Fraunhoferdiffrakció

Fraunhofer diffraction is the far-field regime of optical diffraction from an aperture or obstacle, observed when the incident wave is effectively planar or when the diffracted light is collected in a distant plane or in the focal plane of a lens. It is named after Joseph von Fraunhofer, who studied diffraction patterns in the early 19th century. The Fraunhofer approximation contrasts with Fresnel (near-field) diffraction, which occurs at shorter distances or with more curved wavefronts.

In this regime, the complex amplitude in the observation plane is proportional to the Fourier transform of the aperture function. The resulting intensity is proportional to the square modulus of that transform. For practical cases, simple patterns arise: a single slit of width a yields I(θ) ∝ sinc^2(π a sin θ / λ), and a circular aperture of radius R yields the Airy pattern I(θ) ∝ [2 J1(k R sin θ) / (k R sin θ)]^2, where J1 is a Bessel function and k = 2π/λ. The far-field pattern can also be produced by placing a lens to form the focal plane image, which then represents the Fourier transform of the aperture (pupil) function.

Applications of Fraunhofer diffraction include characterization of optical systems, determination of aperture shapes, and analysis of diffraction-limited resolution. It provides the theoretical foundation for angular resolution limits (for a circular aperture, approximately 1.22 λ/D) and underpins many techniques in imaging, spectroscopy, and laser beam shaping.