Diode collimator determination - theories and methods?

[tribble]

I found a lot of threads comparing different collimators commonly used by hobbyists, but wanted more/better background on what the tradeoffs were for each variable in the equation, and, hopefully, a method to pick the correct focal length high-quality collimator for optimal beam shape. There's lots of talk about the "G-2" lens, or the "three-element lens," or the "acrylic lens," but little information on their actual shapes or focal lengths. And, of course, most of the "comparison" information is about POWER, which for me is a distant, secondary consideration. There is some, but not much, beam comparison information, and what there is is probably particular to the diodes used in the particular test.

I'm going to be building an RGB projector based on single-mode diodes and 3mm scanner aperture, so I'm interested in forming a 2.9mm beam with the best divergence characteristics I can get from each diode, and eventually, each PBS'd diode pair.

The question is, "how do you determine the collimator FL to produce a desired beam width w for a given diode?"

I started by trying to find out the FL of the commonly available lenses, but didn't come up with much. My starting assumption is that a high-quality molded aspheric collimator with AR coating will produce a much better beam than the "three-element glass lens" or the "G-2 lens." If that's wrong, well, I can stop now. But, since these lenses are expensive, one wouldn't want to select by trial-and-error.

I drew this diagram to try to help me work out the geometry, but not knowing the emitter sizes, or even the ballpark emitter sizes, makes it hard to know where to start.



If you figure that n/2 should be = (w/2) / tan(divergence half angle), then considering a fast-axis divergence of 22 degrees, one might expect a FL of ~ 7.7mm from the 'virtual origin' of the beam. But, since the emitter has non-zero size, where along the diagram do we place it, and how do we calculate the real needed FL?

And then, having fixed one axis, can we expand the other axis and get it to diverge at the same rate?

I am sure I am missing something basic, and perhaps when I get all of the required parts I can just set up them on a table somewhere and try to do some measuring, but it sure would be nice to have the theory down correctly before I start.

Thanks for any corrections or ideas.

[danielbriggs]

I ran the calcs for three diodes in 5 mins for a variety of common in production, quality, aspheric lenses.

It assumes the thin lens approximation, and obviously does not consider divergence. It also doesn't compensate for the refraction variation by wavelength.
Take the 2d.p. diameters with a pinch of salt, as the manufacture's datasheets give quite a wide tolerance on emitter angle; typical values were taken for all cases.
Two ticks means is will not clip and can be a considered lens.

FL = Focal Length
NA = Numerical Aperture
CA = Clear Aperture

i.e. THESE ARE BACK OF THE ENVELOPE CALCS - it'll get you close, but nothing beats doing your own physical testing + quality measurements.


638nm - HL63603TG






445nm - NDB7A75





520nm - NDG7475





Hope that helps.
Dan

[tribble]

I ran the calcs for three diodes in 5 mins for a variety of common in production, quality, aspheric lenses.

Dan, that's a fantastic start, thank you! I guess I have two follow-up questions: 1, are these formulas something public domain that can be looked up and learned, or proprietary? I was unable to find emitter size information on my diodes of interest; where do those come from? I have found spec sheets for many diodes, but emitter size is not on it.

And 2, does far-field divergence differ if you arrive at a given final beam diameter at aperture using a single long FL collimator vs. a short-FL collimator and a beam expanding telescope?

Thanks again,
Mike

[danielbriggs]

Mike,

1.
They sure are public domain!
I've a detailed old-old tech guide from Melles Griot somewhere which explains the steps very well. I'll have to root it out this weekend if it's of use.
If not, I'll paste the formulae in from LaTex, such that they are formatted half-decently.

The "BOTEC"s do not take into account emitter size; there are models which do, but you're dangerously close to ray tracing / Zemax territory.
If you want emitter sizes, you have to measure them yourself...
http://www.photonlexicon.com/forums/...Quantification


2.
Assuming you end up with the same diameters in either case, the divergence will either be exactly the same or slightly worse.
Perhaps looking up Etendue will help; basically the "entropy" of an optical system if that aids understanding. Etendue can either stay the same or increase, never decrease.
"No free lunch" etc. etc.
(Focused spot size can however be reduced (to the diffraction limit) using beam expanders and then subsequent lenses, but that's not what you're after. )


Regards,
Dan

[tribble]

Dan, I would appreciate the guide if it's readily available; hate to put you out over the holiday, and there's always the chance that I won't understand it. But, I love to learn! If all else fails just the equations are a great place to start; I can plug them in to Excel and have them for reference when poring over optics catalogs.

The optical entropy concept is interesting; it makes sense that the fewer components you have in your train to achieve the desired result the better, component quality allowing.

Thanks!

Mike

- - - Updated - - -

BTW, that diode reference thread looks fabulous! Hope you have time to keep it going.

[logsquared]

Here is the equation I use: Diameter at lens = 2(Fl of lens) tan(diode raw divergence).

Because the emitter is very small compared to the Fl of the collimator it doesn't have a great affect on the beams exit diameter. Emitter size only affects the divergence for a given Fl lens. The FL of the lens is the distance (roughly) from the emitter to the lens.

Also, keep in mind the datasheet raw divergence can be much different in practice. Generally the divergence increases with current too.

[planters]

I am always using secondary lens pairs for my spatial filters, but when I produced the video I also mentioned that an added benefit is the ability that this gives you to adjust the size of the beam to match the scanner mirror. I like your approach above, but you may find that the "perfect" lens based on your calculations is not quite available commercially. At that point you can select a pair of lenses that will tweak the size up or down to get the most out of your scanners.

And 2, does far-field divergence differ if you arrive at a given final beam diameter at aperture using a single long FL collimator vs. a short-FL collimator and a beam expanding telescope?

I will differ with Dan here. Because of the asymmetry of the emitter there are aberrations such as coma that a radially symmetrical collimator will be unable to compensate for. In theory, the aspheric lens is corrected for spherical aberration (it should not produce the spherical aberration that a spherical lens would) when it is positioned at its focal length from a point source. So, the optimal position is often a tiny bit off this value to get the best compromise for the tightest beam in the two orthogonal axises. By using a cylinder pair as a beam expander you gain an asymmetric degree of freedom. I find when I use a number I call the beam product (I don't think I made this up, just don't know where it comes from), which is the exit diameter x the far field divergence that I can get this number smaller when using the cylinder pair. This does not work when using a prism pair. This isn't a free lunch just like proper focusing isn't a free lunch, but it is significant enough to more than compensate for the beam deterioration that comes as additional elements are added.

[tribble]

OK, interesting...

What happens if you use a cylinder pair as the collimators? Thought experiment... since the beam diverges at fast and slow rates, it seems there should be room to put the fast-axis cylinder closer to the emitter and the slow-axis cylinder farther away, which (in my imagination) would produce a closer-to-square beam. The only thing I can't picture is if the combination of beam expansion due to collimator FL and post-collimator divergence could leave the beam square over a long distance, or at least over a significant 'butter zone' distance, say, 10 to 20 meters, or if it would only be square at a single, fixed distance from the exit aperture. I'm not sure which axis is which with respect to the emitter geometry and the rectangle I'm used to seeing after the collimators. Does the longer axis of the emitter produce the slower-diverging beam, or vice-versa?

Planters, where do you get your lenses? The edmund cylinder lenses I looked up after watching your 'improving beams' video were in the neighborhood of $50 each. The kits are more cost effective if you can use all of the sizes, but I suspect only a few sizes would end up being useful. Kits are nice for experimenting, though. Edmunds' aspheres are in the $100 range, though Optima's are closer to $20, which is more palatable, but their long FL collimators have small NA.

Thanks guys for all of the inputs!

[planters]

The lenses I use for collimators are the 2mm "Dave" lenses, pre-mounted in a 9 x 0.5 threaded barrel or the Optima 4mm lenses. The cylinders are all from Edmund Optics. If you use a -25mm FL, 12.5 x 25 mm, rectangular style, negative cylinder first then the choosing can be left to the round style, positive cylinder. I use a +50mm that gets me close to a 4.5mm to 5mm beam with the Optimas. My advise would be to choose the collimator and except for the alignment tolerances the ultimate performance will be the same. Then add the negative cylinder and determine what you think will be a reasonable guess for the positive cylinder and order two lenses that bracket this guess, or nail it and also bracket it (with three lenses). On the off chance you missed the mark you will now be very confident as to exactly what you need and the extra lens (or two) will sit in your drawer as a tool for future work.

I love thought experiments and I have worked on the idea of a pair of... a pair of cylinders to accomplish the beam management. When the discussions of FAC lenses for hugely divergent red and IR diodes was going on there were references to Doric, a company that manufactures and installs these very small lenses. The problem, as they describe it, is that at these very short focal ratios and I mean ratios, not focal lengths, the collimation will produce a lot of spherical aberration unless an aspheric of a multi-element, aberration corrected lens is used. Aspheric cylinder lenses are rare and very expensive. So, I believe that if the bulk of the collimation is made with a single aspheric lens then the residual aberration that results from the asymmetry ( primarily the longer, slower axis) can be reduced with the cylinder pair.

[tribble]

Thanks for the details! If I may impose, another question...

I recall from your discussion of the spatial filter telescope that you can use unequal FL to expand the beam, e.g., a 50mm followed by a 100mm would give you a 2x telescope, and the beam would be double the "diameter" (or 4x the area, since we're not working with circles) and have half the divergence (in each axis, with spherical lenses) upon exit. For the spatial filter, the filter is pretty much at the focus of each lens. I think I grok all that.

In another discussion of magnification in the cylinder train, I think I recall your saying that the magnification depended on something else, or that it could be varied, and in this case I am a bit puzzled. Does this have to do with the use of a negative FL first lens? What is the expansion coefficient for the arrangement with the -25mm cylinder and a, say, +50mm cylinder, and if it's not constant, how do you adjust it?