Gravitational deformation and astigmatism of tiltable radio telescopes

An ideal telescope structure would deform, when tilted, in a homologous way, from one paraboloid of revolution to another one. Conventionally designed telescopes approach this condition already to some degree, special designs to a very high degree, and a measure for the degree of this approach is suggested. An equation is presented for the deviations from homology if an antenna is adjusted at zenith angle and observes at angle ; it contains only two structural parameters for alt-azimuth mounts (three for polar mounts). The choice of the best adjustment angle is discussed; this is basically different for both types of mount, and examples are given. Supported at two elevation bearings, conventional telescopes will generally show a strong gravitational astigmatism which may be corrected at the secondary mirror, thus improving the astronomical performance considerably. Two possible correction methods are suggested. Several of the equations presented are checked with the example of the 140-ft telescope at Green Bank, W. Va. Good agreement is obtained between detailed computer analysis and equations, and between analysis and astronomically obtained data. Suggested improvements for the 140-ft (applicable also to other telescopes) would diminish the deviations from homology by a factor of 2.5, and the remaining residuals then are brought below the internal inaccuracy of the surface panels. The astigmatic correction thus is advisable as well as sufficient.