For what it's worth, I happen to agree with most points you made in your post above.
Using an even more extreme example, based upon practical observations, no one will ever convince me that a 21x 25mm binocular image of any object ( yielding a factor of 105 on the Adler Index scale ) is "roughly equal" in any way to looking through a 15x50 ( also 105 on the Adler Index scale ).
Indeed, ( and however ) even the "Bishop Index" ( of 21 x 25 = 525) versus (15 x 50 = 750) in no way comes close to being truly representative of the real world superiority of the 15x50 in comparison.
When this binocular group of the day were discussing these issues back in the period around 2004 - 2006 ( many extracts of which can still be read in the "Best Of" archives compiled by Ed Zarenski ) I gave the matter a lot of thought for a long time, and came close to providing an alternative formula that took EXIT PUPIL much more into account as an extra, significant ingredient factor, and cannot for the life of me remember now why I didn't go ahead with the suggestion.
I seem to recall being unsure whether to MULTIPLY either the Bishop or Adler figure by the exit - pupil, or multiply one or the other by the square root of the exit-pupil, or something along those lines, anyway.
I calculated a bit on it and find multiplying the Adler or Bishop idex numbers by the square rot of exit pupil very interresting.
Multiplying AI and BI by the exit pupil makes no sense though; all configurations of same aperture within each index get the same rating undependent of magnification.
With BI magnification and aperture have the same importance. Multiplying AI with square root of EP 10x50 gets twice the value as 10x25. Multiplying BI with square root of exit pupil 10x50 gets ~2,8x the value as 10x25. Multiplying AI with square root of exit pupil 20x50 gets ~2,8x the value as 10x25. And multiplying BI with square root of exit pupil 20x50 gets 4x the value as 10x25.
If we compare 21x25 with 15x50 multiplying square root of EP gives:
AI: 114,5/193,5 ~ 1,69times difference
BI: 573/1369 ~2,39 times difference
It's a known fact that the eyes perception of brightness differences isn't linear and a common belief is that 4 times brighter is perceived as twice. This matter is now and then discussed in the flashlight community I participate. While I can agree that 4 times brighter often does not feel like 4 times I still perceive it feels more than 2 times. Therefore the 2,8times difference between 10x50 and 10x25 by multiplying BI with square root of EP seems to be very interesting. I am leaning towards the belief that multiplying BI with square root of EP may be the best way to measure performance under pretty clear sky.
But the more polluted the sky is the more BI without square root of EP, or AI may be applicable.
Edited by Swedpat, 14 November 2019 - 04:44 AM.