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.