Project Cyclops, A Design... - Department of Earth and Planetary ...

ightness distributionoverthecommonfieldofviewof
theantennas. Finally,thetwo-dimensional Fouriertransformof
themeasured dataistakento getthedesired
map.TheproposedVLAsystemwillusethistechnique,
calledaperture synthesis. It is obvious that neither of
these methods produces a real-time image of the sky.
and at an azimuth a will be received by an antenna at
x,y with a delay.
x sin a +y cos a
rr(X,Y) = - sin 8 (36)
The greater the resolution desired, the greater is the
time required to map a given area of the sky. With the
resolution available from the Cyclops array the times are
very long indeed. Assume that we have 1000 dishes
spread over an area 10 km in diameter, and operating at
a wavelength of 10 cm, If we allow 3 dB gain falloff at
the edges of each elemental area scanned, the number of
resolvable directions is about 1.5 (Ird/X) 2 = 1.5×10 II
(see Chap. 6). With an integration time of only 1 sec per
elemental area scanned, it would take 1.5× 1011 sec or
about 5000 years to map the entire sky. Even to map an
object such as M31 (the Andromeda galaxy)would take
about 126 eight-hour observing days, or 4 months. But
with 1000 elements in the array, we can form I000
independent beams simultaneously, and thus map the
whole sky in 5 years, or M31 in an hour.
where c is the velocity of light. At the received
frequency w r this delay causes a phase shift
% = rrW r (37)
The delay and, if the spectrum has not been inverted,
the phase shift are preserved by all the heterodyning
operations and thus are present at the IF outputs.
Even with an imaging system, the field of view is
limited by the beamwidth of the antenna elements.
Moreover, in an array, there are additional grating lobes
within this field that confuse the picture and reduce the
usable field area by the filling factor. Thus, for the
Cyclops array with a filling factor of 1/10, ten times as
many fields of view would be needed to synthesize a
picture of a given region as would be needed with a
single 100-m dish. The advantage of the array is that the
final picture contains 10,000 times the detail. Thus, the
array with its 1000 dishes is 1000 times more powerful
for map ing, as one should expect. In fact, if blurred
areas in the map made with the single antenna are
resolved into sharp points by the array, the integration
time can be reduced, making the array even more
powerful.
General
Principles
To simplify our thinking let us initially assume that
the Cyclops array is pointed at the zenith. A signal
received from the zenith will then produce the same IF
output signal at the central station from every antenna
element.
Let us take Y to be the north-south axis of the array
and X to be the east-west axis as shown in Figure 11-I 6a.
A signal received at a small angle _ from the zenith
SIGNAL PLANE _ V _
...."_ 0/
IMAGE
/
PLANE
Figure ll-16. (aj Antenna and source coordinate.
[b ) Imaging coordinates.
Let us imagine the IF outputs to be arranged
physically in a plane, forming a small scale map of the
array, so that in Figure ll-16b x' = ox andy' = oy
where o is the scale factor. Now let us arrange a second
lattice of points with coordinates u, v in a second plane,
which we will call the image plane, and let us connect
each of the IF outputs in the signal plane to every lattice
point in the image plane via a transmission path having a
phase shift
_i = - k(ux + vy) (38)
At the image plane point at radius r and at angle a, the
phase will be _bi = -k r (u sin a + v cos a) while at the
angle Ir + _ the phase will be
¢i = kr (u sin a + v cos _) (39)
142