How to quantify beam shape? And discussions on many related topics: optics - TIR & reflector, thrower vs flooder, throw calculation, beam angle, cd/lm parameter, etc., etc. Did I miss anything? :-)

I just want to add that I think that the best measure of the flashlight inherent throwiness tendencies - which accounts for LED+optics combination but doesn’t care how hard you drive the light may be:

Beam Acuity ≈ √(π×cd/lm)

It’s the property of the flashlight, not how bright you make it.

It has nice properties:

  • it gives 1 for the floodiest of flashlights - a bare lambertian or a mule
  • it produces 0.5 as the lowest limit of any light - omnidirectional naked bulb
  • it is proportional to range - given the same lumens the light with twice the Beam Acuity will throw twice as far no matter how the range is defined (ANSI terminal cutoff is ¼ lux, I prefer 1 lux which is simply √cd or ½ ANSI range).
  • it is also proportional to the beam divergence flat angles and hotspot diameter - we are not intuitively compatible with solid angles in steradians and comparing areas.
  • It’s likely about proportional to our perception of brightness - a target at fixed distance should look nearly twice as bright when illuminated with a flashlight with double the Beam Acuity, given the same lumens.
  • the scale values are in a moderate range that goes from 1 (or 0.5 but that’s not a flashlight) to some 50’s for LEPs and it’s easy to interpret (as above). Also a granularity of ±1 or lower is probably sufficient and smaller than the uncertainties of lm and cd measurements used to construct it - no need for decimals.

In summary: it’s just awesome.