Abstract. The far-field behavior of an antenna under test(AUT) can be obtained by exciting the AUT with a planewave. In a measurement, it is sufficient if the plane wave isartificially generated in the vicinity of the AUT. This can beachieved by using a virtual antenna array formed by a probeantenna which is sequentially sampling the radiating near-field of the AUT at different positions. For this purpose, anoptimal filter for the virtual antenna array is computed in apreprocessing step. Applying this filter to the near-field mea-surements, the far-field of the AUT is obtained according tothe propagation direction and polarization of the synthesizedplane wave. This means that the near-field far-field transfor-mation (NFFFT) is achieved simply by filtering the near-fieldmeasurement data. Taking the radiation characteristic of theprobe antenna into account during the synthesis process, itsinfluence on the NFFFT is compensated.
The principle of the plane-wave synthesis and its applica-tion to the NFFFT is presented in detail in this paper. Further-more, the method is verified by performing transformationsof simulated near-field measurement data and of near-fielddata measured in an anechoic chamber.
1 Introduction
Today’s wireless communication, radar or direction findingsystems make use of electrically large antennas like parabolicreflectors or antenna arrays to generate far-field radiationcharacteristics suitable for the particular application. Afterfabrication the far-field of the antenna under test has to beexamined by measurements to verify that it meets the re-quirements on phase and magnitude. Due to the large sizeof the antenna relative to wavelength, an accurate measure-ment under far-field conditions inside an anechoic chambercan hardly be accomplished, simply because of the enormousmeasurement distance required. Thus, performing measure-
ments in a reduced distance in the radiating near-field regionof the AUT and subsequently applying a near-field far-field(NFFF) transformation is an attractive alternative.
The radiated fields of the AUT and the probe are usu-ally represented by a truncated series of orthogonal spheri-cal, cylindrical or planar field modes to formulate a transmis-sion equation describing the coupling between both antennas(Hansen, 1988). Solving this equation for the modal coeffi-cients the far-field can be computed by evaluating the fieldmodes for the radial distance going to infinity.
For the plane-wave synthesis approach (Hansen, 1988; Ya-maguchi et al., 2009; Bennett and Schoessow, 1978), there isno explicit transmission equation needed. The probe whichis sampling the near-field successively at different locationsis considered to form a virtual array of probe antennas on ameasurement surface. This array is then used to synthesizea plane wave in the vicinity of the AUT through a weightedsuperposition of the fields radiated by the elements of thevirtual probe antenna array. The appropriate weights form afilter which is gained from the solution of an inverse problem.
The proposed method allows shifting most of the compu-tational expense of the NFFF transformation and probe cor-rection to a preprocessing step whose result is a set of filterscontaining the weighting factors for the probe signals. Thesefilters are used to compute the far-field directly from the ac-quired measurement data in a near-field far-field transforma-tion step.
The paper is structured as follows: in the following partthe principle and the results of the plane-wave synthesis isshown. How the synthesis is employed for near-field far-fieldtransformation is given in the third part. In the forth part, themethod is applied to simulated and real near-field measure-ment data of a Yagi-Uda and a patch antenna. The results ofthe transformation together with some accuracy considera-tions are presented.
Published by Copernicus Publications on behalf of the URSI Landesausschuss in der Bundesrepublik Deutschland e.V.
48 R. A. M. Mauermayer and T. F. Eibert: A fully probe corrected NFFFT technique employing plane-wave synthesis
2 The probe corrected plane-wave synthesis
2.1 Principle
The principle of the synthesis of plane waves by a virtual ar-ray of probes which are positioned at different locations inthe near-field of the AUT is visualized in Fig.1. The probes
are excited according to the filter vectorw(k,E0
), which
consists ofN complex coefficients, one for each probe posi-tion and polarization orientation. The objective is to generatethe field of the plane wave
Epl (r) = E0e−jkk·r (1)
H pl (r) =1
Z0k × Epl (r) (2)
in the vicinity of the AUT by superimposing the probe fields.The propagation direction of the plane wave is described bythe unit vectork and its polarization is given by the electricfield vectorE0. Z0 describes the free space wave impedance.
The virtual array is equivalent to a probe antenna withideal polarization purity positioned in the far-field of theAUT in direction −k and exciting the AUT with a quasiplane-wave field with the same polarization as the synthe-
sized plane wave. The power wavebFF1
(k,E0
)at the feed
point of the AUT in Fig.1 is proportional to this far-fieldmeasurement.
For the wave field synthesis process inside a volume, theAUT is enclosed by a Huygens’ surface. A filter must befound that enables the synthesis of the tangential field com-ponents of the desired plane wave on the surface. The unique-ness theorem (Harrington, 2001) guarantees that if the super-imposed tangential field components of the virtual probe ar-ray correspond to those of the plane wave, the plane-wavefield is also present inside the source free test volume.
The probe antenna is modeled by its equivalent electricJ n
(r ′
)and magneticMn
(r ′
)surface currents located at the
n-th probe sampling position. Its characteristic electromag-netic field is computed from the surface integrals
En (r) =
∫∫A
[GE
J
(r,r ′
)· J n
(r ′
)+ GE
M
(r,r ′
)· Mn
(r ′
)]dA′ (3)
H n (r) =
∫∫A
[GH
J
(r,r ′
)· J n
(r ′
)+ GH
M
(r,r ′
)· Mn
(r ′
)]dA′, (4)
whereGE/HJ/M
(r,r ′
)are the dyadic Greens’ functions for free
space. The tangential components of the probe field are sam-pled at discrete locationsr i (i = 1, . . . , I ) on the Huygens’surface. In order to avoid the excitation of resonance modes
2 R. A. M. Mauermayer and T. F. Eibert: A Fully Probe Corrected NFFFT Technique Employing Plane-Wave Synthesis
2 The probe corrected plane-wave synthesis70
2.1 Principle
The principle of the synthesis of plane waves by a virtual ar-
ray of probes which are positioned at different locations in
the near-field of the AUT is visualized in Fig. 1. The probes
are excited according to the filter vector w(
k,E0
)
, which
consists of N complex coefficients, one for each probe posi-
tion and polarization orientation. The objective is to generate
the field of the plane wave
Epl(r)=E0e−jkk·r (1)
Hpl(r)=1
Z0k×Epl(r) (2)
in the vicinity of the AUT by superimposing the probe fields.
The propagation direction of the plane wave is described by
the unit vector k and its polarization is given by the electric
field vectorE0. Z0 describes the free space wave impedance.
The virtual array is equivalent to a probe antenna with ideal
polarization purity positioned in the far-field of the AUT in
direction −k and exciting the AUT with a quasi plane-wave
field with the same polarization as the synthesized plane
wave. The power wave bFF1
(
k,E0
)
at the feed point of the
AUT in Fig. 1 is proportional to this far-field measurement.
For the wave field synthesis process inside a volume, the
AUT is enclosed by a Huygens’ surface. A filter must be
found that enables the synthesis of the tangential field com-
ponents of the desired plane wave on the surface. The
uniqueness theorem (Harrington, 2001) guarantees that if
the superimposed tangential field components of the virtual
probe array correspond to those of the plane wave, the plane-
wave field is also present inside the source free test volume.
The probe antenna is modeled by its equivalent electric
Jn(r′) and magnetic Mn(r
′) surface currents located at the
n-th probe sampling position. Its characteristic electromag-
netic field is computed from the surface integrals
En(r) =
∫∫
A
[G
EJ (r,r′) ·Jn(r
′)
+ GEM (r,r′) ·Mn(r
′)]dA′ (3)
Hn(r)=
∫∫
A
[G
HJ (r,r′) ·Jn(r
′)
+ GHM (r,r′) ·Mn(r
′)]dA′, (4)
where GE/HJ/M (r,r′) are the dyadic Greens’ functions for free
space. The tangential components of the probe field are sam-
pled at discrete locations ri (i= 1,...,I) on the Huygens’
surface.
In order to avoid the excitation of resonance modes inside the
test volume, the combined field vector (Hansen, 1988)
F n(ri)=En(ri)|tan−Z0n×Hn(ri) (5)
is used, with n being the normal vector of the Huygens’ sur-
face. The constraint that the tangential components of the su-
perimposed probe fields have to be equal to that of the plane
wave leads to the equation system
F 1(r1) ... FN (r1)F 1(r2) ... FN (r2)
.... . .
...
F 1(rI) ... FN (rI)
︸ ︷︷ ︸
F
w1
(
k,E0
)
...
wN
(
k,E0
)
︸ ︷︷ ︸
w(k,E0)
=
F pl(r1)...
F pl(rI)
︸ ︷︷ ︸
F pl
(6)
of the inverse problem with F pl(ri) being the combined field
vector evaluated for the plane wave. As there are usually
more sampling points I on the Huygens’ surface than probe
positions N , the equation system is over-determined. There-
fore, it is solved for the filter coefficients in a least mean
square error sense in form of
w
(
k,E0
)
=F+F pl (7)
using the pseudoinverse F+ of matrix F in Eq. ( 6). This
solution also minimizes the norm of the filter vector and the
power radiated by the virtual probe antenna array, respec-
tively.75
bFF1(k,E0) E0
k
virtual probe
filter w(
k,E0
)
a2
w1
(
k,E0
)
w2
(
k,E0
)
w3
(
k,E0
)
wN
(
k,E0
)
array
AUT
Fig. 1: The principle of plane-wave synthesis by a virtual ar-
ray of probes positioned in the near-field region of the AUT.
The AUT consists of six antenna elements. The power wave
bFF1
(
k,E0
)
is measured at the feed point of one antenna ele-
ment.
In order to avoid 3D measurements, it is also investigated
whether it is possible to synthesize a plane-wave field in a flat
region around the AUT using a virtual array of probe anten-
nas positioned on a closed curve around the test region. The
motivation for this idea is to improve the accuracy of far-field80
measurement results for an antenna measurement facility that
only allows to record near-field data for some great circles
but not on a complete measurement surface.
For this synthesis problem, the field components of the probe
are directly sampled in the flat area instead of sampling the85
tangential field components on a Huygens’ surface. However
the kind of inverse problem remains the same and it is solved
in the same way as described above.
Fig. 1. The principle of plane-wave synthesis by a virtual array ofprobes positioned in the near-field region of the AUT. The AUT
consists of six antenna elements. The power wavebFF1
(k,E0
)is
measured at the feed point of one antenna element.
inside the test volume, the combined field vector (Hansen,1988)
F n (r i) = En (r i)|tan− Z0n × H n (r i) (5)
is used, withn being the normal vector of the Huygens’ sur-face. The constraint that the tangential components of the su-perimposed probe fields have to be equal to that of the planewave leads to the equation system
F 1 (r1) . . . FN (r1)
F 1 (r2) . . . FN (r2)...
. . ....
F 1 (rI ) . . . FN (rI )
︸ ︷︷ ︸
F
w1
(k,E0
)...
wN
(k,E0
)
︸ ︷︷ ︸w
(k,E0
)=
F pl (r1)...
F pl (rI )
︸ ︷︷ ︸
F pl
(6)
of the inverse problem withF pl (r i) being the combined fieldvector evaluated for the plane wave. As there are usuallymore sampling pointsI on the Huygens’ surface than probepositionsN , the equation system is over-determined. There-fore, it is solved for the filter coefficients in a least meansquare error sense in form of
w(k,E0
)= F+F pl (7)
using the pseudoinverseF+ of matrix F in Eq. (6). This so-lution also minimizes the norm of the filter vector and thepower radiated by the virtual probe antenna array, respec-tively.
In order to avoid 3-D measurements, it is also investigatedwhether it is possible to synthesize a plane-wave field in a flatregion around the AUT using a virtual array of probe anten-nas positioned on a closed curve around the test region. Themotivation for this idea is to improve the accuracy of far-fieldmeasurement results for an antenna measurement facility thatonly allows to record near-field data for some great circlesbut not on a complete measurement surface.
Adv. Radio Sci., 11, 47–54, 2013 www.adv-radio-sci.net/11/47/2013/
R. A. M. Mauermayer and T. F. Eibert: A fully probe corrected NFFFT technique employing plane-wave synthesis 49
For this synthesis problem, the field components of theprobe are directly sampled in the flat area instead of sam-pling the tangential field components on a Huygens’ surface.However the kind of inverse problem remains the same andit is solved in the same way as described above.
2.2 Measurement setups and sampling conditions
The measurement setup has to be defined for the synthesisprocess. There are two setups for the investigation of theplane-wave synthesis inside a volume and on a planar area.
For the synthesis in a volume the spherical measurementsetup depicted in Fig.2a is considered. The probe is posi-tioned on a spherical measurement surface with radius 1m.At each position of the regular sampling grid inϑ andϕ di-rection the probe is oriented with vertical and horizontal po-larization. The probe sampling rate, which depends on wave-lengthλ and the radiusρ of the minimum sphere, is derivedfrom the sampling condition (Yaghjian, 1986)
1ϑ = 1ϕ ≤λ
2(ρ + λ)(8)
for conventional NFFFT using spherical multipoles. TheHuygens’ surface is formed by the minimum sphere whichencloses the AUT and has a radius ofρ = 0.5m.
For the synthesis of a plane wave on a planar area the setupshown in Fig.2b is used. The intention here is to generate afield distribution on the disc with radius 0.5m that is moresimilar to a plane wave than the field of the probe antennaitself. The probe is positioned on a measurement circle inthe xy plane with radius 1.98m. Again the probe samplinginterval inϕ direction is chosen following Eq. (8).
The sampling point distance of the probe fields on theHuygens’ surface and on the disc is chosen to be smaller thanλ/2 according to the Nyquist-Shannon sampling theorem.
2.3 Filter coefficients
For the spherical measurement, an open ended rectangularwaveguide probe operating at 2GHz is used. It is positionedon the measurement surface in 5◦ steps inϑ andϕ direction.The tangential field components on the Huygens’ surface arealso sampled on a regular grid inϑ andϕ direction in 6◦ in-tervals. For all probe positions the probe fields are computedon the Huygens’ surface by Eq. (3) and Eq. (4). The sampledtangential components result in the columns of matrixF inEq. (6). The plane wave that is to be synthesized is propa-gating in positivex direction and is vertically polarized as itis given in Fig.2a. The necessary filter coefficients for theoptimal synthesis of the plane wave are gained from the so-lution of the equation system according to Eq. (7). In Fig. 3the resulting normalized magnitude of the filter coefficientsis shown. As the probe is vertically and horizontally orientedthere is one filter coefficient for each of the probe polariza-tion states. It can be clearly seen that most of the power is
R. A. M. Mauermayer and T. F. Eibert: A Fully Probe Corrected NFFFT Technique Employing Plane-Wave Synthesis 3
2.2 Measurement setups and sampling conditions
The measurement setup has to be defined for the synthesis
process. There are two setups for the investigation of the
plane-wave synthesis inside a volume and on a planar area.
For the synthesis in a volume the spherical measurement
setup depicted in Fig. 2a is considered. The probe is posi-
tioned on a spherical measurement surface with radius 1m.
At each position of the regular sampling grid in ϑ and ϕ di-
rection the probe is oriented with vertical and horizontal po-
larization. The probe sampling rate, which depends on wave-
length λ and the radius ρ of the minimum sphere, is derived
from the sampling condition (Yaghjian, 1986)
∆ϑ=∆ϕ≤λ
2(ρ+λ)(8)
for conventional NFFFT using spherical multipoles. The90
Huygens’ surface is formed by the minimum sphere which
encloses the AUT and has a radius of ρ=0.5m.
For the synthesis of a plane wave on a planar area the setup
shown in Fig. 2b is used. The intention here is to generate a
field distribution on the disc with radius 0.5m that is more95
similar to a plane wave than the field of the probe antenna
itself. The probe is positioned on a measurement circle in
the xy-plane with radius 1.98m. Again the probe sampling
interval in ϕ direction is chosen following Eq. ( 8).
The sampling point distance of the probe fields on the Huy-100
gens’ surface and on the disc is chosen to be smaller than λ/2according to the Nyquist-Shannon sampling theorem.
2.3 Filter coefficients
For the spherical measurement, an open ended rectangular
waveguide probe operating at 2GHz is used. It is positioned105
on the measurement surface in 5◦ steps in ϑ and ϕ direction.
The tangential field components on the Huygens’ surface are
also sampled on a regular grid in ϑ and ϕ direction in 6◦ in-
tervals. For all probe positions the probe fields are computed
on the Huygens’ surface by Eq. ( 3) and Eq. ( 4). The sam-110
pled tangential components result in the columns of matrix F
in Eq. ( 6). The plane wave that is to be synthesized is prop-
agating in positive x direction and is vertically polarized as
it is given in Fig. 2a. The necessary filter coefficients for the
optimal synthesis of the plane wave are gained from the so-115
lution of the equation system according to Eq. ( 7). In Fig. 3
the resulting normalized magnitude of the filter coefficients
is shown. As the probe is vertically and horizontally oriented
there is one filter coefficient for each of the probe polariza-
tion states. It can be clearly seen that most of the power is120
radiated by the vertically polarized probes which are radiat-
ing in propagation direction of the plane wave whereas the
horizontally oriented probes are excited with less power be-
cause their radiated fields have a dominant horizontal electric
field component and fit less to the vertically polarized plane125
wave.
probe
measurement surface
Huygens’ surface/minimum sphere
z
y
x
ϑn
ϕn
k
E0
(a) Spherical measurement setup. A plane wave
is synthesized inside the minimum sphere en-
closing the AUT with propagation direction k=
ex and vertical polarization E0 =−ez
probe
measurement circle
disc
ϕn
y
x
E0
k
(b) Measurement setup for plane-wave synthesis
on a disc. The probe is rotated on the measure-
ment circle.
Fig. 2: Measurement setups for plane-wave synthesis inside
a volume (a) and on a disc (b).
A horn antenna probe, also operating at 2 GHz, is used for
the synthesis on a disc. It is rotated on the measurement cir-
cle in 5◦ steps. Due to the high polarization purity of the
probe field on the disc, it is only oriented in vertical polariza-130
tion to synthesize a vertically polarized plane wave propagat-
ing in positive x direction. Fig. 4 shows the normalized mag-
nitude of the resulting filter coefficients. As for the spherical
setup, most of the power is radiated by the elements of the
virtual probe antenna array which are already pointing in the135
propagation direction of the plane wave, i.e. probes on the
measurement circle with ϕn around 180◦.
2.4 Wave field synthesis results
The elements of the virtual probe array are excited according
to the computed filter coefficients. The most important ac-140
Fig. 2. Measurement setups for plane-wave synthesis inside a vol-ume(a) and on a disc(b).
radiated by the vertically polarized probes which are radiat-ing in propagation direction of the plane wave whereas thehorizontally oriented probes are excited with less power be-cause their radiated fields have a dominant horizontal electricfield component and fit less to the vertically polarized planewave.
A horn antenna probe, also operating at 2 GHz, is used forthe synthesis on a disc. It is rotated on the measurement circlein 5◦ steps. Due to the high polarization purity of the probefield on the disc, it is only oriented in vertical polarization tosynthesize a vertically polarized plane wave propagating inpositivex direction. Figure4 shows the normalized magni-tude of the resulting filter coefficients. As for the spherical
www.adv-radio-sci.net/11/47/2013/ Adv. Radio Sci., 11, 47–54, 2013
50 R. A. M. Mauermayer and T. F. Eibert: A fully probe corrected NFFFT technique employing plane-wave synthesis4 R. A. M. Mauermayer and T. F. Eibert: A Fully Probe Corrected NFFFT Technique Employing Plane-Wave Synthesis
s11
v01
v02
v03
v04
ϕ in degree
ϑin
deg
ree
0 30 60 90 120 150 180 210 240 270 300 330
2.5
27.5
52.5
77.5
102.5
127.5
152.5
177.5
(a) vertical polarization
ϕ in degree
ϑin
deg
ree
mag
nit
ud
ein
dB
0 30 60 90 120 150 180 210 240 270 300 330≤ -60
-40
-20
02.5
27.5
52.5
77.5
102.5
127.5
152.5
177.5
(b) horizontal polarization
Fig. 3: Normalized magnitude of the filter coefficients for a vertically (a) and a horizontally (b) polarized open ended
waveguide probe synthesizing a vertically polarized plane wave propagating in positive x direction.
Fig. 4: Normalized magnitude of the filter coefficients for the
synthesis on a disc.
curacy measure of the synthesis method is the quality of the
wave field which is generated. Since the quality of the plane
wave determines the accuracy of the following NFFF trans-
formation process. Therefore, the deviation of the magnitude
and phase of the synthesized wave field from the ideal plane145
wave is regarded.
In the case of the spherical setup, the errors are computed
on lines which are crossing the minimum sphere in different
directions to get an impression of the electrical field distribu-
tion inside the volume. The deviations are shown in Fig. 5.150
The magnitude error of the generated wave field is lower than
−80dB. The phase error is smaller than 0.006◦. As only the
z-component of the synthesized electric field is considered,
the polarization purity was checked to be above 80dB in-
side the minimum sphere. It is possible to further increase155
the quality of the synthesized plane wave by increasing the
sampling rate of the probe on the measurement surface.
The errors of the plane wave synthesized on the disc are
shown in Fig. 6. The magnitude shows a maximum devia-
tion of about −17dB and the phase of about 2◦. It should be160
mentioned that the errors increase below and above the con-
sidered planar region in z direction. Nevertheless, as it was
intended, the superimposed field on the disc of the virtual
array is more similar to a plane wave than the field of only
one probe on the measurement circle, which would result in165
a maximum deviation of −11dB in magnitude and 140◦ in
phase.
In general, a closed boundary surface with the appropriate
impressed equivalent surface currents is mandatory for the
accurate generation of a desired wave field. For the synthe-170
sis of the plane wave on a disc, this assumption is violated
since the virtual probe array only forms kind of a line cur-
rent around the disc. Therefore an accurate synthesis of the
desired wave field cannot be achieved.
3 NFFFT based on plane-wave synthesis175
To find a relation between the near-field measurements and
the AUT far-field, the signal flow in Fig. 1 is inverted so
that the transposed system shown in Fig. 7 is obtained. This
can be done due to the assumption of the reciprocity prop-
erty of the whole system. The far-field of the AUT in direc-
tion −k, which is now proportional to the power wave signal
bFF2
(
k,E0
)
, is computed by
bFF2
(
k,E0
)
=
N∑
n=1
wn
(
k,E0
)
bNF2,n (9)
applying the filter coefficients wn
(
k,E0
)
to the power wave
signals bNF2,n received by the probe at position n in the AUT
near-field. From Eq. ( 9) it is obvious that the NFFF trans-
formation employing plane-wave synthesis is just a filtering
of the near-field data.180
Although the filter is computed for only one specific direc-
tion k, the propagation direction of the plane wave can be
rotated in ϕ direction by a cyclic rotation of the filter coef-
ficients taking advantage of the rotational symmetry of the
probe sampling points on the measurement and of the Huy-185
gens’ surface. This allows to determine a horizontal cut of
Fig. 3. Normalized magnitude of the filter coefficients for a vertically(a) and a horizontally(b) polarized open ended waveguide probesynthesizing a vertically polarized plane wave propagating in positivex direction.
4 R. A. M. Mauermayer and T. F. Eibert: A Fully Probe Corrected NFFFT Technique Employing Plane-Wave Synthesis
s11
v01
v02
v03
v04
ϕ in degree
ϑin
deg
ree
0 30 60 90 120 150 180 210 240 270 300 330
2.5
27.5
52.5
77.5
102.5
127.5
152.5
177.5
(a) vertical polarization
ϕ in degree
ϑin
deg
ree
mag
nit
ud
ein
dB
0 30 60 90 120 150 180 210 240 270 300 330≤ -60
-40
-20
02.5
27.5
52.5
77.5
102.5
127.5
152.5
177.5
(b) horizontal polarization
Fig. 3: Normalized magnitude of the filter coefficients for a vertically (a) and a horizontally (b) polarized open ended
waveguide probe synthesizing a vertically polarized plane wave propagating in positive x direction.
Fig. 4: Normalized magnitude of the filter coefficients for the
synthesis on a disc.
curacy measure of the synthesis method is the quality of the
wave field which is generated. Since the quality of the plane
wave determines the accuracy of the following NFFF trans-
formation process. Therefore, the deviation of the magnitude
and phase of the synthesized wave field from the ideal plane145
wave is regarded.
In the case of the spherical setup, the errors are computed
on lines which are crossing the minimum sphere in different
directions to get an impression of the electrical field distribu-
tion inside the volume. The deviations are shown in Fig. 5.150
The magnitude error of the generated wave field is lower than
−80dB. The phase error is smaller than 0.006◦. As only the
z-component of the synthesized electric field is considered,
the polarization purity was checked to be above 80dB in-
side the minimum sphere. It is possible to further increase155
the quality of the synthesized plane wave by increasing the
sampling rate of the probe on the measurement surface.
The errors of the plane wave synthesized on the disc are
shown in Fig. 6. The magnitude shows a maximum devia-
tion of about −17dB and the phase of about 2◦. It should be160
mentioned that the errors increase below and above the con-
sidered planar region in z direction. Nevertheless, as it was
intended, the superimposed field on the disc of the virtual
array is more similar to a plane wave than the field of only
one probe on the measurement circle, which would result in165
a maximum deviation of −11dB in magnitude and 140◦ in
phase.
In general, a closed boundary surface with the appropriate
impressed equivalent surface currents is mandatory for the
accurate generation of a desired wave field. For the synthe-170
sis of the plane wave on a disc, this assumption is violated
since the virtual probe array only forms kind of a line cur-
rent around the disc. Therefore an accurate synthesis of the
desired wave field cannot be achieved.
3 NFFFT based on plane-wave synthesis175
To find a relation between the near-field measurements and
the AUT far-field, the signal flow in Fig. 1 is inverted so
that the transposed system shown in Fig. 7 is obtained. This
can be done due to the assumption of the reciprocity prop-
erty of the whole system. The far-field of the AUT in direc-
tion −k, which is now proportional to the power wave signal
bFF2
(
k,E0
)
, is computed by
bFF2
(
k,E0
)
=
N∑
n=1
wn
(
k,E0
)
bNF2,n (9)
applying the filter coefficients wn
(
k,E0
)
to the power wave
signals bNF2,n received by the probe at position n in the AUT
near-field. From Eq. ( 9) it is obvious that the NFFF trans-
formation employing plane-wave synthesis is just a filtering
of the near-field data.180
Although the filter is computed for only one specific direc-
tion k, the propagation direction of the plane wave can be
rotated in ϕ direction by a cyclic rotation of the filter coef-
ficients taking advantage of the rotational symmetry of the
probe sampling points on the measurement and of the Huy-185
gens’ surface. This allows to determine a horizontal cut of
Fig. 4. Normalized magnitude of the filter coefficients for the syn-thesis on a disc.
setup, most of the power is radiated by the elements of thevirtual probe antenna array which are already pointing in thepropagation direction of the plane wave, i.e. probes on themeasurement circle withϕn around 180◦.
2.4 Wave field synthesis results
The elements of the virtual probe array are excited accordingto the computed filter coefficients. The most important ac-curacy measure of the synthesis method is the quality of thewave field which is generated. Since the quality of the planewave determines the accuracy of the following NFFF trans-formation process. Therefore, the deviation of the magnitudeand phase of the synthesized wave field from the ideal planewave is regarded.
In the case of the spherical setup, the errors are computedon lines which are crossing the minimum sphere in differentdirections to get an impression of the electrical field distribu-tion inside the volume. The deviations are shown in Fig.5.The magnitude error of the generated wave field is lower than−80dB. The phase error is smaller than 0.006◦. As only thezcomponent of the synthesized electric field is considered, thepolarization purity was checked to be above 80dB inside theminimum sphere. It is possible to further increase the qual-
ity of the synthesized plane wave by increasing the samplingrate of the probe on the measurement surface.
The errors of the plane wave synthesized on the disc areshown in Fig.6. The magnitude shows a maximum devia-tion of about−17dB and the phase of about 2◦. It should bementioned that the errors increase below and above the con-sidered planar region inz direction. Nevertheless, as it wasintended, the superimposed field on the disc of the virtualarray is more similar to a plane wave than the field of onlyone probe on the measurement circle, which would result ina maximum deviation of−11dB in magnitude and 140◦ inphase.
In general, a closed boundary surface with the appropriateimpressed equivalent surface currents is mandatory for theaccurate generation of a desired wave field. For the synthe-sis of the plane wave on a disc, this assumption is violatedsince the virtual probe array only forms kind of a line cur-rent around the disc. Therefore an accurate synthesis of thedesired wave field cannot be achieved.
3 NFFFT based on plane-wave synthesis
To find a relation between the near-field measurements andthe AUT far-field, the signal flow in Fig.1 is inverted sothat the transposed system shown in Fig.7 is obtained. Thiscan be done due to the assumption of the reciprocity prop-erty of the whole system. The far-field of the AUT in direc-tion −k, which is now proportional to the power wave signal
bFF2
(k,E0
), is computed by
bFF2
(k,E0
)=
N∑n=1
wn
(k,E0
)bNF
2,n (9)
applying the filter coefficientswn
(k,E0
)to the power wave
signalsbNF2,n received by the probe at positionn in the AUT
near-field. From Eq. (9) it is obvious that the NFFF transfor-mation employing plane-wave synthesis is just a filtering ofthe near-field data.
Although the filter is computed for only one specific di-rectionk, the propagation direction of the plane wave can be
Adv. Radio Sci., 11, 47–54, 2013 www.adv-radio-sci.net/11/47/2013/
R. A. M. Mauermayer and T. F. Eibert: A fully probe corrected NFFFT technique employing plane-wave synthesis 51R. A. M. Mauermayer and T. F. Eibert: A Fully Probe Corrected NFFFT Technique Employing Plane-Wave Synthesis 5
Fig. 5: Magnitude and phase error of the synthesized plane wave evaluated on several lines crossing the minimum sphere in
different directions.
x in m
yin
m
mag
nit
ud
eer
ror
ind
B
1.6 1.8 2 2.2 2.4≤ -60
-55
-50
-45
-40
-35
-30
-25
-20
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
(a) magnitude errorx in m
yin
m
ph
ase
erro
rin
deg
ree
1.6 1.8 2 2.2 2.4
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
(b) phase error
Fig. 6: Magnitude and phase error of the synthesized plane wave on a disc.
the AUT far-field pattern (E-plane) without having to solve
the inverse problem of Eq. ( 6) for eachϕ angle of plane wave
incidence again.
a1
filter w(
k,E0
)
bFF2
(
k,E0
)
w1
(
k,E0
)
w2
(
k,E0
)
w3
(
k,E0
)
wN
(
k,E0
)
bNF2,1
bNF2,N
AUT
Fig. 7: Considered system for the NFFFT employing plane-
wave synthesis.
4 Application of the NFFFT based on plane-wave syn-190
thesis
4.1 Simulated and measured near-field data
A spherical near-field measurement is simulated with FEKO
(EM Software and Systems, 2011) for the verification of the
proposed method of synthesizing a plane wave inside a vol-195
ume. A three element Yagi-Uda antenna composed of wire
elements is used as AUT. It is vertically polarized and its
main beam direction is pointing in positive x direction. The
simple structure of the antenna makes a low computation
time possible needed for the simulation of about 5,000 near-200
field measurement points. Fig. 8 shows the normalized mag-
nitude of the received probe signal for copolar orientation of
the waveguide probe.
The NFFFT based on the wave field synthesis on a disc is
verified applying it to simulated near-field data acquired by205
the horn antenna probe in the near-field of a patch antenna.
This simulation scenario is also built up in an anechoic cham-
ber, shown in Fig. 10, and real measurements are recorded.
Fig. 7. Considered system for the NFFFT employing plane-wavesynthesis.
rotated inϕ direction by a cyclic rotation of the filter coef-ficients taking advantage of the rotational symmetry of theprobe sampling points on the measurement and of the Huy-gens’ surface. This allows to determine a horizontal cut ofthe AUT far-field pattern (E-plane) without having to solvethe inverse problem of Eq. (6) for eachϕ angle of plane waveincidence again.
4 Application of the NFFFT based on plane-wavesynthesis
4.1 Simulated and measured near-field data
A spherical near-field measurement is simulated with FEKO(EM Software and Systems, 2011) for the verification of theproposed method of synthesizing a plane wave inside a vol-ume. A three element Yagi-Uda antenna composed of wireelements is used as AUT. It is vertically polarized and itsmain beam direction is pointing in positivex direction. Thesimple structure of the antenna makes a low computationtime possible needed for the simulation of about 5000 near-field measurement points. Figure8 shows the normalizedmagnitude of the received probe signal for copolar orienta-tion of the waveguide probe.
www.adv-radio-sci.net/11/47/2013/ Adv. Radio Sci., 11, 47–54, 2013
52 R. A. M. Mauermayer and T. F. Eibert: A fully probe corrected NFFFT technique employing plane-wave synthesis
6 R. A. M. Mauermayer and T. F. Eibert: A Fully Probe Corrected NFFFT Technique Employing Plane-Wave Synthesis
Since the AUT represents one element of a circular antenna
array it is mounted to a construction made from Rohacell so210
that the patch antenna pattern is not disturbed by the mount-
ing. The normalized, simulated and measured probe signals
are plotted in Fig. 9.
Both AUT antennas are positioned in 0.3m distance to the
rotational axis as they represent the antenna element of a cir-215
cular antenna array which is sketched in Fig. 1.
The simulated and real measurement setups, including the
probe and sampling rates, are the same as for the synthesis
processes, so the computed filters can be directly applied to
the simulated and measured near-field data for NFFF trans-220
formation.
-150 -100 -50 0 50 100 150
0
50
100
150
� in degree
�in
deg
ree
-60
-50
-40
-30
�2�
���
0
mag
nit
ud
e in
d
Fig. 8: Normalized magnitude of the probe signal for copolar
orientation of the waveguide probe.
measurement
simulation
-20 dB
-10 dB
0 dB
30
210
60
240
90
270
120
300
150
330
180 0 ϕ
Fig. 9: Simulated and measured near-field data acquired on
the measurement circle.
4.2 NFFF transformation results
For the spherical NFFF transformation the filter of Fig. 3
is directly applied to the acquired near-field data of Fig. 8.
Evaluating Eq. ( 9) for the cyclically rotated versions of the225
filter coefficients leads to the horizontal cut (E-plane) of the
far-field pattern. The transformation result compared to the
reference solution computed by FEKO is given in Fig. 11. As
positioner
Fig. 10: Measurement setup in an anechoic chamber for the
NFFFT based on the plane-wave synthesis on a disc.
it is to be expected from the high quality of the synthesized
plane wave in the vicinity of the AUT there is no difference230
recognizable between reference and NFFFT results. Regard-
ing the errors of the transformation in Fig. 12, it can be seen
that the error of the normalized far-field magnitude is below
−80dB and the phase error is in the range of some thou-
sandths of one degree. So the transformation errors are in the235
range of the magnitude and phase errors of the synthesized
plane wave.
Already from the quality of the synthesized plane-wave field
on the disc it can be derived that the transformation results of
the near-field data acquired on the measurement circle cannot240
reach the accuracy as the one of the complete spherical mea-
surement. Fig. 13 shows the results of the NFFF transforma-
tion for the simulated and measured near-field data. For the
simulated data, the transformation result matches very well
to the reference of the patch antenna far-field pattern.245
The positive effect of the transformation is also visible for
the measured near-field data. However, there is still a major
deviation from the reference compared to the transformation
results of the simulated near-field data. The main reason for
this seems to be that the measurement was done in a facility250
that is not appropriate for near-field measurements, so that
the exact positioning and orientation of AUT and probe an-
tennas could not be guaranteed. This means that the probe
field on the disc which was assumed for the synthesis might
have been different from the probe field during the measure-255
ment in the anechoic chamber. This also explains the dif-
ference between simulated and measured near-field data in
Fig. 9.
Fig. 8.Normalized magnitude of the probe signal for copolar orien-tation of the waveguide probe.
The NFFFT based on the wave field synthesis on a disc isverified applying it to simulated near-field data acquired bythe horn antenna probe in the near-field of a patch antenna.This simulation scenario is also built up in an anechoic cham-ber, shown in Fig.10, and real measurements are recorded.Since the AUT represents one element of a circular antennaarray it is mounted to a construction made from Rohacell sothat the patch antenna pattern is not disturbed by the mount-ing. The normalized, simulated and measured probe signalsare plotted in Fig.9.
Both AUT antennas are positioned in 0.3m distance to therotational axis as they represent the antenna element of a cir-cular antenna array which is sketched in Fig.1.
The simulated and real measurement setups, including theprobe and sampling rates, are the same as for the synthesisprocesses, so the computed filters can be directly applied tothe simulated and measured near-field data for NFFF trans-formation.
4.2 NFFF transformation results
For the spherical NFFF transformation the filter of Fig.3 isdirectly applied to the acquired near-field data of Fig.8. Eval-uating Eq. (9) for the cyclically rotated versions of the filtercoefficients leads to the horizontal cut (H-plane) of the far-field pattern. The transformation result compared to the ref-erence solution computed by FEKO is given in Fig.11. Asit is to be expected from the high quality of the synthesizedplane wave in the vicinity of the AUT there is no differencerecognizable between reference and NFFFT results. Regard-ing the errors of the transformation in Fig.12, it can be seenthat the error of the normalized far-field magnitude is below−80dB and the phase error is in the range of some thou-sandths of one degree. So the transformation errors are in therange of the magnitude and phase errors of the synthesizedplane wave.
Already from the quality of the synthesized plane-wavefield on the disc it can be derived that the transformationresults of the near-field data acquired on the measurementcircle cannot reach the accuracy as the one of the completespherical measurement. Figure13 shows the results of the
6 R. A. M. Mauermayer and T. F. Eibert: A Fully Probe Corrected NFFFT Technique Employing Plane-Wave Synthesis
Since the AUT represents one element of a circular antenna
array it is mounted to a construction made from Rohacell so210
that the patch antenna pattern is not disturbed by the mount-
ing. The normalized, simulated and measured probe signals
are plotted in Fig. 9.
Both AUT antennas are positioned in 0.3m distance to the
rotational axis as they represent the antenna element of a cir-215
cular antenna array which is sketched in Fig. 1.
The simulated and real measurement setups, including the
probe and sampling rates, are the same as for the synthesis
processes, so the computed filters can be directly applied to
the simulated and measured near-field data for NFFF trans-220
formation.
-150 -100 -50 0 50 100 150
0
50
100
150
� in degree
�in
deg
ree
-60
-50
-40
-30
�2�
���
0
mag
nit
ud
e in
d
Fig. 8: Normalized magnitude of the probe signal for copolar
orientation of the waveguide probe.
measurement
simulation
-20 dB
-10 dB
0 dB
30
210
60
240
90
270
120
300
150
330
180 0 ϕ
Fig. 9: Simulated and measured near-field data acquired on
the measurement circle.
4.2 NFFF transformation results
For the spherical NFFF transformation the filter of Fig. 3
is directly applied to the acquired near-field data of Fig. 8.
Evaluating Eq. ( 9) for the cyclically rotated versions of the225
filter coefficients leads to the horizontal cut (E-plane) of the
far-field pattern. The transformation result compared to the
reference solution computed by FEKO is given in Fig. 11. As
positioner
Fig. 10: Measurement setup in an anechoic chamber for the
NFFFT based on the plane-wave synthesis on a disc.
it is to be expected from the high quality of the synthesized
plane wave in the vicinity of the AUT there is no difference230
recognizable between reference and NFFFT results. Regard-
ing the errors of the transformation in Fig. 12, it can be seen
that the error of the normalized far-field magnitude is below
−80dB and the phase error is in the range of some thou-
sandths of one degree. So the transformation errors are in the235
range of the magnitude and phase errors of the synthesized
plane wave.
Already from the quality of the synthesized plane-wave field
on the disc it can be derived that the transformation results of
the near-field data acquired on the measurement circle cannot240
reach the accuracy as the one of the complete spherical mea-
surement. Fig. 13 shows the results of the NFFF transforma-
tion for the simulated and measured near-field data. For the
simulated data, the transformation result matches very well
to the reference of the patch antenna far-field pattern.245
The positive effect of the transformation is also visible for
the measured near-field data. However, there is still a major
deviation from the reference compared to the transformation
results of the simulated near-field data. The main reason for
this seems to be that the measurement was done in a facility250
that is not appropriate for near-field measurements, so that
the exact positioning and orientation of AUT and probe an-
tennas could not be guaranteed. This means that the probe
field on the disc which was assumed for the synthesis might
have been different from the probe field during the measure-255
ment in the anechoic chamber. This also explains the dif-
ference between simulated and measured near-field data in
Fig. 9.
Fig. 9.Simulated and measured near-field data acquired on the mea-surement circle.
6 R. A. M. Mauermayer and T. F. Eibert: A Fully Probe Corrected NFFFT Technique Employing Plane-Wave Synthesis
Since the AUT represents one element of a circular antenna
array it is mounted to a construction made from Rohacell so210
that the patch antenna pattern is not disturbed by the mount-
ing. The normalized, simulated and measured probe signals
are plotted in Fig. 9.
Both AUT antennas are positioned in 0.3m distance to the
rotational axis as they represent the antenna element of a cir-215
cular antenna array which is sketched in Fig. 1.
The simulated and real measurement setups, including the
probe and sampling rates, are the same as for the synthesis
processes, so the computed filters can be directly applied to
the simulated and measured near-field data for NFFF trans-220
formation.
-150 -100 -50 0 50 100 150
0
50
100
150
� in degree
�in
deg
ree
-60
-50
-40
-30
�2�
���
0
mag
nit
ud
e in
d
Fig. 8: Normalized magnitude of the probe signal for copolar
orientation of the waveguide probe.
measurement
simulation
-20 dB
-10 dB
0 dB
30
210
60
240
90
270
120
300
150
330
180 0 ϕ
Fig. 9: Simulated and measured near-field data acquired on
the measurement circle.
4.2 NFFF transformation results
For the spherical NFFF transformation the filter of Fig. 3
is directly applied to the acquired near-field data of Fig. 8.
Evaluating Eq. ( 9) for the cyclically rotated versions of the225
filter coefficients leads to the horizontal cut (E-plane) of the
far-field pattern. The transformation result compared to the
reference solution computed by FEKO is given in Fig. 11. As
positioner
Fig. 10: Measurement setup in an anechoic chamber for the
NFFFT based on the plane-wave synthesis on a disc.
it is to be expected from the high quality of the synthesized
plane wave in the vicinity of the AUT there is no difference230
recognizable between reference and NFFFT results. Regard-
ing the errors of the transformation in Fig. 12, it can be seen
that the error of the normalized far-field magnitude is below
−80dB and the phase error is in the range of some thou-
sandths of one degree. So the transformation errors are in the235
range of the magnitude and phase errors of the synthesized
plane wave.
Already from the quality of the synthesized plane-wave field
on the disc it can be derived that the transformation results of
the near-field data acquired on the measurement circle cannot240
reach the accuracy as the one of the complete spherical mea-
surement. Fig. 13 shows the results of the NFFF transforma-
tion for the simulated and measured near-field data. For the
simulated data, the transformation result matches very well
to the reference of the patch antenna far-field pattern.245
The positive effect of the transformation is also visible for
the measured near-field data. However, there is still a major
deviation from the reference compared to the transformation
results of the simulated near-field data. The main reason for
this seems to be that the measurement was done in a facility250
that is not appropriate for near-field measurements, so that
the exact positioning and orientation of AUT and probe an-
tennas could not be guaranteed. This means that the probe
field on the disc which was assumed for the synthesis might
have been different from the probe field during the measure-255
ment in the anechoic chamber. This also explains the dif-
ference between simulated and measured near-field data in
Fig. 9.
Fig. 10.Measurement setup in an anechoic chamber for the NFFFTbased on the plane-wave synthesis on a disc.
NFFF transformation for the simulated and measured near-field data. For the simulated data, the transformation resultmatches very well to the reference of the patch antenna far-field pattern.
The positive effect of the transformation is also visible forthe measured near-field data. However, there is still a majordeviation from the reference compared to the transformationresults of the simulated near-field data. The main reason for
Adv. Radio Sci., 11, 47–54, 2013 www.adv-radio-sci.net/11/47/2013/
R. A. M. Mauermayer and T. F. Eibert: A fully probe corrected NFFFT technique employing plane-wave synthesis 53R. A. M. Mauermayer and T. F. Eibert: A Fully Probe Corrected NFFFT Technique Employing Plane-Wave Synthesis 7
-15 dB
-10 dB
-5 dB
0 dB
30
210
60
240
90
270
120
300
150
330
180 0 ϕ
reference
NFFFT
Fig. 11: Magnitude of reference and transformed far-field.
2 4 6 8 2 4 6 82
8
6
4
2
2 4 6 8 2 4 6 8.
.
.
.
.
.
erro
r o
norm
ai
ed m
agnit
ude
in d
phas
e er
ror
in d
egre
e
� in degree
Fig. 12: Errors of normalized magnitude and phase of the
transformation result for the spherical near-field measure-
ment.
5 Conclusions
The presented near-field far-field transformation technique260
based on plane-wave synthesis allows to split the transfor-
mation process into two steps.
In the first step, the plane wave is synthesized by solving an
inverse problem for the filter vector for the virtual probe ar-
ray, which might be time consuming.265
In the second step, the transformation of the near-field data
can be performed by a faster filtering procedure.
The method was verified by applying it to simulated and real
near-field measurement data.
If the computed filters are stored they can be reused for270
the transformation of near-field measurement data of differ-
ent AUTs as long as the measurement setup including probe,
probe sampling rate, frequency, measurement surface and the
shape of the Huygens’ surface do not change.
The synthesis of arbitrary field distributions inside arbitrarily275
shaped volumes is an issue of further investigation.
reference
near-field data
NFFFT
-20 dB
-10 dB
0 dB
30
210
60
240
90
270
120
300
150
330
180 0 ϕ
(a) Simulation
-20 dB
-10 dB
0 dB
30
210
60
240
90
270
120
300
150
330
180 0 ϕ
(b) Measurement
Fig. 13: Results of the NFFF transformation of the simulated
and measured near-field data acquired on the measurement
circle.
References
Bennett, J. and Schoessow, E.: Antenna near-field/far-field trans-
formation using a plane-wave-synthesis technique, Proceedings
of the Institution of Electrical Engineers, 125, pages 179 –184,280
doi:10.1049/piee.1978.0048, 1978.
EM Software and Systems: FEKO Suite 6.1, http://www.feko.info,
2011.
Hansen, J. E.: Spherical near-field antenna measurements, IEE
Electromagnetic Waves Series 26, Peter Peregrinus Ltd., London285
U.K., 1988.
Harrington, R. F.: Time-Harmonic Electromagnetic Fields, Wiley,
J., Weinheim, 2001.
Yaghjian, A.: An overview of near-field antenna measurements,
IEEE Transactions on Antennas and Propagation, 34, pages 30290
– 45, doi:10.1109/TAP.1986.1143727, 1986.
Yamaguchi, R., Kimura, Y., Komiya, K., and Cho, K.: A far-field
measurement method for large size antenna by using synthetic
aperture antenna, in: 3rd European Conference on Antennas and
Propagation, pp. 1730 –1733, 2009.295
Fig. 11.Magnitude of reference and transformed far-field.
R. A. M. Mauermayer and T. F. Eibert: A Fully Probe Corrected NFFFT Technique Employing Plane-Wave Synthesis 7
-15 dB
-10 dB
-5 dB
0 dB
30
210
60
240
90
270
120
300
150
330
180 0 ϕ
reference
NFFFT
Fig. 11: Magnitude of reference and transformed far-field.
2 4 6 8 2 4 6 82
8
6
4
2
2 4 6 8 2 4 6 8.
.
.
.
.
.
erro
r o
no
rma
ied
mag
nit
ud
e in
d
ph
ase
erro
r in
deg
ree
� in degree
Fig. 12: Errors of normalized magnitude and phase of the
transformation result for the spherical near-field measure-
ment.
5 Conclusions
The presented near-field far-field transformation technique260
based on plane-wave synthesis allows to split the transfor-
mation process into two steps.
In the first step, the plane wave is synthesized by solving an
inverse problem for the filter vector for the virtual probe ar-
ray, which might be time consuming.265
In the second step, the transformation of the near-field data
can be performed by a faster filtering procedure.
The method was verified by applying it to simulated and real
near-field measurement data.
If the computed filters are stored they can be reused for270
the transformation of near-field measurement data of differ-
ent AUTs as long as the measurement setup including probe,
probe sampling rate, frequency, measurement surface and the
shape of the Huygens’ surface do not change.
The synthesis of arbitrary field distributions inside arbitrarily275
shaped volumes is an issue of further investigation.
reference
near-field data
NFFFT
-20 dB
-10 dB
0 dB
30
210
60
240
90
270
120
300
150
330
180 0 ϕ
(a) Simulation
-20 dB
-10 dB
0 dB
30
210
60
240
90
270
120
300
150
330
180 0 ϕ
(b) Measurement
Fig. 13: Results of the NFFF transformation of the simulated
and measured near-field data acquired on the measurement
circle.
References
Bennett, J. and Schoessow, E.: Antenna near-field/far-field trans-
formation using a plane-wave-synthesis technique, Proceedings
of the Institution of Electrical Engineers, 125, pages 179 –184,280
doi:10.1049/piee.1978.0048, 1978.
EM Software and Systems: FEKO Suite 6.1, http://www.feko.info,
2011.
Hansen, J. E.: Spherical near-field antenna measurements, IEE
Electromagnetic Waves Series 26, Peter Peregrinus Ltd., London285
U.K., 1988.
Harrington, R. F.: Time-Harmonic Electromagnetic Fields, Wiley,
J., Weinheim, 2001.
Yaghjian, A.: An overview of near-field antenna measurements,
IEEE Transactions on Antennas and Propagation, 34, pages 30290
– 45, doi:10.1109/TAP.1986.1143727, 1986.
Yamaguchi, R., Kimura, Y., Komiya, K., and Cho, K.: A far-field
measurement method for large size antenna by using synthetic
aperture antenna, in: 3rd European Conference on Antennas and
Propagation, pp. 1730 –1733, 2009.295
Fig. 12.Errors of normalized magnitude and phase of the transfor-mation result for the spherical near-field measurement.
this seems to be that the measurement was done in a facilitythat is not appropriate for near-field measurements, so thatthe exact positioning and orientation of AUT and probe an-tennas could not be guaranteed. This means that the probefield on the disc which was assumed for the synthesis mighthave been different from the probe field during the measure-ment in the anechoic chamber. This also explains the dif-ference between simulated and measured near-field data inFig. 9.
5 Conclusions
The presented near-field far-field transformation techniquebased on plane-wave synthesis allows to split the transforma-tion process into two steps. In the first step, the plane waveis synthesized by solving an inverse problem for the filtervector for the virtual probe array, which might be time con-suming. In the second step, the transformation of the near-field data can be performed by a faster filtering procedure.
referencenear-field dataNFFFT
-20 dB
-10 dB
0 dB
30
210
60
240
90
270
120
300
150
330
180 0 ϕ
(a) simulation
-20 dB
-10 dB
0 dB
30
210
60
240
90
270
120
300
150
330
180 0 ϕ
(b) measurement
Fig. 13. Results of the NFFF transformation of the simulated andmeasured near-field data acquired on the measurement circle.
The method was verified by applying it to simulated and realnear-field measurement data.
If the computed filters are stored they can be reused forthe transformation of near-field measurement data of differ-ent AUTs as long as the measurement setup including probe,probe sampling rate, frequency, measurement surface and theshape of the Huygens’ surface do not change. The synthesisof arbitrary field distributions inside arbitrarily shaped vol-umes is an issue of further investigation.
www.adv-radio-sci.net/11/47/2013/ Adv. Radio Sci., 11, 47–54, 2013
54 R. A. M. Mauermayer and T. F. Eibert: A fully probe corrected NFFFT technique employing plane-wave synthesis
References
Bennett, J. and Schoessow, E.: Antenna near-field/far-field trans-formation using a plane-wave-synthesis technique, Proceed-ings of the Institution of Electrical Engineers, 125, 179–184,doi:10.1049/piee.1978.0048, 1978.
EM Software and Systems: FEKO Suite 6.1,http://www.feko.info,2011.
Hansen, J. E.: Spherical near-field antenna measurements, IEEElectromagnetic Waves Series 26, Peter Peregrinus Ltd., Lon-don, UK, 1988.
Harrington, R. F.: Time-Harmonic Electromagnetic Fields, Wiley,J., Weinheim, 2001.
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