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Fresnel diffraction is the diffraction pattern of an electromagnetic wave obtained a small number of wavelengths away from the diffracting object (often a source or aperture). This is also often called near-field diffraction. Diffraction is the bending and spreading of waves when they meet an obstruction. ...
Electromagnetic radiation is a propagating wave in space with electric and magnetic components. ...
In optics, an aperture is something which restricts the diameter of the light path through one plane in an optical system. ...
 Diffraction geometry, showing aperture (or diffracting object) plane and image plane, with coordinate system The electric field diffraction pattern at a point (x,y,z) is given by: Image File history File links Diffraction_geometry. ...
Image File history File links Diffraction_geometry. ...
 where  Analytical solution of this integral is impossible for all but the simplest diffraction geometries.
The key to the Fresnel approximation is the observation that:
 for ![z^2 gg {1 over 4}[(x-x')^2+(y-y')^2]^2](http://upload.wikimedia.org/math/7/2/0/7204acfd73a9cf67f602515abe641cee.png) This is a fairly weak condition which allows all length parameters to take comparable values, provided the aperture is small compared to the wavelength of the light.
Unlike Fraunhofer diffraction, Fresnel diffraction includes the curvature of the wavefront, thus the relative phase is not constant. Fraunhofer diffraction is diffraction of light through an aperture for small values of the Fresnel number, F<<1. ...
In geometrical optics, a wave front (or crest of the wave) is defined as the locus of points having the same phase of vibration. ...
Waves with the same phase Waves with different phases The phase of a wave relates the position of a feature, typically a peak or a trough of the waveform, to that same feature in another part of the waveform (or, which amounts to the same, on a second waveform). ...
For Fresnel diffraction the electric field at point (x,y,z) is given by:
![E(x,y,z)=-{i over lambda}{e^{ikz} over z}iint E(x',y',0)e^{{ik over 2z}[(x-x')^2+(y-y')^2]}dx'dy'](http://upload.wikimedia.org/math/9/e/4/9e4c442405da7991234f337e7cbcb9a0.png) The expression for Fresnel diffraction is valid for: ![z^3 gg {pi over 4lambda}[(x-x')^2+(y-y')^2]_{MAX}^2](http://upload.wikimedia.org/math/5/e/b/5eb2b06a7ddbb26957503345e1331156.png) Analytical solution of this expression is still only possible in rare cases. For a further simplified case, valid only much larger distances from the diffraction source see Fraunhofer diffraction. Fraunhofer diffraction is diffraction of light through an aperture for small values of the Fresnel number, F<<1. ...
See also
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