A Deformable Subreflector for the Haystack Radio Telescope

Joseph Antebi, Melrdi S. Zarglramee, Frank W. Kan, Simpson Gumpertz & Heger Inc. 297 Broadway Arlington, MA 02 174 Tel: (617) 643-2000; Fax:; (617) 643-2009

Haywood Hartwell, Raytheon Equipment Division Mail Stop A6 430 Boston Post Road Wayland MA 01778 Tel: (508) 440-1907; Fax: (508) 440-1707

Joseph E. Salnli, and Steve M. Milner Massachusetts Institute of Technology Haystack Observatory Route 40 Westford, MA 01886 Tel: (617) 981-5400; Fax: (617) 981-0590

1. Abstract

A deformable subreflector was designed and implemented to compensate for part of the gravity deformations of the primary reflector of Haystack, a 37-m- (120-A-) diameter Cassegrain radio telescope. This was done to allow it to operate at 100+ GHz, as compared to the 1-to-10 GHz range for which it was originally designed. The design, analysis, construction, testing, and the results of preliminary measurements of performance are presented. The deformable subreflector consists of a fiberglass shell, supported on an aluminum back structure. The homologous components of deformations are compensated for by optimal positioning of the subreflector, which can be displaced axially and laterally, and tilted. The deformation modes of the subreflector compensate for astigmatic deformations of the back structure of the primary, and for part of the symmetric and anti-symmetric components of gravity sag of the panels of the primary reflector. Analyses show that, due to the deformable subreflector, the surface rms due to gravity has been reduced from 494 mm (19.4 mil) down to 146 mm (5.7 mil), as the antenna travels over its operating range of 15 to 70 degrees elevation. Combining the reduced gravity effects with surface adjustment and thermal errors results in a predicted combined surface error of 250 mm (9.8 mil), at the extremes of the operating range.

2. Introduction

his paper describes the design and construction of a T deformable subreflector, the surface of which is controlled to compensate for part of the gravity deformations of the primary reflector of the Haystack antenna. Haystack is a radome-enclosed, filly steerable Cassegrain-radio telescope, with a 37-m- ( 120-flt-) diameter primary, and a 2.8-m- (1 12-in-) diameter subreflector. Designed in 1960 for high-power transmission and low-noise reception in a variety of modes, over a frequency range from 1 to 10 GHz, it is being upgraded to operate at 100+ GHz.

The concept of deforming the subreflector to compensate for the deformations of the primary was described by von Hoerner [ 11, who applied it for compensation of astigmatic deformations. Parker [2], Cowles [3], Langley [4], and Mayer [SI performed analytical and experimental evaluations of the concept, from the performance point of view. Zarghamee [6] evaluated the effect of adjusting the position of the subreflector to compensate for certain deformations of the primary. The present work is primarily involved with the mechanical design of a subreflector which can be translated, tilted, and deformed, to compensate not only for astigmatism, but also for local-surface deformations of the primary reflector.

The conceptual development, design and analysis were performed by Simpson Gumpertz & Heger Inc. ESSCO fabricated the subreflector. Haystack Observatory designed the control system, and tested the completed subreflector on the ground, and in place, on the antenna.

3. Antenna structure

Haystack is an altitude-over-azimuth-Cassegrain antenna. The primary reflector is a parabolic-shell structure, supported by a back structure which rotates in elevation. The elevation bearings are supported on a yoke which, in turn, is supported on an azimuth bearing at the top of a fixed pedestal and tower (Figure 1).

The back structure consists of five interconnected concentric-ring trusses. The rings, counting from the center outward, are referred to as Rings 1 through 5. Ring 3, the main- support ring of the reflector structure, is 18.5 m (30 fl) in diameter. It is supported by two parallel-trunnion trusses, which carry the loads to the elevation bearings.

A Teflon-coated slip joint, at the elevation bearing on one of the yoke arms, allows the aluminum back structure to expand with respect to the steel yoke. The force that develops between the elevation bearings before slip occurs causes deformations of the

I€€€ Antennas and Propagation Magazine, Vol. 36, No. 3, June 1994 19

Figure 1. The Haystack antenna.

Back structure

Panel sag

primary, which are primarily astigmatic. Although the magnitude of the force is limited by the slip joint, the resulting astigmatism is unacceptable for the upgraded performance.

The reflector shell consists of wedge-shaped panels, supported on the ring trusses by adjustable standoffs. Inboard panels extend From the center to a 25.4-mm (1.0-in.-) thick “splice plate,” supported by Ring 3, and outboard panels extend from the splice plate to the outer perimeter. The panels are connected to each other along their radial edges. In addition to the standoffs at the ring trusses, the shell is supported against in-plane motion by shear studs at the trunnion trusses.

Deformation Compensation Components

Homologous components Adjust position of subreflector Astigmatic Deform subreflector by diametral

loads Higher order None Axisymmetric Splice-plate temperature control plus Antisymmetric deform skin of subreflector in mne

between projections of Rings 3 and 4 Local effects at shear Deform skin of subreflector at studs projection of aRected areas

deformation of the primary. The measured strains can therefore be used as input to the subreflector-astigmatic correction.

Had actuators been used to deform the entire surface of the subreflector, to compensate for the non-astigmatic deformations of the primary, a large number of actuators (about 28) would have been required. However, we have determined by analysis and test that active control of the temperature of the splice plate can be used to cause, and can therefore compensate for, both axisymmetric and antisymmetric panel sags, similar to those due to gravity, except in the area between Rings 3 and 4 [7]. Therefore, by using active control of the splice-plate temperature, we can limit the actuators required for non-astigmatic deformations of the subreflector to the area between Rings 3 and 4, and the local areas corresponding to the shear studs.

The deformation components of the primary reflector, and the compensation for each deformation component, are shown in Table 1.

The effects of diffraction, resulting from the surface deforma- tions of the subreflector, were computed, and were found to be small at 100+ GHz. For example, for the deformation of the subreflector, necessary to compensate for an axisymmetric sag of the primary reflector between Rings 3 and 4, with an amplitude of 940 mm (37 mil), the loss of aperture efficiency is 2.6 percent at 120 GHz. This deformation corresponds to the maximum-surface deformation of the subreflector in the operational-elevation range. For larger deformations of the subreflector, the phase compensation is degraded and the illumination is redistributed. For a hypothetical surface-deformation amplitude of 2030 mm (80 mil); the loss of efficiency increases to 35 percent. The results obtained are consistent with the results of an analytical and experimental study by Langley and Parker [4]. At lower frequencies, the compensation for axisymmetric sag of panels by subreflector deformation is not as effective. However, gain degradation at, say, 12 to 22 GHz frequencies does occur for these lower frequencies. For example, at 22 GHz, the loss of efficiency due to the diffraction effect of subreflector deformation is 2%, and it is 7% at 43 GHz [8].

The gravity deformations of the primary reflector may be considered as the sum of the back-structure deformation and the panel sag between the rings. The back-structure deformation consists of a homologous component, an astigmatic component, and higher-order terms (homologous deformations transform a parabolic surface into another parabolic surface). The panel sag consists of an axisymmetric component, an antisymmetric component, and local effects near the shear studs.

4. Design concept

The homologous component of the deformations of the back structure can be compensated for by optimal positioning of the subreflector [6] . The astigmatic deformation of the subreflector can compensate for not only the gravity deformations of the back structure, but, in an active mode, for the astigmatic component of the distortion of the primary reflector, resulting from the non-repeatable slip between the aluminum back structure and the steel yoke.

The non-repeatable component of the astigmatic deformation of the primary can be measured indirectly, by using strain gages to measure the force in members of the back structure which span between the elevation bearings. By analysis, we know the relations between the force in those members, the force between the elevation bearings, and the magnitude of the resulting astigmatic

5. Design goals

The design goals of the deformable subreflector are, conse- quently, as follows:

Correct for the axisymmetric and antisymmetric homologous deformations of the back structure, by adjustment of the position of the subreflector.

Table 1 Compensation for gravity deformations of primary

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- - - -__ -~ ~ -~

Correct for the astigmatic deformations of the back structure, by imposing an astigmatic mode of deformation on the subreflector.

Correct for the axisymmetric and antisymmetric components of panel sag between Rings 3 and 4, and for the local effects of shear studs, by deforming the skin of the subreflector locally at corresponding areas.

The requirements to be considered in the design of the deformable subreflector include:

The support system must allow the subreflector position to be adjustable in three directions-one axial and two lateral-and in two tilt modes. The required amplitudes for compensation of gravity effects are 6 mm (+1/4 in.) axial, and 12 mm (+U2 in.) lateral. To allow for certain experiments using a defocused surface, and for initial alignment, the required motions were set as 64 mm (*2.5 in.) axial, 38 mm (*1.5 in.) lateral, and f 10 milliradians tilt. The tolerance on repeatability of position must be of the order of 25 mm (1 mil).

The deformed shape of the subreflector must match the deformations of the primary reflector which are to be compensated for, with negligible extraneous components, to a tolerance of 50 to 75 mm (2 to 3 mil).

cyclic-fatigue loads into account. Stresses must be less than the maximum allowable, taking

The actuator loads needed to deform the subreflector must be in the range of available, lightweight actuators: a capacity of, say, 500 kg (1,000 Ib), and a weight of less than, say, 5 kg (10 Ib).

The subreflector surface and its back structure must be designed so that it can be fabricated to the required tolerances, at reasonable cost.

possibility of arcing in the radar mode of operation. Slits in the reflector surface are to be avoided, because of the

Figure 2. The deformable subreflector.

0 0 0

Support Rings

Figure 3. A rear view of the deformable subreflector.

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~

21

Pyramid Member

c I n. Support Clevis w

Support

Figure 4. A cross section of the deformable subreflector.

=T Standoffs E ox Bonded To &eh 0

L FRP Shell - Silver Coated

Figure 5. The connections from the radial rib to the support ring, and the connections to the standoffs and to the shell.

\ ,.A, Mechanical Adjuster , r Actuator

\

- 1 \

L S t a n d a f f

pport Ring

Ring A FRP Shell - Silver Coated

L S u p p o r t Ring

Figure 6. The actuator beams.

The reflector must have a conductive-surface skin, of sufficient thickness not to cause unacceptable temperature rises, when the antenna is used in the radar mode.

The weight of the subreflector must be acceptable with respect to the strength of the existing quadrupod-support structure, and with respect to its effect on the natural frequency of the

quadmpod. The original subreflector weighed 148 kg (325 Ib), and the deformable subreflector should weigh no more than, say, 500 kg (1,000 Ib).

6. Description of deformable subreflector

The deformable-subreflector assembly (Figures 2, 3, and 4) consists of an aluminum back structure, supporting a 2.54-mm- (O.IOO-in-) thick hyperbolic shell of revolution, made of FRP (fiber-reinforced plastic). Five “support” rings, Rings 1 through 5, which correspond to the structural rings of the back structure of the primary reflector, are attached to the back of the shell by aluminum standoffs. The standoffs (Figure 5) (which are tees, one-half inch long, spaced oneinch on center) are designed to be flexible in bending, so that the rings constrain the normal deflections of the shell, but do not add to the membrane stiffness of the shell. Four “floating” rings, denoted as Rings A through D and located between the support rings, are also attached to the shell by similar standoffs.

Four orthogonal-radial ribs are connected to the back of the five support rings, and bypass the floating rings (Figure 4). The radial ribs are rigidly connected to each other at the center of the back structure and, together with the five support rings, provide a stiff back structure with respect to which the floating rings can be displaced.

A series of short radial beams, referred to as actuator beams (Figure 6), span between the support rings. The floating rings are connected to these actuator beams either by a linear actuator, or by a mechanical adjuster. Linear actuators are used only in the areas where active control is needed, namely, on Ring C; the floating ring between Rings 3 and 4; and on the part of Ring B corresponding to the shear-stud locations on the primary reflector. Mechanical adjusters are adjusted and locked. The design allows for the replacement of mechanical adjusters by linear actuators, in the future, if active control is desired over a wider area.

The astigmatic deformation is achieved by using only one linear actuator, in a four-member-pyramidal-space truss, behind the subreflector. The pyramidal-space-truss members are attached to the ends of the radial ribs, and the actuator is mounted in-line with one of the members (Figure 7). An extension of the linear actuator causes compression in one pair of members, and tension in the

22 E€€ Antennas and Propagation Magazine, Vol. 36, No. 3, June 1994

Tilt mode of Ring C (tilt about the x-axis)

Equal displacements of the four actuators on Ring B.

7. Construction and testing

Figure 7. The pyramidal space truss. for astigmatic deformation and subreflector support, and the position-control structure.

other pair. The resulting reactions at the ends of the radial ribs deform the subreflector astigmatically. Contraction of the actuator causes deformations in the opposite sense. The radial stiffness of the radial ribs, and their connection to the support rings, allows the point loads to cause smooth astigmatic deformation of the subreflector.

The entire subreflector assembly is supported by clevises at three points. These clevises are mounted on the back of the radial ribs at the 3, 9, and 12 o’clock positions. A pair of members connects each of the three clevises to the quadrupod. These six members support the subreflector, and allow unrestrained subreflector deformation (Figure 7). In-line actuators in the six members allow the subreflector to be translated and tilted. Note that, to obtain astigmatic deformation with no rigid body motion, the pyramidal actuator and the six support actuators must be used.

The linear actuators selected are manufactured by Industrial Devices. They are specified to have a rated capacity of 363 kg (800 Ib), and to be controllable to within 13 mm (0.0005 in).

The modes of positioning and deformation of the subreflector are as follows:

parallel to the elevation axis, and the z-axis is along the RF axis).

Astigmatic.

Translation in x, y , and z, and tilt about x and y (the x-axis is

Piston mode of Ring C.

The subreflector shell was made of an FRP laminate, consisting of 12 plies of woven-fiberglass cloth, pre-impregnated with epoxy. The first 1 1 plies-a balanced bi-directional woven-glass fabric, oriented at 30-degree angles-serve as the structural components of the laminate. The outer ply-a thin, balanced, bi- directional, tightly-woven fabric-serves as the finishing-surface ply, to ensure optimum surface smoothness, The epoxy, a low- temperature-curing resin, was selected for its low shrinkage and long-term stability.

The construction sequence was as follows:

A precision female mold was fabricated as an aluminum casting, stress relieved, and machined to an rms accuracy of 38 mm (1.5 mil).

vacuum-bagging process. The FRP shell was constructed on the female mold by a

The back structure components, nine rings and four radial ribs and 12 actuator beams, were first fabricated and stress-relieved, Other components were precut, machined, drilled, and was then assembled and bonded to the inner-shell surface, while the shell was secured by vacuum to the female mold.

verify its surface accuracy. The surface of the shell was surveyed, as described below, to

The shell was then painted with a reflective, 70% silver-filled- lacquer paint. To protect the silver lacquer, it was coated with a 25- to-50 mm (1 to 2 mil) layer of gray-enamel paint.

The pre-assembled pyramidal space truss and actuators were assembled onto the back of the subreflector, and the linear actuators were installed and wired.

To ensure that the constructed subreflector met the design goals, a number of tests were planned and conducted. The tests conducted were as follows.

7.1 Material tests

The material tests were performed to verify the calculated laminate properties, and to select the best material for construction of the shell. These tests were as follows:

7.1.1 Laminate. Tests were conducted for tensile modulus and ultimate tensile strength (following ASTM D638 Standard Test Procedure), flexural modulus and ultimate flexural strength (following ASTM D790 Standard Test Procedure), and for interlaminar shear strength (following a modified version of ASTM D1002 Standard Test Procedure). The tests proved that the laminate was isotropic, with a maximum of 7% difference of properties in different directions.

7.1.2 Adhesive. Nine different adhesives were tested in lap shear, following ASTM D-1002 Standard Test Procedure, and in tension. The tension test was designed to simulate the actual

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combined-tensile/peeI-stress state between the standoffs and the FRP shell. For the adhesive selected, the failure surface was through the FRP laminate, rather than in the adhesive.

7.1.3 Paint. The silver paint was subjected to radiation testing, to determine the ability of the paint to withstand the radiated energy when the antenna is used as a radar, without excessive rise in temperature. The silver paint and the top coat were also subjected to strain cycles, to prove that no degradation, lifting, cracking, or peeling of the paint would occur, even if the temperature rose to 60" C (140" F).

7.2. Fatigue test

A test was developed and conducted to evaluate the perform- ance of the bond between the aluminum standoff and the FRP shell, for a design life of 20 years. The test was repeated at both room temperature and at 60" C (140" F) temperature. The specimens, with standoffs corresponding to the selected design, withstood the test without failure.

7.3. Subreflector measurements

These measurements were performed to verify the accuracy of the finished assembly.

7.3.1 Thickness. The shell was measured at 200 locations. The average thickness was found to be 2.565 mm (101 mil), with +229/-178 mm (+9/-7 mil) of dispersion.

7.3.2 Mold-surface accuracy. The mold was machined and measured in the same milling machine. Special care was exercised to minimize distortions resulting from the restraining forces. The rms of 1,036 sample readings of the surface resulted in an rms accuracy of 30 mm (1.2 mil).

7.3.3 Finished-surface accuracy. The surface of the deformable subreflector was measured after assembly, with the pyramidal-support structure removed. The measurements were made over 280 targets on the subreflector surface, performed with three theodolites. The positions of the theodolites were determined by sighting the end points of bars of known lengths. The angular measurements from the theodolites were post-processed, to compute the coordinates of the targets with an accuracy of not more than 38 mm (1.5 mil) rms. The measured surface showed an rms accuracy of 94 mm (3.7 mil), with an astigmatic component oriented at 45 deg, that is, orthogonal to the component which can be corrected by the pyramidal-space truss. This astigmatic component, which had been built into the shell due to the erection and bolt-torquing process, can be rigged out at the primary reflector in the surface-alignment process. The surface rms accuracy of the subreflector, &er removal of astigmatism, was 53 mm (2.1 mil).

7.4. Assembly tests

Prior to installing the subreflector in place on the antenna, the subreflector was mounted on a test stand which simulated the antenna quadrupod, and which allowed the assembly to be rotated in elevation from zenith to horizon. The tests were used to debug the actuator-control system, to verif) the magnitude of actuator motion needed to produce a given displacement or deformation,

and to verify that the deformed shape of the subreflector agreed with the shape predicted by analysis.

7.5. Operational tests

The subreflector was installed on the antenna. The subreflector is now undergoing tests, to verify the amplitude of the required actuator motions, and the variation of gain with elevation. Preliminary results of the variation of gain with elevation are given below.

8. Analysis

A finite-element model of the antenna structure, which had been developed previously, was used to compute the surface deformations of the primary reflector, and the displacements of the feed and the subreflector resulting from the effects of (a) gravity on the structure with change of elevation, (b) temperature changes in the splice plate, and (c) change of thrust load at the elevation bearings. A finite-element model of the subreflector assembly was developed, and used to compute the surface deformations of the subreflector resulting from the effects of (a) gravity on the subreflector with change of elevation; (b) astigmatic adjustment; (c) axisymmetric, piston-mode displacement of the actuators at Ring C; (d) antisymmetric, tilt-mode, displacement of the actuators at Ring C; and (e) symmetric displacements of the actuators at Ring B.

The finite-element model of one-half of the subreflector consisted of 1,895 grid points with 11,370 deg of freedom and 2,328 elements. The shell is represented by quadrilateral-plate elements: 38 elements in the radial direction, and 32 in the circumferential direction over 180 deg. Beam elements represent the support and floating rings, the radial ribs, the actuator-support beams, and the pyramidal-space truss. Actuators are modeled as linear elements, and their motions are simulated by applying temperatures to those elements. The standoffs, which connect the shell to the rings, are modeled by equivalent short-beam elements, and rigid links are used to tie these short-beam elements to the centroids of the rings. Finer-mesh models of a wedge of the subreflector were used, to verify the adequacy of the idealization in the overall model.

The finite-element models were used to calculate the gravity deflections of the primary between Rings 3 and 4 with splice-plate temperature control, and the compensating deformations of the subreflector. The results showed good agreement in the profile of the deformations of the primary reflector and the compensating deformations of the subreflector. These profiles agreed with the deformed shapes measured during the assembly tests.

To obtain an accurate prediction of the magnitude of the actuator motion needed to produce a given surface deformation, detailed models of the local flexibilities of all structural components between the rings and the actuators were developed. With these effects included, the results agreed with the measurement results.

To verify the adequacy of the design with respect to strength, the finite-element model was used to compute the amplitudes of the anticipated stresses in the skin, due to normal operations; the forces and moments at the attachments of the standoffs to the skin; and the required forces in the actuators, as well as the forces and moments in the subreflector-back structure. The stresses computed for these operational conditions were compared to the allowables for fatigue loadings.

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_ _ -__

Figure 8. The RF-path-length errors, due to deflections of the primary due to gravity a t zenith: the surface rms is 1,412 mm (55.6 mil).

Before splice-plate temperature-

Figure 9. The RF-path-length errors, due to deflections of the primary due to gravity a t zenith, with temperature control of the splice plate and with astigmatism removed: the surface rms is 935 mm (36.9 mil).

mm (mil) E=15 E=70

447 535

Figure 10. The RF-path-length errors, due to astigmatic deformation of the subreflector.

- adjustment After subreflector surface adjustments at Rings B and C

In addition, the subreflector will be subject to more-severe loads if, due to a malfunction, the actuators move to the limits of their strokes. Therefore, the stresses for worst-case combinations of actuator travels were computed, and compared to the allowables for static loadings.

(11.7) (14.3) 104 146

(4.1) (5.7)

9. Predicted performance

The RF-path-length errors, due to gravity deflections of the primary due to loads at zenith pointing, Figure 8, are dominated by astigmatism and the sag of panels between rings. The errors, &er

the removal of astigmatism and the application of temperature control of the splice plate, are shown in Figure 9. Note that Figures 8 through 12 are drawn to the same scale.

The FW-path length errors, due to astigmatic deformation of the subreflector and of the piston-mode displacement of Ring C, are shown in Figures 10 and 11. The other modes of deformation of the subreflector are the tilt of Ring C, and symmetric displacements of the actuators at Ring B. These deformation modes, together with temperature control of the splice plate and positioning of the subreflector, must be combined with the effects of gravity to

Figure 11. The RF-path-length errors, due to piston-mode displacement of Ring C of the subreflector.

Figure 12. The change in the RF-path-length errors as the antenna travels from elevation 35 deg to 90 deg, with tempera- ture control of the splice plate and deformation of the subreflector: the surface rms is 203 mm (8.0 mil).

Table 2 Surface RMS due to gravity deformations of primary reflector,

before and after compensation due to travel from E = 35 to E = 15 and E = 70

I Condition I R M S I

offset correction 1 (17.6) I ( 21 .O) After splice-place temperature-offset I 4 13 I 494 correction 1 (16.3) I ( 19.4) After subreflector astigmatic I 297 I 3 64

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lot

0

minimize the changes in RF-path-length errors, as the antenna travels from its bias-rigging elevation angle. The total surface errors are then these residual errors, combined with the surface errors at the bias-rigging angle.

The operating range of interest for observation is 15 to 70 degrees elevation. Table 2 shows the surface rms values resulting from gravity deformations of the primary reflector, as the antenna travels from the bias-rigging angle of 35 to 15 and 70 degrees elevation, before and after compensation by controlling the splice- plate temperature, and deforming the subreflector. In each case, the subreflector is at its optimum position.

These results show that the surface rms, resulting from gravity deformation of the primary reflector, can be reduced very significantly by the astigmatic and non-astigmatic surface deformations of the subreflector. This is illustrated in Figure 12, which shows the change in RF-path-length errors, as the antenna travels from the rigging angle to zenith, after deformation of the subreflector.

To obtain the surface errors at any elevation, the surface accuracy at the bias-rigging angle is combined with the above errors due to the antenna travel away from the bias-rigging angle. At the bias-rigging angle of 35 deg, the total surface accuracy of the antenna is the sum of the surface accuracy of the primary reflector and the surface accuracy of the subreflector, based on geometric optics. The subreflector-surface accuracy is 53 mm (2.1 mil), and the expected surface accuracy of the primary-reflector panels, thermal effects on the antenna, residual of surface adjustments, and error in the control of the splice-plate temperature, is 196 mm (7.7 mil), for a total of 203 mm (8 mil).

Combining the results of Table 2 with the surface accuracy at the bias-rigging angle, the resulting surface values are as follows:

rms = 228 mm (9.0 mil) for E = 15 deg

rms = 250 mm (9.8 mil) for E = 70 deg

10. Preliminary gain measurements

Preliminary tests of gain variation with elevation have been performed at 86 GHZ, the results are shown in Figure 13. From

these results, the calculated effective surface rms, due to a change in elevation from 35 deg (the bias-rigging position), to 15 and 60 deg elevations, are 168 and 142 mm (6.6 and 5.6 mil), respectively. The corresponding predicted values are 104 and 109 mm (4.1 and 4.3 mil).

Some of the difference between the measured and predicted values is due to diffraction effects at 86 GHz, which will diminish hrther at 100+ GHz, and the fact that the splice-plate-temperature offsets were not at their optimum at the time of such measurements. In addition, the bias model for the adjustment of the position of the subreflector, astigmatism, and other imposed deformations was not at its optimum.

Note that without the subreflector deformation to compensate for the deformations of the primary reflector, the comparable surface rms at 15 and 60 deg elevation would be 414 and 391 mm (16.3 and 15.4 mil), respectively.

11. Conclusions

A deformable subreflector, the surface of which can be deformed in the local-normal-to-the-surface direction, to compensate for astigmatic and non-astigmatic gravity-induced surface deformations of the primary reflector, was designed, built, tested and installed on Haystack, a 37-meter (120-ft) diameter antenna. Based upon finite-element analyses, and mechanical tests and measurements of the deformed surface of the subreflector in a test stand, the surface rms of the antenna, due to gravity deformations, will be reduced from 494 mm (19.4 mil) at the extremes of the elevation range of 15 deg to 70 deg elevation, to 146 mm (5.7 mil). Combining these reduced gravity effects with surface adjustment and thermal errors results in a combined predicted-surface error of 250 mm (9.8 mil), at the extremes of the operating range. This will allow an increase in the operating fre- quencies from the original design range of 1 to 10 GHz up to 100+ GHz. This has been confirmed by preliminary gain measurements, with the deformable subreflector in place on the antenna.

Although the design described here is specific to Haystack, the concept which has been successhlly demonstrated here is appli- cable to the upgrading of other antennas. The concept requires a) identifying a limited number of modes of gravity-surface deforma- tions of the primary which, when compensated, will produce the required improvement in surface rms; and b) designing a subreflector to compensate for those modes by actuator-adjusted surface deformation.

12. Acknowledgment

This work was carried out under sponsorship of the National Science Foundation, Division of Astronomical Sciences, through a grant to the Northeast Radio Observatory Corporation, Massachu- setts Institute of Technology, Haystack Observatory.

13. References

1. S. von Hoemer, “The Design of Correcting Secondary Reflectors,” IEEE Transactions on Anlennas and fiopagatiolir, AP-24, May 1976, No. 5, pp. 336-340.

2. E. A. Parker and P. R. Cowles, “A Method for Compensating for Reflector Antenna Surface Errors with Long Correlation Lengths,” Electronic Letters, 8, 1972, pp. 366-367.

26 /€€€Antennas and Propugation Mugazihe, Vol. 36, No. 3, June 1994

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3. P. R. Cowles and E. A. Parker, “Reflector surface error compen- sation in Cassegrain antennas,” IEEE Transactions on Antennas and Propagation, AP-23, 1975, pp. 323-328.

4. R. J. Langley and E. A. Parker, “Wave Scattering from Error Compensating Secondary Reflectors,” IEEE Transactions on Antennas andPropagation, AP-27, No. 7, July 1979, pp. 527-530.

5 . C. E. Mayer, J. H. Davis, and H. D. F o b , “Texas 5-m Antenna Aperture Efficiency Doubled from 200-300 GHz with Error Compensating Secondary,” IEEE Transactions on Antennas and Propagation, AP-39, No. 3, 199 1, pp. 309-3 17.

6. M. S. Zarghamee, and J. Antebi, “Surface Deformation of Cassegrain Antennas,” IEEE Transactions on Antennas and Propagation, AP-33, No. 8, August 1985, pp. 828 - 837.

7. R. P. Ingalls, et al., “Upgrading the Haystack Ratio Telescope for Operation at 1 15 GHZ,” Proceedings ofthe IEEE (“Design and Instrumentation of Antennas for Deep Space Telecommunication and Radio Astronomy”), 1993.

8. A. E. E. Rogers, “Diffraction Effects of Subreflector Deforma- tion,” Haystack Memorandum, 22 May 1991.

Introducing Feature Article Authors

‘*A Joseph Antebi

Joseph Antebi received the BA degree, in mechanical sciences, from Cambridge University, England, in 1956. He received the SM and ScD degrees in structural engineering from the Massachusetts Institute of Technology, Cambridge, Massachusetts, in 1957 and 1961, respectively. He is a Principal of the consulting engineering firm of Simpson Gumpertz & Heger, Inc., Arlington, Massachusetts. He has been involved in structural engineering of antennas and optical telescopes in the conceptual-development phase, analysis, design, and performance prediction. Projects in which he was involved in this field include ALTAIR, a 45.7-m- diameter radar antenna; a Ft. Huachuca, Arizona, 21.3-m-diameter compact-range-radar reflector; the MMT optical telescope, currently being upgraded to 6.5-m aperture; Haystack; a 27.5-111- diameter earth-station antenna in Pleumeur-Bodou, France; and hardened phased-array-radar antennas.

Steven M. Milnet was born in Winchester, Massachusetts, in 1947. He received the BS and MS degrees in Electrical Engineering from Northeastern University, Boston, Massachusetts, in 1984 and 1988. From 1975 to 1990, he was on the research staff of the MIT Lincoln Laboratory, where he was an engineer developing electro- optical space-surveillance systems. Since 1990, he has been a staff member of the MIT Haystack Observatory, Westford, Massachusetts. His interests include the design and construction of radio and radar telescopes. His principal focus at Haystack has been the electrical and mechanical upgrade of the 37-m antenna, and the design and construction of the 12-m Haystack Auxiliary Radar.

Mehdi S. Zarghamee received the Bachelor of Civil Engineering degree from Georgia Institute of Technology, Atlanta, Georgia, in 1962. He received the MS and PhD degrees from the University of Illinois, Urbana, in structure engineering, in 1963 and 1965, respectively. He also received the ScM in mathematics from the Massachusetts Institute of Technology, Cambridge, Massachu- setts, in 1968. He was a Professor of Mathematics and Computer Sciences, from 1968 until 1979, at the Arya-Mehr University of Technology, Tehran, Iran. He is currently a Principal of the consulting engineering firm of Simpson Gumpertz & Heger Inc., Arlington, Massachusetts. He has been involved with the analysis, design, upgrading, surface adjustment, and performance analysis of many large radio-telescope and radar antennas, including Haystack; an 18.3-m radio telescope in Onsala, Sweden; the 13.4-m ALCOR Millimeter Wavelength Augmentation Radar; and the family of phased-array Ground-Based Radars.

Frank W. Kan

Frank W. Kan received the Bachelor of Civil Engineering and Engineering Mechanics degree from McMaster University, Canada, in 1985, and the MS degree from the Massachusetts Institute of Technology, Cambridge, Massachusetts, in 1987. He is a Senior Engineer of the consulting engineering firm of Simpson Gumpertz & Heger Inc., Arlington, MA. He has been involved with structural analysis, performance analysis, upgrading and surface adjustment of large radio-telescope and radar antennas, such as Haystack and the family of phased-array Ground-Based Radars.

IfEf Antennas and Propagation Magazine, Vol. 36, No. 3, June 1994 27

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Joseph E. Salah received BS and MS degrees in electrical engineering, from the University of Illinois at Urbana, in 1965 and 1966. He received the PhD in upper-atmospheric physics from the Massachusetts Institute of Technology, in 1972. He was on the research staff of MIT Lincoln Laboratory from 1966 to 1983, and served as a group leader in the radar and the aerospace divisions. He joined the MIT Haystack Observatory in 1983, where he has held the position of Director. His research interests include the application of radio techniques to the study of the earth’s ionosphere, and the development of instrumentation for radio astronomy. Dr. Salah is a member of the American Astronomical Society, the American Geophysical Union, and the International Union of Radio Science.

Haywood Hartwell received BS and MS degrees in mechani- cal engineering, from the University of New Hampshire, in 1979 and 1983, respectively. He is a Senior Development Engineer in the Mechanical Systems Laboratory of Raytheon’s Equipment Division, Wayland, Massachusetts. He is currently involved in the design of a transportable tactical mount to support a phased-array radar antenna. From 1988 to 1992, he was a Mechanical Engineer in the Antenna Systems Department at ESSCO, where he was responsible for the design and development of composite structures for reflectors for large antennas. From 1983 to 1988, he was engaged in the design, fabrication, and qualification of prototype aircraft structures, using superplastic sheet-metal forming and diffision-roll bonding technology at Texas Instruments, Inc.

AMTA WORKSHOP MODERN IMAGING AND DIAGNOSTIC

TECHNIQUES FOR ANTENNAS AND RCS

Friday June24, 1994

Held in conjunction with the 1994 IEEE AP-S Symposium. University of Washington.

To register see: IEEE AP-S Symposium Registration Form

F a information contaa:

Yahya RahmPr-Samii Technical Coordinator Tel: (310) 2063847 Fax: (310) 2068495

Greg MdLner AMTA Vice Resident Tel: (707) 577-2961 Fax: (707) 577-5666

the Kyoto GA? UNION RADIO-SCIENTIFIQUE INTERN ATlON ALE

IWTERNATIONAL UNION OF RADIO SCIENCE

All scientific participants received membership of the network of URSI Correspondents which provides a numbered membership card and

a three-year subscription to the new Radioscientist & Bulletin (1994-96),

substantial discounts for subscriptions to URSI sponsored jour- nals (RADIO SCIENCE and JATP),

discounted registration fees to URSI conferences held jointly with other bodies with membership discounts.

You can still get all this! for the 1994-96 triennium for US$40 by applying to the URSI Gen- eral secretariat. Payment must be by credit card (VISA or MasterCard). Apply by surface, airmail or fax but not by telephone or electronic mail since the application must be signed. Provide the following details where relevant:

Name in full with title

Professional position and years of professional experience

URSI Commissions (A - K) of interest

Mail address for the Radioscientist &Bulletin and membership card, and phone, fax and Internet emad

Credit card type, number and expiry date (signed and dated)

URSI General Secretariat C/- University of Gent St Pietersnieuwstraat 41 B-9000 GENT Belgium Fax: +32 9 264 3593

(Note: The library and institute subscription for the Radioscientist & Bullerin is US$25 for 1994 only)

Eighth South African AP-S/ MTT-S Symposium

The 8th South African Symposium on Antennas and Propa- gation and Microwave Theory and Techniques will be held on October 3, 1994, in Stellenbosch, South Africa. Abstracts are due June 20, 1994. Abstracts and requests for hrther information should be sent to Dr. David B. Davidson, Department of Electrical and Electronic Engineering, University of Stellenbosch, Stellen- bosch 7600, South Africa; Tel: (+27) 21 808 4458; Fax: (+27) 21 808 4981; e-mail: davidson@firga.sun.ac.za . Three additional IEEE-sponsored symposia will be held in conjunction with this meeting: the Computer Systems Symposium, also on October 3, and the Signal Processing Symposium and Small Satellites and Control Symposium, on October 4.

IEEE Antennas and Propagation Magazine, Vol. 36, No. 3, June 1994

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