# Misapplication of the inverse square law



## Curious_character (Sep 16, 2007)

[Note 9-16-07: Some numbers in the original posting were based on an incorrect second measurement distance. They've now been corrected. This doesn't affect the conclusion.]

It's well established that the light intensity (technically, illuminance, measured in lux) decreases in inverse proportion to the square of the distance to the source. This follows directly from simple geometry, where the source is at the center of a sphere, and its light shines on the surface of the sphere.

But the end of a flashlight isn't like a point source of light. So the square law assumption can't be applied to distances measured from the front of the light. I recently made some careful measurements of one light at a distance of about 3 meters and, compared to measurements made at 1 meter, the square-law adjusted 3 meter measurement was off by 19%. Another type of light was off by less than 4%.

I'm proposing a theory that the light can be extrapolated back from the test surface to an apparent converging point, and that the square law holds for the ratio of distances to that converging point, not to the end of the flashlight. The converging point appears to be behind the end of the flashlight by a surprising amount. Looking at the geometry, it looks like the converging point is farther back in flashlights with larger reflectors, and ones with more tightly focused beams. I thought I'd confirmed the square law for flashlight lux measurement quite some time ago, but I did it with lights with relatively small reflectors and wide beams. A light with one inch diameter reflector (a CPF reference light) was extreme enough, and my measurements carefully enough made, to make the problem apparent. Using careful measurements at two distances, the distance from the front of the light to the convergence point can be calculated. For the one inch diameter reflector light, it works out to 0.14 meter, or about 5.5 inches. That is, when the front of the light is 1 meter from the measurement surface, the apparent source of the light is 1.37 meters from the surface. I also ran a set of careful measurements at both distances with a P3D which has a very constant output level and a reflector diameter of 0.6 inch. The apparent convergence point for that light worked out to be 0.027 meter, or about 1.1 inches. That results in an error at the approximate 3 meter measurement distance of less than 4%, which is probably why I missed the problem earlier. If my conjecture is correct, measurements taken at any distance greater than 1 meter and adjusted to 1 meter by the square law will be higher than actual 1 meter measurements. It also impacts assumptions about "throw" distance, although probably not by enough to have practical implications.

When time permits, I hope to run some tests with several types of lights at several distances, to see if this apparent converging point model is reasonably good. But if it is, it means that you'd have to make at least one set of measurements at two distances for each type of light to determine where the convergence point is. Or, possibly, a measurement of the width of the main beam (at, say, the half brightness levels) at a single distance combined with a little geometry might provide a good enough estimation.

On quite a number of occasions I've promoted making measurements at distances greater than one meter, mainly because it's easier to place the beam hot spot over the light meter aperture. I think in some cases at one meter, the beam can be narrow enough so it's not constant over the light meter aperture area, in which case you'd be reading the average of the brightest part of the main beam along with portions which aren't so bright. But my recent measurements convince me that measurements taken at distances other than one meter could be significantly in error. So I apologize to anyone whom I've led astray, and retract my recommendations.

c_c


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## thunderlight (Sep 16, 2007)

Speculation here, I don't claim expertise:

The inverse square law might not fully apply because the beam is being focused/reflected in an attempt to send out the light in parallel beams. So, behavior might be better than what would be suggested by the inverse square law. I'm thinking of a laser beam at the extreme. That is, everything else being equal. 

However irregularities in the reflector and/or lens and/or absorption or spreading of beam due to the flat bezel lens, etc., might affect the output in the opposite manner, making it worse than inverse square laws might imply. 

Once again, I am not an engineer, nor am I familiar with the physics of light and optics.


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## SilverFox (Sep 16, 2007)

Hello Curious_character,

I believe we standardized on measuring from the front of the bezel just to make it easy for everyone to make the same measurement. The actual spot of the measurement should be from the plane of the LED.

You may want to re-measure using the plane of the LED, and the plane of the filament of the lamp in the incandescent light as your reference point.

I have actually had very good results using the inverse square law. I haven't tried using the CPF benchmarking lights, but it works well with a TigerLight and an Aleph 3.

Tom


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## scottaw (Sep 16, 2007)

Man, do NOT try to understand any of this post after a few drinks....trust me. maybe i'll try again in the morning. Or maybe i should go back to college first.


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## lctorana (Sep 17, 2007)

thunderlight said:


> The inverse square law might not fully apply because the beam is being focused/reflected in an attempt to send out the light in parallel beams. So, behavior might be better than what would be suggested by the inverse square law.


 
My thoughts exactly. Might be wrong, but that is exactly what I was thinking myself.


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## LuxLuthor (Sep 17, 2007)

My 4:30 am take on this just from simplistic level assumes the inverse square law is quantifying a point light source radiating without any alteration in 360°. Once you are capturing some amount of light emanating backwards into a reflector 150° to 190° and reflecting it in the same direction of your measurements, you have increased the torch lumen output.

It seems if you start with torch output as your light source, the inverse square should then work.


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## wakibaki (Sep 17, 2007)

Ahhh, this is the astronomical telescope in reverse.

Reflectors are parabolas, which are the only curves with a point focus (for incoming plane waves, e.g. from a star).

So if you think of your torch as a Newtonian telescope in reverse, then if the source is a point then all the wavefronts leaving the torch should be parallel planar and orthogonal to the axis. This means they have an apparent spherical source an infinite distance behind the reflector, or if you think of it in terms of ray-tracing, all the rays should be parallel with the axis and there should be NO divergence (without thinking about diffraction).

Of course sources aren't points at the exact focus, reflectors aren't parabolas, light is neither wave nor particle and beams do diverge.

So unless (and even if) you want to model each torch individually, there will be a degree of inaccuracy in calculations.

w


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## Codeman (Sep 17, 2007)

Like SilverFox, I've had good results applying the IS law. The two most important factors that can impact accuracy, based on my experience, is that measurements must be made at or beyond the minimum distance at which the beam's hotspot is fully formed, or focused. Secondly, you have to adjust the aim so that you read the brightest spot in the hotspot at every distance. With practice, doing that becomes easier. Errors will still exist, of course, but they can be minimized reasonably well with practice. If you don't measure the brightest spot every time, though, errors will compound quickly.

Since a light meter alone can only measure a small portion of a light's complete beam, in this case just a portion of the hotspot, the shape of a reflector is only indirectly relevant, namely in how much light it concentrates into the hotspot along a direct path from the light source/reflector to the meter. Uniformity of brightness in the hotspot will also impact the accuracy of the IS law. If the hotspot isn't uniform, inaccuracies will grow as the distance to the meter increases.

Accuracy will also improve when reflected light is prevented from reaching the meter's sensor. The amount of reflected light, if allowed to reach the sensor, will always vary as measurements are made at different distances, in addition to those differences directly due to the IS law. The distance that reflected light follows is always further than the direct path from the light source. If reflected light is allowed to reach the sensor, application of the IS law becomes extremely complex. For purposes of a hobby, it's effectively impossible to apply. The IS law only applies to light arriving along a single path. To take multiple paths into account, the calculations are far from simple. You'd need to block all paths except for the one being measured, then do a measurement and IS law calculation for that path. Then repeat that for each possible path and combine the readings - calculus and/or computer modelling anyone? It's much easier to simply block reflected light.

If a particular light doesn't have a fully-focused beam at 1 m, I measure at whatever distance it is fully-formed. A second reading at a distance slightly beyond that usually comes close to matching the IS law.

The IS law always applies. When results don't agree with it, that is an indication that something in the setup and/or system being measured is causing the error. Either some variables aren't being taken into account, or invald assumptions were made.

The notion of a convergence point behind the source isn't realistic. The light starts at the source, not behind it. Nothing exists behind it that is relevant to this measurement. The laws of physics can't be bent, especially as a means to explain our mistakes in applying them.

Knowledge without understanding is knowledge wasted - Gas station bathroom wall, Gray, TN, 1988


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## wasBlinded (Sep 17, 2007)

I suspect there are two very confounding procedural problems leading to the disparities. First, at 1 meter a flashlight is not a point source of light, so the IS square law will fail at increasing distances until the light is effectively a point source. Second, the measuring dome of the light meter occupies a fairly large area itself, and is sampling a larger percentage of the beam at near distances than it is at greater distances. Both of these will lead to nonlinearity in measurements at different distances.

Try doing the measurements at 3 meters and 6 meters. I'll bet that the measurements at these greater distances will be more closely predicted by the IS law.


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## Timaxe (Sep 17, 2007)

I thought this out some time ago, and can explain it.

Explanation:
Intensity = Power / Area

Assuming the power from a source is constant, then the intensity varies only by the area we're interested in.

What can change the area of the projected beam?

...

Distance from the source.

This is why it is the inverse SQUARE law*. The area is some distance squared** (d^2), or an area. And this fits on the bottom half of the Intensity = Power/Area equation.

*The inverse square law is actually for the special case of a point source where the radius/distance from the point makes the area...it is still Intensity = Power/Area.
**That is, unless you have a beam with no divergence - which isn't practical.



So how do we properly apply the inverse square law?

We need to measure the divergence of the beam of our flashlights. Which can be slightly complicated because we don't have perfect point sources or reflectors.

----------------------------------------------------------------------

It is much easier to measure the divergence of a laser because the beam is so nice and round (if you have a quality laser). Then knowing the distances the radius of the beam is measured at, you can back track it to find the area of the source and determine the original intensity. Then you can find the intensity at any distance away from the source because you can find the area at that distance, and knowing the initial power you can solve for the intensity.







The equation for the diameter as a function of distance in my above graph is y=D=0.0018x + 0.0043
The area of a circle is 0.25*Pi*D^2.
The initial power can be say...5mW.
Therefore for the source x=0, and the initial diameter is 0.0043m so the initial area is 0.00001451465m^2.
The source intensity is 5mW / 0.00001451465m^2, etc.

If we want to find the distance where the intensity is 1% of the original...





Note: It's been a while since I went through the stuff below the -----, so it might be unpolished and confusing. Sorry about that. Goodluck.


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## lctorana (Sep 17, 2007)

So, let me get this straight.

If we had some theoretically-impossible reflector and collimator that gave us NO diffusion whatsovever, so strictly parallel rays, then the beam intensity would be the same, however close or far from the source we measure it?

Am I on the right track?


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## Art Vandelay (Sep 17, 2007)

Hello Curious_Character,

Here is a good link on the topic. It is a 2.25 MB PDF document, so if you have slow connection it may take awhile. It has a good description of "point source approximation", and the “five times rule” for irradiance measurements. I hope you find it helpful.

http://www.uni-mannheim.de/fakul/ps...ikel/Alex_Ryer_Light_Measurement_Handbook.pdf

Here is another link
http://books.google.com/books?id=lXNFnybj9wwC&pg=PA354&dq=%22point+source+approximation%22+%22five+times+rule%22&sig=SICuR1GxneWZ7Sowb_aPhxhloLE


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## Codeman (Sep 17, 2007)

Excellent link, Art! :thumbsup:


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## Codeman (Sep 17, 2007)

lctorana said:


> So, let me get this straight.
> 
> If we had some theoretically-impossible reflector and collimator that gave us NO diffusion whatsovever, so strictly parallel rays, then the beam intensity would be the same, however close or far from the source we measure it?
> 
> Am I on the right track?



It means that at a given distance, the intensity would be the same no matter where in the beam you took a measurement _at that distance_. Up, down, left, right or center - they would all read the same for a given distance. A reading taken at any other distance, would relate to the first measurement according to the IS law.


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## Nitro (Sep 17, 2007)

lctorana said:


> So, let me get this straight.
> 
> If we had some theoretically-impossible reflector and collimator that gave us NO diffusion whatsovever, so strictly parallel rays, then the beam intensity would be the same, however close or far from the source we measure it?
> 
> Am I on the right track?



Yes I believe you are correct. However, you'd have to be in a vacumn. Air would diffuse the light.

PS This is my final answer.


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## lctorana (Sep 17, 2007)

lctorana said:


> If we had some theoretically-impossible reflector and collimator that gave us NO diffusion whatsovever, so strictly parallel rays, then the beam intensity would be the same, however close or far from the source we measure it?


 
Actually, I think this is right. This is the theory behind optical fibre.


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## Timaxe (Sep 17, 2007)

Optical fiber has the goal of maintaining the same intensity over very long distances, but it does this in a different way.

It relies on total internal reflection to work properly, which is why the diameter of the fiber is so small and why you don't get to make very tight radius bends with it. Basically the 'fiber' has a very high refractive index (somewhere between 4 or 5), and the jacket has a very low refractive index (ideally 1). Because of the difference, you can achieve total internal reflection between the surfaces beyond certain angles. To see it, you can go under water at a pool and look up - you can see straight up, but at some angle you see a reflection of the bottom of the pool and this keeps up for the rest of the view.

Of course the medium absorbs some of the light...which is another factor influencing light intensity at distances away from some source. The inverse square law doesn't account for this loss.


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## That_Guy (Sep 17, 2007)

Using lux @ 1m to measure throw has been a pet hate of mine for quite a while now. I've been planning on making a thread to rant about it, but had never got around to it, until now. What follows is my rant.

Lux @ 1m is fine when used for lights with small reflectors, but it becomes increasingly inaccurate as reflector size rises. The reason why I am so against lux @ 1m is because I'm mostly into spotlights which have large reflectors, and at these sizes lux @ 1m is so inaccurate that it becomes worse than useless and is actually downright _deceptive_. What I mean by deceptive is that it doesn't just make a far throwing light with a large reflector appear to throw less far than it does in reality, but can actually make it appear to throw _less_ far than lights with smaller reflectors which in reality only have a fraction of the throw of the larger light. I'll post an example of this when I get home.

There is a very simple solution to this. Everyone in this thread is vastly overcomplicating things by talking about things such as calculating the divergence, and convergence point etc. 

The simple solution is this: measure lux at a longer distance. I take all my throw measurements at the longest distance possible, from one side of my house to the other, a distance of 13.5m.

However this creates another problem, the fact that there is now no standardised distance to take measurements from. But this too has a very simple solution: use the proper unit for throw, not the dodgy lux @ 1m unit which I hate so much. The proper SI unit for throw is candela. However, most people are probably more familiar with its former name: the candlepower. Yes, the name of this site. I don't know why the candlepower is so unpopular here, especially since the site does have it as its name.

One possible reason is because it has been perverted by so many manufactures that it has become useless for comparing lights based on manufacturer’s claims. The biggest offenders are the manufactures of all those cheap yellow Chinese spotlights, which "calculate" their ratings by adding a few million cp to their nearest competitor. Even reputable manufacturers like Maglite and Streamlight lie about their candlepower ratings, although not by nearly as much. The only honest manufacture I know of is Peakbeam, the makers of the Maxabeam. However, the fact that so many manufacturers are dishonest shouldn’t discourage people from using the candlepower, only make them aware that it important to actually measure it rather than relying on the manufacturers claims.

The other possible reason why candlepower is so unpopular is because not many people actually know what it means. Most definitions are very confusing or outright wrong. This includes site I’ve seen linked to from CPF for supposedly having a clear explanation of candlepower (this site, I suggest *not* reading it unless you want to be confused).

The simple definition for candlepower is this: throw. Candlepower _is_ throw. Simple as that. No distance is necessary. If light A is 1000 candlepower and light B is 2500 candlepower light B has exactly 2.5x the throw of light A. Note that this doesn’t mean it will throw two times as far, due to the inverse square law (it will throw sqrt(2.5) times as far, or 1.58 times). It will light up a target with 2.5 times the intensity (2.5 times the lux) as light A. This is true for any distance (unless you get too close to the reflector, which is why we’re having this discussion in the first place).

Calculating candlepower is easy. It’s the same as lux @ 1m, only you don’t have to measure it at 1m. You can measure it at a greater distance and use the inverse square law to get back to lux @ 1m. Since it is the same as lux @ 1m using the term candlepower instead might seem stupid, but it is better because people won’t feel restricted to only taking measurements at 1m. This will create some inconstancies because different people will measure the same light at different distances and therefore get different results, but as long as people take their measurements at “reasonable” distances the error will be so low (<1%) the accuracy of the light meter will make far more of a difference. Knowing what is reasonable is the hardest bit, but this really shouldn’t be too difficult. 10m or more is enough for all but the biggest of spotlights, and 5m or more should be enough for most smaller lights.

Let’s put the “candlepower” back into candlepowerforums. Who’s with me?


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## LuxLuthor (Sep 18, 2007)

That_Guy, good post. What light meter do you use to measure at that 13.5m? Only other issue I see is agreeing on measuring the hotspot vs. average including corona.

PS) I did end up getting a Maxa Beam after all our conversation vs. SuperNova in that spotlight thread.


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## Curious_character (Sep 18, 2007)

wakibaki said:


> . . . So unless (and even if) you want to model each torch individually, there will be a degree of inaccuracy in calculations.
> 
> w


That was the conclusion I reached. In the original posting, I mentioned that I saw quite a difference between the two lights I made careful measurements with. And there's every reason to believe that others will be different from both.

c_c


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## Curious_character (Sep 18, 2007)

wasBlinded said:


> I suspect there are two very confounding procedural problems leading to the disparities. First, at 1 meter a flashlight is not a point source of light, so the IS square law will fail at increasing distances until the light is effectively a point source. Second, the measuring dome of the light meter occupies a fairly large area itself, and is sampling a larger percentage of the beam at near distances than it is at greater distances. Both of these will lead to nonlinearity in measurements at different distances.
> 
> Try doing the measurements at 3 meters and 6 meters. I'll bet that the measurements at these greater distances will be more closely predicted by the IS law.


I agree. If my simple model is reasonably accurate, there's a fixed distance error for a given light which has to be added to the measured distance to give an effective distance. The effective distance is the distance from the observation surface to the apparent convergence of the rays. This effective distance is the one which has to be used in square law calculations. Because the distance error (the distance from the front of the light to the apparent convergence point) is a fixed distance, the error caused by ignoring it will get less and less as the measurement distance gets greater and greater.

c_c


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## Curious_character (Sep 18, 2007)

lctorana said:


> So, let me get this straight.
> 
> If we had some theoretically-impossible reflector and collimator that gave us NO diffusion whatsovever, so strictly parallel rays, then the beam intensity would be the same, however close or far from the source we measure it?
> 
> Am I on the right track?


I believe that's what would happen, yes. In that case, the point of apparent convergence is an infinite distance behind the front of the light.

c_c


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## Curious_character (Sep 18, 2007)

That_Guy said:


> . . .The simple definition for candlepower is this: throw. Candlepower _is_ throw. Simple as that. No distance is necessary. If light A is 1000 candlepower and light B is 2500 candlepower light B has exactly 2.5x the throw of light A. Note that this doesn’t mean it will throw two times as far, due to the inverse square law (it will throw sqrt(2.5) times as far, or 1.58 times). It will light up a target with 2.5 times the intensity (2.5 times the lux) as light A. This is true for any distance (unless you get too close to the reflector, which is why we’re having this discussion in the first place).


I'm all in favor of sticking to established, well defined units of measurement and using them correctly. However, I've never seen a strict definition of "throw" anywhere except in hobbyist writings like these. Many people associate "throw" with a distance, which the candela isn't. Flashlight Reviews defined "throw" as the distance at which a light produces a luminance of one lux. That, of course, is the square root of the luminous intensity in candelas. So while I'm all in favor of expressing a light's luminous intensity (which is a function of direction from the light, but not distance), I'm afraid that calling it "throw" adds confusion rather than clarity to the situation.



> Calculating candlepower is easy. It’s the same as lux @ 1m, only you don’t have to measure it at 1m. You can measure it at a greater distance and use the inverse square law to get back to lux @ 1m. Since it is the same as lux @ 1m using the term candlepower instead might seem stupid, but it is better because people won’t feel restricted to only taking measurements at 1m. This will create some inconstancies because different people will measure the same light at different distances and therefore get different results, but as long as people take their measurements at “reasonable” distances the error will be so low (<1%) the accuracy of the light meter will make far more of a difference. Knowing what is reasonable is the hardest bit, but this really shouldn’t be too difficult. 10m or more is enough for all but the biggest of spotlights, and 5m or more should be enough for most smaller lights.
> 
> Let’s put the “candlepower” back into candlepowerforums. Who’s with me?


Fine with me. But it'll be an uphill battle to convince people that although candlepower is the number of lux at a distance of one meter, it isn't equal to the lux value measured at a distance of one meter from the light.

c_c


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## lctorana (Sep 18, 2007)

Timaxe said:


> Intensity = Power/Area.
> 
> **That is, unless you have a beam with no divergence - which isn't practical.
> 
> ...we don't have perfect point sources or reflectors.


 
OK, so we learn 3 things:
1. Power. For two otherwise identical torches, the brighter one will throw further.

2. Area. For two totally identical torches, the one shining on a bigger target will "throw" onto that target better.

3. Diffusion. To get a perfect beam, you need a perfect, parabolic reflector with a point-source of light at the focal point, with no diffraction gradients ahead of it.
If this could be achieved, our torch could theoretically throw to infinity.


Now I want to take us to a real-world example, which should be readily familiar - compare a showerhead to an Eveready Big Jim. 

The showerhead is all flood and no throw. It has no reflector, no lens and you can see the inverse square law in operation. To catch all the light you need a hemispherical screen.

By total contrast, the Big Jim, whilst consuming the same or less power, is all throw and no flood.

At one metre, the output is a single 5" hotspot with almost no spill. For close-up work, it is frankly useless, unless the operator has very steady hands!

But the further away you go, the better the usefulness gets.

To see why, we need to look at the design of the 4546 bulb. It is a PAR36 sealed beam unit, and when you look at it, the filament area is tiny, and held at what must be the focal point by transparent glass supports. The back of the bulb is parabolic, of course. All of which goes to show why the Big Jim throws so far with only 2.375 watts consumed.

This leads me to suggest that throw comes from the rearward-firing lumens that hit the reflector, the front-firing lumens are what gives the little spill there is.

Perhaps this is why there is a silver cap on some of the more high-powered spotlamps, as even these few lumens are fired back at the reflector for that smidgin of extra throw.

One last thing - people have spoken about flashlight glasses, whether they are lenses or not, and looking closely at the 4546, which is designed for throw only, note the glass is curved. I reckon this is to ease the diffraction gradient from vacuum/glass/air that would otherwise bend the beam and spoil throw. On the other hand, floodlights can have flat glass, as bending the beams can be either irrelevant or helpful as corcumstances dictate.

So, to recap, there are 4 factors to throw:
* power,
* distance/target size 
* reflector design 
* lens/glass design


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## Art Vandelay (Sep 18, 2007)

I like this definition of "throw" from flashlightreviews.com. It seems to me like this is the definition most people here at CPF are using when they use the term throw. The inverse square law would work the same with foot-candles but you would need to convert the numbers if you wanted to compare a light measured with foot-candles to a light measured with lux, otherwise the foot-candle measured light would have a misleadingly high number.

"[FONT=Arial, Helvetica, sans-serif]THROW NUMBERS on the chart actually list *distance in meters* at which the light can illuminate a target with 1 lux of light (about equivalent to the light of the full moon on a clear night). This measurement takes the raw "Lux at one meter at beam center" numbers in the review and applies the Inverse Square law (at double the distance, 1/4 the light strikes any one point on the target). As a result, a light that reads 100 on the chart will put the same amount of light on a target at twice the *distance* as a light that reads 50.[/FONT][FONT=Arial, Helvetica, sans-serif] " [/FONT]http://www.flashlightreviews.com/features/output_vs_throw.htm

You can do conversions from foot-candles to lux or from lux to foot-candles if you want.

FC= 10.76 * Lux

Lux =0.0929 * FC

http://www.fhwa.dot.gov/aaa/metricl.htm


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## Curious_character (Sep 18, 2007)

Art Vandelay said:


> I like this definition of "throw" from flashlightreviews.com. It seems to me like this is the definition most people here at CPF are using when they use the term throw. The inverse square law would work the same with foot-candles but you would need to convert the numbers if you wanted to compare a light measured with foot-candles to a light measured with lux, otherwise the foot-candle measured light would have a misleadingly high number.
> 
> "[FONT=Arial, Helvetica, sans-serif]THROW NUMBERS on the chart actually list *distance in meters* at which the light can illuminate a target with 1 lux of light (about equivalent to the light of the full moon on a clear night). This measurement takes the raw "Lux at one meter at beam center" numbers in the review and applies the Inverse Square law (at double the distance, 1/4 the light strikes any one point on the target). As a result, a light that reads 100 on the chart will put the same amount of light on a target at twice the *distance* as a light that reads 50.[/FONT][FONT=Arial, Helvetica, sans-serif] " [/FONT]http://www.flashlightreviews.com/features/output_vs_throw.htm
> 
> ...


I might be wrong, but I detect a confusion between foot-candle, which is a unit of illumination or illuminance, and candle/candela/candlepower (all the same thing) which is a unit of luminous intensity.

A light producing one candela in a given direction will light up an object in that direction with an illuminance of 1/m^2 lux, where m is the distance in meters. So at one meter (m = 1), the illuminance would be one lux; at two meters, it would be 1/4 lux, and so forth.

A foot-candle is simply an American unit of illuminance, equal to the illuminance produced by a one-candela source at a distance of one foot. Hence the conversion between lux and foot-candle is simply the square of the conversion between one foot and one meter. However, there's no dimensionless conversion factor between a lux or foot-candle and a candela.

Saying only that a light produces a certain number of foot-candles is just as meaningless as saying it produces a certain number of lux. A distance at which it produces that illuminance level is also required before we know anything at all about the light's brightness. Only when you know both the distance (in meters, feet, or any other unit) and the illuminance (in lux or foot-candles) can you know the light's luminous intensity (candles/candelas/candlepower) in that direction. Conversely, you can't know the lux or foot-candle level until you know both the luminous intensity (candles/candelas/candlepower) and the distance.

So here's the problem: Even if we know how many candelas a light is producing, we don't know how many lux (or foot-candles if you prefer) of illumination to expect at some distance from the front of the light, because we don't know the effective distance to the assumed point source. However, we could measure the lux at some distance from, say, the front of the light and if we know the output in candelas, we can then calculate where that effective point source is. And, knowing that, we can predict the lux level at any other distance.

Others have pointed out that if the measurement distance is great enough, the error in assuming the point source of the light to be the front of the light becomes negligibly small. Indeed it is, and for some lights even one meter is far enough for this to be true. As I mentioned in my original posting, I saw only a 5% error between one and approximately three meter measurements with a P3D CE when I made this assumption. But the same assumption applied to the CPF standard white LED light resulted in a 21% error. So one meter wasn't far enough for this assumption to be valid for that light.

c_c


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## Art Vandelay (Sep 18, 2007)

Curious_character said:


> I might be wrong, but I detect a confusion between foot-candle, which is a unit of illumination or illuminance, and candle/candela/candlepower (all the same thing) which is a unit of luminous intensity.
> 
> A light producing one candela in a given direction will light up an object in that direction with an illuminance of 1/m^2 lux, where m is the distance in meters. So at one meter (m = 1), the illuminance would be one lux; at two meters, it would be 1/4 lux, and so forth.
> 
> ...


If you know the lux of a light at 1 meter you know what its lux will be at 2 meters (or 10 meters). If you know the lux at 10 meters you know the lux at 1 meter. 

You can't determine the lumens from the lux, or foot-candles. Lux at one meter (or lux at 10 meters) can be greatly influenced by the how much the lights are focused. It's possible for a light that is highly focused to have higher lux than less focused light with more lumens.

Why would candlepower be a better measure than lumens and lux? I've read that candlepower was replaced by the candela. Most people agree on what a candela is. Candlepower on the other hand can be confusing. Some people think it means lumens, and some people think it means lux. Some people means as bright as as candle, some people think we should use the more modern candela definition.


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## Curious_character (Sep 18, 2007)

Art Vandelay said:


> . . .Why would candlepower be a better measure than lumens and lux? I've read that candlepower was replaced by the candela. Most people agree on what a candela is. Candlepower on the other hand can be confusing. Some people think it means lumens, and some people think it means lux. Some people means as bright as as candle, some people think we should use the more modern candela definition.


The reason candlepower (or candle or candela -- they're all the same) is better than lux is that lux doesn't tell us anything at all about the light. Lux _*at one meter*_ can be a useful measurement, but there's the potential problem of defining where that one meter is measured from. _*If*_ the measurement is made one meter from a point source, then the lux level at that distance exactly equals the number of candelas the light is producing in that direction.

But if my conjecture is correct, there's no guarantee that you can correctly determine the lux level at any other distance (although you can come close enough in a lot of cases) if all you know is the lux level at one meter from the front of the light -- because you don't know where the apparent point source is located.

Lumens are a measure of total light output, which is something different from what's being discussed. It's more useful if you want to know how well you can light up a whole room or large area, while candelas (or lux at one meter) is more useful if you want to know how brightly your light will light up an object in one direction, or how far away it'll light something at a given lux level. Both measures are useful in knowing what a light will do.

c_c


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## Curious_character (Sep 18, 2007)

Art Vandelay said:


> If you know the lux of a light at 1 meter you know what its lux will be at 2 meters (or 10 meters). If you know the lux at 10 meters you know the lux at 1 meter. . .


I disagree, unless you're measuring something like a bare emitter which is a good representation of a point source. I can't think of many more ways to try to explain why beyond what I've already posted.

c_c


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## Art Vandelay (Sep 18, 2007)

Curious_character said:


> I disagree, unless you're measuring something like a bare emitter which is a good representation of a point source. I can't think of many more ways to try to explain why beyond what I've already posted.
> 
> c_c


What about point source approximation? The five times rule of thumb says if you want to have 1% or lower error the distance of the measurement point has to be at least five times the largest source dimension.


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## That_Guy (Sep 18, 2007)

Rereading the opening post it sounds as if the lux readings taken at 1m are considered correct and the problem is that the longer distance readings are in error, and the aim of this thread is finding a way to correct for the erroneous long distance readings. The reality is the opposite. It's the long distance readings which are correct and the 1m readings which are wrong and need correction.

I mentioned earlier that I would provide an example of why lux @ 1m can be worse than useless and why I want it to die a horrible death. Two lights:




Which one do you think throws further? Common sense would tell you the one with the big reflector, but lets see what the supposedly "scientific" lux @ 1m measurement tells us:
Little light: 61 700 lux @ 1m
Big light: 128 700 lux @ 1m
Ok so the results aren't quite as bad as I had hoped. I was hoping that the small light would have a higher reading than the big one. And it would if the distance was even closer (say 0.5m) or if the big light was even bigger. However the reading for the big light is still extremely inaccurate.

These are my results at 13.5m, converted to 1m using the IS law:
Little light: 80 000 lux @ 1m / candlepower
Not a huge difference, the true reading is around 30% higher.

Big light: 1 000 000 lux @ 1m / candlepower
A *huge* difference, nearly 8 times higher, or 700%! That's why we need to move away from the silly lux @ 1m method of measuring throw. By the way the big black light is also rated at 1 million cp, so Lightforce is one more manufacturer I can add to the small list of honest manufacturers.

The candlepower unit is also much more practical than lux @ whatever meters. A good example is this thread in the HID forum. The poster wants to know what a good light for lighting up a target at 300m is. Most posters in the thread are bumbling around, just guessing, with no real idea of what would be suitable. Mtbkndad then helpfully posted some lux reading @ 37.5 feet for a number of lights. Because these are at a distance, they will be accurate, unlike readings taken @ 1m. However they don't mean much. They can only be compared to the other lights that he has measured at the same distance, so they aren't much use. Ra then converted the readings to candlepower. Now we have something useful, which can be compared to other lights, and be used to do calculations with. Ra calculated the N30 to be 250 000 cp which produces 2.7 lux at the distance the poster specified. For his situation, I'd recommend a light which can produce a bare minimum of 5 lux, preferably 10 lux at the distance he specified. We can easily calculate how many candlepower you need to achieve this. For 5 lux you need 5*300^2, or 450 000 candlepower. The Polarion X1 comes close to this at 400 000 cp. For 10 lux you need twice that, or 900 000 candlepower. Apart from exotic lights like the Maxabeam only the Costco HID or the big black light above, the Lightforce Blitz, are capable of that.

Every few weeks a thread similar to the one above pops up somewhere on CPF, with the poster wanting to know what a good light to use at x meters is. And the replies are always the same: wild guesses, no one really has any idea what is suitable, and the replies most likely end up doing more harm than good. With the candlepower it is possible to truly "answer" the thread. The steps are:
1. Determine how many lux the poster needs at the specified distance.
2. Calculate the minimum candlepower required to achieve this.
3. Find which lights meet or exceed the required candlepower.

It's that simple! Candlepower really is a great unit, it is very versatile since it can be used for a lot more than just comparing the throw of different lights, it can be used for all sorts of different calculations.



Luxluther,
I use this light meter. It's just a cheap thing so I doubt its very accurate, but it does the job. Good enough for ballpark comparisons to other peoples lights, and the accuracy doesn't matter for relative measurements of my own lights.

When measuring throw/candlepower you only care about the hottest part of the beam, not the average. My meter has a "max" function which makes this easy. You simply move it through the beam, and it will automatically record the highest reading.

Since candlepower involves only measuring the hottest part of the beam you can see the limitations (a green laser will out throw almost all lights but isn't much use). That's why knowing the lumens is also important, and the best thing, which I've seen a few people here on CPF do, is to measure the entire beam profile and graph it.





Art Vandelay said:


> Why would candlepower be a better measure than lumens and lux? I've read that candlepower was replaced by the candela. Most people agree on what a candela is. Candlepower on the other hand can be confusing. Some people think it means lumens, and some people think it means lux. Some people means as bright as as candle, some people think we should use the more modern candela definition.



Candlepower isn't an alternative to lumens, but an alternative to lux @ 1m. It should be used in conjunction with lumens. Those people who think it means lumens are wrong, candlepower really isn't that hard to understand, it's the same as lux @ 1m.

I have no problem with candela, it is the correct scientific unit, it's just that most people are more familiar with the candlepower (along with Firefox's spell checker it seems). They are both the same unit, just a different name. One candlepower = one candela (actually according to Wikipedia one candlepower is slightly more than one candela, but this doesn't really matter).


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## Art Vandelay (Sep 18, 2007)

How exactly can I measure the candlepower of a flashlight?


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## That_Guy (Sep 18, 2007)

1. Take lux reading at a distance of you choice in meters.
2. Multiply reading by the distance in meters squared.

So if you measure 6200 lux at 8.4 meters then candlepower would be 6200 * 8.4^2 = 437 472 candlepower (but since no light meter is that accurate there is no point in using more than two significant figures so just say 440 000 cp).

You want to take the lux measurement in the "hottest" part of the beam, the easiest way to do this is to use a light meter with a "max" function and then slowly move it through all parts of the beam.


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## mtbkndad (Sep 18, 2007)

That Guy,

I really do not appreciate being misrepresented in this post.
While the information you give afterward is good your premise is still flawed. 
First of all here is the portion of the thread I take issue with-



That_Guy said:


> The candlepower unit is also much more practical than lux @ whatever meters. A good example is this thread in the HID forum. The poster wants to know what a good light for lighting up a target at 300m is. Most posters in the thread are bumbling around, just guessing, with no real idea of what would be suitable. Mtbkndad then posts some lux reading @ 37.5 feet for a number of lights. Because these are at a distance, they will be accurate, unlike readings taken @ 1m. However they don't mean much. They can only be compared to the other lights that he has measured at the same distance, so they aren't much use. Ra then converted the readings to candlepower. Now we have something useful, which can be compared to other lights, and be used to do calculations with. Ra calculated the N30 to be 250 000 cp which produces 2.7 lux at the distance the poster specified. For his situation, I'd recommend a light which can produce a bare minimum of 5 lux, preferably 10 lux at the distance he specified. We can easily calculate how many candlepower you need to achieve this. For 5 lux you need 5*300^2, or 450 000 candlepower. The Polarion X1 comes close to this at 400 000 cp. For 10 lux you need twice that, or 900 000 candlepower. Apart from exotic lights like the Maxabeam only the Costco HID or the big black light above, the Lightforce Blitz, are capable of that.
> 
> Every few weeks a thread similar to the one above pops up somewhere on CPF, with the poster wanting to know what a good light to use at x meters is. And the replies are always the same: wild guesses, no one really has any idea what is suitable, and the replies most likely end up doing more harm than good. With the candlepower it is possible to truly "answer" the thread. The steps are:
> 1. Determine how many lux the poster needs at the specified distance.
> ...



First of all Candlepower is no more accurate a way to determine relative difference between lights then lux at 37.5 feet if you are using the lux at 37.5 feet to get the CP numbers. Unless somebody as actually seen a light with a specific CP being used at a set distance, it is all just a bunch of numbers.
This is particularly true since, as Ra pointed out in the thread I was posting in, different people will feel comfortable with differing levels of light when trying to see things.

Anytime I have ever posted my complete list of lights lux at 37.5 feet numbers, I have always said that is only good for comparing the relative difference of the lights I have personally measured. My reason for posting them in the thread you referenced was so that Ra COULD convert the numbers of lights that I have ACTUALLY USED at 300+ meters to CP in order to find out what CP works for me at that distance. 

Contrary to your post I was sharing my personal experience with the lights I mentioned and the lux @ 37.5 feet numbers were useful for the purpose I mentioned. That purpose was for Ra to convert them to CP numbers that were helpful given ALL of the other information. Without ALL of the information they would have just been more useless numbers to the average person.

I will contend that real CP numbers are terrible to use when dealing with people that have nominal understanding of lights. It is a real nightmare to explain to people that the 10 MCP Thor is a 195,000 CP light. Statements like this generally follow, "Well then I will get the 3MCP Dorcy, I would rather have 3MCP then 195,000CP". :hairpull: Now you have to start all over explaining that the 3MCP Dorcy is really only 138,181
CP. :hairpull: :hairpull: :hairpull:

By using lux at 37.5 feet and explaining the numbers are only relative to the other lights I have tested I have a way to explain the relative difference in lights I have personal experience with without having to open up the CP Pandora's box. 

Once again I do feel the information you presented in the paragraph after the paragraph you misrepresented me in was good. But unless people have real experience with a light whose CP is actually known to them, the CP numbers will just be more numerical nonsense no matter how accurate they are.

Added section.
My two 10 MCP Thors are a perfect example of what I think you were trying to demonstrate in the beginning of post 31.
The Focused Thor actually has a donut hole in the center of its beam, and therfore a very low lux reading, within about 30 inches. While the unfocused Thor posts a real high number. Yet at 37.5 feet the focused Thors posts a higher lux reading and the farther away you shine the lights the more dramatic the difference in the focused Thor's throwing ability becomes. 

Take Care,
mtbkndad :wave:


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## That_Guy (Sep 19, 2007)

mtbkndad,

To be honest I don't really understand what your problem with my post is, I don’t see how I’m misrepresenting you. However I'll try to reply as best I can.



mtbkndad said:


> First of all Candlepower is no more accurate a way to determine relative difference between lights then lux at 37.5 feet if you are using the lux at 37.5 feet to get the CP numbers.


True. Candlepower is no more _accurate_ than lux @ 37.5feet. However it is more _useful_ which is the point I'm trying to make. Lux @ 37.5feet can't be compared to anything, it's just a bunch of numbers, candlepower can. When your lux readings are converted to candlepower I can compare them to my lights, Ra's lights, the Maxabeam, or any light with a candlepower measurement. I can't do anything like that with lux @ 37.5feet numbers; they are only useful for comparing the lights you've personally measured at that distance, not anyone else's.



> Unless somebody as actually seen a light with a set CP being used at a set distance it is all just a bunch of numbers.


That's what I'm trying to change. Right now it's just a bunch of numbers because no one is familiar with candlepower. I am, and find candlepower numbers very useful, and can relate the numbers to the candlepower measurements of other lights. In addition candlepower numbers can be used to calculate lux levels at different distances, making the numbers easier to understand.



> This is particularly true since, as Ra pointed out in the thread I was posting in, different people will feel comfortable with differing levels of light when trying to see things.


This is why using candlepower to describe lights is so useful. The problem with that thread is that lots of posts were along the lines of: "I've used light x, and it works great at y meters". Such a statement isn't of much use, because as you said "different people will feel comfortable with differing levels". If, however, the posts were: "I measured light x to be y candlepower" then the lux at the specified distance can be calculated and the individual the post can decide if that level of illumination is sufficient. 

Take the second post for example: "Boxer 24w will reach the distances you are talking about no problem. I recently used mine at night and this range is definitely within its ability."

I consider a 24W Boxer practically useless at 300m, and I know this even though I have never used one. I know this because I have a good idea of what its candlepower is, and then used the estimated candlepower to calculate how much light it would put on a target at 300m. I know from experience that the light it would put on a target at 300m is what I would consider insufficient.

Imagine instead that the poster had said something like this: “I’ve measured the Boxer 24w to be 100 000 candlepower. It will illuminate a target at 300m with 1.1 lux.” Anyone reading the thread will be able to decide for themselves if they consider 1.1 lux to be sufficient or not. I consider 1.1 lux to be vastly insufficient. Other people seem to have night vision goggles build into their eyes and consider 0.1 lux to be sufficient. How many lux is sufficient is a discussion best left to another thread.



> Anytime I have ever posted lux at 37.5 feet I have always said that is only good for comparing the relative difference of the lights I have personally measured.


That’s why they're more useful converted to candlepower, so they can be compared to lights that other people have measured. When I first read your post in the N30 announcement thread containing all the lux @ 37.5 feet measurements I thought to myself “Wow, throw measurements of all these popular lights, how interesting”. However, because they were at 37.5 feet I couldn’t relate them to anything; they were “just a bunch of numbers”. So I decided to convert them to candlepower for my own personal use. I did that, wrote the measurements down in candlepower, looked at them and thought to myself “Wow, now that is really useful” since I could now compare all the lights you measured to a number of other lights. I then posted my calculations in the thread in the hope that someone else would find them useful (I don’t think anyone did ).



> I will contend that real CP numbers are terrible to use when dealing with people that have nominal understanding of lights. It is a real nightmare to explain to people that the 10 MCP Thor is a 195,000 CP light. Statements like this generally follow, "Well then I will get the 3MCP Dorcy, I would rather have 3MCP then 195,000CP". Now you have to start all over explaining that the 3MCP Dorcy is really only 138,181
> CP.


True, I want to change that.

The following isn’t meant as a reply to your post mtbkndad, but as a general summary of why I’m promoting candlepower.



*Candlepower advantages*

Candlepower vs. lux at 1m
-	much more accurate
-	no more “useful” (since both are the same unit, both can be used for calculations, and are easily related to other measurements)

Candlepower vs. lux at some random longer distance
-	no more accurate
-	much more useful (because lux @ random distance can’t be used in calculations, and can’t be related to any other measurements)

Candlepower gives you the best of both worlds: accurate _and_ useful.


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## Art Vandelay (Sep 19, 2007)

Where did you get that formula for converting lux to candlepower?


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## Curious_character (Sep 19, 2007)

The only problem with using candlepower is convincing people that their traditional measurement of lux at one meter from the front of the light isn't necessarily equal to the candlepower.

I just corrected some of the numbers in my original posting. I discovered that I was using an incorrect second distance for my calculations. The error doesn't change the conclusions, however.

c_c


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## Curious_character (Sep 19, 2007)

I've speculated that lights with a large reflector and a tight beam would have an apparent point source position which is farther behind the front of the light than for other lights. Measurements of these lights would deviate considerably from the square law, if the distances used for the square law calculation are measured from the front of the light. Measurement of an MRV provides evidence that this is true.

I just made some careful measurements at two distances of an MRV (which had been modded with a Q5 emitter, but that won't affect the ratios), using the same protocol as for the CPF pass-around tests. The output level isn't flat with battery voltage, so I took a series of measurements at each distance, starting with a freshly charged 18650 at each distance. I rejected the first measurement at each distance because of the rate of drop of the light level. Then I compared the second measurement at one distance with the second measurement at the second distance, the third with the third, and fourth with the fourth, and calculated the average of the ratios. The ratios were different by a maximum of only 0.8 percent, giving me high confidence in the consistency of the measurements. Here are the results, for the average of the second through fourth readings:

1 meter lux value: 9230
3.25 meter lux value: 1501

If the 3.25 meter lux value is extrapolated to 1 meter using the square law, the result is 15,866 lux, which is _*72%*_ greater than the direct one meter measurement. Using the two measured values to calculate an apparent point source position puts that point source 0.52m (20.5") behind the front of the light(*). What this means is that the "1 meter" measurement was actually measuring the light from a point source effectively 1.52m away from the meter, and the "3.25 meter" measurement was actually measuring the light from a point source 3.77m away. The ratio of light levels (6.15) is the inverse of the square of the ratio of distances from the apparent point source (the ratio of 1.52 and 3.77) , not the ratio of distances from the front of the light (1 and 3.25).

So, what is the "lux at one meter" for this light? Is it the lux level measured at 1 meter from the front of the light (9230 lux), is it the light level measured at 3.25 meters from the front of the light and extrapolated to 1 meter using the square law (resulting in 15,870 lux) or is it the lux level measured at 1 meter from the effective point source (which would be 21,300 lux)? Only the third value can be used with the square law to predict the value at other distances (also measured from the effective point source), so it could arguably be regarded as the main beam's luminous intensity in candelas.

The error you get by extrapolating using the square law from the front of the light is much more obvious with the MRV than something like a P3D LE -- 72% for the MRV vs 4% for the P3D LE. So I'd like to encourage anyone who has the time, light, and meter, to carefully measure the lux level of an MRV or similar light at 1 meter from the front of the light, and at a greater distance -- the farther the better. And report back on how well the results fit the common square law extrapolation. Even better would be measurements at several distances, to see if the distance of the apparent point source from the front of the light is the same at all distances (for a given light). If not, then the simple model I've proposed isn't adequate.

(*)For anybody interested in calculating the effective point source position from lux measurements at two distances,

dx = (R*dm2 - dm1) / (1 - R) where

dx = the distance from the front of the light to the apparent point source
dm1 = The distance from the front of the light for the first measurement
dm2 = The distance from the front of the light for the second measurement
R = sqrt(L2 / L1)
L1 = The lux value measured at distance dm1
L2 = The lux value measured at distance dm2
dm1, dm2, and dx must all be in the same units (e.g., meters or inches)

c_c


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## Art Vandelay (Sep 19, 2007)

If I measured 10,000 lux at one meter I can determine the throw to be 100 based on this definition from flashlightreviews.com:
"[FONT=Arial, Helvetica, sans-serif]THROW NUMBERS on the chart actually list *distance in meters* at which the light can illuminate a target with 1 lux of light (about equivalent to the light of the full moon on a clear night). This measurement takes the raw "Lux at one meter at beam center" numbers in the review and applies the Inverse Square law (at double the distance, 1/4 the light strikes any one point on the target). As a result, a light that reads 100 on the chart will put the same amount of light on a target at twice the *distance* as a light that reads 50.[/FONT][FONT=Arial, Helvetica, sans-serif] " [/FONT]http://www.flashlightreviews.com/fea...t_vs_throw.htm

I get the 100 throw number from the square root of the 10,000 lux number. Saying it has a throw of 100 is a shorthand way of saying at 100 meters it can [FONT=Arial, Helvetica, sans-serif]"illuminate a target with 1 lux of light".

If a[/FONT]t one meter I measure 10,000 lux.
At two meters I expect to measure 2,500 lux (1/4 = 0.25).
At three meters I expect to measure 1,100 lux (1/9 = 0.11). 
At four meters I expect to measure 625 lux (1/16 = 0.0625).
At seven meters I expect to measure 200 lux (1/49 = 0.02).
At ten meters I expect to measure 100 lux (1/100 = 0.01).
At one hundred meters I expect to measure 1 lux (1/10,000 = 0.0001).


This link is on gravity applications of the inverse square law but I liked the chart comparing inverse and inverse square relations and I used part of that. http://www.astronomynotes.com/gravappl/s5.htm
This is another good link http://hyperphysics.phy-astr.gsu.edu/hbase/vision/isql.html#c1


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## mtbkndad (Sep 19, 2007)

That Guy,

First of all I want to say that your informantion is useful when used as part of the whole picture.
What I felt was misrepresented was this section and more more specifically before it was edited.

Mtbkndad then posts some lux reading @ 37.5 feet for a number of lights. Because these are at a distance, they will be accurate, unlike readings taken @ 1m. However they don't mean much. They can only be compared to the other lights that he has measured at the same distance, so they aren't much use. Ra then converted the readings to candlepower. Now we have something useful, which can be compared to other lights, and be used to do calculations with. Ra calculated the N30 to be 250 000 cp which produces 2.7 lux at the distance the poster specified.

I was not just arbitrarily posting lux readings of the 3 different lights at 37.5 feet, that would be giving useless information to markeone. Rather I was specificallly posting these lux readings so Ra could use them to come up with CP numbers so we could see what lux at 300 yards works for me to be able to see fairly well for basic illumination.

Ra's point about seeing deer, and I will add other animals that may not really want to be seen, well at 300 yards will likely need 4 lux or more is also an important consideration. 

The only way I know that number is true for me too is because I have been looking at animals at that distance with different lights. At the same time I have friends that cannot see deer well at 300 yards in the daylight. They will need much more light then 4 lux to be able to see deer well at 300 yards. 

I really commend you for your efforts in getting more people to use and record real CP numbers. What I feel is the biggest uphill battle with these numbers is the fact that manufacturers routinely and intentionally inflate CP values to sell lights.

That is why with the Amondotech Illuminator, when I helped design the box, there was intentionally no reference to it's CP on it. Rather we needed to say it is brighter then other brands of 10MCP and 15MCP lights
or nobody would consider buying it with Thors being so much cheaper.

There is also no reference to CP in the N30 announcement post.
There are, as you know, photos, light box reading, and lux at 37.5 feet readings of lots of lights so people could use ALL of that information to try to get an idea of what the little N30's can and cannot do.

I really do like what you said here in principle-
1. Determine how many lux the poster needs at the specified distance.
2. Calculate the minimum candlepower required to achieve this.
3. Find which lights meet or exceed the required candlepower.

I just think in practice it may not always be that easy to accomplish.

I would venture to guess that more often then not the persons asking the questions do not have the means to accurately determine the lux they need at the distances they want to use lights at to achieve their goals.

Without that important piece of the puzzle even accurate CP numbers become more imcomprehensible jargon.

Now if you could come up with a quick simple way for an individual to determine what lux he/she will personally need at any given distance he/she may want to illuminate objects to see to his/her requirements that does not require purchasing special tools. Then then the accurate CP numbers truly do become useful in determining what lights to recomend.

Last of all, thank you for pointing me to this thread. There is a lot of good reading in it I would never have stumbled across otherwise.

Take Care,
mtbkndad :wave:


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## SilverFox (Sep 19, 2007)

Let me see if I may be able to shed some light in this...  

Let's start by understanding that lux at 1 meter and foot candles at 1 foot and candela are all the same. 1 Cd = 1 fc (at 1 foot) = 1 lux (at 1 meter). We report lux at 1 meter because it simplifies figuring out throw. If we reported lux at 10 meters, we would first have to convert it to lux at 1 meter, then take the square root to determine throw down to 1 lux.

Lux at 1 meter is a reporting convention and is not necessarily be best distance to do the measurement from.

To measure illuminance, you first need to measure the diameter of the light. I use the diameter of the reflector for this measurement. You then need to move back a distance at least 5 times that measurement. So, if your reflector diameter is 2", you need to be at least 10" away for your measurement.

We now have set the minimum distance, but have not dealt with the beam shape. You now have to determine the crossover point within the beam. Your measurement needs to be taken beyond the crossover point for accurate results, but if you take it at exactly the crossover point, you will get inflated results.

Finally, you need to determine the plane that the light is being emitted from. This can get a little confusing in the case of LED's because they have a lens that can move the location of the plane of light slightly.

Now we are ready to take some measurements. We set the light up at a proper distance and make sure it is perpendicular to the meter sensor. We then take precautions to try to eliminate all stray reflections, then take our reading.

If our set up allowed us to measure at 1 meter, we can simply report lux at 1 meter and go from there. If we had to measure at a different distance, we normalize the reading for lux at 1 meter and report that. Or we can report lux at whatever the distance was and let others do their own math.

As I mentioned earlier, if we know lux at 1 meter or foot candles at 1 foot, we know candela. Knowing candela we can figure throw. If we are interested in throw down to 1 lux, we take the square root of candela in meters. If we are interested in throw down to 1 foot candle, we take the square root of candela in feet.

The real questions comes down to how much light we need to identify an object. 

In setting up the light meter benchmarking project, the diameter of the reflector is around 1" and the crossover point is within a couple of inches of the lens. This means that the testing could be done by people measuring foot candles or lux and the measurement would not violate the five times rule. When we sent the lights to the laboratory, we specified that they be measured in the same manner that we were measuring them. They took exception to measuring 1 meter from the front of the bezel and insisted on measuring from the plane of the light. By this time we had observed a sizable scatter in our results, so I did not object. They obtained the plane of light by using the inverse square law and taking two measurements at different distances. This means that our measurements will be slightly lower, and the inverse square relationship a little off.

In hindsight, I should have determined the plane of the light and marked it on the lights and the 1 meter measurement could have been done from that mark. However, I was ignorant of all of this when the project got underway.

In spite of the shortcomings of the measurement techniques, I think we have discovered that there are variations in light meter readings, and that measurements reported to 2 or 3 decimal places should be taken with a grain or two of salt...  

Tom


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## Art Vandelay (Sep 19, 2007)

SilverFox said:


> Let me see if I may be able to shed some light in this...
> 
> Let's start by understanding that lux at 1 meter and foot candles at 1 foot and candela are all the same. 1 Cd = 1 fc (at 1 foot) = 1 lux (at 1 meter). We report lux at 1 meter because it simplifies figuring out throw. If we reported lux at 10 meters, we would first have to convert it to lux at 1 meter, then take the square root to determine throw down to 1 lux.
> 
> ...


Great post. Thanks for summing that up. I learned something.:twothumbs

I think I'll have a margin of error when I apply the inverse square law to lux at one meter to a light with a lens or reflector. Even if no other problems arise, I'd have the 1% error from point source approximation & the five times rule. The questions for me are "is it helpful?" and "is there a practical substitute that's better?". For me, the answer the first question is yes and the answer to the second is no.


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## Codeman (Sep 19, 2007)

Art Vandelay said:


> Great post. Thanks for summing that up. I learned something.:twothumbs
> 
> I think I'll have a margin of error when I apply the inverse square law to lux at one meter to a light with a lens or reflector. Even if no other problems arise, I'd have the 1% error from point source approximation & the five times rule. The questions for me are "is it helpful?" and "is there a practical substitute that's better?". For me, the answer the first question is yes and the answer to the second is no.



X2 on everything Art said!


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## Curious_character (Sep 19, 2007)

I'd be greatly appreciative if someone would use the proposed methodology to measure a light with a tight beam like an MRV or Tiablo at two distances, say one and 3 or 4 meters, and show that the the measurements confirm that it's valid. My measurements indicate it isn't, which is the what prompted me to start this thread.

c_c


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## SilverFox (Sep 26, 2007)

Hello Curious_character,

I took the white LED benchmarking light and ran some measurements. I determined that the plane of the LED is about 7/8" back from the front of the bezel. Using that as the index point for measurement, I get very good agreement at 2 and 3 meters, but the reading at 1 meter is a little over 3% low. At 2 and 3 meters my numbers are very close to what Lighting Sciences got, so I am confident with them. While a 3% error is not extremely precise, it is well within the ball park and is a lot less than the standard deviation of the reported results.

It is interesting to note that at 1.5 meters, I once again get good agreement with the readings at 2 and 3 meters. It looks like the beam of this light becomes fully developed just after 1 meter.

In general, I believe we can get better accuracy by taking the measurement at greater distances and then normalizing the reading to lux at 1 meter for reporting.

Very interesting...

Tom


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## Curious_character (Sep 26, 2007)

SilverFox said:


> Hello Curious_character,
> 
> I took the white LED benchmarking light and ran some measurements. I determined that the plane of the LED is about 7/8" back from the front of the bezel. Using that as the index point for measurement, I get very good agreement at 2 and 3 meters, but the reading at 1 meter is a little over 3% low. At 2 and 3 meters my numbers are very close to what Lighting Sciences got, so I am confident with them. While a 3% error is not extremely precise, it is well within the ball park and is a lot less than the standard deviation of the reported results.
> 
> ...


Thanks very much for making that test! I had theorized that any light with a very well focused beam would show quite an error, considering that (I think) a perfectly collimated beam wouldn't decrease at all with distance (except due to scattering or other effects of the medium). But measurements with a D-Mini, which is in that category, put the effective point source only 3/4" behind the bezel, or approximately the physical LED position. I'm going to re-run the MRV tests to see if it's really as far off as I measured earlier, and also to see what difference an OP reflector makes.

Another thing I've done is looked at the sensitivity of the apparent point source position to errors in light and distance measurements. It's great enough that I need to make a realistic estimate of my measurement accuracy to see just how confident I can be in my conclusions.

Wish I had more time for this, but I'm squeezing in as much as I can spare (and actually a bit beyond that). I sure appreciate your taking a look at it, and hope some other folks will too.

c_c


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