Suitability of Correlation Arrays and Superresolution for Minehunting ...

DSTO-TN-0443
(C&H, p. 149). Note that a product of the component beam patterns is now obtained;
contrast the sum in (2.2). For this reason, outside the beamwidth, the sidelobes fall off
rapidly in all directions and the instrument is very satisfactory. Note also that,
although the left side of (3.10) is an intensity, the sinc functions on the right side are not
squared.
3.3 Traditional Cross Antenna
We now discuss the traditional cross antenna in radio astronomy. Here, while each
subarray consists of dipoles—the analogue of elements in sonar—the voltages from
these dipoles are not individually recorded, nor are any correlations carried out
between an individual dipole voltage and another dipole voltage. Instead, for the first
arm, after the analogue implementation of phase delays to produce steering in one of
the two angular coordinates, the total voltage on the arm is obtained and treated as a
single unit. Similarly for the other arm, which is steered in the other angular
coordinate. The correlation of these two totals is then obtained by analogue means.
The traditional telescope’s instantaneous output is thus given by the first line of the
following:
V
⎧
= ⎨
⎩
=
∑
n
n
E
∑∑
p
n
E
exp
n
F
⎧
−1
⎫
−1
[ j2πλ
( l,
m)
⋅ rn
] ⎬ ⎨∑
Fp
exp j2πλ
( l,
m)
⎭ ⎩ p
∗
−1
exp[ j2πλ
( l,
m)
⋅u
]
p
n p
[ ⋅ r ]
p
⎫
⎬
⎭
∗
(3.11)
where u
n p
is defined below (3.2). (Actually the right-hand side of Eqn (3.11) is to be
averaged over time to eliminate uncorrelated contributions to the instantaneous
product.) Removal of the curly brackets gives the second line. The second line shows
that the resulting output from the traditional telescope is the same as if the following
two steps were carried out: (i) the voltages are multiplied within each element pair to
∗
yield E F n p
; and (ii) delay-and-add beamforming is then applied to the product by
performing a phase shift based on the vector spacing u
np
and then adding. But this is
the very beamforming process described for the updated antenna at Equation (3.1).
Thus in essence the traditional telescope behaves in the same way as the updated telescope.
Of course, an important difference in practice is that, in a given correlation run as
described in the first paragraph, the traditional telescope yields an image intensity for
just one direction in the sky (one resolution cell). By contrast, the updated telescope
would record all the voltage streams from the one correlation run and, by repeated
reprocessing of the same data, would yield the image intensity for all relevant
directions.
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