In 1868, Hippolyte Fizeau realized that the lenses and mirrors in a telescope perform a physical approximation of a Fourier transform. He noted that by using an array of small instruments it would be possible to measure the diameter of a star with the same precision as a single telescope which was as large as the whole array — a technique which later became known as astronomical interferometry.
In a 2008 paper, Tegmark and Zaldarriaga proposed a telescope design that dispenses altogether with the lenses and mirrors, relying instead on computers fast enough to perform all the necessary transforms. His concept is an all-digital telescope with an antenna consisting of a rectangular grid. Building radio telescopes this way should become feasible within a few years if Moore's law continues to hold. Eventually optical telescopes could also be built this way. This technique is already being used in radar applications.
More on Aperture synthesis HERE
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