Antenna feed arrangement for correcting for astigmatism

The present invention relates to an antenna feed arrangement for correcting for astigmatism caused by an offset main reflector. The feed arrangement comprises at least one feed element, a first and a second cylindrical reflector disposed along the feed axis of the antenna with corresponding axes across the reflecting surfaces thereof oriented orthogonal to each other, and a pair of plates comprising a conductive material which are disposed parallel to, and on either side of, the feed axis of the antenna to enclose the area between the at least one feed element and the first reflector while forming an aperture thereof within a predetermined distance from the second reflector. The feed arrangement components are oriented with respect to each other and the aperture of the antenna to provide separate phase centers with a predetermined spacing therebetween on the feed axis for the two principal planes of curvature of a wavefront illuminating the antenna aperture to correct for astigmatism, which predetermined spacing can be selectively changed.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to an antenna feed arrangement for correcting 
for astigmatism caused by the main reflector of an antenna. 
2. Description of the Prior Art 
When a feed is displaced from the focus in a reflector antenna, the loss in 
efficiency is due primarily from astigmatism which is found to be a 
different amount at each location of the feed on the focal surface. 
Antenna systems have been previously devised to correct for certain 
aberrations including astigmatism. 
U.S. Pat. No. 4,145,695 issued to M. J. Gans on Mar. 20, 1979 relates to 
launcher reflectors which are used with reflector antenna systems to 
compensate for the aberration of astigmatism which was found to be 
introduced in the signals being radiated and/or received at the off-axis 
positions. A major portion of such phase error is corrected by using, with 
each off-axis feedhorn, an astigmatic launcher reflector having a 
curvature and orientation of its two orthogonal principal planes of 
curvature which are chosen in accordance with specific relationships, the 
launcher reflector being fed by a symmetrical feedhorn. 
U.S. Pat. No. 4,339,757 issued to T-S. Chu on July 13, 1982 and U.S. Pat. 
No. 4,343,004 issued to E. A. Ohm on Aug. 3, 1982 each relate to an 
antenna arrangement capable of correcting for astigmatism over a broadband 
range. Each of the patented arrangements comprise a main focusing 
reflector arrangment, a feed arrangement and an astigmatic correction 
means disposed between the feed arrangement and the main focusing antenna 
arrangement. The astigmatic correction means comprises a first and a 
second doubly curved subreflector disposed in a predetermined manner in 
the antenna arrangement and which are curved in orthogonal planes to 
permit the launching and reception of an astigmatic beam of constant size 
and shape over a broadband range. 
The prior art arrangements, however, only compensate for astigmatism for a 
predetermined off-axis position on the focal surface. Therefore the 
problem remaining is to provide astigmatic correction feed arrangements 
which can be easily reoriented on the focal surface of an antenna 
arrangement and can be adjusted to cancel astigmatism at the new location. 
SUMMARY OF THE INVENTION 
The foregoing problem has been solved in accordance with the present 
invention which relates to an antenna feed arrangement for correcting for 
astigmatism caused by an offset main reflector of an antenna. More 
particularly, the feed arrangement comprises at least one feed element, a 
first and a second cylindrical reflector disposed along the feed axis of 
the antenna with corresponding axes across the reflecting surfaces thereof 
oriented orthogonal to each other, and a pair of plates comprising a 
conductive material which are disposed parallel to, and on either side of, 
the feed axis of the antenna and enclose the area between the at least one 
feed element and the first cylindrical reflector while extending along the 
feed axis of the antenna to form an aperture thereof within a 
predetermined distance from the second cylindrical reflector. The at least 
one feed element, the first and second cylindrical reflectors and the pair 
of plates being oriented with respect to the aperture of an antenna, 
wherein the feed arrangement is to be used, to provide a first and a 
second phase center for two principal planes of curvature of a wavefront 
illuminating the aperture of the antenna which are a predetermined 
distance apart along the feed axis of the antenna to correct for 
astigmatism. 
It is an aspect of the present invention to provide a feed arrangement 
which can correct for any particular value of astigmatism by the movement 
of two cylindrical reflectors toward or away from each other along the 
feed axis of the antenna to change the distance between two phase centers 
for two principal planes of curvature of a wavefront illuminating the 
aperture of the antenna wherein the feed arrangement is used. 
Other and further aspects of the present invention will become apparent 
during the course of the following description and by reference to the 
accompanying drawings.

DETAILED DESCRIPTION 
As was stated hereinbefore, when a feed is displaced from the focus in a 
reflector antenna, the loss in efficiency due to aberrations is primarily 
attributed to astigmatism. To better understand this statement and the 
present invention, the hereinabove-mentioned loss can be eliminated by 
using a feed with different phase centers in the two principal planes of 
its beam, as shown in FIG. 1. In order to operate efficiently over a wide 
range of frequencies, it is desirable that the two phase centers F and F' 
and the two associated beam widths .theta. and .theta.' in FIG. 1 be 
frequency independent. This can be accomplished by combining a small horn 
with two cylindrical reflectors, as shown in the article "An Improved 
Antenna for Microwave Radio Systems Consisting of Two Cylindrical 
Reflectors and a Corrugated Horn" by C. Dragone in BSTJ, Vol. 53, No. 7, 
September 1974 at pages 1351-1377, and then properly choosing the focal 
lengths of the two reflectors so as to produce over the main reflector 
aperture a magnified image of the horn aperture as shown, for example, in 
the articles "A Satellite System with Limited-Scan Spot Beams" by A. 
Acampora et al. in IEEE Trans. on Comm., Vol. COM-27, No. 10, October 1979 
at pages 1406-1415 and "Satellite Phased Arrays: Use of Imaging Reflectors 
with Spatial Filtering in the Focal Plane to Reduce Grating Lobes" by C. 
Dragone et al. in BSTJ, Vol. 59, No. 3, March 1980 at pages 449-461. 
Such arrangement, however, is not suitable for producing a variable 
distance .DELTA.f between the two phase centers F and F'. In fact if one 
tries to vary .DELTA.f by changing the distances of the two reflectors 
from the horn, it is found that the beamwidths .theta. and .theta.' will 
change, thus causing a decrease in aperture efficiency. This is an 
important limitation for it implies that a given feed arrangement can only 
be used for certain locations in the vicinity of the focus since the value 
of .DELTA.f required to correct astigmatism is a function of the feed 
displacement from the focus. Other undesirable features of the above 
arrangement are relatively large dimensions for one of the two reflectors 
and a large feed aperture. 
To remove such undesirable features, the above-described arrangement is 
modified in accordance with the present invention as shown in the 
arrangement of FIG. 2. In FIG. 2, a feed arrangement is disposed along the 
feed axis 10 of a curved focusing main reflector 11 comprising a feedhorn 
12 and a first cylindrical subreflector 14 located between a pair of 
parallel plates 16, and a second cylindrical subreflector 18. In this 
arrangement, the corresponding flat and curved axes across the reflecting 
surfaces of the first and second cylindrical subreflectors 14 and 18 are 
disposed orthogonal to each other along feed axis 10. Additionally, the 
first and second subreflectors 14 and 18 are arranged such that phase 
center F is disposed between first and second subreflectors 14 and 18 
since it is dependent on the curvature of subreflector 14 and the distance 
of feedhorn 12 from subreflector 14. The second phase center F' is 
disposed between the second subreflector 18 and main reflector 11 since it 
is dependent on the curvature of subreflector 18 and the distances of 
aperture D' at the end of the plates 16 from subreflector 18. 
In the arrangement of FIG. 2, the aperture D of feedhorn 12 is disposed at 
a distance s from first subreflector 14. The wavefront radiated by 
feedhorn 12 is a cylindrical wavefront guided by the two plates 16. After 
reflection by the first cylindrical subreflector, the two plates 16 are 
truncated at a predetermined distance l from the first subreflector 14 and 
a predetermined fixed distance s' from second subreflector 18. The 
aperture defined by this truncation of plates 16 is centered at D', with 
width w' determined by the spacings of the two plates 16, and is 
illuminated by the cylindrical wavefront produced after reflection by 
first subreflector 14. The wave radiated by the aperture at D' illuminates 
second cylindrical subreflector 18. In order to produce, over the main 
reflector aperture, an image of the aperture of feedhorn 12, the distances 
s and s' of D and D', respectively, from the two subreflectors 14 and 18 
must satisfy the lens equation, which requires 
##EQU1## 
where f and f' are the focal lengths of the two subreflectors 14 and 18 
and d' is the distance of the main reflector 11 from the second 
subreflector 18. It can be shown that the angular widths .theta. and 
.theta.' of the image are given by the equation 
##EQU2## 
where w' and w are the plate and the feedhorn 12 aperture dimensions, 
respectively, as shown in FIG. 2. 
The property of the main reflector 11 illumination, obtained with such a 
feed arrangement, is that its wavefronts have different centers of 
curvature F and F' in the two principal planes. The location of F and F' 
are determined by the lens equation. More precisely, let the feedhorn 12 
be tapered as shown in FIG. 4 so that its two side-walls intersect each 
other at a distance p from the first cylindrical subreflector 14. Then the 
lens equation requires 
##EQU3## 
where r is the distance of phase center F from the first cylindrical 
subreflector 14. Similarly, for the distance r' of phase center F' from 
the second cylindrical subreflector 18, 
##EQU4## 
where p'=infinity if the two plates 16 are parallel as in FIG. 2. If, 
however, the ends 19 of the two plates are tapered as in FIG. 4, then they 
will intersect each other at a finite distance p' from the second 
cylindrical subreflector 18. 
If p=p'=infinity and the main reflector 11 is at a large distance from 
feedhorn 12 such that d' is effectively equal to infinity, then 
EQU r=s=f, r'=s'=f' (5) 
and 
EQU .DELTA.f=l+2f'-f. (6) 
The value of .DELTA.f can be varied without affecting .theta. and .theta.' 
by simply changing the distance l of aperture D' of plates 16 from the 
first reflector 14. 
A simple arrangement for permitting the distance l of aperture D' to be 
changed is shown in FIG. 3. There, feedhorn 12 is fixedly mounted to first 
cylindrical reflector 14 at a predetermined distance s therefrom to 
provide phase center F at a fixed predetermined distance r from 
subreflector 14. One or both of plates 16 include a slot 20 therein 
running parallel to feed axis 10 of the antenna arrangement with first 
subreflector 14 including a threaded hole for mounting the plates 16 
thereto with a screw 22 through slot 20. Therefore, by loosening screw 22, 
the combination of feedhorn 12 and first subreflector 14 can be moved 
along slot 20 which correspondingly moves phase center F along feed axis 
10 either toward or away from second subreflector 18. Second subreflector 
18 is fixedly mounted to plates 16 such that the aperture of the plates 16 
at D' is a fixed distance s' from second subreflector 18 which fixes 
second phase front F' to a predetermined location on feed axis 10. 
Therefore, by moving the combination of feedhorn 12 and first subreflector 
14 along slot 20, the distance .DELTA.f between the phase centers F and F' 
can be varied to correct for different values of astigmatism. 
It is to be understood that the above-described embodiments are simply 
illustrative of the principles of the invention. Various other 
modifications and changes may be made by those skilled in the art which 
will embody the principles of the invention and fall within the spirit and 
scope thereof. For example, feedhorn 12 can comprise one or more feedhorns 
or feed elements to form a small array, and in FIG. 3 plates 16 can be 
secured together so that only one slot 20 is required rather than a 
separate slot for each plate where such plates are not secured together. 
Furthermore, in the exemplary arrangement of FIG. 2, the present invention 
does not preclude the use of other subreflectors between second 
cylindrical subreflector 18 and main reflector 11. It is just to be 
understood that in the present feed arrangement as illustrated in FIG. 2, 
the elements of the feed arrangement are oriented such that images of the 
orthogonal first and second focal lines 26 and 28 corresponding to the 
principal phases of illumination over the main reflector 11 are formed as 
lines 22 and 24, respectively, at the respective apertures of feedhorn 12 
and plates 16 via respective phase centers F and F'.