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Collimation - Down the rabbit hole

Junkers

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Or at least it feels that way...

A while ago I got my FAP800 up and running and managed to melt some powdered Aluminium and Stainless steel with it - happy days. However, I did this with the collimator I purchased from Ebay. At the time what I didn't realize was that my collimator was set 2 focal lengths away from the point source hence it was behaving as a focusing lens. When my focal lens actually arrived and I tried to setup my collimator properly I ran into some issues. The beam was still highly divergent when setup 1 focal length away from the point source and therefore the focusing lens (plano-convex f=100mm) wouldn't do its job. It would narrow the beam and produce a clear image of the source (the beam projected by the collimator) but was far from what it needs to be (spot size of 8-10mm). I realize why this is but now am in the depths of figuring out what it is exactly that I need to correct this issue.

Now I know from reading on these forums that FAPs have terrible beam quality and therefore require some 'heavy' beam shaping to get them usable. I've read Alaskan's posts and spoken to him personally but still need help making the right decisions and building a clear understanding for myself. I've also been rummaging around the internet to try and gain a better understanding of the parameters at play but can't rid myself of an intuition that I know to be wrong, but not as to why.

My issue relates to selecting the right aspheric condenser for my setup. I've roughly measured the half angle at FWHM which turns out to be 14.5 degrees ~ NA 0.26. Yikes. I notice that aspheric condensers state their maximum NA and it's matching this that I'm having issues with. My intuition tells me that the outer rays (marginal?) cast from the point source need to be incident on the outer edge (90% or so) of the plano side of the condenser as the steepest radius of curvature exists there and therefore will have the best ability to straighten the beam assuming that it doesn't pass the critical angle . Therefore the NA of the condenser needs to be roughly the same as the point source (slightly larger) to ensure that the projected cone covers most of the lens.

But then I saw this on the Thorlabs collimation tutorial:
A good rule of thumb is to pick a lens with an NA twice of the NA of the laser diode. For example, either the A390-B or the A390TM-B could be used as these lenses each have an NA of 0.53, which is more than twice the approximate NA of our laser diode (0.26). Note that these lenses each have a focal length of 4.6 mm, resulting in an approximate major beam diameter of 2.5 mm
This doesn't fit in with my understanding at all and therefore my knowledge is lacking. Can somebody please help me to better understand this problem?
 
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Junkers

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Yes. If a beam is diverging from the point source, the incident light rays on the condenser are bent due to the refractive index of the lens and the exit point, i.e. the curvature at a particular point relative to the incident ray, from the lens... if I understand things correctly? Based on what they're stating, you should double the NA of your lens which would result in a bigger lens diameter for a fixed focus length. That would lead to the marginal rays not utilizing the sharper curvature of the outer lens thereby not bending the light to the same degree. Why would they suggest that?
 
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Junkers

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Hmmm... I think I have just realized something after looking at the cross section of an aspheric lens. The sharpest curvature of an aspheric lens is closer to the optic axis than it is to the outer lens. Maybe this is why it is recommended to use an NA twice that of your source?
 

Singlemode Laser

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Doubling the NA won't double the beam size, the beam size will stay the same (Only the focal length matters). They recommend 2xNA because 1xNA means that 5% of the beam are clipped and diffraction errors and imaging errorsare introduced. With 2xNA you don't have this problem.

Singlemode
 

Junkers

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When I said bigger diameter for a fixed focus length I was referring to the lens, not the beam. Posting pictures would really help right now...
 

Junkers

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And we've hit 20 posts! Picture time...

fig-3-aaa.gif

The points circled in orange have the greatest ability to bend light as far as I understand (assuming the incident light ray doesn't internally reflect due to the critical angle being exceeded). A lens with double the NA for a fixed focal length will be twice as big in diameter (making an assumption here) and therefore the marginal rays will be closer to the optic axis as the projected cone isn't any larger but the lens is twice as big (or thereabouts). Because of that, at least in the case of the plano-convex lens, the marginal rays won't take advantage of the steepest gradient/curvature. Therefore, there is lesser chance of achieving collimation if you have a particularly divergent beam. I didn't understand why Thorlabs would suggest that but now considering the aspheric profile it's making more sense... unless my thinking is totally wrong.
 

steve001

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And we've hit 20 posts! Picture time...

View attachment 67606

The points circled in orange have the greatest ability to bend light as far as I understand (assuming the incident light ray doesn't internally reflect due to the critical angle being exceeded). A lens with double the NA for a fixed focal length will be twice as big in diameter (making an assumption here) and therefore the marginal rays will be closer to the optic axis as the projected cone isn't any larger but the lens is twice as big (or thereabouts). Because of that, at least in the case of the plano-convex lens, the marginal rays won't take advantage of the steepest gradient/curvature. Therefore, there is lesser chance of achieving collimation if you have a particularly divergent beam. I didn't understand why Thorlabs would suggest that but now considering the aspheric profile it's making more sense... unless my thinking is totally wrong.
I read most of your posts but did you state your objective? I believe what is being said are two things: avoiding beam truncation and spherical aberration.
 
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Junkers

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First paragraph sets the scene. Third paragraph is the problem. I want to focus a collimated light source but I'm struggling to do so due to my current collimator not being up to spec - the beam is still too divergent and the resultant beam waist is too large. I'm trying to pick a better lens to collimate with but don't really understand what parameters I should be focusing on if I have a highly divergent beam.

I thought that having a lens NA that closely matches your source would be important but it seems this isn't so. Can anyone explain why and perhaps what I need to collimate a highly divergent beam so I can achieve a decent beam waist (<0.2mm).
 

Singlemode Laser

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I still don't understand what's your problem is and why stuck with the NA question here, it was answered now multiple times in this thread. I suggest GOOGLE in this case for you.

Regarding your lens that is places 1 focal lenght away: This will collimate a point source but you want to focus it. Try 2x the distance.

Singlemode
 

Cyparagon

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All else equal, a shorter focal length makes for a smaller focal point.
All else equal, a larger initial (collimated) beam diameter makes for a smaller focal point.
All else equal, a smaller emitter size (in this case, that's going to be your fiber diameter) makes for a smaller focal point.

So if you have a large diameter fiber which only reaches a maximum of 3mm before focusing to a point 10cm ahead, you're going to have poor results.
 

Junkers

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I'm stuck with NA question because it hasn't been answered yet. What makes you think I haven't made an effort to Google this?

SingleMode Laser said:
They recommend 2xNA because 1xNA means that 5% of the beam are clipped and diffraction errors and imaging errorsare introduced. With 2xNA you don't have this problem.
Yes, 2xNA will obviously prevent clipping and diffraction errors etc, but it will also under utilize the greater beam shaping capabilities of the lens. This is what I'm struggling to understand. Why would you throw away the most relevant aspects of a collimating lens as a rule of thumb? Couldn't the issues you mentioned be avoided with only 1.x NA lens while achieving tighter collimation by better utilizing the sharper curvature of the lens? I'm guessing this is all dependent on the initial divergence of the beam but there doesn't seem to be any formula relating the NA of the beam to the NA of the lens.

Just to highlight what I'm getting at, and disregarding the physical impracticality - why not a lens NA of 4x, 6x, 8x, or 16x.. eventually you would end up passing the beam through something that resembled a flat plane of glass with no beam shaping capabilities at all. It seems to me that the NA of the lens and the NA of the incident beam hold key information as to how well a divergent beam is collimated. If my observations are correct, then how do I best select the lens NA for a highly divergent beam?
 

Singlemode Laser

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I'm stuck with NA question because it hasn't been answered yet. What makes you think I haven't made an effort to Google this?



Yes, 2xNA will obviously prevent clipping and diffraction errors etc, but it will also under utilize the greater beam shaping capabilities of the lens. This is what I'm struggling to understand. Why would you throw away the most relevant aspects of a collimating lens as a rule of thumb? Couldn't the issues you mentioned be avoided with only 1.x NA lens while achieving tighter collimation by better utilizing the sharper curvature of the lens? I'm guessing this is all dependent on the initial divergence of the beam but there doesn't seem to be any formula relating the NA of the beam to the NA of the lens.

Just to highlight what I'm getting at, and disregarding the physical impracticality - why not a lens NA of 4x, 6x, 8x, or 16x.. eventually you would end up passing the beam through something that resembled a flat plane of glass with no beam shaping capabilities at all. It seems to me that the NA of the lens and the NA of the incident beam hold key information as to how well a divergent beam is collimated. If my observations are correct, then how do I best select the lens NA for a highly divergent beam?
I have the feeling you are troll, and won't post anymore in this thread.

Singlemode
 

Junkers

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Thanks Cyparagon. I calculated the spot diameter incident upon my original collimator to be 5.2mm (half angle of 14.5 deg, F=10mm). From that I gather a beam expansion of 6.5 (5.2mm/0.8mm) should have dropped my divergence down to a half angle of 2.23 deg. That wasn't enough to achieve a decent focal point so I guess I'm in the market for a collimator with a longer focal length.

Singlemode - do you honestly think I like repeating myself only to be met with condescending comments? May I suggest COMPREHENSION in this case for you.
 

steve001

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First paragraph sets the scene. Third paragraph is the problem. I want to focus a collimated light source but I'm struggling to do so due to my current collimator not being up to spec - the beam is still too divergent and the resultant beam waist is too large. I'm trying to pick a better lens to collimate with but don't really understand what parameters I should be focusing on if I have a highly divergent beam.

I thought that having a lens NA that closely matches your source would be important but it seems this isn't so. Can anyone explain why and perhaps what I need to collimate a highly divergent beam so I can achieve a decent beam waist (<0.2mm).
So your objective is to focus a laser beam. It's simple then. Expand the beam by allowing it to expand naturally or by placing a negative focal length optic followed by a positive focal length optic in the beams path. It's practical to use two lenses. The wider a beam is expanded the smaller the focal point diameter.
Laser beams don't have an NA. The focal point is not a beam waist.
You can have NA's of any number but why? For example you have a beam of X diameter. Placing a lens in the beams path with the recommended NA will be enough to do the job. In other words a NA of 4x is overkill for practical reason too.
 
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