Note

Update of an old article by paudie. Original text (from A3553085), with my notes in italics.

This is a work in progress!

Intro

An interferometer is a device that was first used by Michelson and Morley in their famous experiment (this is a particular sort of interferometer using division of amplitude). These days it is usually used in field of optics (although, as a radio astronomer, I have to point out that it is a widely used technique in radio astronomy as well as standard optics).

It can be used to measure the wavelength of a light source, to detect minute changes in distance, as an extremely high precision ruler as well as a number of other uses (mention of gravitational wave experiments such as LIGO, GEO600, etc).

An interferometer is simply a device which uses the principle of interference. Light can be modelled in a variety of ways, and physicists choose the most appropriate model in order to investigate a particular problem. You can think of it either as "photons", small discrete packets of energy which move through space at the speed of light*, as rays which travel along straight paths until they hit an obstacle, or as waves which oscillate as they travel. They all describe the same stuff, it's just that each different description is useful for solving different kinds of problems. Some types of interferometer are best thought about by imagining light as rays, but often the wave description is the most conceptually useful.

Interference is what happens when waves interact. It happens for light waves as well as sound waves and even waves on water. When two waves interfere, their amplitudes add up, producing a new pattern of peaks and troughs that is a sum of the two individual waves. In some cases, this can result in quite complicated patterns.

If you've ever seen swirls of colour in a soap bubble or a puddle on the road, then you've seen the effects of interference. These colourful effects are caused by an effect known as "thin film interference". Light is reflected back towards your eye from the top and bottom of the thin film (the surface of the bubble or the thin layer of oil in the case of the puddle) and the colours are produced as the light interferes with itself - constructive interference between the light from the top and bottom of the film appears in different places for different wavelengths.

By measuring the interference pattern that you see, you can work out what is physically going on and use this information to measure all sorts of things.

The Michelson interferometer

The Michelson interferometer is one kind of experimental setup which uses the principle of interference. It can be used to measure accurately minute distance changes. One of its first uses was in the Michelson-Morley experiment carried out in 1887 to try and detect the "ether", the medium through which (it was thought) light waves propagated. This was one of the most famous "null-results" in physics - the experiment failed to find the ether, but still taught us something about how the Universe works*.

A laser is placed in the end of one of the arms, pointing towards the middle of the cross along the arm. Mounted in the centre of the cross is a mirror known as a beam splitter, set at an angle of 45 degrees so that it reflects light from the laser along one section of the other arm. This mirror only reflects half the light that hits it, the rest passes right through it and carries on down the first arm.

So we now have laser light travelling from the beam splitter passing down two of the arms of the cross, half the light along each arm. At the end of each of these arms is mounted another mirror but, unlike the central beamsplitter, these mirrors reflect all of the light which falls on them. They reflect the incident light beam back to the centre of the cross where the beamsplitter is located.

You might have realised by now that there is nothing in the fourth section of our cross. This is where the detector goes. After the light has travelled from the laser to the beamsplitter, along one of the two arms and back to the beamsplitter, it passes into the fourth arm where the two beams are combined and an interference pattern can be observed by eye or, more usually, recorded by a detector.

How do we get an inteference pattern? Well, if the two normal mirrors located a the ends of the second and third arms are at exactly the same distance from the centre of the cross, then the two beams of light travel exactly the same distance through the apparatus and the final beam is the same as the original beam - the peaks and troughs line up exactly and there in no interference pattern. Usually, one of the mirrors is fixed in position while the other can be moved up and down the arm, lengthening or shortening the distance that one beam travels while keeping the other fixed. Changing the so-called path length of one of the beams relative to the other means that the peaks and troughs are no longer perfectly in sync when the two beams arrive at the detector in the fourth arm, this results in an interference pattern.

The form of the interference pattern observed in this setup can tell you useful information and can be used to measure the properties of the light itself or measure minute changes in the lengths of the arms. This is what Michelson and Morley did in their famous experiment to try and detect the hypothetical ether.

Use of the Interferometer

Well now comes the interesting part. One of the mirrors usually M2 is attached to a micrometer. This is a device which allows M2 to be moved by tiny increments, a millionth of a metre.

This means the distance that beam2 travels can be changed. A millionth of a metre may not sound like that much of a difference, but it is perfect for what we are about to do.

We are assuming that light is travelling as a wave. This tiny difference in the distance that beam2 travels means that a diffent part of the wave hits the mirror than did previously.

Before both beam2 and beam3 travelled the exact same distance so we can assume that both light waves were at a crest, the top of the wave, when they hit the mirrors M2 and M3, respectively.

If M2 were moved a distance equal to half the wavelength of light then when beam2 hits the mirror it will be at a trough, the bottom of the wave. This means that when the two beams recombine at the screen at the end of arm4 they will cancel each other out leaving a dark patch.

In reality we cannot make the light do this exactly because there are in fact millions of different waves making up the beam of light, but they are related to each other so what you do get is a pattern of light and dark fringes, as they are known. This pattern is called an interference pattern, because the two waves are interfering with each other.

For this to work a coherent light source needs to be used. A coherent light source is one from which all the light leaving it is of the same frequency, i.e. a laser.

Uses of the interferometer.

Depending on how much M2 is moved, the interference pattern will change accordingly.

In this way if a light of unknown wavelength is shone onto the beam splitter, careful adjustment of M2 will allow us to calculate the wavelength and therefore the frequency of the light¹.

If M2 is connected by some means to a system in which a tiny movement is occuring this will show up on the screen as the interference pattern changing. This change allows us to work out the size of the movement in the other system.

Uses of interferometers

Radio interferometry

The principle of interferometry is used widely in radio astronomy. A single radio telescope on it's own does not have great resolving power - it can not see much detail on the sky. This is because of the long wavelengths of radio waves. The resolving power of a telescope is determined by two things: the wavelength and the diameter of your telescope. The larger the telescope and the shorter the wavelength at which it operates, the greater the resolving power. At radio wavelengths, even large telescopes have pretty poor resolution. One way around this is to use the principle of interferometry. This sort of array uses several individual telescopes spread out over a wide area. The signals from each telescope are combined electronically and the interference pattern is used to determine the sky brightness distribution, that is, a map of what the sky looks like in radio waves.

Gravitational wave detectors

Another use of interferometry is in the hunt for gravitational waves. Theoretically, these are produced by anything with mass moving through space, but are very weak. Although they are very hard to detect, massive objects such as orbiting neutron stars and black holes should produce signals that we can detect with sensitive equipment. Several experiments have been designed and built to try and detect these elusive signals using interferometers. Experiments such as LIGO use (basically) giant Michleson interferometers with arms many hundreds of metres long. They are capable of detecting very small changes in the length of the arms due to these gravitational waves passing through the Earth and fractionally distorting space-time in one direction more than in another. Another experiment using this technique is even more ambitious. LISA is a space-bourne experiment consisting of a series of satellites set up as an interferometer in space. It is going to require extraordinary accuracy in station-keeping in order to detect the tiny shifts due to passing gravitational waves.