Calculating total output with a single intensity measurement

[QReciprocity42 (efficacy ≠ efficiency)]

Inspired by a discussion from this thread, I present a method to estimate total output of a reflector-based light with a single intensity measurement at the edge of the spill.

The idea is simple: at the boundary of the spill, the light comes directly from the LED without any transformation by the reflector. Since a bare LED follows a Lambertian emission profile, a single intensity measurement at a known angle gives you enough information to calculate the emitter’s total output.

What you need:

• A wall 1m from the LED
• An estimate of the diametrical spill cone angle (2θ)
• A lux meter

What you do: [EDIT: this procedure will be replaced by one more robust to measurement errors, to be updated later today.]

• Position the light such that the LED is 1m away pointing directly at the wall.
• Place the phone just to the interior of the spill boundary, flat against the wall, and take an intensity measurement, say L lux.

Schematic:

The computation:

• The total OTF output of the bare emitter (post reflection losses from glass lens) is given by Ω = πL / (cos(θ))^4 lumens.
• For a more accurate result, perform the measurement at a farther distance of d meters, and the final output is Ω = πLd^2 / (cos(θ))^4 lumens.

This method does not yet account for losses at the reflector (which should be easily to estimate, I will update this post with the calculations later), but should already give a +/-10%-accurate output estimate, assuming a correct intensity measurement.

Quick proof sketch for the formula

At point (1), the illuminance is [1]=Ω/π lux; this is a standard result about Lambertian emitters, which follows by considering the sphere of diameter 1m in front of the emitter–this sphere’s surface has constant illuminance and area π.

Point (2) is also 1m away from the emitter, but offset by angle θ. Thus, a lux meter positioned at (2), facing the emitter, picks up [2]:=[1]*cos(θ) lux.

Point (4) is farther than point (2) by a factor of 1/cos(θ); for this reason, a lux meter positioned here picks up [3]=[2]*cos(θ)^2 lux.

By laying the lux meter flat against the wall at point (4), it is now tilted θ away from the emitter, and thus picks up an intensity of [3]*cos(θ) = (Ω/π)(cos(θ))^4 lux.

[QReciprocity42 (efficacy ≠ efficiency)]

Post reserved for empirical testing of this method.

[Dc38 (The Glutton)]

Try out my diffuser method!

[QReciprocity42 (efficacy ≠ efficiency)]

Could you remind/link me to the method again? I’d like to see if I have the equipment to try it out.

[Dc38 (The Glutton)]

Sure!

I haven’t tested it with Zak’s app yet, so I’m interested as to what you’ll find…The caveat is that you’d need a calibrated/verified light to calibrate to, hypothetically you could set the lux/lumens to default, and use distance to force the readout to match the known value. You can replace the ring stand with a mic stand and light clamp. Let me know if you have any questions!

Simple way to measure the runtimes (TASI TA636B lux meter)

You don’t need to measure all the light. You just need to catch a cross section of all the light. In essence, if you can use a diffuser to catch all the light, you can assume that since all the light is in the diffuser, you can take a lux meter at your set distance to approximate the lumens being put out. It was an alternative method to an integrating sphere that I developed because I didn’t have an integrating sphere. Maybe @QReciprocity42 can refine the maths and equations, but my logic was …

How to quantify beam shape? And discussions on many related topics: optics - TIR & reflector, thrower vs flooder, throw calculation, beam angle, cd/lm parameter, etc., etc. Did I miss anything?

I’m gonna toot my own horn here, and slightly deviate to a related topic, “integrating spheres”. If you take a flashlight with a known/verified lumen count, you could put it through a series of diffusers. One to diffuse the beam, the second to scatter the diffused beam. Then, place all of that into a dark box painted with the darkest non reflective paint you can find, with a lux meter set up affixed to an adjustable platform. Tune the number readings to show what the lumen value is, and you will…

**You might also be able to use a pinhole/diffuser, as the pinhole would be a “slice” of the image of the diffuser, which would hypothetically distribute the beam pretty evenly.

Also, a compound diffuser works better because of double diffusion for more even scattering.

[QReciprocity42 (efficacy ≠ efficiency)]

Thanks for the resource! Unfortunately, all my standard lights (with known output) are too big for dedicated diffusers, but that gives me another idea:

What if I used a flat sheet of printer paper as a diffuser? Just lay it flat across the front glass of the flashlight. I just tried it, and it seems extremely effective at converting whatever beam profile into an ideal Lambertian emitter–the hotspot doesn’t shine through at all, and the brightness per area appears visually identical across all viewing angles. I also like printer paper over a dedicated diffuser because the filtering is much closer to uniform across the visible spectrum.

The only concern I have for this approach is that it may penalize non-reflector lights unfairly–this is due to the reflector’s unique ability to reflector/re-emit light that has been diffused backward. A TIR does not have this ability to reflect diffuse light–it only diffuses light that reaches a certain critical angle.

Perhaps a solution is to use a large sheet of paper positioned with some separation from the light–this way the back-reflected light can be truly lost regardless of optic type. I’m envisioning a device similar to the familiar “integrating shoebox”:

Here we have a box with the interior painted black, and one hole for a flashlight; the other side is a hole for a large sheet of printer paper. When the beam hits the paper, most of it is reflected back, but a substantial amount of it diffuses through the paper and turns the paper into a Lambertian emitter. The rest is easy.

I would expect this technique to yield much more precise results than the conventional integrating shoebox, especially with exceptionally throwy/floody lights, for a couple of reasons:

1. The diffused-through light always achieves a near-Lambertian distribution, regardless of the source beam profile. This is due to 2 reasons:

(i) the flat geometry of the emitter (one flat piece of paper) compared to the more chaotic 3D geometry of a box (many reflecting surfaces). On a plane, you can arrange Lambertian emitters of any shape or size–it can be a 1mm^2 square or 2 giant circles 1m across; the angular distribution of the resulting compound emitter stays Lambertian. In contrast, the inside of a box is a 3D shape that enjoys neither nice invariance property. If you arrange Lambertian emitters in a non-coplanar way, the resulting angular distribution would be arbitrary.

(ii) diffusion through the paper does a much better job at “randomizing the direction of light”, compared to reflection, which strongly favors the direction of reflection more than the direction of the source.

4. The setup is insensitive to the location/distance of the light from the paper. As long as the entire beam is captured, the distance has no effect on the angular distribution of the output through the paper.

In contrast, a conventional “integrating shoebox” requires more precise positioning of the light. If the light is pushed too far in, the distribution of light inside the box changes and concentrates toward the far end and reads lower; if the light is too close, its spill lights up the foreground and runs into the previous issue, reading too high.

Actually, now I am more interested in pursuing this idea more than the one stated in the first post of this thread, because the former does not restrict you to reflector lights. Fortunately, the title of the post still stands! I will try to build the drawn device and run some tests tomorrow.

[QReciprocity42 (efficacy ≠ efficiency)]

It occurs to me that testing this setup for absolute accuracy is impossible, since any reference value I could find does not have a quantitative accuracy guarantee. Hypothetically, if you invent a device that makes exact, 100% accurate measurements, you wouldn’t be able to tell because all existing reference values you can find are wrong.

Instead, I will test the setup for robustness/precision: if you change the measurement parameters a little bit–a slightly different distance or a slightly offset angle, does the measurement remain more-or-less unchanged? If you modify the beam profile but leave the output mostly unchanged–say swapping between narrow/wide TIRs, does the measurement reflect this constancy?

[Dc38 (The Glutton)]

BINGO! A diffusal method scatters light the best! That should yield the most relatively consistent results, provided the diffusal method and media are relatively uniform. that leads to the below issue:

@QReciprocity42

It occurs to me that testing this setup for absolute accuracy is impossible, since any reference value I could find does not have a quantitative accuracy guarantee.

Unfortunately, this is the case for most homebrew models…HOWEVER, there can be a coordinated effort amongst members to standardize against at least one relatively consistent light source…The sun. Regardless of the global coordinates, elevation, and weather, the average sunlight, angles, and losses due to atmo can be calculated with a fair degree of certainty, again, provided that there is sunlight.

Another more dangerous, but much more consistently available standard would be a consistent electrical arc in a controlled environment, where humidity, pressure, electrical potential are all regulated.

The most dangerous thing I can think of is nuclear luminance…but besides inert stuff like tritium, this is really too dangerous…

@QReciprocity42

Instead, I will test the setup for robustness/precision:

^ That’s the goal! Consistency across samples, with readily available materials for the average layman. The only real issue would become deltas across different phone sensors and calibration light sources…but the purpose of the homebrew diffuser setup was never truly about absolute accuracy, but more precision, like how we have Kelvin, Farenheit, and Celcius. The goal is that if the same objective quality is being subjectively quantified, those subjective quantities should scale relative to the others.

If we want absolute accuracy, then we need a unifying standard which every tester can access and control, and to me, the most practical and consistent sources are either sunlight or some form of sustained electrical arcs/filament heating (molten materials, even).

[QReciprocity42 (efficacy ≠ efficiency)]

@Dc38

HOWEVER, there can be a coordinated effort amongst members to standardize against at least one relatively consistent light source…The sun. Regardless of the global coordinates, elevation, and weather, the average sunlight, angles, and losses due to atmo can be calculated with a fair degree of certainty, again, provided that there is sunlight.

This is a working method, but unfortunately only for standardizing the sun. The moment you want to measure a light source with a different beam profile and unknown output, different sun-calibrated devices will behave differently again.

@Dc38

That’s the goal! Consistency across samples, with readily available materials for the average layman. The only real issue would become deltas across different phone sensors and calibration light sources…but the purpose of the homebrew diffuser setup was never truly about absolute accuracy, but more precision, like how we have Kelvin, Farenheit, and Celcius. The goal is that if the same objective quality is being subjectively quantified, those subjective quantities should scale relative to the others.

Yes, I believe this is the most ambitious goal we could possibly hope for, given aforementioned constraints about accuracy. Good point about variation among phone sensors/calibration and possible non-linear scaling of the phone sensor–this we have no control over.

Perhaps the calibration can be done at a few different brightness/intensity levels, to get calibrating parameters that are “uniformly low error across a wide range of inputs” rather than “zero error on a single input and no guarantees for other inputs”. After all, even a simple linear regression takes at least 3 data points to perform…

Also, maybe the goal, instead of “getting the most accurate measurements”, could be changed to “getting measurements that are closest to those from a proper integrating sphere”. After all, absolute accuracy is not as useful as standardization, which makes comparison meaningful against other standardized (even if not necessarily accurate) measurements. Same probably holds for color rendering: the human eye generally prefers pink and oversaturated sources, but these sources do not occur in a consistent and natural enough way to be useful as a standard.

[Dc38 (The Glutton)]

@QReciprocity42

The moment you want to measure a light source with a different beam profile and unknown output, different sun-calibrated devices will behave differently again.

The beauty of diffusers! Whatever settings you have for the sun, if you bring a pre-calibrated integrator outside, set up the series of diffusers or papers such that the final paper is the lambertian emitter inside that sphere and target it in line with the sun, you will get an objective reading of how many lumens one specific sunbeam, as filtered through specific paper/diffuser setup and/or pinhole, actually is…maybe?

[Dc38 (The Glutton)]

Believe it or not, I have given this alot of thought over the years, and other thoughts which are incidental end up refining the idea, lol. I can confidently say that I have not even begun to cover a single one of the many bases of photometry…

I’ve always liked numbers, but hated working with them. I’m decent at spotting patterns, but prefer to focus on the outliers. I prefer to chase those “extraneous” datasets in pursuit of potentially unknown patterns, then drop the patterns for others to verify while chasing the erroneous values in those new data sets…as it relates to the diffuser based “integration”, I believe that the above links have sufficiently plotted the logic/thought process that (you) or someone else could derive or contribute a more precise and consistent consumer-available system. That said, Zak’s app is one such marvel, as are TK’s firmwares, as is DirtyDancing’s UI flowcharts, and Koef’s testing, and many others.

Putting my big, empty-ahh head aside, what other hiccups in consistency have you noticed so far?

[Dc38 (The Glutton)]

@QReciprocity42

If you lux match the calibrated light, you get the height/distance that the new light should be measured from before switching to the lumen setting on Zak’s app.

i.e., if at 1 meter you measure"THROW" to be 5000 (5kcd) with one verified lumen light, plug in the lux per lumen value in “SETTINGS”, you can go back to “THROW” with a new light and adjust the distance either closer or further until that reads 5000. Lock in that distance, then switch over to the “LUMEN” tab to grt a pretty accurate reading.

I’m gonna check the readme to see if I should just start reading instructions before operating things…

Gonna blur that out for now, need to test specific scenarios first

[QReciprocity42 (efficacy ≠ efficiency)]

@Dc38

The beauty of diffusers! Whatever settings you have for the sun, if you bring a pre-calibrated integrator outside, set up the series of diffusers or papers such that the final paper is the lambertian emitter inside that sphere and target it in line with the sun, you will get an objective reading of how many lumens one specific sunbeam, as filtered through specific paper/diffuser setup and/or pinhole, actually is…maybe?

I worry that the substantial UV presence in the solar spectrum would introduce fluorescence in the diffusing paper, which messes with the output.

@Dc38

I’ve always liked numbers, but hated working with them. I’m decent at spotting patterns, but prefer to focus on the outliers. I prefer to chase those “extraneous” datasets in pursuit of potentially unknown patterns, then drop the patterns for others to verify while chasing the erroneous values in those new data sets…

You might have noticed that I enjoy working on the more quantitative/theoretical/analytical side of things, which complements your preference. Doing math is cheap: no fancy, expensive equipment needed, just pencil and paper. And I feel that I have enough training (as a math PhD student with some statistics background and a rudimentary understanding of basic physics) to do a somewhat competent job.

@Dc38

I believe that the above links have sufficiently plotted the logic/thought process that (you) or someone else could derive or contribute a more precise and consistent consumer-available system. That said, Zak’s app is one such marvel, as are TK’s firmwares, as is DirtyDancing’s UI flowcharts, and Koef’s testing, and many others.

Developing such a system would be a Herculean task without more interest/involvement from the community, and not particularly meaningful if not widely adopted.

What I really want to see from all measurement systems is some sort of accuracy/performance guarantee. Something along the lines of “every measurement is accurate within +/- 20% with 90% confidence”. A single data point, without any sort of interval error estimate, is meaningless.

Unfortunately, such is the state of things when it comes to integrating shoeboxes and some intensity measurements I’ve seen. I’ve seen some output/intensity measurements on the subreddit that exceed extremely generous theoretical upper bounds by a good margin, which is sure indication that some part of the measurement process has gone seriously awry. Unfortunately, not everyone performs sanity/consistency checks to make sure that the numbers they get are sensible.

[Ruckusmattster (Ruckusmatter)]

do you have any tips for including those error bounds in calculations, i assume its not as simple as what a lu meter’s sensor’s error is?
do you have any examples of those egregious examples? i want to see if ive been fooled by them

[QReciprocity42 (efficacy ≠ efficiency)]

@Ruckusmattster

do you have any tips for including those error bounds in calculations, i assume its not as simple as what a lu meter’s sensor’s error is?

Yes! It’s generally much easier to give a lower bound for measurement error than an upper bound, and I will only address this half of the problem. One general strategy is to slightly tweak the measurement setup and see how much the result changes.

For example, if you’re performing an intensity measurement, ways to estimate error include:

• Making multiple measurements under identical conditions to get a sense of how much error to expect under said set of conditions, due to uncontrollable factors.
• Measuring at different distances (say 1m versus 10m) and back-converting to lux@1m to get a sense of error introduced by (i) change in beam profile due to measurement distance, and (ii) potential non-linearity of the lux meter’s response.

Such variations in measurement method would sometimes hint at problems with measurement methodology. For example, a flashlight reviewer might measure an extreme thrower at 1m and get, say, 300kcd of intensity, and measure again at 20m and get, say, 1 million cd. The former is quite a common mistake.

Such an inconsistency might alert the reviewer to the possibility that measuring at 1m doesn’t work for super throwers because the beam “has not converged to its final shape”: the beam from a thrower is a very poor approximation of a point source at close distances, and thus does not follow the inverse square law of illuminance at such distances.

Upon further thought, the same reviewer might also think of an ideal, perfectly parallel beam of light, which has infinite intensity in candelas and measures the same illuminance (lux) regardless of distance. As a result, as measurement distance increases, the back-converted lux@1m grows without bound. Such a thought experiment may also help them realize that the measurement distance should be as far as reasonably possible to come close to the true intensity of the light.

@Ruckusmattster

do you have any examples of those egregious examples? i want to see if ive been fooled by them

I vaguely remember someone claiming 2400lm and 1200m out of a M21A SFT25R, but my first guess for the owner of that post is now a deleted account. Unfortunately, reddit doesn’t have any way to search my own comments. I also vaguely recall some unrealistic throw claims from SkyLumen on a compact light with a large SBT90-type round die emitter, but it was a while ago and I couldn’t quite locate it.

[Dc38 (The Glutton)]

@QReciprocity42

I worry that the substantial UV presence in the solar spectrum would introduce fluorescence in the diffusing paper, which messes with the output.

This should be ok, if overall lumen rating of unaltered sunlight includes phosphoresence, then that lumen rating will be the baseline

@QReciprocity42

You might have noticed that I enjoy working on the more quantitative/theoretical/analytical side of things, which complements your preference.

Big thumbs here

@QReciprocity42

Doing math is cheap: no fancy, expensive equipment needed, just pencil and paper. And I feel that I have enough training (as a math PhD student with some statistics background and a rudimentary understanding of basic physics) to do a somewhat competent job.

I don’t know that the emboldened words necessarily go together these days, lol…

@QReciprocity42

What I really want to see from all measurement systems is some sort of accuracy/performance guarantee. Something along the lines of “every measurement is accurate within +/- 20% with 90% confidence”. A single data point, without any sort of interval error estimate, is meaningless.

Agreed…maybe, like with the great thinkers, we have to pass on first before people widely adopt the standards LOL.

@QReciprocity42

Unfortunately, not everyone performs sanity/consistency checks to make sure that the numbers they get are sensible.

Number sense only gets sharper with experience…linear vs logarithmic vs exponential. it only gets more complex to sense when more variables are added in, lol… Personally, my number sense has become about as sharp as a warm, gentle breeze.

[Azirine]

A simpler way would be to remove the optic and measure the candela of the mule head on. For a Lambertian emitter, each candela will be π lumens.

[QReciprocity42 (efficacy ≠ efficiency)]

This is indeed a simpler idea for lights with removable heads–most LEDs, domed and domeless, seem to have a profile that is very close to the Lambertian for most of the emission. Though some lights might have shiny interiors that create unwanted reflections that inflate the reading.

[Oli]

I just read through this thread now. I had not seen it earlier.
My first thoughts are , no you’re not going to get a sense or be able to measure total output by taking one little slice of the spill. But I guess you’ve already moved on from that.
My next thoughts are why does it matter.
When new people come in and ask for recommendations for a light with a specific number of lumens they often don’t understand that the light is going to drop down and that the type of beam that it produces is going to determine how far and wide they can actually see.
While the number of lumens is somewhat useful information it’s not really relevant in understanding how far and how wide your field of view will be with any given flashlight.
Knowing the degrees of the spot and The spill is somewhat useful but again it still doesn’t tell you how much of the light is going into the spot versus The spill so that’s not the full answer either. And that’s why taking any one slice of the spill or spot is never going to get you there.
Maybe for lighting up a room with a light bulb the total number of lumens is useful.
And if a few flashlights have fairly similar spot to spill ratios then I guess the total number of lumens is somewhat useful. But in a lot of cases more lumens just means it will step down sooner.
I’m not saying you should give up but I’m not sure where you’re going.
And the sun is not going to be a standard measure of light or intensity for any two different members here. It is going through different amounts of atmosphere at any given time of the day. Even if you don’t think you see any clouds there are so many variables. Time of year, distance from the equator, pollution that you Don’t SEE and “other”.
Having said all of that, again there are some cases where most of the light is in a relatively certain area where you can see and use all of it to see. But the total lumens is just one part of the picture.

[Oli]

I do want to add that I appreciate all the people that have gone through the effort to build the lumin tubes and get a standardized light.
I just don’t see any way you can beat the system. I believe you need to attempt to capture and integrate all of the light that comes out of the front of a flashlight before you can attempt to measure it at one small spot with a light meter.