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Originally Posted by phlogiston
Thanks. That makes sense.
I'm sure that this question could be answered on paper or with a simulation, but I wouldn't know where to begin. Perhaps I should have paid more attention in math class  I guess I'll just have to make one of both with the same diameter, but very different shapes and see what happens. Next paycheck, that is.
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Actually, I think you wind up with a sharper focal point, depending on the accuracy of the construction. (Spherical gives kind of a 'fuzzy ball of energy' type focus, and parabolic gives the sharpest.) I've also seen commercial microwave dishes with "blinders" along sections of the rim to limit interference, and I've also seen a short cylindrical tube section stuck on the front.
The best way to feed a dish is with a feed horn pointed back at the dish. With an antenna just stuck in front, part of the energy is radiated out directly from the antenna, and will be out of phase with the reflected signal, causing areas of lower signal levels due to cancellation zones.