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

These are some advanced calculators I have made to help me estimate the final performance of the custom flashlights I build, and I decided to share it with you guys so you can do the same :slight_smile:

Some example screenshots:
Aspheric Lens:

Standard Reflector:

Recoil Reflector:

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Using these equations, it is possible to find:
-candela (lux @ 1m)
-throw (ANSI to .25 lux)
-lumens in spot
-lumens in spill (for standard reflectors only)
-total lumens OTF
-max beam divergence (half-angle)
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What you need to input:
-led intensity in cd/mm^2
-led lumens
-led die diameter (if square, multiply by 1.41 (root 2))
-dimensions and focal length of the lens/reflector
-wavien collar (yes or no option)
-number and thickness of arms (for recoil reflector only):
For example, this light here has 3 “arms”:

The arms are what hold the center light source in place. I would guess that these are ~3mm thick.

These values can be set by adjusting the sliders or by clicking the number and typing in your value.
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NOTE the lumen calculations are based on the lambertian emission pattern of a FLAT or DEDOMED led. Using these calculators for an LED with a dome will yield inaccurate results.
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METRIC CALCULATORS (reflector dimensions are in mm):
Aspheric Lens: Lens calculator (metric) | Desmos
Standard Reflector: Reflector calculator (metric) | Desmos
Recoil Reflector: Recoil calculator (metric) | Desmos

IMPERIAL CALCULATORS (reflector dimensions are in inches):
Aspheric Lens: Lens calculator (imperial) | Desmos
Standard Reflector: Reflector calculator (imperial) | Desmos
Recoil Reflector: Recoil calculator (imperial) | Desmos

Bookmarked - thanks for sharing :beer:

subscribed

Can you include that one to calculate the reflector dimensions?
You linked it in the gt thread but it’s hard to find in all those posts.

Great, thanks!

I would be interested in how did you arrive at the collar improvement.
I remember seeing +25% as a lower-bound sanity test. And 60% as a top result. Your calculator uses 116%…

Also, if that’s possible, I would love to see the calculator extended with 2 features:

  • support for pre-collimator lenses. I’m especially interested in how they improve light collection efficiency when compared to collar.
  • support for calculations of lenses being out of focus. I’m especially interested in knowing beam widths in zoomed-out lights.

Very nice! I really like this.

Some things which came to my mind:

  • I would put the required measurement units (metric/imperial) into the name fields of the input values in each calculator (just to make it easier and to avoid user mistakes)
  • The spot size values seem high. I’m getting 88m spot diameter @1km with 1.25mm LED “length” and 75m with 1.06mm LED “length”. From my own experience I can say that this isn’t true. My own calulations with 1,06mm LED “length” give me 11m spot diameter.
    This can actually be checked easily. Lumens = lux/m^2
    So 75m spot diameter at 1km distance would mean that my 1.55MCd light would be putting 6848 lumens into the spot (1.55lux at that distance). I reality it’s around 433 lumens, which your calculator also correctly calculates (if the amount of collected light is indeed true).
    I am also not factoring in the corona which is part of the collected lumens. How do you account for that? I wouldn’t consider it to be part of the spot.
    Of course I can get the actual values by doing the calulation backwards:
    Lets say the spot is 11.27m diameter in 1km distance. So the area is 99.76m^2 and it is lit uniformly with 1.55lux. This means that 155lm are in this spot. Of the 433 “spot lumen” calculated by your calulator (maybe they should be called “reflected lumens” instead?) 433-155=278lm remain for the corona.
  • Maybe we can also calculate the size of the corona? My guess is that it is determined by the minimum focal length of the reflector. In my case that is 2cm. So in 1km distance the outer corona would have a diameter of (0.00106m * 1000m) / 2cm = 53m. If it were uniformely lit (it probably is not) we could calculate it’s brightness by using the same circle-with-hole-in-the-middle-principle as we do when determining the area of a reflector (because the intensity that overlaps the actual hotspot is already accounted for in the lumens of it). So in this case 2206.18m^2-99.76m^2 = 2106.42m^2. Now we divide the Lumens by this to get the intensity: 278lm / 2106.42 = 0.132lux.

*If you do all of this maybe you could also implement a drawing which shows the divergence and intensity of the different parts of the beam (calculating the divergence of the spill is probably easy for you).

  • If you want to be super precise you can add the area of the LED multiplied with it’s luminance and with the transmission rate of the lens to the calculated luminous intensity (throw). :slight_smile:
  • Explaining the different parts of the formulas here would be nice I think. For example you calculate the diagonal of the LED die based on the side length to get it’s maximum width.

I am having problems with the metric version of reflector type 1. What do I input for the focal length?

EDIT: I get it now. The focal length needs to be input in cm, not mm like the other values.

I am testing using the values of the Maxabeam reflector:
Diameter: 118mm - 4.65in
Small opening: 40mm - 1.58in
focal length: 10mm
“max focal length”: 94mm - 3.7in
reflectivity: 75%

EDIT2: I am having problems with the imperial version. There seems to be some problem with the geometrical part (the orange reflector curve is not touching the Y-axis where the focal point is when using the test numbers above). The lumen values are also too high.

sma tested it here (in German). A very high degree of precision is required to get the maximum benefit. So the people who only got 60% benefit simply need to position the collar more carefully.

That’s a very interesting link, thank you.

The BLF GT reflectors measurements might be interesting for some people to play around with:
Diameter: 118mm
center hole diameter: 20.1mm
Max focal length: 11.5cm
Reflectivity: 90%
Cree XHP-35 HI diagonal: 2.9mm (2.5mm side length)

You’re welcome :slight_smile:

I will try to find it when I have time, it seems that I have deleted it from my desmos account so I can’t get it immediately.

That will be really difficult, more of a job for an advanced ray tracing program :confused:
If you want to estimate stuff like that I suggest using this free software here: * OpticalRayTracer Home Page

Thanks, I will double check that everything is in mm and add labels for the units.
Do you know which one of the three imperial calculators you’re having the issues with?

Also, the way I calculated the max spot diameter is by taking the distance from the LED to the closest point on the reflector/lens (which is not equal to the focal point since there is a hole)
Then just using similar triangles, LED diameter / distance * 1km = spot diameter.
This is essentially the outer edge of the “corona”.
Keep in mind I am using the MAX spot diameter, so that means using the diagonal LED diameter, not the side length.

You cannot use lumens=lux/m^2 because the brightness is not uniform, the outer edge of the spot will be much dimmer than the inner part of the spot.

[quote=Enderman]

Reflector1

Ok, that first part is very nice. I hadn’t thought of that. So in my case it wouldn’t be 20mm (only for an ideal point source), but 20mm - sqrt(2 * 1.06mm^2)/2 = 19.25mm

Why don’t you implement both, outer edge corona and actual hotspot? :slight_smile:

Just started playing with that, thanks. :slight_smile:

I will echo what everyone else is saying: Subscribed! Thanks for sharing! This will be a very valuable resource!

Ah, I found the bug, thanks. The new links I post should be fixed.

It will take a lot more calculations to find the true hotspot, because I need to figure out exactly where the projected images of the LED are overlapping the most, at the same time taht the images are changing in shape, and also moving away from the center of the spot.
I’ll have to spend some time thinking about that one and see if I can find an equation that isn’t just brute-forcing the answer.

You’re welcome :slight_smile:

Thank you!

No, the focal length of a parabola is the distance between the focal point and the vertex.

small f

The maxabeam uses a reflector with 10mm focal length.

A parabolic reflector does not have a fixed focal length (is is not a lens). That is why I call it “maximum focal length”. The longest possible distance. Thus, there is also a minimum focal length. It depends on the type of light source used. With an LED it is the horizontal distance between the led and reflector surface (calculated above in post 13). With a bulb (emits light in all directions) it is half of this value, so 10mm.

One always needs to account for differences between the theory and the reflectors and light sources we use in practise.

It doesn’t make sense to argue about the specific designations though. They don’t change how we calculate things.

I’m just going by what the datasheets of optics manufacturers say.
You can take the values from any one of their datasheets and plug them into the calculator and you will get a reflector that is exactly like the one they designed :slight_smile:

I don’t see your point? I never wanted you to use the “maximum focal length” for the calulation of the reflector.
It is only needed for calculating the size of the actual hotspot in a specific distance.

Or are you talking about the problems I had before? I was trying to test the imperial calculator by inputting the measurements (converted from metric) of the Maxabeam reflector. I got a different result. It didn’t look right and the luminous flux values were off compared to the metric version.