I have done some playing with lasers over the years and have occasionally used a beam expander.
Collimated laser beams aren't ever quite parallel and so they spread out, to a greater or lesser extent, with distance. This spread of the beam is known as divergence and it is usually expressed in milliradians (mrad), one-thousandth of a radian, or about 0.06°.
The gas lasers I've used have had a divergence on the order of 1mrad (some rather better than that, but I'm only concerned with order-of-magnitude here).
All other things being equal, if you expand the diameter of the beam by X times, you reduce the divergence by 1/X. This means that, at a distance, you end up with a smaller diameter beam.
A kindly soul explained to me that if you use a telescope in reverse you end up with ... a beam expander! So a cheap plastic x3 or x5 toy telescope can give you a much-improved spot size when you're pointing it at a distant hillside or whatever. It worked like a charm and cost far less than lab-grade beam expanders. I used to saw toy binoculars into two so I got two beam expanders for the price of one!
What has this got to do with thermal imaging, I hear asked by those who are still awake at this point. Well, a quick search on eBay for "CO2 beam expander" yielded beam expanders for 10.6µm CO2 lasers in powers from x2 to x8 available for prices in the region of GBP100.
Looking at the photos, they appear to have ZnSe optics.
Has anyone played with these to see if they will work as a telescope for a thermal camera?
I don't expect performance to be brilliant but for many applications I suspect that, if it works, it would suffice. I have certainly found my x3 telescope useful in certain circumstances.
The image below is taken from one of the ads for CO2 beam expanders and comes complete with the original dodgy spelling. (Their Engrish is far better than my Chinese so it's churlish to complain).