The following 2 ratios seem very similar in my measurements of total output and throw. Is that to be expected? Because they are linearly proportional?
Output per lumen tube at 30 secs/Output per lumen tube at 0 sec = ~96%
Brightness per lightmeter 10 m away at 30 secs/Brightness per lightmeter at 0 sec = ~96%
Whatâs the importance of âfixed beam profileâ? As opposed to some other kind of profile? Thanks.
Yes, thatâs correct.
With fixed beam profile I think you could instead simply say âfor the same flashlightâ (emitter + reflecter combination).
Precisely!
The beam profile determines the constant of proportionality. That is: candela = c*output, where the constant c depends on the beam profile. This condition is important because while a keychain light and an LEP might both achieve 500 lumens, the candela they produce is very different, due to the different beam profile. The constant of proportionality is not changed when comparing different drive levels of the same light.
OT. Thanks for the clear explanation. Calculation examples (from 2 different runs) of Wurkkos TS30S Pro w/ SBT90.2 at 0 sec and 30 sec yield similar constant c, looks correct?
0 sec: c=388000 cd/ 4500 lm = 86
30 sec: c=335000 cd/ 3600 lm = 93
I assume a laser light will have super high c value? TIA
You have rediscovered the cd/lm ratio, which is indeed a great way to quantify how throwy/floody a light is. A laserâs cd/lm ratio would be orders of magnitude higher, likely on the order of 10^5-10^6.
BTW, the discrepancy between 86 and 93 indicates that at least one of your measurement instrumentsâeither the lux meter or the integrating sphereâis unreliable (if you want accuracy within 8%). Within the same light, the cd/lm ratio should be the same regardless of output level.
Yes lots of error sources: 2 different runs (one for output, one for throw), and in particular that 30 sec measurement. TS30S with its off the cliff straight drop within seconds is hell for an amateur. Starts the timer, aims the hotspot (little hand shake from 10 m away changes reading a lot), and looks at the meter (while aiming the hotspot); itâs comical some time.
Thanks for the lesson. In retrospect I actually have seen and saved discussion on this before but didnât realize I was now doing it 
. Below from reddit somewhere, didnât keep note of the source (EDIT: laser number added, found the source on reddit HERE. ):
0.1 cd/lm: light bulb
1-3: flooder
5-15: balanced EDC-style beam;
30: compact thrower
100: dedicated thrower;
500+: extreme thrower;
10000: laser
Cd/lm is super useful indeed. I have found that I particularly like the 20-25lm/cd category as it is strikes a useful balance for an outdoor light, e.g. the Acebeam L35v2, or a Convoy M21B with an ~9mm2 emitter (SFT70, SFT90, XHP50.3 Hi).
I see, your analysis of error makes a lot of sense. Given how fast the output drops, timing is critical to ensure consistency of readings between throw and total output measurements. Perhaps the error does not come from the instruments, after all.
This is pretty neat!
The funny thing is, cd/lm is redundant notation. Since cd=lm/sr (where sr is steradian, or âsolid angleâ), the unit cd/lm just simplifies to 1/sr, which can be interpreted as âinverse of beam (solid) angleâ, which is an intuitive way to measure throwiness.
Furthermore, this measure of âthrowinessâ, i.e., 1/sr, can never take values below 1/(4Ď), since solid angle can never exceed 4Ď, the entire surface area of a unit sphere. This is analogous to regular angles never exceeding 2Ď radians, or 360 degrees. This is why you donât see categories of light sources with cd/lm ratio below 1/(4Ď) ~ 0.08 ~ 0.1, with the minimum achieved by a source that emits uniformly, e.g., a light bulb.
Similarly, a bare Lambertian emitter (e.g., a mule) achieves a cd/lm ratio of 1/Ď ~ 0.3, which is indeed floodier than even the 1-3 flooder category!
Also @sb56637 please feel welcome to move this discussion to a separate thread, for independence and discoverability.
This. I anchored the cd/lm scale to a few lights that I know so that I can guess how the beam of lights Iâm not familiar with may look like:
Sofirn HS21 Flood: ~1
Wurkkos HD12: ~4
Nitecore NU25 (2017): ~5
Sofirn HS21 Spot: ~10
Sofirn IF19/Convoy T6 (SFT25R): ~35
Convoy 3Ă21D: ~150
I wonder if rather than dividing max intensity by the flux (cd/lm) a more perceptually linear index wouldnât be even more useful by replacing candelas with ANSI (0.25 lx) throw in meters (a square root function of max cd). Except nobody uses itâŚ
The problem of this (ANSI meters / lm) unit is that it is self-inconsistent as a measure of how âthrowyâ a light is.
Take 4 copies of the same light, and turn them on simultaneously, aiming at the same place. This does nothing to change the beam profile compared to just a single light, so intuitively, whatever metric for âthrowinessâ should be unchanged (true of cd/lm=1/sr) or greater (true of cd).
However, since quadrupling the light increases the lm by 4x but only increases ANSI meters by 2x, the (ANSI m / lm) metric actually gets halved.
This is a good idea though, and can be accomplished by transforming the cd/lm (equivalently 1/sr) according to the perception scale you believe in. If you believe in square-root perception, then sqrt(cd/lm) works for you.
It is actually quite unclear what the right conversion is. Usually the Weber-Fechner logarithmic law applies (e.g., apparent magnitude as a log transform of lux), but not in this case. Instead of taking any possible positive valueâwhich is arguably a prerequisite for the log transform to be appropriateâthe cd/lm unit can never dip below 1/(4Ď) ~ 0.08.
This should not be surprising: consider any light source that outputs 1 lm. It can achieve arbitrarily high intensity by narrowing its beam, but cannot achieve arbitrarily low intensity: the 1lm has to be distributed across a finite amount of angular space, so regardless of how you do it, at least one direction must receive light as much as the average across all directions, which is 1/(4Ď) cd.
That thought has also crossed my mind. I think the ideal measure would be beam angle. Some manufacturers do actually provide the hotspot and spill beam angles.
However, the cd/lm measure is simple to calculate and simple enough to develop intuition for, as it is can also be described as the inverse of the hotspot size.
I think of the following categories:
< 5 pure flood
5-15 EDC
20-30 Balanced / Outdoor EDC
50 Pocketable Thrower
100+ Dedicated Thrower
That would indeed be ideal, but unfortunately, beam angle can become ill-defined as many lights have smooth intensity gradients across the beam. However, if you know that a light has C cd/lm, you can obtain the effective beam angleâthat is, the beam angle if all the light were crammed into a sharp, circular beam of maximum achieved intensityâby the conversion
radial angle (in radians) = arccos(1-1/(2ĎC)), obtained by inverting the formula for area of spherical cap as a function of angle.
I think the true ideal would be an intensity-vs-angle plot like in LED datasheets:
This would be amazing!
I think Gaggione provides this for some emitters for their TIRs. Super helpful stuff.
This may be a good thing? - 4 lights vs. one may be seen as doubling the reach not quadrupling it. The quad as you described will be more as throwy as each of the contributors? If each of the individual lights is dimmed to a quarter, the combined illumination at a distance (and the ANSI distance) should stay the same as a single not dimmed light?
I thing using the distance in the âthrow indexâ should just compress the scale. But as @14500 mentioned, may not be as easy to compute (but may be mor intuitive) - it would de-emphasize the differences between lights.
For example, the difference between Spot and Flood in HS21 in cd/lm is 1 vs 10. Spot is not 10 times more spotty, intuitively. Itâs somewhat sportier⌠On a square root scale that would be a factor of around 3 which would align more with the visual experience.
Using my lights list from above, that would be in â(cd/lm) units:
Sofirn HS21 Flood: ~1
Wurkkos HD12: ~2
Nitecore NU25 (2017): ~2+
Sofirn HS21 Spot: ~3
Sofirn IF19/Convoy T6 (SFT25R): ~6
Convoy 3Ă21D: ~12
Looks like a reasonable perceptual scale for throwiness to me, though maybe a bit too compressed at the higher end?
The HS21 Flood as the scale basis works well for my intuition too. The scale approximately compares all other apparent beam concentrations to this. A Mule would be some 0.5 and a bare lightbulb around 0.3 on this scale - kind of intuitively persuasive compared to 1 for HS21 Flood.
p.s. Hypothetically one could develop a similar scale anchored on physical limits rather than a headlamp I use (inadvertently). For instance,
Throw (focusing) index = 2âĎĂâx - 1
where x = cd/lm
should output zero for bare lightbulb (full sphere or zero focusing), one for Lambertian mule (like in the basic floodiest, primordial flashlight), around 3 for HS21 Flood like lights, 10 for its Spot, some 20 for T6, and 40 for 3Ă21D.
Letâs name it something sexier than âthrow indexâ for the industry to adopt it and it could be quite informative (and based on light distribution limits as @QReciprocity42 explained).
~0.08?
Not sure about the rest of the industry, but I already adopted the (needs a sexy name) Index, for a day :â -â )
Bare bulb - 0
Mule - 1
Floody - <5
Balanced - <10
Quite Throwy - >20
V. Throwy - >40
LEP territory - >80
I was thinking of calling it the Piercing the Darkness Index, but the name was already taken⌠:â -â )
p.s. Beam (Vanity) Factor?
p.s.s. I just discovered that the so-defined beam factor approximately scales linearly with distances and beam cone planar double-angles. Halving the distance is roughly equivalent to halving the beam angle or (arguably) doubling our perceptive brightness of the object by about quadrupling the target illumination. Intuitive winner! :â -â )
And, come to think of it practically, even if there is no theoretical upper bond, one can think of it as a practical throw percentage, 100% being skinny LEPs on the verge of usability as flashlights.
I got it! âBeam Lick Factorâ
Iâm not sure if I understood your argument. If the quad should be more or as throwy as each contributor, it is certainly not reasonable for the quad to only achieve half the âthrow indexâ, which makes (ANSI m / lm) a poor candidate for âthrow indexâ.
A similar issue appears in the lower end: if you have the same light and dim it arbitrarily, the (ANSI m / lm) index approaches infinity, since the square root is extremely fast-growing near zero. Certainly, a light with the same beam profile and much lesser output should not achieve a greater throw index.
Thanks for the correction!
This does successfully normalize the scale from [0.08, infinity) to [0, infinity), but it is unclear how to explain the coefficient of 2sqrt(pi) and the resulting -1 perceptuallyâI am not aware of any model of perception that uses a scale like this.
It is also unclear how to justify using it over other, equally simple normalizations, e.g., log(4Ďx).
ln(4Ďx)/ln(4) fixes the index for bulb as zero and Lambertian as 1, but the scale would be impractically compressed for higher values.
It maps a Mule (Lambertian) to BLF = 1. It fortuitously has a useful range - LEPs are around 100.
The shape is Stevenâs power law with 0.5 exponent. The factor just attempts to capture beam shape on somewhat intuitive scale. Halving beam angle more or less doubles the index, I think, and at least for moderate values roughly corresponds with experience (the T6 at 20 feels twice as Throwy as HS21 Spot at some 10).
Itâs more a beam shape index, or light concentration index - Beam Lick Factor, or BLF for short :â -â )
I see, it is somewhat pleasing to have the uniform emitter mapped to zero and the Lambertian emitter mapped to 1.
I would personally still prefer just cd/lm because it is difficult to justify why a particular transform (e.g., power law with the very specific power of 0.5) should be used. Also, the post-transform quantity becomes much harder to interpret and use, having lost its status as a physically derived quantity and entered the realm of psychology.
Plus, cd/lm is already very easy to interpret: it simplifies to 1/sr, which reads âinverse of beam spreadâ, a natural description of concentration.
Since the (ANSI m / lm) index is not consistent for the exact same beam at different output levels, it is not a valid measurement for beam shape or light concentration.
You know way more math than needed to verify this yourself, but Iâll give an example anyways. Take a Convoy C8+ with Osram W1, which achieves roughly 1000m at 1000lm at maximum, for a m/lm ratio of 1.
Now dim the output to 1%, that is, 10lm. It still achieves a throw of 1000sqrt(1%)=100m, which gives it a m/lm ratio of 10. So: for the same light, reducing its output to 1% increases its âlight concentration indexâ by 10x, which is not sensible.
Oh, that was the old idea. The latest index returned to scaled square root of cd/lm (which should be independent of light level and scales linearly with ANSI m, and planar beam angle to boot!).
