over 1 million nodes lies within the range 0-1%, apart from two addresses for which it reaches nearly 15%. These nodes are important as a high value indicates that a significant number of transactions are connected to this node. How well they connect communities in the network is left for further investigations. Among the top 20 nodes in this category there are 10 exchange services related addresses and 3 mining pools.

Among the 21 unique addresses identified as most central, none of them belong to the 20 most central addresses in terms of eigenvector centrality. Because the eigenvector centrality awards higher score to nodes connected to other nodes showing a high connectivity, it can be concluded that the most central nodes, from this perspective, are individuals that interact often with major actors, rather than the latter interacting with themselves. Inspecting the interaction of services previously identified as central, according to the in-and outdegree and betweenness centrality, we compute for each of these 21 addresses the percentage of transactions in which they take part that connect each of them to other members of the group. It is found that none of them has more than 1.17% of outbound transactions within the group.

The time-independent network topology was investigated and, as for the node directed connectivity, a sharp asymmetry between the in-and out-degree distribution was noticed. A conjecture on the non-independence between these two features was established. Major actors in terms of number of transactions were identified, as opposed to the vast majority of addresses which are used only once.

V. CONCLUSION

In this paper, quantitative indicators that summarize the internal activity on the Ethereum blockchain were presented.

The study of transaction features temporal variation revealed that the announcement of the Ethereum Alliance creation initiated an increase of the activity by several hundred percent,both in terms of number of transactions and the amount of exchange tokens by unit of time. Thus the subsequent caution in the interpretation of time correlations in a blockchain network was highlighted.

The study of the transaction graph revealed that more than 97% of nodes have been engaged in less than 10 transactions. Oppositely, 40 addresses, among which mining pools and exchange platforms, were found to account for more than 60% of the activity, leaving open the question of the health of the Ethereum economic ecosystem.

  1 https://etherscan.io/ IV. ACTIVITY ON THE ETHEREUM NETWORK A. Evolution in time of transaction main features

Fig. 1 :

 1 Fig. 1: Number of different transactions and value transfered over time. The gray line highlights the creation of the Ethereum Alliance.

Fig. 2 :

 2 Fig. 2: (a) Directed degree distribution (logarithmic color scale) upon in-degree and out degree of user addresses expressed as probability; (b) Cumulated in-degree and cumulated out-degree for the first 100 addresses in descending order of their in-degree or out-degree

  Table I displays the global percentage of the number of transactions and the amount of tokens that each of the three kinds of transactions defined in Section II represents.

		Number of transactions	Value transferred
	user-to-user	64.6%	90.5%
	user-to-smart contract	34.3%	9.5%
	smart contract deployment	1.1%	< 0.1%

TABLE I :

 I Proportions of transactions sent and value transfered through the three kinds of transactions.

TABLE II :

 II Pearson correlation coefficient over time between the USD/ETH exchange rate and the number of transactions validated, for different aggregation periods (month, week, day and hour), and two time windows -bold figures highlight the time-range ending before the creation of the Ethereum Alliance. sharp increase from March to August 2017 (top two figures).

TABLE IV :

 IV Public status of the top 20 addresses according to different measurement of centrality which we assume meaning neither mining poool or exchange platform. Results are displayed in Table

ACKNOWLEDGMENT

This research work has been carried out under the leadership of the Institute for Technological Research SystemX, and therefore granted with public funds within the scope of the French Program Investissements dAvenir.


Alain Hérique

Dirk Plettemeier

Caroline Lange

Jan Thimo Grundmann

Valérie Ciarletti

Tra-Mi Ho

Wlodek Kofman

Benoit Agnus

Jun Du

Alain Herique

Valerie Ciarletti

Tra-Mi Ho

Wenzhe Fa

Oriane Gassot

Ricardo Granados-Alfaro

Jerzy Grygorczuk

Ronny Hahnel

Christophe Hoarau

Martin Laabs

Christophe Le Gac

Marco Mütze

Sylvain Rochat

Yves Rogez

Marta Tokarz

Petr Schaffer

André-Jean Vieau

Jens Biele

Christopher Buck

Jesus Gil Fernandez

Christian Krause

Raquel Rodriguez Suquet

Stephan Ulamec

V Ciarletti

T.-M Ho

Valerie Ciarletti

Tra-Mi Ho

Christophe Le Gac

Rochat Sylvain

Raquel Rodriguez

A radar package for asteroid subsurface investigations: Implications of implementing and integration into the MASCOT nanoscale landing platform from science requirements to baseline design

Keywords: MASCOT Lander, Radar Tomography, Radar Sounding, Asteroid, Planetary Defense, AIDA/AIM

Introduction

The observations of asteroid-like bodies and especially their internal structure are of main interest for science as well as planetary defense. Despite some highly successful space missions to Near-Earth Objects (NEOs), their internal structure remains largely unknown [START_REF] Herique | Direct Observations of Asteroid Interior and Regolith Structure: Science Measurement Requirements[END_REF][START_REF] Herique | A direct observation of the asteroid's structure from deep interior to regolith: why and how?[END_REF][START_REF] Herique | A Direct Observation of the Asteroid's Structure from Deep Interior to Regolith: Two Radars on the AIM Mission[END_REF]. There is some evidence that an aggregate structure covered by regolith ("rubble pile") is very common for medium size bodies, but there are no direct observations. The size distribution of the constitutive blocks is unknown: is it fine dust, sand, pebbles, larger blocks, or a mixture of all of these? Observations of asteroid-like bodies hint at the existence of a whole range of variation between these very extreme objects. Some may be 'fluffballs' composed entirely of highly porous fine-grained material [START_REF] Thomas | Saturn's Mysterious Arc-Embedded Moons: Recycled Fluff?[END_REF]. There are also very large objects that appear to be at least somewhat cohesive [START_REF] Polishook | The fast spin of near-Earth asteroid (455213) 2001 OE84, revisited after 14 years: constraints on internal structure[END_REF], and possibly monoliths bare of any regolith layer [START_REF] Naidu | Goldstone radar images of near-Earth asteroids[END_REF]. Binary systems in their formation by evolution of asteroid spin state [START_REF] Rubincam | Radiative Spin-up and Spin-down of Small Asteroids[END_REF] appear to disperse, re-aggregate or reconfigure their constitutive blocks over time [START_REF] Jacobson | Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems[END_REF], leading to a complex geological structure and history [START_REF] Ostro | Radar Imaging of Binary Near-Earth Asteroid (66391)[END_REF][START_REF] Michel | Science case for the asteroid impact mission (AIM): A component of the asteroid impact & deflection assessment (AIDA) mission[END_REF][START_REF] Cheng | Asteroid impact and deflection assessment mission[END_REF]. This history includes components of separated binaries appearing as single bodies [START_REF] Busch | Radar observations and the shape of Near-Earth Asteroid[END_REF][START_REF] Scheeres | The geophysical environment of bennu[END_REF] as well as transitional states of the system including highly elongated objects [START_REF] Brozivić | Goldstone and Arecibo radar observations of (99942) apophis in 2012-2013[END_REF], contact binaries [START_REF] Pätzold | A homogeneous nucleus for comet 67p/Churyumov-Gerasimenko from its gravity field[END_REF][START_REF] Kofman | Properties of the 67p/Churyumov-Gerasimenko interior revealed by CONSERT radar[END_REF][START_REF] Biele | The landing(s) of Philae and inferences about comet surface mechanical properties[END_REF] and possibly ring systems [START_REF] Braga-Ribas | A ring system detected around the Centaur (10199) Chariklo[END_REF]. The observed spatial variability of the regolith is not fully explained and the mechanical behavior of granular materials in a low gravity environment remains difficult to model.

After several asteroid orbiting missions, these crucial and yet basic questions remain open. Direct measurements are mandatory to answer these questions. Therefore, the modeling of the regolith structure and its mechanical reaction is crucial for any interaction of a spacecraft with a NEO, particularly for a deflection mission. Knowledge about the regolith's vertical structure is needed to model thermal behavior and thus Yarkovsky (cf. [START_REF] Giorgini | Asteroid 1950 DA's Encounter with Earth in 2880: Physical Limits of Collision Probability Prediction[END_REF][START_REF] Milani | Long-term impact risk for (101955)[END_REF]) and YORP accelerations. Determination of the global structure is a way to test stability conditions and evolution scenarios. There is no way to determine this from ground-based observations (see [START_REF] Herique | Direct Observations of Asteroid Interior and Regolith Structure: Science Measurement Requirements[END_REF] for a detailed review of the science rationale and measurement requirements).

Radar Sounding of Asteroids

A radar operating remotely from a spacecraft is the most mature instrument capable of achieving the science objective to characterize the internal structure and heterogeneity of an asteroid, from sub-metric to global scale, for the benefit of science as well as planetary defense, exploration and in-situ resource prospection [START_REF] Herique | Direct Observations of Asteroid Interior and Regolith Structure: Science Measurement Requirements[END_REF][START_REF] Milani | Long-term impact risk for (101955)[END_REF][START_REF] Ulamec | Relevance of Philae and MASCOT in-situ investigations for planetary[END_REF]. As part of the payload of the AIM mission a radar package was proposed to the ESA Member States during the Ministerial council meeting in 2016 [START_REF] Michel | Science case for the asteroid impact mission (AIM): A component of the asteroid impact & deflection assessment (AIDA) mission[END_REF][START_REF] Michel | European component of the AIDA mission to a binary asteroid: Characterization and interpretation of the impact of the DART mission[END_REF]. In the frame of the joint AIDA demonstration mission, DART (Double Asteroid Redirection Test ) [START_REF] Cheng | Asteroid impact and deflection assessment mission[END_REF], a kinetic impactor, was designed to impact on the moon of the binary system, (65803) Didymos, while ESA's AIM [START_REF] Michel | Science case for the asteroid impact mission (AIM): A component of the asteroid impact & deflection assessment (AIDA) mission[END_REF] was designed to determine the momentum transfer efficiency of the kinetic impact and to observe the target structure and dynamic state.

Radar capability and performance is mainly determined by the choice of frequency and bandwidth of the transmitted radio signal. Penetration depth increases with decreasing frequency due to lower attenuation. Resolution increases with bandwidth. Bandwidth is necessarily lower than the highest frequency, and antenna size M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 3 constraints usually limit the lowest frequency. These are the main trade-off factors for instrument specification, which also has to take into account technical constraints such as antenna accommodation or operation scenarios [START_REF] Herique | Direct Observations of Asteroid Interior and Regolith Structure: Science Measurement Requirements[END_REF].

The AIM mission would have had two complementary radars on board, operating at different frequencies in order to meet the different scientific objectives [START_REF] Herique | Direct Observations of Asteroid Interior and Regolith Structure: Science Measurement Requirements[END_REF]. A monostatic radar operating at higher frequencies (HFR) can achieve the characterization of the first ten meters of the subsurface with a metric resolution to identify layering and to link surface measurements to the internal structure. Deep interior structure tomography requires a low frequency radar (LFR) in order to propagate through the entire body and to characterize the deep interior. The HFR design is based on the WISDOM radar [START_REF] Plettemeier | Full polarimetric GPR antenna system aboard the ExoMars rover[END_REF][START_REF] Ciarletti | WISDOM GPR Designed for Shallow and High-Resolution Sounding of the Martian Subsurface[END_REF] developed for the ExoMars / ESA-Roskosmos mission and LFR is a direct heritage of the CONSERT radar designed for ESA's Rosetta mission.

HFR: High Frequency Radar for Regolith Tomography

The monostatic HFR radar on board the orbiter spacecraft is a high frequency synthetic aperture radar (SAR) to perform reflection tomography of the first tens of meters of the regolith with a metric resolution [START_REF] Herique | Direct Observations of Asteroid Interior and Regolith Structure: Science Measurement Requirements[END_REF]. It can image the shallow subsurface layering and connect the surface measurements to the internal structure. The HFR is a stepped frequency radar operating from 300 MHz to 800 MHz in nominal mode and up to 3 GHz in an optional mode. It inherits from the WISDOM radar and is optimized to study small bodies.

Table 1 summarizes the main characteristics and budgets of the radar. It provides a decimetric vertical resolution and better than one meter resolution in horizontal direction, depending on the spacecraft speed relative to the asteroid surface. This high resolution allows characterizing the spatial variation of the regolith texture, which is related to the size and mineralogy of the constituting grains and macroporosity.

A primary objective of the HFR within the AIM mission was the characterization of the regolith of Didymoon, the Didymos system's secondary body or moon of the primary, Didymain.The HFR was supposed to survey Didymoon before and after the DART impact, in order to determine the structure and layering of the secondary's shallow subsurface down to a few meters. The tomography of the DART artificial impact crater would further provide a better estimate of the ejected mass to model the momentum transfer efficiency. With a single acquisition sequence, Didymoon mapping provides the 2D distribution of geomorphological elements (rocks, boulders, etc.) that are embedded in the subsurface. Multipass acquisition and processing is required to obtain the 3D tomography of the regolith. Another primary objective is the determination of the dielectric properties of the subsurface of Didymoon. The dielectric permittivity can be derived from the spatial signature of individual reflectors or by analyzing the amplitude of the surface echoes.

Instrument Design

The HFR electronics (Figure 2) uses a heterodyne system architecture utilizing two frequency generators to form a stepped frequency synthesizer. Transmitted wave as well as the local oscillator frequencies are generated separately and incoherently with phase-locked loop (PLL) synthesizers. A functional block schematic of the radar system shows Figure 1. Its front-end mainly consists of a high output power transmitter and two dedicated receivers. The antenna is fed by a 0° and a 90° phase shifted signal to generate circular polarization for the transmitted wave, using a 90° hybrid divider. The transmitter output is muted during reception by switching off the power amplifier output, in order to not overload the receivers. A separate receiver processes one of the receive polarization respectively. For the SAR operation mode an ultra-stable frequency reference provides a stable reference to the digital and RF electronics. All modules are supplied by a dedicated DC/DC module, which provides all necessary supply voltages for the individual blocks from a single primary input voltage.

The receiver's superheterodyne architecture uses a medium intermediate frequency at the digitizer input. This ensures high performance by eliminating the 1/f noise, thereby improving noise and interference performance. A calibration subsystem allows for a calibration of the horizontal (H) and vertical (V) receiver regarding image rejection, inter-receiver phase and amplitude balance. The received H-and V-signals are compensated subsequently to ensure very high polarization purity.

The Digital Module (DM) is built around a Field Programmable Gate Array (FPGA) and microcontroller. It controls and manages the data flow of the instrument. This includes digital signal processing of the measurement data, short time data accumulation, transfer to the spacecraft and processing of control commands for radar operation.

The antenna system comprises of a single antenna, which transmits circular polarization and receives both linear polarizations. This ultra-wideband dualpolarized antenna system operates in the frequency range from 300 MHz to 3.0 GHz. Figure 3 shows a 3D model and its corresponding antenna prototype. Antenna diagrams are shown in Figure 4.

Operations and Operational Constraints

The requirements for the HFR instrument are strongly driven by the acquisition geometry. Indeed, Synthetic Aperture Radar reflection tomography in 3D requires observations of different geometries and can only be achieved by constraining the spacecraft motion and position with respect to the observed target. For each acquisition geometry, the radar acquires the signal returned by the asteroid as function of propagation time, which is a measure of the distance from the spacecraft to the observed body. This range measurement resolves information in a first spatial dimension. The resolution in that dimension is given by the bandwidth of the radar signal and is significantly better than one meter (~30 cm in vacuum).

M A N U S C R I P T A C C E P T E D

For kilometric-size asteroids, the rotational period is generally in the order of a few hours, much smaller than the spacecraft orbital period during remote observation operations within the Hill sphere. In the Didymos system, the main body's rotation period is 2.3 h. Its moon orbits the primary in 11.9 h and it is expected to rotate synchronously [START_REF] Michel | Science case for the asteroid impact mission (AIM): A component of the asteroid impact & deflection assessment (AIDA) mission[END_REF]. The spacecraft's orbital period in a gravitationally bound orbit of 10 km radius is nearly two weeks. It can also be at rest relative to the system's barycenter while on a heliocentric station-keeping trajectory.

For the processing, we consider the body fixed frame with a spacecraft moving in the asteroid sky (Figure 7). Thus, the relative motion along the orbit plane between the spacecraft and the moon resolves a second dimension by coherent Doppler processing (Figure 5) [START_REF] Cumming | Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation[END_REF]. This brute-force SAR processing takes into account the observation geometry to give 2D images of the body surface mixing in the same pixel surface and subsurface features (Figure 5c). For a spherical body this induces an ambiguity between North and South hemispheres [START_REF] Hagfors | Mapping of planetary surfaces by radar[END_REF] which corresponds to the aliasing of the North target to the South hemisphere in Figure 5a. Therefore, the resolution is determined by the length of the observation orbit arc (i.e., Doppler bandwidth) and is better than one meter for an arc of 20° longitude. For the Didymos system, the surfaces of the primary and secondary object show very different Doppler behavior due to their different periods of rotation. This allows to resolve ambiguities when both are inside the radar's field of view.

In addition, a spacecraft position out of the equatorial plane breaks the symmetry. Shifting the signal partially out of the orbital plane reduces the North to South ambiguities as it is spread and a less powerful alias remains in the other hemisphere (South in Figure 5a). The accuracy requirement for the spacecraft pointing is typically 5° when the reconstructed trajectory accuracy requirement is in the order of hundreds of meters. The orbit restitution accuracy can be improved by the SAR processing itself using autofocus techniques [START_REF] Carrara | Spotlight Synthetic Aperture Radar: Signal Processing Algorithms[END_REF].

To achieve a 3D tomography, the third dimension to be resolved needs to be orthogonal to the orbit plane (Figure 7). To do so, the HFR instrument performs several passes at different latitudes. Typically, 20 passes allow a metric resolution. The spacecraft position evolves in a declination and right ascension window centered around 30° radar incidence of the observed target point (Figure 7). The extent of this window is about 20°. Each pass lasts for one to two hours and is traversed close to constant declination. The spacecraft is in very slow motion of a few mm/s along this axis orthogonal to the orbit plane. Such a velocity is difficult to achieve in operations. A proposed solution is to combine this slow motion to a movement along the orbit axis. All the passes can be done in a single spacecraft trajectory. Each pass corresponds to the period when HFR is facing the moon that is orbiting around the main body (Figure 7). In this multi-pass scenario, the resulting resolution for the third direction is 1 m and it is the limiting one (Figure 6).

The distance between the HFR instrument and its target is limited by the radar link budget for the upper boundary and by the speed of the electronic system for the lower boundary. HFR is expected to operate from 1 km up to 35 km, the nominal distance being 10 km.

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LFR: Low Frequency Radar for Deep Interior Sounding

Deep interior structure tomography requires a low frequency radar to propagate through the entire body. The radar wave propagation delay and the received power are related to the complex dielectric permittivity (i.e. composition and microporosity) and the small-scale heterogeneities (scattering losses), while the spatial variation of the signal and multiple propagation paths provide information on the presence of heterogeneities (variations in composition or porosity), layers, large voids or ice lenses. A partial coverage will provide 2D cross-sections of the body; a dense coverage will allow a complete 3D tomography. Two instrument concepts can be considered (Figure 8). A monostatic radar like MARSIS/Mars Express (ESA) [START_REF] Picardi | Radar soundings of the subsurface of Mars[END_REF] analyzing radar waves transmitted and received by the orbiter after reflection at the asteroids' surface and internal structure or a bistatic radar like CONSERT/Rosetta (ESA) [START_REF] Kofman | The Comet Nucleus Sounding Experiment by Radiowave Transmission (CONSERT). A short description of the instrument and of the commissioning stages[END_REF] analyzing radar waves transmitted by a lander, propagated through the entire body and received by the orbiter. The monostatic radar sounder requires very low operation frequencies, necessitating the use of large antennas. It is also more demanding in terms of mission resources (mass, data flow, power), driving all the mission specifications. In contrast to the monostatic approach, a bistatic radar can use slightly higher frequencies, simplifying the accommodation on the carrier mission as well as on the surface package. The bistatic low frequency radar measures the wave propagation between the surface element and an orbiter through the target object, like Didymoon. It provides knowledge of the deep structure of the moon, a key information needed to be able to model binary formation and stability conditions. The objective is to discriminate monolithic structures from building blocks, to derive the possible presence of various constituting blocks and to provide an estimate of the average complex dielectric permittivity. This information relates to the mineralogy and porosity of the constituting material. Assuming a full 3D coverage of the body, the radar determines 3D structures such as deep layering, spatial variability of the density, of the block size distribution and of the permittivity. As a beacon on the surface of Didymoon, it supports the determination of the binary system's dynamic state and its evolution induced by the DART impact (a similar approach as used for the localization of the Philae lander during the Rosetta mission [START_REF] Herique | Philae localization from CONSERT/Rosetta measurement[END_REF]).

Instrument Design

The LFR radar consists of an electronic box (E-Box) shown in Figure 13 and an antenna set on each spacecraft (i.e. lander and orbiter). Both electronic units are similar: two automats sending and receiving a BPSK code modulated at 60 MHz in time-sharing (Figure 9 and Figure 14). This coded low frequency radar is an in-time transponder inherited from CONSERT on board Rosetta (ESA) [START_REF] Kofman | The Comet Nucleus Sounding Experiment by Radiowave Transmission (CONSERT). A short description of the instrument and of the commissioning stages[END_REF]: in order to measure accurately the propagation delay, a first propagation path from the orbiter to the lander is processed on-board the lander. The detected peak is used to resynchronize the lander to the orbiter. A second propagation from the lander to the orbiter constitutes then in itself the science measurement (Figure 10). This concept developed for CONSERT on board Rosetta [START_REF] Kofman | The Comet Nucleus Sounding Experiment by Radiowave Transmission (CONSERT). A short description of the instrument and of the commissioning stages[END_REF] allows measuring the propagation delay with a raw accuracy better than 100 ns over a few tens of hours of acquisition using a quartz oscillator with a frequency stability in the range of 10 -7 . This accuracy can be increased up to 20 ns by on-ground processing post-processing [START_REF] Pasquero | Oversampled Pulse Compression Based on Signal Modeling: Application to CONSERT/Rosetta Radar[END_REF], yielding a typical accuracy better than a few percent of the average dielectric permittivity. The LFR characteristics and budgets are summarized in Table 1. As the LFR antennas cannot be deployed immediately after separation from the carrier spacecraft due to the need to relocate from the landing area to the LFR operating area, an antenna deployment mechanism is required, which needs to be operable in the low gravity environment on the surface of Didymoon. Astronika has designed a mechanical system deploying a tubular boom with a total mass of ~0.25 kg. It is able to deploy the 1.4 m antennas consuming only ~2 W for ~1 minute.

On the lander, the main antenna (V shape in Figure 11 and Figure 12) is deployed after reaching its final location. It provides linear polarization with high efficiency for the sounding through the body. A secondary antenna set with lower efficiency is deployed just after lander separation to allow operations in visibility during descent and lander rebounds, and for secondary objectives and operational purposes. The use of circular versus linear polarization induces limited power losses but reduces operational constraints on the spacecraft attitude. The LFR antenna on the orbiter is composed of four booms at the spacecraft corners in order to provide circular polarization.

Operations and Operational Constraints

Tomographic sections in bistatic mode are created in the plane of the moving line of sight through the target object between the lander and the orbiter passing by underneath. A full volume tomography is then assembled from a succession of several (as many as feasible) different of such pass geometries adjusted by changes in the orbiter trajectory. Considering the rugged topography of asteroids and the fact that all sections of the target object converge at the lander location, it is advantageous to have multiple landers and/or lander mobility, in order to ensure full volume coverage and uniform resolution of the target's interior. Lander mobility is particularly useful in binary systems where the lines of sight as well as the lander release, descent, landing, and orbiter pass trajectories can be constrained by the two

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 13
objects and their orbital motions relative to the spacecraft. The complex shapes and gravity fields of contact binaries or extremely elongated objects can create similar constraints.

The geometric constraints on the operational scenario for the bistatic experiment are driven by scientific and technical requirements on both the orbiter and lander platform. Considering simultaneously the baseline mission science data volume, the orbiter minimum mission duration in the frame of the AIDA mission, and the worstcase power constraints on-board of the lander, it is not possible to ensure full coverage of Didymoon according to the Nyquist criteria, i.e. λ/2 at the surface of the body. Under this constraint, when a full tomography of the body [START_REF] Barriot | A two dimensional simulation of the CONSERT experiment (Radio tomography of comet Wirtanen)[END_REF][START_REF] Pursiainen | Detection of anomalies in radio tomography of asteroids: Source count and forward errors[END_REF] is not feasible with a priori information [START_REF] Eyraud | Imaging the interior of a comet from bistatic microwave measurements: Case of a scale comet model[END_REF], then statistical tomography allows to characterize heterogeneity scales [START_REF] Herique | A characterization of a comet nucleus interior[END_REF] and to retrieve composition information (for CONSERT see also [START_REF] Ciarletti | CONSERT constrains the internal structure of 67p at a few meter size scale[END_REF] and [START_REF] Herique | Cosmochemical implications of CONSERT permittivity characterization of 67p/CG[END_REF]). However, it is likely that a combination of higher data volume by utilization of additional passes, allocation of more ground station time, or mission extension, together with any better than worst-case power availability on the lander platform can result in a much better tomographic coverage.

To achieve a good coverage of Didymoon, seven to ten tomography slices need to be collected, with each measurement sequence taking about 10 hours. Those slices must also be sufficiently separated in space. Thus, the spacecraft has to be able to operate at various latitudes relative to Didymoon.

A single acquisition sequence is composed of a sequence of visibility, occultation and again visibility between orbiter and lander. The first visibility period is mandatory for a time synchronization between orbiter and lander platform. The science measurements are performed during the occultation period. The last visibility slot is re served for calibration. The accuracy on the orbiter trajectory reconstruction needs to be typically a few meters, whereas the altitude reconstruction accuracy should be in the order of about 5°. The radar link budget constrains the operational distance from the orbiter unit to the lander unit to about 10 km.

Concerning the lander, proper operation of the LFR imposes constraints on the landing site selection (Figure 15 and Figure 16). The acquisition geometry constrained by Didymoon's motion around the main body. Most likely, it is in 1:1 spin-orbit resonance, which means that the side facing the main body is always the same, as with Earth's Moon. With a moving spacecraft on the latitude axis the lander needs to land near to the equator of Didymoon, i.e., between -15° and +15° latitude, in order to achieve alternating visibility and occultation periods. In that case, the orbiter spacecraft will be able to cover a range of latitudes between -25° and +25°. This alternation also constrains the longitude of the landing site to a zone between -120° and +120°, with optimal science return between -60° and +60°. It is also constrained by the lander platform's solar energy availability, which means having to avoid eclipses by the main body, and having a "forbidden zone" between -45° and +45° of longitude. Figure 16: LFR landing site possible areas in green: optimal, yellow: acceptable and red: impossible 0° longitude corresponds to the point facing the main body of the Didymos system.

Integration into the MASCOT2 Lander Platform

The MASCOT2 lander for the AIM mission is derived from the MASCOT lander, originally designed for and flying on the HAYABUSA2 mission to asteroid (162173) Ryugu [START_REF] Ho | MASCOT -The Mobile Asteroid Surface Scout Onboard the Hayabusa2 Mission[END_REF]. In order to integrate a radar instrument into the lander system, originally envisaged for short lifetime and mobile scouting on an asteroid surface, several changes are incorporated to cope with the measurement and instrument requirements of the radar package. Table 2 shows a summary of the main differences and commonalities between the original MASCOT and the proposed MASCOT2 variant of the lander platform [START_REF] Lange | MASCOT2 -A Small Body Lander to Investigate the Interior of 65803 Didymos' Moon in the Frame of AIDA/AIM[END_REF][START_REF] Biele | MASCOT2, a Lander to Characterize the Target of an Asteroid Kinetic Impactor Deflection Test Mission[END_REF].

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

15 The LFR E-Box (Figure 13) is designed in order to be compatible with the MASCOT2 lander platform's available volume. The MASCOT2 lander design is ideally suited to incorporate different suites of payloads, which means that a mechanical integration of the LFR E-Box would have no impact on the overall accommodation. The integration of the LFR's primary antennas and their deployment mechanisms requires a slightly larger effort due to volume restrictions in the bus compartment of the lander

The antenna system is designed to match both, the requirements of the MASCOT2 lander and the influence of surface and subsurface in the vicinity of the lander. EM simulations are used to verify the suitability of the antenna system accommodation.

Figure 17 shows a simulation setup and a typical 3D radiation pattern assuming a flat surface. Figure 18 shows the antenna far field diagrams in two planes perpendicular to the surface for 50 MHz, 60MHz and 70MHz.

From an electrical point of view, the integration of the instrument into the lander platform is challenging in two ways: (1) the operational concept along with the overall architecture had to be optimized in order to be compatible with a long-duration highpower measurement mode and (2) precise timing is needed in order to achieve usable instrument characteristics. Both aspects center on the energy demand of the LFR instrument and related services which are based on the need to support a lot of repeated long continuous runs. In contrast, MASCOT aboard HAYABUSA2 is designed to fulfil a short-duration scouting mission. It is expected to operate only on two consecutive asteroid days of ~7.6 h, each. The design-driving power consumption results from the operations of the MicrOmega instrument (~20 W total battery power for only ~½ hr) and the mobility unit (up to ~40 W for less than 1.5 s). The energy for this mission is completely provided by a non-rechargeable battery. The choice for primary batteries was partly driven by the fact that such, a power system operates independent of the topographic illumination [START_REF] Grundmann | One Shot to an Asteroid -MASCOT and the Design of an Exclusively Primary Battery Powered Small Spacecraft in Hardware Design Examples and Operational Considerations[END_REF]. A short mission duration also implies few opportunities and little time for ground-loop intervention, thus the power subsystem operates permanently hotredundant and provides many automatic functions. This leads to an elevated idle power consumption of about 6.5 W, rising to about 10 W with the continuous activity of the MARA and MasMAG instruments. The simplicity of this concept comes at the expense of a very significant thermal design and control effort, required to keep the primary battery cold during interplanetary cruise in order to prevent self-discharge, and warm during on-asteroid operation to ensure maximum use of the available capacity. This simplicity of the original MASCOT concept comes at the expense of a very significant thermal design and control effort, required to keep the primary battery cold during interplanetary cruise in order to prevent self-discharge, and warm during onasteroid operation to ensure maximum use of the available capacity. The support of the LFR with its long-duration high-power measurement mode requires modifications to the platform design due to thermal aspects.

The MicrOmega (MMEGA, [START_REF] Pilorget | NIR reflectance hyperspectral microscopy for planetary science: Application to the MicrOmega instrument[END_REF]) instrument, accommodated at the respective location in the original MASCOT lander, requires cold operation due to its infrared sensor and optics. The LFR E-Box can operate in the typical "warm" conditions of other electronics modules (Figure 19). Therefore, its mass can be used together with the bus E-Box and mobility mechanisms to augment thermal energy storage around the battery, improving the mass to surface ratio of the warm compartment and saving electrical energy which would otherwise be required for heating. For this purpose, the cold compartment on the payload side of the lander was reduced to a "cold corner" or pocket around the camera, MasCAM [START_REF] Jaumann | The Camera of the MASCOT Asteroid Lander on Board Hayabusa2[END_REF], and the radiometer, MARA [START_REF] Grott | The MASCOT Radiometer MARA for the Hayabusa 2 Mission[END_REF].

The accommodation of the magnetometer, MasMAG [START_REF] Herčík | The MASCOT Magnetometer[END_REF], as on MASCOT was considered for optional use together with the proposed magnetometer experiments aboard COPINS, sub-satellites to be inserted into orbit in the Didymos system by the AIM spacecraft [START_REF] Walker | Cubesat opportunity payload inter-satellite network sensors (COPINS) on the ESA asteroid impact mission (AIM), in: 7th Interplanetary Cubesat Workshop[END_REF]. A triaxial accelerometer, DACC, was added in order to observe the interaction of the lander with the surface regolith during touch-down, bouncing and self-righting, reaction to motion during deployment operations, and possibly the DART impact shock wave.

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For the long-duration MASCOT2 mission, the mission energy demand will be orders of magnitude higher due to the repeated long continuous LFR runs. Thus, a rechargeable battery and photovoltaic power is required. The design-driving power consumption results from the LFR instrument operating for several hours at a time (see Table 1) defining the minimum battery capacity, and the simultaneous operation of the dual mobility mechanism. Both have a similar peak power demand, defining the power handling capability.

A deployable photovoltaic panel is necessary to satisfy the energy demand of LFR operations without too extensive recharging periods between LFR sounding passes. The panel will be released after the MASCOT2 lander relocates to the optimal LFR operations site on Didymoon, self-righted there, and deployed the LFR antennas.

The possibility to recharge the battery and wait for ground loop intervention allows mainly cold-redundant operations and reduces the need for highly sophisticated autonomy within the power subsystem. This alone greatly reduces idle power consumption, and thus battery capacity requirements to survive the night. Further reduction of idle consumption is achieved by optimizing the electronics design.

However, the energy demand of LFR is such that a much deeper discharge of the battery will occur as would usually be accepted for Earth-orbiting spacecraft. This will reduce battery lifetime. Thus, some fundamental autonomous functions are used to protect the system from damage by short circuits or deep discharge of the battery and to ensure a restart after the battery has accumulated sufficient energy. For this purpose, the photovoltaic power conversion section charging the battery is selfsupplied and does not require battery power to start up. In case the battery gets close to the minimum charge level e.g. when a LFR run cannot be properly terminated due to an unforeseen event, all loads are disconnected so that all incoming photovoltaic power can be used for recharge. State of the art rechargeable batteries can operate sufficiently well and with only minor operational restrictions at cell temperatures from about -20°C to +50°C, nearly as wide as the temperature range of the primary battery of MASCOT, but with much better performance in cold conditions below +20°C. In case the temperature is too low to allow maximum charging rate, all excess photovoltaic power is diverted to a battery heater [START_REF] Dudley | ExoMars Rover Battery Modelling & Life Tests[END_REF].

During use and in favorable illumination on the ground, battery life extending charge control is applied [START_REF] Neubauer | The Effect of Variable End of Charge Battery Management on Small-Cell Batteries[END_REF].

As described the features of a long-lived high energy mission can be coped with by a deployable photovoltaic panel. As an alternative a moderate enlargement of the MASCOT-like box shape was also considered as an option for the AIM mission. It could provide the same daily average power level. Depending on which sides of the lander are enlarged, the immediately available photovoltaic power can be adjusted within the daily cycle. A flat shape with a similar top plate area as the deployed panel of MASCOT2 increases power generation around noon while higher or wider sides increase power at sunrise and sunset (assuming a clear view to the horizon at the landing site). The increased volume, if provided by the carrier mission, can be used to accommodate additional instruments or a larger battery, also providing more robustness during the relocation phases. Depending on the antenna design, relocation for more extensive LFR tomography also becomes possible. It is thus possible to combine investigations of the interior and the surface mineralogy as

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carried out by MASCOT. The mass increase is little more than the instrument's, i.e. the bus mass would increase by about 10% with the addition of one relatively large instrument. If the carrier mission provides still more mass allowance, a set of multiple MASCOT type landers based on a common infrastructure but carrying different instruments and individually optimized for these can also be considered [START_REF] Grundmann | Capabilities of GOSSAMER-1 derived Small Spacecraft Solar Sails carrying MASCOT-derived Nanolanders for In-Situ Surveying of NEAs[END_REF].

Design Methodologies for Lander Design Reuse

The "mother" mission of MASCOT, the HAYABUSA2 mission, has benefited greatly from its predecessor HAYABUSA. It reused main portions of the design and optimized its main weaknesses based on lessons learned, such as the antenna, the orientation control and engine as well as the sampling approach [START_REF] Tsuda | Flight status of robotic asteroid sample return mission HAYABUSA2[END_REF]. Other than this particular example, and except for the well-known and documented reuse of the Mars Express Flight Spare Hardware for the Venus Express mission [START_REF] Mccoy | Call for Ideas for the Re-Use of the Mars Express Platform -Platform Capabilities[END_REF][START_REF] Mccoy | The Venus express mission[END_REF], the MASCOT2 re-use exercise is the only known system level reuse of a previously flown deep space system in a new environment and with an almost completely new science case, as described above. The fostered and maximized re-use of an already very precisely defined system for a very different mission recreates the unusual situation of an extremely wide range of subsystem maturity levels, from concepts to already flown designs. The integration of new instruments like the LFR radar is one of such lowermaturity cases. New design methodologies based on Concurrent Engineering and Model Based Systems Engineering methods can enhance the redesign, instrument integration and system adaptation process and make it faster and more cost efficient [START_REF] Lange | Systematic reuse and platforming: Application examples for enhancing reuse with modelbased systems engineering methods in space systems development[END_REF][START_REF] Lange | A model-based systems engineering approach to design generic system platforms and manage system variants applied to mascot follow-on missions[END_REF][START_REF] Braukhane | Statistics and Evaluation of 30+ Concurrent Engineering Studies at DLR[END_REF]. In addition, the general use case of a small landing package piggy-backing on a larger main mission is very lucrative and widely applicable in the context of planetary defense and small body exploration, making the platform approach, already known from Earth orbiting missions, a feasible strategy. A strategically planned MASCOT-type lander platform with an ever-increasing portfolio of technology options will further enhance the applicability of the small lander concept to all kinds of missions. Several of the technologies specifically required to realize the radar mission scenario as described above fall into this category. Other technologies such as advanced landing subsystems and new mobility concepts are also interesting and currently under development [START_REF] Lange | Exploring Small Bodies: Nanolander and -spacecraft options derived from the Mobile Asteroid Surface Scout[END_REF].

Conclusions

Direct measurements are mandatory to get a deeper knowledge of the interior structure of NEOs. A radar package consisting of a monostatic high frequency radar and a bistatic low frequency radar is able to perform these direct measurements. Both radar systems provide a strong scientific return by the characterization of asteroid's internal structure and heterogeneity. Whereas the LFR provides a tomography of the deep interior structure, the HFR maps the shallow subsurface layering and connects the surface measurements to the internal structure. In addition to this main objective, the radars can support other instruments providing complementary data sets. The nanolander MASCOT2 demonstrates, by carrying the mobile part of the bistatic radar, its flexibility. It can carry instruments with a wide range of maturity levels using state of the art design methodologies. As shown, a moderate redesign allows for long-term radar runs in contrast to the original short-term operation scenario of MASCOT.

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The presented radar package and the MASCOT2 lander have been developed at phase A/B1 level in the frame of ESA´s AIM mission study. Although the mission has not been confirmed and the next steps to establish such a mission are not clear. The modification of the MASCOT lander platform to a fixed but longtime radar surface station demonstrates the large range of applications for small landing packages on small airless bodies [START_REF] Ulamec | Landing on Small Bodies: From the Rosetta Lander to MASCOT and beyond[END_REF]. The radar instrument package presented has a high maturity and is of main interest for planetary defense as well as for NEO science.

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Figure 2 :

 2 Figure 2: Module stack of the HFR system prototype: DC/DC Module, Digital Module with FPGA, microcontroller and signal level converters, Low Power Module with synthesizer, receiver and switches for calibration, and High Power Module with power amplifier and preamplifier assemblies.

Figure 3 :

 3 Figure 3: 3D model (left) and prototype (right) of the HFR ultra-broadband dual polarized antenna.

Figure 4 :

 4 Figure 4: Simulated antenna pattern of HFR antenna system (E-plane).

Figure 5 :

 5 Figure 5: HFR mono pass impulse response on Didymoon's surface map for a point target located at 20° latitude and 180° longitude (a). The impulse response power is shown by color mapping, in dB.The same impulse response presented in 3D on a sphere portion that represents the surface of Didymoon (b) and shown in 3D (c). Note that a clear ambiguity along the vertical axis remains in a mono pass. The color scale corresponds to a dynamic range of 100 dB and exaggerates signal distortions. This measurement is simulated, along an arc of orbit or 20°, considering an isotropic point target located. On Didymoon's surface and taking into account propagation delay and geometrical losses. Simulation was done in the frequency domain using the instrument characteristics listed in this paper. A SAR processor, corresponding to a coherent summation after compensation of the propagation delay, processes the simulated measurements.

Figure 6 :Figure 7 :

 67 Figure 6: HFR impulse response with 30 passes for a point target located on Didymoon's surface at 30° latitude and 90° longitude. The HFR observation window is chosen so that it has a 30° incidence angle with the target. The color mapping, in dB, shows the impulse response power; (a) presents a view of the radial/along track plane while (b) presents a view of the radial/across track plane; (c) presents the same impulse response planes in 3D, including the tangent plane (across/along track).The color scale corresponds to a dynamic range of 100 dB. This dynamics exaggerates signal distortions.

Figure 8 :

 8 Figure 8: Bistatic (left) and monostatic (right) radar configuration, Artist view from CONSERT/Rosetta. From [1]. Credit: CGI/Rémy Rogez; shape model: Mattias Malmer CC BY SA 3.0, Image source: ESA/Rosetta/NAVCAM, ESA/Rosetta/MPS.

Figure 9 :

 9 Figure 9: Block diagram of the LFR instrument, orbiter (top), lander (bottom). .

Figure 10 :

 10 Figure 10: Lander synchronization: effect on the measured signal taking into account the periodicity of the calculated signal.

Figure 11 :

 11 Figure 11: Lander antennas: V-shaped dipole and secondary dipole antenna. MASCOT2 accommodation.

Figure 12 :

 12 Figure 12: Antenna in tubular boom technology general architecture with basic subassemblies: (1) Structure (2) Tubular boom (3) Tubular boom guidance system (4) Drive and damping unit (5) Lock an release mechanism (6) Electrical connection.

Figure 13 :

 13 Figure 13: LFR electronic box -housing, global view.

Figure 14 :

 14 Figure 14: Block schematic of the LFR system architecture showing electronic box including transmitter (Tx), Receiver (Rx) and digital module.

Figure 15 :

 15 Figure 15 : Definition of Didymoon reference system.

Figure 17 :

 17 Figure 17: Simulated 3D LFR radiation pattern inside (lower hemisphere) and outside (upper hemisphere) the asteroid at 60 MHz in case of a flat surface, assuming a relative permittivity of 5.

Figure 18 :

 18 Figure 18: Simulated antenna patterns of MASCOT2 antenna system above ground.Left: Φ=0° (perpendicular to the y-axis); right: Φ=90° (perpendicular to the x-axis).

Figure 19 :

 19 Figure 19: Detailed view of MASCOT2 platform showing accommodation of LFR, including E-box and antenna systems.

Table 1 :

 1 Main characteristics and performance of the bistatic low frequency radar and the monostatic high frequency radar.

		Bistatic Radar	Monostatic Radar
		Orbiter	LFR	Lander
	Frequency (nominal)	50-70 MHz	300 -800 MHz
	Frequency (extended)	45-75 MHz	up to 3 GHz
	Signal modulation	BPSK		Step frequency
	Resolution	10 -15 m (1D)	1 m (3D)
	Polarization	Circular (AIM) Linear (Mascot)	Tx: 1 Circular
					Rx: OC and SC
	Tx power	12 W		20 W
	Pulse repetition	5 seconds	1 second (typical)
	Sensitivity	Dynamic = 180 dB	NEσ0 = -40 dB.m 2 /m 2
	Mass
	Electronic	920 g		920 g	830 g
	Antenna	470 g	230 + 100 g	1560 g
	Total w/o margin	1390 g		1250 g	2390 g
	Power max / mean	50 W / 10 W	50 W / 10 W	137 W / 90 W
	Typical Data (Gbit)	1		0.3	300

Table 2 :

 2 Main differences and commonalities of the proposed MASCOT2 lander.

	Differing attribute	MASCOT	MASCOT2
	Main Science Case	surface composition and physical properties	internal structure by radar tomography
		mapper
	Landing site	restricted by thermal and communications	restricted by measurement requirements
		reasons
	Target body diameter	890 m	170 m
	Rotation period	7.6 h	11.9 h
	Lifetime	~16 hours	>3 months
	Deployment wrt to S/C	sideways, 15° downwards	not restricted
	Communications	synergy with Minerva landers	with AIM ISL (Copins)
	interoperability
	Lander mounting plane	15° angled "down"	parallel to the carrier sidewall
	Storage	inside panel in a pocket	outside panel, flush
	Mobility	1 DOF	2 DOF
	Localization	passive, by orbiter	self-localization
	Power	primary battery only	solar generator and rechargeable batteries
	Thermal Control	variable conductivity	passive (MLI, heater)
	Self-awareness	basic	extended sensor suite
	Communication	VHF transceiver from JAXA	S-band transceiver
	Scientific Payload	MARA, MASCam, MasMAG, MicrOmega	MARA, MASCam, LFR, DACC, (MAG)

Acknowledgement

Radar development has been supported by the CNES's R&T program ("CONSERT Next Generation" study) and by the ESA's General Studies Program (AIM Phase A). The High Frequency Radar inherits from WISDOM/Exomars founded by CNES and DLR. The Low Frequency Radar inherits from CONSERT/Rosetta founded by CNES and DLR. The MASCOT2 study was funded and carried out with support of the DLR Bremen CEF team.


Claudio Lobos
email: claudio.lobos@imag.fr

Marek Bucki

Yohan Payan

Nancy Hitschfeld

Techniques on mesh generation for the brain shift simulation

Keywords: Mesh Generation, Brain Shift, Finite Elements, Real-time Models

published or not. The documents may come   L'archive ouverte pluridisciplinaire

I. INTRODUCTION

Accurate localization of the target is essential to reduce morbidity during a brain tumor removal intervention. Image guided neurosurgery nowadays faces an important issue for large skull openings, with intra-operative changes that remain largely unsolved. The deformation causes can be grouped by:

• physical changes (dura opening, gravity, loss of cerebrospinal fluid, actions of the neurosurgeon, etc) and • physiological phenomena (swelling due to osmotic drugs, anesthetics, etc). As a consequence of this intra-operative brain-shift, preoperative images no longer correspond to reality. Therefore the neuro-navigation system based on those images is strongly compromised to represent the current situation.

In order to face this problem, scientists have proposed to incorporate into existing image-guided neurosurgical systems, a module to compensate for brain deformations by updating the pre-operative images and planning according to intra-operative brain shape changes. This means that a strong modeling effort must be carried out during the design of the biomechanical model of the brain. The model must also be validated against clinical data.

The main flow of our strategy can be divided into three main steps:

• The segmentation of MRI images to build a surface mesh of the brain with the tumor. • The generation of a volume mesh optimized for real-time simulation.

• The creation of a model of the Brain Shift with

Finite Elements and the updating with ultrasound images. This paper aims to deal with the second point: the selection of a meshing technique for this particular problem. Several algorithms and applications are analyzed and contrasted.

II. MESHING CONSTRAINTS

Various constraints and statements have arisen in the path to achieve this surgical simulation. These global ideas can be summarized as follows:

• The speed of the FEM computation depends on the number of points the system has to deal with. • A good representation of the tumor as well as the Opening Skull Point (OSP) and the path between them is needed. This path will from now on be referred to as the Region of Interest (RoI). • Consideration of the brain ventricles is desirable.

• The algorithm should consider as input a surface mesh with the ventricles and the tumor. • Obtain a surface representation and element quality throughout the entire mesh.

III. MESHING TECHNIQUES

A. Advancing Front

This is a technique that starts with a closed surface [START_REF] Frey | Delaunay tetrahedralization using an advancing front approach[END_REF][START_REF] Lobos | 3D NOffset mixed-element mesh generator approach[END_REF]. All the faces that describe the surface are treated as fronts and are expanded into the volume in order to achieve a final 3D representation. The selection of points to create the new faces encourages the use of existing points. Additional process to improve the quality of the elements can be made. There are two main drawbacks to this approach. The first one is that this technique is recommended when it is important to maintain the original input faces. This is not a specific constraint in our case. The second is that it would be necessary to use external libraries to produce a local or regional refinement. In our case, this is to have a refined mesh in the RoI and coarse elsewhere. However, the control of internal regions can be easily achieved because inner surface subsets are also considered to expand. All this is shown in figure 1.

B. Mesh matching

Mesh matching is an algorithm that starts with a generic volume mesh and tries to match it to the specific surface [START_REF] Couteau | The mesh-matching algorithm: an automatic 3D mesh generator for finite element structures[END_REF]. The base volume is obtained from an interpolation of several sample models. To obtain a new mesh, in our case for the brain, the problem is reduced to find a transformation function that will be applied to the entire base mesh and in that manner produce the final volume mesh for the current patient. This is shown in figure 2.

The problem with this technique is that even though a good representation of the surface and quality of the mesh can be achieved, it would not contain the tumor information because its position and thus the RoI changes from one patient to another. This technique is recommended for, and has been successfully applied to complex structures such as bones and maxillofacial models [START_REF] Luboz | Orbital and maxillofacial computer aided surgery: patient-specific finite element models to predict surgical outcomes[END_REF].

A good adaptation of this technique to our problem would be to provide tools for local element refinement and with this produce a more refined mesh in the RoI. Then a subset of these elements would be labeled as the tumor, leaving the rest of the mesh untouched.

Fig. 2 The mesh matching algorithm: the segmented lines represent the base mesh that has to match the surface.

C. Regular Octree

The octree technique starts from the bounding box of the surface to mesh [START_REF] Schneiders | Octree-based hexahedral mesh generation[END_REF]. This basic cube or "octant" is split into eight new octants. Each octant is then iteratively split into eight new ones, unless it resides outside the input surface mesh, in which case it is remove from the list. The algorithm stops when a predefined maximum level of iterations is reached or when a condition of surface approximation is satisfied. This is shown in figure 3. The octree by itself does not consider a surface approximation algorithm once the split process is done.

Techniques in mesh generation for brain shift simulation.

Therefore it has to be combined with other techniques in order to produce a final mesh that represents well the surface. Two main approaches are considered:

• Marching cubes [START_REF] Lorensen | Marching Cubes: A High Resolution 3D Surface Construction Algorithm[END_REF]: this algorithm crops the cubes that lie within the surface and produce, in most cases, tetrahedrons. • Surface projection: this technique projects the points of those elements that intersect the surface, onto it. The main problem is that this can produce degenerated elements unless a minimal displacement is needed. The problem with a regular octree mesh is that it counts with a high number of points even in regions where no displacement is expected [START_REF] Hu | Intraoperative brain shift prediction using a 3D inhomogeneous patient-specific finite element model[END_REF]. Therefore, a non-optimal mesh would be the input for the FEM producing unnecessary time consumption for the entire simulation.

D. Delaunay

A Delaunay triangulation or Delone triangularization for a set P of points in the plane is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). Delaunay triangulations maximize the minimum angle of all the angles of the triangles in the triangulation. The triangulation was invented by Delaunay in 1934 [START_REF] Delaunay | Sur la sphère vide[END_REF].

To evaluate this technique we used TetGen [START_REF] Tetgen | a Quality Tetrahedral Mesh Generator[END_REF]. This is an open-source application that generates tetrahedral meshes and Delaunay tetrahedralizations. The tetrahedral meshes are suitable for finite element and finite volume methods. TetGen can be used either as an executable program or as a library for integrating into other applications. A mesh generated by TetGen is shown in figure 4. When used as a stand alone program, a surface mesh must be provided as well as some information to identify regions and cavities. The output is a constrained Delaunay volume mesh that contains quality tetrahedral elements.

Because only one file that describes the surface (and inner regions) can be used as input, this mesh must contain the RoI within itself, i.e. several faces have to be joined in order to produce a closed region that will count with a higher level of refinement.

It is possible to not constrain the volume in the zones outside the RoI. In this case TetGen will produce elements as large as possible in those regions, while satisfying the Delaunay property as well as surface representation.

When used as a library, the situation changes. The decision of which element to split can be controlled by another class that defines some specific criteria like regional refinement. The algorithm would start from a global mesh that is not constrained by a maximum element volume. Then detect every tetrahedron that resides in the RoI and produce a refinement of those elements until a certain condition on point quantity is reached. With these modifications, all the initial constraints as defined in section II would be satisfied, producing an optimal patient-specific mesh. This approach has not been implemented.

E. Modified Octree

The octree structure is very convenient for refining only certain elements in the mesh. As explained before, it splits all the elements that are not completely outside the input domain. A minor conceptual modification would make a significant difference in obtaining an optimal mesh: split all the elements that are not completely outside the RoI. This creates a new category of element: an element that is outside the RoI but inside the input domain.

At this level the mesh is unsuitable for the FEM because it has some element faces that are split by one side and not by the other. In other words, there are faces that count with some points inserted on their edges and even on their surface, as shown in figure 5. A mesh is said to be 1-irregular if each element face has a maximum of one point inserted on each edge and a face midpoint. The mesh produced by adding the refinement constraint at the RoI is not necessarily 1-irregular. To solve this problem, all the elements that are not 1-irregular are split until the entire mesh respects this property [START_REF] Hitschfeld | Generation of 3D mixed element meshes using a flexible refinement approach[END_REF].

It is important to produce a 1-irregular mesh because throughout patterns we can split those octants by adding different type of elements (such as: tetrahedra, pyramids and prisms). This stage results in a congruent mixed element mesh that has different levels of refinement.

The last step is to achieve a representation of the surface. This is done by projecting the points of the elements that are outside the input surface, onto it. Better solutions, such as marching cubes, can be implemented with modifications in order to avoid problems with the junction of other types of elements (tetrahedra, pyramid and prism). The main motivation for changing this sub-process is that projected elements may not respect some aspect-ratio constraints as can be seen figure 6. This modified octree has been implemented with satisfactory results. However it can still evolve further with the achievement of a better surface representation. This technique also complies with the constraints mentioned in section II.

The stop condition for the initial octree is not a certain level of surface approximation, but a global quantity of points. Once this quantity is reached, the only process that will increase the number of points is the 1-irregular process. After that, the management of the transition and the process of projection will not increase the quantity of points.

Fig. 1

 1 Fig.1The advancing front technique: top-left: the initial surface mesh with the expansions directions, top-right: one face (front) is expanded, bottomleft: another expansion using already inserted points, bottom-right: expansion of cavity inner face using inserted points.

Fig. 3

 3 Fig.3Regular Octree: a regular mesh that contains hexahedral elements. Only elements that intersect the surface or the cavity are shown to better appreciate the last one. A real output mesh consider all the hexahedra that where erased this time and all of them have the same size.

Fig. 4

 4 Fig. 4 One output mesh generated by TetGen.

Fig. 5

 5 Fig. 5 Octree transitions: a) RoI output, b) 1-irregular mesh and c) mixed element valid mesh.

Fig. 6

 6 Fig. 6 One output mesh generated by the modified octree technique. The circle represents the tumor inside the RoI. Inner elements remain regular.

IV. DISSCUSION

We have presented several meshing techniques that confront the problem of brain shift. In particular, we have mentioned two techniques that can respect all the initial constraints of the problem (TetGen and Modified Octree) and one technique that can be very useful when time constrain is the most important (Multi-resolution).

At this point we can summarize the future works as: 1. Adapt TetGen to the problem, using it as a library. 2. Improve the quality of the projected elements in the Modified Octree. 3. Compare Modified Octree with TetGen in terms of point quantity and element quality.

V. ACKNOWLEDGMENT This project has been financially supported by the ALFA IPECA project as well as FONDEF D04-I-1237 (Chile), and carried out in collaboration with Praxim-Medivision (France). The work of Nancy Hitschfeld is supported by Fondecyt project number 1061227.

Author: Claudio Lobos Institute: TIMC-IMAG Street: Faculté de médecine, pavillon Taillefer City:

La Tronche Country: France Email: Claudio.Lobos@imag.fr