Fraunhofertilnærmingen

Fraunhofertilnærmingen, also known as the Fraunhofer approximation, is a method used in optics and diffraction theory to simplify the calculation of diffraction patterns. It is applicable when the observation distance is very large compared to the size of the diffracting object and the wavelength of the incident light. This scenario is often referred to as the "far-field" region.

In essence, Fraunhofertilnærmingen assumes that the light rays emanating from the diffracting object are parallel when they reach the observation screen. This is a valid assumption when the source of the light is effectively at infinity, or when a lens is used to focus parallel light onto the diffracting aperture, and another lens is used to observe the resulting pattern at its focal plane. Under these conditions, the diffraction pattern observed is essentially the Fourier transform of the aperture's transmission function.

The mathematical formulation of Fraunhofertilnærmingen involves an integral that describes the amplitude of the diffracted wave at a distant point. This integral's form directly relates the diffraction pattern to the spatial frequency content of the diffracting object. It is a fundamental concept in understanding phenomena like the diffraction from slits, gratings, and circular apertures, and is crucial for analyzing the resolving power of optical instruments. The approximation breaks down when the observation distance is not sufficiently large, in which case the Fresnel approximation must be used instead.