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

where 0 is the angle off axis, and "Iv is the vth order
Bessel function. Now f(O) = fUdA and is unity for all v.
If v = 1, we have a constant illumination over the
circular aperture. If v = 3/2 the amplitude has a
hemispherical distribution, while the intensity 1/212 is a
paraboloid. If v = 1 the amplitude has a paraboloidal
distribution. Several distributions of this family are
shown in Figure 9-3 and the corresponding radiation
patterns are shown in Figure 9-4. For all v > 1 the
amplitude and intensity fall to zero at the rim r = a. As
u-+oo, the distributions approach a gaussian form.
1.0 1_///7- -_-----7 _ T f 1 r !
I kNNN_
\\\\\\\. i
41- \ \\\\x,_ .z
4
7to 2
T 7 _ 7
v=O
-.4 ___ __ i
0 2 4 6 8 I0
2fro
a =---g- 0
Figure 9-4. Sonine distribution radiation patterns.
3
TrO 2
Amplitude
Intensity
distribution distribution v r/
5/2
Uniform Uniform 1 1
Spherical Parabolic 3/2 8/9
Parabolic Bell-shaped 2 3/4
2
i7-0 2
I
-frO2
2 4
1/2 _ X_
I I I l I
.2 .4 ,6 .8 1.0 t.2 1.4
Figure 9-3. The Sonine distributions.
Applying equation (7) to these distributions we find
that
which gives the following values:
mr
0
2v- 1
= _ (12)
1/2
We see no fundamental reason why, in large dishes (50
to 100 m), distributions at least as uniform as the case
v = 3/2 cannot be obtained, and with enough effort we
feel that illumination efficiencies on the order 90% are
realizable.
The simplest way to illuminate a large paraboloid is
with a feed horn at the prime focus, and many radio
astronomy antennas have prime focus feeds. More
recently, Cassegrainian and Gregorian systems involving
a secondary reflector have come into use. The secondary
reflector is typically some 10% to 20% of the diameter
of the primary mirror and thus shadows some 1% to 4%
of the collecting area. Also, just as in optical telescopes,
the hollow pupil produced by the central stop has
somewhat greater near-in side lobes. Finally, the secondary
mirror represents some additional expense. For
Cyclops these disadvantages are more than offset by
several important advantages.
First, the cluster of feed horns and receivers can be
located in the shadow of the secondary mirror near the
vertex of the main dish. This eliminates the shadowing
and scattering that these horns and a prime focus receiver
house would produce, allows convenient access to
the receiver house, and greatly reduces the cabling and
piping costs. Figure 9-5 shows various possible arrangements
for clusters of feed horns disposed in the shadow
of the secondary mirror. Off-axis feeds are obtained by
tilting the _condary mirror.
90