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Interferometer Principles
Interferometers work by distinguishing differences between two images of a star taken by two (or more) telescopes, and comparing them to each other. The two images can be looked at for differences in the phase of the light as it reaches the collecting array. In optical interferometry, the collection point is a pair of mirrors.
Historical Interferometers
One of the first interferometers was used to measure the diameter of distant stars. This is an example of a stellar interferometer, and one of the first ones used was on the Mt. Wilson Observatory in California. It managed to measure the diameter of the red giant star Betelgeuse in the early 1920s. By the 1940s, when radio astronomy was in its infancy, interferometry was used to increase the effective aperture of the radio telescopes, and even after dedicated radio telescopes were built, interferometry was incorporated into the plans, such as at the Very Large Array in New Mexico (and seen in the movie "Contact").
The Rise of Optical Interferometry
There were several technical challenges that needed to be overcome for optical interferometry to become practical. Because optical wavelengths of light are much shorter than microwave and radio waves, they magnify any differences in the beam path that might be caused by the atmosphere. It took improvements in computers--starting in the 1970s and improving steadily since then--to automatically correct for atmospheric disturbances in telescope interferometry.
Arranement of Interferometer Mirrors
In most cases, interferometer mirrors are set up in hexagonal arrays: each mirror is a hexagon, and they're laid out like a honey comb. Two telescopes are made with composite mirrors in this way, situated a particular distance apart. One of the best examples of this is the Keck Interferometer on Mona Kea in Hawaii. The Very Large Telescope in Chile can get angular resolution comparable to identifying the distance between a car's headlights on the moon.
Long Baseline Interferometers
The theoretical resolution limit of an interferometer is a function of the distance between its resolving elements. The longer the baseline, the sharper the resolution will be. However, while resolution improves with the distance between elements, the brightness of the image is largely limited by the size of a single telescope. There are currently interferometer telescopes under construction that contain ten or more elements to improve angular resolution and image brightness; these are massive arrays of interferometer telescope mirrors built as individual telescopes in a large array; one of them--the VLTI, in Chile--is functional now. The ambitious MRO telescope in Socorro, New Mexico is under construction and is expected to be operational by 2020.