The six published scientific articles included in this thesis investigate the imaging of the interior of solar system bodies by using the FETD method to simulate the forward problem in electromagnetic wave propagation. The publications introduce complex-shaped asteroid interior models built inside the surface shape of the aster-oid 25143 Itokawa (from now on: Itokawa) to investigate tomographic inversion in an asteroid target having a higher internal permittivity contrast than the extensively studied comet nucleus models[22, 30, 68]. The FETD solver was initially formu-lated and presented in [64, 74, 75], but it has been further developed during this work and has also been made openly available in GitHub[62, 63]. The numerical investigations with the solver are further validated with data from microwave radar
experiments performed in a laboratory on a permittivity-controlled asteroid ana-logue which was manufactured to match the numerical model. The measured data is also used to investigate and validate the performance of the selected forward and inversion methods to yield meaningful tomographic reconstructions.
Publication I investigates the tomographic inversion of a 2 MHz bandwidth radar signal with five different interior structures, each containing mantle and deep inte-rior details modelling void space, cracks or a high-density boulder in addition to modelling the rubble-pile nature of the other parts of the interior with a Gaussian random field. The specification of the radar simulation was based on the suggested Deep Interior Scanning CubeSat (DISCUS) mission[6]which was further developed to a comprehensive space mission proposal AI3 – Asteroid Interior Investigation -3way mission[5]. The mission proposal participated in European Space Agency’s (ESA) fast class mission call in 2019, and it was among the best six proposals in the call, although was not eventually selected. The results presented in Publication I pro-vided the key evidence for the AI3 mission proposal showing that a bistatic CubeSat measurement configuration equipped with tomographic radar can detect deep in-terior voids, cracks, and boulders in an Itokawa-sized asteroid model, and that the numerical experiments could be performed with the then available computing re-sources within a reasonable amount of time.
Publication II concerns not radar tomography, but the tomographic inversion of the gravity gradient field in two different asteroid Itokawa models. This publi-cation was used to strengthen the science case of the AI3 mission proposal, where the interior of the target asteroid would not only be investigated by a tomographic radar, but also augmented with a gravimetric measurement and seismic waves after the impact experiment. The goal of Publication II was to advance the mathematical inversion methodology in gravimetric measurements, and it sought to find feasibil-ity constraints for resolution, noise, and orbit selection for future space missions utilising gravimetric instruments.
To advance the mathematical methodology in radar tomography, Publication III introduces the formulation, implementation, and evaluation of a higher-order Born approximation in a multigrid FETD framework enabling nonlinear tomographic radar imaging. The introduced method is similar to the frequency-domain solver utilising the distorted Born iterative (DBI) technique[21, 35, 49, 50]in that it relies on sequential linearised approximations with respect to the sought permittivity
dis-tribution. However, unlike the previous literature, the methodology introduced in Publication III has been developed for arbitrary spatial domains and full-wave mod-elling for a complex-shaped target and a sparse set of measurement points in the time domain. The computations were carried out in a 2D test domain previously used in [75] introducing the multigrid methodology for a linearised forward and inverse solver in the tomographic radar problem.
To validate the results of the numerical experiments reported in Publication I, permittivity-controlled, complex-shaped analogue objects were manufactured by 3D-printing. The method and results of this work are reported in Publication IV. A fused fabrication filament material with suitable dielectric properties was found, and ma-terial mixing models were used to match the electric permittivity of the final object with the expected permittivity of an asteroid. The same simplified interior void model within the Itokawa shape as in Publication I was used, and the analogue size was matched so that it could be used for experimental tomographic microwave radar measurements to validate the permittivity and attenuation properties of the manu-factured objects, and to perform tomographic radar measurements in the laboratory.
The methodology of creating 3D-printable wireframes with given electric properties was developed alongside this work and published as an open source Asteroid Wire-frame Package[65].
Publication V reports the comparison of full wavefield simulations to microwave radar measurements. The asteroid analogue manufactured and reported in Publica-tion IV was used as the tomographic target in the laboratory experiments. A mod-ulated pulse matching a 10-20 MHz centre frequency radar to a real-scale Itokawa-size target was used to simulate the laboratory radar measurement. At the core of Publication V is the close international collaboration between two groups with two different solvers, one in the time domain, on which this thesis concentrates on, and the other in the frequency domain, allowing the comparison of two different nu-merical simulation approaches on laboratory measurements and the cross-validation between the simulation methods.
The close collaboration between the time and frequency domain approaches con-tinued in Publication VI, extending the analysis of full microwave propagation and backpropagation for the complex analogue model by investigating a single-point quasi-monostatic data. This final article in this thesis investigates the wave inter-action at given points inside the target body and analyses the effect of direct and
higher-order scattering phenomena on the data and the simple backprojection inver-sion carried out for both the simulated and measured data.