![]() ![]() Where is the inter-atomic distance and is the difference between the incident and the diffracted wave vector (the interaction is elastic scattering so the incident and diffracted radiation have the same energy so the module is constant). The condition is expressed by the formula: The von Laue condition establishes the relationship that exists between the occurrence of constructive interference and the distance of the atoms within a crystal. Laue patterns, first detected by Max von Laue, a German physicist, are invaluable for crystal analysis. When a thin, pencil-like beam of X rays is allowed to impinge on a crystal, those of certain wavelengths will be oriented at just the proper angle to a group of atomic planes so that they will combine in phase to produce intense, regularly spaced spots on a film or plate centered around the central image from the beam, which passes through undeviated. 47, 317-374, 1896.Laue diffraction pattern, in X rays, a regular array of spots on a photographic emulsion resulting from X rays scattered by certain groups of parallel atomic planes within a crystal. "Mathematische Theorie der Diffraction." Math. "On the Diffraction of an Electromagnetic Wave through a Plane Screen." J. Cambridge, England: Cambridge University Press, 1902. "On the Theory of Diffraction by an Aperture in an Infinite Plane Screen. "The Reflection of an Electromagnetic Plane Wave by an Infinite Set of Plates, II." Quart. "The Radiation and Transmission Properties of a Pair of Semi-Infinite Parallel Plates-II." Quart. "The Radiation and Transmission Properties of a Pair of Semi-Infinite Parallel Plates-I." Quart. "On an Integral Equation Arising in the Theory of Diffraction." Quart. ![]() "Some Multiform Solutions of the Partial Differential Equations of Physical Mathematics and their Applications." Proc. "The Reflection of an Electromagnetic Plane Wave by an Infinite Set of Plates, I." Quart. Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, 7th ed.Ĭambridge, England: Cambridge University Press, pp. 370-458 and 556-592, 1999.īouwkamp, C. J. "Elements of the Theory of Diffraction" and "Rigorous Diffraction Theory." Chs. 8 and 11 in Other rigorous solutions have been found to a small number of other mostly two-dimensionalĭiffraction problems (Born and Wolf 1999, pp. 370 and 556-592).ĭepending on the Fresnel number of a system, defined asīorn, M. Schwinger (1948, 1949) have used variational methods to calculate exactly the power diffracted through certain apertures (Titchmarsh 1937, p. 339), leading to exact solutions by Copson (1946) and others (Carlson and Heins 1947 Heins andĬarlson 1947 Heins 1948 Levine and Schwinger 1948 Miles 1949 Bouwkamp 1954 Born and Wolf 1999, p. 557). ![]() Mie (1908) rigorously solved scattering by a sphere having finite dielectric constant and finiteĬertain diffraction problems yield integral equations that can be solved exactly using the method of Wiener and Hopf ![]() Sources, and generalization to a wedge instead of a plane were solved exactly by Carslaw (1899), Macdonald (1902), andīromwich (1916). Variants of this problem dealing with line sources, point Theįirst such rigorous solution was found by Sommerfeld (1896). DiffractionĪround apertures is described approximately by a mathematical formalism called scalar diffraction theory.ĭiffraction problems are among the difficult encountered in optics, and exact rigorous solutions are quite rare. Diffraction - from Eric Weisstein's World of Physicsĭiffraction is a phenomenon by which wavefronts of propagating waves bend in the neighborhood of obstacles. ![]()
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