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.


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!

<p>Hi,</p><p>What laser is suitable and how to select laser for such project?</p><p>I tried with red laser pointer and got no interference picture.</p>
Pavelkh,<br><br>Lasers are not 'one-size-fits-all'. One criterion is their coherence length - this is the distance over which the laser light is coherent (and therefore can produce interferencde).<br><br>But having said that, I'm very surprised that even a simple laser pointer wouldn't be sufficiently coherent.<br><br>For the record, I bought this one from Roithner Lasertecnnik in Vienna. But it's nothing special - 2mW, glass lenses - but certainly not 'laboratory' grade.<br>:(<br><br>Wish that I could be more helpful!<br>
<p>Could you recommend a cheap laser for this project giving a link on amazon or other retailer. Or specs that I should look at selecting a laser.</p><p>Thanks</p>
<p>Great project. Presumably an excessively bright laser with perhaps a focussed lens to recolumate the reflection might alow real world objects to replace the target mirror on the measured end? </p><p>I guess the beam splitter would need biasing or the reference mirror might need an ND filter or something so the fringes are visible compared to the total brightness of the pattern. </p><p>I have a 200mW laser itching for a project, this might be just the task.</p>
<p>Where do you get single surface mirrors, an ebay search didn't return any results at all?</p>
I pulled them from the optics of dead CD drives.
<p>Where do you get single surface mirrors, an ebay search didn't return any results at all?</p>
<p>Dear jrcgarry,</p><p>I love your simple Michelson interferometer!</p><p>As you write, I tried to buy single surface mirrors on ebay, but I couldn't find. Could you help me what is the correct keyword for this?</p><p>I ordered a beam splitter on Aliexpress, I hope it will be good also for this:</p><p><a href="http://www.aliexpress.com/item/1pcs-Beam-splitter-50-50-16-5-21-5-1-1mm/32403113899.html" rel="nofollow">http://www.aliexpress.com/item/1pcs-Beam-splitter-...</a></p><p>Thanks a lot,</p><p>Miklos Vass</p><p>high school physics teacher</p>
<p>Try &quot;first-surface mirror&quot; or &quot;FSM&quot;</p>
<p>What if you squished two different types of cheese together and tried the cheese-o-meter? :)</p><p>Very nice demo. I think I'll be scrounging some materials and giving it a try!</p>
<p>James, thanks for the article. Now to build an optical bench with stages for the beam splitters.</p><p>gb</p>
Wow, fabulous explanation, finally I understand how distance is measured with light. Thanks a lot.
Well, in many applications that use optical methods for measuring distance, a simple geometric approach is used with *no* use of interferometry For example, in a CD, the focusing lens is continually moving up and down to track the 'bumpy' surface of the reflective layer in the disc. The distances involved can be as large as 1mm (warped disc) but the lens is moved exceedingly rapidly using a voice-coil arrangement with an accuracy of a few microns. All of that is controlled simply with geometric optics. http://electronicdesign.com/article/components/measure_micro_displacements_using_a_cd_s_optical_pickup_head.aspx Is the reflected spot small and tight or big and blurry?
It is theorized that the interferometery system can be used to detect spacial dilation/compression, such as graviton bombardment or interaction with dark matter. Very cool that we can make these from home now! 5/5<br />
Absolutely right - there are several laser-based gravitational wave detectors operating around the world. They use the same principal, but bounce the beam back on itself many times, each time the minimum detectable shift halves.<br /> <br /> As partial inspiration I&nbsp;did indeed borrow the idea used in Greg Bear's Eon of a portable space-time flatness meter (a 'pi-ometer' if you will).<br />
Is there a reason, then, that we can't send the beam through another splitter and mirror assembly to achieve the same result? or does it need to travel the exact same distance?<br />
After the beams have been split by the beamsplitter, they can each travel along any path you desire (down a fibre, bounced back and forth among mirrors). The pattern of interference fringes depends only on the *difference* in length of the two paths taken by the beams.<br /> <br /> More accurately, the fringe pattern depends on the fractional number of wavelengths that the beams have in their paths.<br /> <br /> Say that one beam travels 1cm. The number of wavelengths in that distance;<br /> = 0.01 m / 650 x 10^-9 m<br /> = 15384.6<br /> That's how many full 'cycles' the electric field in the light beam makes in travelling that distance.<br /> <br /> Say that the other beam travels 1.1cm, the number of wavelengths in that beam is;<br /> 0.011m / 650 x 10^-9m<br /> =16923.08<br /> <br /> The difference between these two 'numbers of wavelengths' is 1600 or so, but what dictates the type of interference is the fractional wavelength difference. In this case that difference is just over half a wavelength.<br /> <br /> The interference pattern for a difference of 0.5 wavelenghths is exactly the same as one for a path difference of 1.5 wavelengths, or 2001.5 wavelengths.<br /> <br /> Imagine, you've got one 'wave' and you slide another of the same frequency along side it. They'll match shen you slide the 2nd wave a distance of n wavelengths - the interference depends only on the fractional mismatch.<br /> <br /> Hope that I've made it clearer!<br /> <br /> <br />
Gronicle,<br /> Please check out <a href="http://www.britastro.org/iandi/manning1.htm" rel="nofollow">http://www.britastro.org/iandi/manning1.htm</a>.<br /> It shows how an interferometer is used to control a ruling engine.<br /> <br /> Enjoy<br />
Remarkable!<br /> <br /> A&nbsp;lovely piece of work there - thanks papa-ralph!<br /> <br /> Naturally, there is scope for improvement (PM tubes - wow) - but as one who has made crude gratings in the past, I&nbsp;heartily say that this is a lovely starting point for a machining rig!<br />
This is interesting.&nbsp; As an amateur machinist I am used to working to .001&quot; degree of accuracy.&nbsp; Now your comments about using interferometry for lathe and mill work have my head spinning.&nbsp; Something like this mounted to the tool post on a lathe would give you a heck of a run-out checker on chucks, and the odd old rifle receiver that you just squared off....&nbsp; Now how do I add some sort of read out scale and calibrate it??&nbsp; Drawings or pictures would be very nice.&nbsp; Regards, Gronicle
Hi,<br /> <br /> Well, sometimes I&nbsp;imagine that absolute measurements are less useful than relative ones.<br /> <br /> For example, I've some equipment being built right now that requires a plate of 300mm width to be flat and plane to better than 0.03mm (roughly one of those 'thou' things that I&nbsp;hear about). <br /> <br /> A good digital or mechanical clock gauge would be fine for this, but even in its current state my desktop MM interferometer gives you 1/4 lambda (550 nm) precision = 0.0005 mm, almost one hundred times better.<br /> <br /> If you needed an absolute separation measure, you'll need to mount a mirror to the workpiece and then perhaps use an electrical contact between the tool and piece to detect the datum zero. Then, count fringe changes - that's the easy bit - any photodiode and an ADC board would allow a PC&nbsp;to monitor the brightness of a section of the fringe pattern.<br /> <br /> Note, a standard CD drive will give you sub-micron precision, and there's already a convenient rotating table in the middle of the drive assembly, and a radial slideway!<br />
I think I could also imagine that relative measurements may be more useful at times than absolute measures.&nbsp; For me that would be the situation when lapping a newly made part to make it fit with other older parts that are themselves no longer within specified dimentions.<br /> <br /> Metric is fine and easier to work in than feet, inches, and eighths, which is what boat builders still tend to use in USA.&nbsp; You don't mention the width or depth of your plate under construction but 300mm to 0.03 should be quite straight forward with a shaper such as my old AMMCO 7&quot; bench model.<br /> <br /> Thanks for the ideas on measuring a work piece on a lathe or mill.&nbsp; I shall have to ponder that for a while and probably try to build one to really see if I understand it.&nbsp; CD drive with cheap already make components for use is attractive.<br /> <br /> I don't do barrel building for rifles, but can alread see how the MM interferometer could be set up on a floated rifle barrel and linked with a PC to record and map vibrations of barrel when rounds are discharged.&nbsp; Might be interesting to see how barrel virbration relates to accuracy of rounds fired.<br /> <br /> Thanks for the feed back.&nbsp; Appreciate it.&nbsp;
Indeed, holding 0.03mm over a (circular) 300mm plate isn't too challenging, but interference methods would certainly allow for another order of magnitude to be readily achieved.<br /> <br /> Well well - not that I'm in the business of needing such tolerances really.<br /> <br /> Now, your idea of recording barrel flexure is interesting - I&nbsp;would suggest an interferogram arrangement.<br /> <br /> http://starryridge.com/mediawiki-1.9.1/index.php?title=Bath_Phase_Shift_Interferometer<br /> <br /> This will certainly visualize plastic deformation of the barrel after a shot - for a green laser 1/4 lambda is only 1000 atoms.<br /> <br /> But, what one would like to do is to record the distortion over a face of the barrel *during* the firing process. Not impossible, and requiring *only*&nbsp;a very fast camera and a rather bright laser.<br /> <br /> I&nbsp;would imagine that something in the tens of kilo-frames-per-second range will show the 'bulge' of the round passing long the barrel, and such frame rates are almost in the commercial range.<br /> <br /> http://en.akihabaranews.com/21231/image/casio-unveils-1-000fps-compact-cameras<br /> <br /> However, you can rent streak cameras for not too much, and as long as you have enough photons, you'll get an image.<br /> <br /> Sounds like a lark!<br /> <br /> (as for the CD&nbsp;drive idea, I&nbsp;was toying with using one as a very small lathe - the magnetic suspension of the laser lens doesn't give much travel along the lathe's axis, so that would need to be altered...)<br />
JRC,<br /> <br /> Your idea about acquiring a very rapid frame camera to actually picture the &quot;buldge&quot; in a rifle barrel as the slug travels would be a lark.&nbsp; I suppose I was trying to think of a more basic approach.&nbsp; <br /> <br /> Basicly, set up an interferometer (IFM) along the lines of the one desceibed mesuring the defection of the rail road rail in the museum.&nbsp; Get the IFM readings sensed using your idea, and converted to a pluse plot patterm at a high frequency rate for capture on a PC.&nbsp; Hopefully, this could be plotted to whatever scale is needed for visual examination, storage and future overlay/comparison with other &quot;takes&quot;.&nbsp;&nbsp;&nbsp;<br /> <br /> The fun part would come in testing a series of loads as well as free-floating and point constrained barrels to see which conditions produce the best accuracy at at given range.&nbsp;&nbsp; Long range shooters and bench shooters in particular go to a lot of trouble to get accuracy.&nbsp; In the one area of barrels people play with a lot of things.&nbsp; Re-boring old barrels that have been shot out and gone through many heat/cold cycles to releave stress in the barrel.&nbsp; Muzzle crown, Free floating vs. constrained or point loaded barrels.&nbsp; Lots of Ju/Ju in where and how much point pressure to put on a given barrel to make it shoot more accurately.<br /> <br /> The basic one demensional IFM plot might not tell me anything system if all data points plot for randomness.&nbsp; A two demensional or double IFM set up would give richer infomation.&nbsp; And by then I would be trying to get the computer boys at work to do some programing for me.&nbsp; Probably, this has all been done big time at Aberden proving gounds and the info is published in DITEC or somewhere If I looked.&nbsp; But this would be for fun.<br /> <br /> Exactly what size of lathe are you thinking of making?&nbsp; Anything small enough to shave &quot;nanos&quot; off of any material will be a real challenge!&nbsp; Work holding, vibration in the work area, just handling work pieces!&nbsp; Or do I have the wrong idea on size and are you thinking something more like a watch makers lathe with nanos for precision in cutting?<br /> <br /> SSK
Feel free to take this to private email (jay arr cee at hotmail dot com) if you like - otherwise we'll fill the comments page!<br /> <br /> Now - one problem with a simple IFM&nbsp;as it stands is that if you simply glue a mirror to the barrel, you can't distinguish between the barrel bending to one side (unlikely, but...)&nbsp;and the barrel actually expanding. A whole host of harmonics will be excited by the round, and some of those, and the nonuniformity of the barrel will cause bending *and*&nbsp;expansion/contraction waves.<br /> <br /> I'll think about this for a bit - what you really want is a pair of mirrors on opposite sides of the barrel in such a way that the diameter is sensed, and any bending modes are cancelled out. I've just got home and am full of no coffee so will think about this for a bit.<br /> <br /> As for readout speed, photodiodes easily can be readout to 100s of kHz - the trick is having a fast ADC to sample the photodiode voltage. Again, I'll think and do some digging.<br /> <br /> If it's any help, I&nbsp;actually own and run a small physics consultancy here in Vancouver...<br />
Great work!<br /> Even though I will probably (read definitely) never have any use of this knowledge it was still very interesting and informative reading.<br /> <br /> I have one question though.<br /> Isn't there a risk that the beams recombine without the interference?<br /> If the north beam travels exactly one wavelength longer than the south, wouldn't the interference be zero again?<br />
Thanks!<br /> Your question is a perfectly good one. <br /> Due to the imperfections in the optics, and the lack of any converging lenses, the intereference pattern is not quite what a simple analysis suggests. In reality you get a circular (ish) patch of finely divided lines (or even rings)&nbsp;as the interference pattern.<br /> <br /> In the idealized 2-dimensional case (with perfect optics), then 'yes' the 'fringe' is a single patch that oscillates from bright to dark. And thus there is an ambiguity when the phase reaches 360&deg;.<br /> <br /> But you can solve that by adding a second laser with a different wavelength, to the rig. If the wavelengths are not too different you can make the 'distance shift needed to yield ambiguous answers' very large indeed. Or combine it with a separate method, say, an optical encoder.<br />
Oh, I see.<br /> Thanks for the explanation!<br />
nice interferometer.<br /> you should explain the failure of the michelson morely experiment to prove the aether theory on account of the fact it's impossible to measure velocity inside an inertial frame of reference.<br />
<p>I&nbsp; have read, and tried/completed many Instructables. This one goes to the top of my list. Why? Because it is one of the best Instructables I have ever read. Easy as that. 5 out of 5 dude!</p>
&nbsp;Very nice writeup, you explained what interferometers are in terms that the average viewer should be able to understand. I was hoping you would go into how you use it to actually measure something, and what that something would be. I used to work for a company that made grazing incidence interferometers along with a complex software package to perform the measuring of parts. I was very curious as to how you would be measuring with this one.
Hi,<br /> <br /> Glad that you liked it.<br /> As for applications?<br /> Well, ever since I&nbsp;had acces to an AFM&nbsp;at <a href="http://www.esa.int/esaCP/SEMOMQ374OD_index_0.html" rel="nofollow">ESTEC</a> I&nbsp;have toyed with the idea of manipulating stuff at small scales. Clearly, before one uses a sub-micron lathe, one needs to know where things are - and interferometry could allow a very tiny lathe or mill to be constructed.<br /> <br /> As a side note, there are other paths to that goal for the DIY&nbsp;experimenter, even a CD drive head (slide assembly and optical platform)&nbsp;would allow for sub-micron positioning, but interferometry gives a useful factor of 5 or so finer resolving power at little cost.<br /> <br /> Dunno.<br /> <br /> Still thinking. :D<br />
One of the cool things you can do with an interferometer is replicate a science museum exhibit I saw once, titled &quot;How far can you bend this railroad rail with your thumb?&quot;&nbsp; One end of a short length of railway rail was rigidly supported (I think it was welded to the building's steel frame) and one of the interferometer mirrors was glued to the other end, opposite a knob labeled &quot;Press here.&quot;<br /> <br /> With a linear photodiode array from an old scanner, an Arduino and some interface hardware, you could probably build an interferometer that reads out directly in nanometers.<br />
Thanks for the suggestion - I&nbsp;wasn't 100% serious about not having an application in mind, but welcome people to take this and run with it (even with the ever-present Arduino!)<br /> <br /> I&nbsp;actually used interferometry in a real-world application when I&nbsp;was a post-doc in the Netherlands. I&nbsp;needed to measure the thickness of thin films of amino acids that I&nbsp;was condensing from the vapour phase on to silicon discs (this was all for an exobiological spectroscopy experiment). I&nbsp;built a cheap/cheerful interferometer <br /> <br /> <strong>http://www.bipbip.info/jg/make4.html</strong><br /> <br /> that allowed me to measure sub-micron films with 50nm resolution.<br /> <br /> I&nbsp;have had ideas about building a local pi-o-meter, something that (humorously)&nbsp;measures the local curvature of space (just an interferometer on a thermally-stabilized platform) - or a box that tells you how your apartment room expands and contracts over the day from thermal expansion. Daft stuff like that.
Hey, this is pretty neat - I&nbsp;figured that the interference pattern would be on the nanometer scale - but obviously I was wrong! :)<br /> <br /> I'm curious, though, how you actually measure things with this setup?&nbsp; In my mind I&nbsp;can see that if you moved one of the mirrors it would change the interference pattern on a large scale - just like how the interference pattern is 'enlarged' from the nanometer scale.<br /> <br /> I don't have a beam splitter, so I&nbsp;can't set this up and see how it reacts - could you possibly do a movie on YouTube or something showing what happens when the mirrors move forward and backward?<br />
Hi,<br /> <br /> The card that I used as the screen was tilted almost to the horizontal - that way the fringes could be viewed more easily - on a perpendicular card they were compressed and looked like a faint stripe with very many fine lines within it.<br /> <br /> The fact that the fringes here are perpendicular to the rays is 100%&nbsp;down to the astigmatism and poor optics of the rig.<br /> (shrug)<br /> <br /> But in general interference phenomena can be any scale - have a Google for 'Newton's rings' - or 'two-slit interference'. In the latter, the fringes can have spacings of several degrees even for a hand-made pair of slits!<br /> <br /> As for utility, I&nbsp;did actually use this method for a real-world need a few years ago:<br /> <strong>http://www.bipbip.info/jg/make4.html</strong><br /> <br /> I'm re-uploading the movie of the fringes moving - that didn't seem to work when I&nbsp;published it!
While at first, I knew nothing about infterferometry, it sounded weird and made me want to read a little into it.&nbsp;<br /> <br /> Every word of this instructable was interesting, clear and informative. I really, really doubt I'll ever use this new knowledge, but it's cool to think this stuff is possible.&nbsp;<br /> <br /> I especially loved the cheese references.<br /> <br /> <br />
:D<br /> Glad that you found it informative and entertaining - I&nbsp;now spot that the movie I&nbsp;had taken of the fringes moving had not uploaded correctly - and I'm trying to fix that now.<br />

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