Permittivity Maps Research Articles

Measuring and Imaging Permittivity of Insulators Using High-Frequency Eddy-Current Devices

This paper shows that the high-frequency eddy-current (HFEC) measurement devices can be used not only for characterizing conductivity and magnetic permeability related properties of electrically conductive materials, but also for permittivity characterization of insulators. Maxwell's equations, finite-element method simulations, and experimental research are applied to support this hypothesis. An industrial HFEC device is used to measure the change of dielectric properties during the curing process of the epoxy resin L20. The measurement results are in good agreement with the expected behavior of the parameters relative permittivity and tan δ during cure. Using a capacitive reference device, similar characteristics regarding the change of the complex permittivity of the resin can be observed. In addition, HFEC imaging results on polymethyl methacrylate are presented, discussed, and compared with capacitive imaging. HFEC permittivity mapping benefits from a high spatial resolution with a sensitivity and penetration depth that is at least comparable with those of capacitive imaging technology.

Analytical and Experimental Investigation of Substrate Permittivity and Loss up to 67 GHz

In this paper, we characterize the substrate permittivity and overall loss of different planar transmission lines (TL) such as microstrip (MS), coplanar waveguide (CPW) and grounded CPW (GCPW) using on-wafer probes and a thru-reflect-line (TRL) calibration technique. The theory for calculation of the related effective permittivity from S-Parameter measurements is given and numerical simulations are being used for a fast and precise mapping of the effective permittivity to the physical value of the TL's substrate. The method presented can be used for higher frequencies, as long as single mode operation of the TLs is ensured. Thus, an overview on higher order modes in TLs and design rules to suppress them is given. The results up to 67 GHz for the aforementioned TL on a conventional RF substrate are presented and used to evaluate approximate models known from publications.

Superresolution with full-polarized tomographic diffractive microscopy.

Tomographic diffractive microscopy is a three-dimensional imaging technique that reconstructs the permittivity map of the probed sample from its scattered field, measured both in phase and in amplitude. Here, we detail how polarization-resolved measurements permit us to significantly improve the accuracy and the resolution of the reconstructions, compared to the conventional scalar treatments used so far. An isotropic transverse resolution of about 100nm at a wavelength of 475nm is demonstrated using this approach.

Quantitative Imaging With Incident Field Modeling From Multistatic Measurements on Line Segments

In this letter, we focus on an imaging procedure that retrieves the complex permittivity map of an investigation domain from electromagnetic scattered field measurements. The transmitter and the receiver are independently moved along two parallel lines of finite extent. In such a configuration, the antenna effects are of drastic importance. We propose thus a quantitative modeling of the antennas that does not require additional calibration process. The antennas model is completely incorporated in the inversion procedure and allows to recover tubes whose diameters are of the order of [(λ)/5].

Tissue electrical property mapping from zero echo-time magnetic resonance imaging.

The capability of magnetic resonance imaging (MRI) to produce spatially resolved estimation of tissue electrical properties (EPs) in vivo has been a subject of much recent interest. In this work we introduce a method to map tissue EPs from low-flip-angle, zero-echo-time (ZTE) imaging. It is based on a new theoretical formalism that allows calculation of EPs from the product of transmit and receive radio-frequency (RF) field maps. Compared to conventional methods requiring separation of the transmit RF field (B(1)(+)) from acquired MR images, the proposed method has such advantages as: 1) reduced theoretical error, 2) higher acquisition speed, and 3) flexibility in choice of different transmit and receive RF coils. The method is demonstrated in electrical conductivity and relative permittivity mapping in a salt water phantom, as well as in vivo measurement of brain conductivity in healthy volunteers. The phantom results show the validity and scan-time efficiency of the proposed method applied to a piece-wise homogeneous object. Quality of in vivo EP results was limited by reconstruction errors near tissue boundaries, which highlights need for image segmentation in EP mapping in a heterogeneous medium. Our results show the feasibility of rapid EP mapping from MRI without B(1)(+) mapping.

Microwave radar imaging of heterogeneous breast tissue integrating a priori information.

Conventional radar-based image reconstruction techniques fail when they are applied to heterogeneous breast tissue, since the underlying in-breast relative permittivity is unknown or assumed to be constant. This results in a systematic error during the process of image formation. A recent trend in microwave biomedical imaging is to extract the relative permittivity from the object under test to improve the image reconstruction quality and thereby to enhance the diagnostic assessment. In this paper, we present a novel radar-based methodology for microwave breast cancer detection in heterogeneous breast tissue integrating a 3D map of relative permittivity as a priori information. This leads to a novel image reconstruction formulation where the delay-and-sum focusing takes place in time rather than range domain. Results are shown for a heterogeneous dense (class-4) and a scattered fibroglandular (class-2) numerical breast phantom using Bristol's 31-element array configuration.

Full-polarized Tomographic Diffraction Microscopy Achieves a Resolution about One-Fourth of the Wavelength

We present a marker-free microscope that records the phase, amplitude, and polarization state of the field diffracted by the sample for different illumination directions. The data are processed with an appropriate inversion method to yield the sample permittivity map. We observe that the full-polarized information ameliorates significantly the three-dimensional image of weakly scattering subdiffraction objects. A resolution about one-fourth of the illumination wavelength is experimentally demonstrated on complex samples.

Operation of CONSERT aboard Rosetta during the descent of Philae

This paper presents a study investigating the performance of using the CONSERT instrument aboard the Rosetta spacecraft as a radar sounder during the Separation–Descent–Landing (SDL) phase of the Rosetta mission. Gathering scientifically valuable data during this phase will support CONSERT's primary target, the reconstruction of the 3D permittivity distribution within the comet 67P/Churyumov–Gerasimenko, by providing a permittivity map of the surface around the landing site. Simulation results will show the performance of the instrument, using a realistic setup including the antenna characteristics of both orbiter and landing unit as well as a realistic orbitography for the descent phase. It will be shown that operating the CONSERT instrument will indeed provide very valuable data, thereby providing tremendous aid to the experiment's main objective. Furthermore, by including knowledge of the antenna characteristics, it is possible to calculate attitude and descent profile of the Philae lander during descent, using the data of the line-of-sight propagation path and the echoes reflected from the comet's surface.

A feasibility study of magnetic resonance driven electrical impedance tomography using a phantom

Imaging the electrical properties of human tissue may aid in cancer diagnoses or monitoring organ function. Traditionally, the electrical properties are revealed with electrical impedance tomography, where currents are injected into human tissue and voltages are measured on the surface. This paper focuses on a method of measuring the electrical properties using a magnetic resonance (MR) scanner without current injection. In magnetic resonance driven electrical impedance tomography (MRDEIT), the MR phenomenon is used to induce currents in the body and the complex permittivity map is inversely computed from the difference between the modeled electric field and the actual surface electrode measurements. Computer simulations indicate that with noise level under 20%, the contrast is visually discernible in the reconstruction image. A phantom experiment is demonstrated and this supports results from computer simulation studies. The noise level in electrode measurements is evaluated to be approximately 7.8% from repeated experiments, confirming the potential to reconstruct conductivity contrast using MRDEIT. With further improvements in hardware and image reconstruction, MRDEIT may provide an additional contrast mechanism reflecting the electrical properties of human tissue, which may ultimately be used to diagnose a cancer or assist in electroencephalography.

Tomographic diffractive microscopy with a wavefront sensor

Tomographic diffractive microscopy is a recent imaging technique that reconstructs quantitatively the three-dimensional permittivity map of a sample with a resolution better than that of conventional wide-field microscopy. Its main drawbacks lie in the complexity of the setup and in the slowness of the image recording as both the amplitude and the phase of the field scattered by the sample need to be measured for hundreds of successive illumination angles. In this Letter, we show that, using a wavefront sensor, tomographic diffractive microscopy can be implemented easily on a conventional microscope. Moreover, the number of illuminations can be dramatically decreased if a constrained reconstruction algorithm is used to recover the sample map of permittivity.

A large 3D target with small inner details: A difficult cocktail for imaging purposes without a priori knowledge on the scatterers geometry

To accurately image a complex shape but large 3D target whose scattered field has been measured in an anechoic environment at high frequencies (18 and 20 GHz), we have developed a complete imaging process, combining experimental and numerical works. The adopted strategy exploits the maximum of available information related to the measurements, both in terms of quantity and accuracy without any a priori knowledge on the scatterer geometry. We first determine the position and then the dimension of the spatial domain which contains the target. This localization is realized directly from the analysis of the spectrum of the measured fields taking into account the random noise disturbing the measurement points. Then, we construct a quantitative permittivity map of this investigation domain thanks to an iterative inversion procedure based on a Bayesian formulation where the spatial diversity of the real random noise is adequately exploited. By following this strategy, we have been able to quantitatively retrieve the target both in terms of dimension, shape and electromagnetic properties, even with a very limited number of measurement points and for a single polarization case. With such a process, even spheres with a diameter equal to λ/3 are correctly reconstructed at 20 GHz.

Microwave Imaging of Soil Water Diffusion Using the Linear Sampling Method

This letter deals with the monitoring of the volumetric water content of a soil column in a fully controlled environment by means of a noninvasive microwave imaging system. Indeed, soil moisture is an important piece of information to improve fluid flow modeling or to better understand the water uptake by plant roots. In this letter, we address the problem of recovering the footprint of soil moisture evolution with respect to time using a built-in laboratory microwave setup coupled to a robust qualitative microwave imaging method: the linear sampling method (LSM). The evolution of the water content in the soil is ruled by the Richards equations and stored at different time steps. The associated maps of soil water content are converted into permittivity maps using the Dobson model. Electromagnetic scattered fields are then computed with finite-element software. We have tested the LSM in a situation that can be encountered in agricultural soils where the water content is not homogeneous. We show that the evolution of the soil water content can be qualitatively monitored with the LSM. We also point out that the source is more precisely located by considering the evolution in time of the singular system of the multistatic matrix (multiple signal classification method).

Quantitative conductivity and permittivity imaging of the human brain using electric properties tomography

The electric properties of human tissue can potentially be used as an additional diagnostic parameter, e.g., in tumor diagnosis. In the framework of radiofrequency safety, the electric conductivity of tissue is needed to correctly estimate the local specific absorption rate distribution during MR measurements. In this study, a recently developed approach, called electric properties tomography (EPT) is adapted for and applied to in vivo imaging. It derives the patient's electric conductivity and permittivity from the spatial sensitivity distributions of the applied radiofrequency coils. In contrast to other methods to measure the patient's electric properties, EPT does not apply externally mounted electrodes, currents, or radiofrequency probes, which enhances the practicability of the approach. This work shows that conductivity distributions can be reconstructed from phase images and permittivity distributions can be reconstructed from magnitude images of the radiofrequency transmit field. Corresponding numerical simulations using finite-difference time-domain methods support the feasibility of this phase-based conductivity imaging and magnitude-based permittivity imaging. Using this approximation, three-dimensional in vivo conductivity and permittivity maps of the human brain are obtained in 5 and 13 min, respectively, which can be considered a step toward clinical feasibility for EPT.

Improving the resolution of grating-assisted optical diffraction tomography using a priori information in the reconstruction procedure

We provide a numerical study of a tomographic microscope in which the sample is deposited on a periodically nanostructured substrate and is illuminated under various incident angles. The map of permittivity of the sample is retrieved numerically from the complex data of the diffracted far-field. A single-scattering analysis shows that, with an optimized grating of period λ/5, the transverse resolution of the digital imager is about λ/10. To ameliorate the resolution further, a priori information is incorporated in the inversion procedure. Fixing the lower and upper bounds of the sample permittivity permits us to obtain a transverse resolution about λ/15.

Probing dielectric ceramics surface at sub-micrometer scale

Scanning probe microscopy (SPM) with conductive tips has been used to image the dielectric properties of ceramics with giant permittivity. In particular, measurements in impedance mode of local resistivity allowed to image the permittivity map on polycrystalline materials. Such imaging provides correlation between the dielectric properties and the sample structure, in particular focusing on defects inside the single grains.Great attention has been devoted to the possible artefacts due to surface imperfections, such as huge roughness and/or contamination. A reliable surface investigation has been obtained after the definition of both the physical and geometrical criteria to avoid the artefacts due to both the surface or anomalous tip-sample contact area variation (for instance, in grain boundaries, holes and cracks in the ceramic pills).In particular, the power spectral density (PSD) allows to get access to the different periodic components of the surface roughness. The PSD demonstrated to be a sensitive tool to check the surface conditions after the polishing procedures aimed to the progressive decreasing of surface roughness, in order to reach the SPM limits and to avoid artefacts inducing wrong data interpretation.

THREE-DIMENSIONAL NONLINEAR INVERSION OF ELECTRICAL CAPACITANCE TOMOGRAPHY DATA USING A COMPLETE SENSOR MODEL

Electrical Capacitance Tomography (ECT) is a non- invasive and non-destructive imaging technique that uses electrical capacitance measurements at the periphery of an object to generate map of dielectric permittivity of the object. This visualization method is a relatively mature industrial process tomography technique, especially in 2D imaging mode. Volumetric ECT is a new method that poses major computational challenges in image reconstruction and new challenges in sensor design. This paper shows a nonlinear image reconstruction method for 3D ECT based on a validated forward model. The method is based on the flnite element approximation for the complete sensor model and the solution of the inverse problem with nonlinear iterative reconstruction. The nonlinear algorithm has been tested against some complicated experimental test cases, and it has been demonstrated that by using an improved forward model and nonlinear inversion method, very complex shaped samples can be reconstructed. The reconstruction of very complex geometry with objects in the shape of letters H, A, L and T is extremely promising for the applications of 3D ECT.

Helmholtz-Type Regularization Method for Permittivity Reconstruction Using Experimental Phantom Data of Electrical Capacitance Tomography

Electrical capacitance tomography (ECT) attempts to image the permittivity distribution of an object by measuring the electrical capacitance between sets of electrodes placed around its periphery. Image reconstruction in ECT is a nonlinear ill-posed inverse problem, and regularization methods are needed to stabilize this inverse problem. The reconstruction of complex shapes (sharp edges) and absolute permittivity values is a more difficult task in ECT, and the commonly used regularization methods in Tikhonov minimization are unable to solve these problems. In the standard Tikhonov regularization method, the regularization matrix has a Laplacian-type structure, which encourages smoothing reconstruction. A Helmholtz-type regularization scheme has been implemented to solve the inverse problem with complicated-shape objects and the absolute permittivity values. The Helmholtz-type regularization has a wavelike property and encourages variations of permittivity. The results from experimental data demonstrate the advantage of the Helmholtz-type regularization for recovering sharp edges over the popular Laplacian-type regularization in the framework of Tikhonov minimization. Furthermore, this paper presents examples of the reconstructed absolute value permittivity map in ECT using experimental phantom data.

Experimental microwave imaging of three-dimensional targets with different inversion procedures

We consider an experimental microwave imaging system in which the targets are illuminated under various angles of incidence and the scattered field is measured on a sphere surrounding them. We estimate the map of relative permittivity of the objects from the scattered field with an iterative inversion procedure based on a conjugate gradient technique. We derive several formulations of the inversion algorithm and analyze their efficiency on three different targets. We observe that including a priori information on the lower and upper bounds of the permittivity of the sample leads to a spectacular improvement of the resolution of the image.

Experimental Demonstration of Quantitative Imaging beyond Abbe’s Limit with Optical Diffraction Tomography

Optical diffraction tomography (ODT) is a recent imaging technique that combines the experimental methods of phase microscopy and synthetic aperture with the mathematical tools of inverse scattering theory. We show experimentally that this approach permits us to obtain the map of permittivity of highly scattering samples with axial and transverse resolutions that are much better than that of a microscope with the same numerical aperture.

Imposing Zernike representation for imaging two-dimensional targets

To overcome the ill-posedness of the inverse scattering problem, we introduce an appropriate way of representing the unknown permittivity profile which benefits from two a priori pieces of information which are commonly encountered. First, the unknown permittivity map has a limited spatial support which can be contained within a circular investigation area. Second, from physical reasoning based on the scattering operator, there is only a limited number of independent parameters that can be retrieved from the measured fields. Both pieces of a priori information can be adequately introduced by representing the unknown permittivity profile in terms of a Zernike polynomial expansion, correctly truncated according to the number of independent parameters. To investigate the effectiveness of such a Zernike representation, the reconstructions obtained from experimentally acquired data in the circular microwave scanner developed at the Institut Fresnel are analyzed.