Signal Path Variations of VLBI Radio Telescopes

Very Long Baseline Interferometry (VLBI) is one of the space geodetic techniques used for deriving geodetic reference frames such as the International Terrestrial Reference Frame (ITRF) or the International Celestial Reference Frame (ICRF). Gravity-induced deformation of the receiving unit distorts the signal path length w.r.t. the pointing direction of the radio telescope. Global products such as Earth rotation parameters (EOP) or the scales of derived global geodetic reference frames are biased. The deformation is assumed to be repeatable and acting systematically. To compensate for gravity-induced signal path variations, the International VLBI Service for Geodesy and Astrometry (IVS) adopts the resolution on the surveys of radio telescopes for modelling of gravitational deformation in 2019. Present studies imply a telescope-specific deformation pattern for each individual radio telescope. Due to the different reaction to gravity, it is necessary to survey and analyse each VLBI station individually. The goal of the IVS is to provide a suitable correction function for each radio telescope participating in the global IVS network.

The standard approach for modelling gravity-induced deformations on the receiving unit was developed in 1988. This approach considers only homologous deformation of the receiving unit and takes into account three main deformation patterns affecting the signal path, i.e., a deformation of the main reflector surface expressed as a change in the focal length, a shift in the receiver or sub-reflector position and a displacement of the main reflector's apex position w.r.t. the antenna’s reference point. The acting direction of the forces corresponds to the principal axis of the entire receiving unit. Thus, the shape types of the receiving unit components remain unchanged and only the shape parameters are affected by gravitational deformation, i.e., the rotationally symmetric paraboloid of the main reflector is assumed to be retained, but only the focal length changes. The advance of the approach is that the measuring and modelling effort can be greatly simplified because the original spatial problem is reduced to a two-dimensional problem. However, investigation of the the Laboratory for Industrial Metrology demonstrates that the assumption of homogeneous deformation is unfounded, and the receiver unit can be affected by arbitrary deformation patterns. From this point of view, the standard approach is only a first-order approximation. More complex analysis approaches are required for rigorous modelling of the deformations.

Most of the legacy VLBI radio telescopes consist of a main reflector designed as a rotationally symmetrical paraboloid. The curvature of the surface is only defined by the focal length. If the radio telescope points to the zenith, the gravity load acts radially symmetrically. However, if the radio telescope points to lower elevations, the gravity load acts asymmetrically and the main reflector is deformed. Modelling surface deformations w.r.t. to the pointing direction by best-fit paraboloids assumes that the surface retains its paraboloid shape, albeit with different focal lengths.

In contrast to the standard approach, the Laboratory for Industrial Metrology has introduced an innovated approach based on Zernike polynomials. Zernike polynomials describe aspheric surface shapes and aberrations in lenses with circular apertures in the field of optical physics. Each Zernike polynomial represents an elementary aberration having a physical meaning. For instance, a defocused optic is described by a specific Zernike polynomial that represents a paraboloid. Thus, the paraboloid model used in the standard approach is nested within the proposed novel approach. In order to model the entire aperture, specific Zernike polynomials are simply stacked.

Based on a comprehensive dataset the deformation of the main reflector surface was studied in detail. The benefit of the proposed Zernike approach was evaluated by a likelihood-ratio test. This test demonstrates that the Zernike approach outperforms the common paraboloid model, especially for elevation angles of less than 50°. The effects of asymmetric deformations increase at lower elevations, and the paraboloid model is unsuitable for modelling the surface changes in a reliable way.

The signal path variations of the Hobart 26 m radio telescope w.r.t. to the pointing direction were derived by numerical integration applying spatial ray tracing. The time delay varies by about 5.7 ps, which corresponds to the path length variation on 1.7 mm. Compared to reported values for legacy radio telescopes of similar dimension this small deviation is five to ten times smaller. Nevertheless, considering the correction for this systematic error in the VLBI data analysis is recommended to increase the precision and reliability of VLBI especially in the southern hemisphere.