# 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.

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

• I'd like to model it to determine the optimum placement. This is for optical communication and I need to balance light capture from the lens vs. the divergence (and capture at the receiver). I have pretty good measurements of the die and power spread from the LED itself, but I want to estimate how much the beam will diverge given various placements and single lens arrangements. – gallamine Mar 24 '11 at 20:18
• Newport also has a similar (albeit more helpful) article on this: newport.com/store/genContent.aspx/Focusing-and-Collimating/… – gallamine Mar 25 '11 at 14:13
• Thanks - was looking for the melles-griot or edmunds online but couldn't find anything useful – Martin Beckett Mar 25 '11 at 15:13
• Have you got access to an optical design code? Zemax is expensive, I think there is a freeware version called FRED that will handle this stuff in no time... – Nic Mar 25 '11 at 17:15
• FRED isn't Zemax and only a demo version is free. There used to be a free limited surface version of OSLO - but unless you know the details of the LED lens none of these will really help - and if you are treating it as a point source then you can just do it by hand – Martin Beckett Mar 25 '11 at 17:26