[Laser] Notes on obtaining optimal efficiency (Was: Fresnel LED TX - test over 94km)

[C. Turner]

Greetings to the group.

Echoing Chris's notes, what follows is an email that I'd originally 
composed (over the past several days) to Rado and his group, but it will 
probably be of interest to all.

***
***

While I'm putting together something more comprehensive (e.g. web pages, 
article, etc.) here are few things that we have determined that are 
useful in using Fresnel lenses with LEDs.

For many of you, some of this is very basic stuff, but then for those 
who *don't* know it, it will be new!

***

First, in any optical system (and assuming "perfect" optics, no 
atmosphere, and that the wavelength of light was zero - none of which 
are true) the divergence of a given system is related to the proportion 
of the aperture of the lens and the size of the emitter.  (Note:  Laser 
pointers have relatively low divergence by virtue of the fact that the 
area from which the light is emitted is *extremely* small - so this 
ratio is maintained even with physically-small lenses.)

What this means is that using such an impossible system (perfect optics, 
zero wavelength light, no atmosphere, etc.) the collimated beam would 
have zero divergence *IF* its source size were infinitely small and the 
lens were of a finite size.  Clearly, this cannot be true so let's 
back-track to a real-world system using Fresnel lenses and LEDs.

In a system using Fresnel lenses we can ignore the wavelength of light 
as our optics will be too imperfect to even get close to the diffraction 
limit, and if we use monochromatic light we can also ignore chromatic 
aberration.  What we are (mostly) left with, then, is the "quality" of 
the lens itself and the ratio of the source size versus size of the lens.

For the size of the emitter (the LED) we are kind of stuck.  With LEDs 
we can only achieve a certain amount of "current density" for the LED in 
terms of amps per square millimeter and this factor correlates directly 
with the number of lumens emitted by that surface per square 
millimeter.  With the present technology this limit is roughly 1-2.5 
amps per square millimeter for LEDs constructed in a manner similar to 
the SST-90.  This limit is imposed, in large part, by the fact that heat 
dissipation becomes problematic at such current densities and further 
(dramatic) increases are likely to require highly exotic materials and 
techniques and would therefore not likely find their way into widespread 
production anytime soon.  The other factor has to do with the quantum 
efficiency of the LED itself as well as the very ability to construct an 
LED such that the photons emitted within the material can escape and be 
useful to the designer.

So, with our number of photons per square millimeter being somewhat 
"fixed" by the current technology, we must make do with what we have.

Now, one oft-repeated fallacy is that a "bigger, more-powerful emitter" 
will increase the higher far-field flux  (e.g. the "brightness" as seen 
by the distant observer.)  With a simple lens system, this is just not 
true:  A larger emitter will simply produce a larger, wider "spot" of 
light (which would be a bit easier to aim!) but at a long distance there 
is NO difference between the perceived brightness of large emitter and a 
small emitter, assuming that each one was producing "X" number of 
photons per second per square millimeter of the emitter.  The key to 
improve far-field flux density, then, would be to somehow increase the 
*effective* number of photons being emitted per square millimeter of 
emitter surface.

That's not easy.  Since we really can't increase the luminosity-per-unit 
area of the LED, we are stuck with trying to decrease the *apparent* 
size of the emitter.  While it's easy to go the other way, reducing the 
apparent size of the emitter WHILE still maintaining high efficiency 
(e.g. not losing most of the photons in the process) is a very difficult 
task:  In 2009 during a visit to the optics department at the University 
of Arizona, I posed this very question to a number of the professors and 
after thinking about the problem for a while, they agreed that it was a 
vexing issue and that they'd have to think more about it, but didn't 
think that whatever solution there might be would be particularly easy 
to do.  My own searches on the "GoogleWeb" about this topic have also 
proved fruitless.  (The use of LED-based "fiber optic" launchers come to 
mind, but these devices often have rather poor overall efficiency - that 
is, they usually harvest relatively few of the photons emitted by an LED 
of large source size.)

Now, several things may come to mind if the goal is simply to *decrease* 
divergence:

- The use of a negative lens between the LED and the Fresnel.  This will 
certainly reduce divergence, but it also spreads the light being emitted 
from the LED over a wider area and most of it will "miss" the Fresnel 
entirely, lighting up the area beyond the edges of the lens.  The 
overall result is a much LOWER far-field flux than if you'd done nothing 
at all!

- Mask the source.  By placing a mask with a hole in front of the LED 
(and as close to LED as possible) one can reduce the divergence of the 
beam.  Doing this will NOT reduce the amount of light reaching the 
distant observer, provided that this pinhole is large enough to overcome 
the optical inaccuracies of the lens itself:  This statement may 
surprise some, but it's true!  What IS reduced, again, is the 
beamwidth.  Doing this has pros and cons:  On the plus side, since 
divergence is reduced, crosstalk may be reduced in a full-duplex system 
as the beams are better-contained and less transmit energy is likely to 
be intercepted by a parallel-aimed receive system due to light 
"spillover" from Rayleigh and other types of scattering as the transmit 
and "receive" beams diverge.  On the downside, with reduced divergence 
it is more difficult to aim the system.  It should also be noted that 
putting a mask in front of such an LED can affect it thermally as it 
will prevent energy (in the form of light) from escaping the immediate 
environs of the emitter and this additional heat source should be taken 
into account.

Neither of the above will actually improve far-field flux - which is our 
desired goal.  What can we do, then, to improve that?

What we are left with is to make sure that as much light as possible is 
directed toward the Fresnel lens.  For this, a positive lens is 
typically used to "confine" the cone of light being emitted by the LED 
to the apparent angular dimension of the lens at the focal length.  
Taking the (imperfect) analogy of "illuminating" a parabolic dish for 
transmit purposes, the energy that "spills" around the outside edge of 
the dish is simply wasted as it never hits the dish and has no 
opportunity to be directed toward the distant station.  On the other 
hand, if one were to confine the beam excessively - that is, produce a 
small diameter "spot" - one would, using the dish analogy, be using only 
a small portion of its aperture and lose efficiency that way - and this 
analogy applies to "illuminating" the back of the Fresnel lens.

What is the optimum, then?  Based on in-field empirical measurement 
where I had a system in which it was possible to measure the far-field 
optical flux while being able to vary the distance of this "secondary" 
lens to the LED (thus affecting how "wide" the circle of light from the 
LED was) AND the distance between the secondary lens/LED assembly and 
the Fresnel lens (to adjust overall focus) I determined that optimum 
far-field flux occurred when, using a square lens, the edge of the 
"circle" of light from the LED just hit the edges and the corners were 
slightly darkened.  This shouldn't be too surprising, as that's about as 
good a "fit" as one can hope for when trying to impose a circle atop a 
square!

One point that is worth mentioning is that as one reduces the size of 
the "spot of light" from the LED/secondary lens assembly, two things happen:

- As the spot of light is reduced by moving the positive secondary lens 
farther away from the LED, the apparent size of the LED is magnified.  
This will increase divergence.
- As the lens is moved farther away, less of the light being emitted by 
the LED will actually hit the secondary lens.

In reality, it is this second point that contributes the most to 
inefficiencies in the system.  If one studies the "beamwidth" charts for 
the LED that plot intensity with the off-axis angle, one can see that as 
one moves off-axis, the intensity deceases.  However, if you consider 
that as you widen the angle of the light from the LED, the area being 
illuminated increases exponentially and one sees how it can be that a 
very large portion of the light being emitted by the LED is not being 
directed forward!  It is important, therefore, that the lens be situated 
such that it "gathers" up as much light from the LED as possible.

Practically speaking, DCX (Double Convex) secondary lenses are 
undesirable for two reasons.  The first of these is that in order to be 
"strong" enough to be useful, they will probably be somewhat "fat" and 
this will prevent one from placing the LED very close to the plane of 
the lens to achieve the desired result.  The other problem with that 
type of lens, light that is far off-axis (which means that it's also 
near the edge of the lens itself) will more likely reflect off the 
curved surface lens - if it hits the lens at all.  (That is, eventually 
the angle gets to be too steep!)

At the very least, a PCX (Plano-Convex) lens is the best of the most 
common types, with the flat surface toward the LED.  A positive meniscus 
(PMN) lens works very nicely, but these are much more difficult to find.

When adjusting such a system, optimal far-field flux will occur when the 
following are true:

- The "circle" of light from the LED just spills beyond the edges of the 
square lens.
- The lens is as close to the LED as possible.

For the systems that I have built, the LED and secondary lens either 
touch, or are within a millimeter or two of touching.  What this means 
is that the "strength" of the secondary lens system should be chosen 
appropriately:  Too "strong" of a lens and you "under-illuminate" the 
area of the Fresnel when the LED and lens touch each other (that is,  
the circle of light is too small) while too "weak" a lens means that 
it's placed so far away from the LED that much of its light doesn't even 
hit the secondary lens.  This also means that, compared to the size of 
the LED, the secondary lens will be quite large (e.g. 48mm diameter in 
the case of a Luxeon III LED.)

Now it is true that the use of any positive secondary lens will increase 
divergence, but the fact is that you will end up with better far-field 
flux with a well-matched system as described above with higher overall 
divergence than a mis-matched lower-divergence system.

***

This brings to mind another consideration:  The F-Ratio of the Fresnel 
being used.

If the F-Ratio (the ratio between the len's diameter and focal length) 
is too low (less than 0.5 or so) we can see that it might be difficult 
to spread the light over a wide-enough angle to effectively illuminate 
the lens while if the F-Ratio is larger (say 2 or more) then the problem 
of being able to narrow the LED's beam to "just" illuminate the Fresnel 
arises.  If one runs the numbers it becomes clear that it is simply not 
possible to efficiently illuminate a hypothetical Fresnel with a very 
high F-ratio with a *single* lens as that would imply a lens with 
impossible-to-make attributes.

In my opinion, the optimal F-Ratio is somewhere in the range of 0.6 to 
1.5 - with the preferred range being somewhere around 1.0.  In this 
range the incident angles aren't unreasonable and it is practical to use 
a single lens for the secondary.  I have constructed Fresnel-based 
systems at each extreme of this range and I have found a slight 
advantage (10-15% overall far field intensity) at the short end of that 
range - but this difference represents only a few dB of recovered 
signal.  One of the difficulties of a system with a very short F-Ratio 
is that uniform illumination of the Fresnel itself becomes problematic 
as the distance from the light source to the edges of such "short" 
Fresnel lenses is significantly greater than the distance from the 
center of the lens to the light source and naturally, falloff in light 
intensity occurs toward the edges.

***

For aligning an LED-based Fresnel optical transmitter I set up a "test 
range" over a distance of about 175 meters in which I place, at the far 
end, an LDR (CdS cell) attached to a 555 oscillator feeding the audio 
input of a low-power FM transmitter (a Handie-Talkie on a 40dB 
attenuator, actually) over which an audible tone would be transmitted:  
The higher the frequency of the tone, the more light being detected.  By 
using a laptop running the Spectran program I can make repeatable 
measurements of relative intensity by measuring the frequency of the 
tone, and by varying the current of the LED being tested by known 
amounts, direct ratios of tone pitch and light intensities could be 
established, allowing indirect comparisons between different 
arrangements and LED transmitters.

At a distance of 175 meters it seems that this is sufficient to be 
deemed "infinite" for purposes of focusing a Fresnel/LED system:  This 
isn't quite true, but the actual difference seems to be only a fraction 
of a dB and the extra difficulty in testing over a much longer range 
wasn't considered to be worth it.  (30 meters, on the other hand, is too 
short for proper focusing!  A much longer test range would make it more 
awkward to set up (having to traverse to opposite ends of the range) 
while very far distances (e.g. several kilometers) may make the path 
more subject to the vagaries of atmospheric attenuation and 
scintillation, thus complicating measurements.

As it turns out, optimal far-field flux occurs coincident with the 
"sharpest" image of the LED die being projected.  For LEDs like the 
SST-90 in which the emitter is on a flat plane, this is fairly easy to 
do, but for other types of LEDs - particular the "TIP" (Truncated 
Inverted Pyramid) such as the red to yellow members of Luxeon family -  
there is a degree of ambiguity as there is not single plane from which 
light is emitted:  In the case of these LEDs the optimum far field flux 
seemed to occur somewhere between achieving a sharp image of the "top" 
of the LED and its reflector cup although the difference isn't all that 
great (only a few percent.)

***

Having tackled that topic, a brief word on the lenses themselves.

I've had the opportunity to "test" a number of Fresnel lenses of 
different manufacture, sizes and F-ratios to determine how "good" they 
are.  While it is well known that Fresnels would be a poor choice if the 
intent was to use them for imaging, the question is "How good/bad are they?"

To answer this question, I first did some analysis using the star Vega - 
which, at the time, was conveniently very close the Zenith at a 
reasonable hour.  Using this "infinitely-distant" and, for all practical 
purposes, "point source" of light, I determined that most Fresnel lenses 
would produce a "blur circle" of under 1mm diameter.

Because stars are rather awkward to use (they "move", they are fairly 
dim - which makes initial setup rather difficult, they can be at awkward 
angles, and one as at the mercy of weather) I decided to make further 
measurement using another system.

For this, I drilled a 0.25mm hole (yes, I have a 0.25mm drill bit) in a 
piece of 0.16mm sheet brass and placed behind it a high-brightness red 
LED.  The LED unit - the current of which could be switched between 
"high" (about 60mA) and "low" (about 1mA) was placed a reasonable 
distance away (about 13 meters).  The "high" setting allowed quick setup 
as it was bright enough to project a red spot onto a piece of paper to 
determine aiming and focusing of the Fresnel while the "low" setting 
avoided saturation of the camera's imager.  The use of an LED provided a 
monochromatic light source to minimize chromatic aberration which, with 
white light, can make precise focusing more difficult.  While this light 
source was neither a true "point source" nor was it infinitely distant, 
it was suitable for analysis of lenses of the quality of the Fresnels - 
and comparisons between results obtained using the star Vega and the 
LED-based test range using the same lens tend to bear this out.

To determine the size of the blur circle, a CCTV camera was used with 
its CS lens removed.  The imager of this camera was of known size and 
thus, the dimensions of the individual pixels of the digitized picture 
could be calculated.  Light from the test source was optimally focused 
directly onto the CCTV camera's imager and digitized so that the result 
could be analyzed later.

The result of this testing was that almost every Fresnel lens produced a 
blur circle with a size that was less than 1/1000th of its focal length 
- and some where much better than this.  In short, it would appear that 
the size of the blur circle of an optimally-focused lens or reasonable 
size (e.g. at least 200mm on a side) and focal length was well under 1mm 
diameter.  Unlike with conventional lenses, Fresnels don't produce a 
nice, fuzzy circle (much less, diffraction rings!) but rather a 
less-defined blob with streaks emanating from it, so the *exact* 
determination of the size of the blur circle and the area over which 
most of the energy is focused is a bit of guesswork.

This has several implications for a Fresnel-based transmit/receive system:

- If the size of the emitter is significantly greater than that len's 
blur circle, it is likely that the divergence of that system will be 
most strongly determined by the ratio of the emitter's size and the size 
of the aperture, rather than the quality of the lens.
- One would probably NOT use a detector with an active area less than 
the size of the blur circle.  Practically speaking, to intercept the 
most energy and make aiming a bit easier the diameter of the detector 
should be at least 2-3 times that of the "blur circle."  One may not 
want to use too-large a detector, as its capacitance can submerge weak 
signals into the noise and the field of view may be unnecessarily enlarged.

In these tests, several things were noticed:

- Overhead projector lenses are NOT good candidates for this use.  
Simply put, these aren't usually designed to focus at infinity, so they 
produce VERY poor results.  If you have a Fresnel from an overhead 
projector, don't bother with it UNLESS you have thoroughly tested its 
performance!
- Larger F-ratios and/or focal length imply larger detector sizes for 
optimal performance.  Such lenses - since the grooves need to be made 
with greater precision in order to provide a sharp focus at the greater 
distance - tend to produce wider blur circles than "shorter" lenses.  
Since these lenses tend not only to be more expensive and require a 
larger physical structure to support the lens and accompanying 
electronics, they aren't recommended for such use, anyway.
- This lenses with fine groove pitch (e.g. more grooves per millimeter) 
appear to have higher scattering losses than those with "coarser" groove 
pitches.  The resulting blur circle of the "finer" lenses were slightly 
"fuzzier" and it is likely possible that scattering losses would be 
higher.  Examples of lenses with "fine" pitches are those intended more 
for imaging purposes (such as video screen enlargement) and those 
imprinted on flexible vinyl.

***

These "page magnifier" lenses are relatively small, with a typical 
"active" lens area of around 200mm x 260mm (although the size varies) 
and often (but not always) include an "un-grooved" border along the 
edges.  This size makes them fairly easy to use and they are, in fact, 
large enough to provide reasonable performance.  Unfortunately, they are 
rectangular, which means that their overall efficiency is reduced 
somewhat because - as determined from previous experimentation and 
measurement - optimal far-field flux seems to occur when the "circle of 
light" from the LED is adjusted to *just* hit the edges of the long 
dimension of a rectangular lens - and this also means that a portion of 
the light will be cut off in the "narrow" dimension and lost.  (This 
amount of degradation appears to be approximately proportional to the 
difference in area to the rectangular lens and a square lens of the same 
"long" dimension.)  Considering how cheap these lenses are, however, 
they are certainly worth considering!

One surprise was that the very cheap, rigid "page magnifier" lenses 
available from stationary/office supply stores (and, in some discount 
outlets) provide very, small blur circles on par with or exceeding those 
obtainable from much more expensive lenses!  As it turns out, these 
lenses tend to have relatively coarse groove pitch - an advantage in our 
case.

About these rigid "page magnifier" lenses, there are a few things to 
consider, however:  They seem to be available in two ranges of focal 
length.  Most have a focal length the 250-330mm area (although most seem 
to be at the longer end of that range), and others are around 600mm.  
Again, the "longer" lenses (with an F-ratio of 2 or greater) aren't 
particularly useful for our purposes as that F-ratios is awkwardly large 
(implying difficulties in obtaining optimal LED transmission efficiency) 
and would require a fairly large assembly to support the lens and its gear.

I am working on a web page that discusses comparative "quality" of 
different molded Fresnel lenses - complete with pictures showing the 
resulting blur circles.  It will be another couple of days before I put 
it online.  However, the upshot of the tests is this:

- Using a good-quality Fresnel lens (including those rigid "Page 
Magnifier" types with around 330mm focal length) you will be "safe" in 
using a photodetector of 1mm diameter or greater.  (The BPW34, for 
comparison, is around 2.7mm on a side).
- This also implies that if the apparent source size of the emitter is 
larger than 2-3 times the "blur circle" of the lens you use that the 
primary contributor of the divergence angle of a given system will be 
the ratio of the apparent source size and the aperture and NOT the 
quality of the lens.  For the lenses that I have tested, that would mean 
that as long as the apparent source size was 1mm or larger, you were 
"source-size" limited rather than "lens-quality" limited in the amount 
of divergence.

73,

Clint
KA7OEI


> Hi Jim,
>
> we were a bit hurry, because I finished the optics and driver a day
> before the test. Optical alignment is not optimal. I need to do more
> iterations to find optimal position of Fresnel and condenser lens. But I
> think we rather make it in new equipment.
>
> Beam width is about 100mRad (2m spot at 20m distance). We know that it
> is very bad. But there is way how to deal with it. We need to have
> better lenses and beeter mechanical enviroment. Clint KA7OEI has good
> results - his beawidth is less than 10mRad.
>
> About the way of the communication - Robo saw the red light  visualy and
> he heard it very weak - audio signal.
>
> Kind regards
>
> Rado om2zz
>
>