Newbie's ~2.5"dia ~1.25"fl aspheric lens with AR coating measured 37k lux with a cree xre at 3.some watts, IIRC. Way back I remember some mag luxeonIII measuring 10-12k lux. Point is, we have a lot of data points on this.
What I am missing in these boards, is guidance towards a theoretical and numerical approach to this as well. So that's what I am fishing for here. I have the feeling that ballpark numbers could be found without expensive and complicated raytracing.
To start with a simple question, if I were to scale an aspheric to half the dimensions, would I get 1/4 as many lux? I'm thinking that degrees in=degrees out; If I am sitting on the flat surface of the lens, the LED is covering x degrees of my view; and that is the resulting beam angle as well. If I and the lens gets two times closer to the LED, then the beam angle is doubled - resulting in the light being spread over an area four times as large.
There are lots of factors which may or may not be relevant to a napkin-class calculation - I would very much welcome the discussion of these.