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

Corrugatedhornssupportingbalancedhybridmodes
hav equalE-plane and H-plane patterns with zero cross
polarization component and are therefore well suited for
illuminating reflectors having axial symmetry (refs. 2-4).
In the focal plane the field amplitude as a function of
radius is very nearly given up by the classical Airy
distribution
Zll(2gOop/X)
u@) = Uo (17)
2_OoP/_
the wave off axis, increases the convexity of the
wavefront at the axis and thus serves to guide the energy
flow away from the axis. Since all transitions can be
many wavelengths long, very low standing wave ratios
should be expected. The major problem with such a
horn might be the loss of the dielectric and the
consequent elevation of the noise temperature. If this
proves to be the case, artifical dielectrics might be
preferable.
for values of the (maximum) convergence angle/9o from
zero to 30° . For /9o > 30° the energy in the rings
increases at the expense of energy in the central spot. In
addition, for Oo _ 60 ° regions of reversed energy flow
appear in what, for lower values of 0o, were the dark
rings. Thus for wide angle feeds the focal plane matching
must include severalrings to obtain high efficiencies.
Thomas (refs. 5, 6) has shown that it is possible to
match the focal plane fields of a reflector having 8o = 63°,
and to obtain efficiencies within 0.1% of the theoretical
values of 72.4%, 82.8%, 87.5%, 90.1% and 91.9%
for feed diameters capable of supporting one to five
hybrid modes, respectively. The match requires that the
relative amplitudes of the modes of different orders be
correct. Mode conversion can be accomplished in various
ways such as by irises or steps in the waveguide or horn.
Whether the ratios between the mode amplitudes can be
made to vary in the appropriate fashion to preserve the
distribution of equation (17) as X varies is another question.
The efficiencies cited above assume that the guide
radius at the mouth equals the radius of the first,
second, third, fourth or fifth null of equation (16), a
condition that is only possible at discrete frequencies.
Thus, although bandwidth ratios of 1.5 to 1 have been
reported (ref. 7) for single mode horns, it is not clear
that multimode horns designed to match focal plane
fields over several rings of the diffraction pattern can
achieve high performance over such bandwidths.
For broadband operation the second approach of
generating a spherical cap of radiation several wavelengths
in diameter to match the field some distance in
front of the focal plane appears more promising. Higher
order modes are involved here also, but since their role
now is simply to maintain the field at a nearly constant
value over the wavefront at the mouth of the horn, the
higher order mode amplitudes are less than in the focal
plane horn where field reversals are required. Thus the
mode conversion process is less critical and might take
the form of a dielectric cone lining the horn as shown
purely schematically in Figure 9-8. The dielectric slows
Figure 9-8. Dielectric loaded corrugated feed horn.
With this type of feed horn, the spherical cap of
radiation illuminates the secondary mirror in the same
way that the spherical cap of radiation generated by the
secondary illuminates the primary mirror, except that
for the feed horn the cap dimensions are less and the
secondary spillover is therefore greater for a given
illumination at the rim. However, the secondary spillover
represents side lobe response aimed at the sky, so the
effect on noise temperature is negligible.
The reradiation reflected in the transmission mode by
the secondary onto the primary in the shadow region of
the secondary is reflected off the primary as a parallel
wavefront that is intercepted by and re-reflected by the
secondary. After this second reflection off the secondary,
most of this radiation is refected by the
primary to a distant focus on the beam axis after which
the radiation diverges. The net result is a general rise in
the side lobe level at modest off axis angles. By applying
spherical wave theory to the design of Cassegrainian
systems, Potter (ref. 8) has shown that it is possible to
shape the secondary mirror near the vertex so that the
radiation that would normally be reflected into the
shadow region is redirected into the unshadowed region
where it combines constructively with the rest of the
radiation. This reduces the shadowing loss and improves
the side lobe
pattern.
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