Advanced calculators for theoretical lumens, lux, beam divergence, and more, of custom LED flashlights

By the way, the focal length of a parabolic reflector is the distance between the focal point and the vertex, that is the definition.
https://www.google.ca/search?q=parabola+focal+distance
So 10mm for the maxabeam.

I also checked and the metric vs imperial versions of the calculators should give the exact same lumen/lux values when you convert your measurements form mm to inches.

Ok, yes, I see it works. Sorry for being confusing. I never use the actual focal length for anything so I didn’t think you might need it. I was inputting the wrong number. The metric and imperial reflector1 variants work nicely this way.

BTW: the imperial version still has some metric input boxes and calculates the reflector size in square millimeter. :wink: How about luminance in cd/inch^2? :smiley:

I still think calculating the actual hotspot size (the smalles possible spot) makes sense. That is what we measure with lux meters. That is what people want to know.

Can’t we just do it with the standard parabola equation? Please note that these are for an upright parabola centered on the y-axis. Yours is rotated 90 degress so you would need to switch the x and y designations.
We take half of the reflectors diameter, c/2, as the x-coordinate of the reflector point which is farthest away.
We then use the parabola equation y=((c/2)^2) / 4f to get the y-cordinate (f being the real focal length). So know we have the coordinates of a point on the rim of the reflector.
Now we just need the coordinates of the corner of the LED. That would be x=(sqrt(2*(s^2)))/2 and y=f.
So now we have two points and we can just calculate the distance between them.
dfmax = sqrt(((x2-x1)^2)+((y2-y1)^2))
dfmax is what I have been calling “max focal length”.
This allows us to calculate the actual “minimum” hotspot diameter:
dhot = diameter_of_LED * distance_to_hotspot / dfmax
(This last calculation might require converting some of the units)

Yeah the imperial version still calculates mm^2 of the reflector because the standard way to measure intensity is cd/mm^2.
Since you don’t have to care about the area of the reflector, it’s just an intermediate value in the calculation, I left it as mm^2.

The problem with the “inner hotspot” is that for the type-2 reflector the shape of the reflected LED is getting smaller and smaller as you approach 90 degrees (the edge of the reflector) causing a “ring” of light that is not going to the center.
The farther off angle that the lens/reflector is from the LED, the more “skewed” the image is.
If you look at an LED from 45 degrees, it looks like a trapezoid.
If you look at it from 180 degrees, it looks like a line.

Also, it doesn’t matter if the parabola is vertical or horizontal, you can literally just switch the x and y in your equation to turn it sideways.

Well it’s not a “standard” calculator :stuck_out_tongue: . Somebody who thinks in inches probably doesn’t have a feel for square millimeters. Personally I think the imperial version is not needed at all, but then again I’m not from the US.

You don’t have to do it for both. You can just add it to reflector1 which is what 99.9% of lights have.

Yeah, that’s why I mentioned that.

Yeah I’ll do that.
The reason I made a metric version was because I originally had only made an imperial version, because both optiforms and phoenix have all their reflector specs in inches.
For people who plan to order reflectors from them it is really easy to take the values straight from the data sheet and put them in without having to convert to mm :slight_smile:

I guess I could have also built in a “mm or inches” option into the calculator to choose between the two. Maybe in a future update.

WOW. Great tools you've developed here, very interesting stuff! :THUMBS:

Thanks for putting such time and effort into all of this, I know it is appreciated and will be put to good use :)

-Ben

Thank you :slight_smile:

I have also started to play around with the lens calculator. Have you thought about how the Wavien collar impacts otf Lumens? sma calculated here is collects 75% of the light and 25% goes through the hole. Since you assume 2.19x the luminance using the collar, the lumens coming out of the hole would be 2.19 x 25% = 54.75% of the LED lumens. After this you would multiply, as before, with the lens transmission rate to get otf lumens.

Yes, the OTF lumens also takes into account whether the wavien collar is on or not.

The only thing is that I do not set the limit for emission angle for when the wavien collar is activated, so if the green lines are going through the collar then that will give incorrect numbers.

I just read this over, and the problem with this method of calculation minimum hotspot diameter is that the point on the edge of the reflector, depending at what angle from the LED it is, will give a different “reflection” image.
For example, if your reflector has the furthest edge at ~60 degrees to the side from the LED, the LED will no longer be square (when viewed from that point)
Which means the reflector will be projecting an image like this:

And not like this:

.
As the angle gets bigger, this effect increases, up until your reflector point is at 90 degrees to the side of the LED and only reflects a line, making the theoretical spot size the same as the reflector diameter.
Then when you add all these ‘lines’ together you end up with a circle, which is why reflectors make a more circular spot than lenses.
.
So this “minimum spot diameter” would only be accurate for a lens/reflector directly in front of the LED.
Since a lens usually does not collect at large angles from the LED, this would be an OK approximation for the spot size with a lens.
For a type-1 reflector it would only be accurate for a deep reflector, and for a type-2 reflector it would only be accurate for long focal length and small diameter (large F-number).
.
.
What get-lit did on CPF is make a program that brute-force calculates this by taking many points and then adding up the projected images:

AFAIK this kind of calculation isn’t possible using a simple calculator like desmos, this would require a coded program.
.
I can probably do that in matlab, but it will take a lot of time which I currently do not have, and I’m not sure if there is a way to make the program available online for anyone to use.

1 Thank

Can you explain in more detail why it is inaccurate and how so?
A nice example are lights with incandescent bulbs. The filament of a typical halogen or xenon bulb is just a straight line. Typically you can get a standard spot that doesn’t seem as small as the width of the filament would make you think.
There must be a reasonable way of calculating this.

Because the red square in the first picture is actually smaller than the red square in the second picture.
The points at a larger angle from the LED will be reflecting the image of the LED die at an angle, not straight on.

There are an infinite amount of points on the reflector reflecting light, which is why a thin line from a filament gets reflected around 360 degrees and creates a circular spot.

Remember the post I made about this?

Now just imagine an infinite amount of those squares around in a circle.
But for large angles, such as in reflectors, instead of squares they look like this:

Which causes the “hotspot” to actually be smaller.
Just imagine multiple of these rotated around a circle.
The diameter will be less than if it was a full square.

1 Thank

I get your point, I just never thought about that it might make the hotspot even smaller.
So we basically need to find a way of calculating the reflector angle at the rim to the be able to calculate the size of the visible LED die from that point. This should be possible with standard triangle geometry. More importantly we need to find a formula to calculate the reduced apparent size of the DIE based on the angle.

Yup.
And what makes it even harder is that depending on where you’re looking from, the square can also be rotated and look like a diamond shape.

Maybe this winter or next summer I will have more time to work on this :slight_smile:

I found an omission in reflector type 1 calculator.
When calculating throw, it includes only intensity of light bounced off reflector, but not of that coming from the LED directly.
It is surely trivial with the sizes that you care about and very small in nearly all cases, but I think it’s at least worth being aware of.

Without having looked into the calculations, here’s my thought. The light rays bounced from the reflector are all parallel, and this contributes to throw/intensity. From all the rays that are emitted that are not hitting the reflector, there is only one ray that travels parallel to all the other rays from the reflector. This means the contribution of that single ray is infinitesimal = 0. Hence this is absent in the equation.

Nope, the LED is not a point source. It is a flat surface of a specific size. This surface contributes to the total surface of the light source as seen from the hotspot. How much of the surface it contributes depends on the size ratio of the reflector to the LED, of course. What also needs to be noted here is that the luminance of the LED is higher than that of the LED reflected by the reflector. Only the losses of the lens need to be acounted for.

This might be interesting for pen lights.

You guys are right, I need to add the LED die area times the lens transmission to the intensity equation.
Thanks :slight_smile:
It will make a significant difference when dealing with reflectors not much bigger than the LED itself.

:+1:

Enderman, in your Lens calculator I see that for working area you take clear aperture.
At the same time I notice that in the inside the part of the lens that passes light is CA while on the outside - it’s the entire lens area.

I’d like to understand that better. Could you give some pointers on why is CA the correct value here?