# The proper way of calculating lux / cd / candlepower

The more the better, because the margin of error when calculating lux and measuring the spot size is lower.
Although it should be in the tens of meters, not hundreds, because then the lux values are too low to be read by the meter

you are wrong
if the convergence point would be 100000m behind the flashlight just the divergence would be really low about 0.000001mrad if the lens diameter is 10cm
at 0.000001mrad the Lux value between 10 and 20m would be almost the same
lets say at 1m I got 100cd
now I got to to 10km

you are just not understanding the difference between a flashlight and a laser

take a laser pointer with 3mm beam and 0.25mrad single Mode diode

I measure at 0m 10000cd

calculated 8521cd

calculated 7346cd

I got 15 years experience with lasers also calculating things trust me

I understand the principle here but I can see why it’s sorta hard to explain and actually using it is also quite a trick. I have a question for EasyB though that may clear some things up, how did you measure the spot, it is of course square so did you measure it’s width or diagonal. I think the correct measurement should be diagonal if you are using the lens diameter as the aperture.

I’m going to do some more extensive tests shortly but as I’ve thought about this in the past I sorta came to the same conclusion as DBC in that in the end it doesn’t matter because numbers are great but if everyone else is just measuring lux at at distance then you are “cheating” kinda, I mean you may be more accurate but for instance in my case selling a light using this more “correct” math means that when people measure it they will come up short and it will be hard to compare with other lights measured in the same fashion. As in for personal uses it’s fine but it’s hard to move out from there.

Then there is the measurement problem, it’s not exactly easy to get really accurate hotspot sizes, sure you’ll be close but there is a lot of messing about and guessing required since the beam is not clearly enough defined at that range. You would have to move the lux meter around to chart the lux change.

However, because this effect gets more and more pronounced the higher the kcd using the “basic” measuring setup may cause some issues because the “basic” measurements will rapidly start generating higher kcd with longer and longer measurement distances. So maybe this is really needed for 1Mcd+ lights. I’m going to try to get some different tests done with our 1-3Mcd prototypes and see if I can get some good comparison numbers.

EXACTLY
THIS IS MY POINT

You can’t take a lux measurement at 20m and then just calculate it back to 10m by 1/r^2 by doing lux*20^2/10^2
Because the flashlight is not where r=0 is!
If the divergence is really low, just as you said, the lux will barely be any different! It will not be 4x higher at 10m compared to 20m!

Good point!
The farther you calculate it, the closer you get to the true value, but users usually do less than 20m measurements so they would get a smaller number than yours.

Measuring the spot size is hard unless you have a highly collimated light with a sharp projection, so tbh this method is not really useful for typical flashlights and reflector lights, it is more for aspheric throwers and sky beams and stuff like the maxabeam.

Also, IIRC the maxabeam was measured at 3M lux at 1meter, but the candlepower is 12 million. So yeah, goes to show how misleading lux can be when calculated incorrectly for those types of lights.

if the convergence point would be 100000m behind the flashlight just the divergence would be really low about 0.000001mrad if the lens diameter is 10cm
lets say at 1m I got 100cd

now I got to to 100.000m then my spot is exactly 20cm
so at 100km of the flashlight I get 25cd
if I calculate that lux to 1m I get 25,000,000,000cd
if I measure at 300.000km or one light second
I get a spot of 600m
0,0000027cd
If I calculate that to 1m
I get 250,000,000,000cd

so for this almost perfect thrower the distance to get an accurate reading would be a couple of light seconds away

there will be a point where the cd doesnt raise anymore
how far that is away depends on the divergence and lens diameter

as flashlights are really bad on divergence that point is really close to the light 5-10m should be fine

just go further out and when the calculated CD value dont increese anymore the reading is accurate

you are just not understanding the difference between a flashlight and a laser

take a laser pointer with 3mm beam and 0.25mrad single Mode diode

I measure at 0m 10000cd

measured 8521cd

measured 7346cd
if I calculate that to 1m I would get 29384cd

measured 115cd
if I calculate that to 1m I would get 1,150,000cd

measured 0,00144cd
if I calculate that to 1m I would get 1,440,000cd

for a Laser that will be in the range of a couple hundred meters to kilometers
it all depends on ratio for divergence and lens diameter

I got 15 years experience with lasers also calculating things trust me

Yes good job, now you’re basically saying the same thing I did in the original post.
For most people with regular flashlights, it doesn’t really matter.

For HIGHLY COLLIMATED lights such as aspheric lights or short arc lights (eg the maxabeam) then YES there is a significant difference between just measuring lux at a few hundred feet vs actually calculating the real candlepower due to the highly collimated sub-1 degree of divergence.

It does NOT need to be a laser, anything that partially collimates light is affected by this property.
This is why if I measure my light at 5m it gets a different cd rating than if I measure it at 10m or 15m.

I honestly don’t understand why you’re even trying to argue, you’re basically proving my point a second time…

I mean it’s not like there is some magic point where etendue compensation is suddenly needed, in effect you are both right the question is what magnitude are we talking here. Lexel is probably right up to surprisingly high kcd/lens size/collimation. Surely well in the range of even the best off the shelf “throwers”, or least that’s how it seems to me, seems like the error with them would be well within the numerous other factors involved. But after 1Mcd things start to get different, we aren’t dealing with the 3mm aperture Lexel used in his example, we are dealing 100mm+ lenses. The divergence is surprisingly small. I of course don’t have measurements yet but things sure look awfully small. If I recall that tree line is 1300m away. So I guess my seat of the pants opinion is that there is some compensation needed at these ranges and perhaps it’s enough to be worth taking into account.

Okay I just took a screen shot of the reading.

This is at 5 meters. Cree XML2 and I did not install this one. This is one I believe to actually be a real Ultrafire, so no clue of bin or color

I can tell you it is the whitest of any XML2 I jave seen. Let me know what else you need .

Normal flashlights have a hotspot of 10-20 degree with 1” diameter

The virtual sorce point is often not even behind the body of the light, if its a short reflector
We are talking here about 10-30cm, if you measure at 3-5m the difference is very small

A extreeme thrower has less divergence and big head
Lets say you get 2 degree with 10cm head the virtual point is less than 3 meters behind the flashlight

The fact that your luxmeter has a big aperatur catching light compensates the virtual source behind the front of the flashlight, ideally the luxmeters aperature should be 0mm2
So often the measurement at too low distance is still correct as both values negate each other

The whole calculating cd to 1m is not really useful to get the real brightness if there is not a defined distance for measurement set for beam angle/head diameter, as well how big the aperature of the luxmeter has to be

Yes I used the width. Not sure whether the width or diagonal is the correct measurement, but it doesn’t make a big difference. My measurements are still inconsistent with the model proposed here.

I’m not convinced the model is accurate for our flashlights, at least not to the extent to which that calculator is predicting. We should be able to test the predictions, and, again, my measurements show them to not be accurate.

We need some more carefully done measurements on largish diameter lights. The tester should be careful to keep the output the same for each measurement. Also there is another effect that I have mentioned that would change the measured cd; at distances too close to the lens, the lens is not filled by the image of the LED. The tester should only measure at distances where the entire lens is filled with light. (tested by looking into the beam at the lens from the distance in question) This distance for my 1504 lens with XPL HI was roughly 2m.

All this talk is nice, put it to pictures for provenance. We have an old saying around here, pictures or it didn’t happen.

Reading the spec sheet on the Thrunite TN42 from it’s light… a mile away

Reading the same spec sheet by the light of my 200wW green laser that was used to aim the camera and TN42, same mile away.

(Yes, I know, my wife missed focus on her camera)

The hot spot from the TN42 was some 40’ in diameter at a mile. The hot spot on the 200mW green laser was about 6’ at a mile.

The TN42 from the lights end…

The 8 1/2 x 11 sheet of paper on a tripod can be seen in the middle of the picture, as can my wife in her pink shirt and black slacks, illuminated from a mile away by the factory Thrunite TN42. Sure, it’s fun to do the math. Much more fun to prove it.

I didn’t have her take a picture of the 3.3W blue laser, she couldn’t see where it was hitting with her eye protection on…

Thank you! Someone that actually read the whole post

From my last measurement, my beam has less than 0.25 degrees divergence.
I need to take longer distance measurements though to get the exact divergence.
As I said, for regular flashlights this isn’t really important, but for highly collimated lights it is.

Although this is true, I do find it important to realise what REALLY is going on with any flashlight, and what kind of simplifications are used and for what reasons. Your thoughts and this thread are much appreciated. Bravo!

I will say again that the phenomenon that Enderman is explaining makes sense, but actual measurements disagree with the proposed model.

Below is a graphical representation of the data and the two models: measuring the distance from the lens and measuring the distance from 2.14m behind the lens, as the calculator predicted.

This plot shows the measured lux vs distance. The blue diamonds are the data points in the quote above that I measured. I estimate the uncertainty at about 100lux. The red line is the lux according to the inverse square law, measured from the lens. The equation is lux=265000cd/(d^2). The blue line is the predicted lux when the distance is measured from 2.14m behind the lens, as the calculator predicts for the measurement. The equation is lux=390900cd/((d+2.14m)^2). The two lines cross at 10.29m because that is the measurement that was input to the calculator.

The two models predict different lux numbers and the measurements are consistent with measuring distance from the lens and not from a point behind the lens.

Yep. I’ve read your post, so I’m also interested what on earth is going on. This makes it all so interesting.

Interesting. I am in the process of reassembling my “lightcanon” and will do more tests, hopefully a lot more accurate than that quick and dirty test I did at the start.
I will do longer distance, hopefully 5, 10, 15, 20, 25m or even 50m.

This recent thread brought me back to thinking a bit about this method. As I talked about above, this method seems to make sense, but my measurements disagree with this method of calculating the candela.

I just thought of a thought experiment which makes me further question this method. Say you have a aspheric lens light with an XPL HI. You take aperture and beam size measurements and the calculator linked in the OP tells you the distance behind the lens the light appears to emanate from and you use this to calculate the candela. Now you put a mask right over the LED which decreases its size to 1mmx1mm instead of the original 2mmx2mm. The lux measurement and aperture size stay the same, but the beam diameter decreases by a factor of 2. Now the calculator says the light is emanating from further behind the lens and the calculated candela goes up. But we know the beam candela would not actually change; the center of the LED is left unchanged and so the properties of the center of the beam should also remain unchanged.

Yes I agree, see this post specifically: The proper way of calculating lux / cd / candlepower - #35 by EasyB
I made this thread to explain the concept that I read about on CPF, but after some further research it seems to be incorrect.

The light coming out of a lens is not a single cone of light that diverges from one point, it is an infinite amount of light cones coming from the surface of the lens.

Based on this, the total lux of the flashlight is simply the sum of all these cones of light.
Since each cone behaves according to 1/d^2, then the sum of all cones also behaves proportional to 1/d^2

So in fact the light converges at the lens, not behind it.

What is still important though is that the flashlight needs to be measured at a far distance to allow all the cones of light to overlap at your luxmeter, in order to measure the maximum possible intensity.