Cup Horns from Olver, et al., Microwave Horns and Feeds, IEE Electromagnetics Series, 1994, Kumar (Wade W1GHZ, Ch. 6-3) 1985,  EuCAP 2006, and Volakis p 14-38, 2007
A complete zip file: containing results of analysis of various published designs and CST time-domain and CHAMP (TICRA) templates can be downloaded.
Page 220 Single Cup Choke Horn, Olver, et. al., 0.57λ deep, 0.603λ wide cup, 0.1λ Extension Opt. f/D = 0.34
CHAMP geometry
Figure 1 CHAMP geometry of Olver, et al., Single Cup Horn, p. 220
Phase Center = -1 mm at center frequency (10 GHz)

Figure 2 Pattern at 10 GHz (10 GHz Center Frequency)