Ifoschematic

Basic schematic of LIGO's interferometers with an incoming gravitational wave depicted as arriving from directly above the detector. [Credit: 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!

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.

 

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. [Image 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 identical wave, they cancel out.  [Image Credit: www.explainthatstuff.com]

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 (its size equal to the sum of the heights of the two waves). In total destructive interference, the peak of one wave meets the valley of an identical wave, and they totally cancel each other out (i.e., '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 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. When perfectly in sync, they will either totally constructively interfere or totally destructively interfere. But a little out of sync, partial constructive or destructive interference occurs. 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 of each wave at each point along the static horizontal line, the resulting wave (black) experiences a full range of heights from twice as high (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 fo 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. [Animation 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 this case, in water, the wave disappears; in light, the light also disappears, which means no light (i.e., darkness) results. Conversely, when the peaks of one beam perfectly meet the peaks of another, total constructive interference occurs. Relating this back to water, the height of the resulting wave is equal to the sum of the heights of the two waves; 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 Parallels between contstructive 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 when they merge, which means no light, a little light, or a light as bright as the original laser beam reaches the photodetector. The flicker appears!

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 makes one arm of the interferometer 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 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 continuously merge while the wave is passing.Again, this results in a flicker of light reaching the photodetector. This process is nicely illustrated in the clip at right from Einstein's Messengers

[Animation Credit: Einstein's Messengers, U.S. National Science Foundation (NSF)]

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.