Re: FEED for parabola
"Antenna Theory and Design" by Stutzman and Thiele, Chapter 7, Section 7 has a good discussion about feed antennas for reflectors, and many references.
Is your antenna a parabolic dish with circular aperture, or a parabolic cylinder? For a parabolic dish, you have a very small f/D of 0.21 (a very deep dish), and you seem to want a feed with an inverse taper to generate an almost uniform aperture illumination. Is this correct? Do you have a very special application in mind? The high illumination of the reflector edge will have a significant effect on the antenna performance for many applications (high spillover; high sidelobes...)
The usual practise is to taper the feed so that the illumination at the edge of the dish is reduced by 10dB or so. This typically gives a reasonable compromise between efficiency and spillover. A popular choice from earlier days is to use a dish with f/D around 0.41 - 0.44, where you find that a simple open-ended circular waveguide of diameter around 1 wavelength gives quite a usable feed.