Basic schematic of LIGO's interferometers with an incoming gravitational wave depicted as arriving from directly above the detector. (Caltech/MIT/LIGO Lab)

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-o-meter', or interferometer. 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!

Interferometers were pioneered in the mid-to-late 1800s by many scientists including Hippolyte Fizeau, Martin Hoek, Éleuthère Mascart, George Biddell Airy, Eduard Ketteler, in their attempts to measure the velocity of light through various media (first and foremost, air and water, then others) and especially through moving media (like flowing water). This work was part of a study to understand the wave properties of light, and their dependence on the medium that light traverses.

As it was believed at the time that all waves require some medium for propagation, scientists such as the famous Augustin-Jean Fresnel proposed the existence of a "luminiferous ether", an amorphous substance permeating everything and serving only as a medium for the propagation of light waves. This theory was a prime target for experimental tests using interferometers. Among the scientists from around the world working on this question were American physicists Albert Michelson and Edward Morley, who invented a self-named optical configuration, the Michelson-Morley Interferometer. Results from their experiments published in 1887 are often cited as the first conclusive experimental evidence against the existence of ether, in favor of light (indeed, all electro-magnetic radiation) propagating without a medium - i.e., in vacuum. This discovery was one of the foundation stones of Einstein's theory of special, and later general, relativity - as Einstein identified the vacuum paths along which light propagates, tracing out the very curvature of space-time itself.

As a part of common knowledge and wide use almost a century later in the late 1960s, the particular interferometric configuration used by Michelson and Morley was identified as a natural fit for the detection of gravitational wave strain on space-time, given its precise measurement of the phase change of light traveling along two perpendicular arms. As such, the Michelson interferometer’s optical configuration is a core, critical piece of all of today’s gravitational wave interferometric detectors, including LIGO.

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.


What is an Interference Pattern?

To better understand how interferometers work, it helps to understand more about 'interference'. Anyone who has thrown stones into a flat, glassy pond or pool and watched what happened knows about interference. When the stones hit the water, they generate concentric waves that move away from source. And where two or more of those concentric waves intersect, they interfere with each other. This interference can result in a larger wave, a smaller wave, or no wave at all. The visible pattern occurring where the waves intersect is simply 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. [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 identical wave, they cancel out. [www.explainthatstuff.com]


The principles of interference are simple to understand. Two or more waves interact. You add the heights of the separate waves together as they interact, and the resulting wave is the 'interference' pattern. The figure at right shows two specific kinds of interference: total constructive interference and total destructive interference. Total constructive interference happens when the peaks and troughs of two (or more) waves perfectly meet up. When added together, you 'construct' a larger wave, the size of which is equal to the sum of the heights (and depths!) of the two waves at each point where they are physically interacting. Total destructive interference occurs when the peaks of one or more waves meet and match the troughs of an identical wave. Adding these together results in them cancelling each other out (i.e., they 'destroy' each other).

In nature, the peaks and troughs of one wave will not always perfectly meet the peaks or troughs of another wave like the illustration shows. Conveniently, regardless of how in-sync they are when they merge, the height of the wave resulting from the interference always equals the sum of the heights of the merging waves along each point where they are physically interacting. So when waves meet a little out of sync, partial constructive or destructive interference can occur. The animation below illustrates this effect. The black wave shows the result of adding together the peaks and troughs of the red and blue waves as they move through (interfere with) each other. Adding up the heights/depths of each wave at each point as they move through each other results in the black wave. Note that it experiences a full range of heights from twice as high/deep (total constructive interference) to flat (total destructive interference). In this example, the black wave is the interference pattern (the pattern that results from the continuing interference of the red and blue wave). 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. [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 troughs of another, total destructive interference occurs. In water, the result is no wave. In light, the result is no light! Conversely, when the peaks of one beam perfectly meet the peaks of another, total constructive interference occurs. Again, in water, the height of the resulting wave is equal to the sum of the heights of the two waves; in light, the result is a light equal to the sum of the intensities of the two separate light beams. Carrying this analogy to the end, in water, as waves pass through each other they can experience a full range of interference from partial to total constructive and destructive (bigger wave, smaller wave, no wave). In light, the result is a full range of brightness, from darkness to the sum of intensities of the interacting beams.

Water vs Light Interference

Parallels between constructive and destructive interference in water and with light. (Adapted from www.explainthatstuff.com)

Returning to 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 are no longer in sync as they merge, which means no light, a little light, or a light as bright as the original laser beam reaches the photodetector. And if the arms are changing length over time, a flicker appears as the beams experience a range of interference depending on how they are meeting up in any given moment.

How do Gravitational Waves Affect LIGO's Interferometer?

Gravitational waves cause space itself to stretch in one direction and simultaneously compress in a perpendicular direction. In LIGO, this causes one arm of the interferometer to get longer while the other gets shorter, then vice versa, back and forth as long as the wave is passing. The technical term for this motion is "Differential Arm" motion, or differential displacement, since the arms are simultaneously changing lengths in opposing ways, or differentially.

As described above, as the lengths of the arms change, so too does the distance traveled by each laser beam. A beam in a shorter arm will return to the beam splitter before the beam in a longer arm, then the situation switches as the arms oscillate between being longer and shorter. Arriving at different times, the waves of light no longer meet up nicely when recombined at the beam splitter. Instead, they shift in and out of alignment or "phase" as they merge while the wave is causing the arm lengths to oscillate. In simple terms, this results in a flicker of light emerging from the interferometer. This process is illustrated in the clip at right from Einstein's Messengers [Credit: U.S. National Science Foundation (NSF)].

While in principle the idea seems almost 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 telltale 'flicker' of light caused by a gravitational wave.