U.S. patent number 3,828,352 [Application Number 05/277,670] was granted by the patent office on 1974-08-06 for antenna system employing toroidal reflectors.
This patent grant is currently assigned to Thomson-CSF. Invention is credited to Bernard Daveau, Serge Drabowitch.
United States Patent |
3,828,352 |
Drabowitch , et al. |
August 6, 1974 |
ANTENNA SYSTEM EMPLOYING TOROIDAL REFLECTORS
Abstract
A microwave antenna consists of two toroidal reflectors turning
their concave sides toward a common axis of rotation, i.e., a main
reflector farther from that axis and an ancillary reflector closer
thereto. The main reflector has a parabolic generatrix with a focal
point situated on a point between the axis and the vertex of the
ancillary reflector in a common equatorial plane of the two
reflectors; the ancillary reflector has a hyperbolic generatrix
whose foci substantially coincide with the focal point and with the
vertex of the parabolic generatrix.
Inventors: |
Drabowitch; Serge (Paris,
FR), Daveau; Bernard (Paris, FR) |
Assignee: |
Thomson-CSF (Paris,
FR)
|
Family
ID: |
9081622 |
Appl.
No.: |
05/277,670 |
Filed: |
August 3, 1972 |
Foreign Application Priority Data
|
|
|
|
|
Aug 9, 1971 [FR] |
|
|
71.29057 |
|
Current U.S.
Class: |
343/837;
343/840 |
Current CPC
Class: |
H01Q
19/19 (20130101) |
Current International
Class: |
H01Q
19/10 (20060101); H01Q 19/19 (20060101); H01q
019/10 () |
Field of
Search: |
;343/781,837,840,912 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Lieberman; Eli
Attorney, Agent or Firm: Ross; Karl F. Dubno; Herbert
Claims
What we claim is:
1. An antenna structure for the focusing of microwaves, comprising
a first toroidal reflector and a second toroidal reflector centered
on a common axis of rotation, each of said reflectors having a
surface which is concave toward said axis of rotation and has a
generatrix substantially in the form of a segment of a conic
section having a focal point located between said axis of rotation
and a vertex of the respective surface in a common equatorial plane
of said reflectors perpendicular to said axis of rotation; said
second reflector lying between said axis of rotation and said first
reflector, the generatrix of said first reflector being a segment
of a parabola, the generatrix of said second reflector being a
segment of a hyperbola having a focus substantially coinciding with
the vertex of said parabola, said parabola and hyperbola having a
common focal point between said second reflector and said axis of
rotation.
2. An antenna structure for the focusing of microwaves, comprising
a first toroidal reflector and a second toroidal reflector centered
on a common axis of rotation, each of said reflectors having a
surface which is concave toward said axis of rotation and has a
generatrix substantially in the form of a segment of a conic
section having a focal point located between said axis of rotation
and a vertex of the respective surface in a common equatorial plane
of said reflectors perpendicular to said axis of rotation; the
surface of said first reflector following a great circle of radius
R in said equatorial plane and the surface of said second reflector
following a great circle of radius r in said equatorial plane, said
radii substantially satisfying the relationship r = 2R/3.
3. An antenna structure as defined in claim 2 wherein the ratio of
said radii is substantially given by r/R = 0.675.
Description
BACKGROUND OF THE INVENTION
The present invention relates to improvements in microwave antennas
and more particularly to antennas including a toroidal reflector,
with a view to reducing some aberration.
Antennas with toroidal reflectors whose surface is generated by a
curve known as a generatrix, situated in a plane rotating about a
straight line contained within this plane, are known and possess
certain important and interesting properties which have been put to
good use in certain constructions.
If the generatrix is a circle, the surface is a torus in the strict
sense of the term. If the center of the circle is a point on the
straight line taken as the axis of revolution, the torus is a
sphere.
The properties of a spherical reflector are known and are recalled
in what follows. Whatever the angle of incidence of a plane wave
may be, it is focused, at least approximately, near a point
situated on the straight line parallel to the direction of
incidence and passing through the center of the sphere, half way
between this center and the point at which that line intersects the
sphere. The locus of the focal points is therefore a sphere of
radius approximately half the radius of the sphere forming the
reflector. Such a reflector allows an aerial to be constructed with
multiple beams or with a beam scanning a very large angle in all
spatial directions. However, such an antenna has a spherical
aberration which becomes apparent from the fact that the equiphased
front of the wave radiated by the spherical reflector is not plane,
as would be the case with an ideal parabolic reflector, for
instance. Obviously means have been sought for correcting, at least
partially, this spherical aberration.
One of these means has been to use a reflector of sufficiently
large radius for the sphere to be considered, in a first
approximation, equivalent to a paraboloid. A second means of
compensating for spherical aberration has been to operate directly
on the primary sources or to provide correcting lenses. A third
means is to alter the surface of a paraboloid by deforming it in
steps approaching the shape of a sphere. In this case the spherical
aberration is reduced. A transverse cross-section of the reflector
thus obtained shows a staircase profile with steps of the order of
half the operating wave-length. However, a reflector of this type
introduces diffraction on the steps and the bandwidth is relatively
small.
If the generatrix is a parabolic arc rotating around an axis
parallel to the directrix of the parabola, a parabolic torus is
obtained.
If it is desired that the multiple beams or the directions of
incidence are all situated approximately in the same plane, the
reflector should be so designed that the geometric focus of the
parabolic arc coincides with the optimum point of focus, i.e., the
center of the straight-line segment joining the center of the torus
to the apex of the parabolic arc. The locus of the primary sources
to be considered is then a circle of radius equal to half the
length of that line segment situated in a plane perpendicular to
the axis and passing through the center of the torus. In this case
focusing is improved in every plane containing the axis of
revolution of the toroidal reflector and the direction of
incidence. Nevertheless, this toroidal reflector with parabolic
generatrix always shows a certain spherical aberration. Another
drawback of toroidal reflectors is the poor accessibility of the
primary sources, especially if the assembly is of large size. The
installation of the sources also brings with it certain drawbacks.
For example, in an installation situated on the surface of a
planet, if the directions of incidence are situated above the
horizon, the primary sources are necessarily oriented below the
horizon and are exposed to the risk of receiving, on account of the
"overspill" effect, the planetary thermal noise coming from
directions outside the periphery of the reflector.
SUMMARY OF THE INVENTION
The object of our present invention is to remedy the defects which
have been cited.
An antenna structure according to our invention comprises a first
and a second toroidal reflector centered on a common axis of
rotation, each reflector having a surface which is concave toward
that common axis and has a vertex located in a common equatorial
plane perpendicular thereto. The surface of each reflector has a
generatrix which is substantially in the form of a segment of a
conic section having a focal point located, within the equatorial
plane, between its vertex and the axis.
Advantageously, the two generatrices have a common focal point
lying between the axis and the vertex of the smaller, ancillary
reflector disposed closer to that axis. The generatrix of the
other, main reflector preferably has a parabolic curvature whereas
the generatrix of the ancillary reflector is hyberbolically curved,
the second focus of the hyperbola substantially coinciding with the
vertex of the parabola.
Other features will appear in the course of the description which
follows, which is given by way of example with reference to the
appended drawing.
BRIEF DESCRIPTION OF THE DRAWING
FIG. 1 represents an antenna structure according to the
invention;
FIG. 2 represents a section through the structure of FIG. 1, in the
equatorial plane;
FIG. 3 represents a section through the structure of FIG. 1 in the
equatorial plane in the case of a beam divergent from the axis of
that structure;
FIG. 4 represents a structure according to the invention in a
system with three-dimensional axes;
FIG. 5 represents a structure according to the invention with a
mobile exploratory beam; and
FIGS. 6 and 7 represent illumination patterns in elevation and
azimuth obtained with an aerial according to the invention.
SPECIFIC DESCRIPTION
As has been indicated above, the object of the invention is to
establish a class of antennas operating at microwave frequencies
which possess the advantages inherent in toroidal reflectors and
avoid their disadvantages, in particular spherical aberration which
ought to be reduced as far as possible.
The use of two coaxial reflectors to define this new class of
antenna allows certain of the characteristics and advantages
inherent in twin-reflector antennas or so-called Cassegrain or
Schwarzschild antenna to be introduced. However, it should be noted
that the configuration of a twin-reflector aerial which may be
described as conventional is different from that conforming to our
invention. In fact a conventional twin-reflector antenna is
produced by the rotation of two coaxial curves around their common
axis and not around an axis perpendicular to this common axis.
FIG. 1 shows the structure of a system of reflectors according to
the invention.
It comprises a surface described by a first curve 1 and a second
curve 2 both bisected by the same axis 3. The two curves 1, 2
perform the role of generatrices for the system obtained by
rotating the two curves around a straight line 4 which is situated
in their common plane and perpendicular to their common axis 3. It
is worth noting that the axis of revolution 4 lies on the concave
side of these curves.
By rotating around the axis 4, curves 1, 2 generate two coaxial
toroidal surfaces ST1 and ST2. Surface ST1 forms what may be termed
the outside or main reflector and surface ST2 defines the inside or
auxiliary reflector.
The generatrices 1 and 2 have curvatures compatible with the
desired properties as regards the focusing in any plane passing
through the axis of revolution of the system.
In particular these curves are conic sections each having a focal
point, namely to point F, located before the axis of revolution 4
and the corresponding vertex S, S.sub.1 in a common equatorial
plane of surfaces ST.sub.1 and ST.sub.2. Thus the curve 1 may be a
parabolic arc and the curve 2 a hyperbolic arc. The focus F of the
parabola 1 coincides approximately with one of the foci of the
hyperbola 2, while the other focus F.sub.1 of the hyperbola is near
the apex S of the parabolic arc. The primary source is situated at
this focus F.sub.1 which in practice merges with the apex S of the
parabola.
A study of the operation of the system shown in FIG. 1 will enable
a determination of the optimum structure to be adopted for the
antenna according to the invention.
FIG. 2 shows a section through the structure of FIG. 1 in the
equatorial plane, i.e., the plane orthogonally intersecting the
axis of rotation 4 of the system and containing the common axis 3
of the reflectors.
In the case of FIG. 2 it is assumed that the focus F.sub.1
associated with the curve d.sub.1 (i.e., with a great circle of
toroidal surface ST.sub.2 of FIG. 1) merges with the apex S of the
parabola 1 so as to come to lie on a great circle of toroidal
surface ST.sub.1 represented in FIG. 3 by the curve d. A primary
source is located at this point S. A beam S-M issuing from the
point S is reflected from the convex ancillary mirror ST.sub.2
toward the concave main mirror ST.sub.1 on which it impinges at P
and from where it is again reflected in a direction S-O parallel to
the axis 3. Conversely, an incident wave whose direction of
incidence is situated in a plane perpendicular to the axis of
revolution, corresponding to a line V-P, is first reflected by the
main reflector ST.sub.1 which redirects it along line P-M onto the
auxiliary reflector ST.sub.2. The latter in its turn redirects it
to focal point F.sub.1 coinciding with the apex S of the main
reflector.
In the case of FIG. 2 it has been assumed that the Gauss
approximation applies, i.e., that the beams are but slightly
inclined with respect to the optical axis of the system. It is then
possible to establish a relationship between the radii R = OS of
the main reflector and r = OS.sub.1 of the auxiliary reflector.
Applying the classic laws of optics one obtains:
1/S.sub.1 S + 1/S.sub.1 F = 2/S.sub.1 O
or ##SPC1##
whence r = 2R/3.
Under these conditions the aerial structure is stigmatic for
paraxial rays.
However, when the beams emitted from the point S or impinging
thereon diverge sufficiently from the axis for the Gauss
approximation to be no longer valid, it may be advantageous to
slightly modify the ratio of the two reflectors r/R if it is
desired that the aberrations be kept at an acceptable minimum level
for a given aperture (scanning angle) of the system.
FIG. 3 shows a plot of the aberrations in the equatorial plane. In
this Figure an axis S-X passes perpendicularly to the axis S-P
through the apex S, and the projection of the point P of the main
reflector on this axis S-X is designated T. At t we have shown the
angle between the line S-M and the horizontal axis and at s the
angle at which the point of incidence M of the incident beam on the
auxiliary mirror ST.sub.2 (represented by curve d.sub.1) is viewed
from the center O. In this case the line P-V is no longer parallel
to the horizontal axis but diverges from it by an angle equal to
2s-t and the extension of line O-P intersects the axis S-X at point
Q.
An aberration parameter D is then given by:
D = SM + MP - QP - 2S.sub.1 S
where SM = MP = (R.sup.2 + r.sup.2 - 2 Rr cos s).sup.1/2
and QP = R 1 - cos 2 s/cos (2s - t)
If this parameter is developed with respect to s to the fourth
order it is found that:
SM = R - r + [rR/2 (R - r)] s.sup.2 - [ rR/24 (R - r)] (1 + [3rR/(R
- r).sup.2 ]) s.sup.4
To find the distance QP, recourse is had to the fact that the
relation OM/sin t = OS/sin (t + s) allows the angle t to be
calculated from its tangent which is tan t = r sin s/R - r cos
s
It can be shown that, with the exception of the sixth-order term of
s, QP = ST = R (1 - cos 2s) where T is the intersection of the axis
S-X with the extension of the path P-V of an emitted or incident
beam not parallel to the horizontal axis S-O, whence
QP = R (2 s.sup.2 - [2/3] s.sup.4)
and the aberration D = [R/R - r] (3r - 2R) s.sup.2 + [R/12] [8 -
[r/R - r] (1 + [3rR/(R - r)] 2)]s.sup.4. D is a fourth order
function of s if r = 2/3 R, in which case D = - 2/5 R s. With the
exception of the third-order term of s, SQ = ST = 2 Rs = X from
which D = (5/32) (X.sup.4 /R.sup.3).
This relationship shows that the phase error, at a point of the
reflector for which the coordinate X is given, varies in inverse
ratio to the cube of the radius R. Put another way, any reduction
in R intended to reduce the size of the system results in a rapid
increase in aberrations.
However, it should be noted that the twin-reflector system
according to the invention enables, in comparison with a single
reflector of the same size, the phase error to be reduced by a
considerable proportion. In an actual example this proportion has
been found to be of the order of 1.6.
When the angle s increases, it is possible to compensate for the
rapid increase in the aberration D by means of the second-order
term of s by taking a value for the radius r of the auxiliary
reflector greater than 2R/3. If the relationship D/R is calculated
as a function of X/R for r/R = 2/3 and r/R = 0.675, it is found
that, for this latter value, the maximum phase error on a reflector
of diameter 2R/3 is minimal.
A study of the aberrations may be performed for the general case
and FIG. 4 shows the system which makes this study possible.
However, the detailed calculations will not be made here. The
calculation of the path-length difference D = (SM + MP - PT) - 2
(SS1) requires that the hyperbolic meridian d.sub.11 and the
parabolic meridian d.sub.10 be determined to calculate the
coordinates of the various points M, M.sub.0, P.
The phase-error as a function of t and s may be stated as E (t,s) =
[360 D (t,s)/.lambda.] in degrees where .lambda. is the operating
wavelength and D(t,s) is the difference in path length as a
function of the angles s and t.
It may thus be seen that the class of antennas according to the
invention offers a certain number of advantages derived both from
the properties of antennas with toroidal reflectors and from
antennas with twin reflectors.
In particular, the primary sources become accessible, being
situated behind the main reflector, and they are directed towards
the sky, which shields them from the disturbances of terrestral
radiation.
These antennas with double toroidal reflectors operate with a large
aperture (scanning angle), the radiation characteristics becoming
independent of the direction of incidence. As for spherical
aberration, which is highly inconvenient in antennas with a single
toroidal reflector, this is reduced for a toroidal aerial with twin
reflectors of the same size.
According to the principles set out above, an antenna has been
produced capable of exploring in a given azimuth an area of space
included within a considerable angle of elevation, of the order of
40.degree.. The sweep is carried out by means of a mobile beam
whose angular width corresponds to a radiation aperture of the
order of 30 m and whose wavelength is 30 cm (1,000 Mhz).
The antenna is formed by two coaxial toroidal reflectors, i.e., a
main reflector 5 and an auxiliary reflector 6 (FIG. 5).
The primary source is situated in the vertical plane of symmetry of
the system, near the main reflector 5.
To carry out the elevational sweep of the space to be explored,
this primary source oscillates about the axis of revolution of the
system.
FIG. 5 shows in schematic fashion such an antenna system with two
extreme positions 7 and 8 of the primary source and the directions
of the beams in these cases.
The relationship of the radii of the main and auxiliary reflectors
is so chosen, in accordance with what has been indicated above,
that the spherical aberration is reduced in considerable proportion
with respect to what it would be for an antenna with a single
toroidal reflector of the same size.
For an antenna so defined the polar diagrams (illumination laws)
may be plotted according to the main elevation and azimuth
diagrams.
FIG. 6 gives the illumination pattern in elevation, whereas FIG. 7
gives the illumination pattern in azimuth from which it will be
noticed that there is a masking effect due to the auxiliary
reflector; this effect does not exist in elevation, where it would
be a good deal more inconvenient.
* * * * *