Wow. You are one scary Dr Mr Jones. Thanks.
Prometheus:
Reflector depth has only a small influence on throw: It affects the size of the reflector's 'dead hole'. An XM-L emits light into the full hemisphere, so those parts of the parabola which would be behind the LED cannot contribute. The deeper the reflector, the smaller that area is. With 'typical' reflectors you get about 10% dead apparent area (that's the factor of 0.9 in the equation), deep reflectors have a few percent less.
A deeper reflector has about the same throw, a smaller spot core, but a wider corona.
However the "deep reflector for throw" rule comes from older times when the typical LED was the XR-E, and the XR-E's collar reduced the maximum emission angle to about 120° (instead of the ~180° hemisphere); that results in a bigger dead hole (about 30% dead area for a typical reflector) and then a deeper reflector gave a more substantial improvement. BTW the XP-E thus does have an advantage over the XR-E regarding throw in a reflector due to it's smaller dead hole.
There is no principal limit to the d to D relation, however the bigger the reflector gets, the better it's quality must be to still reflect the LED precisely into the center beam. Still much less quality than for a professional astronomy telescope of the same size for example, but the price for a D=2m reflector with sufficient quality would be astronomical none the less (16km NEMA-throw...).
If you have access to a, say, 25cm reflector telescope and can get a LED into it's focal plane... -> 2km NEMA-throw. More if you use an XR-E EZ900 R2 :)
1 Thank
thanks for the reply Tecmo and DrJones 
Damn impressive knowledge on this subject. Greatly appreciate you sharing it with us.
Very good info. Thank you very much DrJones. You answered some questions I have been pondering and much more. It has to be a challenge to translate such technical knowledge into concepts laymen can understand. I'm struggling to wrap my mind around something. Recap as I understood your write up:
- Dedome causes less lumen (F) output due to more photons not escaping the led crystal because there is about 13° less critical angle.
- The photons that don't escape bounce around until they finally escape, get absorbed, or reused in the phosphor layer. This increases luminance (L).
- The beam pattern of both dome and dedome are both approximately lambertian.
Since less photons are emitting out the front of our dedomed lights, it just seems the reused photons is not enough to explain enough of the increase in L. At least when considering the typical magnitude of throw increase we experience in our lights after a dedome.
You may have said it and it just went over my head, but is the biggest contributor to the lower L of the dome the actual surface area of the dome itself being much larger than the surface area of the led crystals?
EDIT: Sentence added to clarify.
This may be a silly question, I don’t know…why can’t we buy LEDs with no dome? Wouldn’t that be easier to manufacture?
ImA4Wheeler said: Since less photons are emitting out the front of our dedomed lights, it just seems the reused photons is not enough to explain enough of the increase in L.
It actually is. Hypothetically assuming you have a flat protection layer without photon reuse (photons above critical angle just get absorbed), it would have the same luminance as the domed LED. The dome would get more photons out, but the apparent die would be bigger, so more flux divided by more area gave the same luminance. It's the total inner reflection (photon reuse) that increases luminance.
I have one question DrJones, since after de-doming the LED tint would be shifted to warmer side, does that mean the CRI of the light improved as well?
It seems to me that the main advantage of de-doming is that the light is spread more to the sides so the reflector catches more of it. An other is that eliminating this converging element makes the spot smaller. Since these are optical advantages, they can be achieved as well by other changes in the optics. An aspheric zoomie catches the light that goes forwards so it will focus more light with the dome in place. A longer focal length gives a smaller spot. A long focal length lens tends to lose a lot of light around the sides and makes the flashlight long, but those can be fixed by using a Fresnel lens.
I found a sketch of a Fresnel flashlight lens in a Chinese Web page. It is similar to the lighthouse lenses, some of which were made by Fresnel himself, with the center of the lens refracting and the outer segments working by total internal reflection (more TIR than the lighthouses). It appears to have little or no reentrant form, so it would come out of a two piece mold. The center focal length is short, so the light focused by the center forms a fairly broad beam, but as one goes out the lens and mirror segments are sections of longer focal length lenses and TIR reflectors, so they contribute a small spot at the center. So the result is a nice gradual transition from throw to “spill” with maximum throw for the physical length of the light.
The question is how can a hobbyist make or obtain such a lens. Maybe such things are used in aircraft beacons. The lighthouse lenses were made by hand, but the effort was prodigious. Maybe the Chinese that posted the drawing are making them already? I don’t read Chinese. I only know that Google found the page when I asked for images of flashlight lenses.
Searching for Fresnel in BLF, I find hits including short focal length Fresnel lenses for sale .
I see the argument that the luminance limits the throw for fixed optics or within a given size constraint. But I don’t think there has been enough thought yet about the optics and the requirements.
So why dedoming a LED improve throw on aspherical lights as well?
Uhm, no, the light isn't spread more to the sides (except with XR-E), and a smaller spot isn't per se better. A "converging element" itself does not decrease luminance. I noted that somewhere in the OP.
I must say I am surprised at that. I did say I agreed with the value of luminance but I am not sure that is the answer. An other possibility would be that eliminating a converging optical element at that location decreases the spot size.
I dedomed a sst90 RED led in an ur-t20 aspheric and although it made the hotspot/die image smaller I do not think it is as bright as before.
any thoughts on dedoming red leds??
After reading this informative thread, I thought I post this here. The angles may be off a little but they should be close. It shows that the flux would quadruple or at least triple. Does that sound right for halving the angle?
The smaller apparent emitter size (resulting indeed in a smaller spot) itself is not the point at all: For example you could use a concave lens to spread the beam and get a smaller apparent die size (and also a smaller spot) - but you won't gain any more throw from that, neither in a reflector, nor with an aspheric lens. The reason relates to the etendue or optical invariant, which can't be made smaller for a beam using any lens etc., and the luminance being inversely proportional to the etendue, and luminous intensity I being luminance L times (effective) area A. Throw really comes down to just luminance and area (well, and losses due to scattering, absorption, reflection, imperfect shapes,...).
I’ve read much of what you’ve written and I’ve not seen mention of a reflector size to emitter size ratio or more precisely, reflector distance (from emitter) to “effective” emitter area. That ratio is directly proportional to beam angle. However, you sorta say that here:
It’s not the area per se of the reflector determining the beam angle, it’s the ratio I mention above. Decreasing the apparent size of the emitter has the same effect on beam angle as increasing reflector size. Since an unmagnified, dedomed emitter appears smaller but emits about the same amount of light, compacting that light in 1/4th the area effectively doubles the throw.
Yes, the beam angle is determined by LED size divided by focal length (i.e. distance from reflector to LED). But luminous intensity (and thus throw) is only determined by luminance multiplied with area. I admit that this is counterintuitive and nothing that is taught in school or even basic university lectures, so you need to look up some more special resources. I tried my best to give a simplified summary in the OP. The Wikipedia article on etendue is not easy and the articles on luminance and luminous intensity are somewhat lacking for this purpose.
From what I gather, etendue is a problem with lens but not reflectors. Focused to infinity, a lens has obvious problems towards the outer edges and you can only redirect a limited amount of forward light from the emitter so brightness is extremely limited. With reflectors, light can be gathered from all sides at any distance so etendue is simply limited to emitter size, reflector diameter and of coarse, surface quality.
This document contains some info that’s easier to understand. Skip down to page 2.3 and 2.3.1:
http://www.physics.princeton.edu/~mcdonald/examples/lamp.pdf
BTW, any idea of what % of energy gets lost/wasted in the dome or does it all get recycled?
Lenses are mostly used as examples because 'input' and 'output' are on different sides, which makes things a bit more clearly structured, but it's the same with reflectors.
Nice document :) Will read it later thoroughly, but 2.3.1 sums it up quite well, same holds for dedoming and that Wavien collar.
Flux/energy losses in the dome itself are negligible, ~4% reflection back to the die with a chance of recycling, maybe a bit of absorption, but not much.