  The Five-hundred-metre Aperture Spherical Telescope (FAST) uses adaptive
spherical panels to achieve a huge collecting area for radio waves. In this
paper, we try to explore the optimal parameters for the curvature radius of
spherical panels and the focal distance by comparison of the calculated beam
patterns. We show that to get the best beam shape and maximum gain, the optimal
curvature radius of panels is around 300 m, and a small shift in the focal
distance of a few cm is needed. The aperture efficiency can be improved by ~10%
at 3 GHz by this small shift. We also try to optimise the panel positioning for
the best beam, and find that panel shifts of a few mm can improve the beam
pattern by a similar extent. Our results indicate that accurate control of the
feed and panel positions to the mm level is very crucial for the stability of
FAST's observational performance.

Instrumentation and Methods for Astrophysics