# Formula for calculating throw using aspheric lens



## Walterk

Ra said:


> (Lenssurface divided by sourcesurface) x lux @ 1 meter x lensefficiency



*Summary: *(from posts in this thread )

 - Definition of throw: The abillity to enlighten distant objects.. It's as simple as that!
But: Different objects have different levels of reflection when enlightened, so we have a problem. Ok, then lets agree on specify the throw of a torch by stating the distance from the torch at which 1 lux is measured . 

- There is a simple ' inverse square law' formula to recalculate distance and lux to go from candlepower to throw-distance and vice versa from Lux-measurement to candlepower. 
Rephrased by Walter this comes to: Source intensity (Candlepower) = Intensity (Lux measurement at chosen distance ) / Distance x distance (in meters, of chosen point where the Lux-measurement was or will be). 

- 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)
Basic formula for calculating throw: 

(lenssurface divided by apparant sourcesurface (all in mm2)) x [email protected] meter (bare source) x Throw-efficiency lens (or reflector).

- Surface brightness of the source; measure the candlepower-output of the bare source first, divided by the surface-area of source. The only way to do this without much uncertainty, is to do a lux-measurement on the bare source at one meter (with a calibrated lux-meter) and determain the source size, then divide the lux-measurement by the mm2 surface of the source. 

- 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 !)
For throw-efficiency: A high quality lens copies the surface brightness of the source, minus the losses caused by surface reflections, absorbtions and stuff like that. So we need to know the effective transmission of the lens: Uncoated, that will be about 90%, when coated with anti-reflective coating this can be 95%.

- 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).
- Within the range of aviable lenses: For all lenses with the same diameter: The focus length does absolutely not affect throw!
- For all lenses with the same diameter: Focus length does affect the amount of lumens, collimated into the beam, affecting the wideness of the beam.
So what is important about focal length: Angle of emittance that is grabbed: 
Most sources emit their lumens in a wide area (for most led's about 140 degrees), so the more you cover that area with a lens or reflector, the more lumens you collimate into the main beam. But we're not talking about lumens on this thread, we're talking about throw.
- Lenses more easily give high throw: With led's, which are front-emitting ofcource, lenses are best suited as they grab the light in front of the source. Conventional reflectors are designed mostly for use with side-emitting sources and are less efficient with led's (but still work to certain extend, when you accept the lower efficiency..)
- Throw is not lumens related: A laser pointer throws far but has very poor lumens output !

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

Theoretical example of calculations:

If a omnidirectional source emits 250 lumens, the lux measurement at 1 meter should give 20 lux (250 divided by 4 times pi) This is called MSCP (Mean Spherical Candle Power)
That also means, that when you know the size of the source, for example led-die 1x1mm, you can calculate the surface brightness: 1x1x20 equals 20 lux/mm2
(Although usually the source will be a unidrectional source like a high power starmounted Led. Then calculate surface brightness from Lux-measurements/mm2).
Then you simply need to know the surface of the collimator in use: For example, 30mm diameter aspherical lens.. 15x15xpi=706.85 mm2

So here we are:
- Source: 20 lux at one meter comming from a 1x1mm source size
- Effective lens surface (always 2-D, seen from a distance..): 706mm2
- Lens efficiency 90% (note that this is the efficiancy for surface brightness, not for lumens output!!)
Source has 1mm2 surface, measures 20 lux at 1 meter: Source + lens will give:

(Lenssurface divided by apparant sourcesurface) x lux @ 1 meter x lensefficiency: (706/1)x20x0.9= 12708 lux at one meter ! 

So there is your formula...well not quite..with the inverse square law, you now can calculate the throw:
Taking the square root from 12708 (which is the actual CP-output, as this already is at 1 meter) gives 113 meters as the distance at which 1 lux should be the measurement result.

- Another formula for throw: Take a calibrated measurement at any distance from the source, but far enough to be sure that the entire lens- or reflector-surface plays along,
and multiply that measurement with the quadratic of the distance.

- When does one know, he (or she) has enough distance for an accurate measurement:
Double the distance: according to the inverse square law, you should measure 1/4 of the measurement at half the distance. 

If this doesn't apply to your results, something is wrong in the way you measure. 
Most likely flaw; second measurement too close with the first measurement. 
The amount of lux that is received by the object is only determined by the (apparent !!) diameter and surface brightness of the light-source (sun, torch, candle...)
When you focus at infinity, the reflector or lens is not fully lit when you look at it from close by!
This causes the spot not change much in surface brightness, when you increase the projection distance (to prevent more confusion: Here I mean the surface brightness of the projected spot)
That's what I meant when I said one could be too close to the torch for a reliable lux-measurement. That can only be done at a distance at which the entire reflector or lens plays along. And from that point further away, the lux-readings should follow the inverse square law... (note that on very long distances atmospheric conditions play along as well)

Edit 24.06.2010: My thread-starting-post was : _I really would like to see a formula that predicts beam intensity and throw, and then calculated back from real life measurements corresponds (for the larger part ) to the assumptions._
I am happy with the results, I think we 've got it pretty much covered ! It sure helped me understanding light and lenses. Now will start experimenting and build me a light !


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## Batou00159

somone else with numerical dislexia

If this thred is as good as some of the others have beenit will make my life so much easier cpf rules

sorry this dosent help much dose it


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## Walterk

Thx anyway, it shows there are people appreciating the search to this truth !


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## gcbryan

There is info on here regarding throw. The only problem is that the threads get so long with definitions and theory that it quickly loses its usefulness.

As far as I know it comes down to surface brightness of the led and the diameter of a reflector or optic and depth of a reflector plays a part as well as to it's usefulness.

Everything else is related to surface brightness and reflector/optic diameter.

The XR-E R2 has the greatest surface brightness. The other bright emitters that have greater output are larger but don't have greater surface brightness.

The larger the diameter of a reflector the more light collected but the main factor is that the further from the emitter the more the light is like a point source and so it will be brighter and more tightly focused (collimated).

With optics there are some factors to be considered (I don't have as much practical experience here) but practically speaking I think closer with a greater diameter is better for capturing the light and a longer focal length is better for focusing the light so I guess there is some optimal balance here.

I don't think in terms of formulas so I'll leave that to others.

Good thread. I hope we all learn something.


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## gcbryan

I should add if someone understands throw they should be able to briefly and concisely describe it. In the past no one did this.

I'd hate to see this thread turn into a long illustrated textbook of confusion.

Throw is how far a light will shine. The individual has to decide after what point the light isn't useful. A laser throws a long way but the spot isn't large enough to be useful but it does throw.

Some people will choose a thrower with a reflector because the spot of light may be larger and more useful and some will chose an optic which may result in a smaller spotspot and may be less useful to some.

This is all throw however and doesn't need to be defined beyond this as the rest is all individual preferences.

I hesitated to even post all this but I'm hoping it will eliminate the thread from going in this direction (as all other such threads have).


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## kengps

What you're gonna find is that "Throw" is a subjective thing. Look at Saablusters post about "the mechanics of throw" Or something like that. Maybe the title changed since I seen it last.


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## Walterk

Thanks for your input. Hope this thread will not get muddy. Indeed let us not talk definitions and throw. 

I want to be able to predict the Lux measurent within the spot at a known distance and spot-size, so I am about halfway:
Surface-area of the lens x *Geometric correction factor* x Surface brightness of the Led-die gives Beam-intensity expressed in Lux. 
Inverse-square law gives the light fall-off at a distance.

How do you do it ?


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## gcbryan

I'm not a numbers guy but in chatting with someone who is I've been playing around with the following (just to get a framework for how all this fits together in my mind).

To predict potentially how far a particular light will throw you take a lux reading at 3 meters or so and convert it back to 1 meter.

(by the way does anyone have a lux reading for the Uniquefire HS-802?)

You also have to come up with a minimum lux figure so let's say 1 lux.

If the lux reading from 1 meter is 30,000 (for instance) the math would be squared(30,000/1) or 173 meter would be the throw at which your subject would still be receiving 1 lux.

If we standardize on an emitter (XR-E R2) driven at 1A then the only changes would be in the reflector or optics.

I think 1 lux might be a reasonable figure to use for the minimum illumination.

I'd like to know what the optical laws say regarding increasing diameter as it relates to lux. It's not linear I don't think so what is it?

If you have an aspherical lens of 30 mm with a lux reading of 15,000 lux what is the predicted lux with a 60 mm lens?


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## Walterk

Throw is determined by surface brightness (lux/mm2) x diameter (mm2) x efficiency.

So if efficiency and surface brightness is the same, then:
Diameter lens 30mm, then surface is 706mm2.
Diameter lens 60mm, then surface area is 2827mm2.
So, two times the diameter is 4 times the surface area.

30mm Lens then 1 x 15.000Lux.
For 15.000Lux inverse square gives 1 Lux reading at 122 meter. 
60mm Lens then 4 x 15.000 => 60.000Lux.
For 60.000Lux inverse square gives 1 Lux reading at 244 meter.
So, two times bigger lens gives two times effective throw-length.

That the beamshape might be different, makes no difference for inverse square.
I don't know if the focal length/Geometric correction factor makes a difference, I think it should.


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## gcbryan

Walterk said:


> Throw is determined by surface brightness (lux/mm2) x diameter (mm2) x efficiency.
> 
> So if efficiency and surface brightness is the same, then:
> Diameter lens 30mm, then surface is 706mm2.
> Diameter lens 60mm, then surface area is 2827mm2.
> So, two times the diameter is 4 times the surface area.
> 
> 30mm Lens then 1 x 15.000Lux.
> For 15.000Lux inverse square gives 1 Lux reading at 122 meter.
> 60mm Lens then 4 x 15.000 => 60.000Lux.
> For 60.000Lux inverse square gives 1 Lux reading at 244 meter.
> So, two times bigger lens gives two times effective throw-length.
> 
> That the beamshape might be different, makes no difference for inverse square.
> I don't know if the focal length/Geometric correction factor makes a difference, I think it should.



I don't think it does make a difference in throw. It's more of a lumen or spot size thing rather than an intensity thing (focal length that is).

I think it's interesting to be able to adjust for environment as well. 1 lux at 122 meters may allow for subject identification if the subject is a white building and 2 lux may be more reasonable if the subject is non-reflective such as trees in the forest so throw then becomes 86 meters at 2 lux.

I'm running into this in testing some of my lights. People are listing throw figures that are more than I'm getting but in looking at their beamshots I see that their subject is a white building while my local test environment is (non-reflective) trees.


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## Walterk

Edit - Deleted confusing miss-information


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## gcbryan

Walterk said:


> But what about the GAP between calculation and measurement!!
> 
> Surface lens 706mm2 x 250Lux/mm2 x 60% efficiency = 123.550 Lux
> 
> That is 10 times more the Lux then you expected from measurements.....
> 
> How to explain this?



I'm sorry but I don't understand what you are trying to say here?


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## Walterk

I've edited-ed the post, hope it is more clear.
Anyway, still working on it, and waiting for my Lux-meter.


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## gcbryan

Walterk said:


> I've edited-ed the post, hope it is more clear.
> Anyway, still working on it, and waiting for my Lux-meter.




Where are you getting this figure...250Lux/mm2.

I guess I don't understand what you are referring to when you end up with 123,550 lux from a 30 mm diameter lens? That's not happening anywhere that I know of.

Is the 250 Lux really meant to be 250 lumen (max output for a XR-E)?


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## Walterk

Sorry, got the formula screwed up: have corrected it as follows:

706mm2 x 250 Lux/mm2 x 0.6 efficiency = 105.900 [email protected]

Where indeed 250lux/mm2 is the surface brightness of the Led.
For [email protected] at typical Ampere:
250 Lumen / Surface area of the die 1 mm2 = 250 Lux / mm2


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## gcbryan

Walterk said:


> Sorry, got the formula screwed up: have corrected it as follows:
> 
> 706mm2 x 250 Lux/mm2 x 0.6 efficiency = 105.900 [email protected]
> 
> Where indeed 250lux/mm2 is the surface brightness of the Led.
> For [email protected] at typical Ampere:
> 250 Lumen / Surface area of the die 1 mm2 = 250 Lux / mm2



I don't think it works like that. You are using lumen figures for lux figures and then wondering why there is a gap between calculated and observed values.

250 lumen/surface area of 1 mm2 = 250 lumen/mm2

It's still a lumen figure and therefore doesn't belong in the formula for throw (unless I'm missing something obvious).

The 250 lumen /mm2 figure is a way to compare XR-E to other emitters to see which has the greatest surface brightness but the number itself isn't a brightness (lux) figure. It's simply figuring lumen output as a ratio to size.


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## Walterk

Now THAT is an interesting view, makes sense, so... 

Can anyone confirm or deny this?


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## Th232

Concur with gcbryan, you're mixing up lux and lumens, all that bit is good for is the relative surface brightness between different LEDs.

1 lux is defined as 1 lm/m^2, and is a measure of intensity. Don't forget that 1 m^2 = 1,000,000 mm^2.

BIG catch though. Lux is the light that hits a surface, not the light emitted.

Further thoughts:
The problem with this is that the physics are simple for a single photon, but when you have to take into account every angle it gets rather messy, especially since an aspheric lens may not have a nice geometric formula. The jump from a single case to making a simple formula is quite tricky if you want it to be right. How much error are you willing to tolerate?

I personally can't be bothered doing all this myself, but try this:

* Find several lenses, different focal lengths, same diameter. If you can't do that, tape off the lenses from the flat side so they have roughly the same effective diameter. Note that this will break down at shorter focal lengths.
* Test each of them and plot the width of the beam vs the focal length. Find a relationship (if any).
* Find several lenses, same focal length, different diameter. Put them in and test flux. Find a relationship (if any).
--- Optional: Make readings at points in, say, a 10x10 grid. See how different they are. This could be very useful later on.
* Go through the datasheet for the LED you're using, calculate the total output over a set angle from the axis. Find out how many lumens are being collected by each aspheric.

By that stage you'll have a good idea of how focal length and diameter actually influence both the lumens and lux. I'm not trying to say this in a condescending manner, but as long and tedious as the above procedure is, it'll really give you a much better idea of how it all works.

That'd be a good start, and at least get you a fair formula for the LED you're using. Then repeat the process with other LEDs. To be honest, I'd start off this whole process with LEDs that have a Lambertian emission pattern (i.e. not XR-Es), so then you can easily determine differences due to apparent die size. They obviously won't throw as well as an XR-E, but at this point you're just looking for a formula, aren't you?

On focal length, here's an additional step in the above experiment you might try. The following aspherics have different focal lengths, but both collect the same amount of light:






See what happens. The bigger one will throw further, because the LED more closely approximates a point source. How much further it'll throw is something I leave to you.


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## Launch Mini

Without getting into numbers , I think the following makes sense.

I would think that the tighter & smaller the beam, from any light source, the further your throw will be. Yes a larger lense can collect more light, but there is only so much light being emitted from the LED.

Think of this in terms of a garden hose with and without a nozzle.
How far does your water spray without anything? ie no lens
Then restrict that same flow into a narrow opening ( lens) and you get greater distance. 
Disperse that flow over a larger area and less distance.
Now gravity takes effect with water, but this is my thought on the matter.

You still need the math to determine ulitimate throw but I'll leave that to the experts.


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## get-lit

Throw can be defined. A common standard for search lights is the distance at which luminance is 1 lux.



Here is a key relation:

*Relative Candlepower* = Relative Source Intensity x Relative Light Gather x Optic Efficiency x (Relative Optic Focal Length)^2

*Relative Throw* = sqrt(Relative Candlepower)

*Relative Throw* = sqrt(Relative Source Intensity) x sqrt(Relative Light Gather) x sqrt(Relative Optic Efficiency) x Relative Optic Focal Length

For this relation, light gather is the percent of source light utilized by the optic. For a lens, optic efficiency is the light transmittance of the lens as a percent, and also the light reflectance of a reflector as a percent.

You will see that optic diameter is not a part of the relation, but optic diameter is involved because optic diameter provides for increases in light gather and focal length, but optic diameter alone does not indicate the relative amounts of light gather and focal length. Optic diameter can be used for general comparisons, but it's not as accurate as using the actual light gather and focal lengths.


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## gcbryan

get-lit said:


> Throw can be defined. A common standard for search lights is the distance at which luminance is 1 lux.
> 
> 
> 
> Here is a key relation:
> 
> *Relative Candlepower* = Relative Source Intensity x Relative Light Gather x Optic Efficiency x (Relative Optic Focal Length)^2
> 
> *Relative Throw* = sqrt(Relative Candlepower)
> 
> *Relative Throw* = sqrt(Relative Source Intensity) x sqrt(Relative Light Gather) x sqrt(Relative Optic Efficiency) x Relative Optic Focal Length
> 
> For this relation, light gather is the percent of source light utilized by the optic. For a lens, optic efficiency is the light transmittance of the lens as a percent, and also the light reflectance of a reflector as a percent.
> 
> You will see that optic diameter is not a part of the relation, but optic diameter is involved because optic diameter provides for increases in light gather and focal length, but optic diameter alone does not indicate the relative amounts of light gather and focal length. Optic diameter can be used for general comparisons, but it's not as accurate as using the actual light gather and focal lengths.



When considering throw should focal length really be in the computations? My understanding is that two optics of the same diameter will throw the same distance regardless of focal length. 

Focal length will only affect the amount of light not the intensity (which is all that affects throw).


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## Walterk

@GetLit:


get-lit said:


> Here is a key relation:


 Most interesting posting ! Thx. Finally a leap forward. And reading your NightSword thread I think you know pretty well how it works. I will need some time to get related with this.

@TH232: Thanx for the input. Measuring and testing surely will follow,(waiting for meter) but probably not as elaborate as suggested . 
Can you explain more about ‘The bigger lens will throw further, because the LED more closely approximates a point source.’ ? 
Is that because the actual led is relatively smaller for the big lens, and thus the beam more narrow and thus more intense/concentrated ?









@GcBryan: It may be 'just' another approach. You are right in that you propably can’t just mix principles.

Just a quote from GetLit:
Longer focal distances enlarge the size of the reflector in relation to the luminance area, which in turn decreases the overall angle of incidence to the target, thus increasing collimation. 

Focal length is just the name for a certain set of parameters.


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## get-lit

Walterk said:


> Most interesting posting ! Thx. Finally a leap forward. And reading your NightSword thread I think you know pretty well how it works. I will need some time to get related with this.


 
Thanks. I put a lot of work into deriving that relation. It was most useful for me in determining optimal design of the Nightsword, which is on hold due to lack of funds for now.




gcbryan said:


> When considering throw should focal length really be in the computations? My understanding is that two optics of the same diameter will throw the same distance regardless of focal length.
> 
> Focal length will only affect the amount of light not the intensity (which is all that affects throw).


 
No. Lens diameter alone is useless without focal length. With no focal length, there is absolutely no gain in throw, you would have a light bulb with a just a flat piece of glass that does no good for throw, no matter how big it is. As you increase focal length, the etendue relation is increased for more throw, and with the same diameter optic, light gather diminishes, until a point is reached at which further gains in throw due to increased focal length are no longer achieved due to losses in light gather. The optimal utlization of focal length and light gather is then reached.

Increased diameter allows for increased light gather and focal length. For the same diameter, you can increase focal length by lessening light gather and vice-versa. For any given diameter there is always an optimal utilization of focal length and light gather, based solely upon the light source angular intensity profile.

Focal length has a square relation to candlepower and thus a direct relation to throw.

Light gather has a direct relation to candlepower and thus a square root relation to throw.

Optic diameter provides for increased focal length and light gather. When the utilization of focal length and light gather remain relatively the same, optic diameter has a square relation to candlepower and thus a direct relation to throw.


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## get-lit

Walterk said:


> Just a quote from GetLit:
> Longer focal distances enlarge the size of the reflector in relation to the luminance area, which in turn decreases the overall angle of incidence to the target, thus increasing collimation.


 
I'm glad you located that quote. You've really been looking into this 

Taken from an earlier post I made on the subject:

Here's a decent article for learning a bit more about the inverse relation of luminance area to focal length to produce collimated light output, and in this article Etendue is the key term you want to review:
http://thomann.net/uhp.pdf

In that article, there are many sections describing the Etendue effect, and section 3.4 about arc length is particularly useful.

Here's more about Etendue:
http://en.wikipedia.org/wiki/Etendue

Although the formulas become complex, the concept is really quite simple. To produce the most candlepower, we want the the optical system to produce the most photons going the same direction. If we reflect an infinitely single point source of light with a perfectly parabolic reflector, we would have perfectly collimated light, and candlepower would simply be the amount of light emanating from the point light source. But since an infinite point source of light is impossible, we always have imperfect collimation because photons emitted further from the focal point are never perfectly collimated, and it is impossible for any reflector shape to perfectly collimate photons emitted from different points. As the size of the luminance area continues to increase, more and more photons emit further from the focal point and those photons divert further and further from collimation. If we then increase the focal length of the parabolic reflector, we increase the size of the parabola, which proportionately decreases the diversion of the photons that are further from the focal point.

Please refer to the following diagram:






In the diagram, the blue rectangles are the luminance area. The orange lines are the collimated light from photons emitted at the focal points of the parabolic reflectors. The blue lines are the diverted light from photons emitted at the opposite end of the luminance areas furthest from the focal points. The green lines are the extent of the angles from the luminance area captured by the reflector.

With optical system "A" as a reference, Optical system "B" has double the luminance area, and with the same focal length reflector, double the diversion.

Optical system "C" also has double the luminance area of system "A", but system "C" has also double the focal length of system "A", so the net effect on collimation is nil, and they collimate with exactly the same amount of diversion. System "C" is simply larger in relation to system "A", both the luminance area and the focal length are double in size. Divergence is the same because scaling size does not affect divergence angles.

But if you look at the green lines for system "C", you will also notice that it is capturing less of the angles from the luminance area. It now has less "light gathering" than both "A" and "B". The extent of this amount is dependent upon the luminance distribution pattern of the luminance area.

--- The above is from a discussion about reflectors, but the same relation applies to lenses.


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## gcbryan

Get-lit, I wasn't saying "no focal length" as in a flat pane of glass!

I was referring to comparing, for instance, a 28 mm diameter aspheric with a fl of 24 mm with a 28 mm diameter aspheric with a fl of 48 mm.

The center beam in the focal point is the same with either lens. It's only the beam off center that is larger or smaller and that doesn't contribute to max throw. It contributes to lumen.

https://www.candlepowerforums.com/threads/143017

Read post #23 for the point I was trying to make.


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## Th232

gcbryan said:


> The center beam in the focal point is the same with either lens. It's only the beam off center that is larger or smaller and that doesn't contribute to max throw. It contributes to lumen.
> .



While you and Ra are correct that only the light that's perfectly on the focal point will go parallel to the lens' axis, I think I know what's missing. 

Take an image of the die that is a few microns off from the axis. While almost none (or none at all?) of this light will go exactly parallel to the axis, that light is still going to be projected roughly forward. This overlaps with the on-axis beam, but as we go down range this beam gets wider and moves further away from the on-axis beam. However, at a distance of, say, 100 metres the beam will still cover most of the area that the original beam did. 

The definition of lux (as per my previous post) is lumens/m^2. You're now putting more lumens on roughly the same surface area, therefore lux increases, therefore throw increases.

At a range of infinity, then yes I'd agree that only the beam at the focal point matters, all other die images will have widened to the point of uselessness. That said, I can't see out to infinity with any reasonable degree of resolution.:shrug:




gcbryan said:


> Get-lit, I wasn't saying "no focal length" as in a flat pane of glass!
> 
> I was referring to comparing, for instance, a 28 mm diameter aspheric with a fl of 24 mm with a 28 mm diameter apheric with a fl of 48 mm.



Practically speaking, he is right. Why not instead compare aspherics with focal lengths of 24 and 72 mm, or 24 and 1200 mm, or 24 and 10^6 mm? By that last example, you're practically at a pane of glass.

I've often found taking extreme cases of something to be good, not just for finding upper and lower bounds, but also as a sanity check.


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## gcbryan

TH232, I disagree (by the way, I'm no expert and I'm hear to learn and discuss).

For instance, let's say a flashlight with a 28 mm aspheric lens with a fl of 15 mm puts a spot 5 feet wide on a building 300 feet away 

Let's say a flashlight with a 28 mm aspheric lens with a fl of 20 mm puts a spot 4 1/2 feet wide on that same building 300 feet away.

Is one throwing further than the other? No, the spot is just larger with one.

You're agreeing that at infinity throw isn't affected by focal length and you (I think) would agree that at the 300 foot example above it's not about throw as you can see both spots (one is just bigger) so to me it's not about throw.

I assume you would argue that at some point the dynamic would change and it would be like a laser. I have a smaller green pointer laser that I guess you could say does project further than I can see it. However, that doesn't fit the definition of throw either. If I can't see it...that's where throw stops.

The point-like beam of my laser does diverge and therefore I can see it for a long way (it makes the same size image on my retina). When it no longer does that its reached the limits of throw. If the beam had sidespill and was wider for part of it's distance that wouldn't be throw anymore than it is with a flashlight.

If you can see it without the less intense beam then it's just lumens and not increased lux (intensity).


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## Walterk

@GetLit; Can you correct me or give an example in a way that we can follow where the numbers and units come from ?
The F-number dictates light-gathering (viewing-angle) and collimation, so really keen on understanding how to work the numbers. 

*Relative Candlepower* = Relative Source Intensity x Relative Light Gather x Optic Efficiency x (Relative Optic Focal Length)^2

Source Intensity :250 Lux/mm2 ( Suface brightness of Cree XRE 250Lumen/1 mm2 Led-die Area)
Light Gather : 40 (40% from FluxvsAngle Led-datasheet following viewingangle lens. )
Optic Efficiency : 90 ( 90% for standard condensor lens made of B270 glass.)
Optical Focal Length: 0.7 (For a lens with f# 0.7 , focal length 70mm and a diameter of 100mm ) 

250 x 40 x 90 x (0.7x0.7) = 441.000 Relative Candlepower

How do you get from the calculation (Relative) to real life measurements (Absolute), do you use a correction factor, interpolated from measurements of other lights?
As in the end I want to be to predict the beam intensity, and relate/verify the outcome to real-life Lux-measurements at distance.
(FYI: Relative Divergence = Luminance Area / Focal Length showed me to be close to my own estimates. )


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## Th232

I'd have to disagree that the above example isn't about throw, the reason one isn't throwing further than 300 feet than the other is that there's (obviously) a building in the way, nothing more. You're failing to take into account the brightness of each spot, which is how we can demonstrate which one throws better (note how everyone measures flashlight throw in terms of lux at a certain distance, from Saabluster to Selfbuilt). 

Let's extend your example. Suppose I swap out the aspheric in your second light with an aspheric that has a focal length of infinity (yep, that's actually just a flat piece of glass and yes, it's still actually an aspheric lens). Given the focal length, it doesn't matter where we place it, so we'll do a straight swap with the original lens It lights up the whole building, but to such a low degree that you can't actually tell any difference. All I've done is changed the focal length of the aspheric, yet that one will definitely not throw far at all, it's now a mule.

By your same example, I can take a DEFT and a bare XR-E at the end of a black cardboard tube to make a similar size spot, shine them both at a wall 1 metre away. Using your logic, because I can see the same sized spot in both, I can therefore safely conclude that having an aspheric in place or not doesn't affect throw. Evidently this is wrong, because the intensity of the spot isn't being taken into account.

In the explanation I gave in my previous post, the dynamic doesn't suddenly change. The further the target is, the less important focal length becomes, until you're at infinity, where focal length is irrelevant. For much shorter distances (say, closer to 0 than to infinity), focal length remains very important.

I think we have a fundamental difference of the definition "throw" (didn't this happen in Saabluster's thread as well?). You mention that:



gcbryan said:


> If I can't see it...that's where throw stops.



I think the issue with this is that it and takes into account usefulness (a subjective quality) as well as throw.

Suppose you can only see out to 100 metres for some medical reason. You have two flashlights, the first manages to put out a spot 2 metres in diameter with an intensity of 10 lux. The second manages to put out a spot, again 2 metres in diameter, but with an intensity of 100,000 lux. By your subjective definition, because you can't see past 100 metres anyway, both of those lights throw equally far.

For a person who can see further than 100 metres, suppose they take those two lights and shine them out to 600 metres, and sees only the spot from the second light. By his definition, the second one throws better. From what you've said above, both of these definitions are right?

For reference, my personal definition of throw is in terms of on-axis intensity, and makes no reference whatsoever of its usefulness. That includes lasers. For comparing usefulness, throw and flood beams, then I take FWHM into account.



gcbryan said:


> If you can see it without the less intense beam then it's just lumens and not increased lux (intensity).



Was that supposed to be "with" the less intense beam? If it is, then all I have to say is that lux = lm/m^2, for a given size spot, more lumens = more lux.

Out of curiosity, how much experimentation have you done with aspherics? I'm not trying to say I've got better credentials than you or anything, I just want to see if I can describe things in terms of your past experience with them.


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## gcbryan

Th232 said:


> I'd have to disagree that the above example isn't about throw, the reason one isn't throwing further than 300 feet than the other is that there's (obviously) a building in the way, nothing more. You're failing to take into account the brightness of each spot, which is how we can demonstrate which one throws better (note how everyone measures flashlight throw in terms of lux at a certain distance, from Saabluster to Selfbuilt).



You're missing my point (my fault). Yes, I'm aware that the building is keeping the beams from throwing and I'm aware that throw is measured in terms of lux.

My point was that the difference in the two beam diameters in that (obvious) case was just a difference in size (lumens). So if you moved the building out of the way the one with the greatest intensity (collimated beam) would throw the furthest and the size of the off center beam wouldn't have an effect.



> Out of curiosity, how much experimentation have you done with aspherics? I'm not trying to say I've got better credentials than you or anything, I just want to see if I can describe things in terms of your past experience with them.


I have some experience and I'm not claiming to have more than you or anyone else (I'm not saying that is what you are saying either).

I understand that there is a fine line between Z axis collimated max intensity lux and the contribution of off Z axis lumen output. I posted a question in the RA Optic thread to this effect as I still have a few questions along these lines.

In general I've found there to not be many "experts" around here on this subject and therefore some misinformation. So I try to work things out for myself through experimentation and by asking questions. I still have a few questions.


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## Th232

gcbryan said:


> You're missing my point (my fault). Yes, I'm aware that the building is keeping the beams from throwing and I'm aware that throw is measured in terms of lux.
> 
> My point was that the difference in the two beam diameters in that (obvious) case was just a difference in size (lumens). So if you moved the building out of the way the one with the greatest intensity (collimated beam) would throw the furthest and the size of the off center beam wouldn't have an effect.



Thanks for the clarification, I think I can what you're trying to get at now.

Just to further clarify terminology, when I'm talking about the on-axis beam, I'm talking about just that one projected image that is collimated perfectly (i.e. all the rays are 100% parallel to each other and the aspheric's axis), this coming from the part of the die that is directly below the aspheric's axis. The off-axis beam for me is every other image that doesn't come from that spot. Are those your definitions?

Here's an optics applet:
http://webphysics.davidson.edu/applets/Optics/intro.html

It's rather basic, only has point sources and so on, but the laws of refraction are simple for point sources, and it helps to illustrate my point. Here's what I've done with it:






Fairly simple, one point source, one lens (note that refraction happens at the centre, but that's irrelevant for the purposes of this exercise) and one aperture, since the applet doesn't allow us to change the lens diameter. Same effect though.

Top image is the bit of the die that's directly under the lens' axis. Obviously, everything is parallel to the lens' axis. Second image is for a bit of the die that's a bit off-axis. Note how at short distances, the second beam still covers the first, but as we reach the right side of the image, we've almost got two completely separate projections.

Observe here that in real life, you've got much smaller "steps" in the off-axis distance, and this happens in 360 degrees around the axis. Lots of overlapping.

In the third image, I've extended the focal length. Obviously, since the lens (well, aperture in this case) is still the same size, the beam coming out of the lens is tighter. Fourth image is the same offset that I've introduced in the second image.

Observe the differences between the 2nd and 4th images and where the rays cross the centreline. (Side note: the bottom ray of both has been cut off, note that while this affects both, it makes the 4th image look a fair bit worse than it actually is). In the second, let's put an object where the bottom ray crosses the axis. It's now lit up by both projections, and there's a 50% overlap between them, leading to a doubling of the brightness in that region.

In the 4th image, put an object at the same distance. Now observe that although the beam is tighter, the off-axis projection covers a greater proportion of the on-axis projection. Also note that the angle those rays make with the lens axis is much less than that created by the rays in the second image, confirming that this second setup results in a more collimated beam. That bit can be done by visual inspection or just by using trig.

As I've said before, as the target approaches infinity, the focal length becomes less important. This is due to the fact that for the light from a certain point to still light up the target and not completely miss it, it must be ever closer to the axis, until you hit infinity and no other projection ever hits the target.

Therefore we can conclude that by only changing the focal length, while the first setup will gather more light (which I think we all knew), the second will result in a more collimated beam. Hence the throw will increase, but with the reduction in light being gathered the usefulness of such a beam will decrease.

Finite element analysis would be great here, since it would allow us to more accurately quantify the effects of focal length.


Walter, my apologies, I only just noticed this:



Walterk said:


> Can you explain more about ‘The bigger lens will throw further, because the LED more closely approximates a point source.’ ?
> Is that because the actual led is relatively smaller for the big lens, and thus the beam more narrow and thus more intense/concentrated ?



That is correct. :thumbsup: It can be described either way, depending on whether you're looking at things from the point of the lens or the LED.


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## gcbryan

TH232, can you tell me how you define "infinity"? Thanks.

(I'm asking as in one sense (to me) it means an infinite distance never reached and in another sense as marked on camera lenses it can be quite close.).


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## Th232

In this case, I'm defining it as a distance never reached.


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## gcbryan

I guess my question regarding the charts you've provided is whether that's the way it works regarding the off axis beam.

When you talk about a subject being at a point where the off axis beams overlap you say the throw (intensity) increases.

I would ask...does it? For intensity to increase I would think that you would have to add collimated beams to collimated beams.


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## Th232

I would say so, since lux is defined as lumens/m^2 on a given area. In both examples, say we have each projection putting out 1 lumen*, the overlapping areas will have the same intensity, but in the second example we'll get an overlapping area for a much greater distance when compared to the first.

Shine two dim lights onto a surface from an equal distance, and the intensity increases, regardless of where the lights are positioned. The catch there is that the beams are nowhere near parallel, so with a focus that's decidedly not at infinity, it won't throw. You can do similar with a magnifying glass and the sun, the output from the magnifying glass most definitely isn't collimated, but it gets intense enough to burn paper, leaves, small insects &c. The lumens captured is identical, but it gets concentrated into a smaller area, resulting in a higher lux.





*For the physicists, engineers, mathematicians and others who know integration, yes, I know I should be using an "infinitesimally small number" instead.


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## gcbryan

It only happens at a point in time and one in which the beam isn't at max throw anyway. By the time the beam needs any "extra throw" the beams have already diverged haven't they?


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## Th232

Bit uncertain about what you mean by "extra throw" and "max throw", could you define those terms?


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## gcbryan

Th232 said:


> Bit uncertain about what you mean by "extra throw" and "max throw", could you define those terms?



Not very scientific I'll admit...my point is that we were talking about focal length not effecting throw.

You say in effect that although at the limits of throw fl may not have much effect at practical ranges it does.

Your chart shows a cross over of less collimated beams at a certain point. You say that throw is improved at this point. That would be at a certain distance. After that distance throw would not be improved because the beams would have diverged.

So for the throw to be increased this cross over would need to occur close to the limits that we can perceive throw otherwise it would not be increasing throw at a point where it would make much difference.

In other words this cross over doesn't by definition continue on to infinity so it doesn't extend throw in that sense.


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## Th232

Ahh, right. Got it.:thumbsup:

You've got to remember that this is two points out of what is practically an infinite number (or at least the number of molecules in the phosphor). I wish the applet was able to show non-point sources, because it would clear things up with much greater ease.

You're indeed correct that the particular off-axis point in my example will be useless at certain points, namely before and after it overlaps with the central beam. But there're also points closer and further from the axis, and when our example point fails to overlap, there will be other points that do overlap. If you work out the integral, I'm pretty that increasing the distance will cause the intensity to fall off in line with the inverse square law.

When comparing the focal lengths, as mentioned previously, for a given point the projection through the lens with the shorter focal length will go off at a greater angle. If we break this down and take the molecule right next to the one that's under the lens' axis, that projection will continue on to "nearly infinity", but for the lens with the longer focal length, the projection will be "closer" to infinity.



gcbryan said:


> In other words this cross over doesn't by definition continue on to infinity so it doesn't extend throw in that sense.



And that's why I've been saying that at infinity, focal length doesn't matter. More and more projections diverge until at infinity, none of them overlap. The focal length determines the rate at which they diverge.


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## gcbryan

I'm sure you've seen the RA thread on Optics.

What is your argument to his description of a viewer standing in front of a reflector not being able to tell if it's deep or not (which is focal length)?

It's only by moving off of the Z axis that someone can tell if it's a deeper reflector or not which shows that it produces a wider beam but not a brighter one.


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## Ra

Hi guyzzz,

I think it is about time for me to step in..

Reading this and other threads where the throw discussion starts (or is the main issue..) I cannot help getting the thought that, propably unintentionally, these discussions end up in very long threads that incorporate some confusing remarks, definitely when they are not true! Don't get me wrong here, but this is not very helpfull for the ones that are not quite into this, but still want to know how things work..

Question is: Do you want to know the facts about throw, and live with them without understanding the detailed law's behind them, or not..? (most do propably not..)

We have to face that some members do not have the abillity to understand it all, and when those members are not satisfied with this, long, uninformative threads start to grow..

I sinceraly hope you're not offended by the above, it's absolutely not my intention to lose CPF-friends, but to some, these are maters which are quite demanding to the brain, and so don't allow space for complicated discussions..



Maybe it's a good idea for the OP to edit the first post with a section in which the short conclusions we all agree about are summed up, so members can find a short summary with all the facts about this matter, and can decide for themselves if they want to read how we came up with those facts..



That said,

It's time for a little input from myself:

Definition of throw: The abillity to enlighten distant objects.. It's as simple as that!

But: Different objects have different levels of reflection when enlightened, so we have a problem.

Ok, then lets agree on specify the throw of a torch by stating the distance from the torch at which 1 lux is measured (like most do..) 

Don't forget to post the simple square law formula for people who want to recalculate the throw-distance when they need for example 3 lux.


-Throw is not lumens related: A laser pointer throws far but has very poor lumens output!

Years ago, I experimented with lenses and led's on a testbench, and came to the following hard conclusions: (all theoretical, based on actual tests)

-Within the range of aviable lenses: For all lenses with the same diameter: The focus length does absolutely not affect throw!-

If it does, something else is wrong, like difference in quality, or transmittance of the glass,
or the entre surface of the lens doesn't play along. Those are only a few things that can be wrong.

-For all lenses with the same diameter: Focus length does affect the amount of lumens, collimated into the beam, affecting the wideness of the beam.

So what is important about focal length: Angle of emittance that is grabbed: 

Most sources emit their lumens in a wide area (for most led's about 140 degrees), so the more you cover that area with a lens or reflector, the more lumens you collimate into the main beam. But we're not talking about lumens on this thread, we're talking about throw.

-Lenses more easily give high throw: With led's, which are front-emitting ofcource, lenses are best suited as they grab the light in front of the source. Conventional reflectors are designed mostly for use with side-emitting sources and are less efficient with led's (but still work to certain extend, when you accept the lower efficiency..)

Theoretical:

If a omnidirectional source emits 250 lumens, the lux measurement at 1 meter should give 20 lux (250 divided by 4 times pi) This is called MSCP (Mean Spherical Candle Power)
That also means, that when you know the size of the source, for example led-die 1x1mm, you can calculate the surface brightness: 1x1x20 equals 20 lux/mm2

Then you simply need to know the surface of the collimator in use: For example, 30mm diameter aspherical lens.. 15x15xpi=706.85 mm2

A high quality lens copies the surface brightness of the source, minus the losses caused by surface reflections, absorbtions and stuff like that. So we need to know the effective transmission of the lens: Uncoated, that will be about 90%..

So here we are:

-Source: 20 lux at one meter comming from a 1x1mm source size

-Effective lens surface (always 2-D, seen from a distance..): 706mm2

-Lens efficiency 90% (note that this is the efficiancy for surface brightness, not for lumens output!!)

Source has 1mm2 surface, measures 20 lux at 1 meter: Source + lens will give:

(Lenssurface divided by sourcesurface) x lux @ 1 meter x lensefficiency:

(706/1)x20x0.9= 12708 lux at one meter ! So there is your formula...well not quite..

with the inverse square law, you now can calculate the throw:

Taking the square root from 12708 (which is the actual CP-output, as this already is at 1 meter) gives 113 meters as the distance at which 1 lux should be the measurement result.

Another formula for throw: Take a calibrated measurement at any distance from the source, but far enough to be sure that the entire lens- or reflector-surface plays along,
and multiply that measurement with the quadratic of the distance:

Example:
Torch-luxmeter distance is 100 meters reading 24 lux: Beam-CP output is 100x100x24= 240,000 B-cp


Now there is a catch: Omnidirectional means emitting in all directions.. (like the sun does)
Led's are not omnidirectional. So IMO, the only way to do this without much uncertainty, is to do a lux-measurement on the bare source at one meter, with a calibrated lux-meter,
and determain the source size
The remaining of the theoretics do have less uncertainties.


Notes: When a torch does not give the theoretically calculated lux reading at one meter, chances are that, among other things, the entire surface of the lens does not play along: You are too close to the torch, or you need to focus the torch.

When does one know, he (or she) has enough distance for an accurate measurement:

Double the distance: according to the inverse square law, you should measure 1/4 of the measurement at half the distance. If this doesn't apply to your results, something is wrong in the way you measure..Propably too close with the first measurement. 


Like I said, this is matter that is not easy to understand for some. This is my effort to be clear about the facts in a post that hopefully isn't too long..

Any question's?


Regards,

Ra.


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## Th232

My reflector theory isn't quite up to scratch compared to my optic theory. Truth be told, I fail to see the logic in his argument, it seems to go:

* The object sees a 2D object
* Deep reflectors collect more lumens, resulting in a wider beam (I personally dispute this bit, see below), and vice versa for shallow reflectors.
* Therefore focal length doesn't matter

Could you try explaining it to me if you think I'm completely missing his argument (which I think I am)? Because as is, I just flat out can't see the logic.

Ok, deep reflectors collecting more lumens. While depth is one function, width also plays a role. Here are two parabolae I plotted.








The green one is obviously deeper than the blue one. Focal points for both are at 0,0. The green one is obviously deeper than the blue one (also wider and with a greater surface area), but as is obvious, the blue one will collect more light due to its width:depth ratio, which is better than that of the green parabola.

In case anyone's curious, that's y = x^2 and y = 3x^2, adjusted so the focal point is at (0,0).

The blue reflector will, however, result in a wider hotspot and less throw for the same reasons that a shorter FL aspheric will result in less throw as in my previous posts.

As for the object seeing a 2D surface. I'm not quite sure what Ra is trying to get at, but think about this for a minute. Take an object with a reflector + LED illuminating it from 100 metres. Now take a single point on the object. All light striking it comes from the reflector or the LED. These rays are evidently not parallel to each other, regardless of their source, or whether this point is on the axis of the reflector or not. Draw the lines from each point on the reflector/LED to the point on the object. As the rays are not parallel, this is the only point where every one of those rays will coincide.

Move the object back 1 mm. Now we have an almost completely new set of rays striking the object. The sole exception is one ray parallel to the reflector's axis. It's either coming LED or the reflector, and note that some points won't have this ray at all.

Move the object back another mm. Same process repeats itself. Note the similarities between this process and the aspherics mentioned previously. Same deal, new projections shine on that point, but eventually we're out at infinity and the only rays are from the point of the die that is perfectly in focus with the reflector. Again as with aspherics, focal length determines the rate at which the other projections diverge from the axis for the same reasoning detailed in my previous post.

In short, as with aspherics, focal length is irrelevant if we go out to infinity, otherwise it plays a role. Also like aspherics, the longer the focal length the less light gathered, and the usefulness of the beam diminishes.


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## Th232

And in the meantime Ra posts! Thank you very much for that.

One small question though. Regarding your calculations, I agree with most of it, but you seem to be making the assumption that the whole LED is in focus, when (as we know) a reflector or aspheric has a focal point, not a focal plane, and hence while one point on the LED will be in focus, the other projections diverge and/or will not be parallel to the reflector/aspheric's axis as per the diagram in my earlier post. 

How do you account for the fact that nearly none of the LED die will be in perfect focus? In my experience the focal length determines the rate of this divergence (again, as with the raytracing diagrams in my previous post), and hence the intensity of the beam over long distances. At short ranges the difference is quite small, but the effect becomes more pronounced over longer distances.


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## Ra

@Th232,

As for post #42:

Yup, you're missing the point: When I talk about the deepness of a reflector, then I talk about a reflector with the same diameter! So now draw two reflectors with the same diameter and different focal lengts: You'll see that there is a difference in angle from the source that is covered by each reflector..

And about the 2-D approach: Look at the sun! (use a filter!!) It's a giant ball right? WRONG!!
it's a flat disk!! Due to astronomics, you know that the sun is a ball. Now forget everything you know about the sun and look again.. Can you tell that it's a ball? It's not brighter at the center (not that much that we'd notice it) No, it's a 2-D disk with a certain (very high!) surface brightness..

It's the same with reflectors! look at them from a distance, and you cannot tell wether they have depth at all !

Lets post a picture:







Two operating torches seen from a distance: Can you see the deepness, no silly, it's a picture!! But it's not different when you look at the torch from a distance, with one eye, right? Same as the sun: From a distance, the enlightened object only 'sees' a 2-dimensional disk or surface, with a certain diameter and a certain surface brightness!

The amount of lux that is receved by the object is only determined by the (apparent !!) diameter and surface brightness of the light-source (sun, torch, candle...)
When you have lower surface brightness (halogen at the left) you need a larger reflector diameter: Both torches displayed have the same throw! At the right my Mini-HID..


Hope this more clearly shines some light at the subject..


Regards,

Ra.


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## Ra

Th232 said:


> And in the meantime Ra posts! Thank you very much for that.
> 
> One small question though. Regarding your calculations, I agree with most of it, but you seem to be making the assumption that the whole LED is in focus, when (as we know) a reflector or aspheric has a focal point, not a focal plane, and hence while one point on the LED will be in focus, the other projections diverge and/or will not be parallel to the reflector/aspheric's axis as per the diagram in my earlier post.
> 
> How do you account for the fact that nearly none of the LED die will be in perfect focus? In my experience the focal length determines the rate of this divergence (again, as with the raytracing diagrams in my previous post), and hence the intensity of the beam over long distances. At short ranges the difference is quite small, but the effect becomes more pronounced over longer distances.



You posted just before me...

Yep, when you want to have optimal throw, the one thing you should make, is the assumption that the led is in focus!! It is: With a high quality lens (in focus) an image of the light-chip (or die) is projected at the wall further away, proving that the entire die is in focus! The size of the projection at the wall is (only!!) exactly determined by the size of the die itself, the focal length of the lens, and the distance to the wall !

And:

Every lens or reflector has a focal plane!!
An infinitely small lightsource doesn't exist, so with a led die of 1x1mm, you already are using a focal plane, right?
Indeed: One point of the led-die will be in focus, but the other parts are in focus as well, but will be projected away from the optical axis, forming the image on the wall.
I now assume we have a high quality lens, when we use a low quality lens, you will not get a distinct image of the die, but a blurry spot with a bright center, more like when you use a conventional reflector.
Now the of-axis part of the source (die, arc or filament) causes what we call sidespill..


Regards,

Ra.


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## Th232

I think we're getting somewhere now!



Ra said:


> Every lens or reflector has a focal plane!!
> An infinitely small lightsource doesn't exist, so with a led die of 1x1mm, you already are using a focal plane, right?
> Indeed: One point of the led-die will be in focus, but the other parts are in focus as well, but will be projected away from the optical axis, forming the image on the wall.



Let's just make sure we're on the same page.

Focal plane: The plane along which the rays from a point source will be projected, parallel to each other, in a certain direction, as per the second and fourth images in my previous post. Would that be your definition?

For points on the focal plane but not directly on the axis, they will be projected at an angle to the axis. Would you agree that the angle they make with the axis is dependent on their distance from the axis and the focal length? Specifically that with a shorter focal length, the projections from a certain point on the focal plane will diverge at a greater angle.

Ah-ha! I think we have a definition problem.

I am defining as the "hotspot" of a beam as the on-axis part. I note that you're defining the off-axis part as the sidespill. Let's use that definition for this next bit. At short distances, the sidespill will still overlap with the hotspot, as per the raytracing diagram in my earlier post, hence increasing its brightness. After a certain distance however, it will no longer overlap, and instead illuminate an area outside the hotspot. Yes/No?


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## Ra

Th232 said:


> For points on the focal plane but not directly on the axis, they will be projected at an angle to the axis. Would you agree that the angle they make with the axis is dependent on their distance from the axis and the focal length? Specifically that with a shorter focal length, the projections from a certain point on the focal plane will diverge at a greater angle.




Yep, you got it !!! 


Regards,

Ra.


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## Ra

Th232 said:


> I am defining as the "hotspot" of a beam as the on-axis part. I note that you're defining the off-axis part as the sidespill. Let's use that definition for this next bit. At short distances, the sidespill will still overlap with the hotspot, as per the raytracing diagram in my earlier post, hence increasing its brightness. After a certain distance however, it will no longer overlap, and instead illuminate an area outside the hotspot. Yes/No?



Yep.

Edit: As most of the sidespill is created at the reflector part close to the source (inner rim), it needs some projection distance to free itself from the central spot..

Regards,

Ra.


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## Th232

And so when we have a longer focal length, the off-axis projection will overlap with the on-axis projection for a greater distance, increasing the intensity of the hotspot over that distance.

In all cases though, the off-axis projections will move off the on-axis projection as we approach infinity and become irrelevant.

Funny, that's what I said back in post 26.

Ahh well, I think we've cleared all the confusion up?


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## Ra

Th232 said:


> And so when we have a longer focal length, the off-axis projection will overlap with the on-axis projection for a greater distance, increasing the intensity of the hotspot over that distance.



No, not quite... There is another matter you don't include: When jou project over a great distance, you focus your setup at that distance, so closer to the torch, depending on the source dimensions, only part of the reflector will play along!

Edit: To be more clear: When focused at great distance, the source is not in the focus-plane for the shorter distance, so does not use the entire lens for that shorter distance!
For that, the lens is too close to the source!

When you focus at infinity, the reflector or lens is not fully lit when you look at it from close by!

This causes the spot not change much in surface brightness, when you increase the projection distance (to prevent more confusion: Here I mean the surface brightness of the projected spot)

That's what I meant when I said one could be too close to the torch for a reliable lux-measurement. That can only be done at a distance at which the entire reflector or lens plays along. And from that point further away, the lux-readings should follow the inverse square law... (note that the atmospheric conditions must play along as well)

With Maxablaster (and it's very small source..) I need a distance of several hundered feet to obtain a decent lux-measurement! And for lux-measurements close to the end of the throw of the beast, at 6-7 miles, Sure atmospheric conditions are going to interfere!!
Mostly Maxablaster doesn't reach much over 4-5 miles (if that's not enough...!)
I only once reached 9 miles, under perfect conditions !!


Regards,

Ra.


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## Th232

Good point, didn't consider focussing the source for dedicated long distance beams.


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## Ra

I found some pics from an early throw-test I did with lenses with various focal lengths..

Lens with short focal length:






Longer focal length:






Even longer focal length:







Notice that the lux-readings are (almost..) the same! (plus or minus 0.2... imperfections in the setup..)

And notice the difference in projected spots: The shorter focal lengts grab more lumens from the source, not resulting in higher throw, but bigger spot's !

I needed to cover the sensor, leaving a tiny hole, small enough to make a possible point-measurement within the smallest projected spot (longest focal length..)

Edit: In all situations, the lenses were placed at exactly the same distance from the sensor (within 1-2 mm.). And for each situation, the same diafragm was used
to exactly obtain the same diameter during each measurement..


Regards,

Ra.


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## Walterk

Thank you all for your contributions these last productive days!
And welcome Ra, glad you helped me out. 

One question: You say;


Ra said:


> -Source: 20 lux at one meter comming from a 1x1mm source size
> -Effective lens surface (always 2-D, seen from a distance..): 706mm2
> -Lens efficiency 90% (note that this is the efficiancy for surface brightness, not for lumens output!!)
> 
> Source has 1mm2 surface, measures 20 lux at 1 meter: Source + lens will give:
> 
> Lenssurface x sourcesurface x lensefficiancy:
> 
> 706x1x0.9= 635.4 lux at one meter ! So there is your formula...



I wonder, is it correct that I do not see the surface brightness in the calculation?
You take for sourcesurface the figure of 1.
Why not 20? 
Would it be 9 in case of a 3x3mm Led-die?


----------



## Ra

Walterk said:


> I wonder, is it correct that I do not see the surface brightness in the calculation?
> You take for sourcesurface the figure of 1.
> Why not 20?
> Would it be 9 in case of a 3x3mm Led-die?



If a 1x1mm source gives 20 lux at 1 meter distance, the surface brightness is automatically embedded in that fact..
I take 1 because most led-die's are one square mm..

EDIT: Uhh... :thinking: Wait a minute.. Walter, I think you're right. I forgot something very important !! It's 706x20x0.9 !!!!

EDIT2: Maybe indeed a bit confusing, taking a 1x1mm source because it doesn't change anything and so can be left out... The right formula: (706/1)x20x0.9) = 12.708 lux @ 1 meter

Now when the led-die is bigger, lets say 2x2mm (4 square mm), with the same 20 lux output at one meter, then the torch would give: (706/4)x20x0.9) = 3.177 lux @ 1 meter



Wait, I'm going to correct that right away !

Thanks for pointng this out !



Regards,

Ra.


----------



## Walterk

Thank you Ra ! Finally this thread brought me the answer to my question.

I am pretty sure I've read the same in the Optic theory-thread, but not clear enough to trust as only source.
I found al sort of hints here and there, but no one could state me a satisfactorily and watertight answer.
Although most people (38.3%) claim to know few care to share. 
Many thanks to the people that did help, by contributing to this thread or by PM ! 
Finally I will accept the formula is as simple as that, and nothing more. Stubborn me. 

Just wonder: How much variation is there in Lux within the complete spot ? I suppose close to none at near infinity?

NB In time I might rephrase some of the content in the first posting. 
I leave the thread open for further contributions on light, rays, lenses and the distribution and properties of all this.


----------



## gcbryan

Thanks WalterK for starting this thread! TH232 I'm picturing focal length and how it affects the sidespill better now and thanks especially to RA for contributing and especially for bringing up the focus issue.

That seems to clear up the focal length aspect.

I have a couple of practical questions that many of you can answer I'm sure.

1). The formula for determining lux at 1 meter is based on a lens so pi R ^2. How would this formula be changed to work with reflectors?

2). In many threads I see lux at 1 meter vastly overstated according to the formula above.

Would the explanation for this be not moving away from the source to the point where the sidespill is starting to diverge from the hotspot before taking the reading?


----------



## gcbryan

gcbryan said:


> 1). The formula for determining lux at 1 meter is based on a lens so pi R ^2. How would this formula be changed to work with reflectors?



Anyone?


----------



## Walterk

1). The formula is the same for lenses as reflectors. Only difference is lenses are more efficient. The shape of the reflector works the same as F-# for lenses. (See also post44)

2) Inaccurate measurements, to close by.
Note that High power Leds are not omnidirectional.
In the White led test-thread, the Cree XRE shows to have 170Candela surface brightness on axis, not 250 or 340.


----------



## gcbryan

Walterk said:


> 1). The formula is the same for lenses as reflectors. Only difference is lenses are more efficient. The shape of the reflector works the same as F-# for lenses. (See also post44)
> 
> 2) Inaccurate measurements, to close by.
> Note that High power Leds are not omnidirectional.
> In the White led test-thread, the Cree XRE shows to have 170Candela surface brightness on axis, not 250 or 340.



Since led's aren't omni directional is that the reason for the 4 * pi part of the equation? 360 degrees/90 degrees (XR-E beam angle) =4 ?


----------



## Ra

gcbryan said:


> Since led's aren't omni directional is that the reason for the 4 * pi part of the equation? 360 degrees/90 degrees (XR-E beam angle) =4 ?



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.. So that is why I ommited that part, and took the road of measuring the [email protected] for the bare source first and calculate the surface brightness using the (apparent..) source-dimensions.


And for the throw formula for conventional reflectors:

Walterk already said it but forgot to complete his remark: Lenses are more efficient than reflectors... on throw!!...




This is important: We're still talking throw here ! So the things below are about the reflector and lens efficiencies for throw.. If we do this for lumens-output, the results will be different (and TIR will be the king of all !!! Only with led's ofcource..)




Formula is the same, indeed you must incoporate the lower efficiency of reflectors: It has a central hole that does not play along, and the reflectivity of the reflective layer can be lower as well.
Lenses more easily have high effectivity (for throw) because they have less different factors that can ruin things.

Example: You only have to polish a lens to make it reach a transmission of 90%. Aplying a simple antireflex coating can increase the transmission to 95%.. That's what you need for throw..
Note that this is the same for glass based TIR optics: In a TIR there is no reflection layer, the angle of the lightrays inside causes 100% internal reflection at the inner-side of the reflector.

Now with conventional reflectors: The best reflection layer is silver at 97% minimum, but this degrades very quickly by oxidation of the silver. Second best is aluminium at 88%, but you have to work hard to reach that! More likely is a surface reflection of about 80-85%, which already is much lower than the transmission of an uncoated lens.

And... for throw, the entere surface must play along: Conventional reflectors have this black hole in the center, which only further decreases throw-efficiency!

Cleaning conventional reflectors almost always cause a decrease in efficiency, by damaging the reflective layer.


All these factors and their inconsistencies make it impossible to calculate the throw of all types conventional reflectors by only one formula !! The solution for that would be an efficiency-spec, delivered with the reflector... But then again, how many manufacturers lie about the specs of their products (30 Million CP Thor for example ??)
I wouldn't be surprised by reading a claim of 150% reflector-efficiency some day.. :thinking:

BTW: When conventional reflectors are used with led's you can somewhat increase throw by glueing a lens on the front window which coveres the 'black hole' of the reflector and brings some of the lost light in collimation as well.. Could mean 5-7% improvement on actual 'throw-surface'..



Regards,

Ra.


----------



## Dr.Jones

Ra said:


> 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.


----------



## Ra

Dr.Jones said:


> 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.


----------



## Ra

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 [email protected] 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.


----------



## ma_sha1

Ra said:


> 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":
https://www.candlepowerforums.com/threads/240742
.
.


----------



## Dr.Jones

Ra said:


> (lenssurface divided by sourcesurface (all in mm2)) x [email protected] 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.)




ma_sha1 said:


> 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".


----------



## 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- 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.


----------



## Ra

Dr.Jones said:


> 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


----------



## Ra

Walterk said:


> 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.


----------



## saabluster

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



Ra said:


> -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. 





Ra said:


> 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.


----------



## 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.



> 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...


----------



## saabluster

Dr.Jones said:


> 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.


----------



## Dr.Jones

saabluster said:


> 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?


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## saabluster

Dr.Jones said:


> I know you do have some experience


 :wave:


----------



## gcbryan

saabluster said:


> :wave:



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?


----------



## saabluster

gcbryan said:


> 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?






saabluster said:


> I really don't have the time to get into a long drawn out discussion...


----------



## gcbryan

Originally Posted by *saabluster* 

 
_



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

Click to expand...



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.
_


----------



## Dr.Jones

saabluster said:


> :wave:


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.)


----------



## Walterk

Dr.Jones said:


> 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.


----------



## 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.


----------



## 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 )

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.


----------



## gcbryan

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!


----------



## Dr.Jones

Walterk said:


> 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...


----------



## ma_sha1

Dr.Jones said:


> 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.


----------



## Dr.Jones

ma_sha1 said:


> 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.


----------



## Ra

Dr.Jones said:


> 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.


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## Walterk

Dr.Jones said:


> 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.


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## 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)!!!
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.


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## Ra

Walterk said:


> 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...


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## saabluster

gcbryan said:


> _
> 
> 
> 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.
> _






Ra said:


> 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.


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## Walterk

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


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## Ra

ma_sha1 said:


> 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.




My lens experiments have enough variance in focal length to prove the theory right.. Lenses with shorter focal length act the same, as long as the entire surface plays along, like said earlier. Lens distance to the source does not matter (at least, within the focal length's I used during my experiments..). Apparent surface brightness is not affected by source-lens-distance..

Extremely short focal length's bring difficulties for the shape of the lens: Apart from the fact that they need to be extremely aspheric, the extreme radius of curvature brings a limit as well.. The shorter the focal length, the harder it is to make the entire surface play along.. (needed for throw..)


Regards,

Ra.


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## pepko

Hi all,

can you help me ? 
What should I do to get more throw in my setup ?
https://www.candlepowerforums.com/threads/280018

I use 3" aspheric lens 74(70)mm diameter, 28mm height. Distance from led is about 40mm.

Thanks.


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## Dr.Jones

Walterk, you're right, ... but I can't resist (Ill keep it short):
Saabluster, I'm not a professor (no one said so (except you)), but I have a doctor's degree in experimental physics (related to optics). I bring up arguments from Ra, because they are correct, also arguments I learned in university, for the same reasons. All that stuff isn't actually new. Furthermore, gcbrian and I know each other already from another forum.

Back on topic, beam expanders:


> For beam-expanders / telescope / eyepieces (working all the same ) there are several principles based on plain convex lenses, all effective.


Yes, eye pieces can be very complex, mostly for two reasons: avoiding chromatic aberration and getting a good field of view with low image distortion. For expanding a collimated beam, the latter is often unimportant, because the beams have rather small angles to the optical axis already, so a simple setup often suffices, although the use of achromatic lenses (duplets) is advisable for white light.


Back to pre-collimating:

I present my newest super-thrower, the *Sloppy270*:






I guess you can see why it got that name.... and I didn't even apply a battery yet (and probably never will; on the other hand, I might take it out for some field test...)

There are three versions: 
ver1: no pre-collimator, 
ver2: low-NA (high-f#) pre-collimator, f=150mm
ver3: higher-NA (lower-f#) pre-collimator, f=150mm

The spot brightness, measured at 18.3m, is nearly the same for all three, it's a bit lower for ver3 because the pre-collimator is only a spheric lens with quite some aberrations at that NA (or f#).
While the spot brightness is roughly the same, with the pre-collimator the spot size increases (5cm/10cm/15cm).
And of course a bigger spot with the same illuminance (lux) means more flux (lumen).


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## Dr.Jones

pepko said:


> What should I do to get more throw in my setup ?


Really nice light...  Would like to have one 

Other than getting a bigger lens or a LED with higher luminance (surface brightness) - none, as far as the optics basics go.
Then there's anti-reflex-coating the lens, using a lens with better quality (if yours isn't already very good), better heat sinking for less thermal sag, ...

Regarding basic optics, there are ways to increase the spot size and total flux (lumen) though.


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## saabluster

Dr.Jones said:


> Saabluster, I'm not a professor (no one said so (except you))





gcbryan said:


> Dr. Jones (as I recall) has a Phd in Physics.







Dr.Jones said:


> Back to pre-collimating:
> 
> I present my newest super-thrower, the *Sloppy270*:
> 
> 
> 
> I guess you can see why it got that name.... and I didn't even apply a battery yet (and probably never will; on the other hand, I might take it out for some field test...)
> 
> There are three versions:
> ver1: no pre-collimator,
> ver2: low-NA (high-f#) pre-collimator, f=150mm
> ver3: higher-NA (lower-f#) pre-collimator, f=150mm
> 
> The spot brightness, measured at 18.3m, is nearly the same for all three, it's a bit lower for ver3 because the pre-collimator is only a spheric lens with quite some aberrations at that NA (or f#).
> While the spot brightness is roughly the same, with the pre-collimator the spot size increases (5cm/10cm/15cm).
> And of course a bigger spot with the same illuminance (lux) means more flux (lumen).



Agree with everything you show in your experiment and it falls right in line with my own.

*Benefits of additional optic*
(1)With the additional optic there was 60% more light getting out.
(2)There is a huge reduction in chromatic aberration.
(3)It now throws slightly farther.
(4)The field of view is bigger due to a larger projected die size.


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## ma_sha1

Bravo, Dr.

First of all, the 116mm lens with Q5 @0.9A converts to 274,000 Lux at 1 meter, beating DEFT FTP 135Lux at 1 meter by 200%. The New King of LED thrower, if you can pack them into a flashlight.
(Please check my math 820x18.3x18.3 =~270K lux)

Size does matter, no matter how you work it :devil:

Second of all, the only thing that the pre-colinmator did that could be of benefit to a flashlight is to reduce the system EFL, thus, allow led to move closer to the lens & make it more compact.

So if a single lens could fit in a flashlight, there's no "throw advantage" on introducing a pre-lens, 
if anything, it'll reduce lux by failing to transmit 100% of the light through. But it does make a much bigger spot.

This is a myth buster on pre-collimation will increase throw, nice job! 
.


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## Dr.Jones

Having a PhD does not imply being a professor, at least not around here.



> Benefits of additional optic
> (1)With the additional optic there was 60% more light getting out.
> (2)There is a huge reduction in chromatic aberration.
> (3)It now throws slightly farther.
> (4)The field of view is bigger due to a larger projected die size.



(1) Actually ver2 has ~300% more light; ver3 ~700% more light (flux)
(2) No, it actually gets worse, especially ver3.
(3) No, ver2 slightly less, ver3 even worse.
(4) Yes.




> *ma_sha1* said:
> (Please check my math 820x18.3x18.3 =~270K lux)


That's what I mean with 270kcd.
1 cd is equivalent to 1 lux at 1 m - if the light source size is negligible. With well collimated throwers it isn't, so it should be measured at a bigger distance.
I measured it at 11.9m and 18.3m and got consistent results.

BTW... ver1 has a very narrow beam... good laser pointers have 1 mrad, bad laser pointers have 2 mrad, ver1 has 3 mrad... A 'light pointer'?


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## Ra

Dr.Jones said:


> Really nice light...  Would like to have one
> 
> Other than getting a bigger lens or a LED with higher luminance (surface brightness) - none, as far as the optics basics go.
> Then there's anti-reflex-coating the lens, using a lens with better quality (if yours isn't already very good), better heat sinking for less thermal sag, ...
> 
> Regarding basic optics, there are ways to increase the spot size and total flux (lumen) though.



I hope you don't mind Dr.Jones.. But: To complete this answer..

When you can create better heatsinking, you can increase power to the led (somewhat..), which brings higher surface brightness, and therefore better throw..


Regards,

Ra.


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## saabluster

ma_sha1 said:


> Second of all, the only thing that the pre-colinmator did that could be of benefit to a flashlight is to reduce the system EFL, thus, allow led to move closer to the lens & make it more compact.
> 
> So if a single lens could fit in a flashlight, there's no "throw advantage" on introducing a pre-lens,
> if anything, it'll reduce lux by failing to transmit 100% of the light through. But it does make a much bigger spot.
> 
> This is a myth buster on pre-collimation will increase throw, nice job!
> .


Yeah it is not quite busting any myths. It did and does increase throw on the DEFT as it corrects for aberration in the lenses I make. As I have mentioned before the biggest effect is more throughput and broader beam. Given perfectly made lenses then yes the throw will not increase. However it is also folly to say there is no benefit for flashlights other than a reduced FL. Since the beam becomes broader that means your field of view is larger. Given an aspheric's propensity to have an extremely narrow beam this is a huge benefit in a flashlight application. 



Dr.Jones said:


> Having a PhD does not imply being a professor, at least not around here.


It is true that the word professor can be taken more than one way. One of those refers to someone who has had and graduated from a school of higher learning and is now no longer a student. That is the sense I called you a professor and it is because of comments made not by myself. 




Dr.Jones said:


> (1) Actually ver2 has ~300% more light; ver3 ~700% more light (flux)
> (2) No, it actually gets worse, especially ver3.
> (3) No, ver2 slightly less, ver3 even worse.
> (4) Yes.



You totally missed the point of that part. That was a link back to tests I did of *my* light. *I* got 60% more throughput. *I* had mine throw slightly farther.


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## ma_sha1

Dr.Jones said:


> That's what I mean with 270kcd. 1 cd is equivalent to 1 lux at 1 m



Thanks, I didn't know what a cd was


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## Ra

ma_sha1 said:


> Thanks, I didn't know what a cd was



I know what a cd is.... I'm listening to one now..!! 

Sorry, couldn't resist...


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## Dr.Jones

@saabluster: Ah, I see.

Hm, somehow we seem to agree now. 

It had a few rough words, but was an otherwise interesting discussion.

I'll hit the bed now... Have fun


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## bshanahan14rulz

So a pre-collimator increases the final image size, while keeping the lux the same? 

So would it also cut down on the divergence of the beam then? the image is larger, would the divergence be smaller?


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## Walterk

I put some theory to the test about beam diameter, and look for verification.
I did a maseurement using a XRE and a 66mmm lens, and measured the spot. Set it out in Cad, with the advantage of zooming in- and out without loosing resolution. 
It appears to my findings that the spotsize is plainly resulting from the absolute diesize and the distance of the plane side of the aspheric lens:







- Is it correct that the line from the widest part of the source (here 1mm) through the center of the plane of the lens forms the half beam cone ? (wouldn't that be easy)
- Is it correct that: beam diameter = source size / focal length ? 
- Using the apparent die size for calculating candlepower has to do with units and light, and not the geometric ray-path ? (just throwing in interesting words here)
- The dome makes that the theoretical focus length is different form the empirical witnessed focal length ?


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## Dr.Jones

bshanahan14rulz said:


> So a pre-collimator increases the final image size, while keeping the lux the same?


Basically yes. Minus some additional losses, and maybe plus a small gain from reduced aberration. 



> So would it also cut down on the divergence of the beam then? the image is larger, would the divergence be smaller?


No. A bigger final image size means a wider beam angle and thus a bigger beam divergence.



Walterk said:


> It appears to my findings that the spotsize is plainly resulting from the absolute diesize and the distance of the plane side of the aspheric lens:
> 
> - Is it correct that the line form the widest part of the source through the center of the plane of the lens forms the half beam cone ? (wouldn't that be easy)
> - Using the apparent die size for calculating candlepower has to do with units and light, and not the geometric ray-path ? (just throwing in intersting words here)
> - The dome makes that the theoretical focus length is different form the empirical witnessed focal length ?


I'll start from the end:

- The dome creates a virtual image of the actual die. This virtual light source can be seen as the effective light source for all following optics. This virtual light source is magnified and sits a bit behind the real light source (in your picture: below).
- Thus in your drawing, you should use the apparent die size.
- The line from the die edges of the virtual light source through the lens center forms indeed the half beam cone (effective at larger distances). However, the lens center is not at the plane side, but somewhere in the middle of the lens.
- Thus it should be more like "the spot size is plainly resulting from the apparent die size and the distance to the effective center of the aspheric lens."


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## bigterk

After reading this thread I have determined that I need 2 things, opiates and some pie. :shrug:


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## Genzod

Walterk said:


> Surface brightness of the source; measure the candlepower-output of the bare source first, divided by the surface-area of source. The only way to do this without much uncertainty, is to do a lux-measurement on the bare source at one meter (with a calibrated lux-meter) and determain the source size, then divide the lux-measurement by the mm2 surface of the source.



There is indeed one other way to accurately estimate the axial intensity of a domeless LED, which is the preferred LED type for throw. 

The peak axial intensity of the bare LED at 1 meter is simply the maximum lumen output divided by π divided by the area of the emitter. We divide by the area of the die to get surface brightness.

In the case of an Osram Oslon Flat Black tested at Taschenlampen Forums, cooled with a fan and copper heat sink within the operating temperature range of 25-35C, having a peak lumen output of 937 lm and a die area of 1.122 mm2​:
SB=LTOT​/π/s2​, where LTOT​ is total lumens (usually the peak lumens but it can be whatever value you are designing around) and s2​ is die area in mm2​

SB=937/π/1.122 mm2

​SB= 266 cd/mm2 

​(Peak intensity is 298 cd)​

And this result is consistent with the surface brightness of 260 cd/mm2 ​that is the measured peak this LED. It is derived here from the data in the same link and experiment mentioned here.



*Proof:*

Approximating the domeless LED as a lambertian emitter, the intensity is I(*θ*)=I(0)*cos *θ *from -90 to 90 degrees.

One can then multiply this intensity with an infinitesimal area element on the hemisphere of radius 1 meter to get lumens in that element. Summation of these elements within a boundary defined by the half angle of the beam determines total lumens in that given field. (Integration).

Long story short, the percentage of total lumens from the emitter in the boundary of the beam angle is sin2​*θ* where theta is the half angle of the beam.

The area of this sector is different, and at 1 meter radius, the area of the sector is given as 2 π * (1-cos *θ* ) square meters.

So the average intensity in a defined sector is
IAVG ​(*θ*)= [LTOT​ * sin2​*θ* ] / [ 2 π * (1-cos*θ*) ] ......(lumens / square meters)

Where LTOT​ is total lumen output of the emitter across teh hemisphere.​
To get the intensity of the axial vector at 1 meter (cd), you take the limit of the function as *θ* approaches zero. This is indeterminate at first due to dividing zero by zero when *θ*=0 is plugged in. So the numerator and denominator are independently solved for the corresponding derivatives until the ratio become determinant. (From this point on, I will solve for surface brightness, then correct to solve for axial intensity.)

SB=LTOT​*(1/2π)/s2​* lim *θ*--->0​ [(2* sin*θ**cos*θ)* / sin *θ] *(dividing sines here is a big mathematical no-no



)​
SB=LTOT​*(1/π)/s2​* lim *θ*--->0​ [(sin*θ**cos*θ*) / sin *θ*]​

Again, you get an indeterminate ratio, so you take the derivatives _one more time_.
SB=LTOT​*(1/π)* lim *θ* --->0​ [(cos2​*θ* -sin2​*θ*) / cos *θ*]​

Taking the limit of theta approaches zero, we enter *θ*=0, LTOT ​=937 lm and die area =1.122 mm2​.

SB=937*(1/π) [(1-0)/1]/1.122

*SB=266 cd/mm2 ​*





(Peak intensity on the axial is SB * s2 ​= 298 cd)​

One can easily check this result by placing a very small half angle (say 1 degree) into the formula and finding a value that is very close to the limit.

SB=LTOT​/s2​* lim *θ* --->0 [ sin2​*θ* ] / [ 2 π * (1-cos*θ*) ]*

*SB=937/1.122* [ sin2​*1*°] / [ 2 π * (1-cos*1*°) ]​
SB=937/1.122* [ 3.04586e-4 ] / [ 9.56960e-4 ]

SB=266 cd/mm2​ (rounded to three significant digits)

I(1°)=266 cd/mm2​ * 1.122 mm2​ = 298 cd​


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