Reflector width vs depth for throw?

djozz: The parabolic mirror for LEDs does not have one single focal length; the reflector parts near the LED have a short focal length, those at the edge have a long focal length. Focal length = distance to LED. A deep reflector usually produces a smaller hotspot core, but with a wider corona. Not more throw though.

Rockspider: That's the idea - except that the angle is not 125°, but nearly 180°. Take an XM-L, apply a small current, and view it from the side: you'll get light even at nearly 90° to the side. Those 125° are the full angle for half the intensity, not the maximum angle.

You might now say that the intensity to the sides is lower, thus the light near, say, 85° doesn't contribute much, but that's wrong: The luminous intensity goes down, but not the luminance, and it's the luminance that is important for throw.

To get the most throw from a single point emitting light, (of course leds are not single point, still)

i think you need a fixed width to depth ratio and a fixed parabola shape.

Any deviation from this (i don’t know what it is but i’m sure it’s known/given or can be calculated) will result in less throw.

It will either increase the size of the hotspot or create flood around the hotspot or both. (depending on the new ratio and the parabola shape)
A deep reflector will have less spill and more ‘enlarged’ hotspot and flood but not more throw.

Example: assume the ‘proper’ width to depth ratio is 1 to 1 then a reflector with double the depth (1x2 vs 1x1) would not throw more. It will have less spill, more light in the wider hotspot area but not more throw.
(i like deep reflectors for bike lights)

If the reflector really is a parabole, it indeed has one focal length (f) that determines the magnification of the led, similar to the parabolic mirror of a telescope (but instead of imaging infinity into the focal point, the focal point -actually focal plane, where the led is- is imaged at infinity, so the other way around). If parts of the reflector have a different focal point, the reflector is not parabolic.

I may be missing something that is happening in the real world of flashlight reflectors (leds not precisely in the focal point, reflectors that have different than parabolic shapes, just a cut-off portion of the parabole is used because a led does not emit 360deg, which will have its influence on the image), but the above is what a true parabolic curve does as far as I know

Ok, I see that what I was trying to explain is referred as point (1a) 'dead hole' and my drawing above would have been an explanation of this, and the fact that a reflector for a halo would not be as good for a led.

Anyway DrJones it's hard to me to understand your last sentence, if the light emitted past the 125° and up to 180° is lesser, how comes it's so important for throw? Luminance is the surface brightness, right? So also the brightness is lesser when viewed from the side, isn't it?

Coming to practical examples, I've had some lights in which placing a washer between reflector and emitter it resulted in a smaller hotspot (with larger corona) which in my impression gave more throw because the hotspot looks brighter now, more concentrated. Thus by doing this washer shimming I lost some side light, as the light emitted at very large angles approaching 90° now hits the washer and not the reflector.

Still indoor and outdoor it looks to me it throws more now. Am I wrong?

Johm: There is no ideal depth to diameter ratio. Indeed having a very deep reflector won’t increase throw, but it won’t decrease it either.

djozz: Telescope mirrors and typical flashlight reflectors differ in one way: Telescopic mirrors have a quote long focal length compared to their diameter - for a reason. That way, all parts of the mirror have nearly the same distance to the focal point, thus nearly the same focal length. With those flashlight reflectors it’s different, they are sort of built around the focal point. Every part of the reflector has to have the same focal point of course, but since the different parts have different distances to that focal point, and the distance to the focal point is the focal length, they have different focal lengths and thus cast images of different sizes. This is what makes the corona around the hotspot core. I suggest an experiment: Take a light with a quit big reflector. Take a piece of cardboard and punch a hole into it and put it in front of your light. Move the hole around: When at the edge of the reflector, only light from an outer part of the reflector gets through, and you get a small image of the LED. Move the hole inwards, and the image gets bigger.

Rockspider: “Luminance is the surface brightness, right?” Yes. “So also the brightness is lesser when viewed from the side, isn’t it?” No: The apparent area of the LED seen from the side gets smaller, and that smaller area multiplied with the same luminance gives the lesser luminous intensity to the side. Throw however depends on luminance, not on that apparent area.

The eye is fooled quite easily; it especially is sensitive to contrast. Less corona gives a sharper shape to the spot and thus more contrast, so it looks more distinct and seems brighter. But actually you loose light that would otherwise be directed into the hotspot, too, so throw decreases.
It may only really have increased throw if the LED was misaligned before and you also shifted the LED relative to the reflector into a better spot.

Aha, that was new to me, thanks dr., every day something to learn!

So by adjusting the curvature of the reflector at the various distances from the focal point you can make a precisely calculated non-parabolic reflector that creates a better image of the led than a parabolic reflector can, and thus get more lux in the hotspot, right? If so, do flashlight manufacturers use them?

  • I love this kind of discussion. DrJones is doing a good job but it would be great if Bill Nye decided to stop here and weigh in :nerd_face:

Awesome thread, guyz :smiley: :beer: Thanks!
Always wanted to see a good comparison between reflectors - grab a current regulated driver with, lets say, XM-L emitter. And than put one reflector - white walling and lux meter, change reflector - white walling and lux meter… same driver and LED for all reflectors. It’s the best way to see the differences. Those who do DYI mods and stuff can do that pretty well :smiley:

Thanks for the explanations DrJones

For sure in one of the flashlights the original emitter position was not optimal, because when I shimmed the reflector the hotspot and corona become bright and tight, then I tried to add another washer to see any difference and the beam was bad again with fuzzy hotspot.

On other flashlights maybe it's more a matter of preferences... instead of a big hotspot with thin corona, sometimes I get a smaller concentrated hotspot but with a bigger corona... Some compromise has to be accepted I think.

I respectfully disagree with this comment.
If you take a reflector of good proportions for throw (i would say ideal ) most, if not all the surface of the reflector would direct the light hitting it towards a ‘small’ hotspot.

If you then stretch this reflector to a bigger depth, then the curvature of the reflector would not be able to direct light to the center but rather close to it.
The actual reflector area that sends light to the center in smaller in the deep reflector.

The curvature of the parabola that redirects from point to point (like throw with led) is determined by a mathematical equation, is it not?

BTW: I love your work.

I'm a layman, so I can't get into the theory, but I can tell you an example of two reflectors where the shallow one gives a tighter hot spot, than the deeper one.

http://www.cnqualitygoods.com/goods.php?id=1429

http://www.cnqualitygoods.com/goods.php?id=1372

The first one is 29.5mm deep and the second one is 40mm deep. The shorter one is better at throwing a small center spot, with less side spill. The deeper one is better at flooding an area, with a much less defined hot spot and a lot of spill. Both tested with the same light (Maglite) and emitter (XM-L T6).

It's just an example that depth does not make the difference.

That’s what I was talkin’ about, Old :smiley: Thank for that info :beer: (it’s a pity you don’t have a lux meter :bigsmile: )

Johm: If you stretch the parabola, then the focus shifts, but it will be perfect for the new focus then. Every parabola is ideal in that sense.

Ok, for fun and because my life is busy I took paper and scissors and did the quick experiment (how is the light coming from deeper part of the reflector different from the outer part). The flashlight is a budget 57mm xml-thrower on 5%low, 3 meter from wall:

Three times the same flashlight, without masking, with outside masked and with inside masked (first flashlight picture looks smaller, but was taken a bit further away, the beamshots were taken from exact the same distance, exposure was on automatic because what was relevant was spatial distribution, not brightness.

Bit roughly performed, but this shows nicely what you explained, drJ

djozz

By the way, the experiment with the small hole in the cartboard also worked well

djozz

I understand where you’re coming from with your argument, although your argument that increasing the depth of an ideal reflector reduces throw does not necessarily agree with the logic that let you conceive your ideal reflector [see (1) below]. But I believe you’re onto something.

However unreasonable it would be in real life, consider a reflector with a fixed diameter and infinitely adjustable depth. Assume it’s made from shape-shifting metal like the T1000 from Terminator 2 :cowboy_hat_face: .

Ignore the Inverse Square Law for a minute, and consider the ramifications of significantly increasing the reflector’s depth. This is not the same as changing the equation of the parabola; you are rendering the equation so the vertex [focal point] remains on the x-axis as you ‘stretch’ the ‘wide end’ of the reflector toward +∞ [see (2)]. The resulting beam from this reflector becomes closer to perfectly collimated as you approach the point when Depth/Diameter ≈ Depth/1. A white-wall shot would reveal the beam has uniform intensity, with no hotspot, corona, or spill.

(1) Our flashlights have reflectors small enough with emitters bright enough that we can essentially ignore the Inverse Square Law for our purposes [if reflectors have equal diameters, slightly different depths, and identical LEDs]. The ISL describes the relationship between light intensity and distance [Lux decreases exponentially with distance]. Thus, it’s imperative for any difference in distance that light has to travel [differences between reflectors of various depths and identical diameter] is kept “reasonably small” when drawing conclusions.

We can make these assumptions because the differences in depth between our various flashlight reflectors is tiny, or reasonably small compared to the distances our lights typically throw. There are other reasons, but that is probably the most pertinent and encompassing. These logical assumptions let you conclude that under most circumstances involving flashlights, a deeper reflector shouldn’t directly influence peak hotspot intensity compared to a shallower one. Unless the shallow reflector is too shallow too begin with…but that’s a special case.

(2) Analogous to plotting y(x)= x2 on a graphing calculator, and then zooming out so far that you can see x=∞ and y=∞ (obviously, not realistic but you can ascertain the significance in theory)

I’m just musing here, I’m no expert. So feel free to bash and put a dunce cap on me if I’m wrong :party:

Some damn fine results, djozz. Thanks for posting them.

The bottom line with throw is diameter and emitter (surface brightness).

If you want more corona, which won’t increase throw but may be useful (depending on your purposes) then go for a deeper reflector as well. This may be useful at intermediate distances.

If you want still more throw then replace the reflector with an aspheric lens. You’ll have no spill and a hotspot shaped like the emitter but it will throw further.

The greater the diameter the smaller and brighter the hotspot and therefore the greater the throw.

If you want a larger hotspot use a larger emitter (XL-M). If you want the greater surface brightness (throw) use XR-E or something similar.

That’s more or less all the factors other than driving the emitter as hard as is productive.

Keep in mind that the inverse squared law is the one that applies to throw so gains in lux have to be large to make much of a difference in reality.

Explanations given in these forums were thusfar always too unclear to me (and often not true), but, thanks to this thread, for the first time i get an actual grip on why xre-leds are, with their narrower radiation angle, so good in throw compared to newer leds

djozz

Uhm, actually XR-E’s narrower emission angle doesn’t help for throw, it’s just their higher luminance, or simpler put, their higher emitted lumens per square millimeter ratio.

Nice experiment :slight_smile: Physics is fun, isn’t it? :slight_smile: