Long distance ~2km invisible laser

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That is so aptly put across!
I fully understand now what is possible.
Should I say what is the minimum spot size I can achieve at 2 km with present day available options?
Is it 400mm as you say?
Why can't the beam expander be 20x or 40x to get it even smaller?

Thanks, I really appreciate your effort!

I'll weigh in some regarding a 40X expander, if you have one with a wide enough input aperture (and output collimator diameter for that much expansion) to use with a 2mm wide laser beam, the beam width would then be expanded to more than 3 inches, 2mm x 40 is 80mm, of course. Sure, it will reduce the divergence or the amount the beam spreads as it travels forward, but now you have a 3+ inch diameter fat beam on its output which only gets bigger as the beam travels forward.

You can use this online spot size calculator to determine the size of a spot at a given distance for a specific mRad: pseudonomen137's JScript Diameter Calculator

As a rough example which is closer to what you will probably be dealing with, if you had a 5mm diameter IR beam, which is a more reasonable diameter for IR, and had an initial divergence of 3 mRad and shot it through a 40X beam expander, your beam would be expanded to about 200mm (5mm X 40) and at 2 km of distance the beam would diverge to be about 350mm wide! This figure is if the optics were theoretically perfect, I'm not sure you could achieve close to that in the real world.

A member went through some calculations here in the past to come up with some reasonable real world divergence numbers for a diode I was interested in using and due common optical imperfections, the best he figured I could get using a single mode IR diode (which has much less divergence than the above example) using an expander with a 10cm/100mm wide output lens would be about .05 mRad. Even if having an extremely low divergence such as .05 mRad, 2km away the beam will expand to twice that diameter to be about 200mm. The thread where those numbers were run can be found here: http://laserpointerforums.com/f49/10-bucks-via-pp-individual-who-calculates-me-95521-2.html

I don't know, I'm a bit confused about the final figures given in that thread because first we were talking about the best divergence we might get with a single mode IR diode with a 1x3um emitter size, then a Blu-ray single mode diode was thrown into the mix with a statement due to optical imperfections the best divergence which could be had using a 10cm diameter lens with a 405nm diode was perhaps .05 mRad, but what about the 1x3um emitter sized single mode diode which is much smaller? Maybe someone with more experience in this area here can help figure this out better for you, this would be helpful for me too because I am unsure of what the results would be using a single mode diode with that small of an emitter, maybe much lower divergence with a far smaller diameter lens?

Out of curiosity - how much power do you need?

BTW, you can try to a Gaussian optics variation when the beam is focused in between ~1km.

Anyway, you should be more open and realistic with specs - how large, weight, power. Will it be a commercial product? A student project?
Otherwise, yes it's possible :na:
https://www.youtube.com/watch?v=-a4E6tnOIxY

I've been wondering if using the correct lens a beam can be focused to a tight spot in the far distance, but when I asked other members I was told that isn't possible at great distances. Are you saying at close to 1 km this is possible? How about at much further distances if the collimating lens has the right diameter?

You just need to be realistic about a spot size, a distance, a lens (optical system), and a source.
Russian were doing similar research as the US army about shooting flying objects like 30-40 years ago. Their conclusion was that it was possible but not practical, and there were other ways to do that (shooting).
Apart military applications, scientists use tight beams in lidars. Telescopes are commercially available at Laser Beam Expanders - Optical Surfaces Limited | Optical Surfaces Limited
Just don't ask about a price, you'll not like it

I looked at their page, that's what I need to build, an off-axis parabolic beam expander for the R,G,B project I want to build someday, would take care of the focus problem I would have with the different wavelengths and reduce the loss too. Now to google how to build one, if I can get the parts, I know I don't want to afford the price of a high quality one like they make.