Simulation Study for Numerical Effects of Polarized vs. Non-Polarized Signal Propagation in Radar Tomography of Asteroids

Several landmark space missions have focused on characterizing small bodies and advancing planetary defense, including NASA’s DART and ESA’s Rosetta and Hera missions [4]. The DART mission successfully demonstrated kinetic impact as a viable asteroid deflection technique by altering the orbital period of Dimorphos, the smaller body in the Didymos binary asteroid system [5]. The Hera mission will follow up on this event by conducting a detailed post-impact survey of the same system. HERA includes two CubeSats, Juventas and Milani. Juventas is equipped with the low-frequency monostatic radar JuRa, which will perform the first direct probing of an asteroid’s subsurface structure. JuRa transmits a binary phase-shift keyed signal with a 20 MHz bandwidth and a 60 MHz carrier frequency, powered at 5 W. The signal wavelength is approximately 5 m in vacuum and about 2.5 m within the asteroid, assuming a relative permittivity consistent with typical porous silicate materials [4].

Electromagnetic (EM) tomography [3, 2, 1] offers a non-invasive means to investigate the internal structure of asteroids, aiming to recover spatial variations in relative permittivity and density by analyzing scattered wavefields. This study focuses on simulated monostatic radar tomography, where both transmission and reception are conducted from a single satellite platform. Special attention is given to the role of wave polarization in the accuracy of structural reconstructions. Polarization, which describes the orientation of the electric field vector, is an intrinsic property of EM waves. Neglecting it can reduce computational complexity, but may affect the fidelity of the reconstructions.

The primary objective of this research is to determine how accurately a synthetic asteroid model’s internal structure can be reconstructed without modelling polarization: a strategy that can significantly reduce computational cost. To this end, the study compares simulations of EM wave propagation and tomography using single-component (scalar) and three-component (vectorial) field models. The performance of these two alternative approaches is evaluated in terms of their ability to resolve internal voids and structural boundaries.

In this study, a numerical solution for the wavefield is found via leapfrog time-stepping [6]. The Green’s function, which characterizes the impulse response of the medium, is estimated using Tikhonov-regularized deconvolution and Born approximation [7], allowing for tractable linearization of the forward problem. Several inversion strategies are explored for reconstructing the spatial distribution of relative permittivity, including tomographic back-projection and total variation (TV) regularization.

The results present the reconstructions generated from both single- and three-component models, under noiseless and noisy signal conditions. Accuracy is quantitatively assessed using overlap metrics between the reconstructed regions and ground-truth internal features, specifically focusing on voids alone and voids with surrounding structural boundaries. For noisy simulations, Gaussian noise is added to the synthetic data, and reconstruction robustness is visualized using box plots depicting overlap quantiles. Additionally, the influence of the signal envelope is investigated in a similar fashion, providing further insight into reconstruction stability and performance. The results suggest that omitting polarization does not necessarily deteriorate the quality of the structural maps, especially in the presence of uncertainty factors, such as modelling discrepancies due to signal carrier and measurement noise.

References

[1] Jian Deng et al. “EI+ FWI method for reconstructing interior structure of asteroid using lander-to-orbiter bistatic radar system”. IEEE Transactions on Geoscience and Remote Sensing, 60 (2021), pp. 1–16.
[2] A. Dufaure et al. “Imaging of the internal structure of an asteroid analogue from quasi-monostatic microwave measurement data—I. The frequency domain approach”. Astronomy & Astrophysics, 674 (2023), A72.
[3] Mark Haynes et al. “Asteroids Inside Out: Radar Tomography”. (2020).
[4] Patrick Michel et al. “The ESA Hera Mission: Detailed Characterization of the DART Impact Outcome and of the Binary Asteroid (65803) Didymos”. The Planetary Science Journal, 3.160 (2022), pp. 1–21. doi:10.3847/PSJ/ac6f52. URL.
[5] Andrew S. Rivkin et al. “The double asteroid redirection test (DART): Planetary defense investigations and requirements”. The Planetary Science Journal, 2.5 (2021), p. 173.
[6] John B. Schneider. “Understanding the finite-difference time-domain method. School of Electrical Engineering and Computer Science, Washington State University”. URL: http://www.eecs.wsu.edu/~schneidj/ufdtd/ (2010).
[7] Liisa-Ida Sorsa et al. “A time-domain multigrid solver with higher-order Born approximation for full-wave radar tomography of a complex-shaped target”. IEEE Transactions on Computational Imaging, 6 (2020), pp. 579–590.