  The Five-hundred-meter Aperture Spherical radio Telescope (FAST), the largest
single dish radio telescope in the world, has implemented an innovative
technology for its huge reflector, which changes the shape of the primary
reflector from spherical to that of a paraboloid of 300 m aperture. Here we
explore how the current FAST sensitivity can potentially be further improved by
increasing the illuminated area (i.e., the aperture of the paraboloid embedded
in the spherical surface). Alternatively, the maximum zenith angle can be
increased to give greater sky coverage by decreasing the illuminated
aperture.Different parabolic apertures within the FAST capability are analyzed
in terms of how far the spherical surface would have to move to approximate a
paraboloid. The sensitivity of FAST can be improved by approximately 10 % if
the aperture of the paraboloid is increased from 300 m to 315 m. The parabolic
aperture lies within the main spherical surface and does not extend beyond its
edge. The maximum zenith angle can be increased to approximately 35 degrees
from 26.4 degrees, if we decrease the aperture of the paraboloid to 220 m. This
would still give a sensitivity similar to the Arecibo 305 m radio telescope.
Radial deviations between paraboloids of different apertures and the spherical
surfaces of differing radii are also investigated. Maximum zenith angles
corresponding to different apertures of the paraboloid are further derived. A
spherical surface with a different radius can provide a reference baseline for
shape-changing applied through active reflector technology to FAST-like
telescopes.
