Fresnel GeometryFor the Fresnel case, all length parameters are allowed to take comparable values, so all must be included as variables in the problem. The usual geometry assumes a monochromatic slit source and the problem is set up in terms of a parameter v as defined below. This parameter is used with the Cornu spiral or a table of elliptical intgrals. 
Index Diffraction concepts Fresnel diffraction  

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Fresnel v ParameterThe vparameter in Fresnel diffraction analysis can be thought of as the arclength along the amplitude vector diagram called the Cornu spiral. In the Fraunhofer diffraction case where the source wavefront was assumed to be planar, the different elements of the wavefront had a constant phase difference and the incremental amplitude elements added to form the arc of a circle. In the Fresnel diffraction case where the curvature of the wavefront is included, the relative phase is not constant and the amplitude elements bend into the spiral curve. Just as in the Fraunhofer case, the resultant amplitude is represented by the chord of the arc. 
Index Diffraction concepts Fresnel diffraction  

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