# Laser Sheet Optics

1. Jul 8, 2013

### TerraForce469

Hello,

I've been helping a graduate student out with his project which is planar laser-induced fluorescence. Part of the procedure involves generating a laser sheet with which to illuminate over the flame under study.

Now, typically a usual procedure involves using a beam expander to spread the beam out followed by a cylindrical lens to focus the beam along a projected line.

But now, my question is, would this procedure be possible using only spherical lenses, e.g. double convex lenses, plano concave, plano convex?

And what are the equations involved to quantify these relationships between the source and the optics? I don't think that the regular $$\frac{1}{f}=\frac{1}{d_0}+\frac{1}{d_i}$$ equation will be applicable as we're talking about a collimated light source.

Any advice would be greatly appreciated.

2. Jul 8, 2013

### Andy Resnick

Not unless you are scanning the beam. Maybe if you had an ungodly amount of astigmatism...

3. Jul 8, 2013

### TerraForce469

By scanning, do you mean deflection of the beam so as to sort of steer it? Sorry, I don't exactly get what it quite means...

4. Jul 9, 2013

Yes.

5. Jul 9, 2013

### TerraForce469

But then, how would that possibly aid in creating a thin laser sheet?

6. Jul 10, 2013

### Andy Resnick

I envision an f-θ optical system (no cylindrical optics) producing a gaussian beam with a Rayleigh range somewhat longer than the dimension of your imaging volume- the beam will be approximately constant diameter through the imaging volume. Then, scanning the beam (using a galvo, rotating mirror, etc. located at the appropriate plane) will linearly scan the beam through your imaging volume.

7. Jul 13, 2013

### TerraForce469

Ah, I have never heard of this set up, but it should be interesting enough to consider.

How wide is the image scanning range usually for an $f{\theta}$ system? Does it only work for a specific wavelength as well as repetition rate of the laser, e.g. pulsed or CW?

Thank you so much for your input on the matter!

EDIT:

I've been trying to come up with an optical setup for an adjustable laser sheet, i.e. able to vary the length of the sheet. I get that spreading the sheet would lessen its power per unit area, but I just don't know whether there are commercially available optics to be able to do this kind of stuff already...

Last edited: Jul 13, 2013
8. Jul 14, 2013

### Andy Resnick

9. Jul 16, 2013

### TerraForce469

We are looking to illuminate a pre-mixed OH flame and collect the fluorescence emitted by the OH. This is a typical planar laser-induced fluorescence setup, which consists of an Nd:YAG, dye laser, and wavelength extender. The output is a ~300 nm laser beam with about. Take laser beam diameter is about 4 mm.

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Alright, let's forget about the constraints and consider a regular laser sheet optical setup.

We would normally use a cylindrical plano-concave lens to expand the beam and a spherical plano-convex lens to collimate it. The thinnest possible laser sheet width is at the focal point of the spherical lens, which should be less than the beam diameter. I also want to be able to image the 2D profile of this flame, so I need to make as thin of a laser sheet as possible. I should probably add a cylindrical lens somewhere in this optical setup, but I’m not sure whether it would be better to place it before or after the spherical lens.

Any thoughts? Should I just keep to the simple two-lens setup or would it help to add another lens to better achieve my purpose?

10. Jul 17, 2013

### Andy Resnick

Let's back up a bit- the beam post-lenses can't have certain properties in excess of the 'original' beam. Specifically, if the beam is Gaussian (which it probably is, but I don't know what the 'wavelength extender' does), the product of minimum beam waist (ω) and beam divergence (θ) is constant. If you expand the beam (increase the beam waist), you decrease the divergence ('collimating the beam')- and vice-versa. You provided a measure of the waist but not the divergence. The product ωθ is important to determine because it will set a constraint on your probe volume- how 'thin' the laser sheet is, and the length over which the sheet is sufficiently thin.

But you haven't specified the probe volume, either.

Here's an example- say the original beam has a waist of 2mm and divergence of 1 milliradian. Then, if I want a laser sheet with a minimum (half-)thickness of 0.05mm, the divergence is 40 millirad, meaning the laser sheet is .45mm (half-) thick 1cm away from the 'best focus'. Does that meet your spec? Another way to specify the probe volume is that the sheet thickness does not vary by more than 50% over than 1 cm distance, and that will provide a bound on the minimum thickness.

Next- you are using a wavelength of 300nm. This *severely* constrains the suitable materials, meaning the optical components are going to be expensive. Also, since the wavelength is not visible, do you know how to align the optics?

IMO, based on the contents of this thread, you are well-advised to simply use a cylindrical lens (you still need to calculate the focal length that will result in a suitable probe volume).