Hey Greg,
No offense, but I think you are confusing this thread with insignificant technical detail.
As a general rule with a dive light, 5x lumens = 2x perceived brightness. A 500-lumen light will appear about twice as bright as a 100-lumen light.
As I already said, this is a highly simplified heuristic. In an ideal world, everyone would also consider the beam angle, which makes a huge difference in how those lumens are spread over the target surface.
But the reality is that most manufacturers quote only lumens, not lux@distance and/or beam angles. And these lights are generally used in short-medium range applications where most of the light is reflected back to our eyes. So the 5x output = 2x visible rule is close enough for sport.
As for photopic vs scotopic vision...it is not a major factor here. The current generation of LED dive lights output 100+ lumens, and again, they are typically used at short-medium range. Also, they are frequently used in daytime dives, where you have lots of ambient light but you need to look in a crevice, or restore color to a patch of reef at depth.
Hope this helps.
-Jeff
Ok, I'll try to break this down (this is not insignificant detail, and no offense has been taken):
Lumens != brightness, brightness is a luminance measurement, and it is very subjective. Please stop confusing the units (and me in the process). If you changed your equation to equate to cd/m^2 (luminance) it would make sense according to the research you linked to (although it is closer to 6x).
You say that a 50% drop in lumen output does not equate to a noticeable difference in perceived lightness.
I say it does. Again, you should buy a light that has half as many lumens if you can't tell the difference and save yourself some money .
The scotopic response changes the perceived lightness function to be more sensitive when using cool white LEDs and in dark conditions (as in the cold waters here in the Pacific Northwest). The function you referred to is old and does not account for lumens, nor the scotopic response, nor the cool color (wavelength) of LED light.
Lumens is what this whole discussion has been about (not lux, not cd/m^2). I do not buy the small beam angle and all light is reflected back to the eye. At the end of the day, you have reduced lumens (.: lux) on the illuminating subject and cannot see as much as before, regardless of how bright the center appears. If I went to the USCG, ICAO, IALA, CCG, DOE, USAF or the FAA with a LED light that was quoted in the terms you are saying, I would not be making a sale. That is based solely on safety and divers should be no different.
Here is a quick calculation for you to try:
Light = ? lumens, beam angle 6 degrees
Lux @ center, 1 m away = 1 lx
Lux @ 6 degrees or 52mm on each side of center = 0.5lx
You can't figure out the lumens as you don't know the gradient or change in lumen output as it approaches the divergence angle points. Believe me, more than one engineer I work with has tried to do this with a goniometer and it near impossible unless you measure EVERY point. You can compare lx at a single reference point if you prefer though.
Hopefully this has clarified some misconceptions you may have had.
BTW this thread has gotten way of topic, hopefully Gcbyran won't be too upset.
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