An Explanation of "Nested Hotspot"/"Sharp Corona"

Flashlight Modding and DIY Parts
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A couple of months ago I posted a discussion on reddit about “nested hotspots” but no luck, I was still not sure if the nested hotspot is normal and why some lights have that and some do not.

But later I found a slide( LED optics in Flashlight, Flashlight Collimating System) made by a enthusiast, it talks about the formation of corona (mistranslated by the author as “coma”), and I observed my Fenix PD32V2. In short, for a normal reflector, this is normal. But some manufacturers will eliminate the nested hotspot by optimizing the curve of the reflector.

For example, like in the picture, the reflector curve at the bottom of the Fenix PD32V2 is noticeably different, which may be the key to eliminating the sharp corona.
IMG

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This makes a lot of sense. When I position myself at the corona and look into the reflector, the part that is lit up is precisely the bottom of the reflector near the base. So that is the part that must be perturbed in order to affect the corona. I do suspect that such a perturbation loses some throw, but probably not noticeable and well-compensated by a more pleasant beam profile.

Coma is an interesting choice of word, does make sense when one looks at a picture of a comet. If the core corresponds to the hotspot, then the coma would correspond to the corona.

That document is very interesting. I had my own derivations for an upper bound for throw for an arbitrary emitter+optic combination, assuming a Lambertian emitter; it works well in practice but does not involve some of the variables from the formula in the slides. Looking into it…

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The explanation of coma is interesting :joy:, but since both the author and I are Chinese, I’m inclined to think that “coma” here is probably just a mistranslation of the word “光晕(halation/corona)”, it literally “light + faint/coma” in Chinese.
Sorry for my preconceived notions, the author used words so professionally that I misinterpreted him. Coma is the right word, someone reminded me on reddit. I just hard to believe that in a different language a word can also mean both diffusion and faint.

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How interesting, didn’t know you are Chinese. I am too!

Redid the derivations and what I got for intensity@1m is LA/(a \pi), where L is luminous flux, A area of the optic, and a the area of the emitter, and it is an upper bound for assuming perfect efficiency. The calculations from the document are somewhat obscure and I’m trying to reverse-engineer the numbers they started with…

EDIT: using L=1000, A=\pi (0.025)^2, a=(0.002)^2, and omitting the n_receiver/n_emitter term, the bounds we got are within 1%, so perhaps the derivations were essentially equivalent.

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btw, I forgot to mention that this slide was made in the era of dome emitters, and its corresponding reflector design may have been different from today’s common practice of using flat-top emitters. Although the author casually mentioned years later that the ideal dome emitter could be considered a flat-top emitter with an enlarged area, but if you go to the XPL datasheet, the spatial radiat of the HD and the HI are clearly different, and there may be a dispute here.

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This makes a lot of sense! The author used 2mm by 2mm as the emitter size for XM-L, which suggests that the refractive index ratio term compensates for the presence of the dome. Indeed, domed emitters have a different angular distribution compared to domeless, it seems that some of the mass is pulled from the tails and closer to the center.

I wish these datasheets also included a reference circle for the perfect Lambertian distribution, so that we can get a sense of how luminance varies with angle. This variation seems to exist (with luminance being higher closer to the center) and manifest as longer throw achieved by deeper reflectors of the same diameter–the additional throw is more than explainable by the reduced truncation at the base.

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Thank you for sharing this document, I should have read it in its entirety before initiating this conversation, and this file really should be pinned somewhere!

I realized that the file does have plots for how reflector depth affects intensity, though does not seem to provide an explanation. It also mentions that reflector depth affects hotspot size, but does not describe this relationship. I suspect that this relationship is not monotone: given fixed reflector width, as the height increases from some quantity very close to 0, I’d expect the hotspot size to begin very small (since intensity is conserved under Lambertian assumption while only a tiny fraction of light hits the reflector), eventually reach a maximum, and then drop off again as the spill angle approaches 0 arbitrarily. It would be interesting to determine where the maximum occurs.

It was very eye-opening to see the different TIR designs!

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My knowledge actually hard to understand what’s in the document, but the author did say many years later that a deep reflector would increase throw, mainly because of the smaller bottom hole. Like you said in your last comment.

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When you say “the author did say many years later”, do you mean there is another writeup released by the same author? If so, would you share it?

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He has joined a discussion and answered some questions at Tieba, and I happened to know about this document because I saw that thread.
See the 21st, 23rd, and 24th floors in the thread.

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A couple years ago probaly during one of my question session with you about reflector & hotspot, throw, etc., I also found this same article. I actually screen captured the slides and posted them on imgur.

BTW I also made the grave error of under-estimating author regarding coma vs. corona. Even added notes to correct him. Anyway, does this answer your question? As depth increase, hotspot gets smaller.

My question though, what happens if depth KEEPS increasing, does hotspot become infinitestimally tiny? Is that what you meant by a “monotone” relationship? My background is biological, not physical, sciences; this stuff gives me a headache.

Imgur

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Another slide I captured since I thought it was interesting. Although I cannot understand what it entails when the peak luminance plateaus, the consequences to the beam. Hotspot gets smaller but not brighter? Maybe you could explain in terms I understand. TIA.

Imgur

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Thank you for sharing this resource!! I am completely out of touch with the Chinese flashlight community, this is a good reminder that I can learn from them.

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No wonder the original screenshots look familiar!

Not quite: I don’t believe this to always be true. More to follow.

What I mean is the following: fix the emitter size, and fix the reflector diameter. Start the reflector depth at 0, and increase it from there. Does the hotspot size always increase with reflector depth, always decrease, or vary in some more subtle way? The former 2 relationships are monotone; I suspect that the latter is true, i.e., the relationship goes up and down at different points.

Here’s my argument for the hotspot size being small for very shallow reflectors, assuming a Lambertian angular distribution for the emitter. Since the reflector is very shallow, the proportion of the light that gets collected is very small, so the hotspot has low total luminous flux. At the same time, by the Lambertian assumption, luminance of the emitter is direction-independent, which implies the intensity projected should not change. Since the hotspot maintains equal intensity with less luminous flux, it must therefore be narrower.

This argument does not fully check out for real-world systems because (1) the LED is not perfectly Lambertian, and (2) shallower reflectors have a larger truncation at the bottom which loses projected intensity. The former issue (1), I think, can be resolved by noting that hotspot size is actually independent of total flux (or even intensity given other variables fixed) and dependent only on the dimensions of the emitter and optic; therefore, the argument holds for any emitter that has the same angular size as the ideal Lambertian emitter when viewed from every direction; this includes all domeless emitters.

The problem with reflector truncation can be resolved by considering recoil throwers; these have the LED mounted on a floating heatsink pointing back into the light, and at a very, very shallow, non-truncated reflector.

I think that as depth increases, the hotspot must become arbitrarily small because the spill angle gets arbitrarily small, and the hotspot must be smaller than the spill.

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I think this is right: given a fixed emitter, the maximum achievable intensity of the system is bounded by the diameter of the optic, with the bound being the horizontal asymptote of the blue curve. So a natural question to ask is, what happened to the light from the previously-larger hotspot?

Part of it ends up in the corona. But most of it eventually ends up in a part of the beam–which I shall refer to as “scatter”–that only occurs in extremely elongated reflectors. See, with a conventional reflector, each photon bounces at most 1 time on the reflector: with 0 bounces it becomes spill, and with 1 bounce it becomes corona/hotspot. But with a very elongated reflector, a photon may bounce many times on the reflector before exiting the head of the light, and this exit may be at an angle that is even wider than the spill.

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