The proper way of calculating lux / cd / candlepower

LED Flashlights – General Info
1

NOTICE

This method has been found to be incorrect, thanks to the tests of another forum member as well as my own. Please see these posts for more information:

https://budgetlightforum.com/t/-/43158/35

https://budgetlightforum.com/t/-/43158/39

NOTICE

So I found a pretty old post on the other flashlight forum about why just taking a random lux measurement and then calculating it back to 1m is wrong.

I did some research, and yes, it makes sense both mathematically and in practice.

Before doing all this math, I wanted to see for myself irl, so I took my tiny P5r.2 aspheric flashlight and put it horizontally.

I was very careful to get all the measurements right, and the peak lux in the hotspot:
At 1.00m I measured 12000 lux (12000 cd).
At 2.00m I measured 4500 lux. Now logically, based on 1/r^2, you can calculate this back to 1m by 4500*(2^2)/(1^2) and you get..........18000 LUX???

YES that is correct! The farther you measure lux from, the higher the cd value you get!
At 2m shouldn't it have been 3000 lux? Let's see why not:

So now, let me explain why almost every lux/cd/candlepower you have ever seen is (somewhat) wrong:

First of all, there is this scary-sounding thing called etendue: https://en.wikipedia.org/wiki/Etendue

It seems complicated, but the main thing you need to know is just the inverse law of light:

Pretty simple right? 2x distance, 1/4 lux.

Now, the reason for this is because light is emitted in a 360 degree sphere. Taking a look at a slice of a sphere, you see this:

Looking good?

Well here comes trippy part:

The head of a flashlight is NOT a point. The beams coming out of (most) flashlights is NOT spreading out by 1/r^2 (the spill is, but the beam is not)

Imagine a perfect thrower, perfectly collimated light ways, with 0 degrees divergence. The head of the light is 100mm, the spot at any distance is 100mm.

Ignoring the resistance of air in the way, the lux at 1m would be exactly the same as the lux at 10m, or 100m, because the spot is not increasing in size. All photons at 1m are the same as the number of photons at 100m.

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Now imagine a flashlight like aspheric or large reflector throwers, which are CLOSE to collimated:

As you can see, the light coming out of a flashlight is actually a SECTION of the inverse square light law, a section that does not begin at r=0.

This means that the light is diverging LESS than if the flashlight was the source. How much less will depend on how well your flashlight collimates the light.

This is easy to calculate by just measuring how wide the beam is at the head of your flashlight, and how wide the spot is at a distance.

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Fortunately, there is another really smart person who made a web calculator for this: http://nightsword.com/uniformbeamcalc/

But at first I didn't trust it, so here is some math to check:

Say we have a flashlight with a 100mm lens, and the full lens is being used, so there is a 100mm diameter beam coming out of the flashlight.

The beam is fairly collimated by the lens, and I measure a 300mm spot at 10m distance, with 50000 lux.

The point of the triangle is behind the light by some distance we do not know, so we find it using some simple trig that you probably learnt about in high school:

Except we know the tree is 300mm tall and the person is 100mm tall, and the ditance between the tree and the person is 10m.

(you might be thinking I should have used 150mm and 50mm, but the truth is the ratio between 300 and 100 is the same as the ratio of 150 to 50, and only the ratio matters!)

so 300/100 = (10+x)/x where x is the distance behind the light

3x = 10+x

2x = 10

x = 5

The light rays converge to a point 5m behind the light, and the 10m you measured at is actually 15m from the origin.

NOW we take the 50000 lux (50k lux) we measured and apply the inverse law of light,

(lux @ 1m) / (50000) = (15m)^2 / (1m)^2

lux @ 1m = 225 / 1 * 50000

lux @ 1m = 11 250 000 lux = 11.25M lux = 11.25M cd = 11.25M candlepower

Since some american made that calculator, we are inconvenienced and need to use google to convert m to feet and mm to inches....

BUT IT WORKS!

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Why you might not want to care:

-lights with a small head diameter have pretty large beam divergence, just look at any reflector EDC flashlight, which means the convergence point behind the flashlight is not that far behind, so lux measurements are fairly accurate.

-the farther the lux is measured at the more accurate it is (basic trig, imagine the triangle above, the ratio of measurement distance/total distance gets closer to 1), so it's not like you're actually getting less lux from your light, the rating on the light is an underestimate

-maybe you don't care about lux/cd throw at all :P

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Why I care:

-I have been underestimating my lux output of my aspheric throwers. I need to go outside and measure the spot size at about 50-100m distance, then properly calculate the candlepower/cd/lux.

-measuring indoors is not very accurate because of the way lenses work, you can end up with incorrect values due to the rays crossing over eachother if not focused correctly, which is why accurate results should use a measurement of "a few hundred feet" as it says on the website :)

-I hope you learnt something, I certainly did, and I'm looking forward to finding out the real values of my flashlight.

2

Makes a lot of sense. I had kind of wondered about that myself when measuring from 5 meters, a 4inch spot on the wall that came from a 2inch lens.

But I foresee difficulty changing the longtime “standard” way people measure/calculate lux/cd. Though the fact that the new “correct” method results in better numbers should help make people want to adopt it. :stuck_out_tongue:

3

Ummmm..... okay....

If it's broke I can fix it... From now on if it's math I'm sending it to you...

4

Hello Endermann,

Very nice research and good explanation :slight_smile:

5

My math is not as bad as I make it sound. However I do use a phone app for the calculations. It's an app I use for work mostly that happens to include lighting calculations lol.

6

Most flashlights are not that highly collimated so the lux measurements are “accurate enough”, and you can’t get sued for it because the true numbers are actually higher, the numbers on the box are an underestimate.
If everyone agreed to measure lux at 10m or something standard like that then it would be easier to compare between flashlights, but that’s not gonna happen :stuck_out_tongue:

Hahaha and I’m not even a math major xD
Thanks though

Thank you :slight_smile:

7

My mistake even using the app has always been either the room was not totally dark or I had my distance wrong. And the angle... well it's always wrong

8

I don’t turn off the lights when taking my measurements, when I set the luxmeter range to x100 the tiny 50lux from my room lights become 0 and do not affect the 50000 lux from my light :stuck_out_tongue:
So for me it’s an insignificant decimal place that doesn’t even get considered.

9

I see your point bu i somewhat remember having the exact same number when measuring my B158 at 5 and 100 meters using the simplified widespread method of calculation, maybe i should try it another time.

I was under the impression that the common wisdom among us was that 1 or 2 meters readings may not be accurate and that around 5 meters was kind of the minimum distance to take readings.

10

I have to say that this possible effect has caused me some confusion regarding my understanding of throw and how to predict it, so I did some measurements to see what is actually happening.

My test light was a UF-1504, with 62mm diameter lens and XPL HI V2 1A. I put in a 8x7135 driver to keep the output more constant with time. I measured the lux at three different distances measured from the lens.

dlux__cd
6.05m7230_264.6Kcd
8.34m3840_267.1Kcd
10.29m2530__267.9Kcd

These measurements are consistent with measuring the distance right from the lens and not at some point behind the lens.

Plugging the 10.29m measurement (the beam size at this distance was 36cm) into the calculator you linked (after converting units), results in:
divergence distance behind aperture: 2.14m
candlepower: 390.9Kcd

The calculator results are not consistent with my measurements and how they vary with distance. There are certainly some things in your explanation of the effect that make sense, but actual measurements tell a different story.

A different effect could have caused your conflicting results when you measured the lux at 1m and 2m. At small distances like 1m, the lens might not be filled with the image of the LED, from the point of view of the lux meter. Moving farther back to where the lens is filled would then result in a larger throw number.

11

I’m pretty sure the reason people don’t measure at 1m is because a luxmeter can only do like 20000 or 200000 lux, and at 1m an aspheric flashlight is above that by a lot.

That’s interesting. Is the entire lens actually being used to focus the light?
I usually check by making sure there is led light spilling off the sides of my lens, and using a water sprayer to put water in the air so I can make sure the beam is filling the lens.
Your results still show that the farther you measure at the higher the cd you get. Maybe try measuring at 50 or 100m? :stuck_out_tongue:
I will need to do more tests with different lights to double check.

12

I really can not follow your story very well, I think that you are simplifying the direction that the rays coming out of a flashlight as if they start from a point source which certainly is not the case, flashlight optics and hotspot size/brightness have everything to do with the led not being a point source.

Hotspot brightness has to do with the fact that flashlight optics are imaging a led at a distance, so it more or less follows the lens maker’s formula creating an image of the led at a distance, smaller led or longer focal distance of the lens=smaller image, . Even reflectors do something similar although the way they ‘image’ is way more complicated.
One consequence is that if the image is created at twice the distance from the lens, the image is twice as large (4 times the surface area) and is thus 4 times less bright.

And my aspheric lights follow that simple: twice the distance from the lens= 1/4 the brightness pretty accurately, even when starting from 1 meter.

Reflector lights need more distance to form their uniform hotspot (they are not focusable like zoomies), but my usual 7 meters indoors is enough, and the simple relation between distance and brightness is followed.

13

But the lens is not producing a point source of light…
That’s why applying the inverse law of light assuming that the lens is at r=0 is incorrect.

If you had an ideal light source behind a lens, the lens would collimate the rays and the intensity would not change by distance, which would be infinite candlepower.

14

[quote=Enderman]

No, ever since i started this hobby back when flashlight where much less bright people pretty much agreed on the wisdom that the closer the measuring distance, the less accurate, one or two meters readings have always been considered irrelevant and met with encouragment to measure from farther as far as i can remember, absolutly nothing to do with luxmeter capabilities.

15

Yes, the entire lens is filled with the image of the LED for the distances I measured. I check by looking into the beam at different distances using sun viewing glasses.

16

I think it is because of the reason I mentioned above; at close distances the lens is not filled with the image of the LED. You cannot tell this by spraying water; you have to actually look into the beam at the lens.

17

There are ANSI standards, developed for and by the lighting industry by specialists in the field. There is probably a reason they don’t use if’s and assuming in their definitions. The primary objective is to establish parameters of comparison, to create an equal and repeatable playing field for the purpose of recreative ability in determining the value of one light versus another as suited to a particular task. At the end of the day, deviation from the accepted standard is disqualified summarily as non applicable to the established criteria.

So, in simple terms, if we don’t all use the same test, our results cannot be compared and as such, the tests themselves are disqualified.

Don’t sell us, sell ANSI, then we will adapt accordingly.

An Enderman’s primary purpose is to create chaos and confusion.

18

it is irrelevant where the imagine source of the flashlight is
you get only higher lumens if you go to a negative distance towards the spot where the light should for a focal point,
but that is physically impossible

if the light has 20mrad divergence it doesnt matter where you put a ideal luxmeter as long as the beam is uniform in brightness,
as a reflector light is not uniform in brightness at close distances, so you have to go further away,
if you are too close you measure too low lumens in the donut hole or too high lumens in the ring where the brightness is concentrated

on a reflector light the spill also affects the measured lux if you are very close

the next factor is that your measurement would need to be taken on an indefinate small point in the middle of the beam,
so the bigger the spot is the less you get a false reading as your luxmeter has a quite big spot to catch light at low distances

19

It does though…
If you take a measurement at 10m you would think at 20m it would be 1/4 brightness, right?
But if the convergence point behind the flashlight is 100 000m behind, then the difference between 10m and 20m is nearly 0 because 100 010^2 and 100 020^2 are almost the same number.
Unlike 10^2 and 20^2 where the second number is 4x bigger.

Hopefully the 100000m exaggeration is enough for you to picture what is happening here.

20

Lol I need you to crunch some numbers for me. Then in about a week there will be a tiny upgrade to 1 of my sk68 and 1 sk98 lights. I'm curious what of any difference will be.

I have some higher output cells coming. I'm told I should notice a difference.

If you are up to it, my light meter is built into my phone app. Just let me know at what distance or whatever you may need.

Let me know if you are up to it. I will be typing up a review so it may take me a few minutes to respond. And if you don't feel up to it that's olay too. I know all about being tired. I'm very good at it.