Basic_ifo_diagram

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-ometer". 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 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 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' (a kind of mirror) which as the name suggests, splits a single beam into two identical beams. One beam passes straight through while the other is reflected at 90-degrees. Each beam then travels down an arm of the interferometer. At the end of each arm, a mirror reflects each beam back to the beam splitter where the two beams merge back into a single beam. In 'merging', the light waves from the two beams 'bump' into (or interfere with) each other before traveling to a photodetector, which measures the resulting beam's brightness. If the two beams travel exactly the same distance (i.e. the arms were exactly the same length) before recombining, the photodetector will either see a beam as bright as the pre-split beam or nothing at all, depending on how the mirrors are set up. LIGO's interferometers are set up so that nothing reaches the photodetector as long as the arms don't change their lengths.

If no light comes out when the arms are the same length, then what comes out if the arms change lengths? In that case, with one arm longer than the other, one beam has to travel farther than the other so it takes longer to return to the beam splitter and recombine with the other beam. Since they don’t arrive at the same time, the beams’ waves will be slightly offset when they merge, which  causes the light waves to interfere in a different way than they did when they traveled the same distance. As a result, the resulting merged beam will be brighter or dimmer than it was when the arms were the same length. In an interferometer, any change in light intensity (higher or lower) indicates that something happened to change the distance traveled by one or both laser beams. Moreover, the interference pattern can be used to calculate precisely how much change in length occurred.

 

What exactly is an interference pattern?

To better understand how interferometers work, it helps to understand more about 'interference'. Anyone who has thrown stones into a pond or a pool and watched what happened already knows a lot 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 (meet up), they interact and in that spot, create new waves that are sometimes larger and sometimes smaller. The pattern of new waves occurring where the concentric 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

Left: When the peaks of two waves meet, their peaks and valleys add up making larger peaks and valleys. Right: When the peaks of one wave meet the valleys of another, they cancel out. This occurs in water and light waves. (Image credit: www.explainthatstuff.com) (Click for larger image)

 

 

The principles of interference are quite 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 an identical 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 peak or valley of another wave. Regardless of how they merge, however, the height of the wave resulting from the interference always amounts to the sum of the heights of the merging waves. When the waves don't meet up perfectly, 'partial' constructive or destructive interference can occur. The animation below illustrates this effect. 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 interact.

 

 

 

 

(Credit: Public Domain via Wikimedia Commons)

 
 

Parallels with Light

It just so happens that light behaves a lot 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 one light beam perfectly meet the valleys of another, total destructive interference occurs, and no light results. And when the peaks of one beam perfectly meet the peaks of another, total constructive interference occurs and the resulting beam is brighter. As with water, a full range of interference (which in light means a full range of brightness) from partial to total can occur depending on how well aligned the waves are when they meet. The parallel with water is easy to visualize, as illustrated in the figure below.

Water vs Light Interference (Image credit: Adapted from www.explainthatstuff.com)

What dictates how well-aligned the beams are when they merge is the distance each one travels. If two laser beams travel exactly the same distance through an interferometer, their light waves will be perfectly aligned when they merge. Depending on the experiment, either total constructive or destructive interference will result. LIGO is set up so that total destructive interference occurs (it's easier to detect a brightening of nothing than to detect a dimming of a bright light). If for some reason the lasers travel different distances, their light waves get out of alignment by the time they merge, and they will only partially interfere. As a result, some light reaches the photodetector with a brightness between twice as bright and nothing at all. But what would cause the lasers to travel different distances?

 

One cause is gravitational waves!

Gravitational waves cause space itself to stretch in one direction and get squeezed in a perpendicular direction. In the wake of a gravitational wave, one arm of an interferometer lengthens while the other shrinks, then vice versa. The arms will change lengths in this way for as long as it takes the wave to pass.

As the length of each arm varies, the distance traveled by each laser beam also varies (farther in the longer arm, not as far in the shorter arm). Consequently, the beam in the shorter arm returns to the beam splitter before the beam in the longer arm. Arriving at different times (one before the other, then after, then before again, etc.) causes the beams to shift in and out of alignment as they merge, experiencing varying levels of destructive and constructive interference while the wave passes. This shows up as a flicker of light in the photodetector. This process is illustrated in the clip at right from Einstein's Messengers (Video Credit: 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 things like earthquakes or traffic on nearby roads) is another story. LIGO Technology describes in detail how LIGO filters out much of that "noise" to make detecting a gravitational wave flicker possible.