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Diffraction is a phenomenon by which wavefronts of propagating
waves bend in the neighborhood of obstacles. Diffraction around
apertures is described approximately by a mathematical formalism
called scalar diffraction theory. Diffraction problems are
among the most difficult encountered in optics, and exact rigorous
solutions are quite rare. The first such rigorous solution was
found by Sommerfeld (1896). Variants of this problem dealing with
line sources, point sources, and generalization to a wedge instead
of a plane were solved exactly by Carslaw (1899), MacDonald
(1902), and Bromwich (1916). Mie (1908) rigorously solved
scattering by a sphere having finite dielectric constant and
finite conductivity [4].
Depending on the Fresnel number of a system, defined as

(6) 
where stands for the "radius" of the
aperture^{2}, stands for the wavelength, and is the
distance from aperture, qualitatively different types of
diffraction occur. In particular, produces a type of
diffraction known as Fraunhofer diffraction or Far
Field diffraction, while produces Fresnel
diffraction or Near Field diffraction.
Thus in the case of Fraunhofer Diffraction, the diffraction
pattern is independent of the distance to the screen, depending
only on the angles to the screen from the aperture. Mathematical
description of Fraunhofer Diffraction is much easier and will be
partly presented later.
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