Interferometry is the applied science of combining two or more input points of a data type, such as optical, and combine these data to form a greater picture based on the combination of the two sources. In astronomy (such as with the Keck telescopes), this is used to "combine" two telescopes.
This technique is the basis for radio telescope arrays which, spread out over a wide area of hundreds of miles, can together produce a picture with resolution similar or equivalent to a single telescope with the diameter of the combined spread of telescopes. The proposed Keck interferometer will have 6 radio telescopes working in tandem for astronomy research.
An interferometer works on the principle that two waves that coincide with the same phase will amplify each other while two waves that have opposite phases will cancel each other out.
The basic building blocks of a Michelson interferometer are a monochromatic light source, usually a laser, a detector, two mirrors and one semitransparent mirror. These are put together as shown in the figure.
There are two paths from the light source to the detector. One reflects off the semi-transparent mirror, goes to the top mirror and then reflects back, goes through the semi-transparent mirror, to the detector. The other first goes through the semi-transparent mirror, to the mirror on the right, reflects back to the semi-transparent mirror, then reflects from the semi-transparent mirror into the detector.
If these two paths differ by a whole number (including 0) of wavelengths, there is constructive interference and a strong signal at the detector. If they differ by a whole number and a half wavelengths (eg, 0.5, 1.5, 2.5 ...) there is destructive interference and a weak signal.
The interferometer setup shown above was used in the famous Michelson-Morley experiment that provides evidence for special relativity. Of course, in Michelson's day, they did not have lasers, so instead they used a gas discharge lamp, a filter, and a thin slot or pinhole to make more-or-less coherent monochromatic light. In one version of the Michelson-Morley experiment, they even ran the interferometer off starlight.
There are many other types of interferometer. They all work on the same basic principles, but the geometry is different for the different types. One familar use of the technique is in radio and optical interferometer telescopes. However, interferometers are perhaps even more widely used in integrated optical circuits, in the form of a Mach-Zehnder interferometer, in which light interferes between two branches of a waveguide that are (typically) externally modulated to vary their relative phase. Such components are the basis of a wide variety of devices, from RF modulators to sensors to optical switches.