Imaging in lossy media

Abstract

We study the effects of absorption in the medium on synthetic aperture imaging. We model absorption using the loss tangent, which is the imaginary part of the relative dielectric permittivity, and study two cases: (i) the loss tangent is known and (ii) the loss tangent is unknown. When the loss tangent is known and used in Kirchhoff migration (KM), we find that images of targets are range-shifted by approximately a central wavelength so that their predicted locations are closer to the synthetic aperture than they actually are. In contrast, we find that when the medium is unknown, the KM image does not exhibit this range-shift. Hence, we determine that it is better to not make use of any knowledge of the absorption when imaging. Using a recently developed transformation of KM images, which we call reciprocal-KM (rKM), we achieve tunably high-resolution images of targets through adjusting the value of a user-defined parameter ε. When rKM is applied to an imaging region containing two targets, we find that their predicted locations shift, especially in range, but within a fraction of central wavelength of their true locations.

Synthetic aperture radar imaging below a random rough surface

“…Additionally, we do not know the loss tangent β that dictates the absorption in the lower medium. In fact, we have shown previously that making use of any knowledge of the absorption is not useful for imaging to identify and locate targets (Kim & Tsogka, 2023a). However, we assume that r is known.…”

“…Assuming a synthetic aperture of length a, and system bandwidth B, we have recently shown (Kim & Tsogka, 2023c) that the resolution of the imaging method in cross-range (the direction parallel to the synthetic aperture) is √ δλL/a and the range (direction orthogonal to cross-range) resolution is √ δc/B with c the speed of the waves, λ the central wavelength and L the distance of propagation. We have also carried out a resolution analysis of this method for imaging in a lossy medium (Kim & Tsogka, 2023a) where we have shown that one should not use the absorption in the medium even if it is known. Although, absorption does not affect significantly the resolution of the imaging method, it does affect the target detectability.…”

Synthetic Aperture Radar Imaging Below a Random Rough Surface

“…Additionally, we do not know the loss tangent β that dictates the absorption in the lower medium. In fact, we have shown previously that making use of any knowledge of the absorption is not useful for imaging to identify and locate targets (Kim & Tsogka, 2023a). However, we assume that ϵ r is known.…”

“…Assuming a synthetic aperture of length a , and system bandwidth B , we have recently shown (Kim & Tsogka, 2023c) that the resolution of the imaging method in cross‐range (the direction parallel to the synthetic aperture) is $$\sqrt{\delta }\lambda L/a$$ and the range (direction orthogonal to cross‐range) resolution is $$\sqrt{\delta }c/B$$ with c the speed of the waves, λ the central wavelength and L the distance of propagation. We have also carried out a resolution analysis of this method for imaging in a lossy medium (Kim & Tsogka, 2023a) where we have shown that one should not use the absorption in the medium even if it is known. Although, absorption does not affect significantly the resolution of the imaging method, it does affect the target detectability.…”