# Fresnel Geometry

For 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.

To calculate the intensity at point P, the geometry is set up in terms of the parameter v which is used with the Cornu spiral.

Index

Diffraction concepts

Fresnel diffraction

References:
Meyer-Arendt
4th Ed, Ch 14.
Pedrotti & Pedrotti
Ch 21.

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# Fresnel v Parameter

The v-parameter 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.

The intent here is to show conceptually how the light amplitudes at different points on a screen can be obtained using the Cornu spiral or the expressions shown in the Fresnel geometry. The amplitude is then squared to get the relative intensity at that field point. It is typical in more advanced optics texts to provide tables of the Fresnel integrals, which could be used for a computer routine to plot the Fresnel diffraction pattern.

Index

Diffraction concepts

Fresnel diffraction

References:
Meyer-Arendt
4th Ed, Ch 14.
Pedrotti & Pedrotti
Ch 21.

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