Far field antenna patterns can be reconstructed from planar near field measurements acquired at a sample spacing of lambda/2 or less. For electrically large antennas, sampling at the Nyquist rate may result in errors due to system electronic drift over long acquisition times. The computer capacity may limit the largest size of the near field data set. The requirement to sample at the Nyquist rate is relaxed for high gain antennas which concentrate most of the radiated energy into a small angular region of the far field. The criteria for sample spacing at greater than lambda/e through the use of a priori information of the antenna radiation characteristics are presented. Far field patterns of a 30 GHz dual offset reflector system with a 2.7 m parabolic main reflector are computed from near field data obtained at sample spacings ranging from 0.1 lambda to 10 lambda. The effects of sampling interval and spectrum cutoff on the far field patterns are discussed

Acosta, R. J.

Lee, R. Q.

English

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https://ntrs.nasa.gov/search.jsp?R=19850001927 2020-03-20T21:40:50+00:00Z
(dASA 8-66872) CASE STUD. ''F SAMPLE 	 N85-10234
SPACING IN PLAN118 dlsaB-Fi.ELD 8111SOREA22T OF
HIGH GAIN ANTENNAS (NASA) 10 p
HC A02/MF A01	 CSCL 20H	 Unclas
G3/32 24257
I
Roberto J. Acosta and Richard Q. Lee
Lewis Research Oenter
Cleveland Ohio
Prepared for the	 T
1984 Antenna Applications Symposium
sponsored by the University of Illinois
Wnticello, Illinois, September 18-21, 1984
i
=3
3 J
r
CASE STUDY OF SAMPLE SPACING IN PLANAR NEAR-FIELD MEASUREMENT
OF HIGH GAIN ANTENNAS
Roberto J. Acosta and Richard Q. Lee
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135
SUMMARY
Far-field antenna patterns can be reconstructed from planar near-field
measurements acquired at a sample spacing of 1,/2 or less. For electrically
large antennas, sampling at the Nyquist rate may result in errors due to sys-
tem electronic drift over long data acquisition times. Furthermore, the com-
puter capacity may limit the largest size of the near-field data set. The
requirement to sample at the Nyquist rate can be relaxed for high gain anten-
nas which concentrate most of the radiated energy into a small angular region
N	 of the far-field. The criteria for sample spacing at greater than V2
through the use of a priori information of the antenna radiation character-
istics are presented. Far-field patterns of a 30 GHz dual offset reflector
system with a 2.7 m parabolic main reflector are computed from near-field data
obtained at sample spacings ranging from 0.1 X to 10 'k. The effects of
sampling interval and spectrum cut-off on the far-field patterns are discussed.
INTRODUCTION
The near-field measurement technique has been used extensively for
electrically large antennas which can not be easily tested on a far-field
range. In reconstructing the far-field antenna patterns from the near-field
measurements, a planar configuration may be used with a computation based on
the Fast Fourier Transform (FFT). The near-field data are generally sampled
over a planar grid at the Nyquist sampling rate of Xo/2 spacing or less.
For electrically large antennas, sampling at the Nyquist rate requires long
data acquisition times over which significant system electronic drift may
occur. Furthermore, the computer capacity may lirrit the largest size of the
data set. Special data filtering techniques for large data sets have been
reported (ref. 1). However, these techniques still require sampling at
1 012 spacing.
E. B. Joy (ref. 2) discussed how the sampling spacing may be increased
through the use of a priori information on the antenna under hest. In this
paper, the criterion of sample spacing greater than ko/2 is examined and
demonstrated using data obtained with an offset Cassegrain configuration.
R. Zakrajsek and R. Kunath provided the near-field data measurements and
Dr. C. Raquet gave many helpful suggestions.
OFIZIGINAL
Of POOR Q IJALI iY
FORMULATION
It is well known that the electric field may be represented as a plane
wave spectrum (ref. 3)
E(x.Y.z) = 4 2 ffF(Kx,Ky) 
a-JK,r 
dKxdKy
where
1/2
K K 
x 
x + K y y + (Ko - Kx - Ky)	 z
K = Wx
°	 o
F(Kx Ay ) is the wave-number spectrum function which may be expressed as
the Fourier transform of the aperture field, E(x,y,o), in the x-y plane as
follows:
JKxx+JKyy
F(Kx ,Ky ) 	 E(x,y,o) e	 dxoy
s
As Y tends to infinity, an asymptotic value of E(x,y,z) may be folind by the
method of steepest descent, namely,
JK cos a iK r
°2*^ e ° F(K o sin a cos .0, Ko sin a sin m)
For plane wave propagating awav from the aperture plane at z = o, the propa-
gation constant in the c direction is
K - CK2- K
2 _ K 2^
1/2	 0
z	 o	 x	 y
Thus, radiating modes exist only in the visible region of the real k-spice
defined by
K2 + K2 < K2
x	 y — o
while evanescent modes exist in its complement space. According 	 the Nyquist
sampling theorem, a function whose spectrum exists and is nonvanishing over
finite region of wave-number space may be exactly reproduced from its sample
values taken on a periodic lattice at a rate of at least two times the maximum
frequency, or in terms of wave number, 
2k 
max ' Since the maximum wave-numbers
2
ORIGINAL PAGE IS
OF POOR QUALITY	 -
k 	 and k	 which Grine the boundary of the visible k space is 2w/-x
xmax	 ymax	 o
the Nyquist sample spacing is given by
	
2K	 AX < 2,r
xmax
or
Ax < X /2
- o
Similarly,
Ay < 
x0/2
For a broad spectrum, the radiated power extends over the entire visible
region and a sample spacing of -ho12 is required. However, for high gain
antennas such as large reflector systems used on communication satellites at
geosynchronous orbit, most or tie spectral components are concentrated in the
central region ( ►f the visible space. Consequently, data acquisition at a
sample rate greater -k
0
/2 is possible..
If only the spectrum within the region bounded by (±K x ,±K y ) is of sig-
nificance, the sample spacing may then be increased by k	 /K	 and k	 /K .
xmax 
x	
ymax y
That is
Ax = ,r/K
x
Ay = A/K	
e
y
where K < K	 and K < k
x	
xmax	 y	 ymax
By expressing the wave-number, kmaxt
kmax = 2,r/xo sin emax• the maximum elevat
emax+ as a function of sample spacing, A,
e	 = sin-1
max
in spherical coordinate, i.e.,
ion angle of coverage,
can be computed from
(a0/2A)
For illustration, a few computations of emax versus a are tabulated
below
A	
a0/2 
X0 
2X0 	13X 5 0 20X
emax	
90°	 30 0 15 0 10 0 60	30
As indicated above when the sample spacing is increased, only a small angular
sector of the far-field can be accurately computed by the FFT. For antennas
with broader beams sample spacings approaching X012 are required.
3
n
DIS'USSION AND RESULT
f`.
The effects of sampling at greater than the Nyquist rate were studied
experimentally for a dual offset Cassegrain Configuration designed by TRW for
NASA Lewis Research Center (ref. 4). The main reflector is parabolic with the
following characteristics:
Dish diameter = 257.89 ko
Focal length = 318.74 'Ko
Offset length = 135.51 )Lo
Centerfrequency f = 28.5 GHz (a0
 = 1.05 cm)
The reflector is illuminated by a linearly polarized feed at the focus with a
18 db edge taper. The hyperboloidal subreflector has a magnification factor
of 2. The antenna was tested with the planar near-field range currently in
operation at the NASA Lewis Research Center, Near-field Centerline data were
acquired at 
'`o/2 spacing. The radiation patterns were reconstructed from
the centerline near-field data set with a one-dimensional FFT algorithm. For
sample spacing greater than ko/2 appropriate subsets were selected from
the original data set. The effects of the sample spacings are illustrated in
the antenna patterns shown in figures 1(a) to (e).
This antenna patterns showed no perceptible changes from data taken at
U.5, 1, and 21,0
 spacing. Sidelobe degradation starts to occur at approxi-
mately 4X0 spacing. The main beam is slightly modified by a sample spac-
ing of up to 8Xo. For antennas used in space communication application
where the beam widths arc in the order of 0.3` are often desired, a good
choice of sample spacing will be between 2 to 4X01
Spectrum characteristics with cut-off power levels at -30, -40, and -50
dB are shown in figures 2(a) to (c). These spectrum plots were obtained with
near-field data taken at a -&0/2 spacing. As shown, spectral components
with higher cut-off power level occupies a smaller visible region of the
K-space, and thus a smaller wave number limit K x and Ky . This corre-
sponds to sample spacing greater than X012.
Figures 3(a) to (c) compares far-field antenna pattern from near-field
data taken at a012 spacing (dotted line) and spacings implied by the
spectrum cut-off plots (solid line). From these figures we can conclude that
neglecting data below -40 dB is consistent with sample spacing.
In general, desired pattern accuracy, desired angular range, and availa-
ble instrumentation dynamic range must be taken into consideration when
selecting sample spacing.
REFERENCES
1. Joy, Edward B.; and Paris D. T.: Spatial Sampling and Filtering in Nea--
Field Measurements. IEEE Trans. Antennas Propag., vol. 20, no. 3, May
1972, pp. 253-261.
2. Joy, Edward Bennett: Spatial Sampling and Filtering in Near-Field
Measurements. Ph.D. Thesis, Georgia Institute of Technology, 1970.
4
. q
3.	 Booker, H. G.; and Clemow, P. C.: The Concept of Angular Spectrum of
Plane Waves and its Relation to that of Polar Diagram and Aperture Dis-
tribution. Proc. Inst. Electr. Eng. Part 3, vol. 97. no. 45, Jan. 1950,
pp. 11-17.
5
Ov POOP QUAI f'l,,
0
-20
-40
-60
(a) ]012.	 (d) 001
00	 0
-20
0a
w
-40
w
-60 (b) No.	 -3	 -2 -1	 0	 1	 2	 3
0	 8, deg
(e) 8X0.
-20
-40
-60
-3 -2 -1	 0	 1	 2	 3
8, deg
(c) 2X.,
Figure 1. - Relative power pattern as a function of elevation angle
for different sample spacing.
,
OF PO
-10
-30
-50
(a)
0
m
CW
-20
a
W7
H
5W	
-40^ (b)
0
-10
-20
-30
-1.0
	
0	 1.0
NORMALIZED WAVE-NUMBER
(c)
Figure 2. - Power spectrum.
1..
i {r
ORIGINAL PACE
OF POOR QU U
9
-20
-40
(a)
a,	 0
W
-20
W
F-
5W
°C -40
(b)
0
-20
-40 1 ►r r1	 1 •	 1	 11 1 	 1
-3 -2 -1	 0	 1	 2	 3
0, deg
(c)
Figure 3. - Relative power pat-
tern as a function of eleca-
tion angle.
,-,
	 Ii


Case study of sample spacing in planar near-field measurement of high gain antennas

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