Enderman
February 17, 2019, 9:13am
600
LouieAtienza:
The surface area of said spherical cone comprises about 13.4% of the total surface area of the hemisphere, yet accounts for ~25% of the light. So ~75% of the light comes from the remaining ~86.6%. So if we “weighed” the luminous intensity coming from said 60 deg. cone, which is between .9-1 relative luminous intensity (I’ll guesstimate on average .96 at any point on that surface) and multiply that by .134 I get a result of .1286. Guesstimating the average luminous intensity of the remainder, using a typical chart, between 0 and .9, I’d say about .6. So multiplying .6 by .866 gives me .5196, which is just about 4 times the result I got from the top section. I’m sure the actual equation is a bit more complicated than this (and I hadn’t done calculus or differential equations in about 26 years) but intuitively it seems to jibe now.
It also makes sense why an RLT collar at 33% efficiency would potentially double the luminous intensity of the light coming out its aperture (given a 30 deg. half angle aperture).
While impractical, it also seems clear to me that given a luminous intensity chart for a given LED, there would be an optimal aperture angle for the RLT factoring in the luminous intensity graph, meaning there is an ideal focal length (ratio).
Of course now for a reflector, even a precision electroformed one with the most reflective coating is only approaching 90% efficiency, so that boosts the percentage of light from said 60 deg. cone to about 27% of total light output, and likely more given a typical flashlight reflector. Which makes me ponder that there is an “equilibrium angle” where the light coming from the top cone is equal to that of the lower section with the included efficiency factor. Not clear to me yet what use this would be of, but it should generate the most OTF lumens.
It’s just integration, it’s easy.
This works only for no-dome LEDs such as the black flat, white flat, or CFT90. (but it can do other LEDs if you put in some effort)
These LEDs have an intensity that follows Lambertian distribution, which means that the intensity of the LED is proportional to cos(angle), making it very simple to put inside the calculator.
[image]
If the LED does not follow the Lambertian distribution, a special function needs to be used instead of cos().
Here you can see that flat LEDs have almost a perfect…
2) there is no optimal aperture, the more light that a wavien collar collects the less lumens are output and the more intense the light becomes.
3) silver coatings are 98, aluminum 90-95, and dielectric coatings can get to 99+
4) the highest OTF lumens are with a mule and no optic. For even highest efficiency, remove the front protection lens too, that will get another 1-3% light output.