Aspheric Lens Theory and Application

Flashlight Modding and DIY Parts
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Howdy!

I've been looking into aspheric lenses a little bit. My research didn't yield a whole lot of definite answers, but I've learned a bit looking through quite a few threads as well as manufacturer sites. Some of you will know most of this (or more). I'm writing it to save the less informed some research. Also note that this might seem like an advertisement for ThorLabs, but I don't know a whole lot about them besides their products look pretty nice and their website is informative so much of the information I've gleaned comes from there. If I have made a mistake, I will gladly fix it if one of you with more knowledge points it out to me. Don't be shy. I have thick skin.

I've run across two manufacturers that publish the specifications of their lenses. Their lenses are expensive(ish).

Thor Labs

http://www.thorlabs.com/navigation.cfm?guide_id=11

Edmund Optics

http://www.edmundoptics.com/optics/optical-lenses/aspheric-lenses/aspheric-condenser-lenses/2454

You will notice that both of those links go to "Aspheric Condenser Lens" pages. Those are the type of lens that we would use for focusing the light of an LED. The theory of the lens is that it takes the point source (really a plane source) and bends the light being emitted into nearly perfectly parallel beam. These lenses are flat on one side and curved on the other.

"Aspheric" simply means not spherical. These lenses have a profile that is roundish in appearance, but follows this equation (from ThorLabs site).

I've tried to figure this equation out and come up short. I'm guessing when I say that I believe z is the height of the dome, R is the radius (perpendicular to light path) and y is the direction parallel to the light path. All of the A's are constants.

Terminology:

Aspherical Condenser Lenses have two surfaces: The Plano(flat) surface and the Aspherical(curved) surface.

-The flat surface is mounted facing the LED die. The curved surface faces out.

Focal length (f): Distance from Back Principal Point(H) to the Focus Point.

This is the number that I was looking at when I was beginning to buy an aspheric for a project. It is NOT the number that we need to determine mounting height.

Back Focal Length (fb): Distance from the flat back plane to the focal point. This IS the number that we need to determine mounting height. It is always a smaller number than the Focal Length.

Edge Thickness(te): Edge thickness is useful for mounting purposes. It is merely the height of the cylindrical ring portion of the lens.

Center Thickness(tc): Center thickness is the height of the lens measured from the Back Plane to the top of the curvature.

Back Principal Point(H): This is the height in the lens that focus length is measured from. You can do math to find out where it is in the lens, but is not specified explicitly on data sheets. That is why we must use Back Focal Length for mounting purposes.

When focused, an aspheric lens will project a beam that closely resembles the geometry of the LED die. I hope ThorLabs doesn't mind me using their pictures, they are nice ones :) Notice the square in the center.

There are a couple of ways to get rid of the square hot spot. One is to mount the lens slightly longer or shorter than it's focal length. The other is to rough up the plano(flat) surface with really fine grit sandpaper. ThorLabs sells 600 and 1500 grit treated lenses as "diffuser lenses". I have one of these ordered and will report on it later. Here is their pic of the same setup with a diffuser lens.

This treatment does reduce light transmittance. I do not know how much. Rougher grit treatment reduces transmittance more than finer grit does.

The next big topic I encountered during my research is the great "Lumens vs. Lux Conumdrum".

Please forgive me if I have this wrong. From what I have read, it seems as though total lumen output will be markedly lower for an aspheric lens when compared to a reflector while the LUX will be markedly higher. Perhaps OL or DrJones will pipe in with more info and/or correct me, but my understanding is that the light emitted to the side is basically lost since the aspheric cannot focus it, thus the lower lumen output. At the same time, the light that is emitted forward directly into the lens is focused extremely tightly, thus the high LUX.

Waiven Collars (patented and trademarked) purportedly help recapture some of the lost lumens by redirecting some of the light lost from side emission. I'm not really convinced they do much, if anything.

Some have asked if a small reflector could be used in addition to the aspheric lens. I believe that OL has tried this and reports that horrible rings were present in the beam such that he determined it was not worth the effort.

Regarding lost lumens, I also believe that the thickness and optical purity of the lens plays a part. Highly transmissive flat lenses with optical coatings can get into the 98-99% light transmittance range. These lenses are comparatively thin though. I wonder what their transmittance would be if they were 10-20mm thick. I'll bet it would look more like an aspheric. Here is ThorLabs graph for a 10mm thick lens. It's right at 90% for the area we are interested in. I'm hoping their AR coating helps that a bit, but I can't find a Transmission graph for that, just one for reflectivity.

Anyway, some of the lost lumens may be to the thickness of aspheric lenses. Some of it may be due to the quality of the lenses such as those sourced from the Chinese sites. The balance is from the unfocused "side light" emitted from the LED.

I believe that some of these lost "side light" lumens can be recouped if we are willing to set the height of the lens lower than the back plane focus length. This will be at the expense of throw however. The beam will not be as tight. I, however don't need a light that will throw a mile or more. I want one that throws well. But some lesser distance will suit me fine. I plan on experimenting with this to see if there is a sweet spot where the lost lumens are minimized while keeping respectable throw.

That's all I can think of right now, but I feel like I'm missing quite a bit. Aside from their expense, these lenses really interest me for future builds. I think I'm going to try and build a zoomie MT-G2 and see how it does.

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For updates.

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“Well, what this equation means is……. the rest we will leave as an exercise to the reader” :wink: :smiley:

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What I see is….

AYE! AYE! AYE! AYE!……

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A collar like that reflects the light that goes sideways BACK to the dye, thus illuminating itself by itself with ‘recycled’ light.
It’s essentially a half sphere with the top off (i.e. a hole)
Focussing the reflected light back on the dye.
(Very important that it’s focussed properly)

Of course reflecting light back to the source, is an ancient technique.
Your average slide projector has a spherical hollow mirror behind the filament, which directs the back spill back to the filament which goes through the filament (area) to the condenser lens (a bulgy aspheric lens with very short focal length).

Old projectors…
The bundled light is heavily reduced by the heat shield-lens that follows… :stuck_out_tongue:

I hear people get up to some 20% gain with it.
I very much like Djozz’s experiment where he ‘mirrorized’ part of the LED dome with silver-something.
Again, light that doesn’t normally hit the lens gets ‘another chance’ to get out the front, but using the dome itself as the reflector-collar
Would be great if it was possible with aluminium vapor like real reflectors.

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What i think would be good is an ‘aspherical positive meniscus’ lense.

in stead of the plano (flat) side, it has a hollow side.
This can catch ALL of the light emitted, and bundle it.
Interesting as primary optics, i think.
I happen to have a 30mm spherical positive meniscus lens, which is essentially a half sphere (so it’s 15mm high) with a concave ‘input side’ (4mm deep).
It really does capture all the light from the LED. :slight_smile:
(You’ll then need a secondary lens if you want throw.)
But it generates doughnuts because it spherical…

some cents from Jerommel…

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Αυτό είναι όλα πολύ ωραία, αλλά ακόμα τα ελληνικά μου. Υποθέτω ότι είναι αλήθεια, δεν μπορείτε να διδάξετε ένα γέρικο σκυλί νέα κόλπα.

That’s all very nice, but still Greek to me. I guess it’s true, you can’t teach an old dog new tricks.

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optics is hella-complicated…

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I liked Djozz's experiment too. In fact, I think that it has a lot of promise if we could precisely deposit the required material where we want it. Some day I will have the ability to vapor deposition.

I agree that a two lens system would be much better, but at some point $50.00 lenses become cost prohibitive. Space is another road block.

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Guess you guys had a sheltered childhood like 99% of kids these days ! …LoL

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Sure Ed, the 60’s were so very sheltered…whatever you say.

So let’s see what you’ve got there, a focal length of oh, say, 90 million miles? Easy enough to reproduce in a flashlight…

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Plus the reality of optics versus our ‘great ideas’… :smiley:
Not that difficult would be taking some aluminium plate making a half-spere-hole / indentation the exact (as possible) size of the LED dome and polish it best you can, and then grind it down until you have the top hole.

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I thought about making a very small hemispherical die set and trying to press some thin polished aluminum to see what happens. It would be easy to glue it on. Whether it works or not...

It is just another idea that I have not found the time to test. Someday.

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I am addicted to throwers since I like lents, have tried all of them in almost whatever imaginable configuration :stuck_out_tongue: have mixed with good results zoom mirrors with lents, now will try to put together lents and reflector in my scratch build. Lots have mixed in wrong way them I will do it the only way it can work, need just a little time to post result, but so far I like it and I am not pleased easy usually :stuck_out_tongue:

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Wavien collars - They already did the work. They work well and there are some custom flashlights already being made with them. Home made ones will not work, unless you go through the due diligence and all the science, to achieve the same thing that is already being done. Been there done that, got the brass ring and tossed it away... = buy a wavien collar and be done with it...Wink

If you want a very long throw light, the aspheric is the way to go. If you want a better beam, then just stick with a reflector, matching a reflector with a led is the key, along with focusing that led in the reflector. Really, the science is already out there, proven methods, results are already out there too in custom flashlights. Defocusing an aspheric amounts to using a reflector, been there done that, got the brass ring and tossed it away...

Still, it's lots of fun to play with even if the answers are already there...

The deft is probably the longest throwing light out and there's (I don't keep track on CPF any more), at least one maker of awesome throwers out there, using wavien collars. Been a long time since I have stopped by CPF, but I remember seeing some amazing lights being sold there, using wavien collars.

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Waiven is very hard to implement agree but I will marry aspheric lens and reflector and even that idea is not new I am surprised why its used so rarely, in fact I haven’t seen any other build build doing properly. Its funny what you say about focusing in advanced optical setups its so true that I spent the last thee days just in focusing my setup. It can be focused even further but I am satisfy with results already and not sure have enough time to spend with focusing. When I finish in the contest will experiment with waiven properly, have some ideas already.
How much a deft can throw? My EBRZM alredy throw over 1 million cd but is way bigger than a deft I must acept and this make it somehow not q fair comparison.

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Magnifying glasses… have been the bane of little green plastic army men and army ants for eons… Death From Above!

I have a large Fresnel lens that will cause a tree to burst into flames in under 1 second. J)

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Frosted back side of aspheric?

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OL, I have looked for proof that Wavien collars work as advertised. I have yet to find anything except for their own literature. I'm not saying that they are falsifying anything, but I'd like something that someone else wrote. I've read some threads that kinda sorta look like proof, but don't raise to my level of "Yep, that proves it to me!" Can you point me in the right direction? Let me explain why I'm skeptical.

First, lumen output of an LED is reduced by heat. I think that a Wavien collar cannot help but to raise die temperature, likely very significantly. I'm talking a lot with all of those photons being reflected back at the die. So, overall output will be down right off of the bat due to heat. (I notice that they use active cooling of the LED in at least one of their videos...) We all know how fast lumen output drops as the LED die heats up. Wavien collars will make it heat up faster.

Second, redirecting photons with a reflector induces some loss. From what I've read, reflector loss is somewhere between 10-35%. The math is bad for the Wavien either way. There is at most 35% of the "lost photons" to be recovered. The problem stems from the fact that the Wavien collar has the same loss number. So if we recover 65% of 35% we only recover 22.8% of the "lost" photons as output. That is the best case and I've often seen the number 20% gain bandied about when talking about Wavien. That's the best case scenario. Worst case is recovering 90% of 10% for a 9% "recovery" of photons.

Whether you pick 22.8% or 9% or something in between, when you factor in the additional heat introduced I think the effect is likely marginal and could even be detrimental for a flashlight with poor heat dissipation qualities.

From this thread:

http://www.candlepowerforums.com/vb/showthread.php?111807-Reflector-efficiency-question

Here is a paragraph that McGizmo wrote about reflectors specifically, but talks about the topic at hand too. I copied the whole post for the sake of completeness, but bolded the last three paragraphs which I think are still as true now as when he wrote them in 2006. I think he is exactly right. The part in blue is what I took to heart.

"At the speed of light, I doubt it takes a specific photon much time to either bounce out of a flashlights optic and window or get absorbed by same. Consider the size of a photon relative to the topography of the optic's and window's surface, at its scale.

If I recall my high school physics correctly (unlikely) a material has what is termed a critical angle. If the angle of incidence of a photon is less than this critical angle, the photon will reflect or bounce off the surface of this material with an angle or reflection equal to the angle of incidence based on a perpindicular to the surface point of contact.

Even a highly polished mirror surface has pits and deviations in its topography from the apparent contour as seen from a macro pont of reference. Individual photons are small enough that they may well encounter a point of contact in which their angle of incidence is greater than the materials critical angle and instead of bouncing off, they go in. If the material is a window and the photon is capable of penetrating or passing through, it will either transit if its angle of incidence is greater than the critical angle of the material when it reaches the boundary surface of the material or it will reflect off this boundary surface if the angle of incidence is less than the critical angle and continue on in a new path within the material. I assume at some point it either escapes or collides with an actual particle within the material and in this collision, the energy of light is converted to kenitic energy of heat?

OK, I now admit that even if I recalled my high school physics, it was only a simple explaination of the physics involved and at some level, incapable of actually explaining what is really happening; limitations of man's modeling to represent reality.

These white and super reflective surfaces are for the most part lambertian in nature and even when they are formed at a macro level in a collimating surface, much of the light reflected will not follow the geometry dictated by the general form but rather the particular case of the surface at contact. At some level of significance a finely machined and surfaced optic is the pits or has the pits and some photons enconter these pits.

For me, it helps to think of the world at a photon's level as not a world of solid objects but rather a world of objects that are a latice work with solid areas where contact or collision will occur as well as areas where a clear path through is posible. In the case of contact or collision, the photon may either glance or bounce of in a new path or splat into the mass leaving the mass in a greater state of energy or motion.

At a very simple level of consideration, we loose light everytime we attempt to make contact with it and alter its course. Whether an optic is based on reflection or refraction, it will not be perfect in nature and photons will be lost.

I have opted for relatively deep reflectors to be used with the Luxeons and when a collimated or concentrated beam is desired. Putting more reflective surface in the way of the stream of photons allows for a greater amount of redirection but at the cost of loss of photons. In simple and general terms, you pay for lux with lumen loss. It is this expense that confuses me when folks seem to expect that high lumen numbers equates to high lux numbers. In my way of thinking the two are typically somewhat inversely related due to loss in management or redirection"



I would like Wavien collars to do what they advertise. It is a really cool concept. I just haven't seen what I need to see yet. It may be that I'm wrong, but I think the numbers are stacked against them.

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Yes, they do work… I know somebody that did a lot of testing on them and uses them. He did a lot of measurements… which he ain’t sharin’ to the public, ’cause he makes his living/reputation off what he builds and has zero tolerance for snake oil.

How much improvement can you expect? Who knows… but in the rarefied world of squeezing another lumen/lux/cd out of a light, you do what you need to do.