An Electromagnetic Time-Reversal Imaging Algorithm for Moisture Detection in Polymer Foam in an Industrial Microwave Drying System

Microwave tomography (MWT) based control is a novel idea in industrial heating systems for drying polymer foam. In this work, an X-band MWT module is designed and developed using a fixed antenna array configuration and integrated with the HEPHAISTOS industrial heating system. A decomposition of the time-reversal operator (DORT) algorithm with a proper Green’s function of multilayered media is utilized to localize the moisture location. The derived Green’s function can be applied to the media with low or high contrast layers. It is shown that the time-reversal imaging (TRI) with the proposed Green’s function can be applied to the multilayered media with a moderately rough surface. Moreover, a single frequency TRI is proposed to decrease the measurement time. Numerical results for different moisture scenarios are presented to demonstrate the efficacy of the proposed method. The developed method is then tested on the experimental data for different moisture scenarios from our developed MWT experimental prototype. Image reconstruction results show promising capabilities of the TRI algorithm in estimating the moisture location in the polymer foam.

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Unified double- and single-sided homogeneous Green’s function representations

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2016.0162 ◽

2016 ◽

Vol 472 (2190) ◽

pp. 20160162 ◽

Cited By ~ 16

Author(s):

Kees Wapenaar ◽

Joost van der Neut ◽

Evert Slob

Keyword(s):

Green’S Function ◽

Multiple Scattering ◽

Green's Function ◽

Time Reversal ◽

Wave Theory ◽

Boundary Integral ◽

Open Boundary ◽

Quantum Mechanical ◽

Holographic Imaging ◽

Scattering Time

In wave theory, the homogeneous Green’s function consists of the impulse response to a point source, minus its time-reversal. It can be represented by a closed boundary integral. In many practical situations, the closed boundary integral needs to be approximated by an open boundary integral because the medium of interest is often accessible from one side only. The inherent approximations are acceptable as long as the effects of multiple scattering are negligible. However, in case of strongly inhomogeneous media, the effects of multiple scattering can be severe. We derive double- and single-sided homogeneous Green’s function representations. The single-sided representation applies to situations where the medium can be accessed from one side only. It correctly handles multiple scattering. It employs a focusing function instead of the backward propagating Green’s function in the classical (double-sided) representation. When reflection measurements are available at the accessible boundary of the medium, the focusing function can be retrieved from these measurements. Throughout the paper, we use a unified notation which applies to acoustic, quantum-mechanical, electromagnetic and elastodynamic waves. We foresee many interesting applications of the unified single-sided homogeneous Green’s function representation in holographic imaging and inverse scattering, time-reversed wave field propagation and interferometric Green’s function retrieval.

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Accurate and efficient computation of the periodic Green's function in multilayered media via a hybrid spectral/spatial summation with optimized complex images

IEEE Antennas and Propagation Society International Symposium. 1999 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.99CH37010) ◽

10.1109/aps.1999.788319 ◽

2003 ◽

Author(s):

R.M. Shubair

Keyword(s):

Green’S Function ◽

Green's Function ◽

Spatial Summation ◽

Efficient Computation ◽

Multilayered Media ◽

Complex Images

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Bidimensional spline fitting procedure for rapid evaluation of Green's function for multilayered media

2009 IEEE Antennas and Propagation Society International Symposium ◽

10.1109/aps.2009.5172083 ◽

2009 ◽

Author(s):

G. Bianconi ◽

S. Genovesi ◽

A. Monorchio ◽

R. Mittra ◽

K. Du

Keyword(s):

Green’S Function ◽

Green's Function ◽

Rapid Evaluation ◽

Multilayered Media ◽

Fitting Procedure ◽

Spline Fitting

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Green's Function Estimation in Homogeneous and Scattering Medium for Time Reversal Signal Processing (TRSP) Communication

10.1109/icdt.2007.56 ◽

2007 ◽

Author(s):

Quy Nguyen Dinh ◽

Woon-Seng Gan

Keyword(s):

Signal Processing ◽

Green’S Function ◽

Green's Function ◽

Time Reversal ◽

Function Estimation ◽

Scattering Medium

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A single-sided homogeneous Green's function representation for holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval

Geophysical Journal International ◽

10.1093/gji/ggw023 ◽

2016 ◽

Vol 205 (1) ◽

pp. 531-535 ◽

Cited By ~ 24

Author(s):

Kees Wapenaar ◽

Jan Thorbecke ◽

Joost van der Neut

Keyword(s):

Green’S Function ◽

Inverse Scattering ◽

Green's Function ◽

Time Reversal ◽

Boundary Integral ◽

Open Surface ◽

Function Representation ◽

Holographic Imaging ◽

Scattering Time ◽

Time Reversal Acoustics

Abstract Green's theorem plays a fundamental role in a diverse range of wavefield imaging applications, such as holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval. In many of those applications, the homogeneous Green's function (i.e. the Green's function of the wave equation without a singularity on the right-hand side) is represented by a closed boundary integral. In practical applications, sources and/or receivers are usually present only on an open surface, which implies that a significant part of the closed boundary integral is by necessity ignored. Here we derive a homogeneous Green's function representation for the common situation that sources and/or receivers are present on an open surface only. We modify the integrand in such a way that it vanishes on the part of the boundary where no sources and receivers are present. As a consequence, the remaining integral along the open surface is an accurate single-sided representation of the homogeneous Green's function. This single-sided representation accounts for all orders of multiple scattering. The new representation significantly improves the aforementioned wavefield imaging applications, particularly in situations where the first-order scattering approximation breaks down.

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