Basic schematic of LIGO's interferometers with an incoming gravitational wave depicted as arriving from directly above the detector. (Image: LIGO)

What is an Interferometer?

Interferometers are investigative tools used in many fields of science and engineering. They are called interferometers because they work by merging two or more sources of light to create an interference pattern, which can be measured and analyzed; hence 'Interfere-meter'. The interference patterns generated by interferometers contain information about the object or phenomenon being studied. They are often used to make very small measurements that are not achievable any other way. This is why they are so powerful for detecting gravitational waves--LIGO's interferometers are designed to measure a distance 1/10,000th the width of a proton!

Widely used today, interferometers were actually invented in the late 19th century by Albert Michelson. The Michelson Interferometer was used in 1887 in the "Michelson-Morley Experiment", which set out to prove or disprove the existence of "Luminiferous Aether"--a substance at the time thought to permeate the Universe. All modern interferometers have evolved from this first one since it demonstrated how the properties of light can be used to make the tiniest of measurements. The invention of lasers has enabled interferometers to make the smallest conceivable measurements, like those required by LIGO.

Remarkably, the basic structure of LIGO's interferometers differs little from the interferometer that Michelson designed over 125 years ago, but with some added features, described in LIGO's Interferometer.


What does an Interferometer Look Like?

Basic Michelson Labeled

Layout of a basic Michelson laser interferometer. (Click for larger image)

Because of their wide application, interferometers come in a variety of shapes and sizes. They are used to measure everything from the smallest variations on the surface of a microscopic organism, to the structure of enormous expanses of gas and dust in the distant Universe, and now, to detect gravitational waves. Despite their different designs and the various ways in which they are used, all interferometers have one thing in common: they superimpose beams of light to generate an interference pattern. The basic configuration of a Michelson laser interferometer is shown at right. It consists of a laser, a beam splitter, a series of mirrors, and a photodetector (the black dot) that records the interference pattern.


How Does it Work?

In a Michelson interferometer, a laser beam passes through a 'beam splitter' that splits the original single beam into two separate beams. The beam splitter allows half of the light to pass through, while reflecting the other half 90-degrees from the first. Each beam then travels down an arm of the interferometer. At the end of each arm is a mirror. This mirror reflects each beam back along its initial path toward the beam splitter where, now coming from the opposite direction, the two beams are recombined into a single beam. As they meet up, their waves interfere with each other before traveling to a photodetector that measures the brightness of the recombined beam as it returns. LIGO's interferometers are set up so that, as long as the arms don't change length while the beams are traveling, when the two beams recombine, their light waves cancel each other out (destructively interfere) and no light reaches the photodetector.

But what happens if the distance traveled by the lasers does change while they are making their way through the interferometer? If one arm gets longer than the other, one laser beam has to travel farther than the other and it takes longer to return to the beam splitter. Though the beams entered the infereometer at the same time, they don't return to the beam splitter at the same time, so their light waves will be offset when they recombine. This changes the nature of the interference they experience. Rather than totally destructively interfering, resulting in no light coming out of the interferometer, a little light will 'leak' out and be seen by the photodetector. If the arms change length over a period of time (say with the passage of a gravitational wave), the pattern of light coming out of the interferometer will also change in-step with the movement of the arms. Basically, a flicker of light emerges. In an interferometer, any change in light intensity indicates that something happened to change the distance traveled by one or both laser beams. Critically, the shape of the interference pattern emerging from the interferometer over a period of time can be used to calculate precisely how much change in length occurred over that period. LIGO looks for very specific characteristics (how the interference pattern changes over time) to determine if it has caught the passage of a gravitational wave.


What is an Interference Pattern?

To better understand how interferometers work, it helps to understand more about 'interference'. If you have ever thrown stones into a flat, glassy pond or pool and watched what happened, you already know about interference. When the stones hit the water, they generate concentric waves that move away from the stone's point of entry. And where two or more of those concentric waves intersect, they interfere with each other, the poitns of intersection being larger or smaller or completely canceling each other out. The visible pattern occurring where waves intersect constitutes an "interference" pattern.

Interference patterns in water

Interference patterns in water. The "interference" occurs in the regions where the expanding circular waves from the different sources intersect. (Credit: Wikimedia commons)

Whats an IFO con and des interference

When the peaks of two waves meet, their peaks add up. When the peaks of one wave meet the valleys of another, they cancel out.  Credit:

The principles of interference are simple to understand. The figure at right shows two specific kinds of interference: total constructive interference and total destructive interference. In total constructive interference, when the peak of one wave merges with the peak of another wave, they add together and 'construct' a larger wave. In total destructive interference, the peak of one wave meets the valley of an identical wave, and they totally cancel each other out (they 'destroy' each other).


In nature, the peaks and valleys of one wave will not always perfectly meet the peaks or valleys of another wave like the illustration shows. Regardless of how they merge, the height of the wave resulting from the interference always equals the sum of the heights of the merging waves. When the waves don't meet up perfectly, partial constructive or destructive interference occurs. The animation below illustrates this effect. If you watch closely, you will see that the black wave goes through a full range of heights from twice as high and deep (where total constructive interference occurs) to flat (where total destructive interference occurs) as the red and blue waves pass 'through' each other (interfere). In this example, the black wave is the interference pattern! Note how it continues to change as long as the red and blue waves continue to interact.





The changing black wave is the interference pattern created by the red and blue waves as they pass through/interact with each other. [Credit: Wikimedia Commons]


Parallels with Light

It just so happens that light waves behave just like water waves. When two beams of laser-light merge, they too generate an interference pattern that depends on how well-aligned the light waves are when they combine. Just like water, when the peaks of the waves of one beam perfectly meet the valleys of another, total destructive interference occurs. In water, the wave disappears; in light, the light too disappears and no light (i.e. darkness) results. Conversely, when the peaks of one beam perfectly meet the peaks of another, total constructive interference occurs. Again relating to water, in water waves the height of the resulting wave is equal to the heights of the two waves added together; in a light beam, the result is a brighter light. As with water, a full range of interference (which in light means a full range of brightness) from partial to total constructive and destructive can occur depending on how the waves align over time.

Water vs Light Interference Paralells betwen contstructive and destructive interference in water and with light. [Adapted from]

In LIGO's interferometers, what dictates how well-aligned the beams are when they merge is the distance they travel before merging. If the beams travel exactly the same distance, their light waves will be perfectly aligned so that they result in total destructive interference (LIGO is deliberately designed to make this happen if no gravitational waves are passing). But if for some reason the lasers don't  travel the same distances, their light waves no longer align when they merge. Depending on how the waves from the two beams meet up as they return to the beam splitter, no light, a little light, or a light as bright as the original laser beam may reach the photodetector.

So, what would cause the lasers to travel different distances?

One cause is gravitational waves!

Gravitational waves cause space itself to stretch in one direction while simultaneously compress in a perpendicular direction. The effect on LIGO is one arm of the interferometer gets longer while the other gets shorter, then vice versa, and so on, oscillating back and forth for as long as the wae is passing (like a buoy bobbing on the water after a boat passes). The technical term for this motion is "Differential Arm" motion, or differential displacement, since the arms are changing lengths differently (i.e., in opposite ways).

As the lengths of the arms change (longer/shorter shorter/longer, etc.) so too do the distances traveled by each laser beam. A beam traveling down the shorter arm will return to the beam splitter before the beam in the longer arm (then the situation switches as the arms oscillate between being longer and shorter.) Arriving at different times, the waves of light in the laser beams no longer meet up nicely when they blend back together at the beam splitter. Instead, they shift in and out of alignment or "phase" as they merge over the time of passage of the wave. In simple terms, this results in a flicker of light reaching the photodetector. This process is nicely illustrated in the clip at right from Einstein's Messengers

(Credit: United States National Science Foundation).

While in principle the idea seems quite simple, in practice, detecting that flicker is not. The change in arm length caused by a gravitational wave can be as small as 1/10,000th the width of a proton (that's 10-19 m)! Furthermore, finding a gravitational wave flicker amongst all the other flickers LIGO experiences (caused by anything that can shake the mirrors, like earthquakes or traffic on nearby roads) is another story. LIGO Technology describes in detail how LIGO filters out much of that "noise" in order to detect the tell-tale 'flicker' of light caused by a gravitational wave.