Updated
Beam profiler/calculator - Interactive
Link to Model description.
Please enter your flashlights using the link above to see how they compare to others. Try to keep model names compact. You need to refresh the page to see new entry. Comments and bugs reports are appreciated.
Very interesting idea to collect this data!
Right now the entries are super clustered at the bottom, with lots of empty space. This is not surprising, as it takes LEPs to achieve a vertical value on the order of 100. I would rescale vertically to distinguish the entries better.
I would add buttons to let users try out different scalings: for example, lm and cd/lm without square root, and log(lm) and log(cd/lm). As more lights come in, log scaling might be necessary to maintain approximate equidistribution across the plot.
Some new entries are showing up in the sheets, but not on the plot.
EDIT: there are now entries with both horizontal and vertical values over 100. To capture very high values but still separate low ones, an option of log scale is strongly recommended.
Thank you!
Briefly:
p.s. The main problem I was trying to address was to highlight differences between lights that are seemingly similar.
Thanks for the quick response!
While this is true, equally convincing arguments can also be made for many other scaling options, including log scale. It is clear that some compressive, i.e., sublinear, transform must be used to visualize the data, but there is no evidence that the square root is a definitively better choice than logarithm. In fact, logarithmic transform is usually chosen for brightness (e.g., apparent magnitude), or more generally, any dataset that is expected to span several orders of magnitude. See Benford’s law and lognormal distributions.
Thank you very much for the clarification! I should not have missed it the first time, so my apologies.
I don’t yet understand this part and would appreciate some elaboration:
Any sort of non-affine transformation already makes equally-spaced intervals hard to compare, so I don’t see how one choice can complicate the situation more than another. If a logarithm is introduced, the square root simply comes out as a multiplicative coefficient.
I see. I imagine this to be a difficult endeavor because lights that are seemingly similar may have measurement errors that exceed the true dissimilarity between the lights. In other words, the noise may overwhelm the signal.
This map would be super helpful for people who are looking for lights with similar beam profiles to a light they own, or throwier/floodier than a light they own.
Looking at the map I noticed that C8 SFT25R and 3x21D have the same cd/lm, and didn’t initially believe it. But the math checks out: the SBT90.2 has 4x the area of SFT25R and thus double the effective diameter, while the 3x21D’s 85mm reflector is also double the C8’s 42mm reflector, so they can be expected to produce the same beam profile.
Here is my justification for choosing the Y variable:
The way I think about it is not how to transform some god-given variable like cd/lm but how to create well-anchored a domain where equal spacing have easy to interpret physical meaning, which also conveniently compresses the range. This part has nothing to do with perception of brightness (if you don’t want it to).
With the Y chosen, √cd for X is the logical and Y-matching choice to compress it as well. While we can debate the perceptive interpretation of it, the screen you’re looking at already uses gamma transform, which is close to it, so it’s probably not too far off from reality and practice for photopic vision.
The red contour lines for the ‘reach at 1 lx’ also work nicely with these two choices - one can increase the reach by either pumping out more lumens or tightening the beam and this family of hyperbolas can tell you what’s easier. BTW while unlabeled, the contours start at 100 m and go to 2000 m, in 100 m steps.
Thank you for the response. Regarding your justification for the sqrt(pi cd/lm) unit, I would argue that points 1, 2, 6 are not special to this transform and easily achieved by a suitable log transform, and that point 5 lacks justification. But I would not go into detail here.
I think this is a great goal, bringing in perception makes it much harder to rigorously justify anything. Regarding the particular point
I would argue that the log transform is much easier to interpret. With sqrt scaling, a unit step corresponds to the change from n^2 to (n+1)^2. How would you physically interpret such a change? In comparison, a log step corresponds to the change from, say, 2^n to 2^{n+1}, which is interpreted as “doubling”.
And as we have already seen, square root is not compressive enough to deal with data spanning multiple orders of magnitude.
I made some changes to graphs - probably not to your liking 
- but please take a look.
For the Y scale a change of 1 on a log cd/lm scale doesn’t double what I care about: for instance the beam divergence angle, the throw potential, or the hotspot diameter at fixed distance. A log step of 2 would, which you can halve, but that means that you’re logging square roots anyway just moving them out of the log’s argument.
On the other hand, if you propose the details of coherent indices, with or without logs, that would work better for the Map and were easier to interpret both numerically and visually than the current system, I’ll be happy to oblige.
What’s a realistic range for depth to rim diameter ratio for flashlight reflectors?
From what I’ve seen, the shallowest reflector has a depth:diameter ratio of around 0.5 (Wurkkos FC11C), and the deepest I’ve seen has around 1.5 (Ultrafire T6), with most concentrating around 1.
You’re unlikely to see deeper reflectors than 1.5 because it would be suboptimal engineering. The only exception to a 0.5 lower bound I could envision are recoil reflectors, but they are no longer found in mainstream lights and should be safe to disregard.
Responding to the other post a bit later!
A lot of this seems to boil down to personal preference. If you personally care about length-based units, the square root transform is sensible. If someone cares about area-based units that scale linearly with quantities like lumens and lux, they would prefer to use a non-transformed cd/lm ratio. If someone believes in the Weber-Fechner law, they could argue for a log transform. Without the need to visualize data, I personally prefer non-transformed quantities for the mathematical simplicity.
I appreciate your giving me the space to do so. For the purpose of the map, I will disregard the issue of perception and try to optimize for visual clarity, followed by interpretability and simplicity. Toward this end, I propose
Visual clarity: so far the lm values already span from 200 to 19000, with more to come. This corresponds to around 7.6 to 14.2 on the log scale of base 2, nothing too crazy. The cd/lm so far ranges from 1 to 7500, which corresponds to 3.7 to 16.5; again, nothing too crazy.
Interpretability: the log transform of lm is analogous to apparent magnitude. For the log-transformed cd/lm, the minimum attained by a bare bulb is 0, and the Lambertian mule 2.
On this pair of scales, the curves of constant intensity/reach are lines of slope -1, rather than hyperbolas. Every single flashlight created by now (and likely for many years to come) falls into the interval [0, 20] in both coordinates.
If you want, you can make the tradeoff of inserting a square root inside the log for the cd/lm transform: this turns the curves of equal intensity into lines of slope -1/2, but normalizes the Lambertian mule to have value 1.
Also: if you’d like, I could go through some reviews and contribute some data on extreme lights that I don’t own.
Thank you kindly - I can see the mathematical elegance attraction of ln2 :-)
Need to think, but I believe that the geometry of distribution of points on the map will be identical to the current Overview version - the only thing that would change will be labels on the axes?
As this is supposed to be a map, I care more about relative spacial relationships than absolute numbers.
For instance, compare Overview and Goldilocks. Is the difference in beam acuity between Q8 C8 and T6 about the same as between T6 and HS21 Spot or gaps are practically not the same? I would argue that the Q8 C8 is further apart from T6 (in throw potential, spot diameter, beam divergence) than T6 from HS21 Spot. Since Q8 C8 and T6 use the same LED and output similar lumens, this is reflected in the relative difference in throws. You can pick some other pairs and compare either x or y distances.
At the moment I tend to think that the Overview and Goldilocks pair may be the best compromise. Overview changes the spacing the way you’d like (I think) but leaves the absolute values of indices I concocted, alone.
Yet another idea is to do away with cooked up indices, and simply show cd/lm vs. lm but both on log-transformed axes. The spacing will be just like in the Overview version but the variable values/units are familiar to most. I’m not comfortable with it but it’s the simplest.
Other than the map distance and brightness interpretation dilemmas, the important thing that either of those maps accomplishes is separating beam shape property from LED output, which keeps confusing me and others when comparing flashlights.
Thank you for the kind message! I must say that logs and square roots are my favorite sublinear transforms. Logs for very large/small numbers or conversion of multiplication to addition, and square roots often come up as a natural scaling in the context of probability/statistics.
I did see the updated map with the nonlinear axes; since the intensity contours are lines, some sort of implicit log transform must have been used. Yeah, I think the only thing that would change is the axis labels, not the visual geometry.
I’ve having some trouble because Q8 isn’t on the Goldilocks map. Also, the Q8 and T6 don’t have the same LED (SFT25R vs LHP531). Did you mean to refer to a different light?
I think this makes a lot of sense. People can simultaneously access familiar quantities and enjoy a visually nice scaling. What it could make difficult is comparing values on the map, but that’s no problem as you also provide the explicit data in the forms.
I think the existing plots already do a great job at this: look horizontally for output, vertically for beam shape, and diagonally (cutting across contours) for absolute intensity.
I’m gonna put in info for some more lights, just out of curiosity about how they’d look.
Sorry, I meant C8.
Ahh got it. I don’t have a HS21 on hand, but it looks like an SFT40 behind a small TIR, perhaps smaller in diameter than the T6’s reflector.
Going from C8 to T6, the emitter stays the same and the reflector diameter halves. Going from T6 to HS21, the optic seems to get a bit smaller, and the emitter diameter increases. In general, TIRs will always have a larger hotspot than a reflector of equal diameter. It seems that the C8-T6 and T6-HS21 gaps should be somewhat comparable.
Thank you for populating the Map! The Imalent fell off the map, but then it probably should :-)
My pleasure! Playing with the map has gotten me some interesting insights. For example:
Please indulge me and predict where the M21K LHP73B would fall and if it’s much different than my guess.
I’ll estimate using Funtastic’s turn-on measurements for M21J, and assume the same optic and same drive power.
Output: at around 20A, the LHP73B has around 40% more lumens than SBT90.2, which suggests a lumen estimate of 4260*1.4=5964. Let’s just say 6000lm. Assuming a 15% optical loss, 20A of drive current seems consistent with the measured output.
Throw: The LHP73B has 25mm^2 against 9mm^2. Thus the intensity changes by a factor of 1.4*9/25 = 0.5, so I’d expect the measured 769m to be brought down to 769sqrt(.5)=544m. I might bump that figure to 550m, maybe even 600m, because floody emitters tend to suffer less from focus issues, and measure on the high side of intensity at close distances.
