A "wide" wave moving forward (like an expanding ocean wave coming toward the shore) can be regarded as an infinite number of "plane wave modes", all of which could (when they collide with something in the way) scatter independently of one other.
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No electronic computer can compete with these kinds of numbers or perhaps ever hope to, although new supercomputers such as the petaflop IBM Roadrunner may actually prove faster than optics, as improbable as that may seem.
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It can be shown (see Fourier optics, Huygens-Fresnel principle, Fraunhofer diffraction) that the field radiated by a planar object (or, by reciprocity, the field converging onto a planar image) is related to its corresponding source (or image) plane distribution via a Fourier transform (FT) relation.