Elsevier

Advances in Space Research

Volume 62, Issue 8, 15 October 2018, Pages 1977-1986
Advances in Space Research

Imaging the interior of a comet from bistatic microwave measurements: Case of a scale comet model

https://doi.org/10.1016/j.asr.2017.10.012Get rights and content

Abstract

Imaging the internal structure of comets and asteroids is an important way to provide information about their formation process. In this paper, we investigate the possibility to image the interior of such structures with electromagnetic waves in the microwave domain (radar system) using an inverse algorithm adapted to take advantage of a bistatic configuration, considering the polarization effects, and which presents low memory requirement. To this end, a scale model of a comet/asteroid was built and was used for an experimental simulation. The scattered fields of this scale model were measured in a perfectly controlled environment, in an anechoic chamber, to avoid measurement disturbances and to focus this study only on which structural information can be obtained with such measurements. To profit from the spatial diversity of information, a vectorial-induced current reconstruction algorithm was used. Two configurations were tested and analyzed including one with very few measurements. From the qualitative reconstructed maps, we have shown that it is possible to detect the presence of a core in both cases.

Introduction

The interior of comets and asteroids, i.e. their structure and composition, is poorly known, but could provide information to understand the early development of the Solar System (Bottke et al., 2002, Festou et al., 2004). Nevertheless, it is a very challenging problem obviously in terms of measurements but also in terms of imaging procedures. To solve such inverse problem, the difficulties are mainly due to the two following problems: such structures are very large and furthermore the number of measurements in a realistic space radar scenario is necessarily very limited.

The appeal of the sounding of these small solar system bodies with electromagnetic waves has been increasing in recent years (Herique et al., 2018). The CONSERT experiment on the European Space Agency’s Rosetta mission is the first instrument designed to reconstruct the interior of a comet. It met the Comet 67P/Churyumov-Gerasimenko in November 2014. The CONSERT experiment has explored the nucleus of this comet using electromagnetic waves in the radiowave regime and exploiting a bistatic configuration (Kofman et al., 2007). One of its scientific aims is to contribute to a better understanding of the composition of the cometary core and of its internal structure (Kofman et al., 1998, Kofman and Safaeinili, 2004). This experiment is based on a transmission travel-time tomography process working with a central frequency of 90 MHz and a bandwidth of 10 MHz. The electromagnetic waves sent by the source on the orbiter Rosetta, propagate inside the comet up to the lander Philae and then are sent back to the orbiter. This experiment takes profit from the rotation of the comet itself to reach several bistatic angles. The first measurements with CONSERT were made immediately after the landing of Philae on the comet (Kofman et al., 2015) and have already shown the ability of such electromagnetic techniques to explore the comets (Kofman et al., 2007, Kofman et al., 2015, Herique et al., 2016).

Modelling the propagation of the electromagnetic signal through such large bodies is not trivial as numerical rigorous models based on the discretization of the Maxwell equations are requiring an extremely high memory capacity. To this end, methods based on Physical Optics and the ray-tracing method have been applied to this problem (Kofman et al., 1998, Virkki and Muinonen, 2016, Hegler et al., 2013, Ciarletti et al., 2015). To image the interior of the structure, radar techniques which fully exploit the bandwidth (or temporal methods) have been developed. Indeed, the temporal echoes due to the interaction of the electromagnetic waves with the different inhomogeneities were detected. This can be seen with a direct temporal visualization of the signals versus time as radargrams or as B-scan images (Asphaug et al., 2010); focusing by migrations methods have also be adapted to process these data (Herique et al., 1999, Barriot et al., 1999, Sava et al., 2015, Grimm et al., 2015).

With such bodies, the non-linear imaging procedures - here named quantitative inversion - which allow to get the complex permittivity maps of the targets are very difficult to exploit, specially for the 3D case. Numerical studies on the imaging of the interior of a body which are based on wave propagation have been conducted in both 2D (Pursiainen and Kaasalainen, 2014) and in 3D geometries (Pursiainen and Kaasalainen, 2015). It is true, however, that 3D inversion for a full wave is still a challenge as the objects are very large compared to the wavelengths, i.e., the number of unknowns is - in the general case - also very large which leads to a huge memory requirement, but also to a high risk of false solution (local minimum solution). This risk is also increased by the small quantity of measurements. For more details on these methods the special section of the Inverse Problems journal devoted to the test of such non-linear inversion algorithms against experimental data on 3D targets can be seen (Litman and Crocco, 2009, Geffrin and Sabouroux, 2009).

First-order diffraction tomography algorithms can be a good solution to reach the structural characteristics of these bodies (and also the electromagnetic characteristics when low-contrasted targets are considered). In these algorithms, the polarizations of the scattered field and the incident field are colinear and the Born or the Rytov approximations are used to formulate this problem with a scalar equation. The contrast map is then retrieved via an inverse Fourier transform (see for example (Gurg and Wolf, 2001, Safaeinili et al., 2002, Devaney, 2012)).

The present study continues with the same spirit, but we fully take into account the entire vectorial nature of the field which is needed for such tridimensional bodies. Furthermore, no linear assumption is made here to retrieve the structural characteristics of the target. The spatial diversity of the information which can be obtained in bistatic scenarios is exploited. This study is conducted on a 3D scale model of a comet, from lab-measurements using a single frequency to reconstruct the images.

The details of the inner structure of this target are explained in part II. Part III is devoted to the lab-experimentations. Two configurations of measurement are investigated and explained. The information content in these configurations is then analyzed in part IV. Experimentally measured scattered fields are used as input data of the imaging procedure which is described in part V. The imaging results are presented and discussed in part VI. Some concluding remarks follow in part VII.

Section snippets

Scale model of a comet

Comets can present a wide variety and a diverse set of morphologies has been proposed for the cometary nuclei such as the fractal aggregate model (Donn, 1990), rubble-pile model (Weissman, 1986), icy glue model (Gombosi and Houpis, 1986), layered pile model (Belton et al., 2007), corresponding to different formation scenarios (Sunshine et al., 2016, Davidsson et al., 2016). In this study, we chose to work with a body supposed to have the morphology described by the layered pile model. A scale

Setup

All the scattered field measurements were made with the equipment of the CCRM in Marseille, which is equipped with a spherical positioning setup inside an anechoic chamber. The working frequencies are in the 1–20 GHz range actually, but will be soon upgraded to 40 GHz for scattering measurements (see Eyraud et al., 2008, Geffrin et al., 2009 for more details). Using the different positioning devices is equivalent to placing the sources and receivers in a large variety of positions on an

Analysis of the information content

The maximal amount of information in far field that can be obtained for an arbitrary transmitter-receiver configuration follows from the size of the target and the illuminating frequency (Bucci and Isernia, 1997). In the case of our scale model, the number of degrees of freedom of the scattered field is equal to 128π2aλ43,500,000 where λ is the wavelength of the electromagnetic wave and a is the radius of the minimum sphere which can enclose our target. On the other hand, in our two

Vectorial diffraction tomography algorithm

To reconstruct a 3D image from the scattered field, we chose to work with a qualitative imaging procedure, i.e., the positions and the shapes of the structure can be reconstructed, but the quantitative value of the permittivity cannot be reached. This kind of algorithms has two main advantages in the present study: the memory requirement is low (it is thus possible to reconstruct a large domain) and these procedures are generally robust against most of the disturbances. In this paper, the

Imaging results

With the present imaging techniques, the maximum size of the imaging domain is directly linked to the chosen sampling in the spectral domain, so that it is possible to reconstruct a large area with a fine spatial sampling. Here, the imaging domain is equal to a cube (respectively square) with a side length of 60λ for the configuration A (respectively B). In a complete configuration, the resolution could be λ2 (Born and Wolf, 1999), but with the limited number of measurements that is available

Conclusion

To extract the structural information on large structures as comets or asteroids, we investigated the possibility to exploit an inverse algorithm especially built to take advantage of the spatial diversity, such as what can be measured in bistatic configurations. The induced currents have been reconstructed with a vectorial tomography algorithm which takes into account the polarization states of the transmitting and receiving antennas. The advantage of this method is to have a low-memory

Acknowledgement

The authors acknowledge the opportunity provided by the Centre Commun de Ressources en Microonde to use its fully equipped anechoic chamber.

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