# Estimate Lux & Lumens with Light Meter? LumenToob



## Bolster (Nov 12, 2011)

EDIT: This thread has evolved into the "LumenToob" project, which is a "reverse engineered" method of making ballpark estimates of lumens using a common handheld photo meter and PVC pipe fittings. 

I need to measure the output of several lights (handhelds & headlamps) so I can write better reviews! Recently my reviews have been questioned because I don't give any sort of brightness measurements. 

I have a nice Gossen light meter, the Luna-Pro Digital F. It can convert from reflective to incident with a sliding dome. It gives output in EV values. How do I use this meter to measure lux, or footcandles -- and is there any possibility to somehow estimate lumens with it? (Even if it's only approximate?) 

For lux, is it as simple as putting the flashlight one meter away from the light meter, taking an EV reading, and then converting to Lux or FootCandles? Is this done with the meter in reflective or incident (dome) mode? This phrase "2 - Your light meter will be set up with 1 meter distance for those measuring in lux (or 1 foot for those measuring in foot candles) between the *dome* of the meter sensor and the outside edge of the bezel ring" makes me think these are incident readings, with the light pointed at the dome -- not simple reflective mode. Correct? 

Is there any way of using a ceiling bounce (or other method) to estimate lumens, other than an integrated sphere? A ceiling bounce or some other home-style method won't do for guesstimation, such as this "integrated tee"? At least for comparative guesstimation, if not absolute? Perhaps not, from this comment: "When you find a Lumen measuring light meter, let us know. There's probably 4,000 of us here on CPF that would like to buy one." I keep thinking sliding incident dome should somehow allow me to estimate lumens. Because the purpose of the dome is to measure light hitting it from any and all angles within half a sphere. 

Certainly all these questions have been asked before, and I've searched and read many 'light meter' threads, but have not found a "how to" thread on this topic, although this one came close. Nothing in 'threads of interest' either. There must be a thread on this somewhere, I just can't find it. 

Related threads: 
lux w/o light box
home made sphere
upscale home made sphere


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## Robin24k (Nov 12, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

Generally speaking, you should only treat lux readings as relative, meaning it's only good for making runtime graphs (that's what I use my Extech light meter for). Without an integrating sphere, you cannot compare different lights because reflectors and bezel size will throw off your readings. In addition, your light meter is probably not calibrated for LEDs (standard light meters aren't), so that will also introduce errors.

The reason lumens is difficult-to-grasp unit is because it's luminous flux, the energy of all light that is produced. Therefore, you need something with a known area in which light is spread uniformly, hence the need for an integrating sphere.


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## MikeAusC (Nov 12, 2011)

*Re: How to Estimate Brightness with a Light Meter?*



Robin24k said:


> . . . . Without an integrating sphere, you cannot compare different lights because reflectors and bezel size will throw off your readings. . . . . .



That's why it's important to take readings many metres away from the light. Especially for tight throwers, you can get inconsistent readings if the Light Meter is less than 10 metres from the light.


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## Robin24k (Nov 12, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

That still won't give a reliable reading, spill is ignored and values for reflector-based lights will be too low. You cannot get flux without integrating over a Gaussian surface (hence, an integrating sphere where the Gaussian surface is a sphere).


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## MikeAusC (Nov 12, 2011)

*Re: How to Estimate Brightness with a Light Meter?*



MikeAusC said:


> That's why it's important to take readings many metres away from the light. Especially for tight throwers, you can get inconsistent readings if the Light Meter is less than 10 metres from the light.



Of course that's only for measuring Lux.


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## Robin24k (Nov 12, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

I see, yes, that would be fine then.

While peak beam intensity can be calculated without an integrating sphere, an LED-calibrated light meter is still required. With a standard light meter, I don't think lux or candela readings conform to the FL1 Standard.


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## Bolster (Nov 12, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

OK, can this egg be cracked with a different approach...perhaps by the application of some statistics...again, I'm not looking for Truth, I'm looking for comparative estimations, so I can relax the parameters a bit and leave the precise lumen counts to the labs. 

Imagine you shone a flashlight into one side of a 2" white PVC 90-degree elbow bend. Imagine you measured the reflected light from the other end of the elbow bend. This would ensure that only reflected light was measured, nothing direct, and it would bounce around in a reasonably small reflective space. 

The light meter uses an incident reading, so it is also diffusing the indirect light it's seeing in the elbow. You should be getting a reasonable mix of reflectance of light from multiple (mostly round) surfaces at this point, regardless if the measured light is spot or flood. Again, this reflectivity gets diffused through the meter's dome, so there's a "second mixing/diffusion" point. 

You record various flashlights of known lumens (in my case, I'm using manufacturer claimed lumens - again, I'm looking to compare manufacturer claimed values, not looking for absolute values.) 

Then you build a regression formula, to predict (in my case, manufacturer's claimed) lumens by EV values shown on the meter. You could also enter degrees of beam spread as a predictor--who knows, it might go significant. You could even enter manufacturer as a variable (although that would complicate things with a categorical variable). The computer would give you a regression formula whose result would predict what the average manufacturer would claim a light to be. (And by "average manufacturer," I mean the average of the manufacturers' advertised lumen counts you used to build your formula.)

Basically you leave the hard work of precise calibration (including the tuning of the light meter to LEDs) to the regression formula. The result would not tell you the lumens. It would tell you what your average manufacturer would claim for lumens. Which is actually what I'm looking for...I would like to place an unknown light into a lineup of other lights.


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## Bolster (Nov 12, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

By the way, never got a confirmation of how to do the lux readings. We jumped over that and into the lumens discussion. 

In post 1, do I have the lux reading procedure correct?


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## Robin24k (Nov 12, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

I don't know about EV, but you would use incident mode. Your meter is designed for photography, right?


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## Echo63 (Nov 12, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

I used my photographic light meter (a minolta flash/ambient meter) to measure lux/convert to CP the other night to measure my Maxabeam (it hit 7.2million cp)

I used mine in EV mode (at 100 iso - some meters change the numbers at different iso, some don't)
Then used a table I found on the Internet to convert EV to lux
Lux x distance from source to meter x distance from source to meter = Candlepower (or lux at 1m) although for smaller lights you could measure it at 1m.

I know one of the review sites had a fairly close way of estimating lumens using a milk carton and a luxmeter, it would require a few lights through it to calibrate it thiugh


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## Swedpat (Nov 12, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

A light meter is good for measuring the lux values of hotspot and spill from a certain distance and make a runtime graph. 
Also this is discussed; but I am personally convinced that you can get a very good estimation of the total output by comparing different light with careful ceiling bounce test.


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## Bolster (Nov 12, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

Yes, Robin, it's a photography light meter. 

I think I am basically doing a "ceiling bounce" using a 2" PVC elbow. I'm testing the concept now, and with only 15 datapoints from 4 lights, printed out on an Excel scatterplot, it looks like I'm so far able to predict the lumens (not lux) within about a 10-15 lumen error from a range of about 20 lumens to 200 lumens. All this is eyeballing it, with not much data, so things could change. I need to get on my work computer to run a regression formula. Then we'll have an r-squared that will tell us whether this approach is worthy or not.


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## Bolster (Nov 13, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

Thanks, Echo! Interesting: 

http://flashlightreviews.com/features/lightbox_output.htm
"It had to be something similar to shining the light at the ceiling of a white room and having the meter on the floor, thereby getting a sense of the overall reflected light that hits the sensor....How about a milk carton? White, cheap, easy to replace..."

http://flashlightreviews.com/features/output_vs_throw.htm#lumens
"Lumen calculation factor..."


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## Bolster (Nov 13, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

Progress on the LumenToob...







$7 for PVC elbows, tees, and caps. Opted not to use PVC pipe to put it together, the masking tape is sturdy enough. The meter cap is milled out to just mate with the meter, which fits in during use. On the right, aluminum foil keeps some of the reflected light in the tube. When you view through the meter slot you see a nice even spread of light, regardless of the beam shape of the light. Now collecting EV values to build the regression formula.

Beam placement on the right is not very critical. You can move the light around a fair amount and not see any difference in the EV values. I take that as a good sign. 

With lumens on the X axis and EV values on the Y axis, I'm getting a curve that looks something like an asymptote, just as you'd expect. Ie, a few more lumens make a big difference in brightness at the low end of the curve, and lots more lumens make a little more brightness on the high end.


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## Bolster (Nov 14, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

What? No criticism? Feedback...?

Here's the data going in... X is EV values from the light meter, Y is lumens claimed by mfgr...unfortunately I only own 7 flashlights for which I have the manufacturer's stated lumen count....wish I had more. 

Still, you can see the curvilinear shape appearing...the fact they're not in a perfect curve represents error--from differing lumen estimation methods of the different manufacturers, from imprecise repeatability of my light meter, from different beam patterns registering differently in my "lumen toob," and so on. 

Next we let the computer sort it out...draw the line through the points that misses them all by the least possible amount. Two independent variables: EV (shown below) and angle of beam (not shown, but including it in case it explains lower readings for full flood lights and perhaps help compensate for my home-made "lumen toob" system).


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## Robin24k (Nov 14, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

That's an interesting idea, but as your data shows, the error is pretty significant and non-linear (parabolic or exponential). I'm still going to say the same thing...you should only treat light meter readings as relative.

As a reviewer, any data you present should be factual, and this type of estimation is unprofessional and negligent. That being said, you do have a fairly controlled environment for making runtime graphs. 



Bolster said:


> What? No criticism? Feedback...?


CPF wasn't working consistently for the past couple days, and it seems like whenever I checked my email to get topic replies, it's always down (or very slow)...


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## Bolster (Nov 14, 2011)

*Re: How to Estimate Brightness with a Light Meter?*



Robin24k said:


> That's an interesting idea, but as your data shows, the error is pretty significant and non-linear (parabolic or exponential). I'm still going to say the same thing...you should only treat light meter readings as relative. As a reviewer, any data you present should be factual, and this type of estimation is unprofessional and negligent. That being said, you do have a fairly controlled environment for making runtime graphs. .



LOL, I like you Robin! Good one. And thanks for the reply, I was beginning to think nobody cared. 

*Error*: Yep, it's there. My guess is, the biggest source comes from the different ways the mfgrs measure their own products, an issue which has been widely commented upon. Another source of error could obviously be my LumenToob...it may not do as well with some beams as with others. In fact, I'd guess that's the case, so am entering a variable (beam spread) to possibly counteract. That said, even with the current data, you could draw out a curve by hand that would give you reasonable estimates. Once the formula comes in, I'll know how "off" it actually is. You can predict your own data and then observe the error. For example, that 25 lumen datapoint would appear to be a gross overestimate by the manufacturer. If it really is 25 it should be putting out 6-7 EV. I need to go back and verify that datapoint, maybe it's me who made the error. Even a low battery could do that. 

FWIW, deviance in the direction of the upper left portion of the graph is "bragadocious," and deviance to the lower right is "humble." 

*Non-linear*: That's not a problem, because I'm introducing nonlinear terms into the equation. I'll be fitting a curve, not a straight line. We have the technology! (More accurately, I will be fitting a number of curves, if the beam spread becomes a significant variable.) 

*Data factual*: I don't work at the University of East Anglia, so _my_ measurements are based on data...I'm not making up the EV values. (If I were making them up I'd have made them up in a more perfect curve! Like the University of East Anglia!) I can't speak for the manufacturers' lumen values, but remember...I'm trying to predict what a typical manufacturer would SAY the lumen output is, not what the ACTUAL lumen output is. The purpose of which, is to be able to place an unknown light in a relative lineup of other lights in the marketplace (for which we almost universally use the manufacturer's own published numbers, for better or worse). 

You have my promise, however, that I won't represent my findings as equivalent to an integrated sphere. I'm reverse engineering this process with $7 of PVC, a photo meter, and a regression program. Perhaps I shall call my estimates: "Bolster's negligent and unprofessional estimates." It has a good ring to it. 

If you are interested in a "blind" test of this, when done, send me a light for which you know the lumen output, and I'll predict it. Then you'd have an n=1 test of how much error is in the system. Of course, the calculation will do that too, it will give us an r-squared. I don't know what it will be but if it's not better than .7 I'll be disappointed. That would say I'm only able to predict 70% of the variance in the DV, by the IVs. 

Yeah, CPF has been achy and breaky for me, too. 

Thanks for the reply!


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## Robin24k (Nov 14, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

FL1 Standard light ouput ratings require an integrating sphere, so manufacturers should be measuring their products in the same way. However, due to manufacturing variation, some manufacturers understate the specifications to guarantee at least the stated spec. If you see nice round numbers (80 lumens, 200 lumens, 160 lumens, etc.), it's probably understated and your calculated result may be higher than expected.

The fact that it's non-linear is what's alarming. Your results will be skewed on the lower and upper ends, but since you're looking for ballpark values, I guess that's not an issue. If you do get significantly different values, keep in mind that it's only one sample and not a statistically significant indication.

It's nothing personal, but the reason I'm nit-picking here is because estimating lumens is dangerous business (plus, there's no correction for the fact that the light meter isn't calibrated for LEDs).


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## Bolster (Nov 14, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

Hey Robin, I _want_ you to nitpick. I appreciate the feedback, and I don't have my ego invested in $7 of plastic so it's OK to pick on it. But I don't think it's ready for the trash yet. Here's why: 

The eye perceives brightness along a logarithmic scale. That's the curve you're seeing, that's bothering you. Graph it logarithmically on the Y axis and you get your straight line (with some error, of course). Trust me when I tell you that the regression program will handle the curvilinear relationship just fine. If there _were_ a straight line _without_ a logarithmic scale..._then_ you should feel alarm, because someone would have either altered the laws of physics, or the laws of biology. 

So, how big a ballpark? With the data I've got, the largest offender so far is that 25 lumen rating that should be about a 10 lumen rating. So my worst datapoint so far is off by 15 lumen. That one point is so bad, it could probably be legitimately labeled an outlier and deleted. That 120 lumen datapoint is off, in the opposite direction, it should be more like 140 lumen.

The fit of the curve gets more accurate (better able to predict) as you give it more data. If I had 50 flashlights graphed I'd be feeling pretty smug. As is, only 7. I could do a lot better than that. 

Same problem as always...I NEED MORE LIGHTS!

PS: About the light meter not being calibrated. That might or might not be a problem. If the light meter is consistently off, let's say it has a harder time reading LED light, so it's always low...then it's not a problem, because the method I'm using adjusts for it. However if my readings are off more for some lights than others...then that's a problem.

If I have an intermittent problem, it would be indistinguishable from any other error, say, different mfgrs measuring lumens differently (at the emitter, out the front, whatever). But it would drag the r-squared down until the regression program told me, "your attempt to predict is crap." For this project, I'd consider an r-squared of .5 to be crap (really big ballpark), and I'd be disappointed with anything under .7 (regular size ballpark). If the r-squared gets to .8 or over, I'd be happy to use it as a guesstimation device.


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## Robin24k (Nov 14, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

The tube is actually a very good idea for making runtime graphs (might be taking an idea or two for my runtime test setup...). However, I was expecting your calculated lumens to be off by a constant since flux (lumen) depends on area. It shouldn't have anything to do with how the eye preceives brightness (lumens has nothing to do with "brightness").


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## MikeAusC (Nov 15, 2011)

*Re: How to Estimate Brightness with a Light Meter?*



Bolster said:


> Progress on the LumenToob..$7 for PVC elbows, tees, and caps. . . . . .



Even if the results closely follow the results from an Integrating Sphere for a few test lights, people won't believe your results simply because your test rig is so obviously different to the industry standard in physical shape.

Also Integrating have a matte interior - even flat white paint works fairly closely to Barium Sulphate in diffusing light.


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## MikeAusC (Nov 15, 2011)

*Re: How to Estimate Brightness with a Light Meter?*



Bolster said:


> . . . With lumens on the X axis and EV values on the Y axis, I'm getting a curve that looks something like an asymptote, just as you'd expect. Ie, a few more lumens make a big difference in brightness at the low end of the curve, and lots more lumens make a little more brightness on the high end.



That's because EV has a Log2 relationship with Lux or Lumens - your meter is "compressing" the data for display, after reading from its linear sensor.

If you want accuracy, you really need to use a Lux Meter which reads a linear output range from a linear-response sensor.


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## Bolster (Nov 15, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

"If you can't drive a Ferrari, then you may as well just stay home."

Hey I appreciate the response. If I'm able to predict the lumens of lights, within a reasonable and known range, then neither the type of meter, nor my $7 plastical tubular wonderment, are of any consequence. If I could get an accurate estimate using chicken bones and eye of newt, I'd be just as happy. (Happier, actually. Did you know, that I can predict the next President of the United States with 84% accuracy? Without taking a single poll or spending a dime.)

But I'm not claiming 'a reasonable range' yet. How about we wait until the results are in? I think criticisms would be much more founded if they were based on actual data and quantifiable error, rather than on "this is not the way we do things around here."

I may have to repeat this with each posting, but: I am not looking to create (or replicate) an integrated sphere. I am looking for the Ford or Hundai solution--or perhaps it will turn out to be the bicycle solution. But chances are high I'm not staying at home anymore. Don't worry--if the measurements turn out to be fairly accurate -- IF -- then I will caveat any estimate I make as being "Bolster's negligent and unprofessional estimate."


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## MikeAusC (Nov 15, 2011)

*Re: How to Estimate Brightness with a Light Meter?*



Bolster said:


> . . . . . I think criticisms would be much more founded if they were based on actual data and quantifiable error, rather than on "this is not the way we do things around here." . . . . .



How sad a response. I try to explain how people will likely to react and it's written off as criticism.

Goodbye.


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## Bolster (Nov 15, 2011)

*Re: How to Estimate Brightness with a Light Meter?*



MikeAusC said:


> How sad a response. I try to explain how people will likely to react and it's written off as criticism. Goodbye.



Time out. I'm soliciting feedback and criticism. Your posts were appreciated; my reply was not combative, it was a caution to wait for data. I think you're going out of your way to be offended. No worries. What seems sad to me is when people write the idea off, without even viewing the r-squared first, which can be used as a test of "goodness of fit." 

So, goodbye, Mike. I'm staying here and will see this thing through. If it predicts horribly, fine with me. But I don't think I should stop the experiment because it's not a multi-thousand-dollar light measuring machine. 

So back on topic: What would help this project immeasurably, is if I could have access to an integrated sphere for a few hours...get accurate measurements of a dozen lights and then enter _those_ lumens into the regression program. That would get me around the whole problem of manufacturer variance, which just adds in all kinds of error. 

Anybody know the whereabouts of an integrated sphere in Southern California?


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## Bolster (Nov 20, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

Update. First a caveat...I haven't populated my regression program with a lot of data yet (as you can see by the graph in post 15). I need to add the data from another dozen lights before I'd feel comfortable. Also the curve is not yet good at low values of under, say, 10 lumens; and low numbers seem to cause me trouble at this point. But the midrange results so far are promising and with additional data I think I can get decent estimates. 

An exponential curve did a good job of fitting the existing line, so the computer plotted out an "ideal curve" where it thought it should be, based on my small dataset so far. The formula it gave me was lumens = 4.9 + (.3*(2^EV)). As seen below, the X axis is EV values from the light meter and the Y axis is estimated lumens. 







The r-squared is exceedingly robust at .975. So I estimated one of my flashlights using the curve (bit of a kludge, advantages the formula, need a fresh light to do it right) and here's what I got: 






Not happy missing the lowest lumen setting by 39%. Considering that 20% lumen increase is often considered "barely noticeable on a side by side comparison," I'd call that lowest estimate marginal. But the other estimates I'm happy with...those are close enough for now; they _should_ improve as I get more data, and/or more accurate data. 

As I mentioned, if I could have access to an integrated sphere for a couple of hours, I could cut out the error that manufacturer estimates introduce. (Suspicious they tend to overestimate.) That would tighten things up considerably. But for now I'll just use manufacturer's advertised lumens and live with the additional error that adds to the estimation.

If anyone wants to send me a light with known lumens, I'll run it through the "lumen toob" and see what the prediction formula says. The additional data would very much help refine the program. (I'm in Los Angeles.)


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## Grizzlyb (Nov 20, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

Keep up the good work mate,
I really like what Your doing. Can't help You thou, its not my line of knowledge.
I do have a light meter (different one as Your using) and want to try stuff like this out on my own lights.


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## Bolster (Nov 20, 2011)

*Re: How to Estimate Brightness with a Light Meter?*

Thanks! (I like your sig line!!) 

What I'm very curious about, is whether it might be possible to simply replicate the LumenToob with any source of 2" PVC elbows tees and caps. Could this same device be built in, say, Europe, with similar results? Then the user would not have to go through the tedium of building a new regression formula. That's probably too much to hope for. But at some point, if my prediction numbers stay high, I'd be interested in building another LumenToob sourced from another home supply store, and test repeatability. If repeatability was high, then a single formula _might_ suffice for rough numbers. Provided the meters agreed. Again, it would be rough estimates. But the reason I'm not having a problem with rough estimates is that the eye is not very precisely calibrated, either. Some say that it takes 100% increase to view one light as significantly brighter than another. If I can keep error at 20% or below, I think this might be a useful ballpark procedure, especially considering $7 vs $2000.

BUT--can I keep it at 20% and below, with more data? That's the big question. I'm not sure yet. NEED MORE DATA!! (And my two new Hi CRI Quarks aren't helping any, since they don't come with any published lumen data!!)

Currently, my *"percent error" column averages to just 0.8%*, (explaining the high r-squared of .975) once I remove estimates at 10 lumens or below (which are wildly inaccurate at this point). But even though 0.8% is the current _average_ miss, my_ worst_ miss is -53% (a light advertised at 25 lumens, I estimate it at 12) and my second worst is +46% (a light advertised with 12 lumens, which I estimate at 18, but it's very close to my 10 cutoff, thus the likely error). So there are some published lumens this method misses by a significant margin. (Cue Hiawatha the Statistician.) 

Here's data from a Fenix P1D-Q5, that shows the up-side of this project: 

Published....Estimated.....Percent
Lumens.......Lumens........Miss

....16...............16..............0%
....95...............93.............-2%
...180..............181.............1%

...hey, if they were all like that...wouldn't that be nice!


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## vaizki (Nov 20, 2011)

Mispost... Somehow ended up posting an SMS I sent earlier... Tapatalk fail.


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## selfbuilt (Nov 21, 2011)

Interesting approach with the PVC tubing. FYI, you may find that you need to use more than one relationship across the range of outputs to better predict estimated lumens. In my case using a lux meter and milk carton, a pair of simple power relationships best fit the data. You can see the result of my comparison attempts here:

How to convert Selfbuilt's Lightbox values to Lumens 

Use of an EV meter will likely alter things for you, since there is a built-in logarthmic adjustment (base-2, if wiki is correct). But I see no reason why the "toob" approach may not yield some sort of consistent relationship. Good luck tracking down additional comparisons.

As an aside (not relevant to the lightbox setup, but you may find it interesting in relation to EV metering), the old saw that we perceive brightness "logarithmically" doesn't seem to be correct. More recent research supports a power relationship - specifically, a cube root relationship for non-point sources of light. See a detailed discussion in this post. As a general rule, logarithmic works quite well, but seems to break down at the really low outputs. But again, that's just referring to perceived brigthness - lumens estimation is based on the collection of all light emitted.

:wave:


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## Bolster (Nov 26, 2011)

UPDATE: 

I added a few more lights to my dataset, took much more careful measurements (recorded highest and lowest readings obtained, and calculated an average for the computation) and also allowed myself to remove one outlier, a Fenix LOD Q4 midlevel that claims 25 lumen and is jarringly out of place (should be around 10). Again, the exponential curve fit well. As before, the R-squared high at .975. However this time I was able to reduce my error. Previously the standard deviation was .20 and now it's down to .13. Or here's another way to view the error...if I turn my "percentage I missed the mfgr's lumens" calculation into absolute numbers, remove the <10 lumen estimates, and take the average of that column, it has reduced my average miss from 14.4% to 9.9%. 
*
So on average I'm missing the manufacturer's stated lumens by around 10%.* As before my estimations for below 10 lumens are not good, so fitting this single curve just doesn't work with the low-lumen numbers. Anything below 10 has been deleted for my overall estimations of accuracy. Some of my estimates are within 1%, and my worst is now 39%...for a Fenix L2D's low level, which mfgr claims to be 11 lumens (close to my cutoff for bad estimates, thus the likely problem). Also, I should add that the range for these estimates is between 10 lumens and 200 lumens. I don't have enough bright lights to extrapolate to the higher lumen counts. In fact, I don't have enough data above the 150 lumen mark to be happy about the dataset on the high end. 

The formula is now: 

Estimated lumens = 3.762 + (.306 * (2 ^ EV))

...where EV is the reading that comes from the Gossen light meter. That last embedded parenthesis, for the non math inclined, means "two raised to the power of EV". (That power conversion converts the curvilinear data into a straight line that's easily digestible by the linear regression program.)

Below: blue = actual mfgr-reported data (jumps around due to differences in how mfgrs measure & report), red X = where the program calculates the prediction (along a theoretical curve). You can see how the curve systematically overestimates lumens under 10, which is why I can't use that part of the curve for prediction. On the high end of the curve--if only I could find a few more 150-200 lumen lights to test. (I just got a nice HCRI 2AA Quark, but unfortunately 4sevens doesn't give lumen ratings for that light...darn it.) 






So, _in theory_, if PVC pipe is relatively similar in composition around the world, and if you have an incident light meter, and if incident light meters measure similarly around the world, then anybody should be able to tape $7 of PVC together and use the formula I've published above, to do their own lumen estimations. It would be nice to verify that assumption. If anyone's interested in trying, let me know. It would be interesting to know if every "LumenToob" has to be recalibrated with a custom formula, or is the formula fairly robust for any PVC toob? 

And once again: if you live in Los Angeles, and have some lights of known lumens, give me a shout. 15 minutes with your lights (I don't even have to touch them, you can!) would certainly add much-needed data. Thanks!


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## Bolster (Nov 26, 2011)

selfbuilt said:


> Interesting approach with the PVC tubing. FYI, you may find that you need to use more than one relationship across the range of outputs to better predict estimated lumens....



Hi there, Selfbuilt! Thanks for your insights. It appears I am trying to re-invent the wheel which you already invented! Somehow I missed your lightbox build when I was doing my background research.

I agree that the lower end of the curve needs a separate regression program built for it. I think that's the best solution, and I see you had to do the same thing...I see you split your high and low range formulas at 25 lumens. When I get some spare time I'll give that a shot. Likely a different relationship down there in the lower part of the curve. I see in your results, it was still a power relationship on the lower portion of the curve, but just less "curvey." 

I like your work, and appreciate your much more complete dataset. 40 lights and 150 datapoints, that's righteous. Mine's currently at 8 lights and 28 datapoints. I see your r-squared is very similar to mine, at .96 and .97. That explains how your curve fits the data so well. Even our formulas look somewhat similar, although mine uses an intercept value (but it's small, 3.8). 

Hey Selfbuilt, I would love to see your carton lightbox if you ever get the chance to snap a photo of it. And your caution to view results of strong throwers with a dash of skepticism is well taken. My suspicion is that the type of mechanism we build to measure lumens (your milk carton, my PVC tubes) would have an effect on the relative performance of floods vs. spots. In my tube design, I worry that the throwers will get an unfair advantage, rather than an unfair penalty.

At the end of your post you say: 




selfbuilt said:


> But at the end of the day, I think the analysis and correlation results tell a pretty compelling story - especially since they consist of the multiple output levels of over 40 lights taken from 6 different sources. You can thus feel fairly confident in converting my lightbox readings to something approximating lumens.



And I have to agree. Your r-squared of .96 to .97 really says it all. Viewing your data, and comparing it to mine, I'm thinking that the layperson can make reasonable estimates of lumens without an integrated sphere.


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## WhiteRabbit (Sep 18, 2014)

Argh! The photos are deleted! Would you please put them back?


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