Fresnel diffraction

Summary

Fresnel diffraction, or near-field diffraction, is the diffraction of a wave observed at a moderate distance from an aperture. At such distances the curvature of the wavefronts still matters. It is computed with the Fresnel integral, a paraxial approximation of the Kirchhoff and Rayleigh–Sommerfeld formulas in which the phase is expanded to second order. It applies when the Fresnel number is of order $1$ or larger, and it reduces to Fraunhofer diffraction when the Fresnel number is small. Famous Fresnel patterns are the fringes at a straight edge, described with the Cornu spiral, and the Arago spot.