Interferometers

Finally,  a physics post! is what exactly none of you are thinking.

When studying with a friend, it was brought to my attention that I cannot for the life of me remember the different types of interferometers and what you do with them. I can name them, I just can't remember what differentiates them. This is kind of a critical topic for my qualifying exam, so I thought I would write a post on it to try and help me to remember it. 

Interferometers are 'old tech' in the world of optics. The main types of optical interferometer were invented back in the 19th century, or very early 20th century. At this point in time, the number of subtypes of interferometers is vast. But except for a few exotic types, the principles of their operation fall into two camps: wave front splitting or amplitude splitting. The wave splitting interferometer splits a beam arbitrarily, either by use of two pinholes/slits, very thin prisms, or cleverly aligned mirrors, which essentially takes chunks of same beam. Amplitude splitting interferometers make use of a beam splitter, which divides the light into reflected and transmitted light, which divides the amplitude evenly.  Each has its uses, because they operate on different optical principles.

Wave-Splitting Interferometers

The wave splitting interferometer is possibly the simplest to explain, and if you've ever heard of or seen a Young's Double Slit Experiment, you know of the oldest, and easiest to replicate, of the wave splitting interferometers. Its success or failure depends on the spatial coherence of light. In other words, how similar is this part of the beam to any other part of  the beam? The way physicists usually quantify this property is in the coherence area. If a source is oddly shaped, and relatively close, it will be spatially incoherent, particularly if it is giving off 'broad band' or white light. You have a large group of random oscillators each creating its own wave, and the waves have nothing to do with each other. You will have a miniscule coherence area. However, oddly enough, if you can get far enough away from the source, the coherence area will increase! Why? Let's go to the ducks!

If you look at the water, and not the adorable ducks, you'll notice that near the ducks, the water waves are chaotic. Each duck is acting as an independent oscillator, going his own rate in his own location. But as the waves get farther and farther from the ducks, they look more and more like perfect spherical waves you would get from tossing in a pebble (a point oscillator). The incoherent bits cancel each other out at a great distance, and only the coherent bits survive, creating a spatially coherent wave. The same thing happens with light. The other way to think about it is the farther you get from something, the more it looks like a point sources. Starlight is highly coherent (that's why they seem to twinkle), but they are just as incoherent as our sun at the source. The only difference is distance. They are so far away, all that reaches us is the coherent waves. You can observe the same effect with a car headlight, if you live somewhere with low light pollution and enough space to walk a couple hundred yards or so away from the car. 

So lets say you've got yourself a spatially coherent source. These days, say a laser pointer will do if you can get your hands on sufficient small double slits. Otherwise, you can do as Young did, which was cut a small hole in the shutter he used to make his room totally dark, cover it with thick paper he had poked a pin hole in, and use the tiny amount of sunlight that filtered in as his source. 

By passing the light through two pinholes or slit, you are creating two identical beams of light, each producing uniform waves of light. If you then place a screen far enough away, you can view the interference pattern of the light, the spacing of which will depend on the separation of your slits and the wavelength of the light. How visible the pattern is is determined by the spatial coherence of the light. 

Dr. Young's original drawing of his experiment

The main use of this type of interferometer is to determine the coherence of a source. You could use it to determine the wavelength of a coherent source, but there are much easier ways to do that that don't require coherence. 

Amplitude Splitting Interferometers

The most basic kind of amplitude splitting interferometer is the Michelson Interferometer. Its many offspring are now more widely used than the original because they are more stable, easier to set up and generally less finicky, but the original is easier to explain I think.

This interferometer depends on a different type of coherence, namely temporal coherence, or how well the beam maintains similarity over time. This makes this type of interferometer very very sensitive to the coherence length of the beam (if a beam is not temporally coherent, a point in the beam that was produced a couple nanoseconds ago, and now a meter away, might not look at all like the beam that is just now being produced.)

The basic set up for this can be seen above.  Your light source is aimed at a beam splitter or a half-silvered mirror which divides your beam into transmitted and reflected portions equally. The split beams travel some distance, then reflect off perfectly aligned mirrors, travel back through the beam splitter and interfere on a screen or a detector. If the difference in the distance the beams traveled is smaller than the coherence length, an interference pattern will form. If the coherence length is short, or not of interest, a compensating plate can be used to eliminate the difference in travel time.

So, what can you do with this thing? You can use it to experimentally find the coherence length of a source by moving one mirror relative to the other until the interference pattern disappears.  You can use it to do metrology (measurements) and test the quality of your optical instruments.  You can use a variation of this in wind tunnels to study air flow patterns, or studying fluid mechanics. A really big version of this can be used in astronomy. Its probably easier to list the scientific fields that don't use some sort of amplitude splitting interferometer than the ones that do. A fiber optics based version of this, the Sagnac interferometer, is used in gyroscopes, but really deserves its own post. 

Interferometers were historically important for a whole host of reasons, including disproving aether, proving the wave nature of light and wave-particle duality of electrons. Today they have a million different uses in research and industry and continue to yield new insights into the universe. Its a shame they don't teach them in every basic science class.

~PhysicsGal