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# Question for the optics savvy in regard to beam expansion to reduce divergence.

#### lazeristasUVISIR

##### Active member
If you want a 1 mm speck on the moon, it's certainly possible to use a lens to focus the laser--essentially making it non-collimated, so we increase the spread in angle to decrease the spread in position. The governing quantity for how small you can focus the beam with a lens is the f-number: the distance between the lens and the focus divided by the diameter of the laser beam when it enters the lens. So, you could place a small lens close to the moon so the beam is focused rapidly to the 1 mm spot, or you could place a huge lens on earth so it converges over its entire journey to the moon.
Would like to know how big is that lens to get a spot of 1 mm on the Moon :drool: (I'm lazy to calculate myself

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##### Well-known member
LPF Site Supporter
I've wondered how far I can converge a beam to a small point using a 12 inch diameter lens, but haven't dived deep enough into the formulas to find out. I was able to get through an intense electronics degree program using math approximations, but since then, haven't had to use much of it again.

#### lazeristasUVISIR

##### Active member
I've wondered how far I can converge a beam to a small point using a 12 inch diameter lens, but haven't dived deep enough into the formulas to find out.
You need to tell a focus length of this lens.
Do you want to use it as a single collimating lens?

Building a telescope should give you a better divergence.

#### Cyparagon

##### Well-known member
I've wondered how far I can converge a beam to a small point using a 12 inch diameter lens...
You'd be approaching a diffraction limited system. The absolute minimum diameter of the spot is equal to the wavelength of light itself, under perfect conditions. This is why a BRD holds more data than a DVD.

#### steve001

##### Well-known member
I've wondered how far I can converge a beam to a small point using a 12 inch diameter lens, but haven't dived deep enough into the formulas to find out. I was able to get through an intense electronics degree program using math approximations, but since then, haven't had to use much of it again.
In the manner you've asked the question the diameter isn't important. The focal length is.

##### Well-known member
LPF Site Supporter
I should have wrote PCX lens if the flat side faces the outside, same issue, FL? What is the best lens for a beam exander, a aspherical lens? I've read a post where the lenses in order of best are: 1. Aspherical 2. PCX 3. Bi-convex. True?

#### steve001

##### Well-known member
I should have wrote PCX lens if the flat side faces the outside, same issue, FL? What is the best lens for a beam exander, a aspherical lens? I've read a post where the lenses in order of best are: 1. Aspherical 2. PCX 3. Bi-convex. True?
Link to that post please. I been looking into your question it's one that i have asked myself. I've not found an answer. I suspect it may not matter at all. I think for our purpose of creating a low diverging beam using lens that are easily mountable would be pcx and double concave or PCB lenses. The important thing to keep in mind is one lens should have as short a negative focal length as practical and the positive should have an appreciably greater focal length. For example : use a -6mm and 30mm would give a 5x expansion.

##### Well-known member
LPF Site Supporter
I found the original post, did a cut and paste:

Krazer:

It of course depends on your application, but for an application where you are taking a collimated beam and focusing it to a spot (as would be used for a telescope or diode collimator), a bestform will outperform a plano-convex which will outperform a bi-convex. You can do better with a doublet (such as an achromatic lens), and for monochromatic light you can always do the best with an aspheric lens.

The difference between a bestform or achromat or ashpere has to do with the level of optimization applied to the lens design. When designing a plano-convex lens your only degree of freedom (for a given focal length and optical material) is the lens thickness, and for almost all applications it works out that the thinnest possible lens will perform best. When designing a bestform lens the lens maker has 3 main degrees of freedom, the curvature of input/output faces and the lens thickness. When designing an achromat you have even more degrees of freedom, there are the input/output curvatures of each optical element, the thickness of each optical element, the spacing between them, and the material they are each made of, which allows the lens maker even more freedom. With an ashpere the lensmaker is no longer constrained to using spherical surfaces, so there is a virtually infinite number of degrees of freedom (a typical asphere will have about 10 coefficients that determine the shape of the surfaces).

You can try playing with OSLO (a limited edition is free for students) http://www.lambdares.com/oslo-university-program which will directly give you plots of the lens performance for different optical designs.

#### steve001

##### Well-known member
I found the original post, did a cut and paste:
Ok. So it would appear that a pcx lens would be the first choice for use in a beam expander, since the goal is to produce a beam of lower divergence and it's easier to mount.

##### Well-known member
LPF Site Supporter
If you want a very large fairly inexpensive collimator for a beam expander a PCX lens is the way to go, but I'd prefer an aspheric lens if I could find a large three inch diameter one with 1/4 wavelength accuracy to its curve, not finding them.

I like my beam expanders to have a collimator lens with several inches diameter.

#### Theodore41

##### Member
If we use the NUBM44 diode,is the Sanwu 3X expander enough,or we need 5 or 10X?

##### Well-known member
LPF Site Supporter
For close to 1.5 mRad divergence which is the most divergence I personally will consider acceptable, you would need an expansion factor of about 8X with that laser diode when using a G2 lens, or similar lens.

#### RedCowboy

##### Well-known member
Enough for what? If you want to extend your bench top burning to across your workshop to say....ignite cardboard at 25 feet then yes it's enough.

The NUBM44 has horrible divergence but you can use a 3-element lens with the 9mm to BE adaptor and set the 3 element to a sharp focus at about 50 feet then screw in your 3X BE, I have locked down the 3-elements focus by loosening the heat sink set screws and pushing the module back then tightening the set screws, it helps to back off the 3-elements focus about an 1/8 turn to take up the thread slack when you snug it back down after tightening down your set screws to hold the focus.

Once you have your 3-elenemts lens locked down focused to a sharp line at about 50 feet you can screw in your 3X BE but because of the NUBM44's horrible divergence you will get too long of a line if you use a G2 so it's better to use the 3-element, however you can use a NDB7875 with a G2 locked down to a focused line at about 50 feet which is essentially infinity then screw in your 3X BE and get pretty good results if you want to extend desktop burning fun across your workshop.

To get the 44 into really tight shape I use a Sanwu G2, 6X cylindrical pair and the 3X BE, the standard G2 wont work with the 3X BE after 6X C lens correction because of the focal length, it's a small difference but it matters.

#### Theodore41

##### Member
For close to 1.5 mRad divergence which is the most divergence I personally will consider acceptable, you would need an expansion factor of about 8X with that laser diode when using a G2 lens, or similar lens.
And which BE of suitable expansion factor do you suggest please?

#### Theodore41

##### Member
Thank you very much RedCowboy.

##### Well-known member
LPF Site Supporter
My interest in low divergence is just to see my beam go out into the darkness of the sky without expanding much, not burning. I haven't been buying beam expanders for that laser diode, what I do for that diode is to defocus my small 6 mm diameter G2 lens so the spot is the right diameter to use with a larger PCX or plano-convex lens at its FL in front which re-collimates the beam back to infinity focus.

If you go searching for a BE just to reduce the divergence to have as little spread as possible in the deep distance, you just need to make sure the diameter of the beam isn't too large for either the beam expander input, or the total resulting expansion so the beam isn't clipped inside the tube, that and that the input lens AR coating, if it has one, won't burn.

If you are going to build a poor mans BE as I have by adding a PCX lens in front of a defocused collimating lens, I'd recommend a PCX lens which is well over 50 mm diameter, probably 60mm will work for you if the spot size is 50 mm diameter but the focal length must be long enough to allow the beam to be defocused that large of a diameter into that lens. If you have a laser pointer with that diode, try defocusing the beam to see how far out the PCX lens needs to be from it to produce a spot size that large without clipping inside the 6 mm lens holder tube, then find a PCX lens which has a diameter of close to 60 mm with a focal length about the same as the distance to the spot on a wall to produce a 50mm spot diameter.

If you want to get a PCX lens cheap for this, look on ebay for condenser lenses used in photography, you can find them at 3 inches or larger diameter cheaper, you don't need to use the whole diameter of the lens for the beam expander but the FL is important.

This lens might work: https://www.ebay.com/itm/Enlarger-Russian-condenser-two-lens-diameter-58mm-2-4-inches-1/282756125289

The NUBM44 laser diode can produce ugly wings, I've been able to eliminate them by using a PCX lens which has a diameter of twice the beam it is collimating, not sure it needs to be that much bigger, I think RCB might be able to give you a better estimate on diameter to reduce or eliminate wings, he's done a lot of work with them.

I have some reservations, regardless I've written this response for others who might come this way.

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