A positioning system for a telescope subreflector.
STELLAR INTERFEROMETRY, which combines the images collected by a number of individual telescopes, has long been a staple in radio astronomy. It is now beginning to be applied to shorter-wavelength radiation in the submillimeter range. This method enables astrophysicists to observe interstellar gas clouds and other protostellar phenomena with unprecedented resolution. The Smithsonian Astrophysical Observatory (SAO) is constructing an interferometric array, called the Submillimeter Array (SMA), for use on Mauna Kea in Hawaii.
Submillimeter telescopes, like common telescopes, consist of a large collecting mirror called a primary, in this case 6 meters in diameter, and a smaller secondary mirror called a subreflector. The primary mirror collects and concentrates the light and reflects it onto the secondary mirror, which in turn reflects it back down through a hole in the primary and onto the focal plane. A four-legged structure, called a quadrapod, supports the secondary mirror assembly.
The quadrapod stands in front of the primary mirror obscuring its collecting area; its legs must be as thin as possible to minimize this effect. Thus the supporting structure is limber and the subreflector deflects under the changing apparent gravity.
Infrared and submillimeter telescopes are susceptible to heat. Warm objects emit radiation in these wavelengths, which swamps the image. To combat this, the secondary mirror is chopped back and forth, permitting rapid comparison of an empty portion of the sky to one with the intended image.
In order to achieve the desired telescope performance, a secondary mirror positioning assembly is required. It dynamically positions the mirror to 2 microns, removing gravitational sag and chopping 26 arcmin in 10 milliseconds to an accuracy of 2 arcsec to remove thermal effects.
The subreflector assembly is divided into three subassemblies: linear actuators to compensate tor gravitational sag, a chopper stage, and a subreflector.
The secondary mirror constantly deflects as the telescope tracks a star. Actuators adjusting the mirmr's position in all three linear axes are required to compensate for this effect and to adjust for misalignment. The three-axis stages must fit in the shadow of the 300-mm-diameter secondary mirror and yet be stiff enough to avoid adding more flexibility. New England Affiliated Technologies (NEAT) in Lawrence, Mass., delivered a small three-axis assembly with the desired stiffness, range, and resolution.
The assembly consists of a single-axis linear stage mounted along the line of sight, a two-axis stage aligned perpendicular to the optical axis, and a custom-made mounting bracket.
The speed of the chopping and the 2 arcsec pointing requirement drive the development of the mirror-pointing control system. The cyclic forces that result when inducing this chopping motion are unacceptable out on the quadrapod because they would cause it to vibrate. Thus the chopping force has to be inertially balanced.
A chopping stage design was selected that is functionally based on a chopping mirror built at the University of Washington. The mirror positioner, which consists of two voice coil motors, operates between the mirror and a pivoted reaction mass. Both the mirror and the reaction mass mount on flex pivots. The mirror and the reaction mass are tuned to the same natural frequency, about 11 Hz. As the mirror is driven in one direction, the reaction mass moves in the other, absorbing the momentum change created by this move. Two Linear Varying Differential Transformers (LVDT) measure the mirror angle.
A model of the system dynamics, including a candidate pointing controller, was developed using MATLAB from MathWorks in Natick, Mass. A number of simulations were run to gauge the effects of external forces and component imperfections, such as mirror flexibility, on the pointing performance. The simulation showed that there is an uncontrolled oscillation in the reaction mass under the influence of the wind. This results from wind gusts at the reaction mass's natural frequency being reacted to by the motors. The simulation also showed that mirror flexibility between the linear motor and the LVDT mounting points makes the control system conditionally unstable. This problem is eliminated as the first mirror mode is raised above 600 Hz.
Two tactics were used to reduce problems related to the wind. First, because energy in the wind decreases with increased frequency, flex-pivots that set the base natural frequency to 11 Hz were selected. Next, since the flex-pivots have little internal damping, the ones on the reaction mass were potted with RTV to increase damping enough to stop growing vibration.
Component selection is complicated by the use of linear components in a limited-angle rotary application. Sufficient side clearance must exist to permit the two stages to rotate as required. The geometry of both the linear motors and the LVDTs has a cylinder riding within a cylinder, and in both cases efficient operation depends on minimizing the side clearance. Selecting components requires a balance of light weight, small size, low power consumption, high resolution, and effective angular range.
The chopper position control loop is closed in a Delta Tau Data (DTD) Programmable Multi-Axis Control (PMAC), a single-card computer that can independently control eight functions simultaneously. The PMAC was selected to control the entire antenna because it permits wide flexibility: It implements component compensation curves, adjusts control law on the fly, and maintains commonality between two very distinct kinds of motion systems--one controlling the dc-motor-driven chopper and one controlling the stepper-motor-driven linear stages.
The chopper stage performance tests showed that it easily meets the 2-arcsec accuracy requirement within a 10-ms settling time.
The subreflector has two distinct sets of requirements, optical and structural. Its front surface shape is defined by the telescope's optical requirements and the substrate material. The structural requirements must take into account the need to operate the chopper positioner within the required pointing accuracy.
Aluminum was selected for the mirror material because it is light, inexpensive to purchase and fabricate, and can be diamond-turned to a mirror surface. A lightweight mirror helps reduce gravity-induced sag. The SAO decided on a mirror design consisting of a thin aluminum face sheet and a deep ribbed backup structure as the best approach to balancing the stiffness requirement with that for a lightweight and low-inertia mirror. Once the ribbed structure was determined, the mirror cutting forces were taken into account. The face sheet stiffness varies with its distance from the nearest rib, an effect that can result in "print through," or replicating the mirror supports onto its surface.
Selecting the rib layout required a whole chopper assembly to be designed, which required finding a location for the motor mount, the mirror position sensors, and the mirror mounting points. A full solid model of the system was made using I-DEAS software, developed by Structural Design Research Corp. in Milford, Ohio. The software permitted us to exchange geometric and structural modeling information quickly. I-DEAS structural models were used to examine the effects of various face sheet thicknesses, rib thicknesses, rib widths, and rib spacings on the mirror stiffness, inertia, weight, and deflection. A mirror design that was predicted to meet the disparate requirements was then selected.
A number of approaches for fabricating the mirror blank were examined. Initially, the plan was to cast or oven-braze the blank before machining the final optical surface. Casting was dropped because no aluminum alloy was found that could be both cast and diamond-turned. Casting requires silicon to help fill the mold, while its presence creates hard inclusions impossible to diamond-turn. It was decided to machine the blank from a solid piece of 6061 aluminum, annealing the material as required to avoid warpage and creep.
II-VI in Saxonburg, Pa., was contracted to both machine the blank and diamond-turn the final mirror. The company specializes in manufacturing high-power mirror substrate and fabricating it into mirrors.
A fully operative prototype system has been tested and will be mounted on the first telescope, now being assembled at Haystack Observatory in Westford, Mass. Five more assemblies are in fabrication. The telescopes will be tested in pairs at Haystack and then moved to their final site.
The author wishes to thank the rest of the design team: Adrian Roy and John Clune for the electronics, James Donaghey for much of the mechanical design, David Brown for all of the detailed design, and J. P. Zhang for the structural modeling.
Peter Cheimets is a project engineer at the Smithsonian Astrophysical Observatory in Cambridge, Mass.
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|Date:||Dec 1, 1994|
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