Physics Reports vol.170


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Description:

The space frame is supported centrally by a pivot which is mounted on the pedestal from the ground. The pivot allows the space frame to be rotated about any azimuthal axis. In the preferred embodiment, the pivot is furnished by the gimbal bearing previously described in conjunction with FIGS. Steering of the space frame and hence the telescope array is accomplished by cables such as , In one embodiment, the cable is fixed at one end to an attachment on the pedestal and loops through a first pulley at the underside rim of the space frame and then through a second pulley on the pedestal adjacent the attachment The cable is then wrapped around a drum traction driven by a stepper motor on the ground.

The other end of the cable terminates on the ground with a system of preload counter weights Each elemental telescope such as is protected by an outside casing Inside the casing is a primary mirror 30 and a secondary mirror 32 held in optical alignment by a mirror yoke The mirror yoke may be tubular and together with the outside casing form a double wall insulation so that the telescope can be used in the daytime.

Forced air cooling would be used to reduce the impact of solar driven thermal loads. The outside casing and the mirror yoke are decoupled by being independently attached to the space frame Thus, perturbations on the outside casing are transmitted to the space frame and not the mirror yoke holding the aligned optics. Each end of an elemental telescope is equipped with a shutter such as , for protection from sudden inclement weather and for dust protection when not in use.

For periods of severe weather or maintenance, an inflatable enclosure not shown based on an existing technology may be used. The spaceframe is preferred although other support structures such as honeycomb panels are possible. Since this telescope was designed to operate without a dome, consideration was given to wind loading. Note that all beam paths are enclosed and actively controlled as discussed below. However, if the structure vibration is too severe, mount pointing errors will result. Since the spectrum of wind gusts is in general below 1 Hz, the structure was designed for a lowest structural resonance of at least 10 Hz.

Static wind loading was not an issue for winds below velocities for which the turbulence would become excessive as well. In terms of cost, it is important to consider that they need to be referenced to work that must be accomplished at the site. On-site work is at least twice as expensive as work at a factory. As a result, the structure is designed to be built in sections and ported to the site for assembly. Various materials were considered for the telescope framework with the decision to use standard mild pipes for lowest cost. Several important features of the invention contribute to the low cost of the telescope.

First, the use of a non-redundant, thinned-aperture array of telescopes specifically designed for speckle imaging provides for substantial cost reduction. Also, since speckle imaging is employed to process the image scrambled by atmospheric turbulence, there is no need to match pathlength better than the random errors introduced by the atmosphere. This allows a relaxation of the pathlength matching tolerance to the coherence length of light, which is about one order of magnitude higher than that of phased-arrays.

This results in a much less stringent, and therefore lower cost pathlength matching system. Second, for conventional large telescopes, the dome, site and civil engineering represent a major fraction of the ultimate cost. The present telescope does not require a classical dome but is capable of operating unshielded in the wind. An inexpensive, inflatable cover may be provided as a cover during daytime and for protection during inclement weather.

For tracking stability, the lowest resonant frequency of the SST should be ten times higher than wind gust frequencies below 1 Hz. Since the lowest structural resonance scales as the inverse cube of the unsupported length, the center-mount structure has a resonance eight times higher than that of the classical side-mount one. Thus, the present structure is much less likely to be perturbed by wind. This allows greater freedom to operate in the wind without the need for a protective dome housing.

Third, the high-altitude sites classically used by astronomers contribute substantially to cost. Ground sites are available that have superb "seeing" large r 0 values and that involves low cost in terms of construction. Fourth, the thickness of the present telescope is much less than that of a conventional monolithic telescope of equivalent aperture. The aperture D of the telescope is the same as the diameter of the primary mirror The thickness of the single telescope is substantial since it is controlled by its f ratio times the diameter D.

In contrast, FIG. The telescope array has a plurality of telescopes, two of which are shown; telescopes spanning laterally to provide an effective aperture D.

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Each elemental telescopes has a primary mirror of smaller diameter d, and a secondary mirror The beams from the elemental telescopes combine at the beam-combining module to form an image. The thickness of the array telescope is now given by its f ratio times the diameter d of the smaller telescopes. As a result, the telescope array is almost two-dimensional rather than three dimensional. This leads to tremendous savings in the mechanical structure.

The two-dimensional structure is well supported by a center-mount platform, thereby assuming resonances sufficiently high for operating without a dome. Since the cost of the present telescope scales as the first power of the aperture, telescopes with very large effective-aperture m and beyond may be contemplated. Extending these concepts to meters and beyond is an issue of construction versus operational considerations. For example, an array of over thirty telescopes would be required for a m effective-aperture telescope--a very expensive proposition. However, images would be obtained very quickly.

An alternative is to use only a few telescopes and measuring visibilities by pair wise combinations. However, that would take a very long time since hundreds of baselines are required. As a compromise the use of a linear array is considered. In one dimension, there are no non-redundant arrays above five telescopes. However, at the eight telescope level, it is possible to obtain an optimal placement.

A one-dimensional telescope design comprised of a center-mount, elongated space frame with eight, 3 m elemental telescopes mounted thereon. The beams from the eight telescopes are combined in a beam combining module The field of view is one-dimensional. Observation of all planes is accomplished by rotating the telescope. The optical system must fulfill four major functions.

The first function is to sample the This is provided by the nine elemental telescopes such as , each having a sufficiently large entrance pupil. The second function is to demagnify the exit pupil to a conveniently compact size.

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The third function is to reassemble the compact exit pupil into a configuration geometrically similar to that of the entrance pupils. The second and third functions are provided by the beam-combining module The fourth function is to optically image it into an accessible space for subsequent image processing.

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The first sampling function is accomplished by the nine elemental telescopes such as with a sufficient large subaperture size of 2. The nine element, non-redundant, circular array illustrated in FIGS. Second, it has the major advantage that all path lengths are equal and all telescope assemblies are identical. This reduces the amount of design time and costs since each telescope is identical. Third, it produces a more compact modulation transfer function MTF given by the autocorrelation of the pupil , as compared to other non-redundant configurations.

For highest quality imaging, the ratio of the telescope spacing to telescope diameter is chosen so that the MTF will not have any internal zeros at its core. In selecting non-redundant arrays, the effective aperture of the array is conservatively defined as the distance to the first zero in the MTF. The distance to the first zero in the MTF was then set to 12 meters, giving an actual physical diameter of The elemental telescope is an afocal telescope which collects collimated light through a 2. It comprises the primary mirror 30 and the secondary mirror 32 held in optical alignment by the mirror yoke The primary mirror 30 has an aperture of 2.

The mirror yoke is supported directly by the space frame In this way, perturbation of the outer casing is not readily transmitted to the mirror yoke. Light from a distant object enters the telescope as an input beam , strikes the primary mirror 30 and the secondary mirror 32 in turn to become an output beam of diameter 0. This beam is deflected by a turning flat into an output beam which exits the telescope via a passageway provided by a beam pipe leading to the beam-combining module The second and third function are provided by the beam-combining module The module has an outside casing similar to the elemental telescopes , which serves as a thermally controlled shroud.

Each output beam entering the beam-combining module is redirected via a turning flat to a primary mirror followed by a secondary mirror of the Cassegrain telescope. The output pupil plane is exactly one focal length of the final recollimating paraboloid past the final paraboloid. In this way, the nine output beams from the elemental telescopes are reassembled as a compact beam bundle.

The beam bundle is a scaled-down circle-of-nine configuration similar to that of the elemental telescope array, and are readily accessible. The pupil scale-down and relay requirements stem from desires to provide for optional addition of adaptive optics and to produce beam sizes convenient for common dielectric filters. It appears that a modest adaptive optical system would substantially improve the performance of the telescope. To accommodate the optional adaptive optical system, a pupil of the appropriate size is made available to an adaptive mirror at an accessible location.

At the pupil plane , the assembly of compact pupils has been scaled down to a diameter of 0. Common deformable mirrors have actuator spacings of several mm, so as many as actuators could be used to cover each compact pupil. That is quite sufficient for implementing a limited-performance adaptive optics for substantially improving the performance of speckle imaging. The fourth function is performed by the conventional optics in the optics box The final beam bundle provided in the optics box has a beam width of about 4 cm.

The nine elemental beams in the bundle are then combined interferometrically to form an image using conventional optics. Prior to the combining, the beam's coherence length is enhanced by band-pass filtering. The image is then detected by a sensor for further speckle image processing. The optical system shown in FIG. An important advantage of the present invention is that the use of speckle-imaging allows at least one order-of-magnitude relaxation in path-length matching requirement.

The path lengths need be matched only to within the coherence length of filtered light, not to a fraction of a wavelength, as in conventional imaging. Thus, for a 12 meter telescope imaging at 1 micron wavelength, the path matching requirement is on the order of 1. There are two major sources of pathlength variation as seem from a macroscopic viewpoint. The most obvious is that the individual paths shown in FIG. Less obvious, is that if the pupil geometry a circle-of-nine in the present embodiment at the entrance and exit pupils are not exact replicas, then even if the pathlengths are equal at some field angle, they will not be so at another field angle.

Referring to FIG. The first is the spacing between the primary mirror 30 and the secondary mirror The pathlength error is given by twice the spacing change.

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The second is the tilting of the elemental, afocal telescope as a rigid body relative to the beam-combining module In practice the error produced in a rigid structure is relatively minor, but the error is easily monitored and corrected. The third, and the most significant, is the position of the turning flat in each elemental telescope relative to the beam-combining module Other movements such as translation of the elemental telescope as a rigid body relative to the turning flat do not produce pathlength error. A summary of the error sources and budget is given in Table 1.

The error budget analysis indicates that if displacements are controlled to within 0. Equivalent elements are labeled by the same numerals in both figures. Without loss of generality, it only shows the pathlength matching between a pair of elemental telescopes , For the circle-of-nine array, there are eight such pairs with the pathlength of a selected elemental telescope acting as a reference in each pair.

In FIG. Thus, the turning flat directs each output beam to a compactor to output a scaled-down beam bundle at the pupil Conventional optics residing in the optics box combines the compact beams in the bundle to form an image at an image plane. A laser metrology system is used to monitor the various pathlengths. To control the first source of pathlength error, the distance between the primary mirror 30 and the secondary mirror 32 is monitored by an interferometer. Retroreflectors cats-eyes , are respectively attached to the primary mirror 30 and the secondary mirror A laser interferometer is used to monitor the distance between the two retroreflectors , The second source of pathlength error due to the tilting of an elemental telescope may be negligible if the space frame is built sufficiently rigid to hold to acceptable tolerances.

However, low-cost autocollimators are readily installed for monitoring this error. To control the third source of pathlength error, the position of the turning flat in the elemental telescope relative to the beam-combining module is monitored. For expediency in the following description, the optical axes of the elemental telescope and the beam-combining module are taken along the z-axis, and the beam path lies in the z-x plane, normal to the y-axis.

It is readily seen that displacement of the turning flat along the y-axis hardly affects the pathlength. However, displacement along the z-axis or x-axis is significant. Thus, the position of the turning flat in the z-x plane must be monitored. This is accomplished by a triangulation scheme in which the turning flat is located at a vertex of a triangle. The triangle has its base fixed in the z-x plane.

By monitoring the dimensions of the triangle, any displacement of the vertex can be calculated. In general, there will be one triangle for monitoring the turning flat of each elemental telescope.

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In a multi-telescope system, a reference frame is set up to form and define the coordinate system within which the position of all the turning flats are measured and monitored. In the preferred embodiment, the reference frame is defined by a pair of retroreflectors , fixed at the beam-combining module For simplicity, the line joining the pair of retroreflectors , is co-incident with the beam-combining module's optical axis. The line of fixed length becomes the common base of each triangle. A commercially available laser interferometer monitors the length of the base.

Sharing the same base for all triangles is advantageous in reducing cost and possibility of errors. The vertex of the triangle for each elemental telescope such as is defined by a retroreflector located at the center of its turning flat The lengths of the sides of the triangle adjacent the vertex are monitored by a pair of laser interferometers , The first local Lorentz transformation local Lorentz transformation means that it satisfies A.

By the use of 5 and 8 , we obtain the torsion scalar and its derivatives in terms of r and 0 as. The author declares that there is no conflict of interests regarding the publication of this paper. From A. Equations A. If this term is vanishing, then A. Hehl, J. McCrea, E. Mielke, and Y. Ne'eman, "Metric-affine gauge theory of gravity: field equations, Noether identities, world spinors, and breaking of dilation invariance," Physics Reports, vol. Wanas and H. Wanas, "The other side of gravity and geometry: anti-gravity and anticurvature," Advances in High Energy Physics, vol. Wanas, N. Youssef, and A.

Youssef and A. Sid-Ahmed, "Linear connections and curvature tensors in the geometry of parallelizable manifolds," Reports on Mathematical Physics, vol. Youssef and W. Elsayed, "A global approach to absolute parallelism geometry," Reports on Mathematical Physics, vol. Hayashi and T. Shirafuji, "New general relativity," Physical Review D, vol. Shirafuji, "Addendum to "new general relativity"," Physical Review D, vol. Bamba, S. Capozziello, S. Nojiri, and S. Odintsov, "Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests," Astrophysics and Space Science, vol.

Geng, C. Lai, L. Luo, and H. Tseng, "Teleparallel gravity in five-dimensional theories," Classical and Quantum Gravity, vol.


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Physics Reports vol.170 Physics Reports vol.170
Physics Reports vol.170 Physics Reports vol.170
Physics Reports vol.170 Physics Reports vol.170
Physics Reports vol.170 Physics Reports vol.170
Physics Reports vol.170 Physics Reports vol.170
Physics Reports vol.170 Physics Reports vol.170

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