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.

Time reversal has been demonstrated to be effective for source and novelty detection and localization. We extend here previous work in the case of a coupled structural-acoustic system, to which we refer to as vibro-acoustic. In this case, novelty means a change that the structural system has undergone and which we seek to detect and localize. A single source in the acoustic medium is used to generate the propagating field, and several receivers, both in the acoustic and the structural part, may be used to record the response of the medium to this excitation. This is the forward step. Exploiting time reversibility, the recorded signals are focused back to the original source location during the backward step. For the case of novelty detection, the difference between the field recorded before and after the structural modification is backpropagated. We demonstrate that the performance of the method is improved when the structural components are taken into account during the backward step. The potential of the method for solving inverse problems as they appear in non destructive testing and structural health monitoring applications is illustrated with several numerical examples obtained using a finite element method.

Abstract We have recently introduced a modification of the multiple signal classification method for synthetic aperture radar. This method incorporates a user-defined parameter, ϵ, that allows for tunable quantitative high-resolution imaging. However, this method requires relatively large single-to-noise ratios (SNR) to work effectively. Here, we first identify the fundamental mechanism in that method that produces high-resolution images. Then we introduce a modification to Kirchhoff Migration (KM) that uses the same mechanism to produce tunable, high-resolution images. This modified KM method can be applied to low SNR measurements. We show simulation results that demonstrate the features of this method.

We present a holographic imaging approach for the case in which a single source-detector pair is used to scan a sample. The source-detector pair collects intensity-only data at different frequencies and positions. By using an appropriate illumination strategy, we recover field cross correlations over different frequencies for each scan location. The problem is that these field cross correlations are asynchronized, so they have to be aligned first in order to image coherently. This is the main result of the paper: a simple algorithm to synchronize field cross correlations at different locations. Thus, one can recover full field data up to a global phase that is common to all scan locations. The recovered data are, then, coherent over space and frequency so they can be used to form high-resolution three-dimensional images. Imaging with intensity-only data is therefore as good as coherent imaging with full data. In addition, we use an $\ell$1-norm minimization algorithm that promotes the low dimensional structure of the images, allowing for deep high-resolution imaging.