Interferometry is the applied science of combining two or more input points of a particular data type, such as optical measurements, 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. It has more recently been used for arrays of optical telescopes such as the Cambridge Optical Aperture Synthesis Telescope (COAST), resulting in the highest resolution optical images ever achieved in astronomy. The proposed Keck interferometer will have 6 optical telescopes working in such an array for astronomy research, while the Magdalena Ridge Observatory Interferometer may have an array of up to 10 optical telescopes.
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 laboratory 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 to the right was used in the famous Michelson-Morley experiment that provided 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. The Michelson interferometer finds use not only in these experiments but also for other purposes, e.g. in gravitational wave detection.
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.
The highest-resolution astronomical images are produced using interferometers (at both optical and radio wavelengths). Here is a description of astronomical interferometry (http://www.geocities.com/CapeCanaveral/2309/page1.html).
Another geometry is the Sagnac interferometer.