Actually, I'm not convinced that the ratio of solid angles should give you concentration ratio. This would be true if intensity is uniform both before and after the lens, but it isn't immediately clear to me whether or not this is the case. I need to think about it a bit more I think.
Thanks for your help so far! It makes sense to me that concentration is the ratio of the solid angle the spot "sees" to the solid angle the lens "sees," and given that, the maximum concentration ratio should be 2/θ^2. (I am still confused as to why this seems to differ from the etendue argument...
I should clarify that all the angles I mentioned in the original post were half-angles (which is the relevant angle for calculating etendue), and that the maximum concentration condition (1/(sinθ)^2) occurs when the outgoing divergence half-angle is 90°. So even if the total angle is 2*45° =...
I'm looking at concentrating light (e.g. sunlight) with a lens, and trying to figure out the maximum concentration I can get. If you have a perfectly collimated source, a lens can focus that light down to a point, but when the source has some divergence, the point you can focus down to will have...