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Graph and image of single-slit diffraction. The width of the slit is W. The Fraunhofer diffraction pattern is shown in the image together with a plot of the intensity vs. angle θ. [10] The pattern has maximum intensity at θ = 0, and a series of peaks of decreasing intensity. Most of the diffracted light falls between the first minima.
Geometry of two slit diffraction Two slit interference using a red laser. Assume we have two long slits illuminated by a plane wave of wavelength λ. The slits are in the z = 0 plane, parallel to the y axis, separated by a distance S and are symmetrical about the origin. The width of the slits is small compared with the wavelength.
Because diffraction is the result of addition of all waves (of given wavelength) along all unobstructed paths, the usual procedure is to consider the contribution of an infinitesimally small neighborhood around a certain path (this contribution is usually called a wavelet) and then integrate over all paths (= add all wavelets) from the source to the detector (or given point on a screen).
Thomas Young's sketch of two-slit diffraction for water ripple tank from his 1807 Lectures [6]: 139 . The effects of diffraction of light were first carefully observed and characterized by Francesco Maria Grimaldi, who also coined the term diffraction, from the Latin diffringere, 'to break into pieces', referring to light breaking up into different directions. [7]
[9] [10] [11] Examining the hypothesis of Duane on quantized translational momentum transfer, as it accounted for X-ray diffraction by crystals, [1] and its follow-up by Compton, [12] Epstein and Ehrenfest had written "The phenomena of Fraunhofer diffraction can be treated as well on the basis of the wave theory of light as by a combination of ...
Joseph von Fraunhofer developed the first modern spectroscope by combining a prism, diffraction slit and telescope in a manner that increased the spectral resolution and was reproducible in other laboratories. Fraunhofer also went on to invent the first diffraction spectroscope. [5]
Fourier optics begins with the homogeneous, scalar wave equation (valid in source-free regions): (,) = where is the speed of light and u(r,t) is a real-valued Cartesian component of an electromagnetic wave propagating through a free space (e.g., u(r, t) = E i (r, t) for i = x, y, or z where E i is the i-axis component of an electric field E in the Cartesian coordinate system).
The detector can either be a long way from the object (i.e. in the Fraunhofer diffraction plane), or closer by, in the Fresnel regime. An advantage of the Fresnel regime is that there is no longer a very high-intensity beam at the centre of the diffraction pattern, which can otherwise saturate the detector pixels there.