Effects of illumination functions on the computation of gravity-dependent signal path variation models in primary focus and Cassegrainian VLBI telescopes

Abstract

This paper sets the rules for an optimal definition of precise signal path variation (SPV) models, revising and highlighting the deficiencies in the calculations adopted in previous studies and improving the computational approach. Hence, the linear coefficients that define the SPV model are rigorously determined. The equations that are presented depend on the dimensions and the focal lengths of the telescopes as well as on the feed illumination taper. They hold for any primary focus or Cassegrainian very long baseline interferometry (VLBI) telescope. Earlier investigations usually determined the SPV models assuming a uniform illumination of the telescope mirrors. We prove this hypothesis to be over-simplistic by comparing results derived adopting (a) uniform, (b) Gaussian and (c) binomial illumination functions. Numerical computations are developed for AZ-EL mount, 32 m Medicina and Noto (Italy) VLBI telescopes, these latter being the only telescopes which possess thorough information on gravity-dependent deformation patterns. Particularly, assuming a Gaussian illumination function, the SPV in primary focus over the elevation range [0°, 90°] is 10.1 and 7.2 mm, for Medicina and Noto, respectively. With uniform illumination function the maximal path variation for Medicina is 17.6 and 12.7 mm for Noto, thus highlighting the strong dependency on the choice of the illumination function. According to our findings, a revised SPV model is released for Medicina and a model for Noto is presented here for the first time. Currently, no other VLBI telescope possesses SPV models capable of correcting gravity-dependent observation biases.