# Characterization of an Implicitly Resistively-Loaded

Authors: Colleen J. Fox; Paul M. Meaney; Fridon Shubitidze; Lincoln Potwin; Keith D. Paulsen
Journal: International Journal of Antennas and Propagation
 (2008-02-07)

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## Abstract

Microwave tomographic imaging of the breast for cancer detection is a topic of considerable interest because of the potential to exploit the apparent high-dielectric property contrast between normal and malignant tissue.  An important component in the realization of an imaging system is the antenna array to be used for signal transmission/detection.  The monopole antenna has proven to be useful in our implementation because it can be easily and accurately modeled and can be positioned in close proximity to the imaging target with high-element density when configured in an imaging array.  Its frequency response is broadened considerably when radiating in the liquid medium that is used to couple the signals into the breast making it suitable for broadband spectral imaging.  However, at higher frequencies, the beam patterns steer further away from the desired horizontal plane and can cause unwanted multipath contributions when located in close proximity to the liquid/air interface.  In this paper, we have studied the behavior of these antennas and devised strategies for their effective use at higher frequencies, especially when positioned near the surface of the coupling fluid which is used.  The results show that frequencies in excess of 2 GHz can be used when the antenna centers are located as close as 2 cm from the liquid surface.


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## Body

## 1. Introduction

Microwave imaging techniques have been investigated for biomedical applications for
nearly three decades, but have received renewed interest because of their
potential in breast imaging based on data which have shown significant property
contrast between normal and malignant tissue [1–3]. Their exploration is particularly timely
given the well documented limitations of X-ray mammography which is the
standard of care for breast cancer screening in most developed countries
[4]. While there have been several early
reports on microwave radiometry as a detection scheme that exploits the
elevated temperatures of tumors [5–7], more recent investigations have focused
on tomographic and ultrawideband (UWB) radar approaches [8–17].The UWB radar methods are intriguing because they may be able to capitalize on the
considerable advances in microwave technology for UWB communications. Indeed, simulations have shown that detection
of tumors as small as 2-3 mm in diameter may be possible [10, 18].
In practice, implementation may prove to be
more challenging because wideband antennas are typically large (i.e., spiral
antennas) or resistively loaded in which case they often have very low
efficiency that limits signal penetration depth for tumor detection [19–21],
although novel antenna designs that are not resistively loaded but offer good
efficiency over a narrower frequency band have been identified [19].In terms of tomographic approaches, while there has been a considerable amount of numerical
modeling [9, 14, 16, 17, 22, 23],
only a few systems have been developed for phantom experiments [24–26]
and for actual breast imaging [13, 15]. Similarly to the radar methods, one of the
important considerations is the antenna design.Some systems (e.g., Semenov et al. [26]) have utilized waveguide
radiators positioned on a large diameter whereas others have implemented
monopole antennas [13, 15]. These
antennas are submerged in lossy liquids (either saline or glycerin-water mixtures)
and subsequently are resistively loaded and also have the associated efficiency
degradation, although experience has shown that transmitted signals can still
be detected down to roughly −140 dBm with well-designed, low-noise receivers
[27].The coaxial monopole antenna is attractive for microwave breast imaging because its size
and shape allow it to be densely packed around an imaging target. The design, constructed by removing a length
of the outer conductor at one end of a rigid coaxial cable, is simple and low
cost. In general, the monopole has a
relatively narrow bandwidth and excites surface currents along its outer
conductor [28, 29] in air where it closely resembles a dipole when baluns and/or
notched outer conductors are applied [30].
However, when placed in a lossy medium the behavior changes dramatically,
and its bandwidth increases significantly with the associated resistive
loading. Additionally, we have found that the rigid coaxial cable interfaces well with an imaging configuration
where liquid coupling and vertical positioning are required.The goal of this investigation is to assess monopole antenna performance. Of particular, concern has been the
measurement behavior when the antennas approach the liquid surface. Images near the surface correspond to planes
closest to the chest wall for breast exams and are important given the
relatively high-cancer incidence in the axilla region which is adjacent to the
chest wall. When the antennas are fully
submerged in a homogeneous coupling bath, the measurement magnitudes generally
decrease monotonically as a function of the distance between transmit and receive
antennas [27]. However, this pattern
degrades progressively as the antennas approach the liquid surface and is most
pronounced for the higher end of our operating frequency range (generally above
1500 MHz). As a result, we have investigated the characteristics of these antennas with respect to the most
readily available parameters-composition of the coupling bath and antenna
length-in order to devise strategies for improving overall performance. In general, we have
found strong correlations between the return loss, the effective beam width,
and beam steering angle as a function of antenna electrical length which is
consistent over multiple bath compositions (i.e., with significantly different
permittivity and conductivity). In addition, these measurements are consistent with trends observed in associated
simulation results. Based on these studies, we have optimized the antenna design to allow operation relatively
close to the liquid surface over the upper end of our operating frequency range.


## 2. Methods

Our breast imaging system operates in a range of liquid coupling solutions with varying
electrical permittivities to improve the dielectric property match to specific
breast density types. Previous results have demonstrated significant variations in permittivity and conductivity as a
function of breast density [31] primarily due to the overall higher-water
content of the fibroglandular tissue compared with fat [32–34]. Breast types vary over a continuum from fatty
(mostly adipose tissue) to extremely dense (mostly fibroglandular tissue) [35]. In light of the variations in breast
parenchymal density, we present data for multiple bath compositions in order to
illustrate the consistency of our techniques. We refer the interested reader to
previous publications for a detailed description of our clinical breast imaging
system [13, 27].


### 2.1. Data Calibration

As part of the calibration procedure for our breast imaging system, a set of
measurement data is acquired for the homogeneous bath for all operating
frequencies and all possible permutations of transmit and receive antennas. Figure1 shows the circular antenna array
configuration used during breast imaging exams.
Beyond minor interreceiver channel gain variations, the magnitudes
exhibit a predictable behavior for a given transmitter where power levels
decrease monotonically with distance.Figures 2(a) and 2(b) show the amplitude measurements with respect to
receiver antenna number for a single transmitter over a range of frequencies
for the cases of the array: (a) at its maximum depth below the 87:13 glycerin-water
bath surface (position 7), and (b) with the antenna centers just 2 cm below the
liquid surface (position 1). Note that all 16 antennas in the array are positioned on a 15.2 cm diameter circle with
an orientation such that relative receivers 1 and 15 are adjacent to the
transmitter while receiver 8 is furthest away.
The plots for frequencies from 500 to 1700 MHz in Figure 2(a) suggest a
monotonic signal decrease with respect to transmitter/receiver
separation distance. However, the corresponding curves in Figure 2(b) exhibit
significant variations primarily at the higher frequencies and for the larger
antenna separations. Given that the only
difference between the two cases is the depth of the antennas below the liquid
surface, the most likely explanation is that unwanted multipath signals
(related to coupling at the bath/air interface) are causing the perturbations.Figure 1
2D schematic diagram of the 16 monopole antennas arranged in a 15.2 cm diameter circular
array surrounding the imaging zone.Signal amplitude versus relative receiver number
associated with a single transmitting, 3.4 cm long antenna for a range of frequencies when the antenna center is submerged (a) 10 cm and (b) 2 cm below the 87% glycerin coupling liquid
surface, respectively.
(a)(b)


### 2.2. Beam Characterization

The horizontal beam pattern of a monopole antenna is isotropic due to its radial symmetry;
however, the vertical pattern in a lossy solution is considerably more
complex. The goal of the first set of experiments was to characterize the vertical plane beam width and beam center
with respect to wavelength. This was accomplished by transmitting from a single, vertically oriented, monopole antenna and
recording the amplitudes measured by a receiving waveguide antenna at different
vertical positions. A waveguide antenna was useful in this role because of its beam symmetry in the E-plane. The main
variables in the investigation were the signal wavelength in the medium and the
relative vertical position of the reference (waveguide) antenna. Secondary variables included the coupling
medium and the length of the transmitting (monopole) antenna.A 3-point support (3PS) mechanical steering system, developed by Meaney et al. [36], was used to position the reference
antenna during these studies. Figures 3(a)
and 3(b) show a schematic diagram and photograph of the 3PS system configured
for the experiments. The waveguide was oriented perpendicularly to the axis of the monopole and was translated in
vertical steps of 2.5 mm under computer control. We did not rotate the
reference waveguide about the antenna under test as would be the case in more
traditional beam characterization measurements because of the symmetry of the
experiments and the logistical challenges of acquiring data in the lossy liquid bath.(a) Schematic diagram and (b) photograph of the setup for beam pattern measurement
involving a 3-point support (3PS) mechanical steering system with the aperture
reference waveguide antenna positioned approximately 6 cm from the monopole
transmitter.
(a)(b)The cylindrical testing tank was filled with a lossy glycerin and water solution similar to that used in clinical breast
imaging. Measurements were taken in a 90% glycerin, 10% water solution and a 40% glycerin, 60% water solution to
provide a range of complex permittivity values and resulting wavelengths similar to those observed in biological tissue.
All measurements were collected using an Agilent 8753C network analyzer
in sweep mode with a frequency range of 300 MHz to 3 GHz.Two complementary waveguide apertures were required to span the full frequency
range of the monopole antennas under test.The operational wavelength cutoff for the waveguides was calculated
using 1 [29, 37]:
(1)λc=2(m/a)2+(n/b)2→TE102a,
where m and n are the mode indices, and a and b are the
larger and smaller inner dimensions of the front face of the waveguide,
respectively. The TE10 mode
results in the lowest cutoff frequency and determines the lower operational
limit of the waveguide. In this
situation, the wavelength for a TE10 mode wave decreases to two
times the width. Table 1 shows the dimensions of both receiving waveguide
apertures along with their corresponding cutoff wavelengths. The dielectric properties for the 90% and 40%
glycerin-water baths are shown in Figure 4.
Given that these waveguide antennas were filled with the surrounding
liquid, and that the complex permittivity of the glycerin-water solutions
varied with frequency, it is instructive to plot the propagation wavelengths
for both solutions versus frequency along with horizontal lines corresponding
to the cutoff wavelengths of the waveguides (Figure 5). The points where the curves intersect
indicate the TE10 and TE01 mode cutoff frequencies as the
lower and upper operating frequency bounds, respectively. From this graph, it is evident that the large
and small waveguides can be used from 610 to 1580 MHz and from 1580 to greater than
3000 MHz, respectively, in the 90:10 glycerin-water bath. Likewise, for the 40:60 glycerin-water bath,
the large and small waveguides can be used from 330 to 660 MHz and from 660 to
1270 MHz, respectively.Table 1
Reference waveguide antenna dimensions and cutoff wavelengths.
WaveguideWidth,a (cm)Height,b (cm)Cutoffλ, 2a (cm)Large5.42.710.8Small2.71.45.4The measured (a) relative permittivity and (b) conductivity of the 90% and 40%
glycerin: water baths used in these experiments.
(a)(b)Figure 5
Plot of wavelength versus frequency for the 90% and 40% glycerin solutions along with
the TE10 cutoff wavelengths for the receiving waveguides.


### 2.3. Antenna Modeling

In addition to the measurements used to characterize these antennas, we have also performed a
series of numerical simulations that exhibited comparable behavior. For this modeling, we utilized a finite
difference time domain (FDTD) approach in a cylindrical coordinate system which
incorporated a rigid 50 Ω coaxial feel line along with the geometry of the antenna radiating a lossy,
semi-infinite medium [38]. The source
was setup to excite only a transverse magnetic field in the coaxial line. The inner and outer conductors of the coaxial
cable were represented through perfect electrical conducting (PEC) boundary
conditions. The coaxial line dielectric was assumed to be lossless with a relative permittivity of 2.0, and the spatial
resolution of the grid was established to represent accurately the vertical and
radial components of the electric field within the coaxial cable. The dielectric properties of the surrounding
bath were the same as those of the medium used in the measurements with the
simulations being performed individually at each frequency due to the property
dispersion over this range. Eight layers of a perfectly matching layer (PML) were used to minimize backscattered signals
from the finite termination of the computational mesh [39]. The simulations were run until the solution
had stabilized, after which a Fourier transform was performed at each of the
measurement sites to recover the steady-state field values. Similarly to the actual measurements, the
z-component of the electric field values was computed at a series of points
along a vertical line parallel to the center of the monopole antenna in 3 mm increments.


## 2.1. Data Calibration

As part of the calibration procedure for our breast imaging system, a set of
measurement data is acquired for the homogeneous bath for all operating
frequencies and all possible permutations of transmit and receive antennas. Figure1 shows the circular antenna array
configuration used during breast imaging exams.
Beyond minor interreceiver channel gain variations, the magnitudes
exhibit a predictable behavior for a given transmitter where power levels
decrease monotonically with distance.Figures 2(a) and 2(b) show the amplitude measurements with respect to
receiver antenna number for a single transmitter over a range of frequencies
for the cases of the array: (a) at its maximum depth below the 87:13 glycerin-water
bath surface (position 7), and (b) with the antenna centers just 2 cm below the
liquid surface (position 1). Note that all 16 antennas in the array are positioned on a 15.2 cm diameter circle with
an orientation such that relative receivers 1 and 15 are adjacent to the
transmitter while receiver 8 is furthest away.
The plots for frequencies from 500 to 1700 MHz in Figure 2(a) suggest a
monotonic signal decrease with respect to transmitter/receiver
separation distance. However, the corresponding curves in Figure 2(b) exhibit
significant variations primarily at the higher frequencies and for the larger
antenna separations. Given that the only
difference between the two cases is the depth of the antennas below the liquid
surface, the most likely explanation is that unwanted multipath signals
(related to coupling at the bath/air interface) are causing the perturbations.Figure 1
2D schematic diagram of the 16 monopole antennas arranged in a 15.2 cm diameter circular
array surrounding the imaging zone.Signal amplitude versus relative receiver number
associated with a single transmitting, 3.4 cm long antenna for a range of frequencies when the antenna center is submerged (a) 10 cm and (b) 2 cm below the 87% glycerin coupling liquid
surface, respectively.
(a)(b)


## 2.2. Beam Characterization

The horizontal beam pattern of a monopole antenna is isotropic due to its radial symmetry;
however, the vertical pattern in a lossy solution is considerably more
complex. The goal of the first set of experiments was to characterize the vertical plane beam width and beam center
with respect to wavelength. This was accomplished by transmitting from a single, vertically oriented, monopole antenna and
recording the amplitudes measured by a receiving waveguide antenna at different
vertical positions. A waveguide antenna was useful in this role because of its beam symmetry in the E-plane. The main
variables in the investigation were the signal wavelength in the medium and the
relative vertical position of the reference (waveguide) antenna. Secondary variables included the coupling
medium and the length of the transmitting (monopole) antenna.A 3-point support (3PS) mechanical steering system, developed by Meaney et al. [36], was used to position the reference
antenna during these studies. Figures 3(a)
and 3(b) show a schematic diagram and photograph of the 3PS system configured
for the experiments. The waveguide was oriented perpendicularly to the axis of the monopole and was translated in
vertical steps of 2.5 mm under computer control. We did not rotate the
reference waveguide about the antenna under test as would be the case in more
traditional beam characterization measurements because of the symmetry of the
experiments and the logistical challenges of acquiring data in the lossy liquid bath.(a) Schematic diagram and (b) photograph of the setup for beam pattern measurement
involving a 3-point support (3PS) mechanical steering system with the aperture
reference waveguide antenna positioned approximately 6 cm from the monopole
transmitter.
(a)(b)The cylindrical testing tank was filled with a lossy glycerin and water solution similar to that used in clinical breast
imaging. Measurements were taken in a 90% glycerin, 10% water solution and a 40% glycerin, 60% water solution to
provide a range of complex permittivity values and resulting wavelengths similar to those observed in biological tissue.
All measurements were collected using an Agilent 8753C network analyzer
in sweep mode with a frequency range of 300 MHz to 3 GHz.Two complementary waveguide apertures were required to span the full frequency
range of the monopole antennas under test.The operational wavelength cutoff for the waveguides was calculated
using 1 [29, 37]:
(1)λc=2(m/a)2+(n/b)2→TE102a,
where m and n are the mode indices, and a and b are the
larger and smaller inner dimensions of the front face of the waveguide,
respectively. The TE10 mode
results in the lowest cutoff frequency and determines the lower operational
limit of the waveguide. In this
situation, the wavelength for a TE10 mode wave decreases to two
times the width. Table 1 shows the dimensions of both receiving waveguide
apertures along with their corresponding cutoff wavelengths. The dielectric properties for the 90% and 40%
glycerin-water baths are shown in Figure 4.
Given that these waveguide antennas were filled with the surrounding
liquid, and that the complex permittivity of the glycerin-water solutions
varied with frequency, it is instructive to plot the propagation wavelengths
for both solutions versus frequency along with horizontal lines corresponding
to the cutoff wavelengths of the waveguides (Figure 5). The points where the curves intersect
indicate the TE10 and TE01 mode cutoff frequencies as the
lower and upper operating frequency bounds, respectively. From this graph, it is evident that the large
and small waveguides can be used from 610 to 1580 MHz and from 1580 to greater than
3000 MHz, respectively, in the 90:10 glycerin-water bath. Likewise, for the 40:60 glycerin-water bath,
the large and small waveguides can be used from 330 to 660 MHz and from 660 to
1270 MHz, respectively.Table 1
Reference waveguide antenna dimensions and cutoff wavelengths.
WaveguideWidth,a (cm)Height,b (cm)Cutoffλ, 2a (cm)Large5.42.710.8Small2.71.45.4The measured (a) relative permittivity and (b) conductivity of the 90% and 40%
glycerin: water baths used in these experiments.
(a)(b)Figure 5
Plot of wavelength versus frequency for the 90% and 40% glycerin solutions along with
the TE10 cutoff wavelengths for the receiving waveguides.


## 2.3. Antenna Modeling

In addition to the measurements used to characterize these antennas, we have also performed a
series of numerical simulations that exhibited comparable behavior. For this modeling, we utilized a finite
difference time domain (FDTD) approach in a cylindrical coordinate system which
incorporated a rigid 50 Ω coaxial feel line along with the geometry of the antenna radiating a lossy,
semi-infinite medium [38]. The source
was setup to excite only a transverse magnetic field in the coaxial line. The inner and outer conductors of the coaxial
cable were represented through perfect electrical conducting (PEC) boundary
conditions. The coaxial line dielectric was assumed to be lossless with a relative permittivity of 2.0, and the spatial
resolution of the grid was established to represent accurately the vertical and
radial components of the electric field within the coaxial cable. The dielectric properties of the surrounding
bath were the same as those of the medium used in the measurements with the
simulations being performed individually at each frequency due to the property
dispersion over this range. Eight layers of a perfectly matching layer (PML) were used to minimize backscattered signals
from the finite termination of the computational mesh [39]. The simulations were run until the solution
had stabilized, after which a Fourier transform was performed at each of the
measurement sites to recover the steady-state field values. Similarly to the actual measurements, the
z-component of the electric field values was computed at a series of points
along a vertical line parallel to the center of the monopole antenna in 3 mm increments.


## 3. Results and Discussion

In this section, we first report on the general characteristics of the monopole antennas in
terms of their return loss and beam characteristics (steering angle and
beamwidth). We then illustrate deviations in the transmit data for antenna positions near the liquid surface
for different tip lengths which demonstrate how the overall antenna performance
can be improved.


### 3.1. Return Loss

The basic monopole antenna consisted
of a 50 Ω rigid coaxial cable with the outer conductor stripped from the
transmitting zone. Tip lengths of 2.0, 2.5, and 3.4 cm were tested with each having broad operating bandwidths
associated with return losses nominally of less than −10 dB across the band for
both the 90% and 40% liquid coupling mixtures (plots of the return losses for
the 90% glycerin bath are shown in Figure6).
As expected, the dominant null in the return loss associated with the
resonant frequency shifts upwards as the length of the transmitting tip
decreases −3.4 cm length at 1 GHz, 2.5 cm length at 1.45 GHz,
and the 2.0 cm length at 2.15 GHz. The lower-frequency limit also shifts upwards with antenna length.
At the higher end of this frequency span, the resistive loading of the antennas generally suppresses the return
loss to −10 dB or less.Figure 6
Measured return loss of the 2.0, 2.5, and 3.4 cm length monopole antennas in the 90%
glycerin: water bath as a function of frequency.


### 3.2. Beam Characterization

Figure7 shows a
plot of the beam pattern for the 3.4 cm length monopole antenna in the 90% bath
at 1596 MHz as a function of the angle between the monopole antenna and the
reference waveguide antenna (0 degree was the horizontal plane cutting through the center of
the monopole antenna) with the 3 dB points indicated on either side of the beam
peak. A second-order polynomial fit to
the beam pattern was superimposed to estimate the beam center location—only the 15 points near the beam center were
used in  the least squares fitting process.
The beam center was readily extracted from the equation of the fitted
curve. In terms of the 3 dB beam width,
measurement points were selected which straddled the 3 dB-power level below the
peak in the beam pattern. From these two
points, an interpolation was used to determine the closest position that would
be exactly 3 dB below the peak.Figure 7
Vertical beam pattern for the 3.4 cm length monopole antenna at 1596 MHz in a 90%
glycerin: water bath. A 15-point 2nd order polynomial was used to estimate the beam center location and is also
shown along with the points 3 dB below the peak value.Figure8(a) shows plots of the beam center angle as a function of wavelength in the medium
for the three antenna lengths in the two glycerin-water baths (90% and 40%).(The vertical
positions of the beam centers have been converted to beam angles.) The trends in these cases are clear. The beam steers increasingly upwards with
decreasing operating wavelength (or increasing frequency). From these curves, it is evident that the
beam steering is a function of antenna electrical length in the medium-longer lengths correspond to higher beam
steering angles. These trends are echoed
in the simulation results for the longest and shortest antenna lengths in the
two electrically distinct baths shown in Figure 8(b). The computed behavior matches the measurement
observations best at the higher frequencies of concern (i.e., where the beam
steers upwards) and supports the validity of the measured behavior. Although the
overall response with respect to the antenna lengths and
bath properties is consistent between the experimental and
simulated data at the longer wavelengths (lower frequencies),
the simulated results suggest a more rapid downward steering effect
as the wavelength lengthens than was found to occur with
the actual measurement data.(a)
Beam steering angles for the 2.0, 2.5, and 3.4 cm length monopole antennas as a
function of the medium wavelength for the 90% and 40% glycerin: water baths(b)
Same as Figure8(a) for simulation results of beam steering angles for the 2.0 and 3.4 cm
length monopole antennas operating in the 90% and 40% glycerin: water bathsFigure9 shows
the corresponding 3 dB beamwidths for the three different length monopole
antennas in both the 90% and 40% glycerin-water baths as a function of medium
wavelength. In general, the beamwidths increase significantly with wavelength and with different coupling baths (which
also directly affects the bath wavelength). To a lesser degree, the beamwidth also appears to be a function of the
antenna length. For the 90% bath, the beamwidth increase from the 2.0 to 3.4 cm length antenna is 2.5 degrees across
the range of medium wavelengths.Interestingly, the effect for the 40% glycerin-water bath appears to be
reversed with the beamwidths for the 2.0 cm monopole being broader than its 3.4 cm length counterpart.
Given that the baths we typically use for breast imaging range from 79% to 90%, the results
from the 90% bath are more relevant. While beams steer higher with increasing
frequency (potentially exacerbating the problem of the fields coupling to the
liquid-air interface), the beamwidth narrows some with a shorter antenna length
which counteracts the coupling effects at the liquid interface. Thus, it appears that a reduced antenna
length causes the beam to steer lower while also slightly reducing the beamwidth.Figure 9
Beam widths for the 2.0, 2.5, and 3.4 cm length monopole antennas as a function of the
medium wavelength for the 90% and 40% glycerin: water baths.


### 3.3. Multifrequency Transmission Characteristics

Figure10 shows
transmission data from a single 3.4 cm length monopole to the corresponding
receiver monopole antennas in the 90% glycerin bath for frequencies ranging
from 500 to 2500 MHz at antenna center depths of (a) 2.0 and (b) 6.5 cm below
the liquid surface, respectively. For the deeper position, the shapes of the curves are nearly parabolic with the
greater transmission loss corresponding to the greater propagation lengths
(especially receiver antennas 7, 8, and 9).
(Note that the array has 16 antennas evenly spaced in a circular
arrangement). However, in the shallower
case, the near-parabolic patterns are noticeably perturbed for the furthest
receivers at frequencies above 1900 MHz.These aberrations are due to signals coupling to the liquid surface and
propagating along an undesired, low loss surface path.Plots of the transmitted signal strength as a function of receiver number over the
frequency range of 500–2500 MHz for the 3.4 cm length antennas with
their centers submerged (a) 2.0 cm and (b) 6.5 cm below the 90%
glycerin coupling liquid surface, respectively.
(a)(b)Figures11(a) and 11(b) show the corresponding plots for the 2.0 cm length antennas. In this
situation there appears to be a minor perturbation in the 2300 MHz case and a
more pronounced effect at 2500 MHz.These results are important because they suggest that we can
operate at higher frequencies with reduced surface coupling effects using the shorter
antennas. They also confirm the beam
behavior exhibited in the previous section where the shorter length antennas
steered towards lower positions minimizing the surface coupling. In addition, we plotted the average
absolute-valued differences in the signal strength at the two antenna depths
for the three furthest receivers as a function of frequency for the 3.4 and 2.0 cm antenna
lengths (Figure 12). The deviation for the longer antenna appears to increase noticeably (i.e.,
nominally above 2 dB) above 1900 MHz while that for the 2.0 cm antenna only
increases significantly at 2500 MHz.Plots of
the transmitted signal strength as a function of receiver number over the
frequency range of 500–2500 MHz for the 2.0 cm length antennas with
their centers submerged (a) 2.0 cm and (b) 6.5 cm below the 90%
glycerin coupling liquid surface, respectively.
(a)(b)Figure 12
Plots of the average differences in signal strengths (utilizing only values for
receivers 7, 8, and 9) between the shallow (2.0 cm) and deep (6.5 cm) measurement cases
as a function of frequency for the 3.4 and 2.0 cm antenna lengths in the 90%
glycerin coupling liquid.


## 3.1. Return Loss

The basic monopole antenna consisted
of a 50 Ω rigid coaxial cable with the outer conductor stripped from the
transmitting zone. Tip lengths of 2.0, 2.5, and 3.4 cm were tested with each having broad operating bandwidths
associated with return losses nominally of less than −10 dB across the band for
both the 90% and 40% liquid coupling mixtures (plots of the return losses for
the 90% glycerin bath are shown in Figure6).
As expected, the dominant null in the return loss associated with the
resonant frequency shifts upwards as the length of the transmitting tip
decreases −3.4 cm length at 1 GHz, 2.5 cm length at 1.45 GHz,
and the 2.0 cm length at 2.15 GHz. The lower-frequency limit also shifts upwards with antenna length.
At the higher end of this frequency span, the resistive loading of the antennas generally suppresses the return
loss to −10 dB or less.Figure 6
Measured return loss of the 2.0, 2.5, and 3.4 cm length monopole antennas in the 90%
glycerin: water bath as a function of frequency.


## 3.2. Beam Characterization

Figure7 shows a
plot of the beam pattern for the 3.4 cm length monopole antenna in the 90% bath
at 1596 MHz as a function of the angle between the monopole antenna and the
reference waveguide antenna (0 degree was the horizontal plane cutting through the center of
the monopole antenna) with the 3 dB points indicated on either side of the beam
peak. A second-order polynomial fit to
the beam pattern was superimposed to estimate the beam center location—only the 15 points near the beam center were
used in  the least squares fitting process.
The beam center was readily extracted from the equation of the fitted
curve. In terms of the 3 dB beam width,
measurement points were selected which straddled the 3 dB-power level below the
peak in the beam pattern. From these two
points, an interpolation was used to determine the closest position that would
be exactly 3 dB below the peak.Figure 7
Vertical beam pattern for the 3.4 cm length monopole antenna at 1596 MHz in a 90%
glycerin: water bath. A 15-point 2nd order polynomial was used to estimate the beam center location and is also
shown along with the points 3 dB below the peak value.Figure8(a) shows plots of the beam center angle as a function of wavelength in the medium
for the three antenna lengths in the two glycerin-water baths (90% and 40%).(The vertical
positions of the beam centers have been converted to beam angles.) The trends in these cases are clear. The beam steers increasingly upwards with
decreasing operating wavelength (or increasing frequency). From these curves, it is evident that the
beam steering is a function of antenna electrical length in the medium-longer lengths correspond to higher beam
steering angles. These trends are echoed
in the simulation results for the longest and shortest antenna lengths in the
two electrically distinct baths shown in Figure 8(b). The computed behavior matches the measurement
observations best at the higher frequencies of concern (i.e., where the beam
steers upwards) and supports the validity of the measured behavior. Although the
overall response with respect to the antenna lengths and
bath properties is consistent between the experimental and
simulated data at the longer wavelengths (lower frequencies),
the simulated results suggest a more rapid downward steering effect
as the wavelength lengthens than was found to occur with
the actual measurement data.(a)
Beam steering angles for the 2.0, 2.5, and 3.4 cm length monopole antennas as a
function of the medium wavelength for the 90% and 40% glycerin: water baths(b)
Same as Figure8(a) for simulation results of beam steering angles for the 2.0 and 3.4 cm
length monopole antennas operating in the 90% and 40% glycerin: water bathsFigure9 shows
the corresponding 3 dB beamwidths for the three different length monopole
antennas in both the 90% and 40% glycerin-water baths as a function of medium
wavelength. In general, the beamwidths increase significantly with wavelength and with different coupling baths (which
also directly affects the bath wavelength). To a lesser degree, the beamwidth also appears to be a function of the
antenna length. For the 90% bath, the beamwidth increase from the 2.0 to 3.4 cm length antenna is 2.5 degrees across
the range of medium wavelengths.Interestingly, the effect for the 40% glycerin-water bath appears to be
reversed with the beamwidths for the 2.0 cm monopole being broader than its 3.4 cm length counterpart.
Given that the baths we typically use for breast imaging range from 79% to 90%, the results
from the 90% bath are more relevant. While beams steer higher with increasing
frequency (potentially exacerbating the problem of the fields coupling to the
liquid-air interface), the beamwidth narrows some with a shorter antenna length
which counteracts the coupling effects at the liquid interface. Thus, it appears that a reduced antenna
length causes the beam to steer lower while also slightly reducing the beamwidth.Figure 9
Beam widths for the 2.0, 2.5, and 3.4 cm length monopole antennas as a function of the
medium wavelength for the 90% and 40% glycerin: water baths.


## 3.3. Multifrequency Transmission Characteristics

Figure10 shows
transmission data from a single 3.4 cm length monopole to the corresponding
receiver monopole antennas in the 90% glycerin bath for frequencies ranging
from 500 to 2500 MHz at antenna center depths of (a) 2.0 and (b) 6.5 cm below
the liquid surface, respectively. For the deeper position, the shapes of the curves are nearly parabolic with the
greater transmission loss corresponding to the greater propagation lengths
(especially receiver antennas 7, 8, and 9).
(Note that the array has 16 antennas evenly spaced in a circular
arrangement). However, in the shallower
case, the near-parabolic patterns are noticeably perturbed for the furthest
receivers at frequencies above 1900 MHz.These aberrations are due to signals coupling to the liquid surface and
propagating along an undesired, low loss surface path.Plots of the transmitted signal strength as a function of receiver number over the
frequency range of 500–2500 MHz for the 3.4 cm length antennas with
their centers submerged (a) 2.0 cm and (b) 6.5 cm below the 90%
glycerin coupling liquid surface, respectively.
(a)(b)Figures11(a) and 11(b) show the corresponding plots for the 2.0 cm length antennas. In this
situation there appears to be a minor perturbation in the 2300 MHz case and a
more pronounced effect at 2500 MHz.These results are important because they suggest that we can
operate at higher frequencies with reduced surface coupling effects using the shorter
antennas. They also confirm the beam
behavior exhibited in the previous section where the shorter length antennas
steered towards lower positions minimizing the surface coupling. In addition, we plotted the average
absolute-valued differences in the signal strength at the two antenna depths
for the three furthest receivers as a function of frequency for the 3.4 and 2.0 cm antenna
lengths (Figure 12). The deviation for the longer antenna appears to increase noticeably (i.e.,
nominally above 2 dB) above 1900 MHz while that for the 2.0 cm antenna only
increases significantly at 2500 MHz.Plots of
the transmitted signal strength as a function of receiver number over the
frequency range of 500–2500 MHz for the 2.0 cm length antennas with
their centers submerged (a) 2.0 cm and (b) 6.5 cm below the 90%
glycerin coupling liquid surface, respectively.
(a)(b)Figure 12
Plots of the average differences in signal strengths (utilizing only values for
receivers 7, 8, and 9) between the shallow (2.0 cm) and deep (6.5 cm) measurement cases
as a function of frequency for the 3.4 and 2.0 cm antenna lengths in the 90%
glycerin coupling liquid.


## 4. Conclusions

We have assessed the antenna design to extend the usable operating frequency range of our
clinical microwave breast imaging system.
The primary difficulties have occurred in the imaging planes closest to
the liquid surface where we have observed significant perturbations in the
transmitted signals in the homogeneous case (which serves as the calibration
data [27]). The planes near the liquid
surface correspond to those closest to the chest wall in clinical breast exams
which are important because of the high prevalence of cancer in the axilla
zone. We have performed several experiments to determine the parameters of the monopole antennas which govern
their overall performance. We have been
able to alter the beam steering angle and beam width by modifying the antenna
length while still maintaining our nominal operating
frequency  bandwidth.The results comparing the transmission plots for the longer and shorter antennas clearly
show that the shorter antennas can operate at higher frequencies for a given
imaging plane close to the liquid surface.
These improvements were achieved with minimal reduction in overall
signal strength (less than 3 dB difference at the higher frequencies).



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*Source: 580782-2008-03-13.xml*