@Cosmos, I am not sure what Frank and I are saying the same thing. I am suggesting ways of using lenses to increase the f-stop of the eye, but purely externally. I mentioned replacing the lens of the eye as a thought experiment. Instead of removing the lens, one could put a divergent lens to cancel it, and then put the optical system I suggested in front of that. The crux of my idea is to have a large lens, then a Barlow, where the combination has a short focal length. The Barlow would be the size of the eye's pupil, but the aperture would be much larger.
But alas... that's impossible. It violates Emmy Noether's theorem. A passive optical system cannot increase étendue; at best it can only maintain it. So, once you preclude modifying the eye itself, it is restricted to its native max étendue, no more than that. That invariance appears under different guises in different contexts (Radiance, Lagrange Invariant, Abbe Sine Condition, distortion conditional, paraxial vs real ray-trace, entropy laws...). What you are inventing is the Free Lunch --- but Mother Nature refuses to serve up loaves and fishes. That's what Emmy realized and formalized, in a context that is so generalized that it applies to all gauge bosons and their associated probability density distribution functions.... much to the astonishment and relief of her contemporary mathematicians and scientists. In our context here, the bosons are photons and the field is electromagnetism. It's that fundamental and that unavoidable. Tom
PS: Here's my Arcane T-Shirt celebrating her achievement. When my son gifted it to me, I immediately recognized it and commented, "Excellent, in integral form!" and then waxed lyrical regarding the implicit conditions under which it can seem to be violated, but is not. Things like del n, where the photons slow down so are bunched up, etc. etc. So, we chatted theoretical and applied physics and I blew out the candles on my Birthday Cake. Tom