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

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

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

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

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

25 29.76%

# Thread: Formula for calculating throw using aspheric lens

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

Originally Posted by ma_sha1
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.

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

Hi all,

can you help me ?
What should I do to get more throw in my setup ?
http://www.candlepowerforums.com/vb/...d.php?t=280018

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

Thanks.

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

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).

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

Originally Posted by pepko
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.

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

Originally Posted by Dr.Jones
Saabluster, I'm not a professor (no one said so (except you))
Originally Posted by gcbryan
Dr. Jones (as I recall) has a Phd in Physics.

Originally Posted by Dr.Jones

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.

(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.

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

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

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!
.

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

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

(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'? :)

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

Originally Posted by Dr.Jones
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.

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

Originally Posted by ma_sha1

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.

Originally Posted by Dr.Jones
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.

Originally Posted by Dr.Jones
(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.

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

Originally Posted by Dr.Jones
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

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

Originally Posted by ma_sha1
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...

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

@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 :)

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

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?

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

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 ?

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

Originally Posted by bshanahan14rulz
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.

Originally Posted by Walterk
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."

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

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

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

Originally Posted by Walterk
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 sin2θ 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 * sin2θ ] / [ 2 π * (1-cosθ) ] ......(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* sinθ*cosθ) / sin θ] (dividing sines here is a big mathematical no-no )

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

Again, you get an indeterminate ratio, so you take the derivatives one more time.

SB=LTOT*(1/π)* lim θ --->0 [(cos2θ -sin2θ) / 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 [ sin2θ ] / [ 2 π * (1-cosθ) ]

SB=937/1.122* [ sin21°] / [ 2 π * (1-cos1°) ]

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

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•