Here's something that impressed me at the time (1981) but didn't [apparently] go anywhere. It is a fabricable Fresnel lens IMHO.
I was prompted by Robert Murray-Smith's
2210 Spirals And Wind Turbines, this would be an Archimedes spiral.
On with the show.
What interests me is that the focus can be in front of, or behind the concentrator. I could see a 'behinder' with an open center over a skylight. It would bring in more light but be unaffected by rainfall. Which it would also concentrate.