Could someone explain aspherics?

[Jarl]

according to this,having a shorter focal length is good, because you grab more emitter lumens. However, the shorter focal length also has a wider beam. I want the most possible emitter lumens in a narrow beam; would that mean short focal length and large diameter?

Also, what is the effect of having the emitter slightly off centre with an aspheric?

 

[Jarl]

are they so hard to understand? o.o

 

[monkeyboy]

It makes sense; shorter focal length means the lens is closer to the LED to focus so more light hits the lens and wider diameter also means that more light hits the lens.

Short focal length spherical (single element) lenses suffer from a lot of spherical abberation hence they make the lenses aspherical.