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02-06-2012, 05:42 AM #1
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jbe
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Distance of laser focus?

Hi yall, newbie here. Ive been lurking for a while and decided to join.

Main thing Ive been wondering is, is there a limit to how far one can focus a to?

For example, would it possible to focus a laser to like 5 light-seconds or so?

02-06-2012, 05:47 AM #2
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Sigurthr
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Re: Distance of laser focus?

5 light-seconds in vacuum is 931,411.985 miles. I don't think we (as a race) could create a lens with a 931,411.985 mile focal length.

Why, what are you planning to point at that is nearly one million miles away?
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02-06-2012, 07:01 AM #3
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Wolfman29
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Re: Distance of laser focus?

Interesting. I never knew that a laser's focus was only within the focal length. Question, then: when one focuses further than the focal length, it is not entirely focused then, is it? I mean, it's certainly easy to get a point of focus that is ~50 feet away without actually being focused "to infinity." So what defines the size of the spot beyond the focal point?

02-06-2012, 07:19 AM #4
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Sigurthr
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Re: Distance of laser focus?

Focusing to infinity is just where the lens is in the right position so that the divergence of the beam is nearly but not entirely canceled out by the convergence of the lens. When set to infinity the beam is actually diverging very slowly. It isn't coming to a focal point at all because the beam isn't actually converging. IIRC to do this the lens has to be placed closer to the laser emitter than the lens's focal length. Placing the lens the exact distance away from the laser emitter as the lens's focal length sets the focal point the farthest out possible.

If you used a divergent beam with a very large diameter and a converging lens with a slightly larger diameter you should be able to achieve a very low divergence or a very far focus (based off the focal length of the lens) - this is the principle behind the beam expander. The stronger the convergence of the beam/lens the closer (shorter) the focal length. The lower the divergence of the beam and the lower the convergence speed of the lens the farther (longer) the focal length.

If any of the above is wrong please do not hesitate to correct me. The only reason I know these thins is the reading I have been doing the last few months. I'm still quite new when it comes to optics, and only have a basic grasp on the subject.
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Last edited by Sigurthr; 02-06-2012 at 07:22 AM.

02-06-2012, 07:34 AM #5
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Wolfman29
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Re: Distance of laser focus?

Yeah, that's all right - I understand that and all. But what about when you are not within the focal length of the laser, and not focused "to infinity," but instead focused about 50ft or so out? What's the phenomenon there?

02-06-2012, 07:45 AM #6
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Sigurthr
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Re: Distance of laser focus?

Increasing the distance between the lens and the emission point beyond one focal length away should just bring the focal point of the beam closer to the lens.

Now that I think about it, I think I may have read something stating that when the lens is one focal length away from the emission point there is more complex math involved in determining the focal point of the beam but I'm not sure.

Give me a complex schematic any day, optics friggin' blow my mind.
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02-06-2012, 07:54 AM #7
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Re: Distance of laser focus?

Yup. Electronics are easy... optics are crazy.

Anyway, thanks for the insights.

02-06-2012, 08:00 AM #8
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Sigurthr
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Re: Distance of laser focus?

Glad to be able to shed some (unfocused) light on the subject. (pun intended and quite cheesy)

I still *feel* lost when it comes to optics, utterly lost. You'd think that seeing the effects of basic optics, refraction, diffraction, and reflection all our lives would impart a basic sense into our heads, but no, it certainly doesn't. We can intuitively calculate trajectories subconsciously, but figuring out a simple two lens setup sets neurons on fire, haha.
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02-06-2012, 01:42 PM #9
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jbe
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Re: Distance of laser focus?

Thanks yall, Im not trying to do anything like this just wondering about some of the stuff NASA and ESA are doing. Check these out:

ESA Science & Technology: Spacecraft

A 1W laser at 5,000,000 km?! Im pretty sure theyre using the lasers to remain fixed to detect gravitational radiation. Would they need to focus it that far or would focusing to infinity do the trick?

NASA - Laser Communications Relay Demonstration (LCRD)

" A typical optical signal, however, will only spread over the equivalent of a small portion of the United States; thus there is less energy wasted."

So obviously, the NASA LCRD wont be worrying about focusing it down very small.

Whats the farthest possible one would be able to focus a laser today with unlimited government funding? What limits us right now? Will it ever be possible to focus a laser to focus a laser out to this type of distance and still have a reasonable amount of energy density left, say enough to be used as a weapon?

Also, is there a limit to the energy density of a laser? I know Pauli doesnt exclude photons but would lasers be any different? I heard of an experiment where they collided a laser and a beam of electrons(both very energetic) and the electric field started generating particle pairs. They said this would catastrophically destroy the beam(interrupt it) in future lasers that were intense enough, without the collision with electrons. Would there be a way around this?

02-06-2012, 05:50 PM #10
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DrSid
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Re: Distance of laser focus?

Diffraction is the problem. At no distance you can focus laser into point. It is always spot. But if you focus closer, the spot is smaller. As you move the focus distance further, the spot will increase in size. Generally double distance - double spot size. This then fluently transforms 'infinity case' .. beam is parallel at aperture (collimated beam) but soon transforms into divergent cone.

Check the beam shape at this page (the red curve somewhat bellow on the page):

Gaussian beam - Wikipedia, the free encyclopedia

When using convergent focus at aperture, the waist of the red curve is the focus point .. when using parallel focus at aperture, the aperture becomes waist of the curve.

You can improve the focus by increasing aperture size, or shortening wavelength of the radiation.
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02-07-2012, 09:16 PM #11
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jbe
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Re: Distance of laser focus?

Yes I know it will never be infitesimally small, and I know of Gaussian beams and that focusing to infinity will give the least possible divergence. But, if one had a huge aperture(50m+) and something like far-UV or shorter, would it be possible to focus out to say 100,000km? Would it be possible in the next century or so?

Also, do you ever see lasers becoming used for anything besides point defense weapons? What is the most efficient laser, as far energy input vs output? What would be the best wavelength to use for a weapon needed to penetrate a hard target (i.e. Steel) in the atmosphere and in a vacuum?

Also, as I said earlier, I know Pauli doesnt Exclude photons, but would be there be any limits to reaching an energy density as high as practically possible(eventually a black hole would probably form)? Would a laser thats intense enough start pair production and destroy the beam?

Sorry for all the questions I just dont know very much about lasers besides the basics. Thanks in advance if you reply.

02-08-2012, 12:29 PM #12
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DrSid
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Re: Distance of laser focus?

I took the formulas from wiki and I found some interesting things. I'd like someone to verify this.

First I had to somehow grasp those 2 different situations. Collimated beam, and close focus .. and transition between them.

For collimated beam with best divergence, there is rather simple formula on the wiki. Aperture of the laser acts as waist of the beam profile, the beam then expands and after some distance it expands in linear fashion.

1) divergence = 2 * wavelength / (pi * aperture)

For close focus I simply swapped spot and aperture. So first we compute divergence (or better convergence) at the aperture, when focusing at some distance:

2) divergence = aperture / distance

Now we use reversed formula one, to get waist size .. ie smallest spot size.

3) spot = 2 * wavelength / pi / divergence

Now the interesting facts. The close focus spot size increases in linear fashion with distance .. at speed of divergence of collimated beam ! I never suspected this. You can simply use first formula to get divergence of collimated beam, and then use it for close focus too. You simply multiply distance by divergence and that's it. This can also be easily derived from the formulas above. The unified formula, no matter if what distance you use, close or far, should be:

4) spot = distance * 2 * wavelength / (pi * aperture)

And one last useful formula, simply derived from the last one. Close distance is distance, at which the spot has same size as aperture. Useful for estimating burning ranges.

5) close distance = (pi * aperture ^ 2) / (2 * wavelength)

Now some examples ..

Common laser pointer:
Wavelength: 550nm
Aperture: 1mm
Close distance: 2.85m

Airborne laser (thingy in my avatar):
Wavelenth: 1315nm (Chemical Oxygen Iodine Laser, megawatt range)
Spot at 600km (expected kill range for liquid fuel missiles): 0.313m
Spot at 300km (expected kill range for solid fuel missiles): 0.156m
Close distance: 3058km
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Last edited by DrSid; 02-08-2012 at 03:59 PM.

02-09-2012, 04:53 AM #13
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jbe
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Re: Distance of laser focus?

So youre saying that after the beam waist, the focused laser will have the same divergence as the parallel at aperture(collimated) laser? How come this isnt witnessed in handheld lasers?

02-09-2012, 11:59 AM #14
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DrSid
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Re: Distance of laser focus?

Not sure what you mean .. but let me give an example:

You have collimated beam with divergence 1mRad .. ie at 1km the spot will be 1m in size.

This is divergence, when beam is focused to infinity.

What I'm saying is that you can use this divergence to compute minimum spot size for any focus distance. If you focus this laser to 1m, the spot size will be 1mm. If you focus to 10cm, the spot size will be 0.1mm.

Will paint picture later but I'm quite busy atm.
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02-09-2012, 12:26 PM #15
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Re: Distance of laser focus?

Quote:
 Originally Posted by jbe Yes I know it will never be infitesimally small, and I know of Gaussian beams and that focusing to infinity will give the least possible divergence. But, if one had a huge aperture(50m+) and something like far-UV or shorter, would it be possible to focus out to say 100,000km? Would it be possible in the next century or so? Also, do you ever see lasers becoming used for anything besides point defense weapons? What is the most efficient laser, as far energy input vs output? What would be the best wavelength to use for a weapon needed to penetrate a hard target (i.e. Steel) in the atmosphere and in a vacuum? Also, as I said earlier, I know Pauli doesnt Exclude photons, but would be there be any limits to reaching an energy density as high as practically possible(eventually a black hole would probably form)? Would a laser thats intense enough start pair production and destroy the beam? Sorry for all the questions I just dont know very much about lasers besides the basics. Thanks in advance if you reply.
Do you work for the government or you just one of those backyard scientists, like the kind on that TV show?

These are pretty complex questions to be asking on a hobbyist laser pointer forum.

02-09-2012, 12:51 PM #16
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DrSid
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Re: Distance of laser focus?

Ok .. here is teh picture ..

1) large scale diagram. Laser is focused to infinity. The beam steadily diverges in linear fashion at some angle. We call this angle divergence, measure it in radians. Since the angles are very small, tangent of the angle equals its size in radians. So while we say it's 1mRad it generally means for each meter it spread 1/1000 of meter.

2) close view of the laser focused to infinity. The linear divergence does not describe shape of the beam well at close distance. The beam is parallel at aperture, and only slowly transforms into cone.

3) close view of laser focused to some short distance. The beam converges to some point. But the beam diameter will never be zero, the beam will form waist with some minimal size, and then expand again.

4) close view of laser focused even closer. The waist size will be smaller than in previous case. Now what I'm saying is that the minimum waist size increases with focus distance at same linear rate as the beam does, when focused to infinity (the gray lines).

So the divergence of the collimated beam has two uses:

1) it tells us spot size at distance, when the laser is focused to infinity. It does not work for short distances though. Useful for long range pointing, signaling, distance measurement.

2) it tells us beam waist size (minimum spot size) for beam focused at some concrete distance. Useful for burning.
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