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Numerical 3-D FEM and Experimental Analysis of the Open-Ended Coaxial Line Technique for Microwave Dielectric Spectroscopy on Soil Norman Wagner, Moritz Schwing, and Alexander Scheuermann

Abstract— Open-ended coaxial line probes (OCs) are systematically analyzed by means of numerical 3-D finite element calculations in combination with experimental investigations for microwave dielectric spectroscopy on fine grained soils. The probes, based on conventional coaxial lines and connectors (N, SMA), are broadband characterized in the frequency range from 1 MHz to 10 GHz. The sensitive region for dielectric measurements is ±7-mm lateral and 7-mm perpendicular to the midpoint of the sensor aperture. The spatial spreading of the sensitive zone is stable for the investigated low-loss and high-loss strongly dispersive standard liquids, as well as the saturated and unsaturated soils. Dielectric spectra are determined based on a bilinear relationship between effective permittivity and complex reflection coefficient of the probe after probe-calibration with known standards. The mean relative error of the real part of the complex permittivity from 100 MHz to 10 GHz is smaller than 3.5% and is less than 10% for the imaginary part. A lower limit of the measurement range of 50 MHz with the used procedure and materials is suggested. Complex effective permittivity of saturated fine-grained soils is determined with the developed probes and procedure. The soil dielectric spectra were analyzed with a broadband relaxation model, as well as a novel, coupled hydraulic-dielectric mixture approach. The results demonstrate the suitability of the investigated OCs for the determination of high resolution soil dielectric spectra. Index Terms— 3-D electromagnetic field calculation, dielectric spectroscopy, open-ended soil moisture sensor.

I. I NTRODUCTION

O

PEN-ENDED coaxial line probes (OCs) were originally developed for the broadband determination of dielectric properties of biological tissues [1], [2] as well as for microwave dielectric spectroscopy of liquids [3]–[9]. In addition, the technique was adapted for remote sensing [10]–[13], agricultural [14]–[16], geotechnical [17], and soil physical applications [18]–[23]. Kaatze and Feldman [24] and Kaatze [25] provided extensive reviews of dielectric spectrometric Manuscript received May 28, 2012; revised January 24, 2013; accepted January 24, 2013. This work was supported in part by the German Research Foundation (DFG) under Project WA 2112/2-1 and Project SCHE 1604/2-1. N. Wagner is with the Institute of Material Research and Testing, Bauhaus-University Weimar, Weimar 99423, Germany (e-mail: norman. [email protected]). M. Schwing and A. Scheuermann are with the Geotechnical Engineering Centre, School of Civil Engineering, The University of Queensland, Brisbane 4000, Australia (e-mail: [email protected]; a.scheuermann@ uq.edu.au). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2013.2245138

techniques, including the open-ended coaxial line technique. In this paper, the performance of open-ended coaxial probes used in combination with a network analyzer for microwave dielectric spectroscopy on soils was investigated with numerical 3-D finite element modeling and with experimental techniques. The electromagnetic field at the open-ended coaxial probe aperture fringes into the sample at the interface. Thus, the reflection coefficient measured with a vector network analyzer (VNA) can be related to the complex permittivity of the sample [24]. Stuchly et al. [1] derived a lumped element parallel circuit approximation for the probe admittance. The advantage is the simplicity of the expressions relating the measured reflection coefficient to the sample permittivity, but due to radiation losses the approach is valid only over limited frequency ranges for appropriate probe dimensions [5]. Marsland and Evans [26] have suggested equivalent circuit models, including radiation effects, and Otto and Chew [27] further improved the calibration technique. However, the overall accuracy of the approach suggested by Otto and Chew [27] in the frequency range around approximately 1 GHz is considerably low. Based on the assumption of wave propagation in the transverse electromagnetic mode, the open-ended coaxial probe from a theoretical point of view has been extensively studied [5], [9], [14], [28], [29]. Commercial openended probes are available from Agilent (high temperature, performance, and slim-form probe) with appropriate analysis software (Agilent 85070E Dielectric Probe Kit), which has been used frequently in several applications [16], [18]–[21], [30], [31]. Nevertheless, the probes are expensive and the software only works in combination with Agilent VNAs. In a porous mineral material, the movement of water is influenced by different surface-bonding forces due to interface processes [32]. The interface effects lead to a number of dielectric relaxation processes [18], [23], [33]–[40]. Hence, dielectric spectroscopy gives insight into soil physical properties, which are related to mineral–water interaction, such as the soil water characteristics. The open-ended coaxial line technique offers an experimental method for a precise nondestructive determination of the frequency-dependent dielectric properties of fine grained soils [16], [18], [23]. Against this background, open-ended coaxial probes were developed based on conventional available coaxial lines and connectors, and analyzed for the use in coupled hydraulic-dielectric investigations.

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Three types of open-ended coaxial line probes were studied: 1) a RG 402/U semi rigid open-ended coaxial line (OC); 2) a modified SMA connector (OSMA); and 3) a modified N connector (ON). The propagation characteristics of electromagnetic fields at the probe aperture and spatial sensitivity of the probes for the determination of dielectric spectra were analyzed in the frequency range from 1 MHz to 10 GHz by means of 3-D numerical finite element calculations in Ansys HFSS, in combination with experimental investigations on low-loss and high-loss strong dispersive standard liquids and nearly saturated soils. In addition, the numerical results were used to analyze the calibration technique for the determination of the dielectric spectra. This allows the quantification of the lower and upper frequency limit in which the technique can be applied. The N-based probe (ON) was used to determine the complex effective relative permittivity of saturated finegrained soils to demonstrate the applicability of the technique to study dielectric soil properties. The soil dielectric spectra were analyzed with a broadband relaxation model, as well as a novel, coupled hydraulic-dielectric mixture approach [40].

Sample

Measurement Plane Port 1

(a)

coaxial line

Probe a1

a1

Vector Network Analyser

S11

S'21

b1

S'11

b1

The complex impedance Z  or admittance Y  that depends on the dielectric properties of a sample is determined from the complex reflection coefficient () at the interface between the flat end of the probe and the sample, where 1 1− = Z0 (1)  Y 1+ and Z 0 is the real characteristic impedance of the probe (Z 0 = 50 ). However, Z 0 of the probe is mostly not known a priori and  is not the actual measured reflection coefficient S11 from the network analyzer, because the latter includes not only information from the interface but also error effects from the coaxial line, connectors, and container [1]. To eliminate these systematic errors, a calibration procedure must be performed prior to the determination of the dielectric spectra [41]. In general, two approaches are applied. 1) A two stage calibration procedure, whereby in the first step, the true reflection coefficient  is determined by calibration with three known reflection coefficients S11 [3], [27], [41], [42]. In the second step: a) permittivity is calculated using the theoretical or numerical formulation of the open-ended coaxial line problem with infinite ground plane and semiinfinite sample size using a quasi-analytical or numerical inversion [14], [41], [42] or; b) lumped element parameters are determined (with or without considering radiation effects) in a further calibration step [27]. 2) A single-stage calibration procedure, which is based on a bilinear relationship between measured reflection coefficient with VNA S11 and complex permittivity εr of appropriate reference materials [7], [8], [25], [26], [43]–[45]. In this paper, a calibration procedure based on approach 2) was applied to avoid appropriate instabilities in the

b2

b2

a2

a2

S'22

S'12

(b) εr,eff C0

Cf

(c) a1

Vector Network Analyser

a2

S'21

S11

II. M EASUREMENT P ROCEDURE

Γ

S'22

S'11 S'12

b1

Γ b2 Sample

Probe

Fig. 1. (a) Schematic diagram of the measurement planes of an open-ended coaxial line probe, (b) its lumped-element equivalent circuit representation, and (c) appropriate two-port error model or signal flow graph.

Z =

determination of the frequency-dependent permittivity due to assumptions in the theoretical formulation of the inverse problem and numerical implementation of the used open-ended coaxial probe. In Fig. 1, the appropriate lumpedelement equivalent circuit of an OC is shown. Using (1) with (23) and (24) from Section V, Marsland and Evans [26] and Bao et al. [7] derived the following bilinear equation: εr =

c1 S11 − c2 c3 − S11

(2)

between measured reflection factor S11 and complex relative permittivity εr = εr − j εr, with complex calibration constants c1 , c2 , and c3 (see Section V). A. Open-Water-Short (OWS) Calibration S ) Substituting the short parameters ( = −1 and S11 = S11 into (29), we have S c3 = S11 . (3)

Substituting the open parameters (εr,O = 1 and O ) and those for a standard liquid (ε  = ε  S11 = S11 r r,L and L ) into (2), leads to S11 = S11

and

O O c1 − c2 − c3 = −S11 S11

(4)

L   L S11 c1 − c2 − εr,L c3 = −εr,L S11

(5)

where superscripts O and L stand for open and standard liquid, respectively, and εL is the dielectric permittivity of

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the liquid. Solving the above complex equations gives c1 , c2 , and c3 . After obtaining these three complex parameters, the unknown relative complex permittivity can be found from the measured reflection coefficient S11 (ω, T ) at each frequency and temperature with εr (ω, T ) =

c1 (ω, T )S11 (ω, T ) − c2 (ω, T )

(6)

S S11 − S11 (ω, T )

and c1 = c2 =

S O  (S S − S L ) − ε εr,L r,O (S11 − S11 ) 11 11  S O (S S − S L ) − ε L S O εr,L r,O S11 (S11 − S11 ) 11 11 11 L − SO S11 11

.

B. Open-Water-Liquid (OWL) Calibration The above described OWS-calibration has limitations in the high frequency range above approximately 500 MHz due to the inaccuracy of the short calibration. Therefore, an additional OWL-calibration is suggested. Equations (3)–(5) were rewritten1 as W   W S11 c1 − c2 − εr,W c3 = −εr,W S11 L ,1 L ,1   S11 c1 − c2 − εr,L ,1 c3 = −εr,L ,1 S11 .. .. .=. L ,n L ,n   S11 c1 − c2 − εr,L ,n c3 = −εr,L ,n S11

O −1 −ε S11 r,O

⎜ W ⎜S ⎜ 11 ⎜ L ,1 ⎜S ⎜ 11 ⎜ . ⎜ . ⎝ . L ,n S11

⎞

⎛

O −εr,O S11

(9) ⎞

⎟ ⎜  SW ⎟  ⎟ ⎛ ⎞ ⎜ −εr,W ⎟ −1 −εr,W 11 ⎟ ⎟ c1 ⎜ ⎟ ⎜  L ,1 ⎟  ⎟ ⎝c2 ⎠ = ⎜ −εr,L ,1 S11 ⎟ −1 −εr,L ⎟ ⎜ ,1 ⎟ ⎟ ⎟ ⎜ c .. .. ⎟ 3 .. ⎟ ⎜ . . ⎠ ⎠ ⎝ .  L ,n  −1 −εr,L −ε S ,n r,L ,n 11

(10)

with deionized water “W” as a standard liquid as well as additional liquids “L, i.” In compact form, this relationship is expressed as M c = e. (11) In the case of three standards, the system can simply be solved numerically as c = M−1 · e and εr (ω) of the unknown sample can be calculated from the measured reflection coefficient S11 according to (2). However, if the system is over-determined due to more than three standard measurements, then the inverse of matrix M has to be rewritten as c = (MT M)−1 MT ·e and numerically solved. 1 This relationship is used for every measured frequency.

OSMA

ON

OE

Probe type

SMA

N

RG 402/U

1.5

3

0.909

2.5 55

5 70

3.02 3.58

Inner conductor - Outer diameter [mm] Outer conductor at the sample aperture - Inner diameter [mm] - Outer diameter [mm] TABLE II

R EFERENCE L IQUIDS Methanol

Ethanol

Toluene

Water

0.05 99.8 0.01 0.001 32.04

0.2 0.05 99.5 0.001 46.07

0.03 0.001 92.14

100 18.02

37.90 5.97 −5.94 −2.76 −13.05 15.72

28.56 4.67 −6.34 −1.4 −13.83 23.11

2.44 2.22 −0.97 −13.15 6.14

87.85 6.22 −4.57 −5.79 −14.23 18.02

Water (KFT) [%] Methanol [%] Ethanol [%] Non fluids [%] Molar mass [g/mol] εm,S [-] εm,∞ [-] a S [10−3 /°C] a∞ [1/°C] log(τ0 [s]) E A [kJ/mol]

III. M ATERIALS AND M ETHODS In Table I, we summarize the geometric parameters of the three types of open-ended coaxial line probes (OCs): 1) a 30-cm RG 402/U semi rigid open-ended coaxial line (OE); 2) a modified SMA connector (OSMA); and 3) a modified N connector (ON).

O O c1 − c2 − εr,O c3 = −εr,O S11 S11

⎛

Probe name

(8)

Even though only the connector of the coaxial line to the probe is taken into account by the scattering matrix in the above derivation, Bao et al. [7] found that other artifacts, such as the effects of the probe or sample container, can also be eliminated.

or as

TABLE I G EOMETRICAL P ROBE PARAMETERS

(7)

W O (S11 − S11 )

3

A. Calibration Liquids For the calibration of the probes, the following liquids were used: methanol, ethanol and toluene (neoLab GmbH, Germany, see Table II), deionized water and tap water (Weimar, Germany). In general, εr depends on temperature T , pressure p, and frequency f . However, the pressure dependence is not considered. All measurements were carried out under atmospheric conditions in a restricted temperature range (20–25 °C) from 1 MHz to 10 GHz. Under these circumstances, εr is modeled with a single Cole–Cole type relaxation function [46] ε(T ) εr (ω, T ) − ε∞ (T ) = (12) 1 + ( j ωτ (T ))βCC (T ) √ with angular frequency ω = 2π f , imaginary unit j = −1, high frequency limit of permittivity ε∞ , relaxation strength ε = ε S + ε∞ with static dielectric permittivity ε S , and stretching exponent or Cole–Cole parameter βCC . For the temperature dependence of ε∞ and ε S , the following empirical relationship was used:  εk,i = εm,k,i · exp ak,i T (13) with the two empirical parameters εm,k,i and ak,i for k = {S, ∞} and the i th material. The temperature dependence

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TABLE III P HYSICAL , C HEMICAL , AND M INERALOGICAL P ROPERTIES OF THE I NVESTIGATED S OIL Texture

Mineralogy

Gravel

-%

Soil properties

Mica

16 wt.%

Total specific surface area

17 m2 /g 11 m2 /g

-%

Smectite

9 wt.%

Specific surface area♣

Silt

81 %

Kaolinite

3 wt.%

Particle density

Clay

19 %

Tectosilicates

36 wt.%

Liquid limit

Organic

1%

Carbonates

36 wt.%

Effective cation exchange capacity

Sand

2.744 g/cm3 26.5 wt.% 10 mmol/100g

 obtained from water vapor sorption isotherms according to the BET - method. ♣ obtained from N adsorption isotherms using the device and software of Quantachrome Instruments (Autosorb Version 1.52). 2

of the relaxation time τ can be characterized according to the Eyring equation [47]

τi (T ) =



G i (T ) h κ exp kb T RT

 (14)

where h denotes Planck’s constant, k B is Boltzmann’s constant, κ ≈ 1 is the transmission coefficient, R is the gas constant and G i (T ) = Hi (T ) − T Si (T ) is the free enthalpy of activation with activation enthalpy Hi (T ) and activation entropy Si (T ) [40]. However, in restricted temperature ranges, an empirical Arrehnius dependence can be assumed [48], such that

E A,i (15) τi (T ) = τ0,i exp RT with empirical parameter: prefactor τ0,i and activation energy E A,i . The static and high frequency limit of the permittivity of water has been extensively studied and well documented [43], [48], [49]. To model the temperature dependence of the dielectric relaxation time of water under atmospheric conditions, the approach suggested by Buchner et al. [50] based on Eyring’s equation (14) is applied, such that  G w (T ) = Hw,298 + c p,298 T − T 

T −T Sw,298 + c p,298 ln T

(16)

with activation enthalpy Hw,298 = 16.4 kJ/mol, acti vation entropy Sw,298 = 20.4 J/(K mol), and heat capacity of activation c p,298 = (∂Hw,298/∂ T ) p = T (∂Sw,298/∂ T ) p = −160 J/(K mol) at a reference temperature T  = 298.15 K [50]. The stretching exponent βCC is assumed to be 1. Hence, (12) transforms to the Debye model, which is valid for water in the studied temperature-frequencypressure ranges [43], [49], [51]. For methanol and ethanol, the extensive database of Gregory and Clarke [52] was used. The permittivity data for toluene are taken from [53]. The unknown parameters εm,k,i , ak,i , τ0,i , and E A,i were obtained from fitting the tabulated Debye parameters with (13) or (15). In Table II, the available permittivity data are compiled.

B. Soil A silty clay loam (SCL) from a levee at the river Unstrut, Thuringia, Germany was used as standard soil in the numerical calculations. The soil is well characterized in previous investigations [19], [23] and also used in previous numerical calculations by Wagner et al. [54]. Furthermore, five finegrained soils were investigated. The soils were sieved by a mesh opening of 0.4 mm in respect to the standardized shrinkage test described in ASTM D4943 [55], in order to eliminate grain sized above 0.4 mm. Afterwards, the soils were mixed with distilled water to reach the desired initial water content. The initial water content was chosen to a water content of 1.1 times the liquid limit. According to investigations conducted by Thomas et al. [56], the wetted soil samples were stored in an airtight container for at least 24 h to ensure a homogeneous water distribution in the soil. In the case of a slightly plastic clay soil (for soil details see Table III), we applied the coupled hydraulic-dielectric mixture approach according to Wagner and Scheuermann [40]. C. Numerical Technique In order to determine the propagation characteristics of electromagnetic waves at the probe aperture and to estimate the spatial sensitivity of the probes for the determination of dielectric spectra, 3-D-FE field calculations (commercial software from Ansys: high frequency structure simulator-HFSS2 ) were performed with electrical and dielectric low-loss and high-loss strongly dispersive standard materials (liquids), as well as with the nearly saturated and unsaturated soils. Ansys HFSS solves Maxwell’s equations using a finite element method, in which the solution domain is divided into tetrahedral mesh elements. Tangential vector basis functions interpolate field values from both nodal values at vertices and on edges (see [57]). The 3-D field calculations were used: 1) to analyze the optimal configuration of the excitation, boundary conditions, and size of the simulated probes; 2) to analyze electrical and magnetic field distributions in the investigated material in contact with the probes as a function of frequency; and 3) to determine the complex reflection coefficient, or scattering function S11 (ω), at the connector of the open-ended coaxial line in equivalence to network analyzer measurements. 1)–3) were used to estimate the spatial sensitivity of the probes. Furthermore, in 3) the 2 Ansys HFSS is a standard simulation package for electromagnetic design and optimization.

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deionized water

5 mm

3 mm

70 mm

air

5

10 GHz

copper ground plane

10 GHz

5 ... 35 mm

sample

Fig. 2.

N - connector

teflon

x z

3-D finite element structure of the ON-probe and tetrahedral mesh at 10 GHz in case of air or water at the probe aperture and in a cross section.

calibration and measurement technique to determine stable dielectric properties were systematically investigated. The complex effective permittivity εr, eff of the standard materials used in the numerical calculations was theoretically calculated (see Section III-A). εr, eff of the soil were examined in the frequency range from 1 MHz to 10 GHz at room temperature and under atmospheric conditions with vector network analyzer technique (Rohde and Schwarz ZVR - DC, 10 kHz–4 GHz, and PNA E8363B - 10 MHz–40 GHz). For this purpose, we used a combination of open-ended coaxial line techniques and coaxial transmission line techniques (see [19], [23], and [38] for details). Since the N-based probe (ON) was used in the experimental investigations by Schwing et al. [44], the results of the numerical calculations are discussed in detail for the case of the ON-probe (Fig. 2). The numerical technique was used in equivalence to the two other probe types. In general, the appropriate presented numerical results for the ON-probe (electrical and magnetic field distribution) are qualitatively similar to those for the two other probes. The possibilities and limitations of the applicability of open-ended coaxial line sensors in determining microwave dielectric spectra are also transferable. D. Experimental Technique The principal experimental setup is shown in Fig. 3. In the first step, the coaxial line with PSC-2.4 to SMA or N adapter was fixed to a probe stand and calibrated at the SMA or N connector with one port calibration (open, short, match) with the Agilent electronic calibration kit N4691B/N4690B using the average of 20 runs. Then, the open-ended coaxial probe was connected to the SMA or N connector of the PSC-2.4 to SMA or N adapter. In total, four calibration measurements were carried out: open, short, methanol (pure, Neolab), and deionized water. Each calibration standard is measured using the average of 20 runs. The temperature of the liquids was measured with an accuracy of ±0.05 K with a Ahlborn NiCrNi thermocouple. For comparison, Agilent high temperature probe (HP85070B, 50 MHz–20 GHz) and Agilent performance probe (500 MHz–40 GHz) with dielectric probe kit HP85070B and electronic calibration kit N4691B were used.

WL Gore 3GW40 2.4 mm flexible coaxial cable SMA or N connector measurement plan probe

sample

P1 Agilent-PNA E8363B 10 MHz - 40 GHz

probe stand

Fig. 3. Measurement setup with an open-ended coaxial probe to determine dielectric spectra.

IV. R ESULTS AND D ISCUSSION A. Numerical 3-D Finite Element Calculations In Fig. 2, the simulated structure is represented in case of the ON-probe. Outer surfaces of the 50  connector in parallel with the y-z plane were used as the wave port (driven modal solution, one mode). The outer surface of the sample is a radiation boundary and the second-order radiation boundary condition was used, which is an approximation of free space. The mesh generation was performed automatically with l/3 wavelength-based adaptive mesh refinement at a solution frequency of 10 GHz. Broadband complex S-parameters were calculated with an interpolating sweep (1 MHz–10 GHz) with extrapolation to DC. The accuracy of the second-order radiation boundary approximation depends on the distance between the boundary and the object from which the radiation emanates. For this reason, a sensitivity analysis was carried out for a total height of the sample between 1 and 35 mm. The obtained reflection coefficient for the specific sample heights was used to calculate the appropriate complex permittivity. In Fig. 4, the normalized complex magnitude of the elec (ω)| at a frequency of 1 GHz trical field E n = | E  (ω)|/| E max obtained along a profile normal to the middle conductor is

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Fig. 4. Normalized complex magnitude of the electrical field E n at a frequency of 1 GHz in a profile normal to the middle conductor as a function of position in the sample for several standard materials, as well as a SCL from a flood protection levee at the river Unstrut, Thuringia (Germany) at three volumetric water contents θ and porosities n (V1: θ = 3 vol.%, n = 0.5, V2: θ = 29 vol.%, n = 0.46, V3: θ = 36 vol.%, n = 0.45).

plotted as a function of position in the sample for several standard materials with and without dielectric and ohmic losses, as well as for a SCL soil at three volumetric water contents θ and porosities n (V1: θ = 3 vol.%, n = 0.5, V2: θ = 29 vol.%, n = 0.46, V3: θ = 36 vol.%, n = 0.45). The lower limit of −40 dB (1%) for E n was used as an estimate of the sensitive region. For estimation of the lateral sensitivity, the normalized complex magnitude of the electrical E n and magnetic Hn profile at a distance of 1.5 mm in parallel to the open-ended coaxial line at the sensor aperture was analyzed (see Fig. 5). The results confirm the results from the sensitivity analysis as well as the qualitative results shown in Fig. 6, and suggest that the influence of the boundary layer can be neglected for a distance of 7 mm from the surface of the open-ended coaxial line. Further, the sensitive region for dielectric measurements is ±7-mm lateral to the sensor surface. Hence, the measurements and calculations have to be carried out with a sample radius ≥ 10 mm. In Fig. 6, the magnitude of the electrical and magnetic field distributions at a frequency of 1 GHz in a cross section of the ON-probe for a sample height of 10 mm is represented for the investigated materials. The electrical field distributions at 1 GHz indicate a stable sensitive area below approximately 7 mm above the probe aperture nearly independent of the electromagnetic material properties of the investigated materials (Fig. 7). The numerical calculations further indicate that this is also true below 1 GHz (not shown here). However, the magnetic field is affected by the appropriate material properties, which becomes clearly obvious in the case of tap water and indicates radiation effects for high permittivity and lossy materials. These effects can lead to appropriate ripples in the spectra around 1 GHz, which will be shown in detail in the experimental section. In Fig. 8(a), dielectric spectra in a frequency range from 1 MHz to 10 GHz are given for the appropriate geometrical configuration of Fig. 2, for standard materials, as well as for a nearly saturated SCL soil. The spectra were determined from numerically calculated S-parameters with the procedure

Fig. 5. (Top) Normalized complex magnitude of the electrical field E n and (bottom) magnetic field Hn at a frequency of 1 GHz in a profile in parallel to the open-ended coaxial line at the sensor aperture. The grey area indicates the minimum size a sample should have for this kind of measurement procedure.

described in Section II. The OWL calibration reproduces the theoretical spectra in the high frequency range above 50 MHz for all materials, but fails for electrically lossy materials below 50 MHz due to the electrically lossless calibration materials. Substantially better results in the low frequency range were achieved with the OWS calibration procedure, which suggests a combination of OWS in the frequency range below 50 MHz and OWL in the range above. The OWL calibration was improved using appropriate standard materials, e.g., tap water, with electrical losses in the range of the losses of the sample (open-tap water-liquid, OTWL-calibration). However, the OWS procedures is unstable in the high frequency range for the SCL especially in the real part. Hence, we suggest to use the OWL-calibration in combination with network analyzer technique in the frequency range above 50 MHz. For measurements in the frequency range below 50 MHz, careful calibration with well defined lossy standard materials is necessary to obtain stable spectra. The spectra determined from the numerical results for different total thicknesses h of the material are represented in Fig. 8(b). The comparison between expected and calculated permittivity also suggests a minimal sample thickness of 7 mm to obtain stable reflection coefficients. B. Experimental Results: Standards In Fig. 9, the absolute value and phase of the reflection coefficient S11 ( f ) measured with the VNA (investigated standards

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air

methanol

ethanol

Soil, V1 θ = 3 vol.% n = 0.50

Soil, V2 θ = 29 vol.% n = 0.46

Soil, V3 θ = 36 vol.% n = 0.45

deionized water

7

tap water

| E | [V/m] 500 400 300 200 100 0

1 GHz

| H | [A/m] 5 4 3 2 1 0

z

1 GHz x

10 mm

Fig. 6. Magnitude of the electrical and magnetic field distributions at 1 GHz in cross for the ON-probe for several standard materials, as well as for the soil with three volumetric water contents (V1, V2, and V3).

air | E | [V/m] 500 400 300 200 100 x

z

0

y

10 GHz

7 mm

sensitive area 14

mm

14

m

m

x

z

y

Fig. 7. Electrical field distribution of the open-ended coaxial line calculated for a frequency of 10 GHz at the probe aperture and two sections, as well as the sensitive area of the probe.

as well as the short circuit measurement) for the three probes are shown. In addition, the time-domain waveform (TDR) of the reflection measurement S11 ( f ) calculated by means of an inverse fast Fourier transform (IFFT) is represented in Fig. 9. The differences between the absolute values as well as the phase shifts of S11 of the electrically lossless materials decrease with decreasing frequency and become close in the frequency range below approximately 100 MHz.

Thus, the sensitivity of the open-ended coaxial line to determine complex permittivity with network analyzer technique below 100 MHz is low and the accuracy of the obtained permittivity substantially decreases with the dynamic range of the instrument. Hence, we suggest a lower limit of the measurement range of 50 MHz with these procedures and materials. In principle, to obtain stable permittivity results down to at least 1 MHz, precisely machined probes with precise geometric data, as well as careful measurements, are necessary [14]. However, the results of the investigation of Sheen and Woodhead [14] also indicate a loss of accuracy below approximately 100 MHz. In the technical overview of the used Agilent high temperature probe 200 MHz is suggested as the absolute lower limit of the measurement range (Agilent Technologies 2008). Nevertheless, all types of open-ended coaxial lines exhibit a high sensitivity to electrical losses, shown in the appropriate inset of Fig. 9 (top) as well as in the TDR plot (bottom). Therefore, the determination of low frequency properties, e.g., electrical conductivity, is possible with an appropriate calibration technique [27]. The sensitivity to electrical losses is highest in case of the ON-probe and lowest in case of the OE-probe, due to the geometrical probe dimensions. The complex relative permittivities of the standard liquids investigated with the procedure given in Section II-B are presented in Fig. 10. The dielectric spectra (50 MHz–10 GHz) of the liquids obtained from the VNA measurements in combination with the OWL-calibration of the probes closely agree with the expected theoretical spectra. The relative error in comparison to theoretical values is given in Figs. 10 and 11. In principle, the three probe types enable an accurate determination of the frequency dependence of the complex permittivity with the used calibration procedure. However, as expected the accuracy is substantially reduced below approximately 100 MHz. This circumstance is particularly distinct

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90 80 OWL tap water ethanol methanol air

70 60

ε 'r

50

soil - V3 OWS OWL OTWL

40 30 20 10 0 6 10

7

10

8

9

10

10

10

10

expected spectra

1000

theoretical experimental determined soil spectra taken from Wagner et al. [23]

ε ''r

100

10

1 6

10

7

10

8

10

9

10

f [Hz] (a)

10

10

f [Hz] (b)

Fig. 8. (a) Dielectric spectra with (top) real part εr and (bottom) imaginary part εr of the standard materials obtained from the numerically calculated S11 in the 3-D FE field calculations based on the introduced calibration procedures (OWS - open, deionized water, short; OWL - open, deionized water, liquid; OTWL - open, tap water, liquid). Within the shaded area, the critical frequency range < 50 MHz is marked for an extended application of open-ended coaxial . line cells with network analyzer technique. (b) Dielectric spectrum of soil determined with the numerical results for different total heights h of the material. Inset: the variation of the permittivity at three selected frequencies with height is shown.

for toluene, with decreasing accuracy below approximately 500 MHz. Furthermore, in the case of deionized as well as tap water in the frequency range around 1 GHz in the real as well as the imaginary part, clearly marked resonances appeared due to the probe geometry and radiation effects pointed out in Section IV-A. Here, the OSMA-probe exhibited the best performance. Moreover, the imaginary part of the obtained permittivity of water in the frequency range below 1 GHz systematically deviates from the expected theoretical values. We suggest that these differences are related to the influence of the direct current conductivity [6], [14]. The deviation is most obvious for the OE-probe. The reason is that, on the one hand, the calibration standards used are electrically lossless, and on the other hand, the accuracy in the determination of the temperature-dependent conductivity of appropriate reference liquids determined the resultant spectra. In the specific case of the ON-probe, especially in the imaginary part for methanol and ethanol, distinct deviations occur in the frequency range below approximately 500 MHz. The permittivity of toluene was most difficult to obtain with all probes, especially for the imaginary part, with the calibration standards air, deionized water, and methanol (Fig. 10). Thus, calibration liquids with similar dielectric properties are suggested, as pointed out by Kaatze [25]. The measured permittivity values with the probes were compared with the permittivities obtained with the Agilent high temper-

ature probe (HP85070B, 50 MHz–20 GHz) in combination with the dielectric probe kit HP85070B software as shown in Fig. 10. This further confirms the mentioned accuracy problem of toluene, when compared to the measured permittivities with the three probes. In the technical overview of the Agilent high temperature probe, 200 MHz is suggested as the absolute lower limit of the measurement range, with a relative error of approximately 5% in the real as well as the imaginary part [58]. In Fig. 11, the relative error is represented for the results of all measured liquids and frequencies as well as for all probes in comparison to the theoretical values. The mean relative error of the real part for all materials and probes from 100 MHz to 10 GHz is less than 3.5% and less than 10% for the imaginary part. The error statistics of the probes are summarized in Table IV. C. Experimental Results: Soils The soil samples were prepared at 1.1 times, the liquid limit with deionized water and placed in the open-ended cell set-up. Then the samples were stepwise dried isothermally at 23 °C under atmospheric conditions and equilibrated. Appropriate mass loss and sample volume change were estimated during the drying process to obtain the appropriate volumetric water content. The complex permittivity was determined from

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Fig. 9.

9

From top to bottom: absolute value, phase shift, and TDR-waveform of the measured reflection coefficient for the three probe types (see text).

TABLE IV E RROR S TATISTICS OF THE P ROBES Box Chart Parameters

OSMA

ON

OE

1.6 0.1 1.9 1.7 −0.2 1.5 8.1 −1.7

1.1 0.2 1.8 1.6 −0.2 1.4 5.8 −1.1

0.2 0.3 2.0 1.0 −1.0 0 4.4 −5.1

−1.5 0.4 7.9 4.9 −3.0 1.9 13.8 −29.9

−3.2 −0.6 6.5 1.0 −5.5 −4.5 2.8 −14.3

−3.8 −1.1 4.8 0.9 −3.6 −2.8 6.1 −28.8

Real part Mean [%] Median [%] Interquartile range (I Q R) [%] Upper quartiles (Q 1 ) [%] Lower quartiles (Q 3 ) [%] Skewness [%] Q 1 + 1.5I Q R [%] Q 3 − 1.5I Q R [%] Imagninary part Mean [%] Median [%] I Q R [%] Q 1 [%] Q 3 [%] Skewness [%] Q 1 + 1.5I Q R [%] Q 3 − 1.5I Q R [%]

50 MHz to 10 GHz. In Fig. 12, selected spectra are represented with close values of the real part of the permittivity around 1 GHz in order to compare the dispersion and absorption directly. Due to the different soil properties the water content,

porosity, and soil matric potential, which means the ability of the soil to hold water against gravity due to capillary and adsorptive forces, varied slightly. The dielectric spectra show a typical frequency dependence for all soils: 1) a slight decrease in the real part of the complex effective permittivity with increasing frequency; 2) a strong decrease in the imaginary part with increasing frequency below approximately 1 GHz, mainly due to electrical induced losses; and 3) an increase in the imaginary part above 1 GHz due to the main water relaxation contribution (for details see [19], [23], and [40]). With decreasing volumetric water content, the electrical-induced losses become dominant. The brick clay and clay soil show the strongest frequency dependence in the real part (dispersion), which is coupled to the highest losses (absorption). The silt soil shows the lowest dispersion and absorption. The observations are in accordance with the expected spectra due to the appropriate particle size distribution and clay mineralogy (see also [40]). To quantitatively characterize the relaxation behavior, an inverse modeling technique using a shuffled complex evolution metropolis algorithm (SCEM-UA, [59]) was applied based on a generalized dielectric relaxation model (GDR, [23], [38])  − ε∞ = εr,eff

N 

εk σDC −j βk ωε0 ( j ωτk ) + ( j ωτk ) αk

k=1

(17)

with high frequency limit of permittivity ε∞ , relaxation

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Fig. 10. Complex relative permittivity εr determined with the appropriate probes of the standard materials of tap water, ethanol, methanol, and toluene. (Center) Relative error of the real part and imaginary part. In the frequency range of the shaded area, measurements are not suggested for the appropriate material class with this technique.

strength εk , relaxation time τk , as well as stretching exponents 0 ≤ αk , βk ≤ 1 of the k-th process and apparent direct current electrical conductivity σDC . In contrast to Wagner et al. [23], only two processes were assumed to act in the investigated frequency-temperature-pressure range: the main free water relaxation and an interface water relaxation. The electrical conductivity of the interface water phase was not explicitly considered. In Table V, the results are summarized. The high frequency range above 1 GHz is dominated by the free water contribution with a mean relaxation time = (7.7 ± 0.5) ps, which is lower than the relaxation time of water at 25 °C with 8.28 ps and thus indicates the variation of porosity and saturation. Moreover, the free water distribution parameter = (0.94 ± 0.02) indicates a narrow relaxation time distribution. The low frequency range below 1 GHz also includes information of adsorbed or confined water as well as free pore water conductivity contribution, counter ion relaxation effects, as well as the Maxwell–Wagner effect typical for the appropriate clay mineralogy. Around

1 GHz, a physically bound water relaxation contribution is expected with a mean relaxation time = (3.9 ±0.6) ns and a mean distribution parameter = (0.77 ± 0.04) indicating different forms of interface water or a superposition of different relaxation mechanisms. Due to the sample preparation with deionized water, the diffuse electrical double layer (EDL) is strong with maximal Debye length and thus the effects due to counter ion relaxation are expected to be weak. For this reason, the interface water contribution should be maximal. However, an electrical conductivity contribution is already visible and increases as expected in the order kaolin, silt, lacustrine clay, clay, brick clay, and loam. We tested the theory developed in [40], upon the experimental results of the SWCC from the study of Schwing et al. [44] in the case of the lacustrine clay. We calculated the dielectric spectra using the complex refractive index model (CRIM), based on the porosity, as well as soil water characteristic curve (see [60]). To account for the dependence of the apparent pore water conductivity σa on water content in the mixture equation, the following empirical relationship with the normalized

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11

TABLE V R ESULTS OF THE I NVERSE M ODELING W ITH (17) AS W ELL AS C ALCULATED S TATIC P ERMITTIVITY OF THE

w [g/g] n θ [cm3 /cm3 ] ε∞ εFW ε S,F W log(τFW [s]) αFW (fixed) log(1 − βFW ) εIW log(τIW [s]) αIW (fixed) log(1 − βIW ) log(σDC [S/m])

F REE WATER T ERM ε S,F W = εFW + ε∞ ( FOR S OIL D ETAILS S EE [44])

Lacustrine Clay

Brick Clay

Clay

Kaolin

Silt

Loam

0.219 0.38 0.374

0.206 0.36 0.361

0.263 0.42 0.416

0.243 0.40 0.396

0.218 0.37 0.370

0.237 0.39 0.393

8.3 ± 0.9 15.4 ± 0.9 23.8 −11.08 ± 0.03 0 −1.6 ± 0.1 13 ± 2 −8.57 ± 0.04 0 −0.62 ± 0.06 −1.04 ± 0.01

6.1 ± 1.1 16.2 ± 1.3 22.4 −11.15 ± 0.04 0 −1.29 ± 0.80 39 ± 3 −8.26 ± 0.07 0 −0.51 ± 0.02 −0.96 ± 0.01

10.47 ± 0.76 13.12 ± 0.70 24.1 −11.03 ± 0.05 0 −1.36 ± 0.20 22 ± 3 −8.57 ± 0.10 0 −0.84 ± 0.41 −0.99 ± 0.05

10.3 ± 0.3 14.80 ± 0.33 25.0 −11.07 ± 0.01 0 −1, 88 ± 0, 27 8.4 ± 1.5 −8.26 ± 0.16 0 −0.97 ± 0.17 −1.47 ± 0.03

3.3 ± 1.1 20.9 ± 1.1 24.1 −11.23 ± 0.04 0 −0.83 ± 0.13 9.1 ± 1.5 −8.60 ± 0, 14 0 −0.71 ± 0.24 −1.40 ± 0.02

6.9 ± 0.6 15.5 ± 0.7 22.5 −11.14 ± 0.02 0 −1.16 ± 0.13 32 ± 3 −8.33 ± 0.09 0 −0.42 ± 0.10 −0.75 ± 0.001

  Fig. 12. (a) Real part εr,eff and (b) imaginary part εr,eff of the effective  complex relative permittivity εr,eff of the investigated soils. (c) Imaginary part reduced with the apparent electrical conductivity σeff at 50 MHz to isolate the contribution due to a low frequency relaxation process. (d) Appropriate representation of the reduced complex effective permittivity in the Cole–Cole plot.

Fig. 11. Top: mean relative error in complex permittivity for all frequencies and different standard materials. Middle: box and whiskers plots for the single probe. Bottom: mean relative error distribution of the probes for all standards and frequencies. Real part (left) and imaginary part (right) of the complex relative permittivity.

matric potential m = m /m1M Pa was used: σa = a · |m |b

(18)

with empirical electrical conductivity coupling a in S/m and shape factor b. The constants were obtained numerically from fitting the forward model according to Wagner and Scheuermann [40] to the measured complex permittivity using SCEM-UA leading to log(a) = −0.36 ± 0.05 and b = 0.572 ± 0.007.

V. C ONCLUSION In this paper, three open-ended coaxial line probes (OCs) based on available coaxial lines and connectors (N and SMA) were manufactured and broadband characterized from 1 MHz to 10 GHz using combined theoretical, numerical, and experimental investigations. The electromagnetic wave propagation characteristics at the probe aperture material interface and resulting sensitivity of the OCs were determined by means of 3-D numerical finite element calculations and measurements on low loss and high loss strong dispersive standard liquids, as well as unsaturated and nearly saturated dispersive soils. The 3-D field calculations were used: 1) to analyze the optimal configuration of the excitation, boundary conditions, and size of the simulated probes; 2) to analyze electrical and magnetically field distributions in the investigated material in contact with

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the probes as a function of frequency; and 3) to determine the complex reflection coefficient, or scattering function S11 (ω), at the connector of the open-ended coaxial line in equivalence to network analyzer measurements. The results were used to estimate the spatial sensitivity of the probes. Furthermore, based on S11 (ω), the calibration and measurement technique to determine stable dielectric properties were systematically analyzed. Since the N-based probe (ON) was used in experimental investigations by Schwing et al. [44], the results of the numerical calculations were discussed in detail in case of ON. The used methodology can be equally applied to the two other probe types. In general, the results for the ON-probe (electrical and magnetic field distributions) are qualitatively similar for the two other probes. The performance of the open-ended coaxial line technique to obtain stable dielectric spectra of lossless and high-lossy materials from 1 MHz to 10 GHz are also applicable to the different probe types. The sensitive region for dielectric measurements is ±7-mm lateral as well as 7-mm perpendicular to the midpoint of the sensor aperture. Hence, measurements and calculations have to be carried out with a sample radius and height ≥10 mm. The frequency- and temperature-dependent complex permittivity εr (ω, T ) was deduced from the measured complex reflection coefficient S11 (ω, T ) by applying a bilinear relationship after calibration using three standards: air and two well known liquids. Additionally, a short-circuit was measured and used to control the purity of the liquid standard in the frequency range below 500 MHz. The differences between the absolute values and the phase shifts of the reflection coefficients S11 of the electrically lossless materials decrease with decreasing frequency and become very close in the frequency range below approximately 100 MHz. The sensitivity of the open-ended coaxial line to determine complex permittivity with the network analyzer technique below 100 MHz is low and the accuracy of the obtained permittivity primary decreases with dynamic range of the instrument. Thus, a lower limit of the measurement range of 50 MHz with the procedures and materials was suggested. In principle, to obtain stable permittivity, results down to at least 1 MHz with the network analyzer technique precisely machined probes with precise geometry, as well as careful measurements are necessary [14]. However, to obtain dielectric spectra in the low frequency range, the probes have to be used in combination with impedance analyzer technique [45], [61]. The mean relative error of the real part of εr (ω, T ) for all investigated standards and probes in the frequency range from 100 MHz to 10 GHz is smaller than 3.5% and of the imaginary part smaller than 10%. To improve the robustness and accuracy of the open-ended coaxial line technique, we suggest: 1) combining the OWS calibration in the low frequency range with the OWL calibration at high frequencies and 2) integrating the numerical 3-D FE model in a global optimization approach in combination with appropriate relaxation models to directly fit the measured reflection factor, in analogy with the procedure demonstrated in [23] and [62] for coaxial transmission line technique. We used the N-based probe (ON) to determine the complex effective relative permittivity of saturated fine-grained soils.

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The soil dielectric spectra were analyzed with a broadband relaxation model as well as a coupled hydraulic-dielectric mixture approach. The experimental results demonstrated that the investigated OCs are suitable for an accurate determination of high resolution microwave dielectric spectra of finegrained soils with the used measurement procedure. This opens the possibility to further develop experimental procedures (e.g., [44]), including open-ended coaxial probes to systematically analyze coupled hydraulic/dielectric soil properties. A PPENDIX Following [7], the applied bilinear relationship will be derived. In general, the scattering matrix is defined as   S S12 a1 b1 = 11 (19)  S b2 S21 a 2 22 where Si j with i, j = 1, 2 are the elements of the scattering matrix S’ = (Si j ), ai and bi with i = 1, 2 are incident and reflected waves, respectively, and i = 1 and 2 corresponds to the port connected to the network analyzer and the port in contact with the investigated material, respectively. With S11 = b1 /a1 and  = a2 /b2 and (19), we get the following equations:   a2 S11 = S11 + S12 (20) a1 and

1  a1  = S21 + S22  a2

which gives

 S11 − S11 1 

Thus, we have =

 − S22

=

 S12  . S21

 S11 − S11 .  S22 S11 − det S’

(21)

(22)

(23)

In a first-order approximation, the interface between probe aperture and sample can be modeled as two parallel capacitors (see Fig. 1, [2], [48], [63]), which gives an impedance

or

Z  = ( j ω · C f + j ω · ε C0 )−1

(24)

Y  = j ω · C f + j ω · εr C0

(25)

where C f is a capacitance determined by fringing-fields effects inside the probe, C0 is a capacitance that depends on effects of the fringing-fields √ outside the probe tip that couple to −1 is the imaginary unit, ω is the the sample, j = angular frequency, and εr = εr − j εr is the complex relative permittivity of the sample. Using (1), (23), and (24), Marsland and Evans [26] and Bao et al. [7] derived the following bilinear equation: c2 + c3 εr S11 = (26) c1 + εr where c1 , c2 , and c3 are given by c1 =

 1 − S22 Cf  ) + C j ωZ 0 C0 (1 + S22 0

(27)

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c2 =

 − S S + S S S11 11 22 12 21  ) j ωZ 0 C0 (1 + S22  + S S − S S ) C f (S11 11 22 12 21 +  ) C0 (1 + S22

and c3 =

 + S S − S S S11 11 22 12 21 .  1 + S22

(28)

(29)

Since Z 0 , C f , and C0 are combined with c1 and c2 , individual estimations of the lumped circuit parameters become unnecessary [6]. The advantage of this derivation is that Z 0 , C0 , and C f are explicitly shown in (27) and (28). ACKNOWLEDGMENT The authors gratefully acknowledge K. Emmerich and H. Kaden from the Center for Material Moisture (CMM) of the Karlsruhe Institute of Technology for the determination of the specific surface area and cation exchange capacity of the samples, and S. Karlovsek and W. Muller for their valuable help in writing this paper. Further investigations on the presented research are ensured by a recently granted Queensland Science Fellowship awarded to A. Scheuermann. R EFERENCES [1] M. A. Stuchly, M. M. Brady, S. S. Stuchly, and G. Gajda, “Equivalent circuit of an open-ended coaxial line in a lossy dielectric,” IEEE Trans. Instrum. Meas., vol. IM-31, no. 2, pp. 116–119, Jun. 1982. [2] M. Stuchly, T. Athey, G. Samaras, and G. Taylor, “Measurement of radio frequency permittivity of biological tissues with an open-ended coaxial line: Part II—Expermental results,” IEEE Trans. Microw. Theory Tech., vol. 30, no. 1, pp. 87–92, Jan. 1982. [3] A. Kraszewski, M. A. Stuchly, and S. Stuchly, “ANA calibration method for measurements of dielectric properties,” IEEE Trans. Instrum. Meas., vol. 32, no. 2, pp. 385–387, Jun. 1983. [4] Y.-Z. Wei and S. Sridhar, “Technique for measuring the frequencydependent complex dielectric constants of liquids up to 20 GHz,” Rev. Sci. Instrum., vol. 60, no. 9, pp. 3041–3046, May 1989. [5] Y.-Z. Wei and S. Sridhar, “Radiation-corrected open-ended coax line technique for dielectric measurements of liquids up to 20 GHz,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 3, pp. 526–531, Mar. 1991. [6] J. Z. Bao, C. C. Davis, L. Li, and M. L. Swicord, “Microwave dielectric spectroscopy of human erythrocyte suspensions with the open-ended coaxial probe technique,” in Proc. 15th Annu. Int. Conf. IEEE Eng. Med. Biol. Soc., Oct. 1993, pp. 1441–1442. [7] J. Z. Bao, C. Davis, and M. Swicord, “Microwave dielectric measurements of erythrocyte suspensions,” Biophys. Soc. All Rights Res. Biphys. J., vol. 66, no. 6, pp. 2173–2180, Jun. 1994. [8] J. Z. Bao, M. Swicord, and C. Davis, “Microwave dielectric characterization of binary mixtures of water, methanol, and ethanol,” J. Chem. Phys., vol. 104, no. 12, pp. 4441–4450, Mar. 1996. [9] O. Goettmann, U. Kaatze, and P. Petong, “Coaxial to circular waveguide transition as high-precision easy-to-handle measuring cell for the broad band dielectric spectrometry of liquids,” Meas. Sci. Technol., vol. 7, no. 4, p. 525, 1996. [10] M. El-Rayes and F. Ulaby, “Microwave dielectric spectrum of vegetation-part I: Experimental observations,” IEEE Trans. Geosci. Remote Sens., vol. GE-25, no. 5, pp. 541–549, Sep. 1987. [11] F. Ulaby, T. Bengal, M. Dobson, J. East, J. Garvin, and D. Evans, “Microwave dielectric properties of dry rocks,” IEEE Trans. Geosci. Remote Sens., vol. 28, no. 3, pp. 325–336, May 1990. [12] B. L. Shrestha, H. C. Wood, and S. Sokhansanj, “Modeling of vegetation permittivity at microwave frequencies,” IEEE Trans. Geosci. Remote Sens., vol. 45, no. 2, pp. 342–348, Feb. 2007. [13] Y. Lasne, P. Paillou, A. Freeman, T. Farr, K. McDonald, G. Ruffie, J.-M. Malezieux, B. Chapman, and F. Demontoux, “Effect of salinity on the dielectric properties of geological materials: Implication for soil moisture detection by means of radar remote sensing,” IEEE Trans. Geosci. Remote Sens., vol. 46, no. 6, pp. 1674–1688, Jun. 2008.

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Norman Wagner was born in Schleiz, Germany, on June 4, 1973. He received the Diploma degree in geophysics from the Faculty of Physics and Geosciences, University Leipzig, Leipzig, Germany, and the Dr. rer. nat. degree from the Faculty of Chemistry and Geosciences, Friedrich Schiller University Jena, Jena, Germany, in 1999 and 2004, respectively. He is currently a Researcher in high-frequency electromagnetic (radio to microwave) techniques with the Institute of Material Research and Testing, Bauhaus-University Weimar, Weimar, Germany. His current research interests include the experimental and numerical analysis and the theoretical prediction of the dielectric relaxation behavior of complex systems, such as soils, for the development of advanced near and subsurface sensing techniques.

Moritz Schwing was born in Karlsruhe, Germany, on November 11, 1983. He received the Diploma degree in civil engineering from the Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany, in 2010. He is currently pursuing the Ph.D. degree with the University of Queensland, Brisbane, Australia. His current research interests include coupled mechanic, hydraulic, and dielectric properties of fine-grained soils.

Alexander Scheuermann was born in Wallduern, Germany, on November 6, 1969. He received the Diploma degree in civil engineering, specializing in geotechnical engineering, and the Doctoral degree from the University of Karlsruhe, Karlsruhe, Germany, in 1998 and 2005, respectively, and Habilitation degree from the Karlsruher Institute of Technology (KIT), Germany, on the topic of "Time Domain Reflectometry (TDR) in Geohydraulics and Geomechanics" in 2012. He has been a Senior Lecturer with the School of Civil Engineering, The University of Queensland, Brisbane, Australia, since January 2010. His research interests include the use of electric and electromagnetic measurement methods in civil engineering, hydraulics and mechanics of unsaturated soils, multi-phase flow, and coupled hydraulic/mechanic/electric parameters of soil and erosion. Dr. Scheuermann was the recipient of a Queensland Smart Futures Fellowship on the further development of Spatial TDR in 2012.