@Rred lumens you kind of talked yourself in a circle there.... Lux is deceptive, lumen is fixed. lux ratings can be skewed by having a tight beam angle, see halcyon, but total lumen output is not able to change.
lux is what you are talking about, which is lumens per unit area measured at a distance. Lux is very deceptive because of the example you gave. The issue there is that the 3ft circle might be more useful for what you are doing.
Perfect example is in cave diving. Halcyon and Dive Rite love to talk about lux instead of lumen because their lights are severely lacking in the lumen department at around 800 lumen each *same as a backup light*, but they have more useful light because of having much tighter beam angles. Conversely, UWLD has a wider beam angle at 8* instead of 6*, but they can put out 4+ x as much light, so the lux numbers are still higher, but the useful light is also considerably higher. Halcyon puts a very tight spot in the middle of their light to crank their lux numbers up, but the spill is pretty weak so it's great for signalling, but not a whole lot else. Great source of tunnel vision.
If we look at the image below, the most similar comparison would be done with the UWLD LD-15 and the Light Monkey 21w HID. They are throwing a similar lumen output of 1300-1500 lumen, but the 21w HID has a tighter beam angle so it has more lux. Notice how much more area around the hot spot is illuminated and how much more you can see. Sure the hot spot is light up brilliantly, and it could punch a hole through granite, but is it useful? I'd argue it isn't. Lux is important, but because the readings can be so variable *a single mm of movement can throw the lux readings all over the place*, having a total light output against a beam angle is a much more useful comparison for lights.
image taken from this link, which has the videos that are important to watch as well
Beam Comparison
your comment about the cheap lights is actually backwards because Lumen can't change so I think you may have talked yourself in a circle.
Halcyon Focus and Flare - Halcyon Dive Systems
Looking at Halcyons site, the exact same emitter is able to produce 11,500 lux on the flare, but go all the way up to 39,300 lux on the Focus. The Focus is able to get the beam angle so tight that it basically tricks the lux meter because the meter is not measuring a large area, only the small bit in the center. Both are 710 lumen. Beam angle can't change the lumen rating, only the lux rating. It can change useful lumens, but since LED's are forward facing emitters, it is essentially all useful lumens vs. something like an HID which is a side emitter and may have non useful lumens if it isn't focused properly.
No one that I know of measures lux with large enough of a sensor to make it a useful measurement which is why I don't know of any dedicated manufacturers of dive lights that use them despite Halcyon claiming it's the industry standard. I only know of them and Dive Rite that use them, everyone else used just wattage in the HID and Halogen era *and Light Monkey still does unfortunately, though that's to hide a lot of other issues with their LED's*, and everyone else uses lumens and beam angle since it's a better way to compare lights.
one word of warning though, most manufacturers are quoting lumen behind the lens because the equipment to test lumens is horrifically expensive, so expect to see up to 20% drop in lumens in the front of the glass in the real world. Thankfully since most everyone quotes behind the glass, it's at least on the same page. Also important to note, there are many manufacturers, with Big Blue being the largest offender, that quotes some pie in the sky theoretical lumen number but can't actually achieve it, and if they do, it is only for a minute or two because they are not using constant output drivers. After about 30 minutes, the Big Blue lights drop to roughly 30% of their claimed lumen output and will maintain that for the rest of their burn. They only achieve about 80% of their claimed lumen output but it is essentially a linear drop from 80% to 30% in the first 30 minutes of their burn. Most of the high end lights do not exhibit this behavior, Halcyon, Dive Rite, Light Monkey, UWLD, etc. so just be mindful when you purchase a light from Big Blue and a bunch of other budget manufacturers, that you should factor that into your purchase
