Antenna Design and Near-field Characterization for Medical ...bioucas/files/ieee_tap_2019_ant_mw.pdfantenna topologies used for MMWI: a Vivaldi-type antenna, a broadband planar monopole

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Abstract— In medical microwave imaging (MMWI), the antennas usually operate at close distance from the body and are required to pick up weak echoes from the inside that are masked by high skin reflection. The near-field antenna behavior strongly determines how the received signals affect the effectiveness of the imaging algorithms. However, these usually simply assume the usual antenna far-field radiation characteristics. Here, we discuss three antenna effects that can deteriorate the overall imaging performance but are rarely addressed in the literature: antenna internal reflections, angular dispersion of the “near-field phase center” and antenna frequency dispersive electric length. We propose dedicated methods to characterize these factors, and present mitigation strategies to be integrated into the inversion algorithms. We demonstrate these effects for three frequently used broadband antennas, using signals from an experimental breast imaging lab setup. In fact, the antenna study and design cannot ignore that it operates in the near-field of breast and interacts with its boundary. The methods and conclusions can be extended to other MMWI applications. To the authors’ best knowledge, this is the first systematic study of the above antenna factors in the context of MMWI.

Index Terms— Antenna calibration, antenna design, balanced

antipodal Vivaldi antenna (BAVA), breast imaging, microwave imaging (MWI), planar monopole antenna, near-field imaging, slot antenna, ultrawideband antenna.

I. INTRODUCTION

ICROWAVE imaging (MWI) is being studied as an complementary screening technology for medical

applications, such as breast cancer screening and head hemorrhage detection [1]-[4]. It is based on monostatic or multistatic radar-type measurements, and benefits from the marked dielectric contrast between healthy and diseased tissues.

Manuscript received… This work was partly funded by Fundação para a Ciência e Tecnologia

(FCT) under projects PTDC/EEI-TEL/30323/2017 and under grant SFRH/BD/115671/2016, and by Instituto de Telecomunicações, and Universidade de Lisboa. It was also funded by FCT/MEC through national funds and co-funded by FEDER – PT2020 partnership agreement under project UID/EEA/50008/2019. This work has been developed in the framework of COST Action TD1301 (MiMed).

J. M. Felício, J. M. Bioucas-Dias and C. A. Fernandes are with Instituto de Telecomunicações, Instituto Superior Técnico (IT-IST), Universidade de Lisboa, Lisbon 1049-001, Portugal (e-mail: [email protected]).

J. R. Costa is with Instituto de Telecomunicações, Instituto Superior Técnico (IT-IST), Universidade de Lisboa, Lisbon 1049-001, Portugal, and also with the Departamento de Ciências e Tecnologias de Informação, Instituto Universitário de Lisboa (ISCTE-IUL), Lisbon 1649-026, Portugal.

The adopted inversion algorithm is based on a method that reconstructs the reflectivity map of the volume of interest. These kinds of methods in Medical Microwave Imaging (MMWI) typically comprise two stages. The first stage aims at eliminating the strong back reflection from the skin that masks the response from the embedded tumors. This is called the skin artifact removal. The second stage aims at reconstructing the reflectivity of the inner tissues.

Antennas play an important role and strongly influence both stages of the imaging process, especially because they need to operate in close proximity of the body for link budget reasons. In fact, the faint scattered signals from tumors are additionally attenuated by the body penetration loss, while SAR considerations limit the maximum incident power. The extreme proximity of the antenna to the body requires that some otherwise overlooked antenna characteristics be properly accounted in the imaging signal post-processing.

Given that there are not many consensual near-field figures-of-merit to help in the antenna selection and design, it is not uncommon to use just far-field characteristics in the first approach. Criteria falls on phase center and radiation pattern stability, unidirectional beam [6], and phase linearity across the bandwidth [5]. Other factors that do not necessarily depend on the observation distance (but are affected by the near-field obstacles) are required as well, such as very wide impedance bandwidth, high pulse fidelity [7] and low pulse stretch. The band falls typically within the 1-10 GHz interval, as a compromise between opposing requirements: highest possible body penetration depth, highest possible image resolution, and smallest antenna size.

Frequently used antennas for MMWI seek the best compromise between the above requirements. Examples include bowties [8], [9], planar dipole- [10] and monopole [11], [12], slot-based [13], Vivaldi [14], [15] and horn [16] antennas. Another possibility to enhance antenna miniaturization is electrically short antennas backed by active circuitry [17].

In the present paper, we show that there are additional antenna factors that are quite relevant in the context of MMWI and need to be tackled. These factors can compromise the effectiveness of the skin artifact removal and image reconstruction algorithms, as will be shown ahead. We identify these factors, present methods to evaluate them and propose strategies to minimize or compensate its adverse effects on the quality of the inverted image.

Antenna Design and Near-field Characterization for Medical Microwave Imaging Applications

João M. Felício, Student Member, IEEE, José M. Bioucas-Dias, Fellow, IEEE, Jorge R. Costa, Senior Member, IEEE, and Carlos A. Fernandes, Senior Member, IEEE

M




2

The first aspect is related to internal reflections that are inherent to any antenna, regardless of its careful impedance match design. Especially with wideband antennas, it is

difficult to obtain 11S f ≤ ‒15 dB throughout the band.

Even with such a low amplitude of S11, this means that a non-negligible fraction of the input energy (compared to the target reflection amplitude) reflects back to the feeding port. Depending on the antenna configuration and design, these internal reflections may extend very much in time, superimposing to the echoes collected from the close body. Some algorithms do not require addressing this problem since they do not rely on the identification of the skin response (e.g. [18]); however, the same algorithms have only been proven to work with uniform breast shapes. Therefore, in realistic scenarios with non-uniform breast shapes, the internal reflections can defeat the algorithms for skin artifact removal and/or the detection of the malignancies, especially those that are close to the skin. Here, we show how the effect of mild but non-negligible internal reflections may be overcome, so that the algorithms perform accurately even in realistic examination scenarios, while having minimum impact on the backscattered echoes.

The second aspect is the “near-field phase center”. Inverse imaging calculations inherently assume that the antenna phase fronts are originated at a fixed point, which is especially not true in the near-field. By studying the antenna near-field with a proposed setup, we are able to find the most representative point for the phase origin location, as well as its dependence with the incoming signal angle of arrival. We use this information to improve the imaging algorithms.

The third aspect is the electrical distance offset associated to the antenna internal flow of electric currents. We demonstrate that this distance exhibits frequency dispersive behavior. Given that MWI algorithms involve distance calculations for different frequencies, it is imperative to compensate for this dispersive offset to ensure the best image focus. We propose a procedure to calibrate the frequency-dependent offset.

We analyze the above three factors for three different antenna topologies used for MMWI: a Vivaldi-type antenna, a broadband planar monopole and a slot-based antenna, all operating in the same frequency band, Δf. The analysis is based on experimental data measured using our demonstrator for breast tumor screening. We image the breast and show that the focusing of the final image improves significantly by performing the proposed characterization of the antenna(s) and considering them in the imaging algorithm. We note that the antenna characterization strategies outlined throughout this paper are a one-time procedure, although the associated corrections need to be used for every acquired signal.

This paper is organized as follows: Section II briefly describes the antenna operation context, while Section III presents the antenna topologies that were selected for comparison. Section IV summarizes the MMWI analytical formulation; the antenna-characterization strategies to improve the performance of the algorithms and antennas are addressed in Section V; in Section VI we show the experimental application of the proposed strategies by applying them to a

microwave breast imaging setup; lastly, the conclusions are drawn in Section VII.

II. ANTENNA OPERATION CONTEXT

In order to highlight the relevance of the near-field antenna characterization for MMWI, it makes sense to define a MMWI scenario as an example. This does not mean that the analysis is conditioned by the example or that the conclusion cannot be generalized for other MMWI applications.

We consider a breast cancer-screening scenario, where the patient is lying in prone position, with the breast pending in a cavity opened in the examination bed, Fig. 1 (a). The study assumes a monostatic single-antenna setup that is mechanically scanned around the breast. The variable antenna distance to the skin is dair, and the distance from the ray entry-point to a generic point inside the breast is db. The image is reconstructed from the antenna input reflection coefficients measured at these antenna positions versus frequency, using a Vector Network Analyzer (VNA).

In the screening scenario, a three-dimensional breast shape

is defined according to the ID 062204 model from the University of Wisconsin-Madison breast repository [19], derived from a MRI exam of a patient in prone posture. In the present work, we consider the breast tissue homogeneous. In the lab setup, it is a 3D-printed polylactic acid shell, (PLA, εr ≈ 2.75 – j0.03 @ 4 GHz [20]), filled with a liquid of permittivity of εr ≈ 4 – j0.17 at 4 GHz that emulates the breast fat tissues. The tumor is represented as a 10 mm × 20 mm ellipsoidal shape, filled with a liquid with the same dielectric properties of malignant tissues (εr ≈ 55 – j3 @ 4 GHz). The recipes of both liquids are described in [21].

Unlike existing examples in the literature, no breast immersion liquid is used in this setup, in order to favor a future more practical examination scenario, comfortable and

Fig. 1: (a) Breast screening scenario; (b) detail of the antenna positioning grid around the breast, and generic distances.

Tumor Antenna positions

p anp a N

np a N

aird

bd

( , , )x y z

(a)

(b)

xy

-z



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faster for the patient, contactless and hygienic. This means that we knowingly give up the advantage of slightly lower skin contrast and potentially e

Further to the already identified antenna requirements, limited compact and lowfollowing candidateVivaldi antenna (BAVA), planar monopole antenna, and planar slotthese antennas were designed using Computer Simulation Technology (CST) Transient solver band

A.

Vivaldiits simple design and manufacturing, broadband characteristics, and reasonably unidirectional radiation [14]dependent phase center and slightly lobulated radiation pattern. Furthermore, miniaturization is some size reduction is still achievable

Forbent microstrip line to minimize reflections from tof the connector. The geometry of the antennaFig. by truncated ellipses to Two exponential curves

describe the “fins” and the feeding microstripThirteen other parameters, marked in remainder geometry.Ca, geometry parameters

Fig.


faster for the patient, contactless and hygienic. This means that we knowingly give up the advantage of slightly lower skin contrast and potentially e

III. A

Further to the already identified antenna requirements, limited space around the breast compact and lowfollowing candidateVivaldi antenna (BAVA), planar monopole antenna, and planar slot-based antenna. Optimized, compact versions of these antennas were designed using Computer Simulation Technology (CST) Transient solver band defined as

Balanced antipodal Vivaldi antenna (BAVA)

Vivaldi-type antennas are widely used for MMWI, owing to its simple design and manufacturing, broadband characteristics, and reasonably unidirectional radiation [14], [15]. [24]. Yet, its main drawback is the frequency dependent phase center and slightly lobulated radiation pattern. Furthermore, miniaturization is some size reduction is still achievable

For this study, we used abent microstrip line to minimize reflections from tof the connector. The geometry of the antennaFig. 2. It consists of two antipodal exponential “fins” capped by truncated ellipses to

wo exponential curves

describe the “fins” and the feeding microstripThirteen other parameters, marked in remainder geometry.

, Pa, At, Ct, and geometry parameters

Fig. 2: Geometry and relevant parameters of the BAVA.

PARAMETERS OF THE EXPONENTIAL CURVES.

Aa 0.141


faster for the patient, contactless and hygienic. This means that we knowingly give up the advantage of slightly lower skin contrast and potentially easier compact antenna design.

ANTENNA TOPOLOGIES UN

Further to the already identified antenna requirements, space around the breast

compact and low-profile. Thereforefollowing candidate types for comparisonVivaldi antenna (BAVA), planar monopole antenna, and

based antenna. Optimized, compact versions of these antennas were designed using Computer Simulation Technology (CST) Transient solver

2 5GHzf


type antennas are widely used for MMWI, owing to its simple design and manufacturing, broadband characteristics, and reasonably unidirectional radiation

. Yet, its main drawback is the frequency dependent phase center and slightly lobulated radiation pattern. Furthermore, miniaturization is some size reduction is still achievable

this study, we used a compact BAVA, fed through a 90º bent microstrip line to minimize reflections from tof the connector. The geometry of the antenna

. It consists of two antipodal exponential “fins” capped by truncated ellipses to achieve

wo exponential curves of the form

expt t t t

a a a a

E v A Pv C

E u A P u C

describe the “fins” and the feeding microstripThirteen other parameters, marked in remainder geometry. The optimized values of

, and Pt are presentedgeometry parameters are presented in

: Geometry and relevant parameters of the BAVA.

TABLE


Ca Pa 0.41 0.17


faster for the patient, contactless and hygienic. This means that we knowingly give up the advantage of slightly lower skin

ier compact antenna design.

NTENNA TOPOLOGIES UNDER TEST

Further to the already identified antenna requirements, space around the breast requires that

Therefore, we have for comparison: balanced antipodal

Vivaldi antenna (BAVA), planar monopole antenna, and based antenna. Optimized, compact versions of

these antennas were designed using Computer Simulation Technology (CST) Transient solver [23], for

2 5GHz .


type antennas are widely used for MMWI, owing to its simple design and manufacturing, broadband characteristics, and reasonably unidirectional radiation

. Yet, its main drawback is the frequency dependent phase center and slightly lobulated radiation pattern. Furthermore, miniaturization is limitedsome size reduction is still achievable [25].

compact BAVA, fed through a 90º bent microstrip line to minimize reflections from tof the connector. The geometry of the antenna

. It consists of two antipodal exponential “fins” capped achieve a compact antenna design.

of the form

exp

exp

t t t t

a a a a

E v A Pv C

E u A P u C

describe the “fins” and the feeding microstripThirteen other parameters, marked in Fig.

The optimized values ofare presented in TABLE are presented in TABLE

: Geometry and relevant parameters of the BAVA.

TABLE I


At Ct 0.108 0.77



ier compact antenna design.

DER TEST

Further to the already identified antenna requirements, requires that antennas

we have considered the : balanced antipodal


these antennas were designed using Computer Simulation , for an operation


type antennas are widely used for MMWI, owing to its simple design and manufacturing, broadband characteristics, and reasonably unidirectional radiation [5]

. Yet, its main drawback is the frequency dependent phase center and slightly lobulated radiation

limited, although

compact BAVA, fed through a 90º bent microstrip line to minimize reflections from the outer part of the connector. The geometry of the antenna is detailed in

. It consists of two antipodal exponential “fins” capped a compact antenna design.

t t t t

a a a a

E v A Pv C

E u A P u C

describe the “fins” and the feeding microstrip line [14]Fig. 2, define th

The optimized values of coefficients TABLE I. The remaining TABLE II.


Pt -0.131



Further to the already identified antenna requirements, the antennas are

considered the : balanced antipodal


these antennas were designed using Computer Simulation operation

type antennas are widely used for MMWI, owing to its simple design and manufacturing, broadband

[5], . Yet, its main drawback is the frequency

dependent phase center and slightly lobulated radiation , although

compact BAVA, fed through a 90º he outer part

is detailed in . It consists of two antipodal exponential “fins” capped

a compact antenna design.

(1)

[14] , define the

Aa, remaining

The fabricated prototype is shown in reflection is bellow an attempt sensitivity to small targets. We highlight the effort undergone in order to achieve a compact design of 44.5 × 66.9 mmconsidering that the lower frequency of operation is 2 GHz.

Fig. 3: (a) Balanced antipodal Vivaldi antenna; (b) simulated and measured

input reflection coefficient in free

B. Planar monopole antenna

This is a very common antenna topology including for MMWI provides a large broad frequency band. It is more straightforward to miniaturize than the Vivaldi antenna [29]. The phase center is frequency range. However, its radiation pattern is quasiomnidirectional, and designed antenna is showninput reflection in

The monopole is printed on Rogers 5880 substrate (tan(δ) = 0.0009) of thickness of 0.254 mm (10 mils). The final area is 29 × 57.5 mmin TABLE [7].

The size of the ground plane of planar monopole antennas is crucial, to prevent currents from flowing into the feeding cable and re-radiating 3.9 GHz in the measured predicted by the simulation because it did not include the measurement cable.pattern. However, we favored a compact design with small ground plane, but used a ferrite bead clamped on the measurement cable to minimize the currents flowing in the cable. The influence of the feeding cable on the antenna performance is a subject that we intentionally discuss in this

BAVA GEOMETRY PARAMETERS DIMENSIONS IN MILLIMETERS.

DIMENSIONS OF THE PARAMETERS OF THE PLANAR MONOPOLE


The fabricated prototype is shown in reflection is bellow ‒15 dB in most of the band (an attempt to reduce internal reflections and increase the sensitivity to small targets. We highlight the effort undergone in order to achieve a compact design of 44.5 × 66.9 mmconsidering that the lower frequency of operation is 2 GHz.

: (a) Balanced antipodal Vivaldi antenna; (b) simulated and measured

input reflection coefficient in free

Planar monopole antenna

This is a very common antenna topology cluding for MMWI

provides a large broad frequency band. It is more straightforward to miniaturize than the Vivaldi antenna

. The phase center is frequency range. However, its radiation pattern is quasi

nidirectional, and designed antenna is showninput reflection in Fig.

The monopole is printed on Rogers 5880 substrate (= 0.0009) of thickness of 0.254 mm (10 mils). The final

area is 29 × 57.5 mm2

TABLE III, keeping the same parameter designa

The size of the ground plane of planar monopole antennas is crucial, to prevent currents from flowing into the feeding cable

radiating [31]. 3.9 GHz in the measured predicted by the simulation because it did not include the measurement cable. It also has a major impact on the radiation pattern. However, we favored a compact design with small ground plane, but used a ferrite bead clamped on the

rement cable to minimize the currents flowing in the cable. The influence of the feeding cable on the antenna performance is a subject that we intentionally discuss in this


W Wa 44.46 28.6

La Lts 43.34 17.74

DIMENSIONS OF THE PARAMETERS OF THE PLANAR MONOPOLE ANTENNA (IN MILLIMETERS).

W 29 57.5


The fabricated prototype is shown in ‒15 dB in most of the band (

to reduce internal reflections and increase the sensitivity to small targets. We highlight the effort undergone in order to achieve a compact design of 44.5 × 66.9 mmconsidering that the lower frequency of operation is 2 GHz.


input reflection coefficient in free-space, 11fsS f

Planar monopole antenna

This is a very common antenna topology cluding for MMWI [11]. It is easy to design


. The phase center is mostly frequency range. However, its radiation pattern is quasi

nidirectional, and unstable at higher frequencies designed antenna is shown in Fig. 4

Fig. 4 (b). The monopole is printed on Rogers 5880 substrate (

= 0.0009) of thickness of 0.254 mm (10 mils). The final area is 29 × 57.5 mm2. The relevant dimensions are presented

, keeping the same parameter designa


An evidence of this is the resonance near 3.9 GHz in the measured S11(f) in predicted by the simulation because it did not include the

It also has a major impact on the radiation pattern. However, we favored a compact design with small ground plane, but used a ferrite bead clamped on the


TABLE II


Wm Wg 10.3 8.99

Lf Lm 24.8 23.56

TABLE III


L W1 57.5 0.64

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The fabricated prototype is shown in Fig. 3 (a). ‒15 dB in most of the band (Fig.

to reduce internal reflections and increase the sensitivity to small targets. We highlight the effort undergone in order to achieve a compact design of 44.5 × 66.9 mmconsidering that the lower frequency of operation is 2 GHz.


11fsS f , of BAVA.

This is a very common antenna topology [7]. It is easy to design, fabricate and


mostly stable over the lower frequency range. However, its radiation pattern is quasi

at higher frequencies (a), and the corresponding

The monopole is printed on Rogers 5880 substrate (= 0.0009) of thickness of 0.254 mm (10 mils). The final

. The relevant dimensions are presented , keeping the same parameter designa


dence of this is the resonance near ) in Fig. 4 (b), which is not

predicted by the simulation because it did not include the It also has a major impact on the radiation

pattern. However, we favored a compact design with small ground plane, but used a ferrite bead clamped on the



Ws1 Ws2 0.93 1.53

Re gap 40.3 3.9

III


L1 r 23 13.8

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(a). The input Fig. 3 (b)), in

to reduce internal reflections and increase the sensitivity to small targets. We highlight the effort undergone in order to achieve a compact design of 44.5 × 66.9 mm2, considering that the lower frequency of operation is 2 GHz.


[7], [26], [27], fabricate and

provides a large broad frequency band. It is more straightforward to miniaturize than the Vivaldi antenna [28],

stable over the lower frequency range. However, its radiation pattern is quasi-

at higher frequencies [30]. The corresponding

The monopole is printed on Rogers 5880 substrate (εr = 2.2, = 0.0009) of thickness of 0.254 mm (10 mils). The final

. The relevant dimensions are presented , keeping the same parameter designations as in


dence of this is the resonance near (b), which is not

predicted by the simulation because it did not include the It also has a major impact on the radiation

pattern. However, we favored a compact design with small ground plane, but used a ferrite bead clamped on the



We 13.1

DIMENSIONS OF THE PARAMETERS OF THE PLANAR MONOPOLE

h 1




paper.

C.

Lastly, we used aof the balanced structure of the XETS provides an extremely stable phase center over the whole frequency band of operation. Furthermore, this antenna shows very good performance in both frealmost flat transfer function, as well as a fidelity indicator well above 90% in the main radiation direction, offering very low pulse distortion. The radiation pattern is very stable with frequency, althoproperties are optimum for imaging applications.

The XETS antenna was intended dimensions are presented in nomenclature of the original reference the antenna is 56 mm.thickness of 0.254 mm.

The XETS to two opposing “petals”. The unbalanced feeding marginally deteriorates the input impedance matching and the antenna performance

Fig.

reflection coefficient

left inset shows the ground plane of the monopole.

Fig.

coefficient


paper.

Planar slot-based antenna

Lastly, we used aof the type described in balanced structure of the XETS provides an extremely stable phase center over the whole frequency band of operation. Furthermore, this antenna shows very good performance in both frequency- almost flat transfer function, as well as a fidelity indicator well above 90% in the main radiation direction, offering very low pulse distortion. The radiation pattern is very stable with frequency, althoproperties are optimum for imaging applications.

The XETS antenna was intended band, as illustrated in dimensions are presented in nomenclature of the original reference the antenna is 56 mm.thickness of 0.254 mm.

The XETS is fed through ato two opposing “petals”. The unbalanced feeding marginally deteriorates the input impedance matching and the antenna performance [32]

Fig. 4: (a) Planar monopole antenna; (b)

reflection coefficient


Fig. 5: (a) XETS antenna; (b) simulated and measured input

coefficient in free-space,

Dimensions of the parameters of the XETS antenna (in millimeters).

Dfront Ds 56 52.2


based antenna

Lastly, we used an exponentially tapered described in [32], in short, XETS

balanced structure of the XETS provides an extremely stable phase center over the whole frequency band of operation. Furthermore, this antenna shows very good performance in

and time-domains, such as linear phase and almost flat transfer function, as well as a fidelity indicator well above 90% in the main radiation direction, offering very low pulse distortion. The radiation pattern is very stable with frequency, although quasi-omnidirectional. Many of these properties are optimum for imaging applications.

The XETS antenna was redesignedband, as illustrated in

dimensions are presented in nomenclature of the original reference the antenna is 56 mm. It is printed on Rogers 5880 substrate of thickness of 0.254 mm.

is fed through anto two opposing “petals”. The unbalanced feeding marginally deteriorates the input impedance matching and the antenna

[32]. In order to mitigate this effect, and to

: (a) Planar monopole antenna; (b)

reflection coefficient in free-space, 11fsS f


: (a) XETS antenna; (b) simulated and measured input

space, 11fsS f , of XETS.

TABLE


Lout Lin 35.1 26


exponentially tapered slotin short, XETS


domains, such as linear phase and almost flat transfer function, as well as a fidelity indicator well above 90% in the main radiation direction, offering very low pulse distortion. The radiation pattern is very stable with

omnidirectional. Many of these properties are optimum for imaging applications.

redesigned to operate in the band, as illustrated in Fig. 5 (b). The final antenna

dimensions are presented in TABLE IVnomenclature of the original reference [32]. The diameter of

It is printed on Rogers 5880 substrate of

n EZ-47 coaxial cable soldered to two opposing “petals”. The unbalanced feeding marginally deteriorates the input impedance matching and the antenna

In order to mitigate this effect, and to

: (a) Planar monopole antenna; (b) simulated and measured input

11fsS f , of monopole antenna. The top


: (a) XETS antenna; (b) simulated and measured input

, of XETS.

TABLE IV


ws w0 2.9 0.21


slot-based antenna in short, XETS – Fig. 5 (a). The



omnidirectional. Many of these properties are optimum for imaging applications.

to operate in the (b). The final antenna

IV, keeping the . The diameter of


coaxial cable soldered to two opposing “petals”. The unbalanced feeding marginally deteriorates the input impedance matching and the antenna


simulated and measured input

, of monopole antenna. The top

: (a) XETS antenna; (b) simulated and measured input reflection


L C0 46.9 11.7


tenna The



omnidirectional. Many of these

to operate in the (b). The final antenna

, keeping the . The diameter of


coaxial cable soldered

to two opposing “petals”. The unbalanced feeding marginally deteriorates the input impedance matching and the antenna


reduce potential pickabsorber

The evaluation of the antennas in the context of MMWI requiresprocessing algorithms.information about that is required

A. Artifact remova

The first step before trying to reconstruct the reflectivity of the imaging from the measured signalfor head and breast imaging

The Multiple Input Multiple Output (MIMO) signal processing used to separate multipath signals

value decompositio

measured at different antenna positionsmatrix representation that allows separating the contributionsfrom the different scatterers. scatteredlinked to a unique singular very precisely the unwanted reflections.

Consider the geometry and Na

The antenna position

remove at positionantennaassume matrix, of dimension

where

containing at position

frequencies

matrix factoriz

where Udiagonal matrix ordered in The notation (.)

According to our formulation, well approximated byTherefore

write a calibrated

p = a antenna position by subtracting from the unwanted

where uV, respectively

simulated and measured input

, of monopole antenna. The top

reflection


reduce potential pick-absorber was clamped

IV. ANALYTICAL BACKGROUND

The evaluation of the antennas in the context of MMWI requires testing them processing algorithms.information about the that is required to understand the antenna role in

rtifact removal

The first step before trying to reconstruct the reflectivity of the imaging domain is to from the measured signalfor head and breast imaging

algorithm that Multiple Input Multiple Output (MIMO) signal processing used to separate multipath signals

value decomposition (SVD) to

measured at different antenna positionsrepresentation that allows separating the contributions

m the different scatterers. scattered signals are orthogonal and, therefore, linked to a unique singular very precisely the unwanted reflections.

Consider the geometry uniformly distributed antenna positions

The antenna position

remove the dominant skin reflectionat position p = a, we antenna positions in the

that skin reflection, of dimension N

a a N a a NS s s s

1p p p NS f S f

s

containing the antenna at position p within the mentioned range,

frequencies distributed

matrix factorization has the form

U and V are diagonal matrix formed ordered in non-increasingThe notation (.)H designates the

According to our formulation, well approximated by

herefore, provided that

write a calibrated calaS

antenna position by subtracting from the unwanted q scatterers:

S S u v

ui and vi are left, respectively. The


-up from the antenna back lobe, a smallwas clamped-on to the SMA connector.

NALYTICAL BACKGROUND

The evaluation of the antennas in the context of MMWI them together with

processing algorithms. This section the involved signal processing

to understand the antenna role in

The first step before trying to reconstruct the reflectivity of is to eliminate

from the measured signal. This challenge is widely reported for head and breast imaging [1]-[4].

that we use shares similarities with the Multiple Input Multiple Output (MIMO) signal processing used to separate multipath signals

n (SVD) to replace the matrix

measured at different antenna positionsrepresentation that allows separating the contributions

m the different scatterers. We are orthogonal and, therefore,

linked to a unique singular value.very precisely the unwanted reflections.

Consider the geometry in Fig. 1 (uniformly distributed antenna positions

The antenna positions have index

the dominant skin reflection, we consider the

s in the interval a – skin reflections are similar

Nf × 2Nn + 1,

n na a N a a N S s s s

1 fp p p NS f S f

antenna input reflection coefficientwithin the mentioned range,

distributed in the band

has the form:

a S UΣV

are orthogonal matricesformed by all the

increasing sequence.ignates the Hermitian operator.

According to our formulation, reflectionwell approximated by the first

, provided that q can be calaS matrix free from skin reflections

antenna position by subtracting scatterers:

0

qcal Ha a i i i

i

S S u v

are left- and right-singular vectorsThe number q i


up from the antenna back lobe, a smallthe SMA connector.

NALYTICAL BACKGROUND FOR MMWI

The evaluation of the antennas in the context of MMWI with the appropriate signal

his section presents the minimum signal processing

to understand the antenna role in th

The first step before trying to reconstruct the reflectivity of the strong skin backscatter

. This challenge is widely reported

shares similarities with the Multiple Input Multiple Output (MIMO) signal processing used to separate multipath signals [22]. We use

replace the matrix

measured at different antenna positions, by an equivalent representation that allows separating the contributions

assume that the are orthogonal and, therefore,

value. This allows filtering out very precisely the unwanted reflections.

(b), representing the breastuniformly distributed antenna positions in each ring

index 1, ap N .

the dominant skin reflection as seen from an antenna the input reflection Nn ≤ p ≤ a + N

similar. We assemble

n na a N a a N S s s s ,

f

T

p p p NS f S f

is a Nf

input reflection coefficientwithin the mentioned range, for

in the band 1,fNf f f

HΣV

matrices, and Σthe singular values

. Max{i} is the rank ofHermitian operator.

reflections from the skin the first q singular value

can be found somehow

free from skin reflections

antenna position by subtracting from Sa the contribution

0

cal Ha a i i iS S u v

singular vectorsis determined


up from the antenna back lobe, a small

MMWI

The evaluation of the antennas in the context of MMWI appropriate signal

presents the minimum signal processing techniques

this process.

The first step before trying to reconstruct the reflectivity of the strong skin backscatter

. This challenge is widely reported

shares similarities with the Multiple Input Multiple Output (MIMO) signal processing

the singular

replace the matrix of 11S f

an equivalent representation that allows separating the contributions

that the different are orthogonal and, therefore, each one is

his allows filtering out

, representing the breast, in each ring.

. In order to

as seen from an antenna input reflection of all

Nn, where we assemble a Sa

(2)

× 1 vector

input reflection coefficients, measured Nf discrete

,fNf f f

. The SVD

(3)

Σ is a square singular values σi of Sa

is the rank of Sa. Hermitian operator.

from the skin are singular values of Σ.

found somehow, we can

free from skin reflections for the

the contribution

(4)

singular vectors from U and s determined by testing

S f




5

successively increasing values of q in equation (4), from q = 0 up, until a skin-reflection removal criterion is reached. This criterion is defined in the following way:

1. For each q test-value, we use the Inverse Discrete Fourier Transform (IDFT) on the vector

1 f

cal cal cala a a NS f S f

s that corresponds to the

antenna position p = a in calaS , to obtain the respective

spatial-domain representation calas d . Variable d

represents the roundtrip distance to the antenna.

2. We then check if any of the relative maxima of calas d

falls on the distance corresponding to the entry breast skin wall d = dair, or on the opposite wall.

If test 2) is true, then q is incremented, eq. (4) is re-calculated to remove one more singular value contribution, and we proceed to steps 1) and 2).

The process above, after finding the q that removes the skin reflection, is repeated for all Na antenna positions, since q may change with p due to the non-uniform shape of the breast. We then assemble the matrix

1 a

cal cal cal cala N

S s s s (5)

where calS contains the calibrated signals along the frequency

at each antenna position. Our algorithm is fully automatable and compatible with

real-time systems. Moreover, it works with the non-uniform shape of the breast and does not introduce distortion in the tumor position, contrarily to other algorithms found in the literature. Lastly, it has been demonstrated that the algorithm can detect tumors very close to the skin, where other methods struggle.

B. Imaging algorithm

The imaging algorithm uses the output signals from the

artifact removal stage, which are organized in matrix calS . It

maps the reflectivity of the imaging domain, r(x,y,z), through

0

1, , exp 2 ,

a f

cala i

N Na f

r x y z jk DN N

s (6)

where k0 is the free-space wave-number, and the term Di comprises the distance travelled by the propagating wave. According to Fig. 1 (b), the latter should be computed as

i air b bD d d n f , (7)

in which bn f is the frequency dependent refraction index of

the breast tissues, and dair and db are the straight-line distances travelled in air and through the tissues, respectively. However, in the next section, we demonstrate that Di should include other terms that depend on the antenna but can be known a prior and, therefore, improve the imaging results. Lastly, the factor of 2 in the exponential argument in (6) refers to roundtrip.

Finally, the image is computed as

2

( , , ) ( , , )I x y z r x y z . (8)

C. Performance metrics

We use five performance metrics to assess the quality of the received signals and the image reconstruction. First, the tumor response magnitude (T) that measures the intensity of the tumor response in the final image. It indicates the amount of “useful” energy that is retrieved from the tumor. Second and third, are the tumor-to-clutter ratio (TCR) and tumor-to-mean ratio (TMR), which measure T relative to the largest and mean intensities of the background clutter, C, respectively. In log units, TCR and TMR are computed as:

10TCR dB =10log max T / max C (9)

10TMR dB =10log max T / mean C . (10)

We evaluate also the tumor-to-skin ratio (TSR), which indicates how much energy is coupled into the body compared to the reflection from the skin. This may be influenced by the antennas. In log units we have:

10 d dTSR dB 10 log T /S (11)

where Td and Sd are the tumor and skin responses extracted from the spatial domain signals. This will be further developed in section VI.A.

Lastly, we calculate the tumor position error (PE), which quantifies the deviation of the detected tumor relative to the actual coordinates.

V. ANALYSIS OF THE ANTENNA PICKED-UP SIGNALS

In this section we discuss the referred three usually overlooked antenna performance aspects that influence MMWI system performance. Fig. 6 schematizes the distances involved in antenna-characterization strategies. In the scheme,

vector as is the measured input reflection coefficient at

position a, ρ0 is the “near-field phase center” from which we assume the wave are radiated, and Δd(θ, ϕ) and deq are distances that calibrate the angular dispersion of ρ0 and radiation mechanism of the antenna, respectively. All of these parameters are defined and analyzed in this section.

By the end of this section and according to Fig. 6, equation

(7) should be modified to

, ,eqi b b airD d n f d d f d (12)

in order to include the calibration strategies addressed in the following sub-sections.

Fig. 6: Illustration of the distances involved in the antenna-calibration

strategies presented ahead. The vector as corresponds to the measured input

reflection coefficient at position a.

AntennaCalibration

plane

Body

( , , )x y zbd

aird0

,d eqd f

as




A.

Rin the same order of magnitude as the skin backscattering and several times mandatory

In order to

convert

spatial

We

a Hamming window

each of the three antenna

Each peak corresponds to athatthe common peak at

microstrip or connector

overall

corresponding

The figure also shows that reflections extend upapproximately 300 mm. This can well superimpose on the echoes from the shadowed. importance of the skin and tumor reflectionantenna internal reyet the more advanced processing from Section highlight the physical

We considelocated 20 mm away from the antenna edge. Tcorresponding

hlt hlta as d S f

dashed lines identify the distances at which the breast wall reflection should be detected for each antenna (the distance is not the same is paper, and is

Fig. fss d

line identifies the connectormm.


Antenna internal reflections

Regardless of how well in the Δf band,

me order of magnitude as the skin backscattering and several times greatermandatory to eliminate this effect from the signals.

In order to comprehend the extent of this

convert the antenna free

spatial-domain,

We just consider

Hamming window

each of the three antenna

Each peak corresponds to athat the three antennas exhibit different behaviorthe common peak at

microstrip or connector

overall relative levels in each curve are naturally related to the

corresponding S f

The figure also shows that reflections extend upapproximately 300 mm. This can well superimpose on the echoes from the shadowed. Therefore, we proceed to finding the relative importance of the skin and tumor reflectionantenna internal reyet the more advanced processing from Section highlight the physical

We consider first located 20 mm away from the antenna edge. Tcorresponding

IDFThlt hlta as d S f

dashed lines identify the distances at which the breast wall reflection should be detected for each antenna (the distance is not the same is paper, and is addressed

Fig. 7: Measured free

fss d , for the three antennas

line identifies the connectormm.


internal reflections

egardless of how well the antennas, the magnitude of these reflections is of the

me order of magnitude as the skin backscattering and greater than the tumor response. Therefore, it is

to eliminate this effect from the signals.comprehend the extent of this

the antenna free-space input reflection

fss d , using an IDFT as

the frequencies

Hamming window to reduce the sidelobes.

each of the three antenna examples

Each peak corresponds to an internalthe three antennas exhibit different behavior

the common peak at d ≈ 3 mm corresponding to the connector

microstrip or connector-coaxial cable transition.

relative levels in each curve are naturally related to the

fsS f levels in

The figure also shows that reflections extend upapproximately 300 mm. This can well superimpose on the echoes from the skin and tumors, in which case they might be

Therefore, we proceed to finding the relative importance of the skin and tumor reflectionantenna internal reflections. At this point, we do not consider yet the more advanced processing from Section highlight the physical interpretation of the results.

r first a healthy breast without tumor; the wall is located 20 mm away from the antenna edge. Tcorresponding spatial-domain antenna input reflection

IDFThlt hlta as d S f is illustrated in

dashed lines identify the distances at which the breast wall reflection should be detected for each antenna (the distance is not the same is

addressed ahead).

: Measured free-space input reflection coefficients in spatial

, for the three antennas considered in this study. The vertical dotted

line identifies the connector-microstrip and connector


internal reflections

antennas’ impedancethe magnitude of these reflections is of the

me order of magnitude as the skin backscattering and tumor response. Therefore, it is

to eliminate this effect from the signals.comprehend the extent of this

space input reflection

using an IDFT as

the frequencies within Δf (Nf

to reduce the sidelobes.

examples is shown in

n internal reflection. the three antennas exhibit different behavior

≈ 3 mm corresponding to the connector

coaxial cable transition.


levels in Fig. 3 to Fig.

The figure also shows that reflections extend upapproximately 300 mm. This can well superimpose on the

tumors, in which case they might be Therefore, we proceed to finding the relative

importance of the skin and tumor reflectionsAt this point, we do not consider

yet the more advanced processing from Section interpretation of the results.

breast without tumor; the wall is located 20 mm away from the antenna edge. T

domain antenna input reflection illustrated in Fig.

dashed lines identify the distances at which the breast wall reflection should be detected for each antenna (the distance is not the same is one of the main topic

space input reflection coefficients in spatial

considered in this study. The vertical dotted

microstrip and connector-coaxial transitions at 3


impedance is matched the magnitude of these reflections is of the


to eliminate this effect from the signals. comprehend the extent of this influence, let us

space input reflection fsS f to the

using an IDFT as in Section IV.A

Nf = 34), and appl

to reduce the sidelobes. The fss d

is shown in Fig. 7.

reflection. It is clear the three antennas exhibit different behaviors, apart from

≈ 3 mm corresponding to the connector

coaxial cable transition. The fss d


Fig. 5.

The figure also shows that reflections extend up approximately 300 mm. This can well superimpose on the


s compared to the At this point, we do not consider

yet the more advanced processing from Section IV.A interpretation of the results.

breast without tumor; the wall is located 20 mm away from the antenna edge. T

domain antenna input reflection Fig. 8. The vertical

dashed lines identify the distances at which the breast wall reflection should be detected for each antenna (the reason why

one of the main topics of the

space input reflection coefficients in spatial-domain,


coaxial transitions at 3


matched the magnitude of these reflections is of the


, let us

to the

IV.A.

= 34), and apply

s d for

clear

apart from ≈ 3 mm corresponding to the connector-

fss d


to approximately 300 mm. This can well superimpose on the


compared to the At this point, we do not consider

to

breast without tumor; the wall is located 20 mm away from the antenna edge. The

domain antenna input reflection The vertical

dashed lines identify the distances at which the breast wall the reason why

s of the

Further tocomparposition and peaks’ position. antenna internal reflections

fsS f

effectivepresence of a diel

The result is validity of the clearly identifiableinternal reflectionsis approximately 12, 7.XETS, respectivelyattributed magnitudestrategy with the corresponding vertical lines

To conclude this analysisthe tumor.

tmr nhlt hlta a as d S f S f

measured antenna input reflection in front of the brethe tumor inside.

domain,


coaxial transitions at 3

Fig. 8: Measured input reflection coefficients in the presence of the breast

without tumor in spatial

in this study. breast reflection should be detected for each antenna.

Fig. 9: Spatial

coefficient,

antennas considered in this study.at which the breast reflection should be detected for each antenna.


Further to a slight ed to Fig. 7, there is no correlation between

position and peaks’ position. antenna internal reflections

S f from hltaS f

effective if the reflections in the presence of a dielectric body in close proximity.

The result is presented in validity of the previous clearly identifiable for the three antennasinternal reflections. The magnitude of the skin backscattering is approximately 12, 7.

, respectively. The attributed to larger aperture with significant electric field magnitude. We emphasize that thstrategy has minimum impact on thewith the corresponding vertical lines

To conclude this analysisthe tumor. We represent

IDFTtmr nhlt hlta a as d S f S f

measured antenna input reflection in front of the brethe tumor inside.

: Measured input reflection coefficients in the presence of the breast

without tumor in spatial-domain,

in this study. The vertical dashed lines identify the distance at which the breast reflection should be detected for each antenna.

: Spatial-domain breast signals after subtraction of free

coefficient, hlt fsa as d s d

antennas considered in this study.at which the breast reflection should be detected for each antenna.


slight increase in the magnitude of the curvesthere is no correlation between

position and peaks’ position. Theseantenna internal reflections. Therefore,

S f to remove

reflections in the antenna ectric body in close proximity.

presented in Fig. 9, previous assumption:

for the three antennasThe magnitude of the skin backscattering

is approximately 12, 7.5 and 19 for the BAVA, monopole and The higher response

larger aperture with significant electric field We emphasize that thminimum impact on the

with the corresponding vertical linesTo conclude this analysis, we perform a similar study for

represent in

tmr nhlt hlta a as d S f S f

measured antenna input reflection in front of the bre


domain, hltas d , for the three antennas considered

The vertical dashed lines identify the distance at which the breast reflection should be detected for each antenna.

domain breast signals after subtraction of free

hlt fsa as d s d , based on measured signals, for the three

antennas considered in this study. The vertical dashed lines identify the distance at which the breast reflection should be detected for each antenna.


increase in the magnitude of the curvesthere is no correlation between

are still dominated by the Therefore, we propose subtracting

to remove its effect. This is only

antenna are immune to the ectric body in close proximity.

, and seems to confirm the : the skin reflection is now

for the three antennas, free fromThe magnitude of the skin backscattering

5 and 19 for the BAVA, monopole and response from the XETS

larger aperture with significant electric field We emphasize that the subtraction calibration minimum impact on the matching of the peaks

with the corresponding vertical lines. , we perform a similar study for

in Fig. 10 the function

s d S f S f , where nhltaS f

measured antenna input reflection in front of the bre


, for the three antennas considered


domain breast signals after subtraction of free

, based on measured signals, for the three



increase in the magnitude of the curves, there is no correlation between the skin

dominated by the we propose subtracting

. This is only

immune to the

and seems to confirm the the skin reflection is now

free from antenna The magnitude of the skin backscattering

5 and 19 for the BAVA, monopole and the XETS is

larger aperture with significant electric field subtraction calibration

of the peaks

, we perform a similar study for the function

nhltaS f is the

measured antenna input reflection in front of the breast with


, for the three antennas considered

The vertical dashed lines identify the distance at which the

domain breast signals after subtraction of free-space reflection



space reflection


The vertical dashed lines identify the distance




It appears that the monopole antenna tumor response. However, the maximum takes place at a smaller not observedwith the higher magnitude, 0.3 compared to 0.1 of the BAVAnyway, these skin’s. vertical markers

It is stressed that the employed differenceremove the skin is not feasible in an examination scenario

because

same patient, andat this point of the paper, without going through the Section

The results presented in this subto detect the skin inside the antennathe input reflection coefficients in presence of the body. As a result, this strategy should precede the signal processing, when implementing an algorithmas is our case as explained in Section IV

B.

Aideal point sourcescenter position. Howeverradiation This affects the involved distance calculations, and the image focusing. concept to the nearfield pseudo phase center”. determine and characterize its dependence with the observation angle.

Consider the geometry in close to the breast. The shaded blue region represents volume fororder to make the concept easy to

reference point within the blue region

that the

Fig.

signals, for the three antennas considered in this study.lines identify the distance at which the breast reflection should be defor each antenna.


It appears that the monopole antenna tumor response. However, the maximum takes place at a smaller distance not possible. In fact, it results from the effect of the cable observed in Fig. with the higher magnitude, 0.3 compared to 0.1 of the BAVAnyway, these magnituskin’s. Both antennas show thevertical markers.


cause nhltaS f

same patient, by definition. and is enough to at this point of the paper, without going through the Section IV.

The results presented in this subto detect the skin inside the antennathe input reflection coefficients in presence of the body. As a result, this strategy should precede the signal processing, when implementing an algorithmas is our case as explained in Section IV

Antenna “near

Antennas in Mideal point sourcescenter position. Howeverradiation point tends to change with the observation angleThis affects the involved distance calculations, and the image focusing. Therefore, concept to the nearfield pseudo phase center”. determine and characterize its dependence with the observation angle.

Consider the geometry in close to the breast. The shaded blue region represents volume containingfor all observation angles order to make the concept easy to


that the electric distance

i b b airD d n f d d

Fig. 10: Tumor response in spatial

signals, for the three antennas considered in this study.lines identify the distance at which the breast reflection should be defor each antenna.


It appears that the monopole antenna tumor response. However, the maximum takes place at a

distance than the skin reflection, which is In fact, it results from the effect of the cable

Fig. 4. The XETS antennawith the higher magnitude, 0.3 compared to 0.1 of the BAV

magnitudes are nearly 60 times lower than the Both antennas show the

It is stressed that the employed difference

remove the skin is not feasible in an examination scenario

S f and hltaS f

by definition. However, thisenough to estimate the tumor signal

at this point of the paper, without going through the

The results presented in this subto detect the skin response, we must eliminate the reflections inside the antenna. This may be achieved by subtracting the input reflection coefficients in presence of the body. As a result, this strategy should precede the signal processing, when implementing an algorithm that relies on identifying the skinas is our case as explained in Section IV

“near-field phase center”

MMWI algorithms are usually assumed as ideal point sources, located atcenter position. However, in the near

point tends to change with the observation angleThis affects the involved distance calculations, and the image

Therefore, we propose to adapt concept to the near-field. Onwardsfield pseudo phase center”. determine and characterize its dependence with the observation angle.

Consider the geometry in Fig. close to the breast. The shaded blue region represents

containing the pseudo phase center positions all observation angles θ’, ϕ

order to make the concept easy to


distance in equation

i b b airD d n f d d

: Tumor response in spatial-domain,

signals, for the three antennas considered in this study.lines identify the distance at which the breast reflection should be de


It appears that the monopole antenna picktumor response. However, the maximum takes place at a

e skin reflection, which is In fact, it results from the effect of the cable

antenna detects the tumor again with the higher magnitude, 0.3 compared to 0.1 of the BAV

des are nearly 60 times lower than the Both antennas show their peaks coincident with the


S f are mutually exclusive

However, this is possible in the lab tumor signal characteristics

at this point of the paper, without going through the

The results presented in this sub-section prove that in order , we must eliminate the reflections

be achieved by subtracting the input reflection coefficients in presence of the body. As a result, this strategy should precede the signal processing, when

that relies on identifying the skinas is our case as explained in Section IV.

field phase center”

algorithms are usually assumed as , located at the antenna far

, in the near-field, this point tends to change with the observation angle

This affects the involved distance calculations, and the image we propose to adapt

nwards, we will field pseudo phase center”. We present a procedure to determine and characterize its dependence with the

Fig. 11, which shows close to the breast. The shaded blue region represents

pseudo phase center positions ϕ’ in the antenna solid angle

order to make the concept easy to apply, w

reference point within the blue region 0 0 0 0

in equation (7) may be modified to

,i b b airD d n f d d

domain, tmras d , based on measured

signals, for the three antennas considered in this study. lines identify the distance at which the breast reflection should be de


picks up the largesttumor response. However, the maximum takes place at a

e skin reflection, which is obviously In fact, it results from the effect of the cable

detects the tumor again with the higher magnitude, 0.3 compared to 0.1 of the BAV

des are nearly 60 times lower than the coincident with the

It is stressed that the employed difference-method to remove the skin is not feasible in an examination scenario

are mutually exclusive in the

possible in the lab characteristics just

at this point of the paper, without going through the process of

section prove that in order , we must eliminate the reflections

be achieved by subtracting Sfs

the input reflection coefficients in presence of the body. As a result, this strategy should precede the signal processing, when

that relies on identifying the skin

algorithms are usually assumed as the antenna far-field phase

field, this virtual point tends to change with the observation angle

This affects the involved distance calculations, and the image we propose to adapt the phase center

ll call it the “nearWe present a procedure to

determine and characterize its dependence with the

, which shows an antenna close to the breast. The shaded blue region represents

pseudo phase center positions ρ(θ’, the antenna solid angle.

apply, we define a fixed

0 0 0 0, ,x y z , such

be modified to

, , (13

s d , based on measured

The vertical dashed lines identify the distance at which the breast reflection should be detected


largest

tumor response. However, the maximum takes place at a obviously

In fact, it results from the effect of the cable detects the tumor again

with the higher magnitude, 0.3 compared to 0.1 of the BAVA. des are nearly 60 times lower than the

coincident with the

method to remove the skin is not feasible in an examination scenario,

in the

possible in the lab just

process of

section prove that in order , we must eliminate the reflections

fs to the input reflection coefficients in presence of the body. As a result, this strategy should precede the signal processing, when

that relies on identifying the skin,

algorithms are usually assumed as field phase

virtual point tends to change with the observation angle.

This affects the involved distance calculations, and the image the phase center call it the “near-

We present a procedure to determine and characterize its dependence with the

antenna close to the breast. The shaded blue region represents the

, ϕ’) . In

fixed

, such

13)

where d

and ρ0, a

between of the pseudo phase center relative to Fig. 12point, (xto the other spherical

It remains to discuss the determination of

d

Fig. 12, in which towards a metallic latter sweeps the

we measure the input reflection coefficient,

captures the response of the sphere. We then

to the spatial domain,

allows inferring the electrical distance

is detected.assumed to be at the physical aperture of the antenna.

, based on measured

The vertical dashed tected

Fig. 11: Representation of the pseudo phase center, with angles volume containing

Tumor

Fig. 12: Twosetup used to characterize setup is three

z

y

Scanning plane


db + dair is the

, and the additional term

between ρ(θ’, ϕ’) andof the pseudo phase center relative to

12 is defined in x, y, z), and ρ0

to the other spherical coordinate


, . To this end, we

, in which the static antenna radiates in the towards a metallic sphere

sweeps the xy-plane with constant



to the spatial domain,


is detected. For each antenna, the reference point (0, 0, 0) is assumed to be at the physical aperture of the antenna.

: Representation of the pseudo phase center, with angles θ’ and ϕ’ in 2D gevolume containing ρ(θ’, ϕ’).

( , , )x y z

Breast

Tumor

: Two-dimensional schematic representation of the measurement setup used to characterize setup is three-dimensional, with a similar representation in the

x

Scanning plane

0

0º

s

s

y

0,0,0

Antenna


the distance between the test point (

additional term

) and ρ0, accounts for the angular dispersion of the pseudo phase center relative to

in spherical coordinates

0. The ϕ’ angle (not shown) coordinate angle.


To this end, we assembled the setup

the static antenna radiates in the sphere with coordinates (plane with constant



to the spatial domain, ss d , and


For each antenna, the reference point (0, 0, 0) is assumed to be at the physical aperture of the antenna.

: Representation of the pseudo phase center, in 2D geometry. The irregular blue shape represents the

).

( , , )x y z

0

( , , )i i ix y z

dimensional schematic representation of the measurement setup used to characterize the “near-field phase center”,

dimensional, with a similar representation in the

0

s

sz

0,0,0

Antenna


distance between the test point (

,d ,

, accounts for the angular dispersion of the pseudo phase center relative to ρ0. Note that

coordinates between the test angle (not shown)

angle.


assembled the setup

the static antenna radiates in the with coordinates (xs,

plane with constant zs. At each position,

we measure the input reflection coefficient, sS f

captures the response of the sphere. We then convert

, and subtract s d

allows inferring the electrical distance sd at which the target


: Representation of the pseudo phase center, ρ(θ’, ϕ’), and variation The irregular blue shape represents the

0

,d

y y

bd

aird

z’

dimensional schematic representation of the measurement field phase center”, ρ(θ,

dimensional, with a similar representation in the y

sx

sd


distance between the test point (x, y, z) the distance

, accounts for the angular dispersion Note that angle θ’ in

between the test angle (not shown) corresponds

It remains to discuss the determination of ρ0 and

assembled the setup depicted in

the static antenna radiates in the +z-direction , ys, zs). The

At each position,

sS f , which

convert sS f

fss d . This

at which the target


), and variation The irregular blue shape represents the

Antenna

0

0y y

x’

y’

dimensional schematic representation of the measurement ϕ). The actual yz-plane.

Spherical target

S f




Tcoordinates of the pseudo phase center in both Eplanes of the antenna

In turn, the following least

in which

target,

average values of the measured

some angular interval

It

d

incorporate it through the IDFTAs an example,

previous three test antennas, airfreescan of the target was perlinear positioner. The175 mm in steps of 5 mm in both

We

point

Moreover, plane for the three antennas, after interpolating over a regular grid. For some angles using the monopole antenna, the target was not detected and so Δ


The coordinates of coordinates of the pseudo phase center in both Eplanes of the antenna

In turn, ρE and ρH

the following least

max

min , 0º , 0ºs

s

E

max

min , 90º , 90ºs

s

H

in which sd is the distance between the

target, ,avgs E s sd


some angular interval

It is noted that

,d depend explicitly

incorporate it through the IDFTAs an example,

previous three test antennas, air as target, at constant free-space wavelength at 3 GHz)scan of the target was perlinear positioner. The175 mm in steps of 5 mm in both

We present in

point �� obtained in the referred test, considering

Moreover, Fig. 13plane for the three antennas, after interpolating over a regular grid. For some angles using the monopole antenna, the target was not detected and so Δ

Near-field phase centers,

proposed method, for

ρ0 (x, y, z) [mm]


he coordinates of ρ0 are determined as the average coordinates of the pseudo phase center in both Eplanes of the antenna (see Figs. 2

0

1

2

H are computed the following least-square problems:

min , 0º , 0ºs

s s s s E s sd d

min , 90º , 90ºs

s s s s H s sd d

is the distance between the

, 0ºs E s s and


some angular interval of interest

noted that, in the way they were defined,

depend explicitly

incorporate it through the IDFTAs an example, the pseudo phase center is calculated for the

previous three test antennas, using a 7 mm , at constant zs = λ

space wavelength at 3 GHz)scan of the target was performed using a Bosch Rexroth XZ linear positioner. The sweep extended from 175 mm in steps of 5 mm in both

present in TABLE V the coordinates of the reference

obtained in the referred test, considering

13 shows Δdρ(θplane for the three antennas, after interpolating over a regular grid. For some angles using the monopole antenna, the target was not detected and so Δdρ(θ’,

TABLE

field phase centers, ρ0, of the three antennas calculated using the

proposed method, for max 30º . The center of the reference frame is

assigned in

BAVA (-10, 0.5, -24.5)


are determined as the average coordinates of the pseudo phase center in both E

(see Figs. 2 – 4):

1

2E H .

are computed as the ρ0 value that minimizes square problems:

,min , 0º , 0ºavgs s s s E s sd d

,min , 90º , 90ºavgs s s s H s sd d

is the distance between the ρ0 under test and the

and , , 90ºavgs H s sd

average values of the measured sd in each plane, restricted to

of interest max 30º .

the way they were defined,

depend explicitly on frequency

incorporate it through the IDFT. the pseudo phase center is calculated for the

using a 7 mm metallic sphere = λ3 = 100 mm

space wavelength at 3 GHz) from the antenna. The linear formed using a Bosch Rexroth XZ

sweep extended from 175 mm in steps of 5 mm in both x and y directions.

the coordinates of the reference

obtained in the referred test, considering

θ’, ϕ’) over the entire scanning plane for the three antennas, after interpolating over a regular grid. For some angles using the monopole antenna, the target

, ϕ’) could not be TABLE V

, of the three antennas calculated using the

30º . The center of the reference frame is

assigned in Fig. 12.

Monopole 24.5) (-7.5, 0, -5)


are determined as the average coordinates of the pseudo phase center in both E- and H

(14

value that minimizes

2

min , 0º , 0ºs s s s E s s

(15

2

min , 90º , 90ºs s s s H s s

(16

under test and the

, 90ºs H s s are the

plane, restricted to

30º

the way they were defined, neither ρ0 n

frequency, rather they

the pseudo phase center is calculated for the metallic sphere (where λ3 is the

from the antenna. The linear formed using a Bosch Rexroth XZ

sweep extended from -175 mm up to directions.


obtained in the referred test, considering max 30º

) over the entire scanning plane for the three antennas, after interpolating over a regular grid. For some angles using the monopole antenna, the target

) could not be inferred.


. The center of the reference frame is

XETS (-0.5, 0.5, -13)


are determined as the average and H-

14)

value that minimizes

15)

16)

under test and the

are the

plane, restricted to

nor

, rather they

the pseudo phase center is calculated for the metallic sphere in

is the from the antenna. The linear

formed using a Bosch Rexroth XZ 175 mm up to


30º .

) over the entire scanning plane for the three antennas, after interpolating over a regular grid. For some angles using the monopole antenna, the target

In the Every stable phase centers

which is relatively broad. Concerning the monopole, the phase center is very unstable due to the measurement cable (this result justifies the option of restricting the calculation of

m ax ). I

was very often not detectedhave reasonably stable phase center up to

again, BAVA and XETS have the best performance. We note that the phase center of the monopole antenna is more stable in the H-plane than in the Ecable is the same for all angles.

The Δstored as a lookup table for proper distance correction in equationexample

C. Antenna

As observed in the sectionwere done in the exact same conditions, the skin reflection does not occur at the same distance 9). Indeed, as the electric currents propagate on the antenna, they add an offset length that depends on the antenna geometry and operation modecable). MMWI; otherwisefocused, leading to inaccurate results. Moreover, the offset length exhibits frequencyan average value may be the simpcertainly not the most accurate. Despite being a critical procedure, this subject is rarely addressed. For instance, in


. The center of the reference frame is

13)

Fig. 13: Variability of nearthree antennas over the entire scanning plane: (a) BAVA; (b) monopole antenna; (c) XETS antenna.phi.


the E-plane, both BAVA and XETS antennas present very stable phase centers


). In fact, for angles broader than

very often not detectedhave reasonably stable phase center up to

again, BAVA and XETS have the best performance. We note t the phase center of the monopole antenna is more stable in

plane than in the Eble is the same for all angles.The Δdρ(θ’, ϕ’) information for the tested solid angle can be

stored as a lookup table for proper distance correction in equation (12), for theexample of this strategy

Antenna offset length

As observed in the sectionwere done in the exact same conditions, the skin reflection does not occur at the same distance

Indeed, as the electric currents propagate on the antenna, they add an offset length that depends on the antenna geometry and operation modecable). It is crucial to account for this additional length in MMWI; otherwise, focused, leading to inaccurate results. Moreover, the offset length exhibits frequencyan average value may be the simpcertainly not the most accurate. Despite being a critical procedure, this subject is rarely addressed. For instance, in

: Variability of nearthree antennas over the entire scanning plane: (a) BAVA; (b) monopole antenna; (c) XETS antenna.


plane, both BAVA and XETS antennas present very stable phase centers in the interval between


angles broader than

very often not detected. In the Hhave reasonably stable phase center up to


plane than in the E-plane, since the influence of the ble is the same for all angles.

) information for the tested solid angle can be stored as a lookup table for proper distance correction in

the image inversionof this strategy will be presented

length

As observed in the section V, although the measurements were done in the exact same conditions, the skin reflection does not occur at the same distance for all antennas

Indeed, as the electric currents propagate on the antenna, they add an offset length that depends on the antenna geometry and operation mode (e.g. phase center and feeding

ucial to account for this additional length in the final image will not be properly

focused, leading to inaccurate results. Moreover, the offset length exhibits frequency-dependent variation, whereby taking an average value may be the simpcertainly not the most accurate. Despite being a critical procedure, this subject is rarely addressed. For instance, in

: Variability of near-field phase center over angle, Δthree antennas over the entire scanning plane: (a) BAVA; (b) monopole antenna; (c) XETS antenna. The radial angle is theta and the polar angle is


plane, both BAVA and XETS antennas present in the interval between


angles broader than max 45º

the H-plane, the three antennas have reasonably stable phase center up to

max


plane, since the influence of the


image inversion. An experimewill be presented in Section

, although the measurements were done in the exact same conditions, the skin reflection

for all antennas Indeed, as the electric currents propagate on the antenna,

they add an offset length that depends on the antenna (e.g. phase center and feeding


focused, leading to inaccurate results. Moreover, the offset dependent variation, whereby taking

an average value may be the simplest solution, but it is certainly not the most accurate. Despite being a critical procedure, this subject is rarely addressed. For instance, in

field phase center over angle, Δdρ

three antennas over the entire scanning plane: (a) BAVA; (b) monopole The radial angle is theta and the polar angle is


plane, both BAVA and XETS antennas present

in the interval between max 30

which is relatively broad. Concerning the monopole, the phase center is very unstable due to the measurement cable (this result justifies the option of restricting the calculation of ρ0 to

45º the target

plane, the three antennas

max 25º , but,


plane, since the influence of the


experimental in Section VI.

, although the measurements were done in the exact same conditions, the skin reflection

for all antennas (recall Fig. Indeed, as the electric currents propagate on the antenna,

they add an offset length that depends on the antenna (e.g. phase center and feeding


focused, leading to inaccurate results. Moreover, the offset dependent variation, whereby taking

lest solution, but it is certainly not the most accurate. Despite being a critical procedure, this subject is rarely addressed. For instance, in [5]

dρ(θ, ϕ), for the three antennas over the entire scanning plane: (a) BAVA; (b) monopole

The radial angle is theta and the polar angle is

30




the authors propose a twoinvolving reference targets. However, it does not accthe frequency dependency of the electrical length. In this section,antenna. All calculations in this section pseudo phase center data computed in the previous section

Let

introduced by the

eq eq eqij i jd f d f d f

the Tx and Rx antennas

center”,

since we consider the propagation speed as being the speed of light in vacuum.

It is known that the phase of a transmission coefficient

between two antennas

distance between the antennas through:

where antennas, electrical distance between the two calibration ports. In fact, dtotal

Tx and Rx antennas

W

In order to fully characterize the offset length this method requires at least two antennas, if they are considered identical. As this is rarely true, we formulate the method for three antennas. To this end, we measure the transmission coefficients between14.

W

2eqd f

12eqd f

Fig. equivalent coefficients.

d f

d f

d f


the authors propose a twoinvolving reference targets. However, it does not accthe frequency dependency of the electrical length. In this section, we show how to calculate the electrical length of any antenna. All calculations in this section pseudo phase center data computed in the previous section

Let us designate the frequency

introduced by the

eq eq eqij i jd f d f d f

the Tx and Rx antennas

center”, ρ0,i. Note that

since we consider the propagation speed as being the speed of light in vacuum.


between two antennas


where n is the refractive index of the medium between the antennas, k0 is the freeelectrical distance between the two calibration ports. In fact,

total can be decomposed into three terms corresponding to the Tx and Rx antennas

arg .ij i jS f k f d d f d f

We can use this information to

In order to fully characterize the offset length this method requires at least two antennas, if they are considered identical. As this is rarely true, we formulate the method for three antennas. To this end, we measure the transmission coefficients between

.

We end up having three unknown

2eqd f and 3

eqd f

12eqd f , 13

eqd f

Fig. 14: Representation of the measurement setup used to calculate the equivalent length introduced by the antennascoefficients.

1eqd f

1eqd f

3eqd f

0,1

0,1

0,3


the authors propose a twoinvolving reference targets. However, it does not accthe frequency dependency of the electrical length. In this

we show how to calculate the electrical length of any antenna. All calculations in this section pseudo phase center data computed in the previous section

us designate the frequency

introduced by the i-th antenna as

eq eq eqij i jd f d f d f as the offset length introduced by

the Tx and Rx antennas relative to their “near

. Note that eqid f

since we consider the propagation speed as being the speed of


between two antennas i and


arg ij totalS f nk f d

is the refractive index of the medium between the is the free-space wavenumber and

electrical distance between the two calibration ports. In fact, can be decomposed into three terms corresponding to the

Tx and Rx antennas and the physical distance,

0arg .ij i jS f k f d d f d f

e can use this information to

arg

eqijd f d

In order to fully characterize the offset length this method requires at least two antennas, if they are considered identical. As this is rarely true, we formulate the method for three antennas. To this end, we measure the transmission coefficients between the pairs of antennas, as sketched

e end up having three unknown

3eqd f . Through

d f and 23eqd f , fro

: Representation of the measurement setup used to calculate the introduced by the antennas

d

21S f

31S f

23S f

0,3


the authors propose a two-stage calibration technique involving reference targets. However, it does not accthe frequency dependency of the electrical length. In this

we show how to calculate the electrical length of any antenna. All calculations in this section are referred topseudo phase center data computed in the previous section

us designate the frequency-dependent offset length

th antenna as

as the offset length introduced by

relative to their “near

d f is actually an electrical length,



and j, i jS f , is related to the


0ij totalS f nk f d

is the refractive index of the medium between the space wavenumber and


and the physical distance,

arg .eqij

eq eqij i j

d f

S f k f d d f d f

e can use this information to infer eqijd f

0

arg.

ijS fd f d

k f

In order to fully characterize the offset length this method requires at least two antennas, if they are considered identical. As this is rarely true, we formulate the method for three antennas. To this end, we measure the transmission

the pairs of antennas, as sketched

e end up having three unknown offset distances:

Through relation (19

d f , from which we infer

: Representation of the measurement setup used to calculate the introduced by the antennas, based on the transmission

S f

31S f

23S f

0,3


stage calibration technique involving reference targets. However, it does not account for the frequency dependency of the electrical length. In this

we show how to calculate the electrical length of any are referred to

pseudo phase center data computed in the previous section. dependent offset length

th antenna as eqid f and


relative to their “near-field phase

is actually an electrical length,



, is related to the

ij totalS f nk f d (17

is the refractive index of the medium between the space wavenumber and dtotal is the


and the physical distance, d:

arg .eq

eq eqij i j

d f

S f k f d d f d f

(18

d f as

.d f d (19


the pairs of antennas, as sketched in Fig.

distances: 1eqd f

19) we calculate

m which we infer

: Representation of the measurement setup used to calculate the , based on the transmission

2eqd f

2eqd f

3eqd f0,3

0,2

0,2


stage calibration technique ount for

the frequency dependency of the electrical length. In this we show how to calculate the electrical length of any

the

dependent offset length

and


field phase

is actually an electrical length,



, is related to the

17)

is the refractive index of the medium between the is the


18)

19)


Fig.

eqd f ,

we calculate

In order to calibrate the offset distance, one needs only to

compensate for the phase delay

to post-

(12). We applied the

three antennas included in this study. setup, we set in Fig. 15

The BAVA and XETS antennas have the largest equivalent distance because of the feeding microstrip and cable, respectively. As for the and the microstrip length is shorter. maximumcorresponds to the freealong frequency for the BAVA, 13.6 mm (0.16monopole, and of 36.3 mm

takes the average value of

distance calculation at each frequency may be significant and lead to lower quality focusing.

As an example of the importance of calibrating t

equivalent offset distance, we illustrate

tmras d

equivalent distance

: Representation of the measurement setup used to calculate the

, based on the transmission

d f

d f

d f

Fig. 15:

spectrum for the three antenna topologies considered in this study.

Fig. 16: Spatial

coefficient and equivalent distance calibration,

measured signals, for the three antennas considered in this study.


1 21 31 32

2 21 1

3 31 1

1eq eq eq eq

eq eq eq

eq eq eq

d f d f d f d f

d f d f d f

d f d f d f


compensate for the phase delay

-processing signals

We applied the equivalentthree antennas included in this study.

we set d = 119 15 along the frequency range of

The BAVA and XETS antennas have the largest equivalent distance because of the feeding microstrip and cable, respectively. As for the and the microstrip length is shorter. maximum-to-minimum variation of 19.7 mm (0.23corresponds to the freealong frequency for the BAVA, 13.6 mm (0.16monopole, and of 36.3 mm

the average value of




s d in Fig. 16

equivalent distances w

: Equivalent offset distance,


: Spatial-domain signals after subtraction of free




1 21 31 32

2 21 1

3 31 1

1

2eq eq eq eq

eq eq eq

eq eq eq

d f d f d f d f

d f d f d f

d f d f d f


compensate for the phase delay correspond

processing signals, as denoted by the term

equivalent-lengththree antennas included in this study.

mm. The calculated distances are shown along the frequency range of

The BAVA and XETS antennas have the largest equivalent distance because of the feeding microstrip and cable, respectively. As for the monopole, it is fed by the connector and the microstrip length is shorter.

minimum variation of 19.7 mm (0.23corresponds to the free-space wavelength at along frequency for the BAVA, 13.6 mm (0.16monopole, and of 36.3 mm (0.42λ

the average value of ( )eqid f , the error introduced in the




16 and Fig. 17

were calibrated.

Equivalent offset distance, eqid f


domain signals after subtraction of free




1 21 31 32

2 21 1

3 31 1

eq eq eq eq

eq eq eq

eq eq eq

d f d f d f d f

d f d f d f

d f d f d f


corresponding to d f

as denoted by the term

length calibration method to the three antennas included in this study. In our measurement

The calculated distances are shown along the frequency range of 2 GHz up to

The BAVA and XETS antennas have the largest equivalent distance because of the feeding microstrip and cable,

monopole, it is fed by the connector and the microstrip length is shorter. Fig. 15

minimum variation of 19.7 mm (0.23space wavelength at fc

along frequency for the BAVA, 13.6 mm (0.16λc) for the XETS. If ones

( )d f , the error introduced in the

distance calculation at each frequency may be significant and


equivalent offset distance, we illustrate hlt fsa as d s d

17, respectively,

calibrated.

d f , over the 2-5 GHz frequency


domain signals after subtraction of free-space reflection

coefficient and equivalent distance calibration, hlt fsa as d s d



d f d f d f d f

. (20)


eqid f prior

as denoted by the term eqd f in

method to the In our measurement

The calculated distances are shown GHz up to 5 GHz.

The BAVA and XETS antennas have the largest equivalent

distance because of the feeding microstrip and cable, monopole, it is fed by the connector

15 shows a minimum variation of 19.7 mm (0.23λc, where λc

= 3.5 GHz) along frequency for the BAVA, 13.6 mm (0.16λc) for the

) for the XETS. If ones

, the error introduced in the

distance calculation at each frequency may be significant and

As an example of the importance of calibrating the

hlt fsa as d s d and

, respectively, after the

5 GHz frequency


space reflection

hlt fsa as d s d , based on





We verify that after the equivalent distance is capeaks are aligned and correspond to the actual separation between antenna andcompare with andin particular the physical distance betwbreast was kept the same, we can observe that the skin and tumor backscattering are not obtained at the same distance for the three antennas. This is a consequence of the location of the pseudo phase center (recallthe three antennas (and therefore the skin and tumor are detected at different distances).

This section three antennasconditionsfactorsthree measurement positions each, separated72). z =

A.

In sections retrieved the largest tumor response of the three antenna17). backscattering was larger for the XETSin these results the higher value presented for the monopole is a consequence of the feeding cable and does not correspond to the tumor. As a result, we cannot conclude that the slotantenna favors the tumorbackscattering.

So, ienergy into the breast, we calculatethree antennas under similar measurement conditionscomplete spatial scan

magnitude tumor response

and

are presented in antenna correspond to positions where the feeding cable precludes the detection of the tumor response (see for instance Fig.

Fig.

distance calibration, based on measured signals, for the three antennas considered in this study.


We verify that after the equivalent distance is capeaks are aligned and correspond to the actual separation between antenna andcompare with Fig. and Fig. 17 werein particular the physical distance betwbreast was kept the same, we can observe that the skin and tumor backscattering are not obtained at the same distance for the three antennas. This is a consequence of the location of the pseudo phase center (recallthe three antennas (and therefore the skin and tumor are detected at different distances).

VI.

This section compares three antennas, conditions, using all the previously presented correction factors. Referring tothree antenna circular pathsmeasurement positions each, separated72). The rings we

= -53 mm (the breast has negative

Energy coupling into breast

In sections V.Aretrieved the largest tumor response of the three antenna

). Nevertheless, we also observed that the skin backscattering was larger for the XETSin these results the higher value presented for the monopole is a consequence of the feeding cable and does not correspond to the tumor. As a result, we cannot conclude that the slotantenna favors the tumorbackscattering.

So, in order energy into the breast, we calculatethree antennas under similar measurement conditionscomplete spatial scan

magnitude tumor response

and Sd is calculated from

are presented in Fig. antenna correspond to positions where the feeding cable precludes the detection of the tumor response (see for instance Fig. 17).

Fig. 17: Tumor response in spatial



We verify that after the equivalent distance is capeaks are aligned and correspond to the actual separation between antenna and skin for the three

Fig. 9. Although twere obtained in similar measurement conditions,

in particular the physical distance betwbreast was kept the same, we can observe that the skin and tumor backscattering are not obtained at the same distance for the three antennas. This is a consequence of the location of the pseudo phase center (recall TABLE the three antennas (and therefore the skin and tumor are detected at different distances).

EXPERIMENTAL

compares the imag tested under the same

, using all the previously presented correction Referring to Fig. 1, we adopted a 6

antenna circular paths, each one measurement positions each, separated

were positioned at53 mm (the breast has negative


V.A and V.C we verified that the XETS antenna retrieved the largest tumor response of the three antenna

Nevertheless, we also observed that the skin backscattering was larger for the XETSin these results the higher value presented for the monopole is a consequence of the feeding cable and does not correspond to the tumor. As a result, we cannot conclude that the slotantenna favors the tumor response relative to the skin

to understand which antenna couples more energy into the breast, we calculatethree antennas under similar measurement conditionscomplete spatial scan around the b

magnitude tumor response, Td,

is calculated from hlt fsa as d s d

Fig. 18. The absent markers for the monopole antenna correspond to positions where the feeding cable precludes the detection of the tumor response (see for instance

: Tumor response in spatial-



We verify that after the equivalent distance is capeaks are aligned and correspond to the actual separation

skin for the three antennas. These results Although the results illustrated in

obtained in similar measurement conditions, in particular the physical distance between the antenna and the breast was kept the same, we can observe that the skin and tumor backscattering are not obtained at the same distance for the three antennas. This is a consequence of the location of the

TABLE V), which is different for the three antennas (and therefore the skin and tumor are detected at different distances).

XPERIMENTAL IMAGING RESULTS

the imaging results under the same experimental setup

, using all the previously presented correction we adopted a 60 m

each one comprismeasurement positions each, separated by 15 degrees (

re positioned at z = -33 mm, 53 mm (the breast has negative z coordinates).


we verified that the XETS antenna retrieved the largest tumor response of the three antenna

Nevertheless, we also observed that the skin backscattering was larger for the XETS (Fig. in these results the higher value presented for the monopole is a consequence of the feeding cable and does not correspond to the tumor. As a result, we cannot conclude that the slot

response relative to the skin

to understand which antenna couples more energy into the breast, we calculated the TSRthree antennas under similar measurement conditions

around the breast.

, is calculated from

2hlt fs

a as d s d .

. The absent markers for the monopole antenna correspond to positions where the feeding cable precludes the detection of the tumor response (see for instance

-domain, tmras d

distance calibration, based on measured signals, for the three antennas


We verify that after the equivalent distance is calibrated, the peaks are aligned and correspond to the actual separation

antennas. These results he results illustrated in Fig.

obtained in similar measurement conditions, een the antenna and the

breast was kept the same, we can observe that the skin and tumor backscattering are not obtained at the same distance for the three antennas. This is a consequence of the location of the

), which is different for the three antennas (and therefore the skin and tumor are

RESULTS

ing results obtained with experimental setup

, using all the previously presented correction mm radius for

comprising 24 antenna by 15 degrees (N

33 mm, z = -43 mm and coordinates).

we verified that the XETS antenna retrieved the largest tumor response of the three antennas (Fig.

Nevertheless, we also observed that the skin Fig. 16). Recall that

in these results the higher value presented for the monopole is a consequence of the feeding cable and does not correspond to the tumor. As a result, we cannot conclude that the slot-based

response relative to the skin

to understand which antenna couples more the TSR for each of the

three antennas under similar measurement conditions over a reast. The maximum

calculated from tmras d

2 . The TSR results


s d , after equivalent



librated, the

peaks are aligned and correspond to the actual separation antennas. These results

Fig. 16 obtained in similar measurement conditions,

een the antenna and the breast was kept the same, we can observe that the skin and tumor backscattering are not obtained at the same distance for the three antennas. This is a consequence of the location of the

), which is different for the three antennas (and therefore the skin and tumor are

the experimental setup

, using all the previously presented correction the

antenna Na =

43 mm and

we verified that the XETS antenna Fig.

Nevertheless, we also observed that the skin Recall that

in these results the higher value presented for the monopole is a consequence of the feeding cable and does not correspond to

based response relative to the skin

to understand which antenna couples more for each of the

over a maximum

2

s d

results


Firstly, maximum and minimum TSR are consistent for the three antennas, proving the measurement conditions are similar. The maximum around the 11to the antenna position that is closest to the tumor and, therefore, maximum energy is retrieved from it. On the contrary, the 19between antenna and tumor suffers the most attenuation, which means thatrelative to the skin backscattering.

Secondly, the BAVA and XETS antenna perform similarly, although the latter is more stable. Given that the Vivaldi antenna exhibits better frontexpected that more energy is coupled into the breast. Yet, the results in better TSR.lead to larger tumor responses relative to skin backscatteras both increase by approximately the same facto

Finally, concerning the monopole, the TSR results are not conclusive, because the cable effect prevents the detection of the tumor at several positions.

B. Discussion of impact of the proposed antenna characterization

To demonstrate we imagethe algorithms briefly presented in Section artifact removal was implemented considering useful frequency points were restricted to Δtotal of imaging metrics the improvement in the tumor detectionplaced at coordinates

The imaging results based on experimental data obtained using all the strategies discussed in previous sections are illustrated in represented in the figure, correspond to maximum intensity was achieved. The elliptical white contour marks the tumor container, whereas the exterior white contour defines the limits of the breast phantom. Itumor container is not marked, the maximum intensity was obtained for a lower value of

, after equivalent


Fig. 18: Tumorantennas considered in this study. The absent markers for the monopole antenna correspond to positions where the feeding cable precludes the detection of the tumor.


Firstly, maximum and minimum TSR are consistent for the three antennas, proving the measurement conditions are similar. The maximum around the 11to the antenna position that is closest to the tumor and, therefore, maximum energy is retrieved from it. On the contrary, the 19-th position is the farthest and the distance between antenna and tumor suffers the most attenuation, which means that the antenna gets a lower tumor response relative to the skin backscattering.

Secondly, the BAVA and XETS antenna perform similarly, although the latter is more stable. Given that the Vivaldi antenna exhibits better frontexpected that more energy is coupled into the breast. Yet, the results in Fig. 18 prove that this does not necessarily lead to better TSR. Therefore, using a more directive antenna does not lead to larger tumor responses relative to skin backscatteras both increase by approximately the same facto


Discussion of impact of the proposed antenna aracterization

To demonstrate the effectiveness of the propose strategiesmaged the breast using

the algorithms briefly presented in Section artifact removal was implemented considering useful frequency points were restricted to Δtotal of Nf = 34 frequency points.imaging metrics detailed in Section

improvement in the tumor detectionplaced at coordinates (

The imaging results based on experimental data obtained using all the strategies discussed in previous sections are illustrated in Fig. 19represented in the figure, correspond to maximum intensity was achieved. The elliptical white contour marks the tumor container, whereas the exterior white contour defines the limits of the breast phantom. Itumor container is not marked, the maximum intensity was obtained for a lower value of

: Tumor-to-skin ratio at different antenna positions for the three antennas considered in this study. The absent markers for the monopole antenna correspond to positions where the feeding cable precludes the detection of the tumor.


Firstly, maximum and minimum TSR are consistent for the three antennas, proving the measurement conditions are similar. The maximum around the 11to the antenna position that is closest to the tumor and, therefore, maximum energy is retrieved from it. On the

th position is the farthest and the distance between antenna and tumor suffers the most attenuation,

the antenna gets a lower tumor response relative to the skin backscattering.

Secondly, the BAVA and XETS antenna perform similarly, although the latter is more stable. Given that the Vivaldi antenna exhibits better front-to-back ratio, we could have expected that more energy is coupled into the breast. Yet, the

prove that this does not necessarily lead to Therefore, using a more directive antenna does not

lead to larger tumor responses relative to skin backscatteras both increase by approximately the same facto


Discussion of impact of the proposed antenna

the effectiveness of the propose strategiesthe breast using each of the three antennas

the algorithms briefly presented in Section artifact removal was implemented considering useful frequency points were restricted to Δ

frequency points.detailed in Section

improvement in the tumor detection(xt, yt, zt) of (-1

The imaging results based on experimental data obtained using all the strategies discussed in previous sections are

19 for the three antennas. Therepresented in the figure, correspond to maximum intensity was achieved. The elliptical white contour marks the tumor container, whereas the exterior white contour defines the limits of the breast phantom. Itumor container is not marked, the maximum intensity was obtained for a lower value of z.

skin ratio at different antenna positions for the three antennas considered in this study. The absent markers for the monopole antenna correspond to positions where the feeding cable precludes the


Firstly, maximum and minimum TSR are consistent for the three antennas, proving the measurement conditions are similar. The maximum around the 11-th position corto the antenna position that is closest to the tumor and, therefore, maximum energy is retrieved from it. On the


the antenna gets a lower tumor response

Secondly, the BAVA and XETS antenna perform similarly, although the latter is more stable. Given that the Vivaldi

back ratio, we could have expected that more energy is coupled into the breast. Yet, the


lead to larger tumor responses relative to skin backscatteras both increase by approximately the same factor.

Finally, concerning the monopole, the TSR results are not conclusive, because the cable effect prevents the detection of


the effectiveness of the propose strategieseach of the three antennas

the algorithms briefly presented in Section IV A and Bartifact removal was implemented considering Nn

useful frequency points were restricted to Δf = [2, 5] GHz in a frequency points. We also compute

detailed in Section IV C, in order to assess improvement in the tumor detection. Lastly, the tumor

10, -5, -32) mmThe imaging results based on experimental data obtained

using all the strategies discussed in previous sections are for the three antennas. The

represented in the figure, correspond to z and x planes where maximum intensity was achieved. The elliptical white contour marks the tumor container, whereas the exterior white contour defines the limits of the breast phantom. In the casetumor container is not marked, the maximum intensity was



Firstly, maximum and minimum TSR are consistent for the

three antennas, proving the measurement conditions are th position corresponds

to the antenna position that is closest to the tumor and, therefore, maximum energy is retrieved from it. On the


the antenna gets a lower tumor response

Secondly, the BAVA and XETS antenna perform similarly, although the latter is more stable. Given that the Vivaldi

back ratio, we could have expected that more energy is coupled into the breast. Yet, the


lead to larger tumor responses relative to skin backscattering, .

Finally, concerning the monopole, the TSR results are not conclusive, because the cable effect prevents the detection of


the effectiveness of the propose strategies, each of the three antennas, using

A and B. The

n = 2 and the = [2, 5] GHz in a

computed the in order to assess

Lastly, the tumor was mm.

The imaging results based on experimental data obtained using all the strategies discussed in previous sections are

for the three antennas. The results planes where

maximum intensity was achieved. The elliptical white contour marks the tumor container, whereas the exterior white contour

n the case where the tumor container is not marked, the maximum intensity was





When all the antennathe tumor is correctly detected with the three antennas. Although the monopole presents the feeding problems discussed throughout this work, it still manages to detect the tumor, despreasonably good with TCR ofthe BAVA, monopole and XETS antennastumorlack of resolution in this measurement planes along remaining

Fig. this study: (a) and (b)respectivelymm, respectivelyx = limits and the tumo

CALCULATED IMAGING METRICS


When all the antennathe tumor is correctly detected with the three antennas. Although the monopole presents the feeding problems discussed throughout this work, it still manages to detect the tumor, despite the error in its reasonably good with TCR ofthe BAVA, monopole and XETS antennastumor retrieved image is elongated along the lack of resolution in this measurement planes along remaining imaging metrics calculated for each antenna.

Fig. 19: Imaging results of the breast obtained with each antenna included in this study: (a) and (b)respectively, using BAVAmm, respectively, using monopole; (e) and (f) image cuts

= 14 mm, respectivelylimits and the tumor container.

CALCULATED IMAGING METRICSCHARACTERIZATION STRATEGIES

Antenna

Positive detection

Detected (xt, yt, [mm]

Intensity, T

TCR [dB]

TMR [dB]

PE [mm]


When all the antenna-characterization techniques are used, the tumor is correctly detected with the three antennas. Although the monopole presents the feeding problems discussed throughout this work, it still manages to detect the

ite the error in its reasonably good with TCR of the BAVA, monopole and XETS antennas

retrieved image is elongated along the lack of resolution in this direction, which results from the few measurement planes along z.

imaging metrics calculated for each antenna.

Imaging results of the breast obtained with each antenna included in this study: (a) and (b) image planes

, using BAVA; (c) and (d) , using monopole; (e) and (f) image cuts

mm, respectively, using XETS. The white contours identify the breast r container.

TABLE

CALCULATED IMAGING METRICSCHARACTERIZATION STRATEGIES

BAVA

Positive detection Yes

, zt) (14,-4,-30)

1.43

5.7

13.1

16


characterization techniques are used, the tumor is correctly detected with the three antennas. Although the monopole presents the feeding problems discussed throughout this work, it still manages to detect the

ite the error in its z coordinate. The detection is 5.7 dB, 2.2 dB and 2.3 dB for

the BAVA, monopole and XETS antennas, respectivelyretrieved image is elongated along the

direction, which results from the few . TABLE VI


Imaging results of the breast obtained with each antenna included in image planes at z = -30 mm and

(c) and (d) image planes at z , using monopole; (e) and (f) image cuts

. The white contours identify the breast

TABLE VI

CALCULATED IMAGING METRICS USING ALL THE ANTENNACHARACTERIZATION STRATEGIES

Monopole

Yes

30) (-4,0,-54)

2.67

2.2

11.8

24


characterization techniques are used, the tumor is correctly detected with the three antennas. Although the monopole presents the feeding problems discussed throughout this work, it still manages to detect the

coordinate. The detection is 2.2 dB and 2.3 dB for

, respectively. The retrieved image is elongated along the z-axis due to the

direction, which results from the few summarizes the


Imaging results of the breast obtained with each antenna included in 30 mm and x = 14 mm,

= -54 mm and x = , using monopole; (e) and (f) image cuts at z = -28 mm and


USING ALL THE ANTENNACHARACTERIZATION STRATEGIES.

XETS

Yes

(-14,-4,-28)

4.76

2.3

13.9

5


characterization techniques are used,

the tumor is correctly detected with the three antennas. Although the monopole presents the feeding problems discussed throughout this work, it still manages to detect the

coordinate. The detection is 2.2 dB and 2.3 dB for

. The axis due to the

direction, which results from the few summarizes the

In order to analyze the importance of the antennacharacterization techniques, three antennascorrections imaging results obtained with the XETSmetrics are summarized for all antennas

Let us start by studying the imaging results when

not subtracted prior to the artifact removal execution. Recall that this strategy has been proved to be extremely relevant, because it removes the antenna internal reflections, thus allowing correctly identifyimaging resul

Imaging results of the breast obtained with each antenna included in = 14 mm,

= -4mm and


USING ALL THE ANTENNA-

Calculated imaging metrics when one of the antenna

Strategy not used

Positive detection

Detected (

Intensity,

TMR [dB]

Strategy not used

Positive detection

Detected (

Intensity,

TMR [dB]

Strategy not used

Positive detection

Detected (

Intensity,

TMR [dB]


In order to analyze the importance of the antennacharacterization techniques, three antennas while corrections at a time. imaging results obtained with the XETSmetrics are summarized for all antennas


not subtracted prior to the artifact removal execution. Recall that this strategy has been proved to be extremely relevant, because it removes the antenna internal reflections, thus allowing correctly identifyimaging results with the

Calculated imaging metrics when one of the antennastrategies is not used, while the other are considered.

Strategy not used

Positive detection

Detected (xt, yt, zt) [mm]

Intensity, T

TCR [dB]

TMR [dB]

PE [mm]

Strategy not used

Positive detection


Intensity, T

TCR [dB]

TMR [dB]

PE [mm]

Strategy not used

Positive detection


Intensity, T

TCR [dB]

TMR [dB]

PE [mm]


In order to analyze the importance of the antennacharacterization techniques, we imaged the breast with the

while excluding at a time. For conciseness

imaging results obtained with the XETSmetrics are summarized for all antennas


not subtracted prior to the artifact removal execution. Recall that this strategy has been proved to be extremely relevant, because it removes the antenna internal reflections, thus allowing correctly identifying the skin backscatter. The

ts with the XETS are shown in

TABLE VII

Calculated imaging metrics when one of the antennastrategies is not used, while the other are considered.

Free-space subtraction calibration

Yes

(-4,0,-14) (

17.39

3

11.3

19

Monopole antenna

Free-space subtraction

Yes

(2,-16,-32)

1.33

1.37

9.6

16

XETS antenna

Free-space subtraction

No

- (

-

-

-

-


In order to analyze the importance of the antennawe imaged the breast with the

one of the discussed conciseness, we only show the

imaging results obtained with the XETS. Nevertheless, the metrics are summarized for all antennas in TABLE


not subtracted prior to the artifact removal execution. Recall that this strategy has been proved to be extremely relevant, because it removes the antenna internal reflections, thus

the skin backscatter. The are shown in Fig. 20

VII

Calculated imaging metrics when one of the antenna-characterization strategies is not used, while the other are considered.

BAVA

Δρ(θ, ϕ) calibration

Offset length calibration

Yes

(-12,2,-32)

1.39

5.5

12.9

4

Monopole antenna



Yes

(-4,2,-54)

2.73

2.73

10.4

12

XETS antenna



Yes

(-14,-4,-28)

4.75

2.1

13.6

5


In order to analyze the importance of the antenna-we imaged the breast with the

of the discussed only show the

. Nevertheless, the TABLE VII.

Let us start by studying the imaging results when fsS f is

not subtracted prior to the artifact removal execution. Recall that this strategy has been proved to be extremely relevant, because it removes the antenna internal reflections, thus

the skin backscatter. The 20.

characterization strategies is not used, while the other are considered.


No

-

-

-

-

-


No

-

-

-

-

-


No

-

-

-

-

-




It is evident that there is a deterioration of the resultsthe tumor is not detectedverified for the BAVA and VIIartifact removal. We note that most artifact removals in the literature rely on the accurate identification of the skin backscattering. Therefore, these results should not be only expectable with the present algorithm, but ratheralgorithms.

We now analyze how the imaging results improve when the angular variation of the pseudo nearϕ), is not compensated. The results using in

In order to grasp the improvement obtained with the compensation of the “near field phase center”, the results in Fig. (alternatively, the reader may compare TABLE of 0.calibrating the angular dispersion of the “nearcenter” is more evident, since it presents the greatest dispersion of tindicate that the prior calibration of the pseudo phase ceand its angular dispersionquality of the final image.

Lastly, we evaluated the impact of not calibrating the offset length introduced by the antenna. TXETS are presented in

Fig. space input reflection coeffprior to artifact removal execution: (a) contours identify the breast limits and the tumor container.

Fig. variation of the near(a) and the tumor container.


It is evident that there is a deterioration of the resultsthe tumor is not detectedverified for the BAVA and VII). This is easily explained by tartifact removal. We note that most artifact removals in the literature rely on the accurate identification of the skin backscattering. Therefore, these results should not be only expectable with the present algorithm, but ratheralgorithms.

We now analyze how the imaging results improve when the angular variation of the pseudo near

), is not compensated. The results using Fig. 21.

In order to grasp the improvement obtained with the compensation of the “near field phase center”, the results in Fig. 21 should be compared with the ones in (alternatively, the reader may compare TABLE VII). Focusing on TCR of 0.2 dB using calibrating the angular dispersion of the “nearcenter” is more evident, since it presents the greatest dispersion of the three antennas (indicate that the prior calibration of the pseudo phase ceand its angular dispersionquality of the final image.

Lastly, we evaluated the impact of not calibrating the offset length introduced by the antenna. TXETS are presented in

Fig. 20: Imaging results of the breast obtained with space input reflection coeffprior to artifact removal execution: (a) contours identify the breast limits and the tumor container.

Fig. 21: Imaging results of the breast obtained with variation of the near-(a) z = -28 mm; (b) xand the tumor container.


It is evident that there is a deterioration of the resultsthe tumor is not detected. The imaging deterioration is verified for the BAVA and monopole

This is easily explained by tartifact removal. We note that most artifact removals in the literature rely on the accurate identification of the skin backscattering. Therefore, these results should not be only expectable with the present algorithm, but rather

We now analyze how the imaging results improve when the angular variation of the pseudo near

), is not compensated. The results using

In order to grasp the improvement obtained with the compensation of the “near field phase center”, the results in

should be compared with the ones in (alternatively, the reader may compare

). Focusing on TCR using the XETS. With the monopole the benefit of

calibrating the angular dispersion of the “nearcenter” is more evident, since it presents the greatest

he three antennas (indicate that the prior calibration of the pseudo phase ceand its angular dispersion may indeed be used to improvequality of the final image.

Lastly, we evaluated the impact of not calibrating the offset length introduced by the antenna. TXETS are presented in Fig. 22.

Imaging results of the breast obtained with space input reflection coefficient is not subtracted to the measured signals prior to artifact removal execution: (a) contours identify the breast limits and the tumor container.

Imaging results of the breast obtained with -field phase center with angle, Δ = -14 mm. The white contours identify the breast limits

and the tumor container.


It is evident that there is a deterioration of the results. The imaging deterioration is

monopole antennaThis is easily explained by the poor performance of the

artifact removal. We note that most artifact removals in the literature rely on the accurate identification of the skin backscattering. Therefore, these results should not be only expectable with the present algorithm, but rather

We now analyze how the imaging results improve when the angular variation of the pseudo near-field phase center, Δ

), is not compensated. The results using XETS


should be compared with the ones in (alternatively, the reader may compare TABLE

). Focusing on TCR we notice slightWith the monopole the benefit of

calibrating the angular dispersion of the “nearcenter” is more evident, since it presents the greatest

he three antennas (Fig. 13 (b)). indicate that the prior calibration of the pseudo phase ce

may indeed be used to improve

Lastly, we evaluated the impact of not calibrating the offset length introduced by the antenna. The imaging results with the

Imaging results of the breast obtained with the XETS when freeicient is not subtracted to the measured signals

prior to artifact removal execution: (a) z = -48 mm; (b) xcontours identify the breast limits and the tumor container.

Imaging results of the breast obtained with the XETS when the field phase center with angle, Δρ(θ,

The white contours identify the breast limits


It is evident that there is a deterioration of the results, since . The imaging deterioration is also

antennas (see TABLE he poor performance of the

artifact removal. We note that most artifact removals in the literature rely on the accurate identification of the skin backscattering. Therefore, these results should not be only expectable with the present algorithm, but rather with most

We now analyze how the imaging results improve when the field phase center, Δdρ

XETS are illustrated


should be compared with the ones in Fig. TABLE VI and

slight improvement With the monopole the benefit of

calibrating the angular dispersion of the “near-field phase center” is more evident, since it presents the greatest

(b)). These results indicate that the prior calibration of the pseudo phase center

may indeed be used to improve

Lastly, we evaluated the impact of not calibrating the offset he imaging results with the

the XETS when freeicient is not subtracted to the measured signals

x = -4 mm. The white contours identify the breast limits and the tumor container.

the XETS when the , ϕ), is not calibrated:



, since

also TABLE

he poor performance of the artifact removal. We note that most artifact removals in the literature rely on the accurate identification of the skin backscattering. Therefore, these results should not be only

with most

We now analyze how the imaging results improve when the

ρ(θ, are illustrated

In order to grasp the improvement obtained with the

compensation of the “near field phase center”, the results in Fig. 19

and improvement

With the monopole the benefit of field phase

center” is more evident, since it presents the greatest These results

nter the

Lastly, we evaluated the impact of not calibrating the offset he imaging results with the

In the absence of this calibrationand, therefore, the tumor is not detected. In fact, this was verified with all three antennasresults demonstrate the importance antenna used fo

From these results we conclude that BAVA and XETS present similar imaging performance underconditions. Yet, the monopole is much more susceptible to any slight modification in the measurement setup, particularly if there are intense

Lastly, we note that although we have illustrated our methods using a sysliquid, the methods are also suitable for systems that use contact liquid. In these cases, the antennas must be characterized inside the same liquid as the one intended for the examination, in the absence of any backscatintroduce clutter in the signals.

Microwave imaging has shown great potential for biomedical applications, such as breast cancer screening or brain hemorrhage detection. One of the elements with most influence on the performanceantenna. In fact, as a nondistortion and clutter to the measured signals. Here, we show how to take advantage of proper antenna calibration, as to improve the imaging performance of the overall sythis end, we perform a detailed study of the antennas and remove some of the adverse effects introduced by it. Although the study is based on experimental signals that were measured using the microwave breast imaging setup we have developed, the results can be extended to other MMWI applications.

Firstly, we input reflection coefficient to the signals in the presence of the body is effective in inside the antenstrategy introduces nearoriginated inside the body. This conclusion is valid, as long as the antenna is immune to the presence of the body, which we proved is reasonably true.

Secondly, we proposed a technique to determine that average nearplanar acquisition data set. From the same measurement setup, we characterized the dependence of the phase center on the angle of incidence.

the XETS when free-icient is not subtracted to the measured signals

The white

the XETS when the ), is not calibrated:


Fig. 22: Imaging results of the breast obtained with length introduced by the antenna is not calibrated: (a) mm. The white contours identify the breast limits and the tumor container.


In the absence of this calibrationand, therefore, the tumor is not detected. In fact, this was verified with all three antennasresults demonstrate the importance antenna used for MMW

rom these results we conclude that BAVA and XETS present similar imaging performance underconditions. Yet, the monopole is much more susceptible to any slight modification in the measurement setup, particularly if there are intense currents on the feeding cable.

Lastly, we note that although we have illustrated our methods using a sysliquid, the methods are also suitable for systems that use contact liquid. In these cases, the antennas must be characterized inside the same liquid as the one intended for the examination, in the absence of any backscatintroduce clutter in the signals.

Microwave imaging has shown great potential for biomedical applications, such as breast cancer screening or brain hemorrhage detection. One of the elements with most influence on the performanceantenna. In fact, as a nondistortion and clutter to the measured signals. Here, we show how to take advantage of proper antenna calibration, as to improve the imaging performance of the overall sythis end, we perform a detailed study of the antennas and remove some of the adverse effects introduced by it. Although the study is based on experimental signals that were measured using the microwave breast imaging setup we have developed,

esults can be extended to other MMWI applications.Firstly, we demonstrated that subtracting the free

input reflection coefficient to the signals in the presence of the body is effective in reducing the internal reflections occurring inside the antenna structure. strategy introduces nearoriginated inside the body. This conclusion is valid, as long as the antenna is immune to the presence of the body, which we proved is reasonably true.

Secondly, we proposed a technique to determine that average near-field phase center along frequency, based on a planar acquisition data set. From the same measurement setup, we characterized the dependence of the phase center on the angle of incidence.

Imaging results of the breast obtained with length introduced by the antenna is not calibrated: (a)

The white contours identify the breast limits and the tumor container.


In the absence of this calibration, the energy does not focus and, therefore, the tumor is not detected. In fact, this was verified with all three antennas (see results demonstrate the importance

r MMWI. rom these results we conclude that BAVA and XETS

present similar imaging performance underconditions. Yet, the monopole is much more susceptible to any slight modification in the measurement setup, particularly if

currents on the feeding cable.Lastly, we note that although we have illustrated our

methods using a system that does not require immersion liquid, the methods are also suitable for systems that use contact liquid. In these cases, the antennas must be characterized inside the same liquid as the one intended for the examination, in the absence of any backscatintroduce clutter in the signals.

VII. CONCLUSION

Microwave imaging has shown great potential for biomedical applications, such as breast cancer screening or brain hemorrhage detection. One of the elements with most influence on the performance of the overall system is the antenna. In fact, as a non-ideal element, it introduces distortion and clutter to the measured signals. Here, we show how to take advantage of proper antenna calibration, as to improve the imaging performance of the overall sythis end, we perform a detailed study of the antennas and remove some of the adverse effects introduced by it. Although the study is based on experimental signals that were measured using the microwave breast imaging setup we have developed,

esults can be extended to other MMWI applications.demonstrated that subtracting the free

input reflection coefficient to the signals in the presence of the reducing the internal reflections occurring

na structure. Moreover, wstrategy introduces near-zero distortion to the backscatters originated inside the body. This conclusion is valid, as long as the antenna is immune to the presence of the body, which we proved is reasonably true.

Secondly, we proposed a technique to determine that field phase center along frequency, based on a

planar acquisition data set. From the same measurement setup, we characterized the dependence of the phase center on the

Imaging results of the breast obtained with length introduced by the antenna is not calibrated: (a)



, the energy does not focus and, therefore, the tumor is not detected. In fact, this was

(see TABLE results demonstrate the importance of characterizing the

rom these results we conclude that BAVA and XETS present similar imaging performance under conditions. Yet, the monopole is much more susceptible to any slight modification in the measurement setup, particularly if

currents on the feeding cable. Lastly, we note that although we have illustrated our

tem that does not require immersion liquid, the methods are also suitable for systems that use contact liquid. In these cases, the antennas must be characterized inside the same liquid as the one intended for the examination, in the absence of any backscatterer that might

ONCLUSION

Microwave imaging has shown great potential for biomedical applications, such as breast cancer screening or brain hemorrhage detection. One of the elements with most

of the overall system is the ideal element, it introduces

distortion and clutter to the measured signals. Here, we show how to take advantage of proper antenna calibration, as to improve the imaging performance of the overall sythis end, we perform a detailed study of the antennas and remove some of the adverse effects introduced by it. Although the study is based on experimental signals that were measured using the microwave breast imaging setup we have developed,

esults can be extended to other MMWI applications.demonstrated that subtracting the free


Moreover, we showedzero distortion to the backscatters

originated inside the body. This conclusion is valid, as long as the antenna is immune to the presence of the body, which we



Imaging results of the breast obtained with the XETS when offset length introduced by the antenna is not calibrated: (a) z = -26 mm; (b)



, the energy does not focus

and, therefore, the tumor is not detected. In fact, this was TABLE VII). These

of characterizing the

rom these results we conclude that BAVA and XETS the same

conditions. Yet, the monopole is much more susceptible to any slight modification in the measurement setup, particularly if

Lastly, we note that although we have illustrated our tem that does not require immersion

liquid, the methods are also suitable for systems that use contact liquid. In these cases, the antennas must be characterized inside the same liquid as the one intended for the

terer that might

Microwave imaging has shown great potential for biomedical applications, such as breast cancer screening or brain hemorrhage detection. One of the elements with most

of the overall system is the ideal element, it introduces

distortion and clutter to the measured signals. Here, we show how to take advantage of proper antenna calibration, as to improve the imaging performance of the overall system. To this end, we perform a detailed study of the antennas and remove some of the adverse effects introduced by it. Although the study is based on experimental signals that were measured using the microwave breast imaging setup we have developed,

esults can be extended to other MMWI applications. demonstrated that subtracting the free-space


showed that this zero distortion to the backscatters

originated inside the body. This conclusion is valid, as long as the antenna is immune to the presence of the body, which we



the XETS when offset 26 mm; (b) x = 26





13

The third calibration procedure we have addressed concerns the offset distance introduced by the propagation of currents. This is absolutely essential in MWI systems, since it directly affects the focusing of the imaging algorithm, which involves distance calculations. Moreover, we showed that the offset distance exhibits dependence on frequency. The proposed calibration method consists of measuring the transmission coefficient of the antennas from which the offset length is inferred.

We applied the calibration strategies to three antenna topologies (BAVA, planar monopole and slot-based antennas) and imaged the breast. The results show very good focusing by all three antennas, proving the calibration methods are effective and do not influence the tumor response. We have demonstrated that the calibration strategies improve the image quality significantly. In fact, we showed that removing the internal reflections of the antenna is absolutely essential and so is the calibration of the equivalent length introduced by the currents for the imaging focusing. Moreover, we proved that the angular characterization of the “phase center” is an effective technique to take advantage of prior knowledge about the antenna and improve the image focusing. Lastly, the results suggest that the proposed techniques are effective when applied to any antenna, if the latter exhibits coherent performance in the presence of the body. This last point is extremely important, since, as we have shown, the imaging results are significantly affected by the feeding cable, as was the case of the monopole. Lastly, the balanced structure of the XETS antenna presented slightly better imaging results, although the dimensions of the XETS do not allow stacking as many sensors around the breast, as would be desired. We plan to extend the methods presented here to multistatic systems.

ACKNOWLEDGMENT

The authors are grateful to António Almeida for his collaboration in the measurements and to Jorge Farinha and Carlos Brito for the setup and prototypes manufacturing.

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[30]“Performance Antennas Wirelles[31]measuring small planar Status and[32]crossed exponentially tapered slot antenna for UWB systems,” Antennas Propag.[33]“Review of 20 years of research on microwave and millimeter‘Instituto de Telecomunicaçõ1, pp. 249

1990. He received the Licenciado and Master degreesComputer Engineering from the Instituto Superior Técnico (IST), University of Lisbon, Lisbon, Portugal, in 2013 and 2014, respectiHe is currently working towards his PhD at IST, Lisbon, Portugal, while doing research at Instituto de Telecomunicações, Lisbon. His main interests include Microwave Imaging, antennaapplications.

the EE, MSc, PhD, and Habilitation degrees in electrical andengineerLisboa (now Universidade de Lisboa),2007, respectively. Since 1995, heand Computer Engineering,problemsResearcherTelecomunicações, which is a private nonHis research interests include inverse problems, signal and imagepattern recognition, optimization, and remote sensing.scientific contributions in the areas ofimage processing, optimization,various imaging applications,was included in Treceived the


[30] M. Koohestani, N. Pires, A. K. Skrivervik, and A. A. Moreira, “Performance study of Antennas Wirelless Propag. Lett.[31] L. Liu, S.W. Cheungmeasuring small planar Status and Future Trends[32] J. R. Costa, C. R. Medeiros, and C. A. Fernandes, “Performance of a crossed exponentially tapered slot antenna for UWB systems,” Antennas Propag., vol. 57, no. 5, pp. 1345[33] C. A. Fernandes, J. R. Costa, E. B. Lima, and M. G. Silveirinha, “Review of 20 years of research on microwave and millimeter‘Instituto de Telecomunicaçõ1, pp. 249–268, Feb. 2015.

João M. Felício 1990. He received the Licenciado and Master degreesComputer Engineering from the Instituto Superior Técnico (IST), University of Lisbon, Lisbon, Portugal, in 2013 and 2014, respectiHe is currently working towards his PhD at IST, Lisbon, Portugal, while doing research at Instituto de Telecomunicações, Lisbon. His main interests include Microwave Imaging, antennaapplications.

José M. Bioucathe EE, MSc, PhD, and Habilitation degrees in electrical andengineering from Instituto Superior TéLisboa (now Universidade de Lisboa),2007, respectively. Since 1995, heand Computer Engineering,problems in imaging and electric communications. He is also a Senior Researcher with the Pattern and ImTelecomunicações, which is a private nonHis research interests include inverse problems, signal and imagepattern recognition, optimization, and remote sensing.scientific contributions in the areas ofimage processing, optimization,various imaging applications,was included in Thomsonreceived the IEEE GRSS David Landgrebe Award for 2017.


M. Koohestani, N. Pires, A. K. Skrivervik, and A. A. Moreira, study of a UWB antenna in proximity to a human arm

Propag. Lett., vol. 12, pp. 555L. Liu, S.W. Cheung, Y.F. Weng and T.I. Yuk,

measuring small planar UWB monopole antennasFuture Trends, Dr. Mohammad Matin (E

J. R. Costa, C. R. Medeiros, and C. A. Fernandes, “Performance of a crossed exponentially tapered slot antenna for UWB systems,”

, vol. 57, no. 5, pp. 1345C. A. Fernandes, J. R. Costa, E. B. Lima, and M. G. Silveirinha,

“Review of 20 years of research on microwave and millimeter‘Instituto de Telecomunicações’,” IEEE Antennas Propag. Mag.

268, Feb. 2015.

João M. Felício (S’14) was born in Lisbon, Portugal, in 1990. He received the Licenciado and Master degreesComputer Engineering from the Instituto Superior Técnico (IST), University of Lisbon, Lisbon, Portugal, in 2013 and 2014, respectiHe is currently working towards his PhD at IST, Lisbon, Portugal, while doing research at Instituto de Telecomunicações, Lisbon. His main interests include Microwave Imaging, antenna

José M. Bioucas-Diasthe EE, MSc, PhD, and Habilitation degrees in electrical and

ing from Instituto Superior TéLisboa (now Universidade de Lisboa),2007, respectively. Since 1995, he has been with the Department of Electrical and Computer Engineering, IST, where he is a Professor and teaches inverse

in imaging and electric communications. He is also a Senior with the Pattern and Image Analysis group of the Instituto de

Telecomunicações, which is a private nonHis research interests include inverse problems, signal and imagepattern recognition, optimization, and remote sensing.scientific contributions in the areas ofimage processing, optimization, phase estimation, phase unwrapping, and in various imaging applications, such as hyp

homson Reuters' Highly Cited Researchers 2015 list and IEEE GRSS David Landgrebe Award for 2017.


M. Koohestani, N. Pires, A. K. Skrivervik, and A. A. Moreira, a UWB antenna in proximity to a human arm

, vol. 12, pp. 555-558, 2013., Y.F. Weng and T.I. Yuk,

monopole antennas,” Ultra Wideband , Dr. Mohammad Matin (Ed.), InTech

J. R. Costa, C. R. Medeiros, and C. A. Fernandes, “Performance of a crossed exponentially tapered slot antenna for UWB systems,”

, vol. 57, no. 5, pp. 1345-1352, May 2009.C. A. Fernandes, J. R. Costa, E. B. Lima, and M. G. Silveirinha,

“Review of 20 years of research on microwave and millimeterIEEE Antennas Propag. Mag.

(S’14) was born in Lisbon, Portugal, in 1990. He received the Licenciado and Master degreesComputer Engineering from the Instituto Superior Técnico (IST), University of Lisbon, Lisbon, Portugal, in 2013 and 2014, respectively.He is currently working towards his PhD at IST, Lisbon, Portugal, while doing research at Instituto de Telecomunicações, Lisbon. His main interests include Microwave Imaging, antenna design and antennas for biomedical

Dias (S’87–M’95–SM’15the EE, MSc, PhD, and Habilitation degrees in electrical and

ing from Instituto Superior Técnico (IST), Universidade TéLisboa (now Universidade de Lisboa), Portugal, in 1985, 1991, 1995, and

has been with the Department of Electrical IST, where he is a Professor and teaches inverse

in imaging and electric communications. He is also a Senior age Analysis group of the Instituto de

Telecomunicações, which is a private non-profit research institution.His research interests include inverse problems, signal and imagepattern recognition, optimization, and remote sensing.scientific contributions in the areas of imaging inverse problems, statistical

phase estimation, phase unwrapping, and in such as hyperspectral and radar imaging.

Reuters' Highly Cited Researchers 2015 list and IEEE GRSS David Landgrebe Award for 2017.


M. Koohestani, N. Pires, A. K. Skrivervik, and A. A. Moreira, a UWB antenna in proximity to a human arm,” IEEE

558, 2013. , Y.F. Weng and T.I. Yuk, “Cable effects on

Ultra Wideband - Current d.), InTech, 2012.

J. R. Costa, C. R. Medeiros, and C. A. Fernandes, “Performance of a crossed exponentially tapered slot antenna for UWB systems,” IEEE Trans.

1352, May 2009. C. A. Fernandes, J. R. Costa, E. B. Lima, and M. G. Silveirinha,

“Review of 20 years of research on microwave and millimeter-wave lensesIEEE Antennas Propag. Mag., vol. 57, no.

(S’14) was born in Lisbon, Portugal, in 1990. He received the Licenciado and Master degrees in Electrical and Computer Engineering from the Instituto Superior Técnico (IST), University

vely. He is currently working towards his PhD at IST, Lisbon, Portugal, while doing research at Instituto de Telecomunicações, Lisbon. His main interests

and antennas for biomedical

SM’15–F’17) received the EE, MSc, PhD, and Habilitation degrees in electrical and computer

Universidade Técnica de Portugal, in 1985, 1991, 1995, and

has been with the Department of Electrical IST, where he is a Professor and teaches inverse

in imaging and electric communications. He is also a Senior age Analysis group of the Instituto de

profit research institution. His research interests include inverse problems, signal and image processing, pattern recognition, optimization, and remote sensing. He has introduced

imaging inverse problems, statistical phase estimation, phase unwrapping, and in

erspectral and radar imaging.Reuters' Highly Cited Researchers 2015 list and

IEEE GRSS David Landgrebe Award for 2017.


M. Koohestani, N. Pires, A. K. Skrivervik, and A. A. Moreira, IEEE

effects on Current

J. R. Costa, C. R. Medeiros, and C. A. Fernandes, “Performance of a IEEE Trans.

C. A. Fernandes, J. R. Costa, E. B. Lima, and M. G. Silveirinha, wave lenses at

, vol. 57, no.

(S’14) was born in Lisbon, Portugal, in Electrical and

Computer Engineering from the Instituto Superior Técnico (IST), University

He is currently working towards his PhD at IST, Lisbon, Portugal, while doing research at Instituto de Telecomunicações, Lisbon. His main interests

and antennas for biomedical

received computer cnica de

Portugal, in 1985, 1991, 1995, and has been with the Department of Electrical

IST, where he is a Professor and teaches inverse in imaging and electric communications. He is also a Senior

age Analysis group of the Instituto de

processing, introduced

imaging inverse problems, statistical phase estimation, phase unwrapping, and in

erspectral and radar imaging. He Reuters' Highly Cited Researchers 2015 list and

Portugal, in 1974. He received the Licenciado and Ph.D. degrees in electrical and computerTechnical University of Lisbon, Lisbon, Portugal, in 1997 and 2002, respectively.He is currently a Researcher at the Instituto de Telecomunicações, Lisbon, Portugal. He is also an Associate ProfessorTecnologias da Informação, Instituto Universitário de Lisboa (ISCTEHis present research interests include lenses, reconfigurable antennas, MEMS switches, UWB, MIMO and RFID antennas. He is the coauthor of four pateapplications and more than 150 contributions to peer reviewed journals and international conference proceedings. More than thirty of these papers have appeared in IEEE Journals. Prof. Costa served as an Associate Editor for the IEEE Transactions on Antewas a Guest Editor of the Special Issue on “Antennas and Propagation at mmand Sub mmPropagation, April 2013. He was the CoCommittee of the European Conference on Antennas and Propagation (EuCAP 2015) in Lisbon and General Vice

Licenciado, MSc, and PhD degrees in Electrical and Computer Engineerifrom Instituto Superior Técnico (IST), Technical University of Lisbon, Lisbon, Portugal, in 1980, 1985, and 1990, respectively. He joined IST in 1980, where he is presently Full Professor at the Department of Electrical and Computer Engineering in the aand antennas. He is a senior researcher at the Instituto de Telecomunicações and member of the Board of Directors. He has cochapter, more than 180 technical papers in peer reviewed internajournals and conference proceedings and 7 patents in the areas of antennas and radiowave propagation modeling. His current research interests include dielectric antennas for millimeter wave applications, antennas and propagation modeling for personaartificial dielectrics and metamaterials. He was a Guest Editor of the Special Issue on “Antennas and Propagation at mmIEEE Transactions on Antennas and Propagation, April 2013


Jorge R. CostPortugal, in 1974. He received the Licenciado and Ph.D. degrees in electrical and computer engineering from the Instituto Superior Técnico (IST), Technical University of Lisbon, Lisbon, Portugal, in 1997 and 2002, respectively. He is currently a Researcher at the Instituto de Telecomunicações, Lisbon, Portugal. He is also an Associate ProfessorTecnologias da Informação, Instituto Universitário de Lisboa (ISCTEHis present research interests include lenses, reconfigurable antennas, MEMS switches, UWB, MIMO and RFID antennas. He is the coauthor of four pateapplications and more than 150 contributions to peer reviewed journals and international conference proceedings. More than thirty of these papers have appeared in IEEE Journals. Prof. Costa served as an Associate Editor for the IEEE Transactions on Antewas a Guest Editor of the Special Issue on “Antennas and Propagation at mmand Sub mm-Waves”, from the IEEE Transactions on Antennas and Propagation, April 2013. He was the Co

mmittee of the European Conference on Antennas and Propagation (EuCAP 2015) in Lisbon and General Vice

Carlos A. FernandesLicenciado, MSc, and PhD degrees in Electrical and Computer Engineerifrom Instituto Superior Técnico (IST), Technical University of Lisbon, Lisbon, Portugal, in 1980, 1985, and 1990, respectively. He joined IST in 1980, where he is presently Full Professor at the Department of Electrical and Computer Engineering in the aand antennas. He is a senior researcher at the Instituto de Telecomunicações and member of the Board of Directors. He has cochapter, more than 180 technical papers in peer reviewed internajournals and conference proceedings and 7 patents in the areas of antennas and radiowave propagation modeling. His current research interests include dielectric antennas for millimeter wave applications, antennas and propagation modeling for personal communication systems, RFID and UWB antennas, artificial dielectrics and metamaterials. He was a Guest Editor of the Special Issue on “Antennas and Propagation at mmIEEE Transactions on Antennas and Propagation, April 2013


Jorge R. Costa (S’97–M’03Portugal, in 1974. He received the Licenciado and Ph.D. degrees in electrical

engineering from the Instituto Superior Técnico (IST), Technical University of Lisbon, Lisbon, Portugal, in 1997 and 2002,

He is currently a Researcher at the Instituto de Telecomunicações, Lisbon, Portugal. He is also an Associate Professor at the Departamento de Ciências e Tecnologias da Informação, Instituto Universitário de Lisboa (ISCTEHis present research interests include lenses, reconfigurable antennas, MEMS switches, UWB, MIMO and RFID antennas. He is the coauthor of four pateapplications and more than 150 contributions to peer reviewed journals and international conference proceedings. More than thirty of these papers have appeared in IEEE Journals. Prof. Costa served as an Associate Editor for the IEEE Transactions on Antennas and Propagation from 2010 to 2016 and he was a Guest Editor of the Special Issue on “Antennas and Propagation at mm

Waves”, from the IEEE Transactions on Antennas and Propagation, April 2013. He was the Co-Chair of the Technical Program

mmittee of the European Conference on Antennas and Propagation (EuCAP 2015) in Lisbon and General Vice-Chair of EuCAP 2017 in Paris.

Carlos A. Fernandes (S’86Licenciado, MSc, and PhD degrees in Electrical and Computer Engineerifrom Instituto Superior Técnico (IST), Technical University of Lisbon, Lisbon, Portugal, in 1980, 1985, and 1990, respectively. He joined IST in 1980, where he is presently Full Professor at the Department of Electrical and Computer Engineering in the areas of microwaves, radio wave propagation and antennas. He is a senior researcher at the Instituto de Telecomunicações and member of the Board of Directors. He has cochapter, more than 180 technical papers in peer reviewed internajournals and conference proceedings and 7 patents in the areas of antennas and radiowave propagation modeling. His current research interests include dielectric antennas for millimeter wave applications, antennas and propagation

l communication systems, RFID and UWB antennas, artificial dielectrics and metamaterials. He was a Guest Editor of the Special Issue on “Antennas and Propagation at mm-IEEE Transactions on Antennas and Propagation, April 2013


M’03–SM’09) was born in Lisbon, Portugal, in 1974. He received the Licenciado and Ph.D. degrees in electrical


He is currently a Researcher at the Instituto de Telecomunicações, Lisbon, at the Departamento de Ciências e

Tecnologias da Informação, Instituto Universitário de Lisboa (ISCTEHis present research interests include lenses, reconfigurable antennas, MEMS switches, UWB, MIMO and RFID antennas. He is the coauthor of four pateapplications and more than 150 contributions to peer reviewed journals and international conference proceedings. More than thirty of these papers have appeared in IEEE Journals. Prof. Costa served as an Associate Editor for the

nnas and Propagation from 2010 to 2016 and he was a Guest Editor of the Special Issue on “Antennas and Propagation at mm

Waves”, from the IEEE Transactions on Antennas and Chair of the Technical Program

mmittee of the European Conference on Antennas and Propagation Chair of EuCAP 2017 in Paris.

(S’86–M’89–SM’08) received the Licenciado, MSc, and PhD degrees in Electrical and Computer Engineerifrom Instituto Superior Técnico (IST), Technical University of Lisbon, Lisbon, Portugal, in 1980, 1985, and 1990, respectively. He joined IST in 1980, where he is presently Full Professor at the Department of Electrical and

reas of microwaves, radio wave propagation and antennas. He is a senior researcher at the Instituto de Telecomunicações and member of the Board of Directors. He has co-authored a book, 2 book chapter, more than 180 technical papers in peer reviewed internajournals and conference proceedings and 7 patents in the areas of antennas and radiowave propagation modeling. His current research interests include dielectric antennas for millimeter wave applications, antennas and propagation

l communication systems, RFID and UWB antennas, artificial dielectrics and metamaterials. He was a Guest Editor of the Special

- and Sub mm-Waves”, from the IEEE Transactions on Antennas and Propagation, April 2013.


SM’09) was born in Lisbon, Portugal, in 1974. He received the Licenciado and Ph.D. degrees in electrical


He is currently a Researcher at the Instituto de Telecomunicações, Lisbon, at the Departamento de Ciências e

Tecnologias da Informação, Instituto Universitário de Lisboa (ISCTE-IUL). His present research interests include lenses, reconfigurable antennas, MEMS switches, UWB, MIMO and RFID antennas. He is the coauthor of four patent applications and more than 150 contributions to peer reviewed journals and international conference proceedings. More than thirty of these papers have appeared in IEEE Journals. Prof. Costa served as an Associate Editor for the

nnas and Propagation from 2010 to 2016 and he was a Guest Editor of the Special Issue on “Antennas and Propagation at mm-

Waves”, from the IEEE Transactions on Antennas and Chair of the Technical Program

mmittee of the European Conference on Antennas and Propagation Chair of EuCAP 2017 in Paris.

SM’08) received the Licenciado, MSc, and PhD degrees in Electrical and Computer Engineering from Instituto Superior Técnico (IST), Technical University of Lisbon, Lisbon, Portugal, in 1980, 1985, and 1990, respectively. He joined IST in 1980, where he is presently Full Professor at the Department of Electrical and

reas of microwaves, radio wave propagation and antennas. He is a senior researcher at the Instituto de Telecomunicações

authored a book, 2 book chapter, more than 180 technical papers in peer reviewed international journals and conference proceedings and 7 patents in the areas of antennas and radiowave propagation modeling. His current research interests include dielectric antennas for millimeter wave applications, antennas and propagation

l communication systems, RFID and UWB antennas, artificial dielectrics and metamaterials. He was a Guest Editor of the Special

Waves”, from the

Documents

Antenna Design and Near-field Characterization for Medical ...bioucas/files/ieee_tap_2019_ant_mw.pdfantenna topologies used for MMWI: a Vivaldi-type antenna, a broadband planar monopole