You're missing my point (my fault). Yes, I'm aware that the building is keeping the beams from throwing and I'm aware that throw is measured in terms of lux.
My point was that the difference in the two beam diameters in that (obvious) case was just a difference in size (lumens). So if you moved the building out of the way the one with the greatest intensity (collimated beam) would throw the furthest and the size of the off center beam wouldn't have an effect.
Thanks for the clarification, I think I can what you're trying to get at now.
Just to further clarify terminology, when I'm talking about the on-axis beam, I'm talking about just that one projected image that is collimated perfectly (i.e. all the rays are 100% parallel to each other and the aspheric's axis), this coming from the part of the die that is directly below the aspheric's axis. The off-axis beam for me is every other image that doesn't come from that spot. Are those your definitions?
Here's an optics applet:
http://webphysics.davidson.edu/applets/Optics/intro.html
It's rather basic, only has point sources and so on, but the laws of refraction are simple for point sources, and it helps to illustrate my point. Here's what I've done with it:
Fairly simple, one point source, one lens (note that refraction happens at the centre, but that's irrelevant for the purposes of this exercise) and one aperture, since the applet doesn't allow us to change the lens diameter. Same effect though.
Top image is the bit of the die that's directly under the lens' axis. Obviously, everything is parallel to the lens' axis. Second image is for a bit of the die that's a bit off-axis. Note how at short distances, the second beam still covers the first, but as we reach the right side of the image, we've almost got two completely separate projections.
Observe here that in real life, you've got much smaller "steps" in the off-axis distance, and this happens in 360 degrees around the axis. Lots of overlapping.
In the third image, I've extended the focal length. Obviously, since the lens (well, aperture in this case) is still the same size, the beam coming out of the lens is tighter. Fourth image is the same offset that I've introduced in the second image.
Observe the differences between the 2nd and 4th images and where the rays cross the centreline. (Side note: the bottom ray of both has been cut off, note that while this affects both, it makes the 4th image look a fair bit worse than it actually is). In the second, let's put an object where the bottom ray crosses the axis. It's now lit up by both projections, and there's a 50% overlap between them, leading to a doubling of the brightness in that region.
In the 4th image, put an object at the same distance. Now observe that although the beam is tighter, the off-axis projection covers a greater proportion of the on-axis projection. Also note that the angle those rays make with the lens axis is much less than that created by the rays in the second image, confirming that this second setup results in a more collimated beam. That bit can be done by visual inspection or just by using trig.
As I've said before, as the target approaches infinity, the focal length becomes less important. This is due to the fact that for the light from a certain point to still light up the target and not completely miss it, it must be ever closer to the axis, until you hit infinity and no other projection ever hits the target.
Therefore we can conclude that by only changing the focal length, while the first setup will gather more light (which I think we all knew), the second will result in a more collimated beam. Hence the throw will increase, but with the reduction in light being gathered the usefulness of such a beam will decrease.
Finite element analysis would be great here, since it would allow us to more accurately quantify the effects of focal length.
Walter, my apologies, I only just noticed this:
Can you explain more about 'The bigger lens will throw further, because the LED more closely approximates a point source.' ?
Is that because the actual led is relatively smaller for the big lens, and thus the beam more narrow and thus more intense/concentrated ?
That is correct. :thumbsup: It can be described either way, depending on whether you're looking at things from the point of the lens or the LED.