Demonstration of Quantitative Microwave Imaging Using an Ideal Veselago Lens

Abstract

Quantitative microwave imaging employing an ideal Veselago lens is demonstrated using synthetic 2D experiments. Reconstructions of the complex-valued dielectric constant of an arbitrary objectof-interest are obtained from noiseless data using a non-iterative technique. A closed-form Veselago lens Green's function is utilized in the formulation of the problem. The contrast sources corresponding to a single illumination of the object-of-interest is recovered using total-field measurements at several receiver points located in the lens' focusing region. Collecting the field in the presence of the ideal Veselago lens produces well-conditioned matrices for the discretized inverse source problem. The contrast is then directly obtained by first calculating the total-field within the object. Synthetic examples having features as small as λ/25 show that the resolution is only limited by the signal-to-noise ratio of data. Experiments with noisy data reveals that the inversion procedure directly mirrors the noise in the data. Two new filtering processes are introduced based on the truncated Singular Value Decomposition of the data operator and the domain operator involved in the inversion process. These successfully deal with noisy reconstructions. Results show that using the new filtering methods, even with a single illuminating source, outperforms the least-squares method with several illuminating sources.

Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging

“…In the last two decades, following Veselago's seminal work on the focusing phenomenon of double-negative materials [18], numerous researchers have undertaken investigations into the properties of these materials for various applications [19], including MWI [20][21][22][23][24]. The utilization of an ideal Veselago lens (VL), a loss-less double-negative material with ϵ r = µ r = −1, in quantitative MWI, has been successfully demonstrated in previous research [25].…”

“…Despite the demonstrated potential usefulness of ideal VLs in various applications, such as MWI, their practical implementation has been hindered by the absence of a natural material with the required properties and the associated technical challenges of fabrication. Nonetheless, recent investigations have revealed that the use of a VL can significantly mitigate the ill-posedness of the inverse source and scattering problems associated with MWI, as reported in [25]. This is accomplished because the VL Green's function (GF), previously derived in closed form in [26], produces a well-conditioned matrix in the discretized ISP.…”

“…This is accomplished because the VL Green's function (GF), previously derived in closed form in [26], produces a well-conditioned matrix in the discretized ISP. It was shown in [25] that the quality of the inversion results was limited only by the signal-to-noise ratio of the collected data.…”

“…Subsequently, we employ the concept of the distributional derivative to state the ISP based on the contrast generated by the VL boundaries. Then, we revise the data equation presented in [25], which was introduced for the case where an actual physical lens was utilized. This revision involves the inclusion of two improper surface integrals along the VL boundaries (line integrals in the 2D problem considered herein), and the accuracy of the ISP solution relies on the precise calculation of these integrals.…”

“…The surface integrals represent the addon data in the VVL ISP and their value must be evaluated and added to the VL data. If it is possible to evaluate the surface-integral contribution the corrected data could then be directly inverted using the VL Green's operator proposed in [25], with the analytic kernel for the VL GF described in [26].…”