A New Spherical Reflector Millimetrewave
Compact Antenna Test Range

1. Introduction

The basic principle CATR's are working on is to collimate the spherical radiated field from a horn feed and to transform it into a pseudo plane wave by a lens or a reflector. The test antenna is placed in the plane wave region. The radiation characteristics of the test antenna can then be obtained by recording the received power for different orientations. The scattering characteristics of the test antenna (or other object) can be obtained by receiving the scattered signal back at the horn feed. This enables radar cross section measurements to be performed in a compact, indoor, secure environment. This ability to perform accurate RCS measurements has been one of the reasons why the compact range has been very successful.

There are several types of CATR suitable for millimetre-wave operation, e.g., the single offset reflector CATR and the dual shaped reflector CATR. The most expensive item in the construction of a CATR is the manufacture of the main reflector because it has to be large to provide a sufficiently large quiet zone and its surface accuracy has to be high to make operation at high frequencies possible. The essence of this study was the new idea of making the shape of the main reflector spherical and to provide the spherical main reflector with a dual reflector feed system (DRFS). The use of the dual shaped feed system introduces degrees of freedom into the design that allow for the control of the amplitude and phase distribution across the aperture of the main reflector. A cross section of this spherical tri-reflector CATR is shown in fig. 1. The arrangement has some important features in terms of cost. The large main reflector is unshaped and it has the advantage that only one radius of curvature is needed. Most optical telescopes have mirrors that are spherical so considerable knowledge exists as to how to produce accurate spherical surfaces. The cost of the main reflector is therefore greatly reduced as compared to that in a dual shaped system. On the other hand, the two shaped subreflectors can be made considerably smaller than the main reflector resulting in comparatively low manufacturing costs. The small subreflectors determine the low frequency limit of the system due to diffraction whereas operation at high frequencies, for which the system is designed, is limited by the surface accuracy of the reflectors.

2. CATR Synthesis

The first aim of the project was to prove the concept of the spherical main reflector CATR. In order to do this, a method suitable for the design of such a system needed to be identified. The synthesis procedure used for the design of the spherical tri-reflector CATR was based on the theory of Geometrical Optics (GO). GO was used as the synthesis process needed to be frequency independent since the CATR was to operate over a very wide frequency range. As a high-frequency asymptotic technique GO meets this requirement. A GO based synthesis code for the design of a dual shaped reflector system has been developed which numerically determines the shape of the two reflectors. This data is used as input for a commercial reflector analysis package GRASP8. The synthesis technique is similar to an advanced synthesis approach published by Kildal[1] in 1990. The synthesis procedure was first applied to design a dual shaped reflector system. The synthesis method was subsequently extended to include a third reflector for the synthesis of the spherical tri-reflector configuration. The synthesis procedure was used as the basis for performing a detailed parametric study of the tri-reflector configuration. In the study, emphasis was put on the need to improve the quiet zone size whilst maintaining an acceptable level of cross-polarisation.

Fig. 1: Schematic view of a tri-reflector CATR with spherical main reflector.

3. CATR Requirements

The requirement of a CATR is to produce a pseudo plane wave in the region in front of the main reflector. Ideally, the plane wave should have a constant amplitude and phase but in practice this is not generally achievable and a set of accepted bounds are employed. The amplitude variation of the plane wave should remain within ±0.5dB and the phase within ±5 degrees. These figures are empirical in the sense that they are not derived from any specific rules but they are very much an accepted industry standard. The requirements imposed on our tri-reflector spherical CATR designs were as follows:-

• System should ideally work between 40 and 200GHz
• Quiet zone specification: ±0.5dB amplitude ripple and ±5° phase ripple.
• High quiet zone usage >=70%.
• Compactness of the configuration.
• Low cross polarisation level <-30dB.

4. Predicted Performance of the demonstrator.

With the above requirements in mind, an extensive parametric study was carried out to assess the effects of varying different system parameters and identify those that have the most significant effect on the CATR performance. The performance of a system was assessed in terms of quiet zone ripple and cross polarisation isolation. The study assessed the effects of varying the following parameters:

• System type: Cassegrain or Gregorian subsystem
• Edge illumination of the first subreflector
• Electrical sizes of the subreflectors
• Edge illumination of the main reflector
• Usage of the main reflector area

The parametric study produced the following results:-

• Configurations with the same subsystems (double Cassegrain or double Gregorian) produced a higher quiet zone ripple than in the case of different subsystems (Cassegrain-Gregorian or Gregorian-Cassegrain)
• The quiet zone ripple is increased by a high edge illumination on the first subreflector, but feed horn constraints do not allow an extremely low edge illumination.
• Cross polarisation isolation goes down (up) with the size of the first (second) subreflector. The average quiet zone ripple increases if the sizes of the reflectors are too small.
• An edge illumination on the main reflector below -20dB does not further decrease the quiet zone ripple. At lower edge illuminations, the effects of slope diffraction start to dominate.
• A trade off has to be made between a high main reflector usage and low quiet zone ripple.

Using the results of the parametric study, it was deduced that a Cassegrain-Gregorian configuration CATR design was the most suitable. The Cassegrain-Gregorian configuration offers the advantage that both subreflectors can be enclosed in an absorbing box and that diffraction may be reduced by a diffraction stop between the second subreflector and the main reflector. Fig. 2 shows a ray diagram of the demonstrator. Obtaining a design suitable for manufacture was the next step. A design was produced in which the main reflector had a radius of curvature of 4m. The average diameters of the subreflectors were approximately 36cm and 31cm for the first and second subreflectors respectively. The first subreflector is almost circular while the second subreflector is super-elliptical (approx. 35x26cm). The edge illuminations of the first subreflector and the main reflector were -16dB and -24 dB, respectively and the system nominally had a 70% usage of the main reflector diameter.

4.1 Performance at the centres of band

The demonstrator was designed to work over a frequency range of 40-200GHz. At the lower frequencies, operation is limited by edge diffraction from the reflectors while at the higher frequencies, operation is limited by the surface accuracy of the reflectors. An average surface error of 8µm rms was specified as a tolerance for the manufacturer. Measurements were planned for three frequency bands centred on 40, 90 and 180GHz, using three corrugated feed horns (approx. 40% bandwidth). Figs. 3a-c show the predicted quiet zone fields at 40, 90 and 180GHz, respectively, at 4m distance from the main reflector. The predicted cross-polar isolation is about 28dB for all three frequencies. The quiet zone ripple, ± 2.5dB at 40 GHz, is very high. The predicted ripple of ± 0.7dB at 90GHz is quite close to the CATR specification of ± 0.5dB. No further improvement in the amplitude ripple was achieved for 180GHz. It was however noted, that at 40 and 180GHz the ripple was mainly concentrated around the reflector axis and could possibly be reduced by introducing a diffraction stop. At 90GHz the ripple is quite uniform across the entire quiet zone. At 40 and 90GHz, the phase ripples are ± 11° and ± 9° , respectively. At 180GHz the phase ripple of ± 4° is particularly low and is within the CATR specification of ± 5° .

Fig.2: Ray plot of the demonstrator with a 1m-diameter spherical main reflector

Fig. 3a: Predicted field amplitude distribution in the quiet zone at 40 GHz.

Fig. 3b: Predicted field amplitude distribution in the quiet zone at 90 GHz.

Fig. 3c: Predicted field amplitude distribution in the quiet zone at 180 GHz.

4.2 Improving the performance by diffraction stops

One attractive feature of the Cassegrain-Gregorian configuration is the presence of a caustic region between the second subreflector and the main reflector. This enables us to enclose the entire double reflector feeding system in an absorbing box with just a small aperture in the caustic region providing shielding the feed system from the main reflector and the quiet zone. In the caustic region, the GO field is concentrated within a small area as can be seen from the ray plot in Fig. 2. When an aperture of suitable size is located in the absorber box in the caustic region, the ripple due to diffraction can be significantly reduced. A study of the precise form of the diffraction stop was carried out to investigate the effect of changing its shape and size. Fig. 4 shows the effect of changing the size of a square aperture on the predicted quiet zone field at 90GHz. Results are shown in the offset plane since simulations indicated that in general the amplitude ripple seemed to be more critical in the offset plane than in the symmetry plane. In our predictions, a 12x12cm diffraction stop was shown to produce a reduction of the amplitude ripple from ± 0.7dB to ± 0.5dB, hence the CATR specification of ± 0.5dB amplitude ripple could be met.

Fig. 4: Effect of a diffraction stop on the quiet zone field at 90GHz.

4.3 Predicted performance across the 90GHz frequency band

The CATR quiet zone fields across the 90GHz band have been predicted with GRASP, taking into account the changes in the radiation pattern of the corrugated feed horn feed with frequency. While a corrugated horn has a wide bandwidth over which the pattern remains relatively constant, there are some changes which need to be accounted for to provide a true representation of the performance across a frequency band. The feed horn patterns were obtained using a modal matching analysis code. The tabulated values of the simulated far field patterns at the centre of band have been used as input for the synthesis algorithm. The beam width decreased with increasing frequency and therefore it was found that the shape of the quiet zone field distribution was concave (convex) towards the lower (higher) edge of band. Fig. 5 shows the predicted behaviour of the overall amplitude ripple and of the crosspolar isolation across the 90GHz band of the corrugated horn (72 to 108GHz).

72 GHz

90 GHz

108 GHz

Fig. 5: Predicted amplitude ripple and crosspolar isolation across the 90GHz band.

4.4 Reflector misalignments

The sensitivity of the magnitude and phase of the quiet zone field with respect to translational and angular misalignments of the feed and the reflectors has been examined. The results indicated that the CATR performance was more sensitive to misalignments of the subreflectors than to feed misalignments. Secondly, the effects of angular misalignments were the most serious ones since angular misalignments tend to change the amplitude distribution in the quiet zone significantly and lead to phase distortion near the edges of the quiet zone. Small displacements did not affect the amplitude distribution in the quiet zone significantly. Lateral displacements mainly result in a linear phase taper of the quiet zone field corresponding to a squinted main beam. Axial displacements are the least serious misalignments. They resulted in a constant phase shift corresponding electrically to once (feed misalignment) or twice (subreflector misalignment) the axial displacement.

4.5 High-frequency limitation of CATR operation

At high frequencies the CATR operation is limited by the surface accuracy of the reflectors. The surface accuracy of the reflectors directly determines the phase quality of the quiet zone. A displacement of the main reflector surface by 0.01 lambda results in a phase change at the quiet zone of 7.2° . Since the generally accepted definition for a CATR quiet zone is one with less than ± 0.5dB amplitude ripple and ± 5° of phase ripple, the surface quality of all reflectors needs to be very high. This is a particularly serious problem for millimetrewave operation and has to date limited the upper frequency of CATR operation to about 200GHz. At 200GHz, the wavelength is 1.5mm for which the surface accuracy for all three reflectors has been specified as 8 microns rms, based on maintaining the corresponding phase ripple to below ± 5° at 200GHz.

However, we have calculated the CATR performance at 300GHz with this 8 micron rms surface accuracy on the first and second subreflector using a facility within the GRASP8 package. The results for the phase distribution in the quiet zone are shown in Fig. 6. A variation of ± 1dB and ± 8° still represents a very good performance, and with high gain antennas the ± 0.5dB and ± 5° criteria is probably an over specification.

Fig. 6: Predicted phase in the quiet zone at 300GHz, when surface distortions of both subreflectors are taken into account.

5. Optimisation of the cross-polarisation performance

In [2], based on the beam-mode expansion method, an expression for the maximum cross-polarisation C with reference to the maximum value of the co-polarisation was derived for a tri-reflector system, composed of conic sections. In order to apply the resulting equation to the tri-reflector CATR, the approximate focal lengths of the two shaped subreflectors are determined by fitting their numerical contours in the offset plane to the parabola with the least square error. Fixing the positions of the reflectors, in general four local optima can be found corresponding to the Double Cassegrain (DC), Cassegrain-Gregorian (CG) , Gregorian-Cassegrain (GC) and Double Gregorian (DG) configurations. Each optimal solution was analysed using the GRASP Physical Optics code. The results for the quiet zone amplitude ripple and cross-polar isolation at the design frequency (90GHz) are summarised in Table 1. It is seen that tri-reflector CATR's with equal type subsystems can achieve an extremely high cross-polarisation isolation but at the expense of a high quiet zone ripple.

Table 1: Cross-polarisation isolation and quiet zone ripple for the four optimal solutions.

6. Conclusions and Further Work

This project has resulted in the design and manufacture of a demonstrator of a tri-reflector spherical main reflector CATR. Extensive parametric studies were performed to arrive at a suitable design and to provide knowledge of the effects of varying different parameters in the system. Delays in manufacture have meant that the measurement phase of the project has not yet been tackled, but these are expected to start very soon. The system is currently being realigned using a two theodolite method to determine the positions of the reflectors and comparing these to known theoretical values. When this is complete, the measurement programme will commence. It is expected that the measurements will be undertaken in the period January - March, 2000 and will be undertaken at QMUL's own expense.

The project has to date generated 9 publications which includes both conference presentations and journal papers. A full journal paper is currently being prepared. It is expected that several more papers will be forthcoming when the measurement programme is completed. It is anticipated that the development of the CATR system will pave the way for more work in the future.

Participants

Dr. Mark Rayner

C. Rieckmann

Prof. C.G. Parini

Sponsor

EPSRC

References

Publications produced by this Grant

• Parini, C.G., Rayner, M.R. and Rieckmann, C., "A Millimetrewave Compact Antenna Test Range with Spherical Main Reflector", ESA Workshop on Millimetrewave Technology and Applications, Millilab, Espoo, Finland, May 27-29, 1998, pp523-8.
• Parini, C.G., Rayner, M.R. and Rieckmann, C., "A Spherical Main Reflector Compact Antenna Test Range for Operation up to several THz", International Conference on Infrared and Millimetrewaves, Colchester, Sept 7-11, 1998.
• Rayner, M.R. Parini, C.G., and Rieckmann, C., "Synthesis and Analysis of a Millimetrewave Spherical Main Reflector Compact Antenna Test Range, URSI UK National Meeting, York 29-30 March, 1999.
• Parini, C.G., Rieckmann, C., and Rayner, M.R., "Design and Construction of a 200GHz Demonstrator of a Tri-reflector Compact Antenna Test Range with Spherical Main Reflector", ESTEC Antenna Measurement Workshop, Noordwijk, May 10-12, 1999.
• Rieckmann, C., Rayner, M.R. and Parini, C.G., "Optimisation of cross-polarisation Performance for a Tri-reflector CATR with Spherical Main Reflector", Electronics Letters, Vol. 35, No. 17, August 1999, pp.1403-4.
• Rayner, M.R. Rieckmann, C., and Parini, C.G., "Design, Manufacture and Testing of a Millimetrewave Spherical Main Reflector Compact Antenna Test Range", URSI General Assembly, University of Toronto, Toronto, Canada, August, 1999.
• Rayner, M.R. Rieckmann, C., and Parini, C.G., "Measured Results from the QMUL Tri-Reflector CATR with Spherical Main Reflector", Millennium Conference on Antennas and Propagation, AP2000, Davos, Switzerland. (Accepted for publication)
• Rieckmann, C., Rayner, M.R. and Parini, C.G., "Diffracted Gaussian Beam Analysis of Quasi-Optical Multi-Reflector Systems", Millennium Conference on Antennas and Propagation, AP2000, Davos, Switzerland. (Accepted for publication)
• Rieckmann, C., Rayner, M.R. and Parini, C.G., "A Modular Gaussian Beam Based Approach for the Analysis of Quasi-Optical Multi-Reflector Systems". (Submitted to IEE Proceedings for Publication)