Spot size at distance vs. negative focal length

Does anyone know where I can find an online calculator which will allow me to know the spot size of a laser beam at a specific distance by inputting the negative focal length of a concave diverging lens? I've googled and googled and not hitting on the answer anywhere yet.

Laser Project said:

Does anyone know where I can find an online calculator which will allow me to know the spot size of a laser beam at a specific distance by inputting the negative focal length of a concave diverging lens? I've googled and googled and not hitting on the answer anywhere yet.

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I can do that from beam angle, but I have not tried from the negative focal length. Do you have a resultant beam angle?

Thanks, no beam angle as I don't have a negative lens yet. I'm trying to determine the appropriate negative focal length lens I need to buy for use with a 10 inch diameter plano-convex objective lens with a 24 inch focal point for a uber beam expander. I suppose many different negative focal length lenses will work, just that the amount of expansion will be affected, more expansion with a shorter negative focal point.

I've been thinking about this project for months now, from time to time, and it appears to me to be able to expand a laser beam to something approaching 10 inches diameter would require more than one stage, perhaps several inter-coupled beam expanders. Since a tightly collimated laser beam from 1 to 10 mrad has such a small diameter the first lens you use with it must be small too, so that the beam falls across a good portion of the diameter of the lens, otherwise if the first lens is too big in relation to the diameter of the laser beam, the beam will pass right through the center which is relatively flat and acts more like a window than a lens. So, I'm having to balance the size of the concave input lens with the size of the laser beam and the objective lens all together, trying to figure this out.

My thought was to determine the spot size of a diverging lens at a distance, if at about 24 inches a negative lens produced a 9 to 9.5 inch spot size, it ought to work fine with my large 10 inch objective lens as a boot strap method of finding the right one but that diverging lens must not be too big either, or it won't diverge my laser beam enough if the majority of the beam is passing right through the relatively flattened center of a lens that is too big. I haven't seen any figures on the relationship of beam diameter to negative/diverging lens diameter but I'm guessing for optimum expansion the first lens should be somewhat close in diameter to that of the laser beam but due to power density limitations of the glass at high power, this might not be practical requiring the use of a larger than theoretically optimum diameter input lens and requiring more than one stage for a large expansion factor. I don't want to use more than one stage, but it appears I will have to do so if I want the beam expanded out to close to 10 inches. However, I have to figure out what is possible for the first stage to know if I need more than one stage or not.

Laser Project said:

Thanks, no beam angle as I don't have a negative lens yet. I'm trying to determine the appropriate negative focal length lens I need to buy for use with a 10 inch diameter plano-convex objective lens with a 24 inch focal point for a uber beam expander. I suppose many negative focal length lenses will work, just that the amount of expansion will be affected, more expansion with a shorter negative focal point.

I've been thinking about this project for months now, from time to time, and it appears to me to be able to expand a laser beam to something approaching 10 inches diameter would require more than one stage, perhaps several inter-coupled beam expanders. Since a collimated laser beam has such a small diameter, the first lens you use with it must be small too, so that the beam falls across the majority of the diameter of the lens, otherwise if the first lens is too big, the beam will pass right through the center which is relatively flat and acts more like a window, than a lens. Because the first lens is so small I then have to deal with a power density issue when using a 50 watt output FAP 808nm laser. I am not convinced this will work using a FAP anyway, but it does have divergence too, as any collumated laser beam so maybe there is no issue.

I just want the beam to be expanded so much that it is easily detectable at a great distance as a spotlight, not as a high power tiny diameter beam which will burn through anything, this is to make a tight but wide low divergence spot beam.

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Detectable as a spotlight...as in acting as a spotlight to put a spot on a distant target, and result in enough lux and spot size on the target to resolve details of the target?

Or detectable as in the target is looking for the spot light, and can see it?

Not to illuminate a target, but for someone at a distance to be able to see it. I'd like to TTL modulate the signal at some point in time and send data across it.

Laser Project said:

Not to illuminate a target, but for someone at a distance to be able to see it. I'd like to TTL modulate the signal at some point in time and send data across it.

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OK.

Would this apply?

Focal length - Wikipedia, the free encyclopedia

Hi, saw that earlier. I was hoping there was a calculator I could find online somewhere so I could put in some variables and have the answer spit back each time to get an idea of the right negative lens to use to project a spot covering most of the diameter of the 10 inch PCX/plano-convex lens I have in a position which is close to 24 inches from it, it's focal length. Guess I will have to pull out my calculator and do it the hard way but I'm so new to optics I have a lot to learn to even do that.

I have one of these FAP lasers, the one shown in this YouTube video does not have a big lens hanging off of it, just a small fiber coupling lens and as you can see, the beam expands a lot in a short distance. Perhaps I don't need a diverging lens in front of a PCX objective lens with as much divergence as this output has? https://www.youtube.com/watch?v=s-Kkg0pxKO4 - Or, maybe I have to have a fully collimated laser beam to start out with and then shoot that through a diverging lens to expand it and recollimate it once more to reduce the divergence. Most of this is magic to me right now, perhaps why I am attracted to lasers.

Any and all advice appreciated, even if only speculation.

Thanks

Here's the output or objective lens I want to use which is 10 inches diameter

Could you just do a mock up and see where it all falls?

Here's what I came up with:
Spot size = ((distance from lens)/(Focal length) + 1 ) * (initial beam diameter)

Distance of 0 means you have the initial diameter
Distance of 1 focal length means you have twice the initial diameter
Distance of 2 focal lengths means you have three times the initial diameter, etc.

That makes sense, thanks, I will work the numbers from that and later do a mock up. I still wonder if a diverging lens is necessary if the output of the cutting lens or FAP800 laser module I have diverges so much on its own, once past the focal point (or fiber output) with such a lens anyway. Anyone know? Or must the beam be tightly collimated first before passing through a concave divergent lens paired with a PCX lens to reduce the divergence from the expansion and re-collimation when using a Galilean setup?

Chris

You can use this tutorial and online calculator that I found a year or so ago. It uses the ray transfer matrix analysis for computing divergence and beam size. Note that the angles are in radians, not degrees (radians = degrees * pi/180).

Laser Project said:

Does anyone know where I can find an online calculator which will allow me to know the spot size of a laser beam at a specific distance by inputting the negative focal length of a concave diverging lens? I've googled and googled and not hitting on the answer anywhere yet.

Click to expand...

Here gausian beam rev 2.0.xls
If you need help just let me know

Thanks again, appreciate the info Steve and Bionic-Badger.

I'm starting to get a clearer focus on this issue, to so speak. I believe the reason I cannot find a calculator which will spit out how wide a spot would be produced from a concave lens with a certain negative focal length (at a specific distance away from it) is because it also depends on how much divergence the light entering the lens has as well as what the diameter of the beam entering the lens is too. Time to just buy a negative lens and see what it does.

Laser Project said:

Thanks again, appreciate the info Steve and Bionic-Badger.

I'm starting to get a clearer focus on this issue, to so speak. I believe the reason I cannot find a calculator which will spit out how wide a spot would be produced from a concave lens with a certain negative focal length (at a specific distance away from it) is because it also depends on how much divergence the light entering the lens has as well as what the diameter of the beam entering the lens is too. Time to just buy a negative lens and see what it does.

Click to expand...

Try that app. It has a graphical presentation
Assume two numbers to input in the first two boxes. Those two numbers are 0.
001 and 10. It's a fun app to use once you understand it.

I'm all thumbs with it right now, will have to look at it for awhile to see if I can get what I'm looking for out of it. I'm an electronics technician and engineer at work, but with optics I'm a fish out of water now.

Ugh, that site with the Flash needs to update its plugin code for modern browsers. It only worked in IE for me.