Measuring the focal length of a deformable lens

[almueller32]

Hello all,

My lab recently purchased a deformable lens, which can change its focal length from 140 mm to 40 mm and anywhere in between, based on current applied to it.

I'm wondering how to use a beam profiling camera to measure the focal length of this lens at various current levels. We have a 767 nm laser to use for this.

 

[Simon Bridge]

Welcome to PF;
how would you normally use the BPC to measure the focal length of a lens?

 

[almueller32]

I really don't know; it has something to do with the Gaussian intensity function. As in I take 2 images and somehow that parameterizes the equation and I can solve for focal length, I guess? I'm not sure. Grad students in my lab know it is possible but aren't sure how either, so of course the job fell to me as an undergrad to find out!

 

[Simon Bridge]

OK - so this is a question about "how to use the BPC"... not about variable focus lenses.
Good.

You'll get better cred if you actually figure it out than have someone tell you ;)
You've tried the simple stuff: i.e. have you got a manual?
Bear in mind the manual is unlikely to have a section entitled "how do determine the focal length..." you have to be able to match the picture you get to optical properties, which means you need to understand how it works.

How would you normally measure the focal length fo a lens without a BPC?
Compare that approach to what the BPC does.
i.e. what sort of thing does the BPC tell you about the beam?

 

[UltrafastPED]

You should learn how to use the beam profiler with the laser beam alone first; be sure to attenuate the beam in accordance with the user manual.

If you don't know what you are doing, get someone to show you. In our laser lab you must be trained by an experienced user prior to using any piece of equipment. The rule is: Learn first!

 

[almueller32]

UltrafastPED: I do already know how to use the BPC with the laser beam alone.

Simon: without a BPC, measuring the focal length would consist of using an IR card to see where the beam is most focused. The BPC tells me the dimensions of the beam and its intensity throughout the profile, so the narrowest profile with high intensity in the middle would be a focal point. But I can't simply slide the camera along until I find that spot...

 

[Simon Bridge]

... but you can change the camera position wrt the lens to take two sets of readings right?

If you have width w1 distance d1 from the lens and you have width w2<w1 a distance d2>d1 from the lens... then where is the focus likely to be? (assuming a well-collimated input beam)

 

[almueller32]

Yes, I can. Ok, so the focal point would be closer to the second position than the first, but based on that information you still couldn't say whether it was between the two positions or past the second.

 

[Simon Bridge]

So you'd need to draw on other information to make the determination right?
i.e. do you know the beam width at the lens? Do you may even have some idea of how far away the focus length is ... i.e. inside the lab, meters away, centimeters?

You can choose d1 and d2 to help narrow down the probabilities.
Worst case, you have two possible locations and you need another reading to confirm.

 

[almueller32]

I think I may have it: measuring in two spots fairly close together so as not to bypass the focal point would allow me to determine theta, the divergence, and if I know the beam width at the lens, then I can use f=d/theta to find the focal length! Does this sound plausible?

 

[Simon Bridge]

That's good enough for now - you should start with some idea of where the focus is anyway - if you think it through right.

If you can factor in the beam width at the lens, then you actually have three sample widths.
The rest is the art of choosing positions far enough apart to get low errors.

 

[almueller32]

Yes, I do have an idea of where the focus is because I already plotted a curve of the focal length response to current just by using an IR card (by hand) to find the focal point.

Any suggestions to improve my method?

 

[Simon Bridge]

Well, since you have a fair idea - well done btw - you can arrange to take your two readings so they are pretty much guaranteed to be either side of the beam waist - or on one side, whichever you feel comfortable with. Like if your preliminary inaccurate tests show the focus to be between 20cm and 70cm, you can take width readings at 5cm and 100cm... or 100cm and 150cm... see what I mean?

This sort of incremental narrowing down is a characteristic of science - you never start from zero information.

The farther apart the readings, the smaller the error in the waist position.
... so don't forget to work out the errors: that usually impresses people.

Naturally make sure you know the geometry of the input beam.
Equally - the more reading you take the more accurately you can locate the waist.