FresnelFraunhofer

Fresnel and Fraunhofer are two distinct approaches to the diffraction of light, named after their respective pioneers, Augustin-Jean Fresnel and Joseph von Fraunhofer. Both theories describe how light bends and spreads as it passes through an aperture or around an obstacle, but they apply to different scenarios and have different mathematical formulations.

Fresnel diffraction occurs when the light source and the observation point are at a finite distance from the diffracting object. This is typically the case in everyday situations, such as when light passes through a small aperture or around the edge of an object. Fresnel diffraction is described by the Fresnel integrals, which are complex functions that account for the phase differences between the various parts of the wavefront. The Fresnel number, which is the ratio of the aperture size to the wavelength, determines the type of diffraction pattern observed.

Fraunhofer diffraction, on the other hand, occurs when the light source and the observation point are at an infinite distance from the diffracting object. This is often the case in optical instruments, such as telescopes and microscopes, where the light is collimated (parallel) before it reaches the aperture. Fraunhofer diffraction is described by the Fourier transform of the aperture function, which relates the spatial distribution of the light to its angular distribution. The Fraunhofer diffraction pattern is typically observed in the far field, where the wavefront is approximately planar.

In summary, Fresnel and Fraunhofer diffraction are two complementary approaches to understanding the diffraction of light. Fresnel diffraction applies to near-field situations, while Fraunhofer diffraction applies to far-field situations. Both theories are fundamental to the study of optics and have numerous applications in science and engineering.