Misapplication of the inverse square law

[Curious_character]

[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

[thunderlight]

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.

[SilverFox]

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

[scottaw]

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.

[lctorana]

Originally Posted by thunderlight

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.

[LuxLuthor]

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.

[wakibaki]

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

[Codeman]

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

[wasBlinded]

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.

[Timaxe]

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.

[lctorana]

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?

[Art Vandelay]

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/psy...t_Handbook.pdf

Here is another link
http://books.google.com/books?id=lXN...Sowb_aPhxhloLE

[Codeman]

Excellent link, Art!

[Codeman]

Originally Posted by lctorana

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.

[Nitro]

Originally Posted by lctorana

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.

[lctorana]

Originally Posted by lctorana

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.

[Timaxe]

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.

[That_Guy]

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?

[LuxLuthor]

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.

[Curious_character]

Originally Posted by wakibaki

. . . 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

[Curious_character]

Originally Posted by wasBlinded

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

[Curious_character]

Originally Posted by lctorana

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

[Curious_character]

Originally Posted by That_Guy

. . .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

[lctorana]

Originally Posted by Timaxe

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

[Art Vandelay]

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.

"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. " http://www.flashlightreviews.com/fea...t_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

[Curious_character]

Originally Posted by Art Vandelay

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.

"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. " http://www.flashlightreviews.com/fea...t_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

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

[Art Vandelay]

Originally Posted by Curious_character

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

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.

[Curious_character]

Originally Posted by Art Vandelay

. . .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

[Curious_character]

Originally Posted by Art Vandelay

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

[Art Vandelay]

Originally Posted by Curious_character

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.