What a great response. You’re the best!
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Basically light does not focus down to a infinitely small point. There is a limit determined by the wavelength. CO2 light has a wavelength an order of magnitude bigger than visible light so the effect is significant.
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Seriously? Did you do the math for the formula used that the drawing attempts to explain? Or any of the math in that article?
Where in the DOF formula does the diameter of the beam stay constant while also progressing toward the limit of the DOF? As the math shows, it’s a continuum. There are no mathematical cliffs where the diameter stays constant. There are no physical cliffs either except at the micron level as I noted originally. The “straight bit” in the picture is an artifact of a simplified explanation of the concept of depth of field. It isn’t meant to demonstrate a constrained beam field.
For someone who was berating another poster’s inaccuracies, this seems exceptionally sloppy if not possibly intentional obfuscation or misdirection.
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No it isn’t absolutely straight but relatively straight compared to a cone. If it was a cone you would get a point of infinite power density which would be great for cutting! In practice there is a limit to how small it gets, about 0.2mm in this case. Far away from focus it will be a close to a cone shape but close to focus it looks more like a real hour glass.
As you pointed out there can’t be any discontinuities in curvature, so given it starts as a cone, has a minimum waist before diverging again as a cone of follows the waist must flatten out and become parallel at the actual point.
The actual equation is shown here: https://en.wikipedia.org/wiki/Rayleigh_length
And looks like:
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To elaborate on palmercr’s reply above:
As I’ve posted before the waist size is listed in the specs of a laser. (The waist size is the minimum cross-section of the beam in the laser cavity.) This is because it is a fundamental property of the laser and determines many other properties of the beam. Focusing a laser beam does not change this property, you will always get a waist, and never a point.
For more information about the properties of laser beams I would refer people to this article:
The article is specific to a ‘Gaussian Beam’ which is what you get if the manufacturer of the laser took care to make sure the laser produced this fundamental mode and not a higher harmonic. It’s called the TEM00 mode. (The laser cavity is a resonant system and as such supports multiple wave modes. An acoustic analogy might be a drum.) The GF specs used to note the that the TEM00 mode was produced:
And there have been posts before that this is not the standard for hobby lasers:
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Well said…
I think a huge part of the problem is that you have responses from people who actually have a GF, have real experience in the real world, and they are trying to help new and old forum folks alike with questions and challenges. Then you have one or two folks who regularly expound on would’a-could’a-should’a about the GF who have never used one and are working from 2nd and third hand hearsay answering those questions and and challenges with nothing but guess work and ill-founded assumptions. I would say the former is of value – the latter not so much…
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Apropos of absolutely nothing…do you guys know the song “Buckle Down Winsocki”?
For some reason that darned thing is running through my head this morning and I absolutely can’t get it out…and I have no idea where I heard it.
Hate it when that happens. 
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LOL. Those one or two you refer to know so much more about the machine than any of us. Have you not followed all the posts?
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Let’s not forgot another type of response that is fairly common:
Those that expend much effort on condemnation of others, but never seem to provide anything of substance to the conversation.
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It isn’t necessary to own a GF to understand the physics of laser beams as it is well documented on the Web and GF cannot break the laws of physics. And, given the beam is about 8 thou in diameter at the waist, does it seem reasonable that a few though away from focus it will be much different in power density?
I don’t see why pointing out reality is “dour and off-putting attitude” or negativity. It is simply how it is.
Gotta jump in here. I just finished binge-watching the Star Trek reboot triplet. Still wiping the tears from my eyes.
@palmercr is clearly the Spock character in this drama. Superbly logical. Doesn’t always understand the emotional blowback to his statements. But ultimately seeks to understand a viable pathway to the success of our mission.
@scott.wiederhold is the quintessential Scotty character. Knows every nook and cranny of the Enterprise. He knows just what buttons to push in a tight spot.
I’m thinking @rpegg is Bones. No nonsense. Rolls his eyes at Spock privately. But perhaps the most grounded character on board.
So who do you think are the others? Sulu, Chekov, Uhura?
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Yes some of my oldest friends, Porg and Trog, call me Spock.
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Obvious…I’m a tribble. (Look at the icon.) 
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So your new picture is about beam diameter and the “waist” at the focal point not about the distance on both sides of the focal point that your first picture showed as a “straight bit”. But your new picture shows the “straight bit” as the appropriate gradually increasing curve of increased beam diameter. And you’re now suggesting that “relatively straight compared to a cone” is justification for your original “misinformation” about the straight bit.
I don’t have a problem with your conclusion that a few thousandths of an inch is not likely to have an impact on the performance based on the science. My issue is how you came down on @dwardio’s post for containing an error of a few thousandths but when you proffer something similarly erroneous it’s okay because it’s relatively straight compared to a cone.
It just seems like a double standard of judgement when others are concerned. That’s what I believe fired up the other posters coming down on you about this.
Again, as I said, I agree with your conclusion about @dwardio’s assessment, just not about the defense that you were simply correcting misinformation with further misinformation of your own. It wasn’t necessary.
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This is what the beam diameter looks like over 10 thou.
Was it misinformation to call it flat?
It is 0.8% bigger at 0.25mm.
This is how it changes over 10 hundredths.
So my assertion it needs to be a few hundredths out to have any noticeable effect is borne out by the formula.
Got irritated a couple times here. Sorry, accidentally shot myself full of Cordrazine.
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You don’t like me. I get it. Move on.