How to determine divergence of a LED source from a single biconvex lens I'm trying to determine the divergence angle of light from a single lens that is completely illuminated by a high power LED. 
Most optics textbooks only deal with imaging optics and I'm having a hard time wrapping my head around what happens when I don't care about the image on the focal plane - this is for a non-imaging application (I'm just projecting the light), and I just want to be able to determine the spot size at any distance. 
The LED will not necessarily be at the focal point of the optic (though it will be along its axis). Furthermore, the LED isn't a point-source, as its size is approximately $\frac{1}{10}^{th}$ of the focal length of the lens.
 A: Determine = design or measure?
A dark-ish room, a white piece of paper and a ruler should do for a bright LED.  Modelling it accurately, especially if the LED has a plastic lens built-in and you don't know the precise details of the die position, is trickier.
If the LED has a builtin lens then about the best you can do is just match the angle coming out of the led to a lens size and put the LED at the focal point (actually just beyond the focal point is better)

But since your lens isn't a single point you will end up with something like this - because the edges of your LED can't both be at the focal point.

See http://alumnus.caltech.edu/~leif/infratag/lens_choice.html for details - it's specifically about IR leds but that doesn't matter.
edit: for free space optical comms. If you can choose the LED then a bare surface mount device with no built-in lens is much closer to a point source. A longer focal length will give the best colimation - for experiments a 500mm camera mirror lens or telescope is a good start
