FIELD OF THE INVENTION The present invention relates generally to antennas and, more particularly, to reflector antennas.

BACKGROUND OF THE INVENTION Conventional reflector antenna designs require a tradeoff between high efficiency and low sidelobes. In general, the aperture illumination is tapered to minimize near in sidelobes. A-15 dB edge taper from the peak is a typical aperture distribution to minimize sidelobes adjacent to the main beam. However, tapering the aperture distribution reduces the illumination efficiency of the antenna aperture. For example, a-15 dB taper can reduce the aperture efficiency by about 25 percent and result in a 1.2 dB loss in antenna gain.

FIG. 1 shows a prior art reflector antenna 10 having a main reflector 12 that reflects energy from the feed 14. Far-out sidelobes due to so-called spillover energy 16, which exits the feed 14 but does not reach the reflector 12, and so-called edge diffraction 18, must also be taken into account.

One prior art attempt shapes a subreflector to redistribute a high taper feed pattern to almost uniform distribution on the main reflector aperture. However, with such a main reflector distribution, the near-in sidelobes are typically too high to meet standard commercial sidelobe requirements, e. g., 29-2510g, o (0) dBi, where 8 is the angle from antenna boresight.

Another attempt to provide low sidelobes and high efficiency includes synthesizing dual- shaped reflectors to produce aperture power distribution defined by 1- (1-taper) (r/a) **2, where taper is the amplitude taper, r is the radial variable, and a is the main reflector radius. This arrangement does not provide low near-in sidelobes without relatively low illumination efficiency.

It would, therefore, be desirable to provide a reflector antenna system that provides relatively low near-in and far-out sidelobes and high aperture efficiency.

SUMMARY OF THE INVENTION The present invention provides an antenna system having a main reflector and a subreflector having geometries that optimize antenna efficiency. While the invention is primarily shown and described in conjunction with a truncated Gaussian distribution over a circular

aperture, it is understood that the invention is applicable to other antenna shapes and configurations.

In one aspect of the invention, a method for synthesizing a dual reflector antenna includes selecting certain parameters for the antenna such as reflector size, feed location, sub reflector midpoint location, main reflector midpoint location, and synthesis interval. The method further includes mapping energy from a known feed pattern to a selected analytical aperture distribution.

From the initial locations of the feed and reflector midpoints, the shapes of the main and sub reflectors are synthesized using wavefront parameters to determine surface normals for each surface point. The resultant reflector shapes are adjusted as necessary to correct an computational errors.

The actual aperture field distribution is modified from the initial truncated Gaussian field distribution, for example, for the final synthesis of the shaped reflectors to allow the near in sidelobes to bump against a predetermined sidelobe requirement for optimizing overall antenna efficiency.

BRIEF DESCRIPTION OF THE DRAWINGS The invention will be more fully understood from the following detailed description taken in conjunction with the accompanying drawings, in which: FIG. 1 is a diagrammatic illustration of a prior art reflector antenna system; FIG. 2 is a side view of a shaped dual reflector antenna system in accordance with the present invention; FIG. 3 is a schematic depiction of the antenna system of FIG. 2 showing a feed angle; FIG. 4 is a schematic depiction of an exemplary feed pattern for the antenna system of FIG. 2; FIG. 4A is a schematic depiction of an exemplary aperture field distribution for the antenna system of FIG. 2; FIG. 5 is a graphical depiction of an exemplary antenna pattern produced by the antenna system of FIG. 2; FIG. 6 is a flow diagram showing an exemplary sequence of steps for synthesizing the shapes of the main and sub reflectors in accordance with the present invention; FIG. 7 is a schematic depiction showing unit vectors used to synthesize the reflector shapes in accordance with the present invention; FIG. 8A is a graphical representation of an exemplary feed pattern showing a portion for mapping to the aperture field distribution of FIG. 8B;

FIG. 8B is a graphical representation of an exemplary aperture field distribution showing a portion for mapping to the feed pattern of FIG. 8A; FIG. 9A is a pictorial side view of a feed pattern about a feed axis of an antenna system in accordance with the present invention; FIG. 9B is a pictorial top view showing an angle of rotation about the feed axis of FIG.

9A; and FIG. 10 is a pictorial representation of a spherical wavefront from a point source feed of an antenna system in accordance with the present invention.

DETAILED DESCRIPTION OF THE INVENTION FIG. 2 shows a dual reflector antenna system 100 having high antenna efficiency and low sidelobes in accordance with the present invention. The antenna system 100 includes a subreflector 102 that reflects energy from a feed 104 to a main reflector 106. The main reflector 106 provides an antenna beam for transmission from the antenna system 100.

In general, the initial curvatures of the main reflector 104 and the sub reflector 102 are determined from a selected aperture energy distribution, such as truncated Gaussian. Certain parameters are selected from which the antenna shapes are incrementally defined. Input parameters include the main reflector midpoint location MRM, sub-reflector midpoint location SRM, and feed center location FC shown in FIG. 3, as well as the reflector size. Additional parameters include feed angle theta and feed taper, which are shown in FIG. 4, and the synthesis interval described below.

The initial aperture field distribution is then selected based upon the requirements of an intended application. The initial field distribution can be selected from a wide variety of suitable analytical, i. e., defined by a function, aperture distributions including truncated Gaussian, cosine function, quadratic function, and the like having a constant pedestal. FIG. 4A shows an exemplary first order cosine field distribution from an aperture AP of the main reflector MR.

In general, the shapes of the main and sub reflectors are incrementally defined based upon the desired aperture field distribution and feed pattern using the law of energy conservation, Snell's law, and equal path length requirements (feed to sub reflector to main reflector). As is well known to one of ordinary skill in the art, the ray path that follows Snell's law is the path such that the reflection angle is equal to the incident angle.

The reflector shapes can be modified in relation to the sidelobe requirements for the particular application. More particularly, the reflector shapes can be modified from the analytical function aperture distribution such as the truncated Gaussian, such that the sidelobes track the

allowable sidelobe envelope with a predetermined margin. By allowing the sidelobes to be as large as possible, yet less than the maximum allowable sidelobes, the resultant dual reflector antenna has optimal overall efficiency ilt. That is, the reflector shapes provide the optimal balance between low sidelobes and illumination efficiency.

In addition, a relatively large portion of the energy, e. g., 95-98%, radiated from the feed with a feed angle of about 45-50 degrees for example, can be captured and efficiently used so as to minimize spillover losses and maximize the overall efficiency.

FIG. 5 shows an exemplary antenna pattern 150 for a 95 cm main reflector at 30 GHz in an azimuth plane. As can be seen, the pattern 150 tracks a sidelobe envelope 152, which can be 29-25 loglo (theta) for example. The pattern sidelobes approach the envelope 152 while remaining underneath. A margin can be built in, which can include production tolerance, to prevent the sidelobes from exceeding the envelope.

This invention can be applied to various antenna sizes as long as the subreflector is "electrically sufficiently large", e. g., in the order of 5 wavelengths or larger. For subreflectors smaller than about 5 wavelengths, the diffraction effect becomes relatively high so that the antenna performance will be degraded significantly. The range of the feed taper is typically from about-dB to about-20dB down, which corresponds to approximately 96% to 99% spillover efficiency. The feed angle ranges can vary widely depending on the desired feed pattern.

However, for minimal spillover lobes, angles from about 45° to about 50 ° half angle have been found optimal. The overall antenna efficiency will depend on the required sidelobe envelope.

Efficiencies from about 70% to about 80% for typical commercial sidelobe requirements have been achieved.

FIG. 6 shows an exemplary sequence of steps for defining a dual reflector antenna in accordance with the present invention. It is understood that the operator has a rough idea of the size and location of the feed, main reflector and sub reflector of the antenna. In step 200, initial information for the antenna is entered including the feed center, the sub-reflector midpoint, and the main reflector midpoint. In step 202, further information for the antenna is entered including main reflector size, feed angle, feed taper, and synthesis interval. The main and sub reflector surfaces are defined from initial information over a feed angle increment defined by the operator.

In step 204, the operator enters a desired aperture field distribution, such as truncated Gaussian, on the main reflector in a linearly piecewise manner, e. g., incrementally across the main reflector aperture. It is understood that the synthesis interval can vary based upon the

degree of linearity of the field distribution, e. g., smaller step sizes near the field distribution peak where the curvature is higher.

An initial antenna coordinate system including unit vectors is established in step 206.

This local coordinate system is determined by the feed center FC, the sub reflector midpoint So and the main reflector midpoint Mo. As shown in FIG. 7, a unit vector system can define the initial components as a starting point for the synthesis process. As shown, a first unit vector u, extends from the feed center FC to the sub reflector midpoint So, a second unit vector t) smO extends from the sub reflector midpoint So to the main reflector midpoint Mo, and a third unit vector umoa extends from the main reflector midpoint Mo to the main reflector aperture AP.

Referring again to FIG. 6, in step 208, a mapping function is generated to map the energy between the known feed pattern (f (O) inFIG. 8A) and the known desired aperture field distribution AFD (p (Q) inFIG. 8B). From the laws of conservation of energy, it is known that every incremental portion of the energy from the feed must equal the corresponding portion of the energy at the aperture. In one embodiment, the energy for a given distance p from the peak of the aperture field distribution is determined by integrating the selected area AA under the distribution curve AFD. The corresponding feed pattern angle theta having the same energy is then determined. This process continues to provide a mapping function p (6) of the energy between the feed pattern and the aperture field distribution.

In step 210, the feed local coordinate system and the total path length of the energy from the feed to the sub reflector to the main reflector aperture is initialized. FIG. 9A is a side view of the feed angle A and FIG. 9B is a top view of the feed pattern FP showing the angle about the feed pattern. In step 212, a theta angle loop is initiated. As described above, the feed angle is measured from the initial feed axis FA, which is determined by the feed center and the sub reflector midpoint. In step 216, a phi angle is initiated. The phi angle loop provides an incremental 360 degree rotation about the initial feed axis FA.

In step 216, wavefront parameters of the input ray are computed for later use in finding each reflector surface normal and surface point. More particularly, as shown in FIG. 10, energy from the feed is reflected by the sub reflector SR to the main reflector MR. Defining the feed as a point source, the feed energy has a spherical wavefront. The initial input ray is then defined by two principal radii of curvature, which ride on a plane. Defining wavefront parameters is well known to one of ordinary skill in the art. Since the energy radiated from the feed is a spherical wave, the radius of curvature of the wavefront to the sub reflector corresponds to the distance

from the feed F to the sub reflector SR. The curvature is the inverse of the radius. Over the theta and phi loops, the wavefront parameters are used to define surface normals for each point on the main and sub reflectors MR, SR. When using the relatively small increments of the theta and phi loops, the wavefront can be considered local with respect to the surface point currently being synthesized with each previous wavefront being used to find the next point.

In step 218, the coordinates are transformed to the local coordinate system of the wavefront parameters to a global coordinate system on which the reflector surfaces can be defined. In order to find the surface normal vectors, the incident vector and the reflected vector are expressed in the global coordinate system. In step 220, the surface normals are incrementally calculated from the transformed wavefront parameter information starting from the reflector midpoints.

The wave parameters are then calculated in step 222, such as by using so-called floating mapping. As known to one of ordinary skill in the art, floating mapping refers to a well known technique that provides some flexibility with respect to a coordinate system. In one embodiment, the reflected rays off the main reflector to the aperture and the rays off the sub reflector from the feed are calculated from the surface normals using Snell's law. The resultant ray calculations are used to determine the wave parameters between the sub reflector and the main reflector, such as by solving a four by four linear equation that includes the mapping function p (6). In step 224, the main reflector parameters are then defined by radii of curvature and location. The reflector surfaces are synthesized over the theta and phi angles until the loops end in steps 226 and 228.

In step 230, any necessary path length adjustments are made to correct computational limitations since the path lengths from the feed to the sub reflector to the main reflector must be equal. In one embodiment, a derivative over dp/dO is used to make adjustments.

One skilled in the art will appreciate further features and advantages of the invention based on the above-described embodiments. Accordingly, the invention is not to be limited by what has been particularly shown and described, except as indicated by the appended claims. All publications and references cited herein are expressly incorporated herein by reference in their entirety.

What is claimed is: