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.

The Five-hundred-metre Aperture Spherical Telescope (FAST) is being constructed in China. With an illuminated aperture of 300-m diameter, it will be the most sensitive single-dish radio telescope in the world. We calculate the beam patterns, gains, and efficiencies of the FAST at 200 MHz, 1.4 GHz, and 3 GHz. A program is developed to calculate the structural parameters and construct the FAST models. The three-dimensional beam patterns are calculated by utilising the shooting and bouncing ray method. We show that, with a coaxial horn feed, the FAST has a beam pattern of high gain and reasonably low first sidelobe over the frequency range of 200 MHz to 3 GHz. Compared with an ideal 300-m parabolic reflector, the un-illuminated spherical part of the FAST would make the power level near both sides of the main beam rise by at least 20 dB and the efficiency tends to decrease at high frequencies. At a zenith angle of 0°, its efficiencies at 200 MHz, 1.4 GHz, and 3 GHz are 71.72%, 66.94%, and 57.55%, respectively. We conclude that the FAST is an excellent telescope at low frequencies. At high frequencies, the triangular spherical panels and the gaps between panels are important factors that affect the performance of the FAST.