Huygens–Fresnel principle

The Huygens–Fresnel principle models wave propagation by treating each point on a wavefront as a source of secondary waves whose superposition forms later wavefronts.

Huygens' principle: A wave-propagation construction in which every point on a wavefront acts as a source of secondary wavelets. Fresnel extended this geometric construction by including interference among the secondary wavelets.
Christiaan Huygens: A Dutch mathematician and physicist who developed an influential wave theory of light in the seventeenth century. His 1690 wave theory introduced the construction later incorporated into the principle.
Wave equation: A differential equation governing the propagation of waves through space and time. The principle is a construction for solutions of wave equations under suitable conditions.
Fresnel diffraction: Near-field diffraction in which the curvature of wavefronts across an aperture matters. The principle provides a direct way to calculate this near-field pattern.
Geometrical optics: An approximation that models light as rays and neglects effects associated with its wave nature. It predicts ray paths but not the interference patterns explained by the principle.
Wavefront: A surface of constant phase in a propagating wave. The principle starts with a wavefront and constructs the next one from it.
Augustin-Jean Fresnel: A French physicist who developed a wave theory of light and analyzed diffraction in the early nineteenth century. Fresnel added phase and interference to Huygens' construction.
Phase (waves): The position within a wave's oscillation cycle, commonly expressed as an angle. Relative phase determines whether secondary-wave contributions reinforce or cancel.
Fraunhofer diffraction: Far-field diffraction in which the observed pattern is approximately the Fourier transform of the aperture. It follows from the same wavefront construction under far-field approximations.
Rayleigh–Sommerfeld diffraction theory: A scalar diffraction formulation derived from wave equations with boundary conditions at an aperture. It provides a more explicit integral treatment than the elementary secondary-wave construction.

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