Minimum lux at target required to recognize a defined target?

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Genzod

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What is the minimum amount of lux required to marginally identify a 2x6" Appalachian Trail white blaze marker at 100 meters?

BLAZE_1024x1024.jpg


SOLVED:
This post poses a question that is ultimately answered in an experiment documented at this post. Not only that, the amount of intensity required at any distance is resolved.

A useful interactive plot is derived there and is used as a tool to solve some problems with light and naked eye target identification here and here.

A forum member brings up the need for scopes for small targets (which isn't necessarily always true as I later proved). Others attempted to use unsound arguments, based mostly in a failure to understand the context of my question, to dismiss any and all hope for ever finding a practical answer to this question.

The math for the scope problem was demystified at this post and several scoping examples are provided here. The triumph of this effort discovers a general formulaic solution adaptable for almost anyone's eyes here.


q03NK.gif



But it's fun to first read the question, watch a small gaggle of obvious reading comprehension failures and irrational attempts determined to "block that kick" and talk me out of finding a practically useful solution. So pay attention, try to get the context, resist the urge to become narcissistically dismissive and intellectually condescending, and try to have some fun. But not too much fun because that would be X-rated!

Purpose:

I'm a fastpacker who enjoys running at night on the Appalachian Trail. I'm replacing my defective headlamp, and I'd like to choose one with enough throw to identify navigational white blaze tree markers at a distance, preferably with a 100 meter constraint for marginally identifying such a marker under ideal nighttime conditions and still have enough foreground spill light for running under technical trail conditions. (Later, I would realize the need for lamp redundancy, so I decided to separate tasks--headlamp for running and a more powerful handheld for marker identification).

But carrying a lot of weight is not expedient for a fastpacker running up mountain inclines, and lamps increase with weight as their performance improves. Therefore, I need to know the minimum amount of light I can get away with so as to keep weight at a minimum. I'm on a budget here, and I can't just buy several $80 lamps and try them out to see what works best. If you aren't on a budget and own Fort Knox, lucky you. ;)


Question:

What is the minimum RECEIVED lux at target (as opposed to REFLECTED lux) required to discern the white blaze target on the tree in photo above? I'm assuming 0.25 lux throw is just a standard used for calculating flashlight range for comparison's sake, not for what most people actually need to recognize a target at a specified distance.

(Did you stop reading here, go to the photo and answer the question? What's the matter with you? Don't you like to be entertained?)

If you need to qualify your answer as a range of distances (for example: "4-8 lux instead of something like "about 10 lux") that's fine, just help me understand why you chose those bounds as an answer. Aw shucks, explain why you chose your answer anyway so I can research it and get a gist for exactly how much fertilizer is in your shed.
:knight: Yes, that kind of fertilizer.


Actually, I like smart people. I like to check their answers, so I can know who to like.

Everyone else...

NO BOOZE FOR YOU! :drunk:

soupnazi.jpg


What, you don't drink? Okay...

NO FISH STICKS FOR YOU!


Given/Assumptions: (PAY ATTENTION!)

Target is as appears in photo above, a 2" x 6" painted white blaze marker placed about 2 meters high on a highly contrasted tree. Assume this is a magic tree and all the trees with white blazes look like this. I like simple things.

Target is 100 meters from searcher in direct line of sight and is anticipated to be on a tree next to a well worn path. (109.4 yards for you Americans who think the metric system is a communist plot designed to confuse the world).

Searcher is old, American and speaks in two measurement systems, but has healthy night vision, which is corrected with glasses but due for a prescription renewal (later learned this was the legal limit for driving of 20/40 at the time I collected my data).

Atmosphere is clear--no precipitation, humidity, fog or Skittles. (Taste the rainbow).

There is no ambient light (edit: or foreground spill) whatsoever. This is not a university graduate level question. Stop making it complicated!

I'm the only person on earth with a flashlight (a magic flashlight) , and no, you can't borrow it.



 
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Offgridled

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In everyday life we describe light subjectively; for example, light is `good' if it enables us to do what we want to do, and `bad' if it doesn't. But light can be measured and described numerically. In particular, we can measure the*intensity*of light; if a given source produces one unit of light, two such sources will produce twice as much light, ten sources will produce ten times as much, and so on. Thus it makes sense to talk about the intensity of light in mathematical terms.

We will need to measure the intensity of light in two different ways. First, we must consider the total amount of light a source - say, a star, or a light-bulb - gives off. Second, we must consider the amount of light from a source which reaches our location. The difference between these two kinds of intensity is part of everyday experience. For example, a 100*watt light-bulb is a fairly powerful source of light; placed a few feet from your desk, it provides plenty of reading light. But even a 1000*watt light-bulb won't provide enough light to read by if it's located a few*hundredfeet away.

Besides i see duct tape on a tree!!
 

Genzod

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I read TEEJ's post linked by Archimedes. Although I don't have a scope, he suggests 1-5 lux is needed to aim at a target or identify it (in other places he goes as low as 0.5 lux). I'm assuming he isn't talking about targeting Bugs Bunny (at other posts he mentions highly contrasted paper targets). Using 100 meters and the 1 lux minimum, that's 100x100x1=10,000 cd at 1 meter, minimum. The Manker T01 II produces 20,000 cd with a 14500 battery and 10,000 cd with a primary AA. At 55g and $50, it appears to be the lightest, reasonably priced option I have available for that range/visibility constraint.

The markers in the photo tend to be placed within 30-50m of each other (except in wilderness areas like the White Mountains of New Hampshire of course, where markers have been spaced farther apart by hungry trolls who like to eat lost hikers). For 50m (164 ft for all you non-NWO communist conspirators out there), intensity would be 50x50x1 to 50x50x5 = 2500 to 12,500 cd. The Jetbeam Jet-I and II MK and the Fenix E15 2016 are 30g, $30 cheapies that are between 4000-5000cd with lithium ion.

The Nitecore EC11 light (45g) and still relatively cheap at $60 and can produce 4300 or 9000cd.

I'm thinking though, if I don't want to be invited to a troll tea party (as the main dish), I'll need to stick with the Manker T01 II.

838.jpg
 
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Genzod

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Okay, here is where my concern is about my particular target. It's such a small target at 2 x 6 inches. It's high contrast, but very small. I'm stuck with my vision unless I carry some kind of telescope, so there is a question of my ability to see the tree blaze at 100 m even if I could paint that tree with 1-5 lux.

TEEJ, who is so clever with lux at a distance and could resolve my problem in a matter of moments with a few keystrokes and a :D, points this out here, saying:

"When closer, objects take up a larger proportion of your field of vision. As objects get progressively farther away, they take up a progressively smaller proportion of your field of vision.

"As to see details, your central 2º cone of vision is required...objects that are smaller than your 2º field of vision are VERY hard to resolve at long distances. (Hence scopes and binoculars helping so much) Your vision within that 2º cone is your sharpest, best at tracking motion, and most sensitive to colors...but, the WORST in low light. So, if you are trying to see something small in your field of view, you need more light to do it than if it were proportionally larger...or closer, etc."


2º cone translates to about 14.3 ft (4.4 meters) for a 6 inch tall target, so for 100 meters, it's safe to say vision will be working inside the 2º cone which operates worst in low light.

It would be great to have this mapped out with a mathematical formula--not because it would make life easier, but because demonstrating mathematical prowess is a surefire thing when it comes to impressing the ladies.

Am I not right, ladies?

main-qimg-c7b742b7971b08c3c6264e74d60df146
 
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Offgridled

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Mathematical equations aren't just useful — many are quite beautiful. And many scientists admit they are often fond of particular formulas not just for their function, but for their form, and the simple, poetic truths they contain.

While certain famous equations, such as Albert Einstein's E = mc^2, hog most of the public glory, many less familiar formulas have their champions among scientists.
The fundamental theorem of calculus forms the backbone of the mathematical method known as calculus, and links its two main ideas, the concept of the integral and the concept of the derivative.

In simple words it says that the net change of a smooth and continuous*quantity, such as a distance travelled,*over a given*time interval (i.e. the difference in the values of the quantity*at the end points of the time interval) is equal to the integral of the rate of change of that quantity, i.e. the integral of the velocity
 

archimedes

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Mathematical equations aren't just useful — many are quite beautiful. And many scientists admit they are often fond of particular formulas not just for their function, but for their form, and the simple, poetic truths they contain....

Off-topic, but e^(i*pi)+1=0 ... :eek:oo:
 

Genzod

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I plotted Range (meters) as a function of Lamp Intensity (candelas) for lines of constant lux (measured at target) from TEEJ's favorite lux picks of 0.5-5 lux ( starting with black 0.5, 1, 2, 2.5, 3, 4, 5 lux, ending with violet). You can see this graph and change parameters to your liking to view the points of interest better without altering the link's compilation.

Move your mouse pointer over the plot and click on the point-on-line icon, then click any point on any line to see the values there. For example, if I wanted to see lamp intensity required at range 100 meters and target intensity of 1 lux, I would follow the red line to 100 meters and click on the point there to get the precise intensity required in candelas. (10,000 cd).
 
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Bdm82

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As noted above, a small target like that would be tough to identify without some sort of scope or binoculars. And using those, it changes all formulas and lux preferences anyway.


The objective lens size on a binocular or scope collects the light. A larger lens and lower magnification and you need less lux from the illumination source. A smaller lens and higher magnification, you need more lux. So whatever lux you like with bare eyes (not bear eyes) will be different based on scope/binocular.

Let's say you've got a 6x50 scope. That's a 50mm lens and a ratio of 8.3. This will allow you to see more light than the human eye alone ever could (unless you have special eyes and pupils that can dilate to 9mm). I have a pair of 15x70 binoculars, and not only do they "zoom" the target in for me, but they collect enough light for me to see the target a bit better. No, not true night vision. 70mm+ binoculars are often used for star gazing as the additional light collection helps other planets and stars become visible.

But if you have say a 10x25 scope, 2.5 ratio, forget about it. That is going to collect less light than your own eyes - and would not help at all in the dark.



Side note... Archimedes... I feel like you might be one post from replying entirely in binary...
 
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Genzod

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Off-topic, but e^(i*pi)+1=0 ... :eek:oo:

The Hippy Dippy news report:

"Citizens were alarmed today when from all across the country, a mysterious stampede of pheromone saturated women too numerous to count, converged on Washington State."

hqdefault.jpg
 

Genzod

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As noted above, a small target like that would be tough to identify without some sort of scope or binoculars. And using those, it changes all formulas and lux preferences anyway.


The objective lens size on a binocular or scope collects the light. A larger lens and lower magnification and you need less lux from the illumination source. A smaller lens and higher magnification, you need more lux. So whatever lux you like with bare eyes (not bear eyes) will be different based on scope/binocular.

Let's say you've got a 6x50 scope. That's a 50mm lens and a ratio of 8.3. This will allow you to see more light than the human eye alone ever could (unless you have special eyes and pupils that can dilate to 9mm). I have a pair of 15x70 binoculars, and not only do they "zoom" the target in for me, but they collect enough light for me to see the target a bit better. No, not true night vision. 70mm+ binoculars are often used for star gazing as the additional light collection helps other planets and stars become visible.

But if you have say a 10x25 scope, 2.5 ratio, forget about it. That is going to collect less light than your own eyes - and would not help at all in the dark.



Side note... Archimedes... I feel like you might be one post from replying entirely in binary...

I'm looking for a constraint, whether it is 1 lux at 100 m or the maximum distance my naked eye can make out a highly contrasted 2 x 6 inch white blaze on a tree and asking what lux is necessary to distinguish it, suggesting a flashlight specification that will ultimately lead to a smart purchase.

My family has a pair of decades old and quite heavy military naval binoculars with large lenses and its ability to collect light and assist with night vision is quite startling.


Edit:
Now that I'm educated on scopes, I can respond to the technical aspects stated by this post:


Let's say you've got a 6x50 scope. That's a 50mm lens and a ratio of 8.3. This will allow you to see more light than the human eye alone ever could (unless you have special eyes and pupils that can dilate to 9mm).

I just want to clarify this statement. The scope will collect more light than your eye ever could (maybe that is what you meant). I think you understand that the extra light gathered by a scope with say, a 9mm exit pupil, used with an eye having a 7mm dark adjusted pupil is wasted.

"Aged eyes may dilate to only about four millimeters. Younger eyes may open up to seven millimeters and even more. An exit pupil much larger than your eye can use is wasted. Like drinking out of a fire hose." (Source)


But if you have say a 10x25 scope, 2.5 ratio, forget about it. That is going to collect less light than your own eyes - and would not help at all in the dark.

A 10x25 scope can be very helpful in the dark provided light on target is increased to compensate for the dimness caused by the smaller exit pupil of the scope, e.g., extra lux will make the scope useful again. I think you said this higher up in your post when you said: "A smaller lens and higher magnification, you need more lux. "

By itself however (no auxiliary illumination from a lamp), a scope with an exit pupil at least as large as the dark adjusted pupil of the eyes is ideal for night use. Again, a scope exit pupil beyond that is wasted.

After field experiment, I determined I can identify a white blaze out to about 30 meters with no supplemental illumination other than about 0.085 lux of ambient illumination on target. With the aid of auxiliary illumination, I can marginally identify a white blaze target
out to about 180 meters with the naked eye, 8 lux on target from a lamp and 0.085 lux ambient light. By "marginally" I mean bordering the ability to see it at all.

Your post pushed me to learn more about scopes, so it was very helpful contributing to this research effort, particular for seeing beyond my 100 m constraint and possibly up to 0.15 miles with the right scope and lamp. I found the information very fascinating. Thank you.




 
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ssanasisredna

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I can answer this but I am on my phone ...

1) assume it's the only white or even mildly reflective element.

2) lots of web resources for minimum detectable candela

3) you know the size and can estimate reflectance/albedo

4) can work that back from lux to get answer

5) need to work out angular size to determine ability to resolve and say yes it is a blaze ... Near impossible unless you know it's on a tree
 

Genzod

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I can answer this but I am on my phone ...

1) assume it's the only white or even mildly reflective element.

2) lots of web resources for minimum detectable candela

3) you know the size and can estimate reflectance/albedo

4) can work that back from lux to get answer

5) need to work out angular size to determine ability to resolve and say yes it is a blaze ... Near impossible unless you know it's on a tree

When I look for blazes below tree line, assuming it's on a tree is a safe bet.

Size is a standard 2 x 6 inches about 2 meters high on a tree.

One day, the ATC will find it in their heart to also add a 1 inch diameter dot of reflector tape to the dried blaze. Except in the White Mountains of course, where hungry trolls hunting lost hikers will remove them.
 

Genzod

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*snip*

2) lots of web resources for minimum detectable candela

*snip*

Regarding #2, could someone direct me to at least one such resource? The web is a very large place, and unless the resource is placed "on a tree", it's near impossible for me to pin it down with my Googles.
 
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Offgridled

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When a sudden bright light hits the eyes, the photoreceptors in the retina that registered that light go into temporary overload. For a while they won't register anything at all. Then, when they do get back to work, they are very likely to produce a reverse afterimage of the light that overloaded them. It's like a photographic negative.

The most common afterimage is the one you get when you stare into a photographer's strobe light. The bright spot of strobe light turns into what appears to be an equally large spot of darkness—sometimes blue, sometimes green—that appears to get between your eyes and whatever you are trying to look at. The dark spot is produced by the overloaded rods and cones on the retina, which are temporarily out of service.
 

KITROBASKIN

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Perhaps one aspect that should be remembered is when a manufacturer will state (hopefully not overstate) maximum lux for a particular flashlight, it is when the battery(s) are fresh and before everything sags performance wise. Or maybe that is not germane to this discussion.
 
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