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A parabolic reflector is imaging, it makes in image of the sun on the
target. Non-imaging concentrators channel radiation without preserving
the relationships between rays which constitute an image. for a given
source, a non-imaging concentrator is Pi times more effective. They
can be designed to not track, track seasonally, or track sloppily.
(with imaging concentrators you design for perfect conditions and get
what you get in the real world).
The complication is that the reflector geometry is more complicated. So, a trade off is having an imaging primary with a non imaging secondary, designed to accommodate the angular uncertainty of the imperfectly tracking primary.
CPC (compound parabolic concentrators) were the first along these lines. More recently, the snail and helmet concentrator.