diffractions

Diffraction is the bending and spreading of waves when they encounter obstacles or pass through apertures, accompanied by interference among the secondary wavefronts emanating from the edges. It occurs for all wave types, including light, sound, water waves, and matter waves such as electrons.

Historically, diffraction was studied to explain observed light patterns and was formalized through the Huygens–Fresnel principle. The phenomenon is described in different regimes: Fraunhofer (far-field) diffraction, where the pattern is the Fourier transform of the aperture function, and Fresnel (near-field) diffraction, which requires a more general treatment of phase variations.

In classic experiments, single-slit diffraction produces a central maximum with minima at a sin θ = mλ (m = ±1, ±2, …). A slit much wider than the wavelength yields a broad central lobe; a circular aperture yields the Airy pattern with the first minimum at sin θ ≈ 1.22 λ / D. Double-slit interference creates a series of sharp fringes modulated by the single-slit diffraction envelope. Diffraction gratings with many slits produce highly directive maxima at d sin θ = mλ, increasing intensity.

Theoretically, diffraction can be described by boundary conditions and integrals such as the Kirchhoff diffraction integral; Babinet's principle relates patterns from complementary screens. Related concepts include the Fraunhofer and Fresnel approximations and the Airy disk in optics.

Applications span optical instruments, microscopy, X-ray and electron diffraction in crystallography, and acoustic wave studies. Diffraction sets fundamental limits on resolution and informs the design of lenses, sensors, and imaging systems.