What theory is connected to this
theoretically?
Do you mean your own research? I haven't made any experience like this until now.
Unfortunately, it's complicated to make reasonable experiments in a way that can be reproduced by others.
And how might "Huygens Ultimate" support the idea that FL matters in your opinion?
(WalterK does
not think so, btw.)
I know that some CPF members believe that FL matters, but I don't.
I would really like to hear about a plausible physical idea behind FL influencing max-lux.
Until now I only know an idea which contradicts it (
conservation of etendue).
This actually seems so simple, that I'm not sure why this isn't brought up more often. Unless my outlook is completely off, in which case if it is, someone would be very helpful to explain why what I am about to explain would not be true in practice.
I will skip the obvious things which I think conflict with LED use, and lux (throw) in the real-world use of available lenses. Remember, these are real lenses we use, not infinitely-thin proposed lens planes using infinitely-small point sources for calculation of collimation angles. An LED is not a point source. It has a real size. It also has a characteristic pattern of light output!
While light, in general, follows very specific rules, an LED is a device. The way it emits light is not equal in all directions. Because it is not infinitely small, and has a size, it also has something CREE themselves take the time to document in their PDFs.
Let's talk about "Spatial Distribution". First let me make things clearer as to what point I'm arguing.
Argument #1:
Two lenses of different F/#s are the same diameter and surface area on the side facing the LED which is also plano (flat) on that side. The lenses are of the same quality, yet their focal lengths vary. One person says, at the same diameter and light entrance area, the same amount of lux (throw) is constant between these two different FL lenses. The only thing different (for arguments sake, I'll keep it simple here) is the output angle of the beam ahead of the lens. The lower F# lens (shorter FL) yields a larger projected square output. The higher F# lens with longer focal point yields a smaller projected square. But, both lenses throw the same distance. That would make the lower F# lens more efficient of course, because it is covering a larger projected output area with the same intensity of light per area covered.
Argument #2:
In the real world, lenses of equal diameter but different F# can have an influence on throw, even though argument #1 may be accurate in "thin-lens" equations. However, argument #1 holds truer when a point-source is used as a light source, and therefore it is not a perfect analogy to use when an LED is used as the light source. Although the general laws of point-source light are accurate for argument #1, an LED is not a point-source, and it emits light in a semi-known pattern known as "spatial-distribution". Because spatial-distribution of angular light does not adhere to a standard law that we know as applied directly to LED output, it is assumed that a circle which captures light (a lens), must also not adhere to the general laws of light gathering when the source has a specific spatial-distribution. If we even attempt to assume that lenses obey a standard of light-gathering based on initial angle of light incidence and lens area, when the angle of intake light changes, we find that spatial distribution itself is what throws a curve ball into the mix.
Okay, so what is the curve ball?
Different F# lenses capture light at different angles from the source, keep this in mind foremost. This means that different F# lenses rely on spatial distribution of light, to predict gathering of light at any given intake angle! General area formulas for circles, and triangulation formulas, must take into account the spatial distribution of the LED, because the LED must be treated as an optical system itself coupled to a lens, not as a simple 1-dimensional object that is illuminated and viewed through a lens.
To better illustrate this problem I see, a simple diagram should help clarify everything.
Now, I am keeping in mind that my example image is only an attempt to display what "linear" distribution actually is as I somewhat conceive it to be. However, this image is more or less there to show that for a given LED, the light captured at a different angle is not a constant, it is a sloped curve that varies. (If the graph were to show 180°, a sphere might demonstrate this more accurately than a triangle.)
Moving on, if a lens is close to the LED and having a lower F#, a given distribution of light is captured. If a lens is further from the LED and has a higher F#, another given amount of light is captured, but we cannot concisely predict them using a general inverse square rule, as that would be acting on a linear spatial distribution of light . In conclusion, due to spatial distribution, nothing can tie these values together as "predictable", without a formula that incorporates the spatial distribution profile into the lens(es). Since the profile is not a standard shape, like a cone or a half-sphere of light, F# means that lux must change, at least somewhat, as incidence angle changes upon the lens face.
All of this, and yet still before even acknowledging that real lenses (not thin imaginary lenses) with large face radii have troubles collimating the light at the high interior angles found closer to the outside of the lens face surface; where light is highly bent. A high F# lens does not capture as much light as a much lower F# lens--that can be said, but it also doesn't suffer from as many internal refractions/reflections as the lower F# lens. In my opinion here only, it seems that some F# within a range of F#s must be most efficient at lux output and therefore throw, at equal lens diameters.
I am eager to know how spatial distribution would NOT effect throw/lux in varying FL positive lenses of equal quality and diameter.