Thermal Design and Thermal Behaviour of Radio Telescopes and their Enclosures Bearbeitet von Albert Greve, Michael Bremer 1. Auflage 2010. Buch. X, 420 S. Hardcover ISBN 978 3 642 03866 2 Format (B x L): 15,5 x 23,5 cm Gewicht: 795 g Weitere Fachgebiete > Physik, Astronomie > Astronomie: Allgemeines > Astronomische Beobachtung: Observatorien, Instrumente, Methoden Zu Inhaltsverzeichnis schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, eBooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte. Chapter 2 Radio Telescope Constructions in View of Thermal Aspects A radio telescope operates with good performance if all relevant structural components remain stable for a considerable period of time. Adverse influences may arise from gravity, temperature and wind. They affect the focus, the pointing, the reflector surface and the path length. Corrections can be made from pointing and focus measurements that may however consume a substantial part of the ob- serving time. Telescopes with active main reflector or subreflector surface can, in addition, upgrade the performance from temperature monitoring and/or metrology measurements and subsequent real time actuator control1. With f the focal length of a telescope, θ =1.2λ/D the beam width (D = reflector diameter, λ = wavelength of observation), σ (rms value) 2 the reflector surface accu- racy and H a characteristic height of the telescope (for instance the distance from the ground to the elevation axis, or the focus), the criteria of good performance demand a focus stability of Δ f ∼< λ/10 (2.1) a pointing stability Δθ ∼< θ/10 ∝ (λ/10)/D (2.2) a surface stability σ ∼< λ/16 (2.3) and for interferometer/VLBI telescopes a path length stability Δ H ∼< λ/10 (2.4) Since these specifications scale with wavelength, it is evident that mm–wavelength telescopes have tighter tolerances than cm–wavelength telescopes. This Chapter deals with the design and construction of radio telescopes and the efforts to cope 1 For units and fundamental constants see Appendix A 2 see Appendix B A. Greve and M. Bremer, Thermal Design and Thermal Behaviour of Radio Telescopes 13 and their Enclosures, Astrophysics and Space Science Library 364, DOI 10.1007/978-3-642-03867-9 2, c Springer-Verlag Berlin Heidelberg 2010 14 2 Radio Telescope Constructions in View of Thermal Aspects with temperature influences by passive means of paint and insulation and by active thermal control of ventilation, if necessary, so that a good performance is obtained. 2.1 Optical Configurations Full aperture radio telescopes use as optics configuration the parabolic reflector, the Cassegrain system with parabolic main reflector and hyperbolic subreflector, the Gregory system with parabolic main reflector and elliptical subreflector, and modifications of these systems. Very low–noise radio telescopes use an off–axis Gregory system or off–axis Cassegrain system. The parabolic main reflector in radio telescopes has a small focal ratio (∼ 0.3) and thus is very deep and steep. The geometric optics properties of radio telescopes are similar to those of the much earlier developed optical telescopes. The optical configurations are explained by Schroeder [1987], Wilson [1999], Love [1978], Kraus [1986], Baars [2007] and others. The mechanical concept of radio telescopes is explained in the textbooks by Mar & Liebowitz [1969], Goldsmith (ed.) [1988], Polyak & Bervalds [1990], Levy [1996], Baars [2007], Cheng [2009] and many articles. 2.1.1 The Parabolic Reflector Figure 2.1 illustrates the optics of the parabolic reflector. The on–axis incident plane wavefront (W) emitted by a point source at far distance is (coherently) concentrated at the focus (f) of the parabolic reflector (R). The receiver (RE) is located at this focus. The path lengths AAfandBBf of individual rays are identical for an on– axis incident plane wavefront so that the individual rays arrive in phase at the focus f. For orthogonal coordinates (x,y,z) with the reflector vertex as origin, the (x,y) plane tangential at the vertex and the z axis pointing in the direction of the reflector axis, the parabolic contour is defined by r2 = x2 + y2 = 2pz= 4fz (2.5) with f the focal length of the reflector. The focal ratio n is n = f/D (2.6) with D the diameter of the reflector. Typical values for radio telescopes are n ≈ 0.3, with exceptions like n = 0.45 of the Onsala 20–m reflector and n = 0.8 of the Kitt Peak 11–m reflector. The perfect parabolic reflector concentrates the on–axis incident plane wavefront (W) in phase at the focal point f. The proof of this property follows the derivation by 2.1 Optical Configurations 15 Fig. 2.1 Geometry of the parabolic reflector (R). The on–axis incident plane wavefront (W) is reflected to the focus (f) and detected by the receiver (RE). Vp is the vertex of the parabola; OA is the optical/radio axis. Rush & Potter [1970] in which the reflector is considered as a transmitting element by reversing the direction of wave propagation. As shown in Fig. 2.1, a ray fA emanating from the receiver under the angle β is reflected at the position A of the surface. The condition of collimation, i.e. parallel rays, requires that the propagation of the ray AA is parallel to the reflector axis. This condition is fulfilled for any ray, i.e. any direction β,if fA + AA = constant = 2f (2.7) With fA =s,AA=scosβ, p = 2 f, Eq.(2.7) becomes s = p/(1 + cosβ)(2.8) which is the expression of a parabola in polar co–ordinates. Radio telescopes can operate in primary focus mode with the receiver installed at f. The geometric optic properties of multi–mirror telescopes are derived in a similar way by tracing principal rays through the systems. Details of the wavefront and principle rays in a Cassegrain system are found in Rush & Potter [1970]. 2.1.2 The Cassegrain and Gregory System The combination of con–focal surfaces leads to the Cassegrain and Gregory system, with the Cassegrain system more often used because of the shorter construction length. The Cassegrain system uses a convex hyperbolic subreflector, the Gregory 16 2 Radio Telescope Constructions in View of Thermal Aspects system uses a concave elliptical subreflector. The receiver is placed at the secondary focus at a convenient position near the vertex of the parabolic main reflector. Fig. 2.2 Geometry of the Cassegrain system. The on–axis incident plane wavefront (W) is col- lected by the parabolic main reflector (R, with focus f) and imaged by the hyperbolic subreflector (SR) to the secondary focus (F). The foci f1 and f2 are those of a hyperboloid of which the subre- flector is a section. The receiver (RE) is placed at the secondary focus (F). Vp is the vertex of the main reflector, Vs the vertex of the subreflector; OA is the optical/radio axis. Figure 2.2 illustrates the optics of the Cassegrain system. One virtual focus (f1) of the hyperbolic subreflector (SR) coincides with the focus (f) of the parabolic main reflector (R), the other virtual focus of the hyperbola (f2) is the secondary focus of the combined system (F, also called Cassegrain focus) located near the vertex of the main reflector. Here the receiver (RE) is installed. The optical path of an on–axis incident plane wavefront (W), emitted by a point source at far distance, is shown in Fig. 2.2. The geometrical parameters that define the Cassegrain system are D = diameter of the parabolic main reflector, f = focal length of the parabolic main reflector, n = f/D the focal ratio of the main reflector, d = diameter of the hyperbolic subreflector, F = M f equivalent focal length of the Cassegrain system, M = F/f magnification of the Cassegrain system, N = F/D = Mn focal ratio of the Cassegrain system, s=VpVs = distance between the main reflector vertex (Vp) and the subreflector vertex (Vs), 2.1 Optical Configurations 17 g=FVp = distance of the secondary focus from the vertex of the primary reflector (+ : behind the vertex, – : in front of the vertex). With the hyperbolic surface of the subreflector given by b2x2 − a2y2 = a2b2, e2 = a2 + b2 (2.9) the construction parameters of the Cassegrain system are N = F/D = Mf/D = Mn (2.10) 2e= f + g (2.11) a = s + g − e = s +(g − f)/2 (2.12) b2 =(g + s)/(f − s)(2.13) d = D(f − s)/f (2.14) s =(Mf − g)/(M + 1)(2.15) Fig. 2.3 Geometry of the Gregory system. The on–axis incident plane wavefront (W) is collected by the parabolic main reflector (R, with focus f) and imaged by the elliptical subreflector (SR) to the secondary focus (F). The foci f1 and f2 are the those of an ellipsoid of which the subreflector is a section. The receiver (RE) is placed at the secondary focus (F). Vp is the vertex of the main reflector, Vs the vertex of the subreflector; OA is the optical/radio axis. Figure 2.3 illustrates the optics of the Gregory system. One focus (f1)oftheel- liptical subreflector (SR) coincides with the focus (f) of the parabolic main reflector 18 2 Radio Telescope Constructions in View of Thermal Aspects (R), the other focus of the ellipsoid (f2) is the secondary focus of the combined system (F, also called Gregory focus) located near the vertex of the main reflector. The optical path of an on–axis incident plane wavefront (W), emitted by a point source at far distance, is shown in Fig.