How to quantify beam shape? And discussions on many related topics: optics - TIR & reflector, thrower vs flooder, throw calculation, beam angle, cd/lm parameter, etc., etc. Did I miss anything? :-)

[Dc38 (The Glutton)]

i have no idea, lol. that’s just the number that popped into my head. Maybe it’s complement to 1 is the significant number? 0.5548714?

[QReciprocity42 (efficacy ≠ efficiency)]

Still nothing that stands out in an obvious way…I guess only time will tell!

[cannga]

@QReciprocity42

Technically, this is an oversimplification: deeper reflector always corresponds to larger corona, but not always a smaller hotspot. For the same diameter (say 1), the largest hotspot is achieved by a depth close to 0.5; the hotspot size shrinks both above and below this threshold.

The oversimplified claim appears consistent with our observations because most reflectors we encounter are deeper than this threshold (i.e., we don’t get a sample of all depth/diameter ratios), so as a result we see hotspot size only shrinking with depth.

Thanks for the detailed explanation. Are these formulas (1st one presented in the slide, 2nd one my googling) not true then? Don’t they describe hotspot size being inversely proportional to focal length, which is D/d?

1. hotspot size/observed emitter size = target distance/focal length

2. Focal length = D square/16 d
D=diameter d=depth

[QReciprocity42 (efficacy ≠ efficiency)]

@cannga

Are these formulas (1st one presented in the slide, 2nd one my googling) not true then? Don’t they describe hotspot size being inversely proportional to focal length, which is D/d?

Could you grab me a screenshot of the slide containing the formula? I’m having a hard time finding it.

The central issue underlying your question is: how do you define “focal length” for something that is not a convex lens? Depending on the definition, the formula might be true or false. What might clarify is that the focal length does not equal reflector depth, in particular. And what does “observed emitter size” mean in this context?

@cannga

1. hotspot size/observed emitter size = target distance/focal length

This formula holds in the small-emitter limit if “focal length” is taken to mean “the distance from emitter to outer boundary of the reflector”, i.e., sqrt(h^2+R^2) where h is depth and R the radius of the reflector. And “observed emitter size” taken to mean “the minor axis of the emitter’s projection in a direction pointing to the outer boundary of the reflector”.

The reason this formula is not monotone in reflector height is the dependence on both quantities “observed emitter size” and “focal length”. For very shallow reflectors, the hotspot is small due to small emitter size, due to projection in a direction almost aligned with the plane of the emitter. For very deep reflectors, the hotspot is small due to long “focal length”.

Of course, all this is just my interpretation because it is unclear what “focal length” and “observed emitter size” meant.

Another way to think about this is taking the reflector as an analogue of a classical convex lens. A very shallow reflector with short “focal length” corresponds to a very thick lens, where the approximations of thin-lens equations begin to break down. The formula you quoted is essentially a thin-lens equation.

@cannga

2. Focal length = D square/16 d
D=diameter d=depth

This formula does not appear to make much sense. It says that as depth increases, the focal length goes to zero. This might make sense for corona calculations, but definitely not for hotspot calculations.

[Dc38 (The Glutton)]

@QReciprocity42

This formula does not appear to make much sense. It says that as depth increases, the focal length goes to zero. This might make sense for corona calculations, but definitely not for hotspot calculations.

Conceptually, I’m imagining an indefinitely long parabolic reflector…I am imagining that the curves are approaching parallel lines, and that the hotspot will eventually become a fixed surface area, and the spill will cover 99.9999999% of the hotspot, as will the corona…I’m thinking that it’s not the focal distance that will change, but rather that the relatively “fixed” divergence will essentially be 0 at any distance **beyond the reflector.

[cannga]

@QReciprocity42

@cannga

2. Focal length = D square/16 d
D=diameter d=depth

This formula does not appear to make much sense. It says that as depth increases, the focal length goes to zero. This might make sense for corona calculations, but definitely not for hotspot calculations.

1. Sorry I just grabbed that off googling here; have no idea about its veracity. Is it wrong?

2. The other formula was found on slide number 26. I think I quoted him erroneously: he switches topic and is talking about the reverse reflector at this point?

[QReciprocity42 (efficacy ≠ efficiency)]

@Dc38

Conceptually, I’m imagining an indefinitely long parabolic reflector…I am imagining that the curves are approaching parallel lines,

It is often very illuminating to consider what happens in the limit! In this case, however, it turns out to be impossible to elongate a reflector arbitrarily, when the diameter and emitter are fixed.

In a parabolic reflector, the emitter is situated within a region known as the latus rectum, the chord within the parabola that contains the focal point. As the parabola elongates, the latus rectum shrinks, eventually so small that it could no longer accommodate the emitter.

@cannga

1. Sorry I just grabbed that off googling here; have no idea about its veracity. Is it wrong?

Thanks for sharing the source! The formula is neither “right” nor “wrong”, it just doesn’t apply to our setup.

The original source is a video in which “focal length” is taken to mean “the height of the focal point above the origin in a quadratic graph centered at the origin”. It has no meaning within the context of this optical discussion about a truncated forward reflector.

However, if you instead had a recoil reflector, the above equation might describe the angle of the corona generated.

@cannga

2. The other formula was found on slide number 26. I think I quoted him erroneously: he switches topic and is talking about the reverse reflector at this point?

It appears that the discussion has switched from a forward reflector to either (1) a recoil reflector or (2) convex lens, and that the equation is indeed a thin-lens approximation. In short, it doesn’t apply to our scenario.

[Dc38 (The Glutton)]

@QReciprocity42

parabola elongates, the latus rectum shrinks, eventually so small that it could no longer accommodate the emitter

brother, you killed me at elongates and rectum. I couldn’t focal on much else after that

[QReciprocity42 (efficacy ≠ efficiency)]

Here’s a quick animation on how the latus rectum, i.e., focal plane, shrinks as reflector depth increases: Focal plane | Desmos

[Dc38 (The Glutton)]

Yessir, I got that, lol…nice simulation though, that’s pretty cool!

[cannga]

@QReciprocity42

@cannga

what happens when depth increases? This statement in one of the slides was helpful: Deep relfector has a smaller hotspot and a larger coma/corona.

Technically, this is an oversimplification: deeper reflector always corresponds to larger corona, but not always a smaller hotspot. For the same diameter (say 1), the largest hotspot is achieved by a depth close to 0.5; the hotspot size shrinks both above and below this threshold.

The oversimplified claim appears consistent with our observations because most reflectors we encounter are deeper than this threshold (i.e., we don’t get a sample of all depth/diameter ratios), so as a result we see hotspot size only shrinking with depth.

I’ve “amateur” google read and searched this topic of reflector depth’s effects for a long time and for me this is the most definitive discussion I’ve come across. Very nice.

The followed explanation for why the over-simplification is often “successful” is also very nice. Good job!

But more importantly, as opposed to hotspot size vs depth, could I pls ask about throw vs depth? It cannot follow the same pattern of “best” at 0.5 and decreasing on either side right? Because if hotspot size is largest at 0.5, throw cannot be furthest (less intense because the similar (?) amount of light is spread over a larger area)?

[cannga]

Combining the information of this curve with largest hotspot being at 0.5 ratio, does it imply that at least from 0.5 ratio and deeper, throw will continue to increase, albeit with ever decreasing amount? TIA

[QReciprocity42 (efficacy ≠ efficiency)]

Thank you! I’m happy that my explanation was satisfying.

For throw vs depth: deeper reflectors always throw more because there is less area truncated away at the base. For real-world reflectors, deeper reflectors also throw more due to the LED’s emission deviating from a cosine-angle distribution, and due to deeper reflectors being less demanding of manufacturing precision.

@cannga

Combining the information of this curve with largest hotspot being at 0.5 ratio, does it imply that at least from 0.5 ratio and deeper, throw will continue to increase, albeit with ever decreasing amount? TIA

This is exactly the right description: as depth increases, the throw levels out and never exceeds a certain threshold. In particular: under ideal assumptions, a depth:diameter ratio of 1 gives you more than 94% the maximum possible throw achievable by any optic of equivalent diameter; there is no point in going beyond that. (For a depth:diameter ratio of 0.5, this figure is around 83%.)

BTW, if you find the subject of reflector geometry interesting, you might be entertained by this simulation!