LEDs & Other Stuff - (Reference Guide)

There is. You need to use a pre-collimator (small spheric lens very close to the LED, LED needs to be de-domed). This is the only way to collect as much light as possible with an aspheric lens. If you then want a small hotspot, you just need to use a suitably small LED.

Here is a formula you can us to calculate the size of the hotspot:

luminous_intensity_in_specific_distance [lux @ xx m] = luminous_flux [lumens] / area [m2]

Generally you need to know how many lumens are actually in the beam. For reflector lights you can assume 75% of the total lumens.

Here you can find some nice calculators to help you.