Desktop Michelson-Morely Interferometer

Over the years I've had to measure some unusual processes in systems, and one of the most common 'tough' problems has been the measurement of displacement. For mm-scale motion I've used mice (mechanical and optical) to record movement, but I once found myself needing to record nanometric scale displacements and so I was led to interferometry.

An interferometer is not something that interferes with meters, nor a method for measuring between iron things. Instead, it is the use of phase differences (which cannot be easily measured) and the wave-like properties of light to form measurable changes in intensity (which can be easily measured).

Here I'll describe how I built a Michelson-Morley interferometer.
Is it useful? Maybe.
Is it awesome in that you can watch nanometer-scale phenomena? Ooh yes.

Step 1: The Parts List

You'll need;

1) A cheap laser diode - red is good, green is better.
I used a 5mW diode that I had bought from Roithner Lasertechnik in Austria many years ago - but I have no reason to believe that a cheapy 3 dollar laser pointer from the local dollar store wouldn't work as well. Actually, there will be reasons, but they lie outside the scope of this article and you can have a dig around with the keywords of 'spatial coherence' and 'astigmatism'.

2) Some single-surface mirrors - I bought half a dozen on eBay for a few US dollars.
These are fancy mirrors that have a highly reflective aluminium coating on one face of a glass slip. They prevent multiple internal reflections, which would occur with normal glass-faced mirrors.

3) A beam-splitter
I bought some de-lasered blue-ray drive heads on eBay, and found a pair of beam-splitter cubes among the teeny tiny spangly bits inside.

In the image you can see the parts.
The two single-surface mirrors are each glued to a piece of aluminium right-angle extrusion that hjave been spruced up with a black permanent marker.

The laser and beam-splitter are glued to two lengths of scrap aluminium, to make positioning a little easier and to ensure that the laser and beam-splitter are at the same height.

Step 2: A Little Theory

The idea behind all of this is that the laser light is split into two separate paths. The beams travel along these paths and then recombine.

In most situations, when you add one thing to another, well you simply add the amplitude of the 'things'.

Put a cheese infront of a cheese-o-meter, and it would read '1'.
Put two cheeses infront of a cheese-o-meter, and it should read '2'.
(yeah yeah - squish the two cheeses together and you have one cheese - it's a bad analogy but it makes me smile)

But, critically, with two cheeses infront of it, the cheese-o-meter never should display zero. It doesn't matter how you arrange them, side-by-side, one on another, the meter should read '2'.

But light can demonstrate wave-like properties. And anything that oscillates can, at any given time, can be said to have a phase with respect to some other thing. I'll explain.

The phase simply describes how far the oscillating thing is along its path, with respect to some other point. Consider two perfectly bouncy balls.

A bouncing ball may be said to be 'in phase' with another similarly excited ball if the two both reach the apex of their bounces at the same time. A fancy way of saying that is that their phase difference is zero.

If the two balls are dropped from the same height at different times, then they will strike the ground at different times, but that difference will not change for subsequent bounces. One might say that their phase difference will be a constant.

Clearly, the balls could be dropped so that one is at the top of its path when the other hits the ground. The balls' motions are then in anti-phase: when one is doing one thing, the other is doing its opposite.

So - back to the two light beams alluded to earlier. If one light beam takes a slightly longer path than another light beam, then when the two are brought back to the same point, there will be a phase difference between the two. If it helps to think of something associated with each beam wiggling back and forth while it travels, well, good for you, but don't imagine that it's the full truth.

Because the wavelength (ie, distance between wiggles) is very very small for light, it doesn't take very much displacement for two beams to end up completely in anti-phase with each other.

And that's where the cheese come in.

See, because cheese hasn't got a phase, it always adds in a simple way.
1+1 = 2

But the electromagnetic fields that make up light have a phase (with respect to other light fields). So if one light beam is in anti-phase with another, when I add them the sum is zero.

So two light particles can be combined to give '0', and '2', and any number in between when shone into a light-o-meter (such as an eye, or a camera).

The fields in a light beam are always oscillating - they wiggle back and forth while the light propagates forward.

Thus, if one light beam is split into two rays, and if the rays cover different distances before recombining, the two rays will have different phases. And unlike cheese, they can cancel each other out, or they can add together.

(phew!)

Step 3:

So here's a theoretical picture of how it should all work.

The laser's ray is split into two paths. One goes north to Mirror 1, one goes east to Mirror 2.

If the path taken by the northbound ray is of a different length to that of the eastbound ray, then when the two rays recombine at the eye / camera / screen, they will have different phases and will display an interference pattern.

No optical rig is perfect, so the rays won't precisely cancel each other out, nor will they exactly boost their amplitude. Instead one should see a fringe pattern of light and dark bands, and the position of those bands will move according to how the 'legs' of the interferometer are changed.

Step 4: The Arrangement

I used a sheet of 6mm thick polycarbonate plastic as the 'optical bench'. It fails quite well in that role, and in a sense, that's a good thing - as it allows one to observe the effect of *tiny* deformations on the intereference pattern produced.

Here's the arrangement.

Now, this all looks very pretty, but the point to observe is the striped pattern at the bottom of the picture.

This is the interference pattern generated by the two rays, and it is an incredibly finicky thing to establish - expect a good half hour of gently poking and tilting the elements till you glimpse this faint but unmistakable banding.

That is being projected onto an almost-horizontal piece of white card. I tilted the card so that the interference pattern would be broadened out and the fringe motion would be more readily observed.

The second picture is a contrast boosted view of the image on the white card.

In the movie you can see the effect of gently poking the polycarbonate 'bench' with a bit of heat-shrink sleeving (I'd have used a feather, but I'm fresh out of them).

What you're seeing is the weak and feeble tubing bending the 6mm polycarbonate. You can't see it actually deflect, but you're altering the relative path lengths of the two legs of the interferometer.

Step 5:

So, there you have it.

A way of measuring nanometric disturbances.

Every time that a bright band is swapped for a dark band, the path lengths of the two rays in the interferometer will have been changed by exactly 1/4 of a wavelength. For red light that's a shade over 100nm.

Now the question is how to engineer a way of generating controlled disturbances at that scale - and for that we'll need a feedback loop and a transducer! But that's another project - enjoy!