## View Poll Results: Do you understand the physics of throw

Voters
84. You may not vote on this poll
• I don't but want to

15 17.86%
• I want to understand better how throw works

27 32.14%
• I understand enough to decide what's working

17 20.24%
• I think or am pretty certain I know how it works

25 29.76%

# Thread: Formula for calculating throw using aspheric lens

1. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by Ra
The 4 * pi part is only part the optical law that states how many lux at 1 meter an omnidirectional lightsource would give based on the total lumens output of that source.
Like I said earlier, led's are not omnidirectional! But it is too difficult to make a formula that overcomes this problem..
Well, if it only emitted into a hemisphere (but uniformly), it would be 2*pi as the solid angle, and using a lambertian emission profile the spheric integral yields 1*pi. You'll have to apply rather generous losses to get realistic values though.

2. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by Dr.Jones
Well, if it only emitted into a hemisphere (but uniformly), it would be 2*pi as the solid angle, and using a lambertian emission profile the spheric integral yields 1*pi. You'll have to apply rather generous losses to get realistic values though.

Yep, that's why it's easier to measure the cp-output of the bare source first, because then you have determined the surface brightness (when you know the source dimensions..) and then go on from there..

Regards,

Ra.

3. ## Re: Formula for calculating throw using aspheric lens

Maybe it's time to sum up the important things in this thread:

I try to do this as simple as possible: No long story's about the why..

-We're talking about throw: Reflectors and lenses have two types of efficiency: Efficiency for throw and efficiency for lumens output (torchlumens).

-Throw-efficiency of lenses is almost always (sometimes much..) higher than of reflectors with the same diameter. (on lumens-efficiency it's mostly the other way around!)

-Throw is determined only by three things: Lensdiameter (or reflector diameter), surface brightness of the bare source, and the (throw-) efficiency of the lens (or reflector)

-F-ratio of the lens (or depth of reflector) does not affect throw, it only affects total lumens output (torchlumens, wideness of the beam and sidespill).

Basic formula for calculating throw: (theoretical)

(lenssurface divided by apparent sourcesurface (all in mm2)) x Lux@1 meter (bare source) x Throw-efficiency lens (or reflector).

Edit:

I think "apparent sourcesurface" needs an explanation (Thanks to Dr.Jones.): I forgot to mention that most sources like led's have domes that somewhat magnify the surface of the led-die, so it appears to be bigger (seen from the front) than stated in the specs of the led. In the formula above, you need the apparent source-dimensions, not the dimensions stated in the specs. Roughly measuring these dimensions still is better than trying to calculate the surface brightness from the lumens output and the geometry of the beam, as these are not omnidirectional sources.

When putting this all to the test: Always use a stable power supply, and the same source (led or bulb). Never use batteries ! It's best to use calibrated equipment (lux-meter)
When comparing collimators on throw: Always check that the entire surface of the collimator plays along at the test-distance !

@Walterk: Maybe you can update the first post with the above??

And: Any votes for making this a sticky ???? And is this the right forum-section for a discussion like this?? (I think yes, but not sure..)

Regards,

Ra.

4. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by Ra
Maybe it's time to sum up the important things in this thread:

-Throw is determined only by three things: Lensdiameter (or reflector diameter), surface brightness of the bare source, and the (throw-) efficiency of the lens (or reflector)

-F-ratio of the lens (or depth of reflector) does not affect throw, it only affects total lumens output (torchlumens, wideness of the beam and sidespill).

Ra.

Ra,

Thanks so much for helping out. The lens pictures lux vs. F is very telling.

deep reflectors often give a smaller spot, since it also collect more lumens, I wonder where does the extra lumens go?

If the extra lumens do show up in the smaller hot spot, then the lux/throw will increase. Since your pointed out that throw doesn't increase by deep reflector with same diameter, one must conclude that non of the extra lumens will end up in the hot spot. Is this correct?

In that case, the smaller spot often preceived as brighter is just an a illusion? I've always wondered about that. I remember a post comparing FM deep reflector vs. Litho, the deep reflect throw a smaller hot spot but didn't make it any brighter.

Is it possible to alter part of the the deep reflector curve shape so that the extra lumens can be put towards the center hot spot?

Edit. I found the link here that supports the principle "deep reflector doesn't increase throw":
http://www.candlepowerforums.com/vb/...d.php?t=240742
.
.

5. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by Ra
(lenssurface divided by sourcesurface (all in mm2)) x Lux@1 meter (bare source) x Throw-efficiency lens (or reflector).
In that case you should use the 'virtual' source surface area as seen through the LED's lens (the 'apparent' source area), which might be not that easy to measure.

(on the other hand, I'm not able yet to distinguish between EZ900 and EZ1000 anyway.)

Originally Posted by ma_sha1
Ra,
deep reflectors often give a smaller spot, since it also collect more lumens, I wonder where does the extra lumens go?
Hm, according to the arguments, throw can't increase, so the spot should be wider (compared to a less deep reflector of the same diameter).

However reflectors are more difficult to understand since the effective focal distance seems to vary from inner to outer rays, and I can't yet put my finger on the definitive reason exactly why it should get wider.

Is it possible to alter part of the the deep reflector curve shape so that the extra lumens can be put towards the center hot spot?
I'm afraid this is not possible by some fundamental principles of optics. A terminology often used in conjunction with that principle is "etendue".

6. ## Re: Formula for calculating throw using aspheric lens

Four questions I wonder:

1- How much variation is there in Lux within the complete spot ? I suppose close to none at 'near infinity' ?

2- Ra said: ' Focus length does affect the amount of lumens, collimated into the beam, affecting the wideness of the beam.'
If you measure a Lux/m2 at a certain distance in the spot, and you calculate this back to the surface area of the spot, what meaning would that have? Would it have some useful relation with the Lumen-output?

3- For Lumens I've read in the Optics theory thread:Lumens output is Diameter and Efficiency of the lens or reflector and the Focal-Ratio.
In a formula that would be?:

Lumen = Diameter x Efficiency x Flux @ viewingangle from the source

4- @Ra: Would this figure give some thumbrule for lens/reflector effciency regarding Lumens-efficiency?

@Ra: Will rewrite first post.

7. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by Dr.Jones
In that case you should use the 'virtual' source surface area as seen through the LED's lens (the 'apparent' source area), which might be not that easy to measure.
Yes, you're quite correct ! I even remember saying that myself earlier (in this thread?)
I'll correct that, thanks..

@ma_sha1:

Deeper reflectors create wider beams, not smaller!. Like said earlier: The extra amount of lumens, collected by a deeper reflector will widen the beam and create more sidespill. Apparent surface brightness does not change, so throw doesn't change.

Note that putting this theory to the test, you need to use the same source for all tests and use reflectors with the same optical quality..
"Deep reflectors often give a smaller spot" is not a valid reason to prove this theory wrong!

For most applications, the parabolic reflector always is the best solution, altering the shape of it, no matter in what region, will cause the optical performance to decrease!

Regards,

Ra

8. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by Walterk
Four questions I wonder:

1- How much variation is there in Lux within the complete spot ? I suppose close to none at 'near infinity' ?

2- If you measure a Lux/m2 at a certain distance in the spot, and you calculate this back to the surface area of the spot, what meaning would that have? Would it have some useful relation with the Lumen-output?

3- For Lumens I've read in the Optics theory thread:Lumens output is Diameter and Efficiency of the lens or reflector and the Focal-Ratio.
In a formula that would be?:

Lumen = Diameter x Efficiency x Flux @ viewingangle from the source

1: There will be much variation! From the center towards the edge of the spot, it will definitely decrease because the outer rim of the reflector stops to play along: Since the outer rim is further away from the source, the beamspread of that section is much less than the beamspread from the center of the reflector. (The source-size is relatively bigger for the inner rim of the reflector, causing a wider spread)

2: Yes, that would have a direct relation to lumens output, but as this is extremely difficult to predict or calculate, I don't want to even think about it !!

3: That's also a difficult one: It all depends on the focal length versus the emittance angle of the source. And lumens-efficiency of a reflector highly depends on what source is used.
Example: With a Cree XR-E, an aspherical lens is quite lumens-efficient, with a halogen bulb it's not.. The already quite narrow output angle of the Cree makes the lens more efficient, a halogen bulb is almost omnidirectional, so when the lens grabbes a 80 degrees cone from a halogen, alot of light is not collimated !

Regards,

Ra.

9. ## Re: Formula for calculating throw using aspheric lens

I really don't have the time to get into a long drawn out discussion but I just have to say something.

Originally Posted by Ra
-Throw is determined only by three things: Lensdiameter (or reflector diameter), surface brightness of the bare source, and the (throw-) efficiency of the lens (or reflector)

-F-ratio of the lens (or depth of reflector) does not affect throw, it only affects total lumens output (torchlumens, wideness of the beam and sidespill).
What you say makes no sense here. If this were true we would not need these really deep reflectors that can be seen on every single dedicated throw light. Are all these light designers just that stupid?

Throw is determined by:
Distance of the reflecting/refracting surfaces
Collection efficiency- both from a quality and quantity perspective(amount of light emitted that can be collimated and the transmissive efficiency)
Source brightness

You say diameter is key but not depth for throw when in actuality it is a delicate balance between the two that is key. Balancing what?

Spatial radiation of the source, and diffraction limitations of a given lens shape/material.

Both diameter and depth are the major physical "tools" to in crease throw. Both increasing depth and increasing diameter will get the surfaces farther away and decrease the divergence, or increase the collimation, of the beam. However if we only focus on one parameter such as diameter we will not really be gaining any ground.

Originally Posted by Ra

For most applications, the parabolic reflector always is the best solution, altering the shape of it, no matter in what region, will cause the optical performance to decrease!
This is incorrect. When dealing with some domed LEDs the apparent position of the source moves. Altering the the shape can help increase performance over a plain parabolic.

10. ## Re: Formula for calculating throw using aspheric lens

I'm afraid Ra is right: The focal length does not have influence on the beam intensity, and he already proved it experimentally with some lenses and the luxmeter.
I did that, too, taking an XR-E and different lenses of the same diameter but different focal lengths. Result: With a shorter focal length the image of the die was bigger, but not brighter. Having a bigger spot is a good thing, and that's why thrower manufacturers do it (well, and it would be quite a waste of flux otherwise).

With a reflector there's another reason, too: With an XR-E there are virtually no beams at an angle >60° to the optical axis, a deeper reflector has a smaller area left in those dead angles in it's center, thus it increases the effectively used apparent reflector area and thus throw.

Other than that (and especially for lenses), throw is only determined by die luminance and apparent lens area (or apparent effectively used reflector area).

Increasing depth at a fixed diameter will move the outer reflector parts away from the LED (resulting in a tighter beam, as you said), but move the inner parts actually towards the LED, widening the beam.

When dealing with some domed LEDs the apparent position of the source moves. Altering the the shape can help increase performance over a plain parabolic.
The LED dome lens creates a magnified virtual image of the die - just put that image into the focus of the 'plain' parabolic reflector. On the other hand, that dome probably induces a few aberrations at higher angles which you might compensate with an adapted reflector...

11. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by Dr.Jones
I'm afraid Ra is right: The focal length does not have influence on the beam intensity, and he already proved it experimentally with some lenses and the luxmeter.
I did that, too, taking an XR-E and different lenses of the same diameter but different focal lengths. Result: With a shorter focal length the image of the die was bigger, but not brighter. Having a bigger spot is a good thing, and that's why thrower manufacturers do it (well, and it would be quite a waste of flux otherwise).

With a reflector there's another reason, too: With an XR-E there are virtually no beams at an angle >60° to the optical axis, a deeper reflector has a smaller area left in those dead angles in it's center, thus it increases the effectively used apparent reflector area and thus throw.

Other than that (and especially for lenses), throw is only determined by die luminance and apparent lens area (or apparent effectively used reflector area).

Increasing depth at a fixed diameter will move the outer reflector parts away from the LED (resulting in a tighter beam, as you said), but move the inner parts actually towards the LED, widening the beam.

The LED dome lens creates a magnified virtual image of the die - just put that image into the focus of the 'plain' parabolic reflector. On the other hand, that dome probably induces a few aberrations at higher angles which you might compensate with an adapted reflector...
His test was faulty from the start. Start with a bad premise and you get bad info. The test only focused on one aspect.

For a beam to have throw it must be collimized. The better the collimization the further the throw all else being equal. Increased focal length is what reduces the divergence or increases collimization. Do this while keeping the same amount of light captured and you will increase throw. To keep the same amount of light in the beam means the lens will have to get larger yes but this goes back to what I said that it is not a focus on any one aspect that is key it is a balance of them all.

If what he says about diameter is true then as long as you make it wider the throw will increase. This may be true in theory land but not in the world we all live in where glass has a diffraction limit. Therefore you can only get so wide before you need to move out away from the source to see any additional gains in throw.

That means focal length is key to throw.

12. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by saabluster
The test only focused on one aspect.
Indeed, it focused on bare throw.

For a beam to have throw it must be collimized.
Yes. To get maximum possible collimation, you put the source into the focus, and that's what we always do when trying to 'throw'.

Increased focal length is what reduces the divergence or increases collimization. Do this while keeping the same amount of light captured and you will increase throw. To keep the same amount of light in the beam means the lens will have to get larger yes ....
Exactly... and exactly that (lens getting larger) is increasing throw.

And didn't Ra's experiment show that the amount of light caught doesn't have influence on the beam intensity, but only on spot size?

If what he says about diameter is true then as long as you make it wider the throw will increase.
And that's true.

This may be true in theory land but not in the world we all live in where glass has a diffraction limit.
If the theory was wrong, they had already made a better one
And with flashlights, we are so much above diffraction limit, we don't need to take any care of it.

Therefore you can only get so wide before you need to move out away from the source to see any additional gains in throw.
That means focal length is key to throw.
You didn't get the point: We have no problem at all increasing or decreasing the focal length as it doesn't have influence on the throw anyway.

Compare different diameter lenses with the same focal length: Throw increases with diameter, while spot size stays the same.
Compare different focal length lenses with same diameter: Throw is the same, but spot size increases with decreasing focal length.

Get some lenses and do it... I know you do have some experience, but maybe only with the same kind of high-NA lenses?

13. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by Dr.Jones
I know you do have some experience

14. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by saabluster
That's not much of a response. We know that you make flashlights. RA is an optical engineer and Dr. Jones (as I recall) has a Phd in Physics.

Is it possible that they might actually know something?

15. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by gcbryan
That's not much of a response. We know that you make flashlights. RA is an optical engineer and Dr. Jones (as I recall) has a Phd in Physics.

Is it possible that they might actually know something?

Originally Posted by saabluster
I really don't have the time to get into a long drawn out discussion...

16. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by saabluster
I really don't have the time to get into a long drawn out discussion...

With all due respect, that's getting a little old as well.

Why are you in this thread if that's the case? You have your unfinished thread (sticky) and you have time to state, yet again, that RA makes no sense (to you?).

It's disruptive to interrupt a thread to only criticize and then to become "busy" when the questions become more detailed. If you understand the subject then it shouldn't take any more time to post a paragraph regarding the subject matter than to post a paragraph disagreeing with RA's point.

17. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by saabluster
Well, as long as you think focal length has influence on throw, you don't have enogh experience, I'm afraid.

I just put some little experiment together: A LED (XP-E Q5 @0.9A), and a lens, f=500mm, 116mm diameter. Quite sloppy design. It yields 250kcd. I'll post an image later.

And before I forget: A pre-collimator won't increase throw either, but increase spot size instead. (Unless it's able to reduce some aberrations, that is.)

18. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by Dr.Jones
A pre-collimator won't increase throw either, but increase spot size instead.
Now HERE it get's interesting again ! Let's change subject to pre-collimator.

19. ## Re: Formula for calculating throw using aspheric lens

A pre-collimator creates a magnified virtual image of the die (just like the LED dome); that image has a smaller viewing angle, and that virtual light source's luminance is the same as the die's, so there's no increase in throw. The bigger size of the virtual image results in a wider beam and thus a bigger spot.

You catch more of the LED flux with a pre-collimator, but again it just increases spot size, not throw.

20. ## Re: Formula for calculating throw using aspheric lens

So, using two lenses as beam-expander or reversed telescope, results in:
- different f-number (only affecting Lumen as the viewingangle changes )
- different diameter ( affecting throw as surfacearea changes )
- different beam angle ( only affecting the spotsize )

I used to think there was more to gain.
In my experimenting it is the best way to get more Lumen lit the full diameter of the large lens.
Large diameter lenses are easy to find, but they have mostly large focal lengths.
Using a precollimator then is great for making use of the large lenses.
Smaller lenses with short focal lengths are less expensive.

21. ## Re: Formula for calculating throw using aspheric lens

I think it's hard to find a host for the larger diameter lenses. I don't know what is considered a longer focal length but most aren't long enough to mount as a simple replacement for the front glass lens.

The hosts are all (of course) made for reflectors and therefore tend to be deep as well as wide. For an aspheric wide and shallow would be good.

There's always cat food cans...right Dr!

22. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by Walterk
So, using two lenses as beam-expander or reversed telescope, results in:
- different f-number (only affecting Lumen as the viewingangle changes )
- different diameter ( affecting throw as surfacearea changes )
- different beam angle ( only affecting the spotsize )
Not sure if I understand you completely, but yes, a beam expander increases the diameter (and thus throw) and decreases the beam divergence (giving a smaller spot), while keeping the same flux (minus losses).
The two lenses of a beam expander should have the same F#.

Using a precollimator then is great for making use of the large lenses.
Again I'm not sure if I understood you correctly...
Without a precollimator the lens is already completely used, since the LED beam is much wider than the lens. But only a fraction of the beam flux is used. The pre-collimator helps getting more flux (lumen) into the main lens, resulting in a wider beam (bigger spot) with the same intensity (same throw).

There's always cat food cans...

23. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by Dr.Jones
Well, as long as you think focal length has influence on throw, you don't have enough experience, I'm afraid.
Dr. or Ra,

Would it be fair to add a qualifier "Assume the same lens efficiency" before the "Focal length doesn't matter" theory?

Ra's exp. is pretty convincing, however, it's done with long EFL lens.
Most Aspheric lens folks used in flashlight has a small focal length, for example 35mm-38mm EFL on a 52" lens, (F number in the .7,-.8 range) where the Led is about an inch away from the flat side.

It makes sense to me when you get "Too close" to the lens, the angle from led to the outside section is getting more wide, which will cause more reflection loss & therefore less light going through the lens.

People always thought led "too close to the lens" cause the lens to reduce "efficiency" due to the colimating angle being too wide, by Ra's formular, reducing lens efficiency = less throw.

So, Is it possible that there's a minimum Focal lens limit where the "Focal length doesn't matter" theory holds true? where the further reduction of Focal length with reduce throw?

Would love to see some experiment like Ra's but with same diameter lens that has small F numbers, really small like 0.5., 0.7, 0.8, 1.0 etc.

Small F numbers is preferred to keep the flashlight compact, especially when trying to fit 3"-4" large diameter Aspheric lens into a flashlight.

Thanks for your contributions, I find your input enlightening, in a place most people are limited by "try & error" approaches.

24. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by ma_sha1
Would it be fair to add a qualifier "Assume the same lens efficiency" before the "Focal length doesn't matter" theory?

It makes sense to me when you get "Too close" to the lens, the angle from led to the outside section is getting more wide, which will cause more reflection loss & therefore less light going through the lens.

So, Is it possible that there's a minimum Focal lens limit where the "Focal length doesn't matter" theory holds true? where the further reduction of Focal length with reduce throw?
Yes, indeed. However, that reflection loss depends on the polarisation. Up to a certain angle (brewster angle, ~56° for glass), light polarized radially actually suffers less reflection loss, while the losses for light polarized tangentially always increases. That gain and loss cancel each other out to some extent, the losses prevail though. That brewser angle however corresponds to an F# of 0.34. Lower F# would be very bad, since both reflection losses increase a lot then.

25. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by Dr.Jones
A pre-collimator creates a magnified virtual image of the die (just like the LED dome); that image has a smaller viewing angle, and that virtual light source's luminance is the same as the die's, so there's no increase in throw. The bigger size of the virtual image results in a wider beam and thus a bigger spot.

You catch more of the LED flux with a pre-collimator, but again it just increases spot size, not throw.
I hope I'm allowed to add the remark that this means that a pre collimating lens is only for getting more torchlumens from the source. By narrowing the beam angle from the led, the pre collimating lens alowes the aspheric lens to grab more lumens within the main beam, causing the wider beam.

Regards,

Ra.

26. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by Dr.Jones
The two lenses of a beam expander should have the same F#.
Sorry Doc, I happen to think to knnow there is more to this then just that !

For beam-expanders / telescope / eyepieces (working all the same ) there are several principles based on plain convex lenses, all effective.
Maybe one more then another but if you have several lenses around then probably you can find a combination that is working.

Especially look for the Kepler, Ramsden and Huygens eyepiece on Wiki.

I see Ra posted, so for clarity:
I like throwing lights, preferable portable, not necessarily compact and pocketsize.
For that I found me a couple of big lenses, bigger then the average flashlight will fit, among them 75 and 100mm.
But having long focal lengths, it's to little Lumen to build me a light from those lenses alone.
But using a pre-collimator lens, I can put the full diameter of the lenses in function.
They give more throw then whatever you carry in your every day.

27. ## Re: Formula for calculating throw using aspheric lens

And regarding Saablusters posts #69 and #71:

I do not have the time, nor the need to react on that right now (or ever)!!!
And even if I did, it would have no use I think..

But those posts can bring some unnessesary doubts for some members, and that is not a good thing, as this already is quite difficult matter for some..(at least for one apparently..)

Regards,

Ra.

28. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by Walterk
I see Ra posted, so for clarity:
I like throwing lights, preferable portable, not necessarily compact and pocketsize.
For that I found me a couple of big lenses, bigger then the average flashlight will fit, among them 75 and 100mm.
But having long focal lengths, it's to little Lumen to build me a light from those lenses alone.
But using a pre-collimator lens, I can put the full diameter of the lenses in function.
They give more throw then whatever you carry in your every day.
To certain extend, yes.. But there is a limit to the usefullness of such a setup: a 75mm lens with a focal length of 300mm already is not very practical for this.. But you definitely will have a very long torch...

29. ## Re: Formula for calculating throw using aspheric lens

Originally Posted by gcbryan

With all due respect, that's getting a little old as well.

Why are you in this thread if that's the case? You have your unfinished thread (sticky) and you have time to state, yet again, that RA makes no sense (to you?).

It's disruptive to interrupt a thread to only criticize and then to become "busy" when the questions become more detailed. If you understand the subject then it shouldn't take any more time to post a paragraph regarding the subject matter than to post a paragraph disagreeing with RA's point.

Originally Posted by Ra
And regarding Saablusters posts #69 and #71:

I do not have the time, nor the need to react on that right now (or ever)!!!
So the question gcbryan is are you going to apply the same standard to Ra as you are to me? I have stated my arguments and they have yet to be addressed. Don't try and put this all on me. And I find it funny this so-called physics professor(although I have yet to see him claim that) has just shown up here regurgitating things both myself and Ra have posted and he is now suddenly the expert in your eyes.

30. ## Re: Formula for calculating throw using aspheric lens

To all: please keep the discussion to Led's, light, lenses and if you can't resist reflectors.

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