# Minimum lux at target required to recognize a defined target?



## Genzod

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

*



*

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.


*






*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. 
 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:






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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## archimedes

Try searching for posts by @TEEJ ....

http://www.candlepowerforums.com/vb...weapon-light&p=4271900&viewfull=1#post4271900

He has like about a thousand posts (really!) discussing this


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## Offgridled

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!!


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## Genzod

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.


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## Genzod

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 , 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?


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## Offgridled

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


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## archimedes

Offgridled said:


> 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 ... oo:


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## Offgridled

archimedes said:


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


Well played arch


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## Genzod

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

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

archimedes said:


> Off-topic, but e^(i*pi)+1=0 ... 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."


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## archimedes

Bdm82 said:


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



_ ... " I'm sorry, Dave. I'm afraid I can't do that " ... _


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## archimedes

Ok, let's try to gently ease this thread back into orbit now ...


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## Genzod

Bdm82 said:


> 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

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


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## Genzod

ssanasisredna said:


> 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.


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## Genzod

ssanasisredna said:


> *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

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.


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## KITROBASKIN

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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## Offgridled

Thats a great point KIT...


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## Genzod

KITROBASKIN said:


> 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.



I view lux/range/lumen figures as "for comparison only". For example: Max range theoretical to 0.25 lux. Outputs are peak values after 1 minute run time. I'm aware of the reputation of certain manufacturers who are either not careful or exaggerate their numbers, and I take that into account. For those, I look for a consensus for data among reviewers. 

Some manufacturers (a name is not my agenda here) assume the larger fraction of uneducated consumers will not understand these facts. _Safe_ assumption, not a good one. I think it is a mistake for a manufacturer to treat the entire consumer base as "stupid" and potentially malicious. A simple legal _disclaimer _is sufficient to cover their sacred...well... you know_... _qualifying that the test data is according to a certain standard and is only for the purpose of comparison, not a measure of the full run time performance, and I think most everyone will get that much except the crankiest of "professional victims".


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## BVH

Spectrolab, the helicopter searchlight manufacturer, provides the figure of 32 Lux at 1 Kilometer output for their 1600 Watt light with a beam of 4 degrees and 40 Lux at 1 Kilometer output for their 500 Watt, 2-degree beam light. Maybe that gives you an idea of what they need to see a target from a typical 500 - 1000 feet away.


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## Genzod

BVH said:


> Spectrolab, the helicopter searchlight manufacturer, provides the figure of 32 Lux at 1 Kilometer output for their 1600 Watt light with a beam of 4 degrees and 40 Lux at 1 Kilometer output for their 500 Watt, 2-degree beam light. Maybe that gives you an idea of what they need to see a target from a typical 500 - 1000 feet away.



Thank you. I would imagine that standard might set the upper limit for minimum lux requiring a much more detailed identification of target. A police chopper for example might be searching for a very specific suspect, what he's wearing, how he's moving, what he's up to, that sort of thing. Whereas my task is a whole lot less complex, being a simple, highly contrasted 2 x 6 inch rectangle on a much larger target, the base of a tree that is not moving.

I'm going to see if I can't do a little experiment tonight with a headlamp of known intensity and fresh batteries. I'll post a white 2x6 marker with similar reflectivity and contrast, then pace off a distance and approach the target until I can barely make out the target. I guess no formula will be a better substitute for my own eyes. Of course I'll be aware to take into account ambient light, full moon, that sort of thing. But I know of a few places where it's extremely dark (no street light) that will work.

*Edit:* *BACK FROM THE FUTURE!

*





I configured the tool I devised much later for modeling blaze identification with the performance of the second copter lamp you mentioned--Plot. The 2 deg spotlight is 40 million candela, and the black line represents lux _received_ at target vs. range. That curve intersects the yellow line (marginal identification of a highly contrasted 2x6 inch blaze) and the red line which is 32X more intense illumination, indicating the range and lux the lamp provides with those constraints. 32X above marginal is probably useful for identifying a moderately contrasted randomly located moving target the size of a man. You can see from the intersections the lux required is 776 lux (226m) for a man and 154 lux (509m) for a white blaze, about 52% and 10% the intensity of the average overcast mid day sun. 

*EDIT: *I replaced the plot with more the accurate formulaic equation. (The 5th order polynomial curve was skewed by an inaccurate point at 175 meters during regression). I adjusted the acuity range needed for a 6 ft tall man rendering him with around 18x72 pixels with each pixel 1x1" (87.5m acuity limit). Sight represented in plot is 7.0mm dark adapted pupil with 20/20 vision (average 30 year old).


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## archimedes

Genzod said:


> ....
> I'm going to see if I can't do a little experiment tonight with a headlamp of known intensity and fresh batteries. I'll post a white 2x6 marker with similar reflectivity and contrast, then pace off a distance and approach the target until I can barely make out the target. I guess no formula will be a better substitute for my own eyes. Of course I'll be aware to take into account ambient light, full moon, that sort of thing. But I know of a few places where it's extremely dark (no street light) that will work. And of course I'll make sure the distance I select puts the target dimensions inside a 2 degree cone.



These types of practical real-world tests are very valuable. Detailed notes of your findings will be greatly appreciated, here on CPF.

Looking forward to hearing your results ....


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## StarHalo

But night vision ability declines with age, and women are typically better at it than men.

So get some women and go out into the forest with your flashlight..


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## Offgridled

I agree with arch.. I will be very interested in your experiment and results. Ive enjoyed your knowledge and humor. Great job.


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## Genzod

archimedes said:


> These types of practical real-world tests are very valuable. Detailed notes of your findings will be greatly appreciated, here on CPF.
> 
> Looking forward to hearing your results ....








One might compare my feeble attempt to establish a baseline for minimum lux required to identify a white blaze trail marker on a tree with "endeavoring to construct a mnemonic memory circuit using stone knives and bearskins", seeing that having a simple lux meter might have made my testing more precise. But then, with Spock as my inspiration, all things technical are possible even without the best of tools. 

Nevertheless, my reasoning is, if I can get some kind of ballpark idea, and it is consistent with TEEJ's much posted expertise on this very topic, I think I can safely rest assured, there is very little fertilizer taking up space in TEEJ's shed.


I can come back later with explaining my stone knives and bearskins methodology, seeing that I'm very tired now, and would like to go to bed. But just to let you in on a little something I learned tonight. There is no fertilizer whatsoever in TEEJ's shed (as far as I am concerned). He is spot on with his minimum bound for simple, highly contrasted targets where aiming is the only concern.
I just have one question now. Just where in NJ do I send this smart fellow this booze?:drunk:


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## Genzod

StarHalo said:


> But night vision ability declines with age, and women are typically better at it than men.
> 
> So get some women and go out into the forest with your flashlight..



One can explain the reason for being so "blind" at such an old age, and I can assure you it has nothing at all to do with women. But then, nothing flies over your head, because your reflexes are quick, and you will catch it, right?


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## Genzod

Offgridled said:


> I agree with arch.. I will be very interested in your experiment and results. Ive enjoyed your knowledge and humor. Great job.


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## StarHalo

Genzod said:


> One can explain the reason for being so "blind" at such an old age, but I can assure you it has nothing at all to do with women.



The younger guys make themselves blind over women all the time, but as to the technical aspect of it, true story bro..


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## Genzod

StarHalo said:


> The younger guys make themselves blind over women all the time, but as to the technical aspect of it, true story bro..



Never had an argument with me "bro"!


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## Genzod

I'd like to repeat the experiment later tonight before posting anything about the one I did last night. I'd also like to see how the requirement for target intensity varies with distance. I have three outputs on my lamp, so I can take three samples at three different distances. That might give me some kind of idea how much more intensity I would need at 100m.


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## StarHalo

Genzod said:


> Never had an argument with me "bro"!



But I'm arguing that "what I perceive" is not a good measure, since you're technically handicapped by gender from the start, not counting any other issues with your vision. Then there's the atmosphere, which is remarkably unpredictable in that no given weather condition ensures best visibility, since particulates in the area could be any range of local phenomenon like trees pollenating or nearby construction. I ran into this issue testing an HID light in the desert all the time; the distance would vary as much as 50% from night to night, and there was no meteorological parameter that could predict it.


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## Genzod

StarHalo said:


> But I'm arguing that "what I perceive" is not a good measure, since you're technically handicapped by gender from the start, not counting any other issues with your vision. Then there's the atmosphere, which is remarkably unpredictable in that no given weather condition ensures best visibility, since particulates in the area could be any range of local phenomenon like trees pollenating or nearby construction. I ran into this issue testing an HID light in the desert all the time; the distance would vary as much as 50% from night to night, and there was no meteorological parameter that could predict it.



I'm not arguing, period!_

This is for me. _My eyes are the best test instrument for answering my question for what kind of light _I_ need to get to search white blazes. Go back, reread the thread and see if you can pick up on that. 

As for agreeing with the lux range TEEJ came up with, for me that range is relevant _under similar conditions_, and for his shooters. He seems to know what he is talking about.

As for weather, (and other variables) did you not read the assumptions in my OP? THERE ARE NO SKITTLES! REPEAT, THERE ARE _NO_ SKITTLES!

I had a maturing puppy once who spied himself an opportunity in a loose thread on the fabric of a love seat. He was teething and his gums were irritating him. By the time I returned from a round trip to Maryland 12 hours later, that love seat was torn to sheds. Bad puppy...baaaaaaaaad puppy!:whoopin:

"You can't teach an old dog new tricks", but a young puppy might be able to teach _us_ something.


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## Genzod

Bdm82 said:


> 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.



I should point out here to _everyone_ that identifying a 2 x 6 white blaze on the Appalachian Trail is a very easy thing to do. You can't equate an object that small to some randomly varying micro-target that could pop up anywhere. That's not what is going on here.

White blazes are not randomly thrown wherever. As a general rule, the white blazes are anticipated about every 30-50 meters, (except in designated wilderness areas where spacing is between 160-400 meters) and they are found on trees at about head height along a well worn trail. Finding the next blaze on the trail is not like trying to target a camouflaged soldier in the bush, shooting chipmunks or searching for a needle in a haystack. 

Although the standard blaze is 2 x 6 inches, sometimes they are a little wider due to tree growth, and then get painted over, but they tend to be the same sizes in such sections. 

If you know what to expect, where to expect it and it's highly contrasted with the object it's painted on, it's very easy to recognize in very low light. No telescope or binoculars required! (with the obvious exception of said wilderness areas).

What is "hard to do" is spend $30 on a cheapy 4300 cd thrower and finding out what you really needed was the $50 compact 20,000cd thrower. :hairpull: 

The clever ones figure out what they need first, then buy themselves one lamp for that one job. The simple ones buy many lamps for the same job, then proudly refer to themselves as _"a flashlight collector". _


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## StarHalo

Genzod said:


> As for weather, (and other variables) did you not read the assumptions in my OP?



Got that, it says "Atmosphere is clear," but what I'm telling you is that you can go out on two different nights that have what appear to be the exact same clear air, and the results can be wildly different. You will successfully see the target reflect one night, and then the very next night with every variable apparently the same, it simply won't reach. Living at the bottom of an ocean of air is an amazing thing..


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## Genzod

StarHalo said:


> Got that, it says "Atmosphere is clear," but what I'm telling you is that you can go out on two different nights that have what appear to be the exact same clear air, and the results can be wildly different. You will successfully see the target reflect one night, and then the very next night with every variable apparently the same, it simply won't reach. Living at the bottom of an ocean of air is an amazing thing..



That's fine, but you're really preaching to the choir here. I'm already aware of these variables. That's the reason I posted assumptions. 

When I ask a manufacturer to supply a range to 0.25 lux, I don't care about variables or being told it's a meaningless parameter. I just want to compare lamp performance between models and brands, not establish what I can see at that range. Likewise, I'm trying to establish a standard for myself through analysis and experiment at one consistent set of variables for the sake of providing some context for that particular parameter. 

We have a computational standard for all things flight related moving through such an "ocean of atmosphere". It's called the US Standard Atmosphere. We use it as a model to provide consistent information for air density, temperature and pressure up to 86000m. 

Of course this "ocean of air" is constantly changing, but that's not an argument for suggesting a standard atmosphere table isn't useful, especially when computationally designing flight vehicles. It's not a denial that the atmosphere is changing. No one is pretending that it isn't changing by having a standard. Neither is my exercise determining a personal range for what target intensities are useful and what are not. 

Tonight I went out in the same clear atmosphere and was able to see the white blaze marker at a substantially greater distance than yesterday. Mystery? A reason to throw in the towel and say it's pointless to analyze? No, there was no direct moonlight hitting the bike trail in the foreground of my field of vision this time constricting my pupils requiring a greater intensity at target to see it. Atmosphere the same, variable for difference accounted for. No amazement or mystery to me whatsoever.


----------



## Offgridled

Current vision systems are designed to perform in clear weather. Needless to say, in any outdoor application, there is no escape from “bad” weather. Ultimately, computer vision systems must include mechanisms that enable them to function (even if somewhat less reliably) in the presence of haze, fog, rain, hail and snow.

Begin by studying the visual manifestations of different weather conditions. For thiS draw on what is already known about atmospheric optics, and identify effects caused by bad weather that can be turned to our advantage. Since the atmosphere modulates the information carried from a scene point to the observer, it can be viewed as a mechanism of visual information coding. We exploit two fundamental scattering models and develop methods for recovering pertinent scene properties, such as three-dimensional structure, from one or two images taken under poor weather conditions.

Next model the chromatic effects of the atmospheric scattering and verify it for fog and haze. Based on this chromatic model we derive several geometric constraints on scene color changes caused by varying atmospheric conditions. Finally, using these constraints we develop algorithms for computing fog or haze color, depth segmentation, extracting three-dimensional structure, and recovering “clear day” scene colors, from two or more images taken under different but unknown weather conditions.


----------



## Genzod

Offgridled said:


> Current vision systems are designed to perform in clear weather. Needless to say, in any outdoor application, there is no escape from “bad” weather. Ultimately, computer vision systems must include mechanisms that enable them to function (even if somewhat less reliably) in the presence of haze, fog, rain, hail and snow.
> 
> Begin by studying the visual manifestations of different weather conditions. For thiS draw on what is already known about atmospheric optics, and identify effects caused by bad weather that can be turned to our advantage. Since the atmosphere modulates the information carried from a scene point to the observer, it can be viewed as a mechanism of visual information coding. We exploit two fundamental scattering models and develop methods for recovering pertinent scene properties, such as three-dimensional structure, from one or two images taken under poor weather conditions.
> 
> Next model the chromatic effects of the atmospheric scattering and verify it for fog and haze. Based on this chromatic model we derive several geometric constraints on scene color changes caused by varying atmospheric conditions. Finally, using these constraints we develop algorithms for computing fog or haze color, depth segmentation, extracting three-dimensional structure, and recovering “clear day” scene colors, from two or more images taken under different but unknown weather conditions.



That...or fly like a bat in an all weather capable EA-6B Prowler! (But, I'll settle for a neutral, minimized spill, narrow beamed light held low in the fog.)


----------



## Genzod

*Experiment Update:

*Sorry that I haven't posted yet. Data collection is still in progress and the procedure is getting better. 

The first night was spent discovering a best location for the elimination of ambient light and glare (pupil contraction) and I want to minimize those effects if I can't altogether eliminate them.

Now that I had the ideal location, the second night I timed my experiment with the moon still below the horizon to eliminate its spill on the bike trail in front of me. I also was able to select and test three distances with the three output selections of my headlamp, up to about 50-60 meters, to give me some kind of idea how greater distances require more lux as the target virtually shrinks relative to the eye.

But I still didn't have good data for 100 meters, which is my desired constraint. My headlamp didn't have enough output to test at that range.

Today I realized all I have to do to get 100 m data is set the lamp on low, and paint the target with various approximate "measured" intensities --0.125 lux, 0.25, 0.5, 1, 2, 4 (determined mathematically by distance knowing intensity at 1 meter, then using a tripod at those distances). Then I walk my eyes over to a predetermined 100 m distance and see whether I can identify the target. The headlamp doesn't have to be with me when painting the target, it can be closer to emulate a stronger output. 


That also eliminates spill light in my foreground and brings my perceived measurement closer to the "mechanical" one. I can then use that data as a ballpark "measured" reference that I can later modify with Stephens Power Law for foreground spill light).

So one more time guys. Hold tight. It's getting better.


----------



## Genzod

*
**Determination of PERSONAL Minimum Required Flashlight Intensity to Identify an Appalachian Trail White Blaze on a Tree as a Function of Distance Utilizing only Stone Knives, Bearskins and a Nerdy Girl with Glasses*
*

EDIT: *At the time of this experiment, subject had 20/40 vision and amazingly wide 8.5 mm dark adapted pupils. That acuity has since been corrected. Also, it was later learned that the experimental curve derived here could be adapted to all pupils and degrees of acuity with a convenient two equation piece-wise function discussed here in post #76 of this thread.


*PREPARE TO BE AMAZED! *(Probably how it will go, too) :laughing:

*


Abstract*

Fast-packing the Appalachian Trail at night over long distances between trail towns requires a reliable headlamp, preferably one with a large enough boost mode that is able to see an appreciable distance when identifying trail markers for navigation (a vertical blaze of white paint, 2 x 6 inches in size, placed about 2 meters high on a tree and spaced about every 140 feet/43 meters). When such a boost is unavailable on the primary lamp because the manufacturer of your favorite headlamp model _lost their minds_ and nixed lithium ion support, procuring a compact, lightweight secondary flashlight that has enough throw to find trail markers is necessitated. (Nah, this experimenter really would have needed redundancy for his lighting needs, either way).

Throw performance of a flashlight is defined by intensity in lux at one meter (e.g., candela) and/or throw distance to 0.25 lux. A minimum requirement to identify white blazes at a distance of 140 ft /43 m is straightforward, but various factors like weather and foreground spill light can impede both flashlight performance and perception. So it was decided a minimum constraint for marker identification at 100 meters under ideal conditions would be expedient. This choice provides brighter, easier identification under normal conditions, while providing some reserve capacity for performance robbing conditions.

An experiment was devised to determine the experimenter's personal minimum useful intensity required to meet this goal. A flashlight of known intensity was set at various distances from target so as to create intensity at marker of 0.5, 1, 2 and 4 lux. At each intensity, the experimenter attempted to identify target marker at 100 meters. The marker was discernible at 4, 2, and marginally discernible at 1 lux. At 0.5 lux, the marker was not discernible at 100 meters but was marginally discernible at 75 meters. 

Experiment establishes that 1 lux provided the most practical minimum cutoff intensity for target identification at 100 m. 1 lux at 100 m is 10,000 lux/candela at 1 meter or 200 meters throw to 0.25 lux. A flashlight meeting those minimum requirements should provide the experimenter useful throw for identifying white blazes on the Appalachian Trail.

At a later date, a more useful set of data was collected at equally spaced intervals of 30 meters from target up to 180 meters. This new data allowed investigation of a suspected acuity limitation that began to deviate the required minimum intensity vs distance curve from the square law curve after about 85 meters. The equal spacing of data also allowed for easier handling of the regression curve fit.

The regressed curve becomes a useful tool for predicting target identification with various sized scopes at distances beyond the 180 meter range of this investigation. Although not discussed in this post, later posts in this thread demonstrate that feature. It was determined that as a rule of thumb, 0.5 lux is a practical minimum intensity for identifying the given target at any virtual sighting distance from an observation distance of 200 meters.

*Methods and instruments*

A makeshift white blaze, 2 x 6 inches in size was carefully cut from the poster-board rigid page of a spent spiral notebook (Did I not tell you this was stone knives & bearskins?). The surface color was white having a cool white tint, not flat and not entirely satin in sheen, either, providing a highly contrasted and highly reflective target for emulating white blazes. Duct tape was looped and placed at three points covering the entire backside of the marker, and placed on a pine tree of about 8-10 inches diameter at a bend in a forested section of a very wide bike path. (I'm taking the 5th on where exactly this was).


*THAT TICKET WILL 
COST YOU..............*





*1 MILLION DOLLARS!
*

A Princeton Tec Quad of current make was utilized for illumination, having the following characteristics and performance:

Three modes: low, medium and high. 

Max output: 78 lm. 
Range (high): 50 m @ 0.25 lux. 
Range (medium): 24m 
Range (low): 17m

(Note: Specifications in manual are no longer valid for this lamp. Correct data was derived from product package labeling.)


Maximum intensity of 625 cd was determined from maximum throw (I=(R^2)/4).

The low mode was used to generate predetermined target intensities for this experiment. The low mode intensity of 72.25 cd at one meter is determined from the 17 m throw and the maximum throw (I=Imax*(R/Rmax)^2).

The headlamp was secured to a tripod and aimed at the marker so the most intense part of the spot illuminated the center of the marker. The following table provides corresponding distances for the four tested target intensities:​
*

Table 1* Target intensities and corresponding distances of headlamp

​0.5 lux....12.00 m
1.0 lux......8.50 m
2.0 lux......6.00 m
4.0 lux......4.25 m​

A set of three fresh AAA alkaline Duracell batteries were used for this test. The lamp on low mode has 10 hours of regulation, and the lamp was allowed to stabilize output before attempting to identify target.

A time of night was selected providing no moon and minor starlight due to high altitude haze (June 13, 2017 between 10:50 and 11:50 PM EDT). Temperature was about 80F and humidity was high at 71%. No rain, no fog, NO SKITTLES. Location had little ambient light and even less in the area where the tree with the marker was isolated by forest. Closest street lights impacting _viewing_ zone while discerning target were 620 meters to the right of viewer. A hand was used as an effective visor to eliminate glare in peripheral vision due to the distant street lamps. The target marker was isolated by trees and bushes on all but the immediate viewing side and was not directly impacted by street lighting or residential light. The marker could be marginally discerned with the naked eye at 30.4 meters in this ambient light. The fox that passed by the target tree did not run off with the blaze marker, although, he may be the reason for the absence of ducks at the pond this year. 


_*mmmmmm.....SNACKS!*_








The lamp on the tripod was set at a predetermined distance, turned on to low mode, aimed and locked, then the experimenter walked quickly to the 100 meter viewing line to identify target, starting with 4 lux and working down to 2, 1 and 0.5 lux. Identification at 100 m was successful for 4, 2 and 1 lux and unsuccessful at 0.5 lux. Identification with 0.5 lux was restored at 75 meters. The identification at 1 lux was considered marginal.

A 50 something year old male with corrected vision was utilized as a testing instrument. This instrument was _ideal_ in that the investigation was conducted for the purpose of determining a useful minimum intensity at 100 meters as a constraint in procuring a _magical_ flashlight for his own personal use. (And no, you still can't borrow it.)









Taken under advisement, a 40 something year old woman with corrected vision (allegedly superior to the geriatric male experimenter's vision) was asked to view the 0.5 lux case at 50 meters and 75 meters to render moot the assertions of love seat rending, irritable puppies once and for all. Identification was successfully made at 50 meters. At 75 meters, identification was successfully made but described by the woman as "marginal", just as it also was for the male experimenter--proving once and for all, that a man _with_ a woman _need not_ go blind. :huh: (This experimenter sees _extremely_ well.)








No scopes or binoculars were used in this target identification. But please, do keep digging for a way to render this effort nebulous and pointless, I'm sure you'll come up with something. You did get an early start, after all. 
​​
*
Discussion and Conclusions*

An intensity of approximately 1 lux was determined to be a boundary constraint for target identification at 100 m for the eyes of the experimenter. (Your results may differ.) Required intensity at target appears to closely approximate a quadratic function of the distance within the range of 0-88 meters. The farther the eyes are from the target, the higher the intensity at target is required in accordance to the square law. 

After 88 meters the intensity as a function of range to target curve deviates noticeably from the square law primarily due to the acuity limitations of the observer (20/40--max range to acuity limit for this target is 88 m). Although suspected _at first_, there is no asymptote the required intensity approaches implying a limit to distance where no amount of light will resolve target.

Although one might imagine that looking for a white blaze marker is like hunting for chipmunks that move in and out of holes and blend in with their surroundings, the white blaze target is highly contrasted, easily anticipated, found typically on _stationary_ trees (when they aren't being chased by a pack of marauding termites) spaced every 140 feet or so at an elevation of about 2 meters and is found more often than not along an easily identifiable, well worn path. But, if you still fancy the marker being an elusive chipmunk, don't worry--I won't interrupt your delusion. 1 lux as a limit will be fine for my purposes. (_Your_ purposes may be different).


_*RUN, FORREST, RUUUUNNNN!*_








_Ambient light:_ On June 11th in the same test location, phase angle of moon was about 27 degrees and Z = 39. Moonlight intensity was calculated at 0.11 lux The ambient light impinging on the isolated marker was substantially darker in comparison. On the following two test nights_ without _moon, the marker was isolated in even less light. Distance for marginal marker visibility was measured on two moonless nights as 30.4 meters. Whatever the intensity of the ambient light impinging on the marker, it was perceived to be substantially less than the moonlight at 0.11 lux plus any background ambient light from the city. So ambient light impinging the marker was much, much smaller than the 0.5- 4 lux added by the lamp. 

Perhaps a _lumen stud_ could enlighten us on what that value is based on the distance needed to marginally identify the target without lamp. _Go, Speed Racer, go! _(In the mean time, see below for how I finally backed it out of the collected data.)









A new data set was collected on July 25th, 2017, 2-3:30am EDT. Crescent moon on opposite side of earth, no rain, very little cloud cover, no haze or pollen, no foxes, no Clint Eastwood running cattle between observer and target, no Skittles. A rectangular box visor was used this time to block the effect of ambient light above tree level, residences and street lights in the distance. Nevertheless, the new data was very similar to the old data with the exception that investigated range to target was extended from 100 meters out to 180 meters. The equally spaced data points made for better regression curve fit determination. Differences in regressed curves between old and new data were primarily due to the spacing of data points and initially imposing incorrect boundary conditions on the data during the regression. Those issues have been resolved and updated.
​*

Table 2* Marginal target identification intensities* (less ambient light) and corresponding distances

​..............*DATA*...............

​Ia + 0.000 lux........30 m
Ia + 0.271 lux........60 m 
Ia + 0.739 lux... ... 90 m 
Ia + 1.640 lux .....120 m
Ia + 3.770 lux......150 m
Ia + 8.800 lux......180 m​
**Ambient intensity at target, "Ia" is unknown at this point. *

*ACHTUNG! *The data above represents the intensity from the lamp ONLY. It is _not _total intensity.* Ia* was later placed as a variable in the above data due to the fact that this forum is PREGNANT with  looking for any _false_ appearance of loose threads to pull to blow off neurotic steam. Future assaults by neurotic combatants vill face military tribunal und be shot.. _den_ zent to zee Russian Front! ​ 

Ambient light intensity impinging target was determined by imposing the boundary condition I'(0)=0 and I(0)=0 on the data set and regressed curve. These constraints simply mean the minimum required light to see target approaches zero as the distance to target approaches zero. Since there is no other light but ambient in the interval between zero and 30 meters, and ambient light is the minimum required light to identify target from 30 m, less light than ambient is required at distances less than 30 m. The trick now is to guess Ia and bend the regressed curve with guesses for *Ia *until the shape of the curve at range equals zero has met the condition I'(0)=0

It is important to differentiate between _ambient intensity_ and _minimum required intensity_ at distances less than 30 meters, as ambient light is constant in the interval (lamp is off and not needed here), but minimum required intensity drops off as the target is approached from 30 m. The minimum required intensity curve from 0-30 m should theoretically follow a square law with approximately zero intensity at zero meters and ambient intensity at 30 meters--And indeed, as shall be seen, it does. 







To find ambient intensity, a guess for ambient is provided as I(0)=-*Ia*. The data set of table 2 and this guess are regressed in a quintic polynomial regression (5th order polynomial), and the derivative is checked to see if I'(0) = 0. This involves monitoring the shrinking of the constant of the 1st order term of the polynomial with each progressive guess until it approaches approximately zero.* Ia*=0.085 lux when that requirement is accomplished. Once the curve has the proper shape with I'(0)=0, the constant term of the polynomial is truncated from the function, vertically moving the curve up the value of *Ia* so that the curve intersects the origin (0,0). The resulting curve represents all values for minimum required intensity to identify target at distances from 0 to 180 meters. Then we add the ambient intensity of 0.085 lux to each of the 6 collected data points and superimpose the curve over the data points.

The value of *Ia* makes sense as it is a small fraction of moonlight intensity plus background intensity (there was no moonlight during this data collection, therefore *Ia* is background from suburban light pollution and anything else in the atmosphere at the time--stars, light reflecting off clouds, etc--approximated as 0.39 lux*). Ambient light impinging on the target blaze in the shaded portion of the test area is 0.085 lux which is about 22% of the local suburban light pollution.


*Two nights prior to the first data collection, the moon was 39 degrees above horizon and estimated from a chart to be about 0.11 lux. Max sighting distance with only ambient light was found to be 34 m. On two test nights that followed much later with no moon, max sighting distance with only ambient light was 30 m. Unshaded suburban light pollution in the test area, P, can be backed out of the intensity square law equation (0.11+P)/P=(34/30)^2. P becomes 0.39 lux. 


*Boundary conditions: I'(0)=0 and I(0)=0*




*

Table 3* Marginal target identification intensities and corresponding distances (with ambient light added)

​...........*DATA*...............

0.000 lux.........0 m
0.085 lux***......30 m
0.356 lux........60 m 
0.824 lux... ... 90 m 
1.725 lux .....120 m
3.855 lux......150 m
8.885 lux......180 m**​
​**Artificial, guessed value used as a "bending point" to force and maintain a horizontal tangent in the regressed curve at point (0,0), i.e. I'(0)=0 . True value of ambient light is Ia=0.085 lux, which comes from the red regressed quintic (5th order) polynomial curve fit.

**EDIT: This one data point was in error due to the fact the correct location down range for marginal identification for 8 lux+ambient on target was over the surface of the lake. I apologize for not only being unable to walk on water like Jesus, but for also fudging this point by making an estimation instead of tossing it out altogether--be assured, it caused me no little grief. I discuss this in greater detail in post #76 where I describe the physics equation governing requirement for increased intensity beyond the acuity limit.*​
*
Red Curve Regression: 


*​*Minimum Intensity to ID Target (lux) Vs. Observation Range to Target (meters)

I(x) * = 7.3990e-05**x*+6.5004e-05**x*^2+1.4421e-06**x*^3-2.1628e-08**x*^4+1.1145e-10**x*^5* 

(Intensity values valid only in the range from 0 to 180 meters. Notice I(0)=0 and that I'(0)<0.0001 which for our purposes is approximately 0. 

PLOT*

*We can determine from the plot, utilizing the point tool, that required intensity of the lamp at 100 meters is 1.0512-0.085 (ambient) = 0.9662 lux, which is consistent with 1 lux determined in the first data set, a deviation with relative error of only 3.4%.​*
*Note: *The blue curve is the square law curve for intensity and distance. The square law appears to be valid up to about 80-85 meters, which in terms of visual acuity represents a focus of 12 one inch square pixels filling the 2x6 inch target for a person with 20/20 vision, three 2x2" pixels for 20/40 vision which I had at the time of the data collection. As the target shrinks smaller than the 3x1 pixel resolution and focus blurs, the regressed curve increasingly deviates from the square law curve. At increasing distance, the target blends into the tree and dims, becoming a point source of light, ever diminishing.
​*
EDIT:* There is no vertical asymptote at a distance that no amount of light will resolve the target. I had suspected that at first, but it is not the case. Once the target rectangle slips inside the pixel dimension of 2x2", distance progressively dims the pixel, which stays the same size relative to the viewer.

_
*Compact Flashlight: *_The 0.966 lux at 100 m constraint requires the performance of a flashlight with at least 0.966x100x100 = 9660 candela. (See plot of Range vs. Intensity for constant target lux of .5, 0.71, 1, 1.41) Since foreground spill can constrict pupils and require more intensity at target to identify it, it is necessary to minimize spill with a deep reflector, narrow beam spot, or impeding the spill light in some way without altering the spot, such as using a tube extended off the head of the lamp or using a sighting tube to isolate the pupil. 

The Manker T01 II seems well suited for the job, capable of 10,000 cd with a primary AA (same battery as my headlamp) and 20,000 cd with an IMR battery for even greater throw. The Manker T01 II has output settings that make it also useful as a back up running light. Plus, it's empty weight is only 55 grams, which is desirable when wanting to keep things light running up hills.

*Manker T01 II*
















​


----------



## Offgridled

Very well done here Genzod. I believe the numbers would have changed if SKITTLES were involved glad you used a females eyesight to keep all happy ( experimental reasons only) not to be taken out of context! I hope you enjoyed doing this as much as ive enjoyed reading it!! Ok back to my red button for now


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## archimedes

Nice work 

As I know you'd be disappointed @Genzod if we didn't have at least _something_ to criticize (lol) ... you might consider calling the "0.000 lux" data point, "no added light" / "ambient moonlight / starlight" or something similar, since truly without _any_ lux you wouldn't be able to see anything at all


----------



## Genzod

archimedes said:


> Nice work
> 
> As I know you'd be disappointed @Genzod if we didn't have at least _something_ to criticize (lol) ... you might consider calling the "0.000 lux" data point, "no added light" / "ambient moonlight / starlight" or something similar, since truly without _any_ lux you wouldn't be able to see anything at all



I appreciate your smartalec humor, but you really should have waited to comment until after I removed the advisory that I was updating:

*I am correcting some data points that were entered incorrectly. Please do not quote article while this advisory is still posted. I will remove it when the article is corrected, thank you

*As you can see, the ambient light has been backed out of the data set and added into the data. I was doing that during your post.

I was aware of this issue as you could see from the request near the Go Speed Racer quote. 

Perhaps you could have met the request and supplied a calculation method instead of just saying the data point was wrong? (That's the helpful way). I don't see that too often around these parts. 

("Geniuses" with no answers, only red pens. (not you, haha) Reminds me of professors who mark tests wrong but don't tell you the correct answer.)

I've taken your advice and update the article.


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## Offgridled

archimedes said:


> Nice work
> 
> As I know you'd be disappointed @Genzod if we didn't have at least _something_ to criticize (lol) ... you might consider calling the "0.000 lux" data point, "no added light" / "ambient moonlight / starlight" or something similar, since truly without _any_ lux you wouldn't be able to see anything at all


Arch you always have me smiling.


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## Offgridled

Genzod the red pen is definetly safer than the red button.


----------



## Genzod

Offgridled said:


> Genzod the red pen is definetly safer than the red button.



Oh, I know he was only "coarse jesting". And he did point out a way to protect myself from a loose thread that would attract sharks. That's been fixed. 

His post simply brought up a lot of bad experiences on threads like this. Sharp people with a lot of technical saavy, and yet all the advice they seem to have gets invested in pointing out what is wrong with something rather than offering help with a solution, even when asked. I've asked such people for a little assistance, yet the only response after the request is unsurprisingly *silence*. Just another smart*ss on another bombing run trying to impress himself with shutting others down.

I'm trying to solve problems here that will _help_ people with similar problems. I would hope people that are that technically saavy to see what is wrong could also be intelligent enough to figure out, there might be a solution they could contribute to.

If you want to be the exceptional rare bird, and not a "Debbie Downer" focused on only what is wrong, it's clear. Be a problem solver rather than a problem-pointer outer. The latter is as common as the litter of cigarette butts and can pull tops in the gutter of a highly trafficked street in the 70's.


----------



## Genzod

Ambient light is 0.0613 lux. Sheesh. That iteration was....well...you know...(and it took forever, too!)

(It took almost forever to realize the actual ambient on target is 0.085 lux and to correct the calculations that followed in later posts.)


----------



## Offgridled

Illuminance is a measure of how much*luminous fluxis spread over a given area. One can think of luminous flux (measured in*lumens) as a measure of the total "amount" of visible light present, and the illuminance as a measure of the intensity of illumination on a surface. A given amount of light will illuminate a surface more dimly if it is spread over a larger area, so illuminance is inversely proportional to area when the luminous flux is held constant.
The choice is ours....


----------



## Genzod

Open the two following links in your browser on two different tabs. Then click back and forth between tabs. 

Camera 1 Camera 2 *

Lamp intensity only, lamp with ambient intensity added in.

I know, I know. It's fun, but don't over do it. (You might go blind).

**Note: *these two graphs are no longer valid once I updated the old data with evenly spaced data more fit for regression analysis and corrected the boundary conditions. However, I left the post the way it is lest any of you OCD cases get panicked that your toy has been removed. See, I'm nicer than people give me credit for. Click away, you coo coo birds!


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## scs

Offgridled said:


> ...
> 
> The choice is ours....



Certainty of doom to the left and empty and unfulfilled promises to the right...


----------



## ssanasisredna

scs said:


> Certainty of doom to the left and empty and unfulfilled promises to the right...


----------



## Offgridled

scs said:


> Certainty of doom to the left and empty and unfulfilled promises to the right...


What flashlight would you take


----------



## subwoofer

Having made it through this thread so far, I'm still not sure if this is a serious question or just for fun. I'll guess fun.

The thread title is VERY interesting; as a night time hunter, target identification is absolutely crucial, and in some cases the only visible aspect are eyes reflecting back the gun lamp light. This is not sufficient to take a shot, even if you think you are confident that the colour, position and movement identify the target, you need more to be sure you are not making a big mistake.

For any one scenario there will be one equation, but with so many variables I can't see there being anything usable for real world situations. The 'observer' being the biggest variable (dark adaptation, spectacles, contacts, age, averted vision, binoculars, scope), not to mention their position relative to the target, the target's reflectivity, size and orientation. Perhaps using a camera with fixed lens and exposure might eliminate some of the variables.

Another major factor is glare. Glare from atmospheric factors (dust, moisture etc) and the spill light hitting the ground near the observer, so making the ground surface (grass, dust, wet etc) a big influence as it affects the relative brightness of target and the observer's immediate surroundings, so affecting target visibility.

Effectively for the best ability to identify a target, it means having the most collimated beam possible with as little spill as possible (a light-sabre like thrower). Very impractical for anything other than target identification. This is one reason the cheapy zoom lights are so popular as their lens can focus the LED's output to a very tight beam with no spill, and while this is very inefficient and the output is actually pretty low, the perceived brightness can be much higher.

An interesting subject to muse over, and one that had many practical uses, but will remain theoretical only. If you think about it in terms of the 'need' to identify a target, then 'minimum' is not really what it is all about, instead you throw as much light as you can and can either identify the target or not (S+R, LE and Military applications).


----------



## scs

subwoofer said:


> Having made it through this thread so far, I'm still not sure if this is a serious question or just for fun. I'll guess fun.
> 
> The thread title is VERY interesting; as a night time hunter, target identification is absolutely crucial, and in some cases the only visible aspect are eyes reflecting back the gun lamp light. This is not sufficient to take a shot, even if you think you are confident that the colour, position and movement identify the target, you need more to be sure you are not making a big mistake.
> 
> For any one scenario there will be one equation, but with so many variables I can't see there being anything usable for real world situations. The 'observer' being the biggest variable (dark adaptation, spectacles, contacts, age, averted vision, binoculars, scope), not to mention their position relative to the target, the target's reflectivity, size and orientation. Perhaps using a camera with fixed lens and exposure might eliminate some of the variables.
> 
> Another major factor is glare. Glare from atmospheric factors (dust, moisture etc) and the spill light hitting the ground near the observer, so making the ground surface (grass, dust, wet etc) a big influence as it affects the relative brightness of target and the observer's immediate surroundings, so affecting target visibility.
> 
> Effectively for the best ability to identify a target, it means having the most collimated beam possible with as little spill as possible (a light-sabre like thrower). Very impractical for anything other than target identification. This is one reason the cheapy zoom lights are so popular as their lens can focus the LED's output to a very tight beam with no spill, and while this is very inefficient and the output is actually pretty low, the perceived brightness can be much higher.
> 
> An interesting subject to muse over, and one that had many practical uses, but will remain theoretical only. If you think about it in terms of the 'need' to identify a target, then 'minimum' is not really what it is all about, instead you throw as much light as you can and can either identify the target or not (S+R, LE and Military applications).



I guess it's a very vigorous mental exercise with real world measurements that has yielded results that might be useful as a rough guide for how many CDs a person should look for.


----------



## Genzod

scs said:


> I guess it's a very vigorous mental exercise with real world measurements that has yielded results that might be useful as a rough guide for how many CDs a person should look for.



No, maybe he's right. Maybe I shouldn't be advising people with guns to go out with 1 lux and shoot a living target at 100 meters. Maybe I did ignore spill light and atmospheric conditions and neglected the idea of collimation as a practical kind of light for this application. Maybe I do need to take a 490,000 cd/1400g cannon with me fastpacking for the absolutely _best_ possible white blaze target identification. Indeed! My serious efforts must seem "amusing" to him in light of his superior knowledge as a professional lighting expert.

And here i was thinking the OP and my meant-for-mere-musing experiment was about learning my personal minimal lux requirement to see a white blaze trail marker at 100 m under ideal conditions, so I can get a bearing for selecting the most suitable compact flashlight for that need. I sure am glad there are professional lighting experts perusing this forum who can set us hokey amateurs straight! 

:bow: My hat's off to him for his generosity and the obvious sacrifice of his time! His review of my "theory" has been considered, and _I stand corrected! _ 

Perhaps he could do one more thing for me? Recommend the _heaviest_ possible collimated hand held thrower for my fast-packing? I want to make sure I'm lugging around the light that has the best ability to identify those white blazes. Don't want to accidentally shoot the wrong trail marker, you know!

*SHHHH...BE VEWY VEWY QWIET, 
I'M HUNTING TWAIL BWAZES!*


----------



## Genzod

_Continuing on with my musings...
_
I created a plot that bounds my candela requirements. It's based on the red curve which is the minimum lux for white blaze identification under ideal conditions (for my eyes). The horizontal axis is viewing distance to target in meters, and the vertical axis is measured target intensity in lux.

The pink line describes the candelas required at distance for that minimum constraint. Just multiply the left hand lux scale by 10,000. (2 lux on the scale would be 20,000 cd).

The blue line describes 4 times the minimum required lux at a distance, an intensity that makes identification very easy.

Since the pink line represents a flashlight with an intensity only strong enough to meet a minimum identification at that distance, the blue line will be 4 times that minimum, which is ample for making this identification under those conditions.

So lets _pretend_ this is your data profile for a moment. You went to a trail and replicated my experiment with you as the viewer, and surprise surprise, you have big beautiful blue eyes that _look _exactly like mine. Mmm, you _lucky_ guy. 

Let's also pretend you are happy with viewing AT trail markers at a minimum constraint of 75 meters. That's about 32 meters beyond the typical average spacing. You use the point tool and click the pink line at 75 meters. The answer is 0.2670 lux, but that's the wrong scale. Multiply by 10,000, so the answer is 2670 cd. Now we're cooking with oil! You need a light with a mode having a minimum of 2670 cd to marginally make out a trail marker under ideal conditions. 

Now follow a vertical rise to the blue line at 75 m. It resolves to 10,681 cd. To see the marker with _4 times_ that minimum intensity, you need a flashlight with an intensity of 10681 cd. Now move the pointer horizontally to the right until you hit the pink line again. You get between 102-103 meters. That is your max ideal range with a 10,681 cd flashlight capable of seeing 4x above minimum required intensity at 75 meters. So your idealized range is 75 meters to a _potential_ 102 meters.

Let's say now the trees are 43 m apart most of the time as they are said to be. Most of the time you will only need about 177 cd to see with minimum required intensity. With 10681 cd, you are seeing the blazes at 43 m with target intensity about 60 times your minimum constraint at that distance. 

Have fun with it, but please, if you're still clicking those two graphs back and forth--STOP IT already. You'll go blind!


----------



## Genzod

A lamp combination that I'm considering is the Zebralight H53w and the Manker T01 II. The intensity of the H53w is about 1200 lux @ 1 meter at 330 lm output. The intensity of the T01 II is 20,000 lux @ 1 meter.

If you start 1 meter away from the target and start stepping back, the lux value at target will diminish with the square of the distance. Add in any ambient light intensity and you have total target intensity.

The linked plot shows this target intensity for the Zebralight and Manker across distance to target in meters. The green curve is the Zebralight and the black is the Manker. The red curve is the OBSERVED not THEORETICAL minimum lux required at that distance to marginally see target. 

One person in particular doesn't seem to understand the purpose of that minimum intensity to ID target boundary limit. I wouldn't question his understanding of the purpose of a throw to 0.25 lux figure for a lamp. He's a smart cookie. It's a figure that quantifies lamp performance. Maybe he'll eventually understand too what I am saying here. The red line is observed data obtained under specific conditions to establish a baseline that quantifies my visual performance. Not other people's visual performance--mine. No theories, no scopes, no contacts, no shiny wet grass, no Skittles, no glowy eyed out of season dead wabbits.

Well, the minimum lux to marginally identify target is a baseline from which we can create a frame of reference and talk about more useful light. 

The "marginal" identification is subtle. I can tell there is a marker there, but it takes me a little effort to be sure. It's not something you would use to hunt a living thing. No one here is talking about hunting living things, except perhaps someone who has strayed off topic for some dark purpose. Maybe this 'expert' didn't read my OP (despite having said he read the thread up to that point). This confuses me. Why would a _clever_ fellow rehash irrelevant issues and "variables" that have already been specified and dealt with in the thread, then dismiss the practical observations I made as mere musings and impractical theory? hmmmmm.

If you increase incident lux on target 4 times the baseline (red line), you get a decent, easy identification. The rectangle is focused. The identification is immediate. There is no question what it is.

So let's take a look at the plots. 

The 330 lm max mode of the Zebralight intersects the red curve at about 60 m. Anything beyond that is useless. It's an upper limit. I can't go beyond that. A practical useful figure. Won't see target at that distance all the time, but I know I can't see beyond it. Useful, useful, useful. Mathematically speaking, boundaries are good. 

Now we move toward the target. We want a useful amount of intensity on the target. We place a vertical line across the red and green curves and move it to the left. We come to the magic number 47 m. Let's check it out. We put the mouse over the graph and up come the orange buttons. Select the one that has a line with a point on it. Now click on the point of the green line at 47 m--0.5432 lux. Now the red line--0.2168 lux. (subtract ambient light from the red only which then becomes the required minimum lamp intensity and compare it to the thrown intensity of the lamp at that distance (green). We get (0.5432)/(0.2168-0.085)= 4.12. That's about 4X minimum required lux to ID target. So 47 m is a good distance that provides plenty of light for easy identification. So the max range of the Zebralight is 47m to a potential 60m. So with 330 lm max mode, the Zebralight can easily identify white blaze targets that have an average spacing of 43 m.

Now in the real world spill light is a problem. But any driver knows as well as I that the solution to glare is to block it out. We see cars coming toward us with their brights on and we put our hand up to cover the lights from our eyes to restore ability to see the road. Glare in the mirror? We turn the mirror up. 

In the case of a trail, the spill light doesn't go very far in the kind of narrow beam lights I mentioned. You only need to see a narrow view and that down the narrow corridor of the spot where the spill doesn't reflect. Why not look through a tube at the target? You could alternatively put a tube on the lamp head to block spill; although, the eye tube visor could block glare from other sources like a moon on the horizon. 

For the "Debbie Downers" who circle the forum in your AC130 gunship looking for an opportune moment to open fire with your negativity cannon: cease from making wet grass in foreground, close trees and glare from spill (and every other detail you can draw from your nix it bag) an issue just to win a warped and pointless argument. 

And it _is_ a pointless argument when it's a _strawman_ argument. If you're going to debate, learn how to debate correctly--don't put arguments in my mouth I never made, then refute those arguments with contrary, irrelevant details to give the false impression you have shut my effort down--it's irrational-- stuff made for the "coo coo for Cocoa Puffs" box. 

In fact, why not go look elsewhere for a debate? There's no debate going on here. I am pursuing the answer to a _question_, not asserting something that ruffles your chips--the _topic_ is about answering a question about a very specific, well defined circumstance I am investigating for my needs. Here I am trying to answer my own question for lack of constructive help (TEEJ must be busy shooting wabbits) and all I get are discontented "Debbie Downers" negating me at every turn--providing no _useful_ help--just reasons or exceptions for why I am "wrong". What kind of circus is this? Go back to reviewing lamps--you are apparently good at that. Reviewing my "theories" while I try to help myself isn't exactly your best forte.

Now we have seen that the Zebralight had a useful distance of 47 meters extending out to a possible maximum distance of about 60 meters. (For AT white blaze targets--no wascally wabbits allowed).

Now we do the same with the Manker. The intersection of black and red is at 115 meters--can't identify beyond that, not even on a good day--_boundaries_. Approaching target with the vertical line we arrive at 86 m and sample the two points on both lines. 2.704 and 0.7456 lux. Subtracting out ambient of 0.085 from the red and taking the ratio, we have 4.09 times the marginal identification intensity, again about 4X, which is plenty of intensity for easy identification. Thus we have a range of 86 meters to a potential 115 meters with the 20,000 cd Manker.

Now it can rain, it can fog we can stop to eat Skittles. We might even skin a wabbit. But none of those things change the performance capacity of the lamp's throw (in candela) and neither does it change the performance capacity of my eyes. We just tuck our head and deal with it until the miserable condition passes.

You can stick any lamp into the 2nd and 3rd equation to the right. Try 10,000 cd in place of 20,000, which is the AA primary battery performance for the Manker. I got 74-99 meters. (Your results may differ.) 

You can check these results on the plot I posted earlier. In fact, it's probably a little easier to use it looking for a 4X lamp intensity difference because ambient light is already subtracted out of the pink and blue curves. Just take the intensity rating of the lamp, divide by 10,000 and use that number to draw a horizontal line across the pink and blue lines. The range is the intersection of the horizontal with the blue (low) and pink (max) curves. For 20,000 cd, the lux of 2 is used, and the intersections are 86 at the blue curve and 116 meters on the pink curve. Very close.

Now I have learned that the National Park System has estimated there are over 165000 white blazes over the 2189 miles of trail. I'm assuming that's ALL of them, both ways. A quick calculation yields an average spacing of 140 feet. Now that's good news to me because I read earlier that the spacing is on average 200 feet. That's a change from 61 meters to 43 meters. That cuts my intensity requirement for the flashlight in half. There are sections through designated wilderness areas and National Parks where the blazes are less frequent, even 0.1 to 0.25 miles apart at times (161m-404m and I would need a much heavier scope for that). Nothing I can do about that. But for the most part, the blazes are supposed to be set up so that one can see the next one from the former. If some areas are spread out that wide, the spacing in places it is not that wide is even closer together than 140 feet. The Zebralight H53w can deliver 4X intensity identification at 154 feet, so even without lithium ion boost, the Zebralight H53 can still work at finding blazes _most of the time, _except in places like national parks and wilderness areas where the blaze spacing is beyond the performance of any narrow beam compact flashlight. But I still need lamp redundancy, and it would be better to have a narrower beam for less spill and glare, especially for fog.

Hey review guy, how about this one? Would that be the best option for a fastpacker? Or should I go larger? Still haven't heard back yet. But then, things to do, bombing runs to complete....


----------



## Genzod

Taken under advisement: 



> "Effectively for the best ability to identify a target, it means having the most collimated beam possible with as little spill as possible (a light-sabre like thrower). Very impractical for anything other than target identification.... If you think about it in terms of the 'need' to identify a target, then 'minimum' is not really what it is all about, instead you throw as much light as you can and can either identify the target or not (S+R, LE and Military applications)."



I've decided that the best route to "have the most collimated beam possible" is to forsake the 490,000 cd/ 1400 gram hand held for a helo spot light. At $1000 an hr, I could rent a helo with a Spectrolab SX-16 Nightsun to follow me around on my next through-hike fastpacking expedition. Figure it will only add about $640,000 onto my hiking budget!


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## archimedes

... better rent two, 'cause "two is one" , and you don't want to risk having to hike in the dark without light ...


----------



## scs

If only someone made a good zoomie headlamp, then you wouldn't have to carry two. I suppose you should still take two of the headlamp then.


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## Genzod

archimedes said:


> ... better rent two, 'cause "two is one" , and you don't want to risk having to hike in the dark without light ...



*REDUNDANCY! 
That was the equation!*


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## Genzod

scs said:


> If only someone made a good zoomie headlamp, then you wouldn't have to carry two. I suppose you should still take two of the headlamp then.



The mechanical engineer @ThinAirDesigns made clear the need for lamp redundancy. He said he has seen one too many racers sidelined at night because their lamp failed. I had a lamp fail on a fastpack outing, and I had to sack it in until dawn. Good idea to have a narrow beam cheapy along for the ride anyway for penetrating light in fog. I've been twice impeded by that as well.

I was originally given a bad estimate of 200 feet for average distance between markers. I've since learned from the National Park System that the average is closer to 140 feet. I read another estimate that indicated the markers tend to vary from 30-50 yards with an average of 120 feet, with the wilderness area one tending anywhere from 0.1-0.25 miles. With a 1 ounce headlamp and a 2.5Mcd cannon, I could cover all bases IF I could even see a blaze with my 20/40 vision at 160-400 meters. :laughing:

But if I wanted to cover all bases, I think the thing to do would be to go with the 1200 cd 30g ZL H53w (40-60 m white blaze targeting range, spill light blocked), get a cheapie 4800 cd thrower like a 30g Jetbeam Jet II-MK (84m max range), then use a lightweight (63g) 5x20mm golf monocular (but I'm still evaluating how far out that might get me to ID a white blaze). Might not be useful in a section with a lot of turns obscuring the next blaze, but above treeline, like in the White Mountains, it would be helpful spotting cairns and blazes on boulders when I do have direct line of sight. That would be a useful circumstance for a scope because the trail isn't so clearly defined then. Really easy to get lost even with a hiking lamp. Also, using a scope eliminates the problem of spill glare pupil constriction diminishing perceived target intensity. Total weight is about 4.3 oz to see as far as I could ever need to see a trail blaze.

Of course I've just begun looking at this option, so I'm not all that aware of options and variables. 

The exit pupil of the model below is 3.3mm (when calculated without the approximation), but I would need 7mm (or slightly less because I'm older-about 6mm)*** for the scope to pull in as much light as my naked eyes can in the dark. If that gets too heavy, I'll have to compensate by increasing my constraint for flashlight intensity, which tends to make the lamp heavier as well. I smell an equation! 

***I've since learned I have an 8.5mm dark adapted pupil, so having the best scope exit pupil is expedient to take advantage of that.

Bushnell 5 x 20 Golf Scope

3-3/8″ long and 1-1/8″ in diameter, 63 g, $25 retail


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## Genzod

My investigation of combining optics with flashlight for white blaze target identification beyond 100 meters ( and up to 0.15 mi) can be satisfied with relatively compact devices, such as a Walters 3.25x25 monocular (34 grams) and a Manker T01 II (55 grams), (about 3.14 oz total). 

Not only that, but the monocular can be used with minimal running light (65 lm) from the Zebralight H53w to identify markers up to 57 meters. No output boosting required. That would help extend runtimes. Only about 25% of the AT has spacing between 161-404 meters (wilderness designated areas). The rest is between 30 and 50 meters. Boosting would only be required then if I really wandered off the beaten path.

The 3.25x25mm Walters Monocular guarantees best brightness with an exit pupil of 5.9 mm. Problem is, products sold as medical devices in the US tend to quadruple the price above what it should otherwise be (shades of medical litigation, Batman!). It's $120 of tiny wonder. 

Anyone know where I can get a *not-so-certified-as-a-medical-device* monocular with a _high_ exit pupil _around_ the same magnification power and objective lens diameter and costing around $30-$45 that looks like the Walters model in the image? I don't really care about high efficiency transmission of 95%--85% is fine, but I pretty much at least expect the glass to be fully and multiply coated as most are.

The prospects so far: :huh:


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## Genzod

I wouldn't mind having a Chinese knock off toy such as this except the magnification and diameter are 2.5x17.5mm and that reduces my max range to under 0.10mi. 3x20mm - 4x28mm is right in the Goldilocks zone for what I want.--the difference between scoping a _wascally wabbit_ and targeting a patch of wabbit fur. I need a little field of view for searching. Don't want to shoot any opulent old ladies dressed in pearls, high heels and mink stoles that happen to go wandering by on the forested trail, you know!

OOPS! My bad!


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## Genzod

*A-looky here, Babbalooee! 
El Kabong has once again saved 
the day!
*








*Left: 3x20mm 25g 

Right: 3.25x25mm 34g 

($39.95 each as predicted)
*
Although I think I see pretty well for being able to run on the empty streets at night without a headlamp, dark adjusted pupil diameter is only an average 5.8mm in the dark (4.4-7.2 range) in my age bracket. But these have the right magnification to get me where I need to go, and they just happen to have larger exit pupils to boot for improving brightness (provides more of the available light). Hard to find ratios that high because most monocular activities like bird watching take place during the day when plentiful sunlight determines a 2-3mm pupil diameter, thus allowing greater magnifications like 5-10x without diminishing brightness. Be nice to find a simple lightweight 5x28-30mm like the ones above, but 3.25 will probably get me to 0.12 mi.

_*And my big, adorable 
pupils keep me from going 
blind, too! *_:naughty:


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## Genzod

The following discussion is based on lamp-scope performance predictions from the following plots: PLOT A *Zebralight H53w* outputs *(green lines)* and the *2.5x17.5* scope *(black curve)* or the *3.25x25 *scope *(red curve)*. Also PLOT B the *Manker T01 II* and the *Nitcore MH12GT* max outputs *(green lines)* with the same scopes.

A very cheap ($4 from Gearbest), lightweight, (20 gram) "ring" monocular as shown above can more than compensate for range loss on the Zebrlight H53w due to discontinued lithium ion support (500 lumen boost mode). Appalachian Trail white blaze target identifications can be resolved up to 69 meters distance with the "castrated" max mode of 330 lm when optically assisted by this monocular. This is a few meters better than the 66 meters available from the 500 turbo boost mode.

Provided foreground spill light glare is blocked by a sighting tube, a scope or a flashlight "snoot" tube, 330 lumens (max output) provides optically unaided target identification up to 69 meters. 65 lumens (standard running lumens) provides optically unaided marginal target identification up to 40 meters. Since most white blazes are between 30-50 meters/yards (about 90-150 feet), 65-198 lm covers all bases (40-52m) except for the designated wilderness areas where blaze spacing is between 0.10-0.25 mile (161-404 m).

20/20 visual acuity range with naked eye for a 2x6 inch blaze (maximum range to still see the blaze sharply) is estimated to be no greater than 175 meters under ideal light and contrast conditions (black and white contrast with at least 807-1345 lux on target NCBI, Fiat Lux: The Effect of Illuminance on Accuity Testing) but is realistically probably someplace between 87-175m (an average 131 m) during the day due to lower contrast a white blaze has with tree bark. With ideal contrast and light, one could discern an "E" made with twelve white 1x1 inch pixels in a 2x6 inch blaze footprint at 87 meters but only a simple "I" with a stack of three 1x1 inch pixels at 175 meters. Anything beyond 175 meters starts to blend in with the tree as the 20/20 acuity pixel widths become larger than the width of the 2 inch wide blaze. 

But scopes extend the acuity limit by their magnification factor, extending visual range. They can also be focused, compensating for deficient vision.

Although magnification isn't required for blazes in the typical 30-50 meter/yard spacing, monocular use can block glare created by foreground spill light, making distant blazes easier to see with lower levels of lamp intensity. 

A monocular allows me as a trail runner to run with standard running light of 65 lumens and _easily_ identify average 40 m spaced AT blazes without the need to boost the headlamp, thus conserving battery life. No need to click through output levels, either.

Although there are typically no blazes found in the extended range of 50-69 meters that the tiny monocular provides when supplemented by the max mode of the Zebralight H53w (57-86 m with the 34 gram 3.25x25 scope) , that extra range becomes useful when meandering down the wrong trail. A quick look ahead 69 or 86 meters for a blaze saves a lot of meaningless forward travel and backtracking--a great time and energy saver. How many times have I come to a road junction at night and wish I could have looked both ways for a blaze. Sometimes at a road junction, the trail follows the road a short space, then turns back into the forest. It's easy to lose 15-30 minutes missing the turn and following the road for 15 minutes and dobling back, 30 minutes wasted. Carrying that extra 20-34 grams potentially saves me a lot of energy and time.

A back up lamp is still required for ensuring running light. Selecting the proper model combined with the right monocular capacity can increase night time range blaze identification for wilderness areas. A low weight low powered monocular (2.5x17.5 or 3.25x-25) combined with a 20,000-33,000 cd compact thrower (Manker T01 II or the Nitcore MH20GT) can extend blaze identification range up to 140-197 meters (0.09-0.12 mi), a sizable chunk of the maximum 0.25 mi wilderness spacing, a 75-123 gram (2.7-4.3 oz) solution.


*(ZL H53w intensity is estimated at approximately 1198 cd based on testing of the 52 series and flux improvement (But don't ask ZL, that figure is classified TOP SECRET! Holy ESPIONAGE, Batman! This is HIGH TREASON! Consumer question about candelas? Block that kick!). The closer the exit pupil of the scope is to the dark adapted diameter of your pupil the better the brightness of the image that is seen (my age bracket implies mine is only about 5.8mm in the human range of 4-9mm--I later had this measured as 8.5mm). An 85% lens efficiency was assumed in the calculations, which for lower quality monoculars is probably accurate. Lenses in these models are assumed "FMC" for minimizing reflection but utilizing lower grade of quality materials and manufacturing than in more expensive optics (about 40% less performance wise). Looking downrange through the monocular reduces glare imposed by spill light.) _

_ *EDIT: This post was reviewed and revised for calculations and conclusions based on updated precision in predicting lamp-scope performance. *_


_*So where can you get a monocular like this?*_
_





Kunming Powerior Optics Co, LTD manufactures the 3.25x25mm monocular, and it is sold at yoycart.com by various chinese vendors. It is also sold at Taoboa.com (chinese numba one ebay, no Engrish--use google transrate to buy "baby"--google translation for "product"). Best price on Yoycart is $23.18 plus $3.97 small parcel post shipping. Taoboa best price is about $15, plus shipping, insurance, fees, whipped topping, sprinkles and cherry (maybe some fava beans and a nice chianti, too....._f-f-f-f-f-f-f-f-f_).

The 2.5x17.5mm ring monocular is manufactured by Bijia I believe.

I'm a little leery of yoycart.com as I've seen two negative reviews so far, one in English and the other is in Russian. Both reviews suggest the site plays dirty pool when things don't go smooth as chinese silk. If you have to return something (only if received damaged or incorrect, there's a surprise waiting for you in the fine print. You _had_ ONLY 3 days to contact them and 7 days to ship it back to them, internationally AT YOUR EXPENSE even if goods are damaged, defective or not as specified. They make you responsible for bank fees, and there is no Paypal, usually only "Alipay" which I believe is the brainchild of Aliexpress (wait a minute, aren't these pay systems supposed to protect you from handing financial information over to a retailer? :laughing: Being that these products are bought from China, you have little recourse legally for making sure they play by the retail book. They know if you spend $10 on something, you won't return it at international postal rates to get your money back.

I'm hoping one of the safer and more popular sites with protection provided by Paypal (like Banggood) carries this monocular in the future. Otherwise the Sammons Preston model, which I believe is manufactured by Kunming, is available at US sites for $40-65 plus shipping.


----------



## Genzod

I've made some incredibly low cost purchases at Banggood, recently. For $21, I got a nominal 1400 lumen Astrolux S1 with optional 18350 tube providing about 10,600 candela for about 58 grams, that I intend to modify to extend range. I also found a Walters/Selsi knockoff  like mentioned earlier in this thread that tends to retail in the US between $39 and $60 plus shipping for only about $10 at Bangood. It's 8X21 [21/(8+1)] mm = 2.333 mm exit pupil) which advances a 200 meter sighting to 25 meters virtual, requiring only about 4.29 x 0.05903 lux = 0.2530 lux at target for my 8.5mm dark adadapted pupil diameter. That resolves to 0.2530*200^2=10120 cd, meaning my scope lamp configuation allows me to see out to 200 meters. Some say scopes like this with exit pupils much smaller than that of the dark adapted pupil don't work at night because it dims the image. Well, if you have a lamp, shine more on target to compensate for the dimming, right? Mass weight is only about 76 grams sans rubber lens covers. 

20,000 cd with an 8X21 optic provides me with 172m (0.11 mi) max of marginal AT blaze identification with only a 4.7 oz cost in carry weight. This is good, because it keeps my flashlight compact and lightweight. I can't imagine needing more than 0.11 miles sighting ability in forested areas due to meandering trail (laterally or vertically). The only place I can even see 0.11 mi and beyond is above treeline in NH and ME. It seems possible with de-doming and spring bypassing, I could get the Astro up to 23000cd. Then I could see up to about 178 m. Even if I don't have that range of line of sight, it makes closer objects brighter.

Of course I'm keeping an eye out for a cheapy Chinese Ebay 3.25x25 or 3x20 knock off. These would be great most of the time for improving headlamp range over shorter distances, then switch over to the 8x21 in the alpine regions. If I can get the Manker Astro S1 up beyond 20,000 cd, there will be no need to buy the $50 Manker T01 II. I_ like_ cheap solutions, don't you?

Both units below are about 3.5 inches long, a little over an inch in diameter and have a mass of 76 grams and 58 grams ( 82 grams with li-ion battery), respectively. 

Optic is shown extended, which is used to focus at very short range. Longer distance viewing is made with the focus retracted most of the way.

 *EDIT: **This post was modified to be consistent with updated scope-lamp performance calculations provided in *this plot here*. The approximation usually made by astronomy buffs in calculating exit pupil of the scope introduces large errors when scope magnifications are less than 40X and even greater error with even less powerful scopes I reference between 2.5-10X. A more precise (and smaller) scope transmittance efficiency of 85% is used for these knock offs that tend to use coatings and manufacturing techniques that are inferior to that used by high quality scope manufacturers (about 40% less performance wise). I also use a corrected dark adapted pupil of 8.5 mm as opposed the the age determined average of 5.8mm. I guess dyslexic eyes have their advantages. (8.5<-->5.8 .... okay I think you got that).*


----------



## Genzod

*
Here is the mathematical procedure I am using to model the tandem use of a flashlight and a scope for marginal identification of a 2x6in Appalachian Trail white blaze marker:*


The following demonstrates two examples of a mid-fifty year old viewer with 20/40 vision and an 8.5 mm dark adapted pupil in 0.085 lux ambient light using an 85% transmittance 8x21mm scope and standing at 160 meters and again at 231 meters from target with a *Manker T01 II* flashlight (20,000 cd). (Your results may be different depending on ambient light, your dark adapted pupil diameter and acuity, the weather, presence of atmospheric Skittles, the price of rice in China and whether or not Clint Eastwood and a steer stampede is passing between you and target.)*
Ride 'em in....

*





*HYAAAAA!



Experimentally Derived Graph of Minimum Required Intensity vs. Distance from Target :* 


Calculations below are made using this plot with the following definitions (the website Fooplot.com isn't configured for labeling):​*

Horizontal Axis:* Range to Target, *x* in meters : (The measured gap between the tree with the 2x6" white paper target and my sexy body)

*Vertical Axis:* Light _Painting_ Target, *I* in lux : (Can represent two things: Either the minimum lux required to paint the target to marginally identify target OR the square law extrapolation of the flashlight's candela rating from hand to target, over range x, _not_ the reflected light back to the sender.)

*Ambient light*: the light painting target when no light is required in hand at a certain distance *xa​*, *Ia​* in lux, which in the graph is 0.085 lux at 30 meters. (This can change with the moon, cloud cover, fullness of trees blocking light ,etc.)​*
RED CURVE:* Minimum required lux *I(x)* at target for "marginal" identification of white blaze on tree, viewer sighting from distance *x*. "Marginal" shall mean a momentary effort must be made to discern target, i.e. it is not "readily" recognized or rather, it is on the border of not being recognized at all. ​*

Extremely important:* This curve is sensitive to acuity and dark adapted pupil variations. If you want to play with data and would like to accommodate it more to your perception consider the following.​
This curve is based on a viewer with a _measured_ dark adapted pupil of 8.5 mm and vision corrected to 20/40 (A recent visit to the optometrist confirms I have incredibly seductive dark adapted bedroom eyes :naughty. This pupil size is not only close to being maximal for _all_ (human range tends to be 4-9mm in all age groups) but it is quite unusual for someone like me in his mid 50's. (And, NO, I was _not_ smoking a doobie at the time. No buds for you! Mooch someplace else!)​





To correct the *red curve* to your specific pupil, adjust the curve vertically by multiplying it by (8.5/*Deye​*)^2, where *Deye​* is dark adapted pupil diameter in mm. For example, if you have a 7mm dark adapted pupil, shift the curve vertically by multiplying each point by (8.5/7)^2=1.474. In other words, jeepers, creepers, your more constricted pupils at 7mm would need 47% more light to identify target than my big beautiful peepers.




20/40 vision makes the *red curve* deviate from the expected square law curve (*blue curve *on this plot) at half the distance of the minimum pixel representation of the target for 20/20 vision. Since the target is 2x6", this cut off point is represented by 20/20 vision as three vertically stacked white 2x2" pixels at 175 meters, this means for 20/40 vision, the white target begins to blur into the highly contrasted pine tree at a shorter distance of about 87.5 meters (half the 20/20 expectation), which is consistent with the experiment results. More light is required to identify the target as it blends into the darker tree with increasing distance. But with 20/20 vision, dimmed blending isn't evident until after about 175 meters. 

After the blaze shrinks smaller than vision's 3x1 pixel resolution, lux required to see it climbs _geometrically_ (not _asymptotically_ as I previously suspected). 

In essence, you can expect the *red curve* to follow the square law *blue curve* up to your minimum pixel resolution distance (175m for 20/20 vision and a 2x6" blaze). Then the curve progressively deviates from this expectation, growing geometrically.​*

GREEN CURVES:* *Zebralight H53w* intensity *IZL ​*in lux painting target plus ambient light on target (0.085 lux) when sourced from a distance *x*. (1200 cd @1 m) (lower curve is 65 lumens output, higher curve is the maximum output of 330 lumens). 

*BLACK CURVE*:* *Manker T01* intensity *IM​* in lux painting target plus ambient light on target (0.085 lux) when sourced from a distance *x*. (20,000 cd) ​
I am making the assumption here that spill light glare is always blocked, either by a tube mounted on the light or by viewing the target through a tube or a monocular, so that glare does not reduce pupil diameter thus reducing light available to the eye. Where these *black* and *green* lines intersect with the *red* line is the _maximum_ distance each output can _marginally_ identify the target, e.g. 45m, 62m and 116m for Zebralight H53w settings of 65lm, and 330lm, and the Manker T01 at full power, respectively. To the left of each intersection provides more light than needed, to the right, not enough light to identify target.​*

FORMULAS:*​

*Dep​=Do​/M : Monocular Exit Pupil = Entrance lens diameter / magnification factor *(an _approximation_ for scopes with large magnification factors, M>40X introduce only about 5% error or less to surface brightness. I AM NOT USING SCOPES WITH LARGE MAGNIFICATION FACTORS)​
Viewer utilizes 8x21mm scope. Exit pupil approximation is 21/8 = 2.625mm.​*
Note:* Although exit pupil diameter is often represented as Objective Lens Diameter / Magnification, this isn't _exactly_ the case. The focal distance of the eye piece is disregarded in the derivation of the formula because in scopes with large magnification such as astronomy telescopes, the focal distance of the objective lens is much, much larger in comparison. Astronomers like to do calculations in their head when they switch out eye pieces, and making that approximation is convenient and accurate for someone using scope magnifications in excess of 40x. But in my case, lightweight monoculars between 2.5-10x power can't accurately use this approximation.​
Therefore, Exit Pupil Diameter _sans approximation_ is accurately represented as: 

*Dep​=Do​/(M+1) : **Monocular Exit Pupil = Objective lens diameter / (Magnification factor+1)* which yields the more accurate 2.333mm not the approximate 2.625mm. 

This is important, because when it is inserted into the equation below, the error compounds itself by squaring it. A 10% error in eye pupil results in a 21% error in total transmittance. That's significant for low powered monoculars in the useful range of 1x-16x, but not for an astronomer with a 100x scope who would have a 1% error compounded to 2% in his surface brightness calculation.​*

SB=(Dep​/Deye​)2​ : Surface Brightness = **(Monocular Exit Pupil Diameter / Dark Adapted Pupil Diameter)^2 *Percentage of light of the sighted object transmitted after undergoing a magnification with a scope and passing into your eye pupil. *


Total Light Transmittance = Optical Transmittance * Surface Brightness *Percentage of light transmitted after losses due to reflection off each optical lens/prism and aberrations due the nature of each optic's material and construction. Lens transmittance is a percentage. For example, a high quality gun scope with 7-10 optics overall might have an optical transmittance of 90%.​
Viewer age mid 50's has a measured 8.5 mm dark adapted pupil. (Assume less if you are _not_ a horny domestic cat on the prowl.)

Assumed monocular lens transmittance is 85%. ​*
Note:* A high quality rifle scope with slow polished glass lenses fully and multiply coated on the entrance and exit of each optical surface with superior coating materials and application quality typically has a 90% efficiency. The reason the differences are so small between a premium rifle scope and a low quality monocular is because a cheap lightweight monocular might have 4-5 optics with 8-10 total surfaces, whereas the high quality rifle scope might have up to 10 optics and 20 surfaces. Each medium and surface presents an opportunity for diffraction and reflection losses. These compound. So for an expensive high quality monocular (Walters brand), I would estimate the transmittance at best is around 95%, but don't quote me on that (choose 95% in your calculations if you have money to burn). My cheap $12 Chinese 8x21 knockoff purchased from Banggood performs remarkably well at 85% efficiency in comparison, and it is probably better than some of the cheaper monoculars out there. *Strain at an insignificant gnat, swallow and expensive camel!*






*For my Suncore 8x21 monocular:*​*

Total Light Transmittance* = 0.85*[((21/(8+1)/8.5)^2]=0.05444 (5.444% of the original light registers with the eye with eye adapted to dark).​
If the area of the exit pupil of the scope is smaller than the area of the viewer's dark adapted pupil area, light is lost and the monocular image appears dim. To compensate, lux requirement must be increased as a quotient of the *red curve* lux at _virtual sighting distance_ (*x/M*) divided by the *Total Light Transmittance*. 

In other words, the smaller the exit pupil diameter of your scope below your dark adapted pupil diameter, the dimmer the image is using it and consequently, _the more light you have to supply to compensate. 

_If your scope has an exit pupil _greater_ than your dark adapted eye pupil diameter (lucky you, you rich *******!), anything extra is wasted, so assume the SB ratio as 1 (representing that you can only see up to 100% of light available _and no more_) and divide only by the lens efficiency to get total light transmittance.


*How to use the experimental red curve plot to solve scope problems *

​Remember, this is _my_ vision. At the time the experimental plot was determined, my acuity was 20/40 and my dark adapted eye pupil was 8.5 mm. The examples used here have virtual sighting distances, determined by scope magnification, of less than 87.5 meters, after which my acuity begins to require more light than predicted by the square law expectation for resolution See this plot to visualize departure-*blue curve* is the square law expectation. Since I am using an 8X power scope, It is safe to use the intensity square law in my calculation provided my actual range does not exceed 8 x 87.5 = 700 meters. For 20/20 it would be twice that or 1400 meters. My scope problems don't involve more than 404 meters, so the square law is always appropriate.​*
Example 1: *If I stand *160 meters* from target with my 8x21 monocular, and my virtual sighting distance is 160/8=20 meters, the *red curve* minimum is 0.03591 lux (from this red curve plot), but my monocular only transmits 5.444% of that light, so it must be amplified by compensation with a flashlight having an effective throw (candela rating). The quotient is 0.03591 lux /0.05444 = 0.6596 lux on target. To get the minimum effective flashlight, the candela rating must by in excess of *Icd​*=(0.6596 lux) *160 *160 = 16886 cd. The 20,000 candela *Manker T01* would work in this case, providing 1.18x the needed light or 18% more light than required.

*Example 2: *If I stand *231 meters* from target with my 8x21 monocular, and my virtual sighting distance is 231/8=28.9 meters, the *red curve* minimum is 0.07840 lux (from this red curve plot), but my monocular only transmits 5.444% of that light, so it must be amplified by compensation with a flashlight having an effective throw (candela rating). The quotient is 0.07840 lux /0.05444 = 1.440 lux on target. To get the minimum effective flashlight, the candela rating must by in excess of *Icd​*=(1.440 lux) *231 *231 = 76,846 cd. The 20,000 candela *Manker T01* would NOT work in this case, providing only 26.0% of the needed minimum intensity. You'd need a flashlight rated better than 76846 cd to marginally identify the target at this distance.​

Remember, spill light must be shielded from both eyes for this to work. If you have spill light hitting your eye in excess of 1 lux intensity, your pupil will constrict its diameter to reduce ingress of light.​







Keep in mind, I'm not an expert in optics like my retired US Navy cousin is. So if my seductively dark, wide pupils have elicited a carnal desire within you to violently hump my deliciously plump ego into the wall like a panting dog in heat, please, feel free to prove me wrong _by showing me through scientific references how to do it right._ Otherwise I might enjoy having you and my dear friend Clarice, over for dinner (with some fava beans and a nice chianti-- "F-F-F-F-F-F-F-F-F!" )  






​


----------



## Genzod

Now we come full circle. We have experimental lux values for marginal identification of a small, regular (rectangular), highly contrasted white paper target. We also now have a mathematical model for scoping that target. We can now compare it to TEEJ's remarks on 0.5 lux being a ballpark minimum for such a target.

I do not know what magnification and "quality of scopes" the _"Lord of Lux--Sir Luxely, Ordained Knight-Light and Protector of the 7 realms of Light" _or *TEEJ* as he is known in the magical kingdom of CPF_, _is thinking of when he talks about his _merry men in tights_ shooting targets at 200 meters. He hasn't been around for a while it seems, so I can't seem to get an answer.

_*TALLY-HO! TEEJ * *HAS LEFT THE BUILDING!*_






His men probably have perfect 20/20-20/20 vision and impressive dark adapted pupils, _almost_ as seductive as mine. They are likely using optics that are superior to anything I could hope to use or afford. All that aside, lets investigate my results with various inferior Chinese knock off scopes (assumed transmittance of 85%) and see how that compares.








*
LOW QUALITY MONOCULAR EXAMPLES:*
*
8X21:* At 200 meters, my 8X scope will provide an image that appears as if seen 25 meters from target. A 21 mm objective lens will reduce light available to my eye with an efficiency of 6.0405%. Lux required at target for marginal identification is 0.05765 lux from 25m, virtual. Dividing by scope/eye transmittance efficiency, the required lux for marginal identification at 25 meters is 0.95 lux.

*5x20:* At 200 meters, a 5X scope will provide an image that appears as if seen 40 meters from target. A 20 mm objective lens will reduce light available to my eye with an efficiency of 13.07%. Lux required at target for marginal identification is 0.1553 lux from a virtual position of 40 meters. Dividing by scope/eye transmittance efficiency, the required lux for marginal identification is 1.2 lux.

*3X20:* At 200 meters, a 3X scope will provide an image that appears as if seen 66.7 meters from target. A 20 mm objective lens will reduce light available my eye with an efficiency of 29.41%. Lux required at target for marginal identification is 0.4411 lux from a virtual position of 66.7 meters. Dividing by scope/eye transmittance efficiency, the required lux for marginal identification is 1.5 lux.​

Okay, there you have 3 scopes and 3 different results between 0.95-1.5 lux, an average of about 1.2 lux. My standard of identification in the red plot was based on effort, moving the eye around, trying to focus the eye, trying to determine a distance it took some effort to identify the target. At 4X this value, target identification is "easy" and instantaneous. No effort is required. TEEJ likewise describes his 0.5 lux as very marginal:_
"My best guys could hit stationary white paper at 200 m with ~ 0.5 lux, and an illuminated scope*, but needed ~ 3.5 lux for the same target with a non-illuminated scope. These are guys that can drive tacs in daylight...and yet miss the entire target 3/4 of the time under these conditions."

*Reticle is lit to center scope on marginally visible target._​
I would imagine my requirements are greater due to differences in scope lens geometry and lower quality lenses and coatings.


*A HIGH QUALITY RIFLE SCOPE EXAMPLE:
*

I'm going to take a shot in the dark (no pun intended) on which scope TEEJ's men use, and work a calculation from it. Sounds like TEEJ is either a military or police marksman instructor. I'd venture a guess his men are using a 4x32 scope common to the USMC, the *USMC AN/PVQ-31B. *:rock:*

*





I'll assume his men are about the age of 20 and have average dark adapted eye pupils of 7.5 mm and like to practice ballet in their tights while adapting their eyes to the dark before shooting. :kiss: The scope is assumed to have the typical transmittance efficiency of a very high quality scope with up to 10 lenses--90%. (At over $1500, I imagine you'd insist on that).​*
4x32:* At 200 meters, a 4X scope will provide an image that appears as if seen 50 meters from target. A 32 mm objective lens will reduce light available to their 7.5mm eye pupil with an efficiency of 65.54%. Lux required at target for marginal identification is 0.2461 lux from a virtual position of 50 meters for a deliciously gorgeous 8.5 mm pupil. To adjust for the inferior pupil of 7.5 mm, the required lux from the graph must be bumped up by a factor of (8.5/7.5)^2=1.284. Dividing by scope/eye transmittance efficiency, the required lux for marginal identification is 0.48 lux. (*Edit:* It turns out, as I demonstrate later, that for any pupil diameter equal to or in excess of the exit pupil of the scope (6.4mm) the marginal intensity required will be 0.48 lux).

Gee, that's pretty close to TEEJ's 0.5 lux,​*
YA THINK?*​



​​
When my scope comes in (China shipment, ordered June 30), I'll be able to run some experiments and confirm my model.
*
0.5 wux and a good scope and he coulda 
hit that wascally wabbit!*


----------



## Genzod

In the last post, a conundrum :thinking: occurred that made me realize back when I first conducted my experiment, I had made a mistake with formulating my *required minimum intensity vs. distance * profile by confusing _ambient intensity_ for _minimum required intensity_ in the interval from 0 to 30 meters from target (range where no assisting lamp light was required to identify target). This error led me to choose an incorrect boundary condition of *I'(30.4)=0* and *I(30.4)*=*Ia* (Ia = ambient intensity) and set the required minimum in the interval from 0-30 m to ambient. The result backed out a calculation for ambient intensity on target of 0.0613 lux. In actuality, the correct boundary condition was *I'(0)=0*, with *the limit of I(x)=0 as x---> 0*, resulting in a determination for ambient intensity on target of 0.085 lux. When I tried to determine the intensity required for the 200 meter scoping problem above using the 8x21mm scope sighting at the virtual distance of 25m (less than 30m where ambient is sufficient to identify target), I realized I needed a value of required minimum intensity that was less than ambient to carry out my calculation.

Fortunately, I discovered my error and finally got around to fixing it. The affected posts with calculations and useful plots that were made for the experiment and afterward have all been corrected. I even revamped the original data set with a new collection of intensities at equally spaced intervals so that the regression analysis would be less awkward, more accurate and include the observations in the extended range from 100-180 meters. This extended range allowed me to investigate where required intensity to identify target deviates from the square law expectation due to acuity limitations. In all, I probably spent about 16 hours redoing the project just to get it right. _(You-lucky-*******s.)_

*PREPARE TO BE AMAZED! *(Probably how it will go, too) :laughing:

And so my prophecy at the header of my experiment about how like Sheldon Cooper's first try (and failure) to "amaze" Leonard and Raj's sister with a card trick under the door of his roomate's bedroom (as they were working toward a passion filled "coitus"), my first attempt to "amaze" you would end in like fashion. So allow me to follow through with the following appropriately expected formality:

_"...Drat."_


----------



## Genzod

Posts #69 and #70 have been substantially updated today.

The commonly used equation for calculating exit pupil, Dep=(Do/M), is merely an approximation and has a dramatically negative effect on calculation accuracy for low power monoculars. I go into greater detail on that in the posts. 

New information has come to light (no pun intended) since visiting my optometrist last week that gives some insight into the experimental results and how the derived lux vs. range curve will change depending on personal acuity and dark adapted pupil diameter. I also suggested a possible scope TEEJ's men use to shoot paper targets from 200 meters and ran these update calculations to see if my methodology is correct.

I've since conducted the promised confirmation experiment with the 8x21 scope I received from Banggood this summer. I'll be posting a short discussion on that soon.


----------



## Genzod

*
Experimental Confirmation of the Procedure for Predicting the Performance of the Tandem Use of a Monocular with a Flashlight*

A few weeks ago, I once again visited the test area with the flashlight and monocular. The near half moon had already set below the horizon for at least two hours. All that was needed before testing with the scope was a check for ambient light on target. Some trees were deciduous and had lost their leaves allowing more light to enter the bike path test area. During the original data collection, it was determined the white blaze target could be seen with 0.085 lux ambient light impinging on target from a distance of about 30 meters. During this confirmation test, I could marginally make out the target at 37 meters. Using the square law, new ambient impinging target is​​*
Ia​* = 0.085 * (37/30)^2 = 0.1293 lux​​
From 37 meters, I now focused the monocular on the target and moved back 2 meters. I found the target again and refocused. I repeated this procedure until losing the target at 77 meters. The distance I accepted for a marginal identification was 75 meters after some repeated checking in that small interval. My distance was confirmed, as always, using landmarks and *Google Earth* with its Path function.​

This plot is a useful format for investigating the predictive power of the math behind this method. Keep in mind the data was based on an observer in his mid 50's with 8.5 mm dark adapted pupils and 20/40 vision. The description of the graph format is as follows:​​*
Vertical axis:* Candela intensity, *Icd​* of a lamp sourced at range *x* in meters.​*
Horizontal axis:* Range, *x* in meters between the target and the source lamp.​*
White Curve:* The telescopically unaided observance of target, and the minimum candela required of the source lamp to marginally identify the 2x6" white blaze target at range, *x*.​*
Black Curve:* 8x21 *Suncore* scope (estimated 85% transmittance) used in tandem with a source lamp to marginally identify target.​*
Red Line:* Maximum candela rating of the *Manker T01* (20,000 cd)​*
Orange Line:* Maximum candela rating of the *Astrolux S1* (10,600 cd) This version is not spring bypass, about 1400 lumen max output with a high current lithium battery.​*
Yellow Line:* This is the equivalent candela output of the ambient intensity of 0.1293 lux impinging target as seen from 75 meters. It's the same thing as a pitch black environment and firing a source light from 75 meters such that 0.1293 lux impinges target.​
*
Discussion:*​
*
Examination of the Plot:* 

First, call Richard Gere, and tell him to return the mouse he borrowed from you.






(This has been a public service announcement intended for educational purposes only.)


Now, bring the mouse pointer over the graph and bring up the orange icons to the lower left corner. Click on the icon represented with a line and a dot. Place the mouse over the intersection of the *white curve* and the *red line*, and click. Make sure the dot is right on the intersection. The info panel shows up with the numbers 115, 20,000. This information means the naked eye requires 20,000 candela rated output at 115 meters to marginally identify this target. In other words, the maximum range (for me) with the *Manker T01* (no scope) is 115 meters.

Again, check the values at the intersection of the *white curve* and the *orange line-*-100, 10,600. This means 10,600 cd output is required at 100 meters to marginally identify the target. In other words, the maximum range of the* Astrolux S1* (no scope) is 100 meters.

Move the pointer to the *red line* and *black curve* intersection and click. The info panel reads 173, 20,000. This point represents the tandem use of the *Suncore* 8x21 scope with the maximum output of the *Manker T01*. Max range to marginally identify target with these aids is 173 meters.

Move the pointer down to the intersection of the *orange line* and the *black curve* and click. The info panel reads 149, 10,600. This point represents the tandem use of the 8x21 *Suncore* scope with the maximum output of the *Astrolux S1* (1400 lm). Max range to marginally identify target with these aids is 149 meters.

*
Method Confirmation:*

Now, your brain should be primed to understand the next point on the *black curve* intersecting the *yellow line*. Here we have the culmination of the confirmation test. 

What does my experimentally derived curve for the _minimum lux to marginally identify target_ combined with the mathematical formulas I'm using for the scope predict my range should be when a scope is used in tandem with a source light (in this case, ambient lux of 0.1293 lux)? 

Clicking on the intersection at *black *and *yellow* reads 77 and 727 cd. Now 727 cd is not from a flashlight, but it is the ambient intensity on target at the real 75 meters I viewed the target from. The prediction is 77 meters (77.08 m if you dig a little deeper). Actual was 75 meters. This is a 2.79% error, and suggests the mathematical model is correct.

*
Error Discussion:*

The error of 2.79% comes from the difference in _minimum required light intensity_ at the virtual sighting distance of 75/8 = 9.375 meters between the 5th order polynomial regression and the square law expectation at that distance. The intensity error between the 5th order polynomial and the square law model (the latter of which is more precise) is about 11.6%. 

The required minimum intensity from the square law is 0.085 * (9.4/30)^2 =0.008345 But the 5th order polynomial under-predicts the square law at this range as 0.007476 lux. The ratio is 0.008345/0.007476 =1.116. The 4th root is 1.0279 or 2.79% greater. If you multiply 75 by 1.0279, you get 77.08 meters, which is the model prediction. Therefore the error is solely due to experimental data collection and regressing that data into a 5th order function, not the mathematical model representing the physics of light going through a monocular, which is now confirmed as used correctly. ​*

Conclusion:*​

The mathematical model is precise with some deviation due to experiment and regression of that information into a 5th order polynomial. Normally, the expected result is the square law but only in the range where acuity is still rendering a sharp image. In the range where the target begins visually blending into its surroundings, more light is required and the curve deviates from the square law, requiring a higher order polynomial to represent it. These extra terms can introduce some error into other parts of the curve, particularly where the curve is best represented by one square term.

When using a scope, more often than not, the virtual sighting distance is going to be less than 175 meters for 20/20 vision, which is the acuity I have now since the care of an optometrist. I can simply rely on a square law function with two points defining it at (0,0) and (30 m, 0.085 lx) in this interval from 0 to 175 m. If my maximum sighting distance is 0.25 mile or about 404 meters, using the smallest scope magnification of 2.5X puts the virtual sighting distance at about 162 meters which is less than 175 meters. I really have no need to use anything more than the square law for this specific problem with my corrected to 20/20 vision.

You could generate your own curve by simply finding a very dark location shaded from direct light, determining ambient intensity on target with a lux meter, then finding the distance you can just marginally make out the target, which would be: ​*

I(x)=Ia​ * (x/xa​)^2*;where* Ia​ *and* xa​ *are constants, in my case 0.085 lux and 30 meters, respectively.​

Or, you could take my equation and modify it with your own measured dark adapted pupil by multiplying it by (8.5/*Deye​*)^2. You will most likely need more light to see than this old horny domestic tomcat.

*Ia​* is ambient intensity hitting target (not bouncing off target--big difference. Ask *TEEJ * , he'll tell ya), and *xa​ *is the distance with ambient light that you can just barely make out the target without aid of any other light.​
Then you could determine your dark adapted pupil for use in the scope equation (post #69). You could ask your optometrist to measure it for you; otherwise, use the procedure below:​​*

How to Determine your Dark Adapted Pupil Diameter Utilizing only Stone Knives and Bearskins

*​






Set your smart phone camera with flash on but with pre-flash off (red eye reduction off). 

Go into your bathroom and close the door. Turn off the light. Wait a few minutes for your pupil to adapt. Yeah, you might want to flush that toilet now. 

Pupil normally adapts after a few minutes in the dark, cones need about 10 minutes, and rods need about a half an hour. We aren't measuring cones and rods. Stop making this complicated. :scowl:​
Only if you accept responsibility for your dexterity, hold a ruler horizontally under your left eye. You'll need it in the photo for measurement purposes.​*Now, you kids don't poke yer eye out with that thing! *In fact, if you _are_ kids, go someplace else. Adult entertainment only--this is completely X-Rated humor. Do your parents know where you are? Why isn't this "dangerous" site blocked? Who made me your babysitter? *

Disclamer: Author is not responsible for your IQ*​





Hold the camera at a 4 o'clock position relative to your head (forward is 12) out about 18-24 inches away. (This puts most light on the right eye and less on the left where the ruler is). 

Find the camera in the mirror and look directly at it (a little ambient light for this is necessary and fine, usually the light from the view screen).

Take the picture and transfer it to a PC. (Why not take a few--there's no limit to how much fun you can have with this. Did I not say this was X-rated?) 

Use *MS Paint* and the _line function_ to measure (x, y) of the line. (If you hate Bill Gates and Microsoft, pardon me for mentioning it.) 

Zoom in on the left pupil and ruler with the magnification function. Maintain a distinct edge on the pupil for measurement, and enough sharpness on the ticks of the ruler to discern distance. Place the dots of the line over the widest edges of your pupil and read (x,y). Use the Pythagorean formula to get distance. 

Now place that distance across your ruler in the image and get a reading from the tick marks. If you have 100 units over the pupil and 400 units over an inch on the ruler, then your pupil is 1/4" or 25.4mm/inch*0.25inches=6.35mm.

Repeat this procedure several times until you get the widest pupil possible.

Check the floor for missing eyeballs.

You're good to go. 
​


----------



## ssanasisredna

Can you please factor in how recent rains impacting the albedo of the targets would impact the calculations?


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## Genzod

ssanasisredna said:


> Can you please factor in how recent rains impacting the albedo of the targets would impact the calculations?



This exploration is about comparing scope/lamp combinations under ideal environmental conditions. Your use of the term albedo suggests to me you know more about that than I do. :laughing:

The white blaze target on the AT is white paint. That has an albedo of 0.8 or 80% reflection. Wetness makes pine bark darker which would provide better contrast, so I'd venture a guess the effect would be slightly favorable to next to none.


----------



## Genzod

*
A Universal Equation for the Minimum Lux Required to Marginally Identify a Highly Contrasted 2x6" White Blaze Target under Ideal Conditions
*




Yea verily, 'tis mine derivation, alone. I -eth thee not. 



It's already been shown that in the range that precedes the limit of acuity, the requirement for light intensity to marginally identify said target is simply determined by the square law.​*

ISL​(x) = Ia​*(x/xa​)2​... (for x<xo​)*,​

where, ​*

xo​* is the acuity limit *xo​=S*175* meters* 

*S* is your snellen ratio divided into a decimal, ex 20/40 vision is S=0.5. 

*Ia​* is the ambient lux _delivered to _target (not _coming off_ of the target)****

*xa​* is the distance you can see the target without any light other than ambient.****​*

***175 m *is a special case for a 2x6" target, it is where the target is rendered by 3 vertically stacked 2x2" pixels for 20/20 vision. It is the last point you can render a sharp focus of the image in its size. For a 4x6" object, you can render it in 3 vertically stacked 4x4" pixels at 350 meters...a 8x12 object at 700 meters and so on.*

***_Ambient numbers_ are simply one point on the square law curve, *x<xo​*, that defines the entire second order curve. Any non-zero point will suffice up to the acuity limit since you only need one point to define the equation. I use ambient values to do this because of their convenience. You can lux meter the light _approaching_ the target _at _the target, then pace off the point you can just barely see the target and get *xa​*. If there is no ambient light, you can still mechanically provide it and determine *xa​* for that intensity at any point *x* less than *xo​*.​



At that acuity limit (blaze is represented by three 2x2" square pixels), some _mysterious_ function deviates away from the square law expectation at a tangent, increasing need for lux above it.


Imagine standing at your acuity limit. Let's say you have 20/40 vision like mine was during data collection for my experiment. Your acuity limit for this 2x6" target would be 87.5 meters.

Now extend in all directions from your eye a sphere of 87.5 meter radius, with 2x2" pixels forming the surface of the sphere. Egad! Shades of John Travolta, Batman! It's a discotheque ball! 
*
Yes, you ARE the Dancing Queen, young 
and sweet, only 17.*








This 87.5 meter radius ball with 2x2" mirror pixels, touches the tree with the target and the target white blaze occupies 3 pixels of it, all stacked vertically, 3 by 1 pixels.

Now, as you step away from the tree, the surface of the ball retreats with you, and the image of the blaze shrinks relative to the 3x1 pixels, as if slipping inside the 3 x 1 pixel resolution, but you can't render this image accurately, only the intensity of the light in the pixels, evenly across the pixels.

The size of the 3x1 pixel image stays the same relative to you since the surface of the pixel sphere travels with you. The light of the ever shrinking blaze is spread out over the relatively larger area of the pixels, decreasing surface brightness of the pixels. Thus, we have two squaring laws, one for the increased need for intensity with distance, and one for spreading the light of the shrinking target over the relatively larger area of the 3 pixels that are fixed in size relative to your vision.

As you step back farther, eventually the entire blaze occupies one pixel, and the light becomes a single dot that progressively dims with increasing distance, all in accordance with this compounded squaring.

Without a drawn out boring derivation involving a little bit of "algeber" as Mr. Reynolds, my Math Analysis instructor, used to say and derivative "calc-useless" as my fellow Calculus peers used to say, (you will eventually see how it fits the experimental data anyway), the formula for the minimum intensity required in the region of acuity loss is very simply:

​
*IAL​(x) = 0.5 * Ia​ * [(xo​/xa​)2​] * [1 + (x/xo​)4​]*,.. *(**for x>xo​)*
​

where, ​*
xo​* is the acuity limit *xo​=S*175* meters 

*S* is your snellen ratio divided into a decimal, ex 20/40 vision is S=0.5)

*Ia​* is the ambient lux _at_ target (not coming _off_ the target)

*xa​* is the distance you can see the target without any light other than ambient.



**175 m* is a special case for a 2x6" target, it is where the target is rendered by 3 vertically stacked 2x2" pixels for 20/20 vision. It is the last point you can render a sharp focus of the image in its actual size. For a 4x12" object, you can render it in 3 vertically stacked 4x4" pixels at 350 meters...a 8x24 object at 700 meters and so on.

​ In my case (your case may be different):


​*xo​=87.5* meters (acuity limit**** of 20/40 vision for a 2x6" target),

*xa​=30.0* meters (distance to see target with only ambient light)*

x>xo​* (distance from the target, variable x in meters, in the range of acuity loss), 

*Ia​=0.085* lux (ambient intensity)


​***To correct the intensity curve for _your_ vision (below), simply provide your Snellen ratio derived *xo​*, (*xo​=S*175), *and shift the curve up or down according to the square of the ratio of *my dark adapted* pupil diameter *8.5mm* to yours, *Deye,​* multiplied by *the square law curve with my constants *plus the *diminishing acuity region with the compounded squaring.* Note that this is a piece-wise function with *logic switches (true=1, false =0).


I(x)=ISL​(x) + IAL​(x)

*Or in its expanded form,
​*
I(x)= **(8.5/Deye​)2​** * { **[(0.085/30*2​*)*x*2​*] *** **(x<=xo​)* + *0.5 * 0.085 * [(xo​/30)2​] * [1 + (x/xo​)4​] * (x>xo​) } *:rock:


This is the complete formula for minimum intensity to marginally identify target (white paper on tree) with the naked eye (no scope) under ideal conditions (no spill, no fog, no skittles) as a function of range *x*, acuity limit for your specifically sized target *xo​*, and your dark adapted pupil diameter.

Note that for smaller eye pupil less than 8.5mm, more light is needed, point for point, and larger pupil (good luck wit dat :ironic:), less light is needed. 

​
:buddies::drunk::buddies:







*Disclaimer:* The characters in the media above are fictional 
and do not necessarily represent real persons and/or 
appropriate behavior (for both minors or adults). Minors who 
are here are not asked where your parents are, but why you 
call them that since obviously that is not what they are doing. 
If you are a minor and your parents have not blocked this 
thread, please leave this thread immediately and seek 
professional counselling and/or medical assistance, 
if warranted, from a professionally licensed psychiatric 
physician.
​*
About albedo: *This target was white paper having a reflectivity (albedo) of between 0.6-0.7. It was posted on a pine tree with albedo of about 0.08-0.09. White acrylic paint has a reflectivity of about 0.8. I would expect because white paint reflects a little better than white paper, that the equation above applied to freshly painted trail blazes overestimates required received lux, probably in the neighborhood of 25-30%. Unfortunately, white blazes tend not to be freshly painted, and seem more often weathered from time, reducing reflectivity. I thought the weathered, satin look of the paper I used to emulate a white blaze was somewhat closer to the typical blaze. Therefore, I feel I can disregard albedo corrections to the equation above, seeing freshly painted blazes for what they are--pleasant bonuses. You know the feeling. You drive for hundreds of miles on faded asphalt with low contrasting, weathered road markings, then you come across a rare stretch of road that is black and has freshly painted markings--ding ding ding--bonus! But that's not what you plan around or expect to see that often. Just be aware that the albedo of the target, and the contrast that it has with it's adjacent background can affect the prediction, soldier... and you'll be O.K. :thumbsup:​

I have a graph demonstrating how the plot lays against the collected data, with the following definitions:​*


Horizontal axis: *range *x*, meters. Where you are standing with the _magical_ flashlight I told you that you could not borrow. COUGH IT UP! :scowl:

*Vertical axis: * intensity *Imin​*, lux. Minimum lux to identify target.​*
Black Curve*: The original regressed curve for 20/40 acuity and 8.5 mm dark adapted pupils. (This experimenter eats carrots and does NOT shoot wascawy wabbits with only 0.5 lux.)

*Blue curve*: Square law expectation

*Red curve:* Acuity loss (20/40) intensity x>87.5 meters (formula)

*Yellow curve:*Acuity loss (20/20) intensity x>175 meters (formula)

*Green Points:* Experimental data (20/40 acuity, 8.5 mm pupil).​


Notice how *20/20 acuity* gives you a longer run with the better values of the *square law curve* than the *20/40 acuity curve*.

You can see (even more clearly with this graph) how the *green points* of the data lay nicely right across the *formulaic red curve* (and *square law blue curve*) _with the exception of the *final data point at 175*_*,* which was made in error because it was an estimation necessitated by the fact I am NOT _Jesus_ and can't walk on water. The shore line of the lake was at 165 meters. I was about 13 meters off in my estimation for where the range was for 8 lux on the target. It was actually at 188 meters (23 meters from shore) according to the formula. I made the approximation it was at 175 meters, and _skewed_ (sic) up my experimentally derived curve for x>165m. 

_*
Hey, guys! C'mon in. The 
misty air is fine!*_






True, I could have moved the test lamp to a distance from the tree to generate about 4.75 lux on target (as opposed to 8 lux that put the distance over the lake), then I could have tested at around 160-165 meters to get that last point right at the shoreline, but why do _that_ when it's easier to just _*fudge*?_ I like *fudge*, don't you?

 No...not that kind of *fudge*.


No wonder the experimentally derived curve was so hard to fit across the last few points. I thought it was just experimental deviation about the true curve. And that is why the experimental *black curve* deviates so profusely away from the formulaic *red curve* after 165 meters. It shouldn't. I'm going to have to own that one :sigh:. My bad.​*
Yes kiddies, the Zodster does have his 
own kryptonite -- shortcut laziness.*







So now we have two simple formulas to represent the data, and those formulas can be adjusted for _everyone_ based on personal Snellen acuity and dark adapted pupil diameter. (Eat yer *carrots* like I do, kiddies.) The simple square law curve up to the acuity limit *xo​*, followed by the 4th order formula described at the top of this post. We can now ignore our dear friend the experimentally derived 5th order curve which is better served by the more robust, simple physical equations, equations that exactly predict my confirmation test with the 8x21 scope in ambient light--75 meters. _Exactly._ Did I not tell you the Zodster is perfect? ​
This graph features an adjustable curve that can be modified by playing with the numbers in the color coded fields to the upper right of the page. The plot as it stands describes 20/20 vision with a 7.5mm dark adapted pupil (typical for a 20-30 year olds).

Just test your acuity with a chart printed from the internet, and measure your dark adapted pupils in a dark room (1 lux or less ambient light).

Then, where you see the number 175 meters (special case for 20/20 acuity limit for this size target) in the formula fields, substitute your acuity limit distance.​

*xo​=175*S*, ​
where,

*S*=Snellen acuity ratio as a decimal fraction. (*xo​*=87.5 for Snellen = 20/40)​

And also substitute the existing number of 7.5 mm in the formula (the typical dark adapted pupil for 20-30 year age bracket) with your measured pupil diameter in mm. A smaller dark adapted pupil will see less light in the dark, so the intensity required curve will be shifted up. This shift up or down is the square of the ratio of pupil diameters). Ask your optometrist to measure your dark adapted pupil or use the home method in the earlier post. _Kids, do you know where your parents are? _

The ambient light on target of your environment is irrelevant (provided you also block out any glare with say, an eye tube or monocular). Any light you need is determined by the equation, whether you get that as ambient or supplied light plus ambient. More ambient means you need less from the lamp.

Now, you can use these values from the graph to determine how much candela power you need in a flashlight to marginally make out the target at that distance. Just multiply the intensity *I(x)* by the square of the range, *x*.

Recognizing what that target is, though, as a point source of light in one pixel is a totally 'nother critter, but if you know what it is in advance, there it is. 

Now against better advice in this thread, you can go ahead and *{{{SHOOT IT}}}* :devil: (You know you want to.)

If you want practical light to see the target, imagine kicking in the high beams of your car to take the edge off. Multiply the minimum intensity by 1.5-1.7.

In the telescope problem, divide your range, x by magnification to get your virtual range. Then use that range to pick a point off the *blue curve* you modified for your dark adapted pupil diameter. Your scope focuses to compensate for acuity, so use only the *square law curve, *safe up to a range of the power of the scope times the acuity limit, *M*xo*. Then square the ratio of your scope's exit pupil divided by your eye pupil diameter and multiply it by the transmittance efficiency of your scope = *E***([Do​/(M+1)]/Deye​ )2​. *Invert that result and multiply it by the lux of the point you picked off *your personalized blue curve*. That is the scope-lamp marginal intensity required. Multiply by 1.5-1.7 for practical lux if you'd like. Then you can take that intensity, multiply it by the square of your range (where you are actually standing with my magical flashlight that you are bogarting). That is the candela power needed to see target with your scope. 

*IMPORTANT!* Remember, if your dark adapted pupil diameter *Deye ​*is less than the exit pupil of the scope *Dep​*, i.e. *Deye​* < *Do​/(M+1), *divide the intensity at virtual range _only_ by the scope transmittance efficiency, *E*. That extra light that is not getting into your pupil is wasted. You can't have better than 100% surface brightness. You can't see the target at range with a scope with less intensity than that which you would need at your closer virtual range.​

_*AND THAT'S HOW YOU DO IT *_​






​


----------



## Genzod

*
Using the Derived Formulas to Analyze Lamp and Lamp-Scope Performance to Find a Minimum Weight Solution that Fulfills My Sighting Requirements*
Now that I have a practical tool for determining light requirements to see that target with any vision (dark adapted pupil and Snellen ratio aspects only, not cone/rod pigment differences, can't help if you don't eat your carrots or you stared into the sun like a fool just because your mother told you _not_ to do it), I can study the problem of my light and scope needs for sighting that wascawy ewusive bwaze.

*Vewy impwessive! *:candle:






This pwot has been adjusted for my cowected 20/20 vision and awurwing 8.5 mm bedwoom eyes. :naughty: The *bwue curve* is the expected square waw for wight intensity ovah distance for naked eye viewing. The *yellow curve* is the deviation from expectation due to acuity limitation for 20/20 vision (x>175 meters).








The *bwack wine* descwibes the can-deh-wuh wee-qui-uh-ments of sight _sans scope _ in this pwot hewuh. Just mut-wih-pie vuh-tih-caw axith by 10,000 to get can-deh-wuh.​

50 m, 2361 cd
100 m, 9444 cd (*Astrolux S1* standard 1400 lm configuration 10,600 cd, Klarus XT1C, 11,025cd, 1.67oz)
161 m, 63,457 cd (0.10 mile)
175 m, 88,579 cd (*Acebeam L16,* 90,800 cd, 4.52oz) (20/20 Acuity limit naked eye)
*200 m, 156,532 cd Armytek Barracuda *160,000 cd, 9.14 oz less ~1-1.5oz for extention tube; *Olight M2X-UT Javelot*, 164,000cd 7.68oz)​241 m, 386,111 cd (0.15 mile)
250 m, 466,839 cd
350 m, 3.1 Mcd (2x 20/20 acuity limt, ID still practical but candela requirements and weight are not)
404 m, 6.9 Mcd (0.25 mile)​

The practical weight limit of the typical flashlight exceeds 10 ounces (284 grams) after 200m. A scope can reduce the weight of the flashlight and provide a focused image extending acuity range by the power of the scope (8x scope extends 20/20 vision range from 175 m to 1400m, 3.25x is 568 m, 2.5 scope is 438m), so the *square law curve* is always used for investigating ranges I need, which never exceed 404 m.

The following data comes from the *red line* of this plot which describes the tandem use of a flashlight and my *Suncore* 8x21 scope (85% transmittance), Compare it to the above data:​

100 m, 2304 cd
150 m, 11,663 cd (*Astrolux S1 18350 IMR cell*, spring bypassed to 1600lm, 12114 cd, 2.12oz)
161 m, 15,480 cd (0.10 mi) *Manker T01 II* 20,000 cd, 1.94 oz 
175 m, 21608 cd (*Astrolux S1 18350 IMR cell*, spring bypassed and dedomed, 23,000cd)
200 m, 36,862 cd (*Nitecore MH20GT,* 33,000 cd, 3.08 oz, *Klarus XT12S*, 40,401cd, 4.62oz)
241 m, 77,719 cd (0.15 mi)
250 m, 89,996 cd* (**Acebeam L16,* 90,800 cd, 4.52oz)
*288 m, 158,500 cd* (*ArmyTek Barracuda,* 160,000 cd, 9.14 oz less ~1oz for extention tube; *Olight M2X-UT Javelot*, 164,000cd 7.68oz)
300 m, 186,615 cd (*Olight M3XS-UT Javelot* 250,000 cd 8.99 oz)
350 m, 345,728 cd 
404 m, 613,744 cd (0.25 mi)​

The *Manker T01 II* with an IMR battery would provide 1.3X minimum required intensity for 161 meters (tenth of a mile) with an 8x21 scope, while providing the same intensity for 20/20 identification (no scope) at 113 meters. This combination is a nice compromise weighing only 4.6 oz or 131 grams. A 3.25x25 scope would provide _slightly better _performance (this plot) for less weight: 3.1 oz or 89 grams. The 3.25x25 scope is depicted by the *green curve* while the 8x21 is again depicted by the *red curve*.

Of course there are other lamps and scope combinations yielding different results. The name of the game is keeping it light while providing the minimum light.

If my *ZL H53w* headlamp failed, I could use the primary lithium from it in the *Manker T01 II* to get half the max lux, while still supplying trail running light at around 60-80 lumens using a diffuser. Really important when you're on foot, deep in the wilderness and 20 miles from any store--oh, yeah, and it's _dark_, too. 

​


----------



## Genzod

*
Comparing Scope-Lamp Combinations using an Intensity vs Range Diagram*

The following plots provide data for various scope-lamp combinations. Use this plot for long range analysis (160-400 meters), and this plot for short range analysis (90-160 meters). 

Remember, this is specified for my vision (20/20, 8.5mm dark adapted pupil). You can modify the equations, as described below, to depict your own vision.​

The plots are color coded for your _ocular pleasure_  (and last time I checked, that was _still_ legal despite many a motherly warning NOT to rub your eyes):​*

Naked eye*, *2.5x17.5*, *3x20*, *3.25x25*, *5x30*, *8x21*, *8x32*, *10x40*. (These are common monocular ratios presently available on the market.)​
Color coded fields to the right hand side of the plot page contain all the functions describing the corresponding curves in the graph. 

The equations for the scope lamp combinations use only the square law and have this form:
​
(x>0)*x*x*(8.5/*8.5*)^2*(0.085*((x/10)/30)^2)/(0.85*(40/11/*8.5*)^2).​​
To own this function, replace *red* emboldened numbers with your dark adapted pupil (mm). Acuity is irrelevant for me since the magnification of even the the smallest power scope (2.5x) extends my 20/20 vision beyond the range of the 404 m that I am studying. If per chance your vision sucks like mine did when I started this experiment (20/40) you are cautioned not to explore ranges exceeding the magnification of the scope multiplied by the acuity limit, *xmax​ = M * xo​*. (Example: 20/40 ---> *xo ​*= 87.5, so using a 2.5X scope, I can't use this function for ranges exceeding 219 m).​

The equation for the *black curve* (naked eye--yes, still legal in public :huh involves both square law and acuity functions and looks like this in the field:​

(x<*175*)*x*x*(8.5/*8.5*)^2*(0.085*(x/30)^2)+(x>=*175*)*x*x*(8.5/*8.5*)^2*0.5*0.085*[(*175*/30)^2]*[1+(x/*175*)^4]


The (x<175) and (x>=175) are logic switches (0 for false or 1 when true) that tell the plotter when to include or exclude each separate function. I hate discontinuities, don't you? I like a nice, smooth, continuous function that doesn't make my baby blues hurt. I find logic switches intellectually titillating. 

To own this function, replace the emboldened *black* *175* (meters) with your acuity limit in meters. (87.5 for 20/40, 117 for 20/30, 175 for 20/20, 350 for 20/10, see the rule? Aren't you the clever one? Move to the head of the class, you precocious genius, you.)​
Replace the red *8.5* (mm) with your dark adapted pupil diameter in mm.

And once again, check the floor for missing eyeballs. (Better safe than sorry. )​

*
*To see a blaze at 1/4 mile (404 m) the maximum blaze spacing in wilderness areas (provided a direct line of site is available) the possible combinations are thus:​

*0.25 MILE RANGE

*​*162,000 cd 10x40 ** Olight M2X-UT Javelot *(164,000cd, 7.68 oz) *Bushnell 10x40* Monocular (5.47 oz) *(1x, 13.2 oz total)*
264,000 cd 8x32
342,000 cd 5x30
585,000 cd 3.25x25
614,000 cd 8x21
950,000 cd 3x20
1,45 Mcd 2.5x17.5
6.94Mcd Naked eye (Helicopter spot, anyone? Maybe two as a backup.)​






That's almost a pound of sighting tools. That's a fairly impractical amount of weight to be carrying while running up mountains. I think I would be better served keeping total weight below 6-7 oz, and compromise by making my maximum sighting range around 0.10 miles (161 m), the minimum blaze spacing in wilderness areas.​

Then I could use this plot to determine the lightest weight lamp and scope combination at 161 meters:​
*
0.10 MILE RANGE*​
4079 cd, 10x40
6667 cd, 8x32
8630 cd, 5x30
*14758 cd, 3.25x25 **Manker T01 II*, (1.94oz) *Kunming 3.25x25* Monocular (1.2) oz *(1.35x, 3.14 oz total)*
15480 cd, 8x21
23973 cd, 3x20
36678 cd, 2.5x17.5
63547 cd, Naked eye (20/20 8.5 mm pupil vision) *Nitecore P30* (95,500 cd, 5.63 oz)​






​3.14 oz is pretty light. Let's increase the range constraint to add some weight, and see what happens. I could set my constraint at the middle, 0.175 mi (282 m) or thereabout. (So many choices, so little time! :huh​*

0.175 MILE RANGE*​
38393 cd, 10x40
*62748 cd, 8x32* *Acebeam L16,* (90,800 cd, 4.52oz) *Levenhuk 8x32* Monocular (6.62 oz) (11.2 oz total)
81229 cd, 5x30 *Acebeam L16,* (90,800 cd, 4.52oz), *Pulsar 5x30* Monocular (7.06oz) (11.6 oz total)​*138906 cd*, 3.25x25 *Olight M2X-UT Javelot *(164,000cd, 7.68 oz) *Kunming Powerier Optics* 3.25x25 (1.2oz) *(1.2x, 8.9 oz total)*​*145639 cd, 8x21 Suncore *(2.68 oz)*Olight M2X-UT Javelot *(164,000cd, 7.68 oz) (10.4 oz total)​225636 cd, 3x20
345224 cd, 2.5x17.5
890476 cd, Naked eye (20/20 8.5 mm pupil vision)​
The practical limit of the flashlight weight is exceeded at the 8x21 scope power requirement.








It seems like from the data above, I might be able to find something in the 6-7 oz range at about 0.15 mile (241m). An *Acebeam L16,* (90,800 cd, 4.52oz) and a *Kunming 3.25x25* is 5.72 oz total and provides 1.17x minimum required intensity at 0.15 mile. I could simply swap out my lighter backup flashlight (Manker T01 II) for the heavier one *Acebeam L16* when in the alpine areas of the AT in NH and ME where direct line of sight is possible above treeline. (Blazes painted on rocks, and rock-piles called cairns mark trail). 

If only a simple, lightweight, 4-5 element optic, 4x32 monocular existed on the market. That would probably be the best compromise between 2.5-10x monoculars, but it doesn't exist except as a 7-10 element rifle scope, and that tends to weigh around 16oz--way too heavy for running up mountain inclines with a pack.











At this point you might be thinking to yourself:_

"Hey Zodster, don't you think all the trouble to minimize the weight of the lamp-scope combination is kind of a going around the elbow to get your thumb waste of time?"_:thinking:

*WHAT? YOU QUESTION THE ZODSTER'S BRILLIANCE? **

NO FISH STICKS FOR YOU! *:scowl:




Run a 50 mile day in the mountains in my trail shoes with a pack full of your philosophy, then ask me that again 
_(if you can still breath, that is.) _


----------



## Genzod

BVH said:


> Spectrolab, the helicopter searchlight manufacturer, provides the figure of 32 Lux at 1 Kilometer output for their 1600 Watt light with a beam of 4 degrees and 40 Lux at 1 Kilometer output for their 500 Watt, 2-degree beam light. Maybe that gives you an idea of what they need to see a target from a typical 500 - 1000 feet away.



In hindsight, now that I can theoretically determine the amount of lux needed for a person with 20/20 vision and 8.5 mm pupils to marginally identify a 2x6 white blaze (Plot), 32 Mcd's of the Spectrolab searchlight gets me to 522 meters. Granted, the blaze is just represented by one pixel of my resolution (3x the acuity limit), but that pixel is just bright enough to marginally see it. 

If I wanted to easily see it with 1.7x intensity like the increase from high beams of a car, I'd have to reduce the max range to 476 meters.

Of course I'd only know that blip was a trail marker if it were the only such highly contrasted target next to the clearly defined trail, but I think I'll SHOOT it, anyway. :devil:

I think maybe "32 lux at 1 km" might just be another industrial standard for saying "0.25 lux at 11314 meters of throw" or "32,000,000 candela", and it doesn't actually represent a figure that describes useful lux for any kind of task since there can be so many (reading, walking, running, reading a license plate from 500 ft altitude, identifying a suspect, etc.)


----------



## Genzod

_*
Meanwhile, back in Sherwood Forest... *_:duh2:





​





 We revisit _Sir Luxly, Lord of the 7 Realms of Light_ AKA _*TEEJ *_ and his _merry men in tights_ shooting 3x3' white paper targets at 200 meters with scoped rifles and 0.5 lux in the darkened recesses of the King's Forest. We assume a 4x32 military grade high quality scope with 90% transmittance, and men about the age of 20 with 8.0 mm dark adapted pupils, a clinically accepted average, almost as adorable as mine. :naughty:​
With 8.5 mm pupils, I can see the same target with my voluptuously sexy, naked eyes with 11.4% less lux as they. However, when we all look into the exact same scope having a 6.4 mm exit pupil, things change. We all now require the same intensity on target. How can this be? 

Since the light coming out of the exit pupil of the scope is 6.4 mm in diameter, it doesn't matter if the pupil is 8mm or 8.5 mm wide, it _all_ gets in. Only when the pupil is below 6.4 mm, does the need for more lux on target arise. The light spilling around the outside of the pupil is wasted. 

The formulaic method more accurately predicts a minimum requirement of 0.463 lux on target to marginally see it, _provided_ dark adapted pupil is in excess of 6.4 mm diameter, as can be seen in this plot of *Lux vs Range* from the *red curve* at 200 meters (all pupils 6.4 mm and greater will fall on this red line). The next (black) curve above it is 6mm, then the next is 5.5mm and so on until the last at 4.0mm. You can see that with less pupil open to the light that is available from the scope (but only for pupils less than the scope exit pupil) the need for more light on target becomes necessary, in this case anywhere from 0.463 lux to 1.185 lux. 

It seems strange but it's true, all evidence considered. As long as your pupil is larger than or equal to the exit pupil of the scope, you will see the target through the scope with the same need for lux as a guy with even a wider, sexier pupil than yours. Is the Zodster wrong? POPPYCOCK! The Zodster has perfect 20/20 EYE-Q! 

Actually, the only clues I have are from the equations and the mulling around I've been doing contemplating this strange, unfamiliar conundrum. I'm not an expert with scopes, so if anyone who is would like to add to the discussion, please feel free to... 

:bow:_*KNEEL BEFORE ZOD, SUPER-BRAIN*_ :bow:








and provide a knowledgeable, preferably well documented, response. 

_*OR ELSE...*_








And now a tribute :candle: to _*TEEJ*_  and his _merry men in tights_. (Blimey, you got to be a _man_ to wear tights! :sweat​
 
​
​


----------



## Genzod

*
An Inexpensive Aspheric Zoomie that Outperforms Most 1x18650 Reflector Flashlights in Terms of Weight, Throw and Distracting Spill *:rock:

My "Marginal Lux as a Function of Range" formula requires that foreground spill not constrict dark adapted pupil diameter. This requirement can be met by utilizing a scope, an eye tube to shade the eye, a snoot tube fixed to the lamp to illuminate most foreground spill or a pencil beamed zoomie. I found an aspheric zoomie that not only meets this requirement, but also allows me to fulfill other requisites such as a back up lamp for my head lamp, which is used for sitting activities, walking, running and short range blaze searching. This is my magical flashlight, _and NO you still can't borrow it!

_:nana:








*SKY LUMEN Aspheric18 - Budget 18650 Zoomie Spotter *​*

LED: *Oslon Black 6500K*
Max Flux: *700 Lumens
*Max Intensity*: 260,000 cd
*Throw to 0.25 lux:* 1020 meters
*Battery:* 1x18650 High drain, unprotected. Sony VTC5A 2600mAh nominal capacity (highly recommended by Vinh for maximum performance).
*Weight:* 170 grams (6.0 ounces) 
*UI:* VN4 Driver--Multiple arrangements of anywhere from 1 to 6 modes as percentages of max lumens. For example, I will use: Firefly, 7lm, 35lm, 105lm, 350lm, 700lm (Zooming in substantially reduces flux but at great gain to intensity because of collimation.)

(At this time, I suspect Vinh may have acquired his T20 hosts from Mountain Electronics or their own vendor, and if so, then I believe the lens material is glass and the pill is brass.)
*
EDIT: *Weight was revised from a vendor misquote of 3.8 oz to 6.0 oz. Vendor acknowledges weight is 6.0 oz. The weight of the standard T20 host using glass lens and brass pill.​

Combined with a $65 3.25x25 monocular weighing 34 grams or 1.2 ounces (below right) from a US supplier, much cheaper for under $15 at a chinese "ebay" site, the scope/zoomie combination has the following performance predicted by this *interactive Intensity (Candela) vs. Range (meters) plot* of my derived formula (8.5mm dark adapted pupil, and 20-30 minutes of retina pigment dark adaptation). _See Adaptation (eye)_.
​*

Definitions for plot:

*​*Black Curve:* Naked eye and lamp.
*Red Curve:* 3.25x25 scope (34 g) and lamp.
*Blue Curve:* 8x32 scope and lamp.
*Yellow Curve:* 10x40 Bushnell scope (155 g) and lamp.
*Green Lines:* Mode Intensities of lamp in narrow beam configuration.










The intersections of the *green lines* with the *colored curves* that represent different scopes is the best marginal range for that combination under ideal conditions and with my highly _shagadelic_ 8.5mm dark adapted pupils. :naughty: 
*
YEAH BABY, YEAH!
*




​

The UI will be used in 6 mode format in accordance to the 3 flood outputs below and the predictions of the Red Curve scope/lamp performance in each of higher 5 modes when zoomed in as follows:
​*

FLOOD*​
FF reading​1% (7lm) sitting​5% (35lm) walking​15% (105lm) running ​*

SPOT* (with 3.25x25 scope--1.2 oz / without scope)
​

1% (up to 105m / 72m) blaze​5% (up to 156m / 109m about 0.10 mile) blaze​15% (up to 206 / 143m) blaze -- naked eye: 66x marginal intensity on target 50 meters away (typical blaze spacing)​50% (up to 278m / 191m) blaze​100% (up to 330m / 223m) blaze

Each zoomed in mode utilizing scope is a step up of about 50 meters throw. 

*Please do not confuse these throw figures with the 1020 meter throw to 0.25 lux of the Sky Lumen specifications. *When I say the max output mode throws to 330 meters, that means it is throwing 2.39 lux to 330 meters (not 0.25 lux) and that I am just barely able to see the target blaze with a 3.25x25 scope. 
​

Notice the 155g *10x40 Bushnell monocular* (above left, and the *yellow curve*) meets with 1.6x marginal intensity at 404 meters (1/4 mile). This is the maximum spacing between trail blazes in wilderness designated areas. It's about the same size as the zoomie flashlight above but a little heaver at 5.47 ounces. I would only need this in the Alpine sections of the AT in NH and ME where trees don't limit line of sight for that distance, if I should so choose to carry it (but I doubt I will). I just show the data to demonstrate what is needed to see that far, and demonstrate that knowing the weight cost allows me to understand that such range capability isn't desirable due to the determined excessive weight. There are no trees here for highly contrasted blazes anyway, and those blazes tend to be on the ground or on a boulder. Cairns (rock piles) mark the way in some alpine sections. Although there tends to be no clearly marked path in many places, these paths tend to be on ridges and generally run straight for long stretches. ​_
_​_"But GenZod, don't you think all this effort to determine the right combination of lamp and scope for finding trail markers to navigate with is a going-around-your-elbow-to-get-to-your-thumb waste-of-time and effort? Why not just carry a light trail map and simple compass to figure out which way to go?_ " :ironic:​







*You've never been up on the 
White Mountains above tree 
line at night trying to handle a
paper topo map; have you, my
windy-lipped genius?*








*WINDY-LIPPED...IS THAT WHERE ALL THIS WIND IS 
COMING FROM? *:laughing:


I'm totally blown away myself that 6.0 ounces of flashlight can punch 260,000 cd. The 1x18650 reflector type flashlights I investigated earlier in this thread were at best 7.68 oz just to get to 164,000 cd and were just as pricey if not more. For example, the *Armytek Barracuda Pro* throwing 160,000 cd at 9.1 oz (maybe 1.6 oz less shortened to 1x18650 with reducing tube) is $140. The zoomie above is $110. For similar weight (as close as I could get to it anyway), I could only find the* Acebeam L16* at 90,800 cd and 0.8 oz heavier at 4.52 ounces.

If you could compare lamps in terms of how many times better they are than another, you might do it this way. Consider, you want to minimize cost (C), maximize candelas (I), minimize weight (W) and maximize candelas/lumens (L) (efficiency of lumens in terms of candelas/lumen). Make the ratio R =(I*L)/(W*C) with quantities you want larger in the numerator and quantities you want smaller in the denominator and seek the flashlight with the largest resulting combination of specs.​

For instance, the *Olite Javelot* R=164,000*(164,000/1020)/(218*110) = 1100

For the *Armytek Barracuda Pro* R=160,000*(160,000/1500)/(210?*140)= 580

For the *Aspheric18 Zoomie* R= 260,000*(260,000/700)/ (170*110)= 5164

*EDIT*: These numbers have been revised due to an earlier error.​

The zoomie wins, hands down. In fact, it's 4.7x more desirable for my task compared to the *Javelot* (5164/1100) and 8.9x compared to the *Barracuda* (5164/580).

Even though the zoomie has a 6500K cool white tint, I believe it will work with short range blaze searches in fog provided I move the beam away from direct line of sight with the target. Fog is a speed killer at night, and the one or two times I needed it in 2200 miles of AT, I really needed it (and didn't have it). The alternative is sitting tight till morning, getting lost at road heads, or moving at a snail's pace when every blaze becomes a new challenge: find a blaze, move ahead in one direction 30 paces, fail to locate next blaze, back-track through the fog, do it again in a new direction, back again, and so on until you find the next blaze.






*
"OH, WHAT FRESH HELL IS THIS? I 
JUST LEFT THE DOOR WIDE OPEN FOR 
A SWARMING INVASION OF BLOOD 
SUCKING DIPTERA NEMATOCERA 
SIMULIDAE*! " 

*_***Translation: Fog and tint pests trolling forums looking for blood._


I know there are all sorts of hypothetical arguments for why tint matters in the fog and various sincere anecdotes of hobbyists comparing their own lamps, but we are talking 30-50 meters here, not going for the full potential to 330 meters (2.39 lux not 0.25 lux) of the highest mode. Consider the scientific argument (by scientists) on light scattering if you are interested.

​
*
Quote: "...large fog droplets scatter all visible wavelengths equally effectively." *​

A friend pointed out to me that it's possible one physical reason there are differences in perception in warm and cool white tint in rain and fog is perhaps because some people's eyes are more sensitive to higher frequency spectrum light, and therefore cool white seems brighter to them than warm tint, as they both equally scatter. That said, I end all discussion on tint and fog and ask others not to debate that here.​
And that is my argument (to me for my own purposes) for why I'm going to at least _try_ this zoomie out and see if it will work for _me_ in fog. What works for you is for another time and another place, but not the same _bat time_, nor same _bat channel.
_













I know the topic of tint as it relates to fog is like nitro-glycerin around these here parts (people shake, and then they explode), but *please keep in mind*, this thread is about identifying blaze targets and the tools I developed to model that for the purpose of finding devices that can help me in that regard. If you want to blow off some steam :touche:and argue flashlight tint and fog, NAFF OFF , maybe _go for a pint_ and _get pished!_ :buddies: _Aggro_ bombing runs on my person :duck: by trans-Atlantic _blighters_ :devil::scowl:  and _flibbertigibbets _:huh: who are trying to _knacker_ my _arse _:tired: :sleepy: with _daft_ _cobblers_ :eeew: should be restricted to those pertinent topics only, as has apparently been the tradition here, anyway. Then get a group hug :grouphug: because you're probably long overdue.​
*

Pip, pip, cheerio and all that rot!*  

(Check out those shiny, straight pearly whites, mate! Aren't they absolutely SMASHING?)


*
His compass set, and his ailerons trimmed, the fearless and determined RAF 
Lancaster bomber pilot ventures onward toward yet another dauntless
bombing run...*






*
From out of the east, he came, riding upon his wings of glory, delivering parcels 
of unparalleled wisdom from since the dawn of man's conscious evolution.
*






_

"...If you think about it in terms of the 'need' to identify a target, then 'minimum' is 
not really what it is all about, instead you throw as much light as you can and can 
either identify the target or not (S+R, LE and Military applications)". 

_




​*

Throw as much light at the target as you can? How about 
we throw as much FLAK as we can...with the biggest, 
heaviest HAT CANNON we can find...and either bring 
down "the target" or not? Would that be considered a 
viable "military application"?*






 
_
*I repeat the original clarification made in **the OP **for contextually 
challenged readers who say **they read the entire thread before 
delivering their dismissive ordinance:*
_​




_


"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."
_​_
__*So no, it's not about the maximum amount of light you
can throw. It really is about the minimum amount of 
light required. *_










​


----------



## Genzod

*
Everyone is Not the Same!*

People have varying degrees of eyesight. The chemical reactions with light acting on pigment in their eyes can be different, their ability to focus and the ability of the pupil to open when adapted to dark.

Assume for the moment everyone eats their carrots and they have similar pigment function. We go to a range and place a 2x6" white paper target against the bark of a pine tree isolated from direct light sources. It is the only white highly contrasted object in the area, and we know where the target is. It is summer time, clear, and humidity is moderate for a mid-atlantic state in the continental US (CONUS). There is no moon.

Dark adapted pupil can vary from 4mm to 9mm across all age groups.

Acuity can vary widely, but lets assume for the moment most people are corrected to between 20/40 and 20/10, 20/10 of course being something a pilot might covet. 20/40 might be something a blind person who wants to drive a car might covet. For a 2x6" sized target, this means acuity range can vary between 87.5 to 350 meters respectively.

To demonstrate what happens with naked eye seeing performance for this 2x6 target using the Intensity vs. Range function described in earlier posts, I plot distributions for *20/40 (red)*, *20/20 (yellow)* and *20/10 (blue) *vision. Each acuity classification retains its color, and I make a plot for dark adapted pupils from 4mm-9mm, incremented by 1mm at a time.

As acuity improves, the color groups shift to the right (increased range, and that makes sense). 

Within each color group, improved dark adapted pupil (wider) shifts the plots to the right (increased range, again makes sense).

Here are the plots for possible range up to 280 meters using a flashlight with up to 500,000 candela.

*CLICK FOR PLOTS*

(Plots should be functioning correctly now. Microsoft Explorer probably couldn't handle the address length when using it with this site's editor.)

Notice how the groups shift to the right as vision improves. 

There is some overlap of curves at this zoom of scale, and that changes the color of curves slightly. You can control scale by changing the limits of the x and y axes.

*
As an example using the flashlight in the photo:

*​




​

With a 260,000 candela flashlight depicted by the *green* horizontial line (my _magical_ flashlight, *Skylumen Aspheric18*, which I am under a contractual obligation for your safety (and Vinh's :laughing not to let you borrow ) and absolutely no additional ambient light (you'd add Ambient*x2​ to the green curve function, i.e. *260,000+0.085*x^2* in the frame for the green curve if your ambient is 0.085 lux on target which is typical of my test site during summer with no moon and light pollution only: this plot):
​

*20/40* vision with *9mm* pupil marginally sees the target at 188 meters (189 m with 0.085 lux ambient).

*20/20* vision with *9mm* pupil marginally sees the target at 228 meters (229 m with 0.085 lux ambient).

*20/10 *vision with *9mm* pupil marginally sees the target at 236 meters (237 m with 0.085 lux ambient).​

​Hopefully I did that correctly, and I won't have another surprise visit from a Lancaster bomber._*

TALLY-HO! Bombing runs to do, sorties 
to complete. Pip, Pip! *_








0.085 lux is ambient light pollution in a city affecting a tree nestled away in isolation from direct light. For backpacking in a forest with good leaf cover and virtually no light pollution, I would assume zero ambient and just use the intensity of the flashlight only in my calculations.

Remember, there is no glare from spill light affecting pupil diameter accounted for in my equation, which is why the concentrated spot of a powerful zoomie with little to no spill complements the plot over range. Also understand while it takes only a minute or so for pupil to adapt to dark from bright light, it can take up to 30 minutes for eye pigments in rods to adapt to dark, and this is the condition the curves were adjusted for.
​​


----------



## Genzod

My *Skylumen Aspheric18* order is in the mail and a Saturday delivery is anticipated. I'll give my initial impressions soon after, and eventually conduct a field test employing the intensity formula to make an estimate of the flashlight's power, specified as 260,000 cd.

Vinh originally had a Cree XPG2 PDT in this T20 host yielding 125,000 cd. (Note: This version is no longer available, the page has been removed and is only available from Google cache--DO NOT ATTEMPT TO ORDER THE OLD VERSION :scowl: Are you DAFT? ). Replacing the XPG2 PDT with the Oslon Black LED represents a 2.1x increase in candlepower, a 17% increase in flux, and a 1.4x increase in throw distance (0.25 lux to 1020m).

That's a lot of punch for a 6.0 oz 1x18650 flashlight! :huh:


----------



## Genzod

ssanasisredna said:


> Can you please factor in how recent rains impacting the albedo of the targets would impact the calculations?



I've done a small amount of research on this, and I think I can make an estimate on the specific problem I am working on (2x6" white blaze target on tree). I'm not trained in this, so take it with a grain of salt. 

First, the contrast coefficient = (intensity of target - the intensity of background)/(intensity of background) or*

C=(It​-Ib​)/Ib​*

where *It​=Io​*At​* and *Ib​=Io​*Ab ​* (I=intensity; A=Albedo; t=target; b=background; o=at target)​

Since the incident lux on target *Io​* is virtually the same whether on the target or background, the albedo is the percentage of intensity coming back to you. Therefore we can divide out the incident intensity *Io​* and use albedo of materials to determine contrast coefficient.*

C=(At​-Ab​)/Ab​*​

But we need more than contrast. We need an idea of how change in contrast of the target and background affects the intensity required to marginally identify it.


TEEJ says:_
_



_

"My best guys could hit stationary white paper at 200 m with ~ 0.5 lux, and an illuminated scope, but needed ~ 3.5 lux for the same target with a non-illuminated scope. These are guys that can drive tacs in daylight...and yet miss the entire target 3/4 of the time under these conditions._​_
_​_If I swap a rusty steel plate for the white target, none of the scopes could FIND the target with that lux level, needing about 3x more light to find that lower contrast plate...let alone aim." _​

I interpret this to mean, TEEJ's _merry men in tights_ need 0.5 lux to FIND the 3x3 ft white paper target at 200m, then to hit it, an illuminated sighting reticle is required for aim. (The target is small in the field of the suspected 4x32 scope and illuminated crosshairs in darkness are required to aim and hit it.) When the albedo of the target changes (paper to rusty plate), he needs 3x the lux to FIND the target--1.5 lux.



I can compare the change in the contrast coefficient for this problem and see how it relates to the change in required intensity to find the targets.
*
Albedo for materials:* (approximate based on internet sources)

White Paper = 0.65 (0.6-0.7)
Rusty plate =0.25 (close to terra cotta tile, autumn foliage)
Dry Pine bark = 0.115 (average conifer forest, 0.08-0.15 would prefer bark because this is as seen from the sky)
Wet pine bark = 0.05 (similar to wet grey dirt or average of wet/dry black soil)​
We'll assume the albedo of the background in TEEJ's target shooting is 0.05--this sort of divides out and doesn't really matter.
*
Cpaper​=(0.65-0.05)/0.05

Crust​=(0.25-0.05)/0.05

Crust​/Cpaper​=0.2/0.6=1/3*​

So the contrast is 3x worse. If it requires 3x more illumination sent to target to compensate for 3x worse contrast, then there seems to be a linear relationship between contrast and intensity.

In my situation with the white paper on pine bark, we can compare dry to wet bark and the white paper:*

Cdry​=(0.65-0.115)/0.115

Cwet​=(0.65-0.05)/0.05

Cwet​/Cdry​=(0.6/0.05)/(0.535/0.115)= 2.58*​

I would need 1/2.58 less intensity sent to target for wet bark as opposed to dry bark or 39% as much intensity required for dry bark. 

This number would be better if I had the albedo for pine bark of a _trunk_ rather than a coniferous forest as seen from the sky, which includes green pine needles and ground cover. Worn/old (cracked) asphalt (rocky grey) like that in front of your residence when your municipality, engorged with your property tax dollars, neglects your street repairs, so that the mayor and his cronies can give themselves raises and bonuses, or more subtly, procuring themselves kickbacks by favoring contractors and bending building codes and zoning regulations, is similar to an oak tree trunk and has an albedo of 0.12, so pine bark being darker might have an even lesser albedo somewhere between dry black soil 0.05 and 0.12 for worn asphalt. If I take the average of that range as 0.085, then *Cwet​/Cdry ​*becomes 1.8 or 56% as much intensity as required for dry bark.

This calculation is untested in my case, but appears to work for TEEJ's case. I'll have to go out to the test site and and see if wet bark really does substantially reduce the need for lamp intensity.

As a generalization, if it rains and bark becomes soaked, my plotted intensities can be halved to predict the threshold intensity required to marginally detect white blazes. 

Also note that average albedo for white paper is 0.65 and white paint is 0.8. There is a small difference between white paper (used in the experiment to emulate a painted blaze) and white blaze paint. The white paper curve of my experiment, therefore, slightly over estimates required intensity for marginal identification of the _painted_ target by a factor of 1.28. The difference, however, would be less than the ability of the eye to detect it, if compared side by side. 

Nevertheless, the 3.25x25 scoped identification range with 260,000 cd pencil beam utilizing my gorgeous 8.5mm dark adapted pupils :naughty: and perfect Twiloite 20/20- 20/20 vision would be extended from 330 meters to 351 meters--See plot.* (dividing the *orange* intensity required curve for white paper by 1.28, shifting it to the right becoming the *red* curve for white paint, and finding the intersection with the *green *horizontal line at 260,000 cd). I would have to experimentally confirm the 0.65 white paper and 0.80 white paint values are representative of my targets and actually would produce those results.

*The *grey* and *black* curves of naked eye viewing represent the 28% improvement shift white paint provides over the albedo of the white paper target used in my experiment (229m ---> 244m @260,000 lux of the max output of the *Aspheric18*). The *second lower green line* is a 1.7 magnitude decrease in max intensity. It represents the distance I can _more easily _recognize the target with max output. While I could barely see the target at 229m/244m with max output, I can more readily recognize the target with max output it if it were 200m/214m (about 30m closer, which has the same effect as bumping up the flashlight 1.7x higher for better clarity). 

*Try it! (It's terrible **)*

(On the FooPlot graph, click the orange icon with the point on the line at the lower left of graph when pointer is over graph and place a point on the curves). What distance can I more readily recognize the white paper target for the _scoped _viewing at max output? For the painted target?  How many meters improvement does paint provide over paper for that situation? (hint: 6.23% improvement)


----------



## hahoo

what have i stumbled onto here?
this confuses me....


----------



## Genzod

hahoo said:


> what have i stumbled onto here?







​


hahoo said:


> this confuses me....







What? You don't understand my _meticulously_ explained posts?







All kidding aside, *Hahoo*, (must...control...urge...), tell me what it is that confuses you, and I'll give it a go to try and explain it a little more clearly. ​


----------



## Genzod

*Why I Prefer a Powerful Zoomie over a Throwy Reflector Flashlight for White Blaze Target Searches*


First photo, *666* :devil: grams of hat taping wonder, the *Thrunite TN42*. Second photo, a zoomie flashlight, the TMA*66* :devil: on full zoom. 
















Reflector types provide spill that is helpful for seeing the immediate foreground while making searches in the distance, but they can provide too much spill when at max output because spill is proportionally increased with spot intensity, and that extra spill while making searches can provide a lot of glare, reducing ability to effectively see targets in the distance, which is probably why you bought the flashlight in the firstplace.

Take for example the *Aspheric18*. If a person with 20/20 vision and 8mm dark adapted pupils (average 20 year old) were to conduct a search for white blazes on the Appalachian trail, his limit of observation would be 217 meters with 260,000cd of max mode. But if he has a reflector that threw the same intensity, the spill light would constrict his pupils. If the glare constricted his dark adapted pupils to 3mm, his limit of observation (for the white blaze) would now be diminished to 136m. That's roughly a 37% loss in range according to this performance plot. (Each yellow line represents a different pupil diameter incremented by 1 mm, left to right is 2mm, 3mm, 4mm.....up to 9mm, and the green line is 260,000 cd intensity). So the TN42 might be a great flashlight, but the max throw range figure is a little deceptive, isn't it? The the equally powerful glare can make that throw in certain situations meaningless and impotent.

And what good is having a big flashlight if it's impotent? 







Most of the time, I'm on a trail with large trunked trees right next to me. The spill light would practically blind me against those close trees. In my case, a zoomie is the answer to doing blaze searches on forested trail. If I need _comfortable_ spill light for walking (10-50 lumens), it's better provided by a separate headlamp that I can keep consistent. Spill from a 2000 lm flashlight is overdoing it for foreground illumination in my case.


​


----------



## Genzod

*
I Just Discovered Recoil Lamps!*
Recoil lamps provide highly collimated beams utilizing nearly 100% of the source light (the heat conductor sinked to the host blocks some of the light). The source is positioned forward of the parabolic reflector and aimed backward, so as to send light to the mirror which is reflected toward the target. 

Since it was recommended contrary to my obviously errant rationale, that minimum lux required to identify a white blaze target correlates to minimum weight of lamp for ultralight fastpacking, that _"__minimum' is not really what it is all about, instead you throw as much light as you can and can either identify the target or not"_, I figure I can't lose with 32,000,000 candela of the Spectrolab Nightsun Sx-16. Not too shabby for 38 lbs (17.2kg)! And I could carry the 72 lb (32.7 kg) battery for it in my backpack, which I could probably keep charged with a pair of crystal pressure pads in my running shoes, although I'm not quite sure yet where to re-position my displaced food and gear. 

Keep sending all the great advice to help me with my only _'for fun'_, impractical and merely _'theoretical_' research, guys! I won't stop giving you the praise and credit! After all, _you deserve it! _:thumbsup:








*BVH*, you actually own this thing? No wonder you mentioned the SX-16 spec--32 lux @1km! Whoa! What a BEAM! :rock:






*
Fry it, baby--YEAH! *_*Lucille likes her eggs sunny-side UP! *
_



*

*​


----------



## Genzod

*
The Ambient Intensity Received at Target Daaaaaabble Check


*





Two things concerned me about my back calculation of ambient intensity received at target. It came from a 5th order regression with one point wildly off, and the entire function f(x) is piece-wise (in two parts) divided at the acuity limit of my vision at the time, xo​=87.5m. You can't regress a piece-wise function and expect it accurately depict both functions, especially outside the domain of the regressed data.

So I re-evaluated the regression, excluding the errant portion of the collected data, utilizing only what experimental data points I had where x<87.5m. This portion of the curve is consistent with the square law for light, so I could regress a second order equation from the data and back out a very accurate value for ambient light received at target, then compare it to what I backed out of the 5th order equation.

Recall that I had set up a headlamp on tripod at various distances from the target, such that lux received at target (lamp only, not ambient) had values of 1/8, 1/4, 1/2, 1, 2, 4 and 8 lux. I went a distance x for each value and determined a corresponding x for each intensity. Those were 46, 58, and 79 meters (for x<87.5m only), respectively.

I also determined a distance x for no _added_ light. This would be the position that has the corresponding value of lux for 'ambient received at target'. Since there is no error introduced by a lamp at this x, I considered it the most valid and accurate point, and therefore weighted it accordingly so that regression would insist the curve go exactly through this point while relaxing the requirement to go exactly through the others.

Keeping in mind the following boundary conditions, that the curve must go through the origin (0,0) (*limit I(x)=0 as x-->0*) and the slope of the curve is zero at the origin (*I'(0)=0,* i.e. FLAT at *x=0*), I regressed the _lamp only_ values corresponding to x, and controlled a point (0, k) where k was free to vary until the boundary conditions are met. 

Since we are dealing with the square law here, the quadratic *f(x)=a+bx+cx*, has *a* and* b* terms will not exist in the final solution. That means simply for our purposes, choose a *k<0 *and keep moving it up in value until term *b=0* (or approximately zero). I evaluated k through multiple regressions until b was of the order of 10-13​, which is essentially zero.

When boundary conditions were met,​*

k=**-.0766685039 

*and* 

f(x)=-0.0817715857788-1.95586304314e-13*x+9.43897759453e-05*x^2*.​

You can readily see that the derivative of the function *f'(x)*-- *f'(x)=0+b+2cx* evaluated at 0 is *f'(0)=b *or *-1.95586304314e-13,* which is essentially zero. This just means the curve is flat at *x=0*.

Then we subtract out the *a=**-0.0817715857788* to move the curve up to the origin to meet the boundary constraint for the limit. 

Now that we have both conditions met, we can plot the curve and determined the value of *f(x) *at 30 meters which is determined to be *f(30)=0.08495* lux. 

See plot. (*Blue curve* is the pre-acuity limit square law of the recent regression sans first two terms, the *red curve* is the derived formula utilizing 0.085 lux ambient at target. *Green points* are experimentally derived data points, and the *black curve *is the former flawed 5th order polynomial regression of the original data (flawed by my penchant for _good fudge_).

I have been using the value 0.085 lux at 30 meters to define the formulaic curve. Since 0.085 is just 0.08495 rounded up to two significant digits, the back calculation of ambient intensity at target formerly derived by the 5th order polynomial is unaffected, and the derived equation is still valid. 

And why shouldn't it be? It passes quite nicely over and through the collected data points depicted by green dots (except over the last, errant data point, which only a hydra-ambulatory Jesus could have accurately determined and obtained for me that inquisitive night at lake's edge, and I shame-facedly had to fudge because I just _can't_ resist good fudge.)

_*?*_

No...still not that kind of fudge.

Who owns this damn horse that keeps pooping on my thead? 








My _magical flashlight_ is out for postal delivery today, delayed perhaps by the thunder-boomer blizzard that passed up the eastern seaboard of the continental US a few days ago, leaving street icebergs in its wake and leaf springs and axles all over the roads. (Yes, I saw these). 








Or maybe the postal guys with the x-ray machines found it and decided to play with it for a while. They, of course, can afford to do this without fear, as they enjoy such a high quality level of healthcare in their compensation package. But then, I would NEVER threaten an agency of the US gov't or its agents! Especially if it were as _tyrannous _as USPS! And if you don't believe that, try telling them that your credit card company does not require them to check your card for $3.00 purchases. 







*
*​


----------



## Genzod

*
The magical flashlight has arrived!*

Pulled out the scale to verify the 3.8 oz empty weight Vinh at Skylumen assured me the Aspheric18 was--twice. It seems to have magically added 2.2 oz in the mail. (Hmmm...Must have had a heavy in flight meal.)

Honestly, (silliness aside) I think his scale must be off. That or there's a little dyslexia going on on his side of the American continent, too. *107 grams* (3.77 oz) vs. *170 grams* (6.00 oz) :huh:. I don't think he intended deception. I validated my scale with 6 oz of coins and determined the theoretical total from their known weights, and my scale matched the prediction.

*EDIT:* Vinh confirms, a wire and some paper were interfering with his scale reads.​
The *Aspheric18* is also in a *T20* host that has a known 6 oz empty weight. I knew this. I should have trusted my instinct on this one that Vinh was somehow not getting the weight right when I asked him to weigh it for me, but I went against my better judgment. He doesn't list product weights, so he was just trying to do me the favor. I guess I have to accept responsibility for the return shipping and count it a lesson learned.

*EDIT: *Vinh assured me the scale read was his error and he has offered to cover my return shipping costs. 

I'm slapping myself. (But I think I'm starting to enjoy that a little too much. )​
I've requested full reimbursement for this order under his assurance of "try it out--no hassle returns". He's complied in correspondence. So credit due where it is due.

We'll see how that pans out. And if it does, you'll certainly find out about it, after all, I do reward those who treat me well with showers of high praises!  

Seriously though, if anyone can put up with a looney toon like me (I prefer to call it--_'entertainer'_), that Vinh is one high caliber dude. I'll give him that.
_*
Tune in next week Bat Fans! *__*Same bat time, same bat channel!*_​






The *Skylumen Aspheric18* is pretty bright though. I don't doubt Vinh's posted intensity spec. I shot it about 8 ft to a white cardboard box at focused max output, and the reflection was actually quite blinding. I think my eyes started to bleed. I was seeing red. Probably need an arc-welding glass using this thing. This light saber is sharp--yeah, baby!








If you don't have any weight constraints like I do for fastpacking, this 6+ oz flashlight is the bomb! He's really got a gem here. *Breaks my heart to have to send it back. *:mecry:I really wanted this to work.

I'll probably end up pimping out a Cree Q5 host now with a remod. That'll run me a little over 2 ounces. It won't hardly come close to 260,000cd, but I really don't want to be carrying a 6+ oz flashlight, either. Trying to keep pack weight below 8 lbs is a pretty difficult task. Every ounce counts. I had room for 3.8 oz, but unfortunately, not for 6 oz.

Vinh has a lightweight 50,000 cd pocket rocket in a Q5 host, the *'Wenger Oslon Zoomie' *but it's only single mode--max. I need max for blaze searches but lower multiple modes as a back up light for tasking, walking and running.






​


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## BVH

Genzod said:


> *
> I Just Discovered Recoil Lamps!*
> Recoil lamps provide highly collimated beams utilizing nearly 100% of the source light (the heat conductor sinked to the host blocks some of the light). The source is positioned forward of the parabolic reflector and aimed backward, so as to send light to the mirror which is reflected toward the target.
> 
> Since it was recommended contrary to my obviously errant rationale, that minimum lux required to identify a white blaze target correlates to minimum weight of lamp for ultralight fastpacking, that _"__minimum' is not really what it is all about, instead you throw as much light as you can and can either identify the target or not"_, I figure I can't lose with 32,000,000 candela of the Spectrolab Nightsun Sx-16. Not too shabby for 38 lbs (17.2kg)! And I could carry the 72 lb (32.7 kg) battery for it in my backpack, which I could probably keep charged with a pair of crystal pressure pads in my running shoes, although I'm not quite sure yet where to re-position my displaced food and gear.
> 
> Keep sending all the great advice to help me with my only _'for fun'_, impractical and merely _'theoretical_' research, guys! I won't stop giving you the praise and credit! After all, _you deserve it! _:thumbsup:
> 
> 
> 
> 
> 
> 
> 
> 
> *BVH*, you actually own this thing? No wonder you mentioned the SX-16 spec--32 lux @1km! Whoa! What a BEAM! :rock:
> 
> 
> 
> 
> 
> 
> *
> Fry it, baby--YEAH! *_*Lucille likes her eggs sunny-side UP! *
> _
> 
> 
> 
> *
> 
> *​



Already done that.

http://www.candlepowerforums.com/vb...ng-completed&p=4341902&viewfull=1#post4341902

Genzod, I hate to say it but it looks like you're talking to yourself in this thread.


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## Genzod

Okay, gang. Vinh at Sky Lumen checked his scale at my request and he found some paper and a wire were impeding the tray and causing a misread. He's accepted responsibility for the error and is covering return shipping. I don't think anyone should have anything to fear about doing business with Vinh. He's a straightforward, honest proprietor.


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## Genzod

BVH said:


> Already done that.
> 
> http://www.candlepowerforums.com/vb...ng-completed&p=4341902&viewfull=1#post4341902
> 
> Genzod, I hate to say it but it looks like you're talking to yourself in this thread.



Why would you say that? The thread has 12,442 hits. It's just that contributions have pretty much dried up. If people want to read my journal on this exploration, have a laugh, maybe learn what I've learned about scopes, lights, vision and targets. Great. But I don't think I'm talking to myself. 

I hope you didn't say that hurtful remark thinking that I was mocking you. I actually appreciate your earlier contribution to this thread about the Nightsun spec possibly indicating what useful light is for identifying targets. It was some other guy that recommended I get the most light I can throw, not the minimum, intentionally contradicting my clearly explained and reasonable rationale, and for that, the sarcasm humor is directed at his 'helpful' advice. I'm sorry if that was taken the wrong way.

I'm not sure what you mean by "already done that". Did you think perhaps I was trying to? I actually got the 72 lb figure for the weight of the battery from the very page you linked since the weight adds weight to the humor of the sarcasm. I wouldn't assume to have copied or plagiarized your work. That kind of hands on project is sort of beyond the skills of this engineer/mathematician.


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## BVH

Genzod, I should have added a big grinning smilie at the end of my post as it was intended in a humorous tone. You're almost the only poster over the last month.

Already done that meaning that I made myself the NightSun battery powered headlamp already. Again, humorous tone which can't be detected over the Internet.


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## Genzod

BVH said:


> Genzod, I should have added a big grinning smilie at the end of my post as it was intended in a humorous tone. You're almost the only poster over the last month.
> 
> Already done that meaning that I made myself the NightSun battery powered headlamp already. Again, humorous tone which can't be detected over the Internet.










The post left me wondering! I knew you had made the _battery pack_ already (video), but the _headlamp? _Hard to see headlamp in "done that" even with a smiley! I had seen your video about the battery pack a few days ago when I made the referenced post, and from reading your voice there, I would have thought you would be the last person to react to a post, and it's clear now you haven't. Yet there it seemed to be. Sorry to imply another meaning to your motives. 

I feared maybe I had confused you myself, using sarcasm to make light of how someone took my thread out of context and dismissed my rationale for the purpose of this thread. I mixed you into that using your light and it's weight to demonstrate how absurd his 'helpful' advice was. I thought I might have provoked a reaction.

I sort of see this thread as a journal as my understanding of light, vision, reflection and optics develops. I doubted myself after so few responses as of late that people weren't reading the thread, yet 1000 hits in the last week and 11,400 more since July when it started. That to me is sort of funny in itself. Didn't see that coming. I sort of just wanted to lighten my pack, whittle it down to perfect lightness. Sought some help, had some fun.

Of course I haven't entirely dismissed the thought that people aren't interested in the material but just want to come and see a geriatric man make a fool of himself. But I don't mind, I just have another 'coke and a smile', and wipe my nose before anyone thinks I'm eating powdered donuts--especially cops, who seem to like donuts as much as I do. But then, you're retired and old enough, so you know about the fellow below and how much he liked to have a coke and a smile, too!

*"SHAZBOT! Leave my donuts alone, you vile Terran 
moochers! EEN EEN EEN EEN!" *


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## KITROBASKIN

It is amazing that this thread has so many views. Thinking a lot of folks enjoy the zany quotient. 



Genzod said:


> That's a lot of punch for a 3.8 oz 1x18650 flashlight! :huh:



The fact that no one commented on the 3.8 oz claimed weight of an aspheric flashlight of that size seems to indicate members do not want to take a chance and mess with your dance. 

The albedo scene was pretty funny, responding full on dead serious with interesting research of yours.

The whole monocular thing smacks impractical big time, based on personal limited use at night with optics. Then adding a light source with virtually no side spill to monocular use... And that is while running with a pack in gale force winds.

I am prepared to get the Genzod browbeat.


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## FRITZHID

IME, most views are due to curiosity... i think many more are just for "marking read" in order to clear a forum, i know i often click on a thread just to peek and clear that particular forum line.
I know i did on this thread in hopes of something relevant. :thinking::shrug:


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## Genzod

KITROBASKIN said:


> It is amazing that this thread has so many views. Thinking a lot of folks enjoy the zany quotient.
> 
> The fact that no one commented on the 3.8 oz claimed weight of an aspheric flashlight of that size seems to indicate members do not want to take a chance and mess with your dance.


​






Are you saying I have the dance floor to myself, not because I dance so well, but because people are guarding their toes? SHAZBOT! And here I was thinking I was the _dancing queen!_ But you have steel toed boots, you clever boy. And you can't resist the urge to get close to these sexy hips. Fortune favors the bold.​​







> The albedo scene was pretty funny, responding full on dead serious with interesting research of yours.




Yes, intriguing stuff. Can't say I'm quite there with it yet. I think it pretty straightforward that an albedo change on an almost fully black, invisible background is linear, but I do wonder about the one case I'm interested in, that has a visible contrasting background like a tree (0.12) surrounding the target, (0.65). My other half has a friend who is an MRI Tech, whom I intend to ask about this subject since Weber Contrast is a topic that entailed part of his studies. 

I might (as an allegorical example) present a seriously detailed exploration of the anatomy and document my understanding of it thus far, but as I pass by the naval, you're going to have to endure the innate joys of the _lint cheese_ there as well. ​



> The whole monocular thing smacks impractical big time, based on personal limited use at night with optics. Then adding a light source with virtually no side spill to monocular use... And that is while running with a pack in gale force winds.




My experience with US Navy field binoculars back in the 70's demonstrated to me that I can see better at night with them, even stargazing, not _simply_ because a large objective lens collects so much light (as is the common misnomer) but because it _also _puts my virtual distance so much closer to the target where less received light is required (square law). Sure, magnification dims surface brightness, but visibility is the combined result of both. Having a large exit pupil is more helpful, but smaller ones can be compensated with more light.

I used an 8x21 scope (a scope selection for night use most people would cringe at) on my target which I could marginally make out at 38 meters (ambient only), and it truly did extend my visual range to 75 meters, without anything other than ambient light received at target, just as the math predicted. What mattered, I discovered, was that I needed to learn how to handle the monocular so I could find the target more readily. Adding a narrow beam of light on target would obviously only help matters provided particulate scattering in the beam doesn't block the direct line of sight to the target. Consider that ambient light might come from the moon, a house light or street lamp. In a forest with virtually no ambient light, I could cast the same amount of lux I have in the city at a tree with a lamp and use the scope at 75 meters to see it. The source is irrelevant. What matters is lux received at target.

Most people would think that an 8x21 scope would be useless in the dark because the exit pupil is so small 21/(8+1)mm in relationship to most young person's dark adapted pupil, but with the math describing the physics, it actually works where most might think it won't work. Remember, TEEJ'S merry men in tights are using scopes at night in tandem with light to hit targets at 200 meters. Even cheap monoculars can work almost as well as these expensive scopes (about twice as much light required I found in the 3 cases I demonstrated), simply because they have much fewer optical surfaces causing transmission losses. 

Actually, I believe it was your introduction to scope math that inspired me to research the use of a scope and a lamp as an aid to finding those sometimes elusive blazes.

By the way, in gale force winds on mountain ridges, I don't run--I put on my rain poncho and glide.  (Remember...I'm BATMAN. SHHHH!) ​









> I am prepared to get the Genzod browbeat.



_*You know you want it... :naughty:*_

​


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## Genzod

FRITZHID said:


> IME, most views are due to curiosity... i think many more are just for "marking read" in order to clear a forum, i know i often click on a thread just to peek and clear that particular forum line.
> I know i did on this thread in hopes of something relevant. :thinking::shrug:


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## KITROBASKIN

If the optic can be stabilized seriously well, the image from an 8X21 can be helpful and more can be seen at distance is what I found. Hand holding an optic is borg-like.


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## Genzod

KITROBASKIN said:


> If the optic can be stabilized seriously well, the image from an 8X21 can be helpful and more can be seen at distance is what I found. Hand holding an optic is borg-like.



8x is on the border of shaky is my experience. I had a hard time with it at first, not having any prior experience with such devices. But with a little thought of what was necessary to make it work, I realized I could thereafter find the target easily.

I prefer the 3.25x25 scope, which would not only be easier to use, but has a larger exit pupil to support brighter images at night, has a larger field of view and it's very light. It also has similar performance to an 8x21, a tad better actually, and it's less than half the 76 grams of the larger, 34-37 grams. 

What I did to find target on the test night was stabilize the scope in my hand while squatting, hold my right elbow with my left hand resting on my leg to dampen movement, aim at the top of the tree where there was contrast with the sky, use that edge to focus, then follow it down to the trunk where I knew the blaze was. I moved back from naked eye maximal range of 38 meters 2 meters at a time, so as to reduce brightness incrementally and be certain of the interval where I do lose it due only to insufficient lux.

This wouldn't be the procedure in the forest while running of course, unless I was really stuck in a lost situation. I would be using more than 1.7x minimal required lux to search a certain range for targets and the optic would be bio-mechanically grafted into my skull in Borg-like fashion for improved stability. The minimal search of the test night was just to confirm the predictive math I was using.

So did you find my trademark 'brow beating' pleasurable and validating? First one is always free.


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## KITROBASKIN

Some of us always carry phone/GPS and have pre-informed 'Home Base' of our intentions, just in case a bailout survival situation evolves as a result of trying to remove an optical implant while gliding through gale force winds looking for little white thingies.


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## Genzod

KITROBASKIN said:


> Some of us always carry phone/GPS and have pre-informed 'Home Base' of our intentions, just in case a bailout survival situation evolves as a result of trying to remove an optical implant while gliding through gale force winds looking for little white thingies.



https://i.imgflip.com/22j4eg.jpg 

Most of these "little white thingies" are easily seen every 30-50 meters with my headlamp, most of the time. I don't really need to "search" for blazes, so to speak. But then, I either wander off the trail, come to a trailhead (road) and the trail picks up someplace else along the road, or I enter wilderness area and the markers are spaced 0.1-0.25 miles apart. When I get to a point I'm wondering if I've gone off trail, I need to look far down trail for a blaze to save myself a lot of time backtracking. So then I stop, pull out the cannon and if necessary, the scope and conduct a search. It's not something I'm really juggling with all the time. 

But the image of running (sometimes gliding) with scope and hand held, pack in tow, gale force winds blowing through my hair does sort of look kind of funny.


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## KITROBASKIN

Been communicating with Genzod via PM and wanted to say that his objective is more clear now. He was able to distill his work for an experiential mind like mine. And he was patient when I kept on countering. Chasing ever bigger lumen counts in a flashlight is not going to solve real-world challenges but it is a lot of fun for some members.


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## Genzod

KITROBASKIN said:


> Been communicating with Genzod via PM and wanted to say that his objective is more clear now. He was able to distill his work for an experiential mind like mine. And he was patient when I kept on countering. Chasing ever bigger lumen counts in a flashlight is not going to solve real-world challenges but it is a lot of fun for some members.



I want you to know I appreciate your vote of confidence. I'm really only after the truth, and I love to share the truth with others once I've confirmed it. 

I'm pretty much a light noob. I know so little about the technical aspects of light and flashlights, but I'm trying hard to get at the truth that will help me accomplish my goals and solve my problems which in turn will perhaps eventually help other's as well. It is fun to discover what is true, what predicts and what works. It is even more fun and pleasant when someone recognizes the fact that that is what I'm really all about and encourages others to join the adventure.


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## Genzod

KITROBASKIN said:


> Been communicating with Genzod via PM and wanted to say that his objective is more clear now. He was able to distill his work for an experiential mind like mine. And he was patient when I kept on countering. Chasing ever bigger lumen counts in a flashlight is not going to solve real-world challenges but it is a lot of fun for some members.



I'm not sure I understand the relevance of the last part of your comment. What exactly is lumen chasing, and how are you connecting that here?


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## KITROBASKIN

Your objective is to be effectively efficient. Others here are having fun and do not care how portable or lightweight their gear is, or if it meets a minimum standard for the job at hand. A person like myself, prefers to get the flashlight and see if it works for the task. If it doesn't, get another! I have a pretty full spectrum of throwers and really do not use the two most powerful because they are heavier and much more power than needed for our terrain.

Also, a lot of folks here do not know that a flashlight that puts a lot of light out nearby will impair the ability to see at a distance (and those that do will sometimes choose to get a light that can also spit out a bunch of lumens at distance, making for a very big, quite inefficient tool). One can guess that very, very few people actually have a bonefide application for some of these blasters but they are having fun, and GOOD for them.


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## KITROBASKIN

Oh, and careful How you question the relevance of other's comments and don't Ever tell me to "exactly" explain anything again. Do you understand?


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## Genzod

KITROBASKIN said:


> Oh, and careful How you question the relevance of other's comments and don't Ever tell me to "exactly" explain anything again. Do you understand?



I certainly don't see the relevance of_ that_ comment! :thinking: Perhaps it's a threat, maybe not. Would you like to clarify that for us? I wouldn't want to read a meaning into a comment that just isn't there, after all. 

Requests for clarification are usually made by those of us who don't want to jump to conclusions, and would rather hear a matter fully before judging it. That's why I ask for clarification, to give yourself a chance to be fully understood. Maybe what you said was with a sense of humor and I didn't see it. Perhaps a smiley emoticon would have been in order. That usually clinches it! 

I didn't question the relevance of your comment. I said I did not _understand _the relevance of your comment. Context, context, context. 

Either way, I'm not afraid of these kind of outbursts. They look kind of silly to me. I hope they eventually look kind of silly to you, if you are of similar age as myself, and have had plenty of time to learn otherwise.

Now please, can we all get back to the subject at hand, not me, not the validity of the enormous number of visits to the thread, not whether I seem to be talking to myself, not the impracticality of my endeavor or the seriousness to which I am pursuing it? And certainly not whether or not I am going through a middle age crisis, as if that had anything to do with it?

I have much more to explore here. I have yet to experimentally confirm the answer to the question *ssanasisredna *posed about albedo. I have a flashlight with specs in mind that I would like to find and test out with the predictive power of the mathematical tool I developed. I have yet to adapt this formula to all sorts of targets as I have with al sorts of eyes. Isn't that valuable and relevant to any of you?

Yet some of you, not all, just a few, a small few, seem intent to disrupt the forum with dismissals or outbursts designed to provoke off topic arguments and have moderators lock down this thread. If you don't have something topical, constructive and soundly documentable or experimentally demonstrable to say, and if not, at least nice or funny or thankful like some who have made this thread an enjoyable experience for me and others, it probably isn't worth saying at all.


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## Genzod

*
THE PURPOSE OF THIS THREAD*

In engineering, students learn mathematical techniques for designing systems, among other things, such as language skills and laboratory procedure, so they can be proficiently astute to qualify for employment at engineering firms which are often contracted by the government sometimes for contracts worth tens of billions of dollars to design a system or vehicle. This is done on "paper" first, utilizing computers mainly, perhaps produce some small scale models (if aerodynamic data is required when computational methods aren't satisfactory), then they build a prototype, flight test it, and work the "bugs" out. When the vehicle is ready, it is usually compared with the product of a rival firm who was tasked with meeting the same design criteria. The products are compared, a decision is made, and an order is placed by the government for 100-200 or so of these vehicles to be delivered over the space of a decade or two for around $140 million per unit.

They do not build a prototype, fail, build another, fail and keep iterating this irrationally expensive process until they get it right. There are much smarter ways of designing costly systems than the tried and true backwoods method of trial and error.

My mother had a dog once that used trial and error to find the center of gravity of a plumber's plunger while carried in his mouth, his mouth of course only inches away from the rubber plunger. My mother, bless her heart, was a farm girl from a foreign country, and she said "look how smart he is!" Saying nothing, I thought, "mom, he has the business end of a toilet plunger in his mouth." :laughing:

Scientists take the time and trouble to develop the mathematical tools for engineers, so they can have the tools to build these expensive systems on paper first. Once the tool is developed, it is tested and confirmed by peer review by likewise intelligent scientists. These sophisticated shortcuts save people a lot of time and trouble and render the design process much easier, quicker and less costly. This process was demonstrated to members here (in a layman sort of way) for the mathematical tool that governs determining throw for a flashlight with an aspheric lens, right here at CPF.

Of course our pocket books are much smaller than the government's, and certain people might prefer not to accumulate a $1000-2000 arsenal of flashlights in an expensive trial and error process.

I am developing a mathematical tool that can be adapted to most eyes and most targets, so that when you get a hankering for a flashlight, you can use the tool to determine the spec of a flashlight that will meet your visual and targeting needs without having to procure a flashlight hobbyist's arsenal of expensive flashlights and then not be able to send your son or daughter to college so he/she can become as smart as a certain handsome, sophisticated, worldy sort of fellow contributing to this forum. 

I realize this procedure is unfamiliar to some people. It might even feel intimidating and rub these persons' grain the wrong way, even to the point of eliciting a narcissistically snubbing and dismissive response. Or, one might be hard pressed to seek some kind of self-validation for they way _they_ approach the selection process for a flashlight, and thinking one did not obtain it, might lash out in fear at the thing or person he doesn't understand.

I am an engineer with a high level of mathematical expertise. What I have been doing is the job of a scientist developing a tool that I will ultimately use to design and fulfill my flashlight needs. If others are lucky, they will stumble across my tool and save themselves a lot of money and hassle choosing a flashlight. Provided firstly, that those with validation natured issues don't disrupt the forum with their kamikaze technique for flaming the thread and sinking it by moving moderators to lock it before it is completed. 






If anyone has such issues, and either feels the need to snobbishly dismiss this _strange, alien_ approach or at least obtain validation before able to return the favor and validate me or it, this is not the place to work out or vent these turbulent, unpleasant emotions. This thread is about flashlights. It is not about psychology or spirituality or your personal emotional needs. Please find a support group and get a group hug. :grouphug: 

If you wish to vent pent up emotions, perhaps you could find the comment section of a Trump news story. He seems to be the popular beating post now. Enjoy. 

If you have an expensive smartphone with GPS and monthly service contract and prefer to use it for backwoods navigation, trying to talk me into doing that is beside the point of this thread. I have patiently explained to one such person why that is not going to work for me. 

If you use maps and a compass in high winds on mountain ridges, feel free to rip your map to shreds. 

If you buy a $1000-2000 arsenal of flashlights and try them out one at a time to select what works best for you, that's your hobby, not mine.

If you think I'm having a midlife crisis, perhaps you can use your psychiatry doctorate to prescribe me the appropriate meds. I obviously need some help.

If this thread is unpleasant for you or is hopelessly irrelevant in your opinion :thinking::shrug:, I might offer that you spare yourself the click and do something you find more interesting or satisfying.

This thread's purpose is not here for validating people or recognizing different approaches. It is not about "you" or "me" or "them" and the ways people prefer to do things or how they have fun. 

And this comment is not here to start a tangential discussion about this point and such issues. _It is here to end them._ Such discussions are _certainly_ irrelevant and off topic in this thread, and I hope _that_ will finally be "understood" by those to whom it pertains.

​


​


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## quinlag

Project:
Determine height of building.
How:
Using known weight of a falling object.
Tools:
Hygrometer, stopwatch, steel ball.

Proceedure:
Measure density of air using hygrometer, call city to block street, drop ball from top of building, measure time to impact, use correct equation to determine height of building.

All the students turned in their paper with the correct answer but there was one student who had the correct answer with no math.
The instructor asked if he cheated; he said no, I just went to the office of the building engineer, knocked on the door and said," I'll give you this hygrometer if you'll tell me how tall the building is.


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## Genzod

Off topic trolling posts are now being flagged as harassment.


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## Greta

This thread is now beyond the limit of childish comments, bickering, trolling and baiting. It is not worth trying to clean up and I'm not into trying to herd cats today.

Thread closed.


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