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practical tips for optical interferometry

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Dr. Slack

Mon Jul 27 2015, 03:16PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

I would like to measure some sub-micron displacements remotely and absolutely, with resolution better than 100nm, ideally 10nm. I should manage to resolve a red light fringe shift to that, but have no need for huge accuracy, so don't need an accurate wavelength for the light.

I've come across all the theory at school and for my degree, but never got my hands dirty actually doing it. I can forsee a number of pitfalls, so would appreciate any practical tips from anybody who has done it.

a) are red laser pointers adequate for coherence? I'm thinking both across the beam (which could be fixed by using a pinhole, if so how big) and in time (so how much path difference is allowed?)

b) beam splitters? make or buy? I can buy 45 degree glass prisms for a reasonable price (work this one out, there's a UK supplier that does roughly polished prisms for Â£2.50, and optically finished ones of similar size for Â£1.80, uh?). I understand the airgap between two would need to be in the order of a wavelength, so sub micron, even for red light. I know a cigarette paper is about 25um thick, so way too thick. Spacing just one side with a paper would give me a wedge gap which would be correct at some point across the width. Are there any other much thinner but easy to get materials, or other ways of spacing. Squidging out superglue would not work as its n is in the same order as glass, what low index glues do get used? Unfortunately, cheap prisms like these don't specify n, so I would need to measure after buying. I can buy ready made two prism beam splitters, but they are much more money, and I have long pockets and short arms.

c) are there cleverer, but potentially less accurate ways than the straightforward Michelson-Morely type two arm interferometer?

Ash Small

Mon Jul 27 2015, 05:25PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

Can you get the 'sub-micron displacement' to displace a mirror by a small amount?

You've not given a great deal of detail, but there is a classic experiment used for measuring C which uses spinning mirrors.

You only have to displace a mirror by a very small amount in order to be able to accurately measure the displacement of the reflected photons.

(I'm assuming a very small mirror)

Wastrel

Mon Jul 27 2015, 05:37PM

Registered Member #4095 Joined: Thu Sept 15 2011, 03:19PM
Location: England.
Posts: 122

Stability over time will be an issue especially for a red laser diode. The prisms will need to be optically flat to a fraction of the wavelength of light.

How fast is the displacement moving? Could you use the gap as a variable capacitor?

Dr. Slack

Mon Jul 27 2015, 07:00PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

What I had in mind was the displacement moving a mirror, which changed the length of one of the MM interforemeter arms, so in fact the ligth path length changes at 2x the mirror displacement.

The displacement is being used to vary a capacitor, the point of the optical method is to give me an independent method to cross check the capacitance method.

I guess the question is really 'can I do optical interferometry for Â£10 with a few clamps on a carpentry bench, or do I need to build an optical bench and spend 100x that?'

Newton's Rings may well be a cheaper and more cheerful way for doing what I'm trying to do.

...

Mon Jul 27 2015, 07:19PM

Registered Member #56 Joined: Thu Feb 09 2006, 05:02AM
Location: Southern Califorina, USA
Posts: 2445

For the beam splitter, you are better off buying a functioning beam splitter, ideally one which is as close to 50% reflection as you can get. One option is to buy a 'real' one (will cost $100-200 from a reputable manufacture), you can also dig around on ebay and the likes to find a used one. Be careful though, most of ones are taken from cd/dvd/etc drives and are actually polarizing beam splitters which will not work correctly (if you split the beam into orthogonal polarizations you fundamentally cannot interfere them). That said, this guy was able to get his interferometer to work with the cube out of a blueray drive

For a proof of concept you can use a simple uncoated piece of glass (such as a microscope slide) which will give you about a 5% reflection. This is enough to see some interference fringes, but the contrast will not be great. Upgrading to a dielectric mirror with ~50% reflection will work correctly if you can scrounge one (if you pull apart enough cd/dvdroms drives you will probably find a suitable mirror). For these applications you need not worry about matching the phase in both paths (using compensator plates and whatnot) since you will not be operating at the zero crossing point anyway.

For the laser, even the crappiest of laser pointers will have a coherence length of a few hundred micrometers, so as long as you are careful to match the path lengths they will work. The usual 660nm ~5mW laser diodes are a good choice and usually have a coherence length of at least a mm or so. ex

The spatial coherence will be fine, so long as you make sure the that laser is well collimated.

The trickiest part is the alignment, you need to have the beams sufficiently parallel that over the beam diameter (~1mm or so) the wavefronts are overlapped to within less than a wavelength (ie, <100nm, corresponding to ~0.1mRadian), while also keeping them overlapped spatially with eachother. You can probably get away with something hacked together using screws and springs, but ideally you will want to buy/make some decent optical mounts. You might look to

for inspiration.

Finally, the real tricky part will be getting a stable interference pattern that does not drift away. At the very least you will need to use a solid metal baseplate (5mm thick should be sufficient for an interferometer with path lengths of a few cm, anything longer I would look into the usual 10-20cm thick baseplate). Furthermore you should try to mount the assembly on some sort of vibration isolation (rubber sheet, etc), and mount it in such an arrangement that if the table it is sitting in flexes the baseplate does not also flex (the simplest way to do this is to single support the assembly on short/fat post, more advanced techniques involved balancing the table in a series of balls and slides).

Ash Small

Mon Jul 27 2015, 08:13PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

How long does the displacement take? Is all this on a concrete floor? Do you have large trucks going by outside?

I think maybe more info would be useful

Should be possible, laser theodolites are pretty accurate over some distance, and I suppose you are using similar technology, but you'll have to isolate everything from vibration, I suppose.

Interferometry may be theoretically more accurate, but will it actually be more accurate than a simple 'deflected laser' or whatever in practice?

Carbon_Rod

Tue Jul 28 2015, 03:25AM

Registered Member #65 Joined: Thu Feb 09 2006, 06:43AM
Location:
Posts: 1155

Sam's Laser FAQ would be the best place to start:

Some use a glass sand-box on air inner-tubes for floating-slab vibration isolation. Optical benches are now usually machined aluminium, but a surfaced CNC Mill Tooling Plate is cheaper and can be a carbon steel (magnets are nice).

Cube beam splitters with AR coatings may still require incident beam dumps (

). Note, some splitters out of optical drives may have polarizing filters and or unwanted apertures.

Cheers,
Rod

Dr. Slack

Tue Jul 28 2015, 10:15AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Handy link, thanks.

Looks like too big and too sensitive a yak to shave just to get somewhere else. I'm surprised by the short coherence length of a laser pointer, but I guess there's no reason to expect more than the order of length of the lasing cavity itself. With alignment, I'd be wondering which of too many reasons was causing a null result.

I have a micrometer screw mount, which I'll use to position my capacitive sensor, and measure/confirm its response at a few points, and then use the sensor to resolve the small movements and interpolate the calibrated points.

Wastrel

Wed Jul 29 2015, 05:42PM

Registered Member #4095 Joined: Thu Sept 15 2011, 03:19PM
Location: England.
Posts: 122

You can get low power SLM laser diodes that will do holography. 10m+ coherence length.

I'm not sure the application is right. If you can do fringes, then a sodium lamp is probably fine. You only need a coherence length of the order of 1um.

If you can use a lever to reduce the micrometer movement to 1 in 10 or lower, that might be the best way.

Shrad

Sat Aug 22 2015, 11:14AM

Registered Member #3215 Joined: Sun Sept 19 2010, 08:42PM
Location:
Posts: 780

please have a look at

you will find designs to make homemade external cavity laser diodes with extended coherence length, and spectrometers with decent resolution

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