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In optics, the Fresnel diffraction equation for near-field diffraction, is an approximation of Kirchhoff-Fresnel diffraction that can be applied to the propagation of waves in the near field.〔M. Born & E. Wolf, Principles of Optics, 1999, Cambridge University Press, Cambridge〕 It is used to calculate the diffraction pattern created by waves passing through an aperture or around an object, when viewed from relatively close to the object. In contrast the diffraction pattern in the far field region is given by the Fraunhofer diffraction equation. The near field can be specified by the Fresnel number, of the optical arrangement. When the diffracted wave is considered to be in the near field. However, the validity of the Fresnel diffraction integral is deduced by the approximations derived below. Specifically, the phase terms of third order and higher must be negligible, a condition that may be written: where is the maximal angle described by , and the same as in the definition of the Fresnel number. The multiple Fresnel diffraction at nearly placed periodical ridges (ridged mirror) causes the specular reflection; this effect can be used for atomic mirrors.〔 http://www.ils.uec.ac.jp/~dima/PhysRevLett_94_013203.pdf H. Oberst, D. Kouznetsov, K. Shimizu, J. Fujita, F. Shimizu. Fresnel diffraction mirror for atomic wave, Physical Review Letters, 94, 013203 (2005).〕 ==Early treatments of this phenomenon== Some of the earliest work on what would become known as Fresnel diffraction was carried out by Francesco Maria Grimaldi in Italy in the 17th century. In his monograph entitled "Light",〔''Light'', by Richard C. MacLaurin, 1909, Columbia University Press〕 Richard C. MacLaurin explains Fresnel diffraction by asking what happens when light propagates, and how that process is affected when a barrier with a slit or hole in it is interposed in the beam produced by a distant source of light. He uses the Principle of Huygens to investigate, in classical terms, what transpires. The wave front that proceeds from the slit and on to a detection screen some distance away very closely approximates a wave front originating across the area of the gap without regard to any minute interactions with the actual physical edge. The result is that if the gap is very narrow only diffraction patterns with bright centers can occur. If the gap is made progressively wider, then diffraction patterns with dark centers will alternate with diffraction patterns with bright centers. As the gap becomes larger, the differentials between dark and light bands decrease until a diffraction effect can no longer be detected. MacLaurin does not mention the possibility that the center of the series of diffraction rings produced when light is shone through a small hole may be black, but he does point to the inverse situation wherein the shadow produced by a small circular object can paradoxically have a bright center. (p. 219) In his ''Optics'',〔''Optics'', Francis Weston Sears, p. 248ff, Addison-Wesley, 1948〕 Francis Weston Sears offers a mathematical approximation suggested by Fresnel that predicts the main features of diffraction patterns and uses only simple mathematics. By considering the perpendicular distance from the hole in a barrier screen to a nearby detection screen along with the wavelength of the incident light, it is possible to compute a number of regions called half-period elements or Fresnel zones. The inner zone will be a circle and each succeeding zone will be a concentric annular ring. If the diameter of the circular hole in the screen is sufficient to expose the first or central Fresnel zone, the amplitude of light at the center of the detection screen will be double what it would be if the detection screen were not obstructed. If the diameter of the circular hole in the screen is sufficient to expose two Fresnel zones, then the amplitude at the center is almost zero. That means that a Fresnel diffraction pattern can have a dark center. These patterns can be seen and measured, and correspond well to the values calculated for them. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fresnel diffraction」の詳細全文を読む スポンサード リンク
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