Of course, with a bucket we are trying to "step twice into the same river". Discussion metal bucket as the horn has already been discussed  on the internet. It is obvious that to draw energy from the twice same amount of space is impossible.
Please note that the effectiveness of the example is superior to the dual mirror system and is comparable with them on bandwidth supports. Use galvanized buckets as the mouthpiece, which probably can be discussed in detail .
And in this example, dispelled some myths. In particular, square (rectangular) patch element easier to manufacture at home, allows you to easily build wideband antenna and can be used in circular polarization. And here are the achievements of some predecessors...