# How to calculate beam spread of a non-point light source via an aspheric lens

I need to determine the angle, or rate of divergence of light from a single aspheric lens when I place a non-point light source (e.g. LED array) at a given distance from the lens which is less than the focal length of the lens.

This seems to fall outside of the normal emphasis on image size and location in all the beginner optic info I'm finding on the WWW; I don't care about the virtual image this creates, I just want to know what the angle of divergence is so I can predict the spot size at an arbitrary distance from the lens.

I can also say that I've seen plenty of examples which have collimated light on one side of the lens; as near as I can tell, they won't work, as they assume the light is collimated and thus don't take into account the light source beam angle.

My best guess is that the equation to solve for the divergent angle would just need: *light source's beam angle *the focal length of the lens, *distance between the light source and the lens, *and possibly the radius of the non-point light source.

I also suspect that the equation is probably the same for other types of lenses.

## 1 Answer

Well, if you were looking strictly at the LED array (no lens) then you can typically find that the intensity of the array will fall off at angle according to the LED manufacturers data sheet AND the cosine of the cross section of your array. Which is to say that an array of LEDs will have a wider viewing angle than a single LED. In theory you could solve your angle of divergence as the point where these angles give a "negligible" intensity output/no light. Since there's also a lens involved, then I would guess that you would need to know the size of the image as it leaves the lens.