This thesis deals with the development of deployable structures, based on the tensegrity concept, for applications in space. A state-of-the-art review of deployable masts and reflector antennas for space applications is presented. A comparison is made between the various reflector antennas in terms of deployed and stowed sizes, mass and accuracy. The key step in the design of tensegrity structures is the form-finding analysis. Several methods proposed for this step are scrutinised and classified into two groups, kinematic and static methods, and the advantages and disadvantages of each method are investigated. Two of the statical methods seems to be identical. It is concluded that several form-finding methods are available, but no single method is suitable for general tensegrities. The force method, for the analysis of the kinematic and static properties of large bar frameworks, is presented. The analysis and design of deployable tensegrity masts, with three struts per stage, is described. A routine for the manufacturing of physical models is proposed and evaluated. Different schemes for deployment are investigated. A way to deploy the struts using self-deployable hinges is introduced and demonstrated by fourand eight-stage mast models. Finally, the tensegrity mast is compared with an existing deployable mast with respect to stiffness. The mast is relatively stiff in the axial direction but very weak in bending. The requirements for a deployable reflector antenna used on small satellites are formulated. A concept, which uses a triangulated cable network to approximate the reflecting surface, is adopted. The kinematically determinate triangulated cable network is thoroughly analysed. The achievable surface accuracy of the net, both to systematic errors arising from the triangular approximation of the surface and random manufacturing errors, is evaluated. The underlying principles and the statical and kinematical properties of the new concept are presented. A physical model is built to analyse the feasibility of the concept and to test various deployment schemes. The scheme using telescopic struts are identified as the most suitable and a preliminary design an antenna, with a diameter of three metres, for a future space mission is performed. Numerical computations show that the antenna is stiff and extremely light.

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Deployable Tensegrity Structures for Space Applications

The Atacama Cosmology Telescope is a 6 m telescope designed to map the cosmic microwave background simultaneously at 145, 215, and 280 GHz with arcminute resolution. Each frequency will have a 32 by 32 element focal plane array of transition edge sensor bolometers. The telescope and the cold reimaging optics are optimized for millimeter-wave observations with these sensitive detectors. The design of each is described.

Optical design of the Atacama Cosmology Telescope and the Millimeter Bolometric Array Camera

Stringent requirements on reflector antenna performances in modern applications such as direct broadcast satellite (DBS) communications, radar systems, and radio astronomy have demanded the development of sophisticated synthesis techniques. Presented in the paper is a generalized diffraction synthesis technique for single- and dual-reflector antennas fed by either a single feed or an array feed. High versatility and accuracy are achieved by combining optimization procedures and diffraction analysis such as physical optics (PO) and physical theory of diffraction (PTD). With this technique, one may simultaneously shape the reflector surfaces and adjust the positions, orientations, and excitations of an arbitrarily configured array feed to produce the specified radiation characteristics such as high directivity, contoured patterns, and low sidelobe levels, etc. The shaped reflectors are represented by a set of orthogonal global expansion functions (the Jacobi-Fourier expansion), and are characterized by smooth surfaces, well-defined (superquadric) circumferences, and continuous surface derivatives. The sample applications of contoured beam antenna designs and reflector surface distortion compensation are given to illustrate the effectiveness of this diffraction synthesis technique. >

A generalized diffraction synthesis technique for high performance reflector antennas

A beam waveguide may include a first set of dual offset reflectors and a second set of dual offset reflectors. The first set of dual offset reflectors and the second set of dual offset reflectors may each include reflector geometries to produce a radiation pattern that is symmetric about a first axis between the first and second set of dual offset reflectors and to produce an axi-symmetric beam from the second set of dual offset reflectors that is unaffected by any rotation of the first and second set of dual offset reflectors relative to one another about the first axis.

Beam waveguide including Mizuguchi condition reflector sets

We present the design of a reflector system that can rapidly scan and refocus a terahertz beam for high-resolution standoff imaging applications. The proposed optical system utilizes a confocal Gregorian geometry with a small mechanical rotating mirror and an axial displacement of the feed. For operation at submillimeter wavelengths and standoff ranges of many meters, the imaging targets are electrically very close to the antenna aperture. Therefore the main reflector surface must be an ellipse, instead of a parabola, in order to achieve the best imaging performance. Here we demonstrate how a simple design equivalence can be used to generalize the design of a Gregorian reflector system based on a paraboloidal main reflector to one with an ellipsoidal main reflector. The system parameters are determined by minimizing the optical path length error, and the results are validated with numerical simulations from the commercial antenna software package GRASP. The system is able to scan the beam over 0.5 m in cross-range at a 25 m standoff range with less than 1% increase of the half-power beam-width.

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Confocal Ellipsoidal Reflector System for a Mechanically Scanned Active Terahertz Imager

The equivalent paraboloid is derived for classical offset Cassegrain and Gregorian antennas. The important practical case of systems with circular exit apertures is discussed in detail, and a condition for a symmetric equivalent paraboloid is derived. For such systems, diffraction effects are investigated using tapered and scanned feeds to illuminate the equivalent paraboloid and the two-reflector system. >

Derivation and application of the equivalent paraboloid for classical offset Cassegrain and Gregorian antennas

A geometrical optics procedure for designing electrically optimized classical offset dual reflector antennas with circular apertures is presented. Equations are derived that allow the size and spacing of the main and subreflectors of the antenna system, along with the feed horn subintended angle, to be used as input variables of the design procedure. The procedure, together with these equations, yields an optimized design, starting from general system requirements. The procedure is demonstrated by designing both an offset Cassegrain and an offset Gregorian antenna, and is validated by analyzing their radiation patterns using physical optics surface current integration on both the main and subreflectors. >

A design procedure for classical offset dual reflector antennas with circular apertures

This work presents a generalized study of classical axially symmetric dual-reflector antennas. The antenna dishes are simply described by conic sections, arranged to reduce the main-reflector radiation toward the subreflector surface. The dual-reflector configuration provides a uniform-phase field distribution over the illuminated portion of the aperture, starting from a spherical-wave feed source at the antenna primary focus. All possible configurations are characterized into a total of four distinct groups. Simple closed-form design equations and the aperture field distribution are derived, in a unified way, for all these kinds of generalized antennas using the principles of geometrical optics. The formulation is applied in a parametric study to establish the configurations yielding maximum radiation efficiency (not including diffraction effects). The design procedure is exemplified in the synthesis of a novel configuration, which is further analyzed by the moment method.

Generalized classical axially symmetric dual-reflector antennas

An efficient algorithm for numerically evaluating diffraction integrals is presented. The algorithm employs a predictor-corrector scheme combined with Ludwig's (1968) integration procedure. The predictor-corrector eliminates the amplitude and phase ambiguities present in the real+imaginary algebra used in machine calculations and provides accuracy self-checking capabilities. The end result is a reliable and efficient integration method that does not require independent integrand phase information, can handle arbitrarily shaped integration domains, and is capable of monitoring its own accuracy as the integration proceeds. The performance of the algorithm is investigated by computing, using the physical optics technique, the electromagnetic field scattered by representative reflector antenna geometries. These tests demonstrate that the proposed algorithm is particularly efficient in the analysis of multi-reflector systems. >

A self-checking predictor-corrector algorithm for efficient evaluation of reflector antenna radiation integrals

A formulation is presented for shaping dual-reflector antennas designed to offer an omnidirectional coverage. The shaping procedure is based on geometrical optics (GO) principles and assumes a uniform phase distribution for the aperture field. Two distinct dual-reflector arrangements, based on the axis-displaced Cassegrain (ADC) and ellipse (ADE) configurations, are investigated. The GO shaping results are validated using the accurate analysis provided by the method-of-moments technique

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A. Prata

Papers

Derivation and application of the equivalent paraboloid for classical offset Cassegrain and Gregorian antennas

A design procedure for classical offset dual reflector antennas with circular apertures

Generalized classical axially symmetric dual-reflector antennas

A self-checking predictor-corrector algorithm for efficient evaluation of reflector antenna radiation integrals

GO Shaping of Omnidirectional Dual-Reflector Antennas for a Prescribed Equi-Phase Aperture Field Distribution