The aperture size requirements of imaging microwave radiometers in geosynchronous orbit ruled out filled aperture antenna systems below 10 GHz. In the regions 10 to 30 GHz, filled apertures are only marginally practical. The size requirements in turn aggravate the problems with a mechanically steered antenna beam. Both the aperture size and steering problems are resolved with a synthetic aperture interferometric radiometer (SAIR). The SAIR imaging is discussed, along with the requirements of the two-dimensional antenna elements

Ruf, C. S.

English

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SYNTHETIC APERTURE
INTERFEROMETRIC RADIOMETER
(SAIR)
_21 9 95_
///
N90-19261
C. S. Ruf
Jet Propulsion Laboratory
California Institute of Technology
Pasadena, CA
PRECEDING PAGE BLANK NOT FILMED
179
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The aperture size requirements of imaging microwave radiometers
in geosynchronous orbit rule out filled aperture antenna systems
below I0 GHz. In the region 10-30 GHz, filled apertures are only
marginally practical. The size requirements in turn aggravate the
problems with_a mechanically steered antenna beam. Both the
aperture size and steering problems are resolved with a Synthetic
Aperture Interferometric Radiometer (SAIR).
SAIR imaging is based on a technically and analytically mature
discipline, synthetic aperture radio astronomy (refs. 1 and 2). A
two-dimensional array of antenna elements can be thinned by more
than 99.9%. The remaining elements are cross-correlated and the
output is recorded digitally. All antenna beams are then generated
simultaneously in software.
THINNED APERTURE RADIOMETERS
, CORRELATION INTERFEROMETRIC IMAGING
-STRONG HISTORICAL PRECEDENT IN RADIO ASTRONOMY
,, > 99.9% SAVINGS IN ANTENNA SIZE/WEIGHT
• NO MECHANICAL SCANNING
180
The cross-correlation of a pair of antenna elements in the SAIR
thinned array produces a measurement referred to as the visibility
function by radio astronomers. The visibility function is the two-
dimensional Fourier transform of the brightness temperature
distribution lying within the mainbeam of the individual antenna
elements. The relative positions of the pair of elements determine
which sample of the visibility function is measured. After enough
different samples are made, the measurements are inverse Fourier
transformed in software to reconstruct the brightness temperature
distribution. The sinusoidal weightings on each sample in the
software reconstruction are exactly analogous to the phase shifter
settings on a conventional electronically steered phased array. One
fundamental difference between a SAIR imager and a phased array,
however, is the inability of the phased array to be thinned without
raising its sidelobe levels.
CORRELATION
INTERFEROMETER
FUNDAMENTAL RELATIONSHIP
(Dx
"t,_" _,=)
S:I ..... .t"
T B (x, y)
¥
- ,,:1"°,__" 5_±]
I)ll
I
I
I
I
ORIGINAL PAGE IS
OF POOR QUALITY
181
Samples are made of the visibility function at a wide variety
of different relative antenna element spacings. There must be close
and distant spacings, as well as a uniform distribution in-between.
Also, the spacings must vary evenly in two perpendicular directions
which lie in the plane of the thinned array. There are many
configurations in which to construct the thinned array. A ring of
elements - pseudo randomly thinned - provides an even distribution
of spacings instantaneously (ref. 3). A "Y" configuration is
presently used by the Very Large Array radio telescope in Socorro,
NM. It relies on the Earth's rotation to produce much of the
spacing. A rotating thinned line of elements would generate the
proper distribution of spacings after 180 ° of rotation. Linear
thinning algorithms have been studied for SAIR Earth remote sensing
(ref. 4).
RING
,,y,,
POSITION CORRELATION
(VARY D x, y)
EXAMPLES OF SAMPLING LATTICE:
• g
• EXCELLENT "SNAPSHOT"
COVERAGE
• VLA CONFIGURATION
• USES EARTH ROTATION
ROTATING
LINEAR
g • MINIMUM REDUNDANCY
THINNED ARRAY
HERITAGE
• ORBIT STABILIZED
ROTATION
182
The spatial resolution of a SAIR imager can be derived from
standard Fourier transform theory. The visibility function is
sampled over a region, the extent of which is determined by the
maximum spacing between antenna elements in the thinned array. This
effectively truncates the visibility function sample space. The
truncation produces a smoothing, or "lowpass filtering" of the
brightness temperature distribution reconstructed in software. The
resulting resolution of the image is the same as would have been
measured by a filled aperture, for example a very large reflector,
with a diameter equal to the maximum spacing between antenna
elements in the SAIR array.
CORRELATION INTERFEROMETRY
SPATIAL RESOLUTION
• V SAMPLE-SPACE HAS FINITE EXTENT
=_ TB IMAGE IS "LOWPASS FILTERED"
• IMAGE RESOLUTION = V-SPACE MAXIMUM
X min h
Dx, y max
]83
Examples of specific SAIR array configurations illustrate the
large savings in size and weight possible relative to conventional
filled array imagers. A SAIR imager capable of I00 km resolution
from geosynchronous orbit at I0 GHz would require 20 array elements,
each approximately 8 cm in diameter, deployed pseudo-randomly in a
rotating line 10.7 m long. A phased array with the same image
resolution would require 795 times as many elements. A 70 element
SAIR imager, with I0 km resolution at i0 GHz, has the imaging
performance of a filled array with 22,743 times as many elements.
This extreme reduction in required aperture is, to a certain extent,
offset by the increased complexity of the cross-correlation
circuitry necessary in a SAIR system. Every possible pair of
antennas is cross-correlated. For the 70 element array, this
implies 2,415 cross-correlators. The streamlining, parallel
processing, and, possibly, digitizing of this step is a key area for
further development.
SPATIAL RESOLUTION
EXAMPLES AT 10 GHz
RESOLUTION (kin) 100 50
21.5
10
Dx, y max (m) 10.7 107.5
# ELEMENTS IN FILLED ARRAY 15.9 K 63.7 K 1,592 K
# ELEMENTS IN ROTATING
THINNED LINEAR ARRAY 20 30 70
% FILLED APERTURE 0.13% 0.05% 0.005%
184
Measurements of the visibility function are made over a region
of its sample space. This corresponds to a range of spacings
between different array elements. The required distribution of
spacings over this range can be specified using Nyquist sampling
theory. The field of view (FOV) imaged determines the incremental
steps allowed between successive spacings. In the case of a filled
phased array imaging the full 2 _ steradian half space, this implies
the standard half wavelength spacing between elements. From a
geosynchronous platform, the FOV is significantly reduced and the
increment between element-pair spacings increases to 2.84
wavelengths. The aliased responses generated by an image
reconstruction from Nyquist samples are analogous to antenna grating
lobes. These grating lobes are positioned off the limb of the Earth
by the Nyquist condition and can be further suppressed, if
necessary, by the individual array element patterns.
CORRELATION
INTERFEROMETER
SAMPLING THEOREM
• TB SPATIAL EXTENT IS FINITE
2-d NYQUIST SAMPLING OF V
EXAMPLE: GEOSTATIONARY PLATFORM
"_- 8.7 °
h=3 28km /I
___ / I
I I
-'_ _-FOV = 12610 km
SAMPLING THEOREM:
/'. = _ = 2.84
185
Incomplete sampling of the visibility function by a SAIR array
configuration results in a loss of beam efficiency in the synthetic
an£enna pattern. A particular example illustrates the sampling
requirements of a SAIR array. Twelve antenna elements are arranged
in a circular ring, either uniformly spaced or thinned according to
an optimal thinning algorithm (ref. 3). The diameter of the ring is
varied and, at each diameter, the beam efficiency of the
corresponding synthetic antenna pattern is computed. The uniform
distribution degrades as soon as the spacing between elements along
the circumference of the ring significantly exceeds the Nyquist
criteria. The performance of the thinned ring degrades when its
diameter exceeds twelve times the Nyquist criteria. This
degradation amounts to a rise in sidelobes near the mainbeam. The
spatial resolution of the array is also plotted. A thinned SAIR
ring with twelve elements can provide 500 km resolution with 90%
beam efficiency. Increasing the resolution to 5 km should raise the
number of elements needed to approximately 120 (ref. 5).
RING INTERFEROMETER
BEAM EFFICIENCY
• ASSUMING 12 ANTENNA ELEMENT ARRAY
• OPTIMAL THINNING (T.J. CORNWELL, IEEE TRANSACTIONS ON
ANTENNAS AND PROPAGATIONS, Vo|. 36, No. 8, AUGUST 1988,
pp. 1165-1167)
• BEAM EFFICIENCY ASSUMES UNIFORM APERTURE TAPER
2700
2300
E
_,._1900
Z
9 15oo
P
_ 1100
700
3OO
f\i I _ I J I t . f I I t i
\
_\"\_JNIFORM_ -\ _'_\\ - . OPTIMAL THINNED RING
\
I l r : I t I I E t 1 ' i
5 10 15 20 25 30 35 40 45 50 55 60 65
RING DIAMETER (x l)
A
9s
)-
90 o
z
ILl
85 _
E
Ii
80 ','
7s _
QI
70
186
The radiometric noise floor of a SAIR image has been studied in
detail (ref. 4). The noise floor of the individual measurements of
the visibility function is simply that of a conventional correlation
radiometer. The two- dimensional Fourier transform of these
measurements can be viewed as a weighted summation of N 2 random
variables, where N 2 is the number of measurements or the number of
independent pixels in the brightness temperature image. The weights
are the sinusoidal kernels of the transform and the resulting image
has a noise floor which is approximately N times that of the
individual measurements. This accumulation of noise is
significantly offset by the fact that all pixels are imaged
simultaneously, thus increasing the available integration time over
that of a scanning imager. The SAIR system temperature can also be
significantly reduced by using small array elements with antenna
patterns much broader than the Earth disc. This technique must be
traded off, however, against grating lobe suppression by the element
patterns.
CORRELATION INTERFEROMETRY
IMAGE SENSITIVITY
• INDIVIDUAL MEASUREMENT NOISE FLOOR
Tsys
AV=_
WHERE Tsy s = TRx + 2_
• RECONSTRUCTED IMAGE NOISE FLOOR
AT = N AV
2
WHERE N = # OF PIXELS IN IMAGE
NOTE:
• Tsy s =TRx +<T B) =TRx + 200 K FOR FILLED APERTURE (PENCIL BEAM)
IMAGERS VERSUS = TRx + 3 K FOR CORRELATION INTERFEROMETER
• TRx IS MAJOR DESIGN DRIVER HERE
187
The noise floor of a brightness temperature image has been
computed for three different radiometer systems: a mechanically
scanning filled aperture, a SAIR ring array, and a SAIR rotating
linear array. Radiometer operating parameters typical on a
geostationary platform are assumed. The filled aperture system must
sequentially sample the pixels in the image and its integration time
per pixel is reduced accordingly. The linear SAIR system must
rotate 180 ° to adequately sample the visibility function and its
dwell time per sample is reduced. The SAIR ring array is assumed to
have the double advantage of longest integration time and lower
system temperature than the filled aperture imager. If this latter
advantage is eliminated, then the filled aperture and ring array
will have comparable noise floors. For i0 km image resolution, only
the rotating linear SAIR array has an unacceptably high noise floor(8.1 K). The ring array, or perhaps some other two dimensional
thinned configuration, becomes a performance necessity at this level
of resolution.
CORRELATION
INTERFEROMETRY
SENSITIVITY EXAMPLE
• TOTAL INTEGRATION TIME
• PRE-DETECTION BANDWIDTH
• RECEIVER NOISE
• # OF PIXELS IN IMAGE
T=I hr
B = 100 MHz
TRx = 150 K
N 2
RESOLUTION (km) 100 50 10
N 126 252 1261
• INDIVIDUAL MEASUREMENT INTEGRATION TIME
• RECONSTRUCTED IMAGE NOISE FLOOR AT:
RESOLUTION (km) 100 50 10
IMAGER "r
MECHANICAL SCANNING T
-- 0.08 0.17 0.83
PENCIL BEAM N2
RING T 0.03 0.06 0.32
T
ROTATING LINEAR 0.26 0.72 8.11
N/2
188
REFERENCES
i. Pawsey, J. L. and Bracewell, R. N.:
Oxford, 1955.
Radio Astronomy. London,
2. Napier, P. J., et. al.: "The very large array: design and
performance of a modern synthesis radio telescope.,, Proc.
IEEE, Vol. 71, no. ii, Nov. 1983.
3. Cornwell, T. J.: "Crystalline antenna arrays."
Memo No. 38, NRAO, Socorro, NM.
Millimeter Array
,
Ruf, C. S., et. al.: "Interferometric synthetic aperture
microwave radiometry for the remote sensing of the Earth.',
IEEE Trans. on Geo. and Rem. Sens., Vol. 26, No. 5, 597-611,
Sept. 1988.
5. Ruzsa, I. Z.: "On difference-sequences.,, Acta Arithmetica, Vol_
XXV, 151-157, 1974.
189



Synthetic Aperture Interferometric Radiometer (SAIR)

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