Far field approximation to Kirchhoff's diffraction formula, i.e. when the plane of observation is far from the object diffracting.
Near field approximation to Kirchhoff's diffraction formula, i.e. when the plane of observation is near the object diffracting.
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The Huygens-Fresnel principle describes propagation by coherent addition of secondary-wave contributions from a wavefront or aperture. Their complex amplitudes, including relative wave phases, must be summed before calculating light intensity. The Fresnel propagator follows by retaining quadratic propagation wave phase in the paraxial approximation.
The Huygens–Fresnel principle is a fundamental concept in the field of wave optics that describes how waves propagate and interfere. Named after Dutch physicist Christiaan Huygens and later expanded by the French physicist Augustin-Jean Fresnel, the principle provides a way to analyze the propagation of wavefronts, such as light waves.