# Focusing laser beams with concave and convex lenses

1. Mar 11, 2014

### Racer_Rob

I'm trying to focus a 3mm diameter laser beam (527nm) to a 0.3mm spot size. According to this online calculator I need a +500mm focal length lens and a -50mm FL lens separated by 450mm. However, in practice this did not produce a focused spot. I'm assuming this calculator has made some simplifications which perhaps my experiment needs to consider?

Any advice of help as to where I'm going wrong would be appreciated.

2. Mar 11, 2014

### jbriggs444

So the 3 mm diameter parallel beam hits the 500 mm convex lens. This causes the beam to converge toward a point 500 mm further on. 450 mm downrange the beam has converged to a diameter of 0.3 mm. The beam hits your -50 mm concave lens and is now parallel once more, but with a beam diameter of 0.3mm

In freshman physics terms you started with an image at ∞ and produced a real image at 500 mm. That fits with a 500 mm lens. No simplifications needed. It's already quite simple.

Then you had a virtual image at 50 mm (further on from the second lens) and wanted an image at ∞. That fits with a -50 mm lens. No simplifications needed. It's already quite simple.

You had expected a "focused spot" with a diameter of 0.3 mm, right? What did you actually see?

3. Mar 11, 2014

### Racer_Rob

That's correct but I actually saw a much larger (around 2cm diameter) and out of focus spot. I tried varying the lens separations and the distance between the convex lens and the laser source but saw no improvement.

4. Mar 11, 2014

### jbriggs444

Warning: I'm no experimental physicist and have no experience with lasers. The idea of eye-balling a setup where you are trying to concentrate a laser beam to increase intensity by a factor of 100 scares the bejesus out of me. You are using appropriate safety measures, I hope.

If you reversed the lenses, that could result in a 3 cm diameter spot that would be in focus. Could this have happened?

If the lenses were shipped with a grease or wax covering, that could result in almost any out of focus behavior. Have you looked for such a possibility?

With results this egregiously out-of-whack you probably need to start testing your tools rather than questioning your setup.

Project the original beam on a screen. What's the spot size? Is it fuzzy?

Put the 500 mm lens alone in the beam and project on a screen 250 mm downrange. What's the resulting spot size? Is it fuzzy?

Put the 50 mm lens alone in the beam and project it on a screen 100 mm downrange. What's the resulting spot size? Is it fuzzy?

5. Mar 11, 2014

### UltrafastPED

I am an experimental physicist, primarily lasers and optics. I have done this sort of thing many times, and I have also taught any number of undergraduate and graduate students how to do this setup correctly. Of course it is much easier in person - then you can show and tell, and watch them check their own work. If the correct equipment is already available it takes ten to twenty minutes to guide a student through this procedure.

They also learn the value of Poisson's rings!
See http://physicsed.buffalostate.edu/pubs/StudentIndepStudy/EURP09/Spot/spot.html
and http://io9.com/5707749/poissons-spot--the-greatest-burn-in-physics

I assume that you have had proper training in laser safety, and have the correct safety glasses, and are able to attenuate the laser beam during all of the setup stages. You must also have lenses which are designed to handle the power levels that are being used.

What you describe is a telescope being used as a beam expander/compressor.
Here is the theory: http://www.edmundoptics.com/technical-resources-center/lasers/beam-expanders/

To make the beam smaller the light must enter thru the converging lens. You should construct the telescope on a small optical breadboard, with a two-axis stage for the second lens. This will allow you to adjust the centering and the focal length later. You will use the post to adjust the vertical centering.

You must also have the incoming beam perfectly centered on _both_ lenses.
You can do this with the aid of a pair of iris diaphragms:
http://www.edmundoptics.com/optomechanics/apertures/iris-diaphragms/stainless-steel-series-iris-diaphragms/1374 [Broken]

Before setting up your lenses you must generate a "sight line" with the laser beam going through both diaphragms; a greater the distance between the diaphragms allows for more precise centering. Now slowly close the first diaphragm so that "Poisson rings" are visible on a test card. These rings should be perfectly round if the beam is well centered on that diaphragm. Use these rings to center the second diaphragm; you may open/close the first diaphragm in order to generate the most useful Poisson rings at the second diaphragm.

With the beam "perfectly centered" on these "pinholes" you can now place your optical telescope in between the two diaphragms. Block the laser beam while doing this. If you have followed good technique with your optical table this placement should be pretty good. Now place the test card immediately behind the converging lens - and check the Poisson rings. Move the telescope breadboard until they are perfectly centered on the lens. For an even better alignment - check the back reflection from the forward lens surface: it should go directly thru the forward pinhole. With these two conditions met you now have the laser wavefront perfectly aligned with the converging lens. Clamp the telescope breadboard down onto the optical table loosely - recheck the centering - and then tighten a bit more: just enough so that it doesn't move around when touched.

Now move the laser test card to the back surface of the expanding lens. Use the adjusters to center the Poisson rings. When it is well centered, move the laser test card behind the second diaphragm. If the compressed beam is well centered - then you are done. Otherwise you will need to make more adjustments to the expanding lens.

Now open both iris diaphragms ... but leave them clamped in place. You will find them useful later to verify alignment. You may have to make slight adjustment from day to day.

You can also use an extra iris diaphragm which is left unclamped so that it is free to move. Set the diameter to your desired beam diameter - or you can use a fixed pinhole of the correct diameter - and slide it along the compressed beam line. Again use the Poisson rings to get its height perfect, and to get it well centered on the beam. Now test again further away - if the beam is well collimated the beam diameter will not change very much. Otherwise your beam is diverging/converging - and the telescope lens to lens distance will need to be adjusted a bit.

If you are still having trouble - then you actually have the wrong lenses! It is easy to check the 500 mm converging lens.

Let us know how things go ...

Last edited by a moderator: May 6, 2017
6. Mar 11, 2014

### Racer_Rob

Thank you both for your detailed responses. I didn't manage to get back on the laser today but I will tomorrow so I can update you on the experimental side of things then.

I've checked and double checked this, they're definitely the correct way around. I also checked the surfaces of the lenses for dirt or dust but they were clean. I hadn't thought of their being a grease or wax coating as you suggested on the new lenses so I'll check this tomorrow.

The original beam is not perfectly circular and the beam edge is also slightly fuzzy however both of these effects are slight.

UltrafastPED, the method you describe is very similar to the one I followed. I'm using a V-rail (similar principle to this for those unfamiliar) for the experiment. It has two sliders with the target mounted in a fixed position at the end of the rail.

I placed an optical mounting stick in each of the sliders and adjusted the rail until the beam struck the tops of both sticks in order to align the rail with the beam. I also marked on the target where the beam was striking. I then placed the convergent lens on the first stick and adjusted the height of the stick until the beam struck the same position on the target. With the target being a fixed distance away, the spot was out of focus but nevertheless in the same position. I then inserted the diverging lens and again adjusted the height until the beam struck the same position.

Unfortunately I don't have access to iris diaphragms or a 2-axis lens holder in order to be able to follow your method to the letter. However, I had hoped that my "short-cuts" would not prove too significant but perhaps I am wrong. I was just surprised a how incorrect the output spot was in my first experiment. Even with the lens alignments out by a millimetre or two (as I suspect mine are) I would still have imagined the output beam to be smaller than the input but this was not the case for me.

I will sanity-check everything tomorrow, including check the lenses for a wax coating and report back.

Lastly just to check my understanding...

I'm guessing the Poisson ring's I'd form would not feature the same very bright centre spot as shown in your links, but the diffraction property causing them is the same, and actually I would see a pattern more like this ?

7. Mar 11, 2014

### UltrafastPED

The Poisson rings also have a spot - it may be a dark spot, or a bright spot. This depends on the distance.
It is easiest (for the human eye) to align with the dark spot - then the ring around it is bright, and the darkened room provides excellent contrast.

With the V-rail system you should have "perfect alignment" along the rail axis. Unfortunately the fixtures applied are often not very well aligned - just good enough for student labs. The first thing to check is that you do have the correct lenses!

8. Mar 11, 2014

### UltrafastPED

The Poisson rings also have a spot - it may be a dark spot, or a bright spot. This depends on the distance.
It is easiest (for the human eye) to align with the dark spot - then the ring around it is bright, and the darkened room provides excellent contrast.

With the V-rail system you should have "perfect alignment" along the rail axis. Unfortunately the fixtures applied are often not very well aligned - just good enough for student labs. The first thing to check is that you do have the correct lenses!

9. Mar 11, 2014

### UltrafastPED

Lenses (as used with lasers in an optics lab) normally are shipped in lint-free containers, and have never had contact with wax, oil, or any other contaminant. This is not to say that they don't get dirty with handling - especially in a student lab!

I suspect something else is going on here. Perhaps the laser beam is not properly collimated, or the lenses are incorrectly labeled. The manufacturers seldom put labels on lenses - there isn't enough room, and anybody trained in optics can either measure the focal length optically, or measure the lens curvature(s) and compare with the manufacturer's specifications for a lens made of BK7, which is the most common glass in use.

We typically mark the edge in pencil with the lens code & focal length, and store them in marked containers. But mistakes do happen!

10. Mar 12, 2014

### Racer_Rob

The lenses were brand new for the experiment so I'm as confident as I can be that they are correct. The convex lens is BK7 and the concave is UV grade fused silica because this could be supplied uncoated and was needed to deal with the high fluences.

I suspect a poorly collimated laser is the problem. I tried putting some burn paper in front of the beam today. At 10cm from the laser aperture a uniform circle is produced, at 50cm it elongates to an ellipse with the major axis normal to the table, at 70cm the major axis has slightly increased and fuzzy corona shapes appear along the longer edges and at 90cm both of these features increase slightly again. At 90cm the major axis of the ellipse was roughly twice that of the circle produced at 10cm. Presumably even if I place my optics 10cm from the laser where the beam is uniform the fact it's not perfectly collimated will still appear further down range?

The purpose of these lenses was to increase the fluence which is important in the laser-polymer interactions which I'm studying. For the time being (and because I need some results for my Master's) I'm thinking of just using the convex lens and placing the sample a set distance from it where I can calculate the beam width and consequently the fluence. I'm assuming the top two equations here are all I need for calculating the beam width at a given distance once I know the minimum waist width. I presume this can be found from:

$w_{0} \approx \frac{\lambda}{\theta \pi}$

But I'm not sure on how to determine theta, wouldn't this depend of the focal length of the converging lens?

11. Mar 13, 2014

### Cthugha

Do you use a VCSEL based laser or a simple diode laser or something like that? These often have very inhomogeneous spots and -even worse - may spread differently in horizontal and vertical directions, so it is pretty hard to collimate them.

Do you have a micrometer stage, a razor blade and some powermeter? In that way you could also determine your spot size by measuring the transmitted power when moving the blade into the beam in a well determined manner.

12. Mar 15, 2014

### Racer_Rob

I'm not sure if it's a VCSEL based laser I'm afraid, all I know is it's a diode-pumped Nd:YAG laser which is really designed for Particle Image Velocimetry (PIV).

Unfortunately I don't have a micrometer stage but the power meter I have does at least show the expected power.

My plan at the moment is to calculate the distance away from the converging lens that I have to place sample to produce the desired beam size assuming a Gaussian beam which is essentially what I have at 10cm from the laser head before it starts to diverge.