The Fraunhofer diffraction pattern is obtained at a very large distance from the aperture, but using a lens, an image of it can be formed at a finite distance. Calculation of Fresnel diffraction is based on an approximation, which eventually breaks down: closer to the aperture more advanced theories are required. This situation is called Fraunhofer diffraction (shown in the image below).Ĭloser to the aperture the diffraction pattern does change with distance. If the observation screen is far enough away from the aperture, the diffraction pattern does not change in structure, but merely changes in size, as the distance is further increased. The light spreads as a result of diffraction. The amplitude at any point is the superposition of these wavelets.Ĭonsider an opaque screen illuminated with a plane wave. No mirror or lenses are used for observations.ĭiffracted light is collected by a lens as in a telescope.Īccording to Huygens, each point on a wavefront serves as the source of a spherical secondary wavelet with the same frequency as the primary wave. The wave-fronts are the plane which is realized by using the convex lens. The wave-fronts are divergent either spherical and cylindrical. The single-double plane diffraction grating is used. The source, and the screen is at an infinite distance from the diffracting aperture.įor obtaining Fresnel diffraction, zone plates are used. The source and the screen are at a finite distance from the diffracting aperture. The difference between Fresnel and Fraunhofer diffraction is as follows: Comparison and difference between Fresnel and Fraunhofer Diffraction S.No. The spreading out of light wave into the geometrical shadow when it passes through a narrow opening is known as the diffraction. ^ a b Born, Max Wolf, Emil (1999).Distinguish, differentiate, compare and explain what is the difference between Fresnel and Fraunhofer diffraction.The factor 1/ rs is replaced with 1/ r ' s ', where r ' and s ' are the distances from P 0 and P to the origin, which is located in the aperture. cos( n, r) − cos( n, s) is replaced with 2cos β, where β is the angle between P 0 P and the normal to the aperture.This allows one to make two further approximations: Another approximation can be made, which significantly simplifies the equation further: this is that the distances P 0 Q and QP are much greater than the dimensions of the aperture. One of the important assumptions made in arriving at the Kirchhoff diffraction formula is that r and s are significantly greater than λ. Analytical solutions are not possible for most configurations, but the Fresnel diffraction equation and Fraunhofer diffraction equation, which are approximations of Kirchhoff's formula for the near field and far field, can be applied to a very wide range of optical systems. This is mainly because the wavelength of light is much smaller than the dimensions of any obstacles encountered. In spite of the various approximations that were made in arriving at the formula, it is adequate to describe the majority of problems in instrumental optics. Kirchhoff's integral theorem, sometimes referred to as the Fresnel–Kirchhoff integral theorem, uses Green's second identity to derive the solution of the homogeneous scalar wave equation at an arbitrary spatial position P in terms of the solution of the wave equation and its first order derivative at all points on an arbitrary closed surface S Fraunhofer and Fresnel diffraction equations The Huygens–Fresnel principle is derived by the Fresnel–Kirchhoff diffraction formula.ĭerivation of Kirchhoff's diffraction formula This formula is derived by applying the Kirchhoff integral theorem, which uses the Green's second identity to derive the solution to the homogeneous scalar wave equation, to a spherical wave with some approximations. It gives an expression for the wave disturbance when a monochromatic spherical wave is the incoming wave of a situation under consideration. The approximationĬan be used to model light propagation in a wide range of configurations, either analytically or using numerical modelling. Kirchhoff's diffraction formula (also called Fresnel–Kirchhoff diffraction formula) approximates light intensity and phase in optical diffraction: light fields in the boundary regions of shadows.
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