Fresneldiffrakció

Fresneldiffrakció, or Fresnel diffraction, is a description of near-field diffraction effects that occur when light passes through an aperture or around an obstacle and is observed at distances where the wavefront remains curved. It is named after Augustin-Jean Fresnel. In contrast to Fraunhofer (far-field) diffraction, the geometry and the curvature of the wavefront play a central role in shaping the interference pattern.

The calculation relies on the Fresnel diffraction integral. The complex amplitude at a point in space is proportional to an integral over the aperture of exp(i k r)/r, which under the paraxial approximation reduces to a quadratic phase term. The resulting near-field pattern can be represented by the Cornu spiral, constructed from the Fresnel integrals C(v) and S(v). This approach provides a compact way to describe how contributions from different parts of an aperture interfere as the wavefront propagates.

A key concept is the Fresnel number, F = a^2/(λ z) for a circular aperture of radius a observed at distance z, with wavelength λ. When F is of order 1, Fresnel diffraction dominates and intricate fringe patterns appear. For F ≪ 1, the pattern tends toward the simpler Fraunhofer (far-field) form, while for larger F the near-field structure becomes increasingly complex.

Typical examples include diffraction by a straight edge, a circular aperture, or small obstructions, where features such as bright and dark fringes and, in some cases, the Poisson spot (bright center) can arise. Fresneldiffrakció is relevant in imaging systems, lithography, X-ray optics, and acoustic settings, where near-field effects influence resolution and intensity distributions.