The Huygens–Fresnel principle (named after Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel) states that every point on a wavefront is itself the source of spherical wavelets and that the secondary wavelets emanating from different points mutually interfere. The sum of these spherical wavelets forms a new wavefront. As such, the Huygens–Fresnel principle is a method of analysis applied to problems of luminous wave propagation both in the far-field limit and in near-field diffraction as well as reflection.

In 1678, Huygens proposed that every point reached by a luminous disturbance becomes a source of a spherical wave. The sum of these secondary waves determines the form of the wave at any subsequent time; the overall procedure is referred to as Huygens' construction. He assumed that the secondary waves traveled only in the "forward" direction, but it is not explained in the theory why this is the case. He was able to provide a qualitative explanation of linear and spherical wave propagation, and to derive the laws of reflection and refraction using this principle, but could not explain the deviations from rectilinear propagation that occur when light encounters edges, apertures and screens, commonly known as diffraction effects.

In 1818, Fresnel showed that Huygens' principle, together with his own principle of interference, could explain both the rectilinear propagation of light and also diffraction effects. To obtain agreement with the experimental results, he had to include additional arbitrary assumptions about the phase and amplitude of the secondary waves, as well as an obliquity factor. These assumptions have no obvious physical foundation, but led to predictions that agreed with many experimental observations, including the Poisson spot.

Poisson was a member of the French Academy, which reviewed Fresnel's work. He used Fresnel's theory to predict that a bright spot ought to appear in the center of the shadow of a small disc, and deduced from this that the theory was incorrect. However, François Arago, another member of the committee, performed the experiment and showed that the prediction was correct. This success was important evidence in favor of the wave theory of light over then predominant corpuscular theory.

In 1882, Gustav Kirchhoff analyzed Fresnel's theory in a rigorous mathematical formulation, as an approximate form of an integral theorem. Very few rigorous solutions to diffraction problems are known, however, and most problems in optics are adequately treated using the Huygens–Fresnel principle.

In 1939 Edward Copson, extended Huygens' original principle to consider the polarization of light, which requires a vector potential, in contrast to the scalar potential of a simple ocean wave or sound wave.

In antenna theory and engineering, the reformulation of the Huygens–Fresnel principle for radiating current sources is known as surface equivalence principle.

Issues in Huygens–Fresnel theory continue to be of interest. In 1991, David A. B. Miller suggested that treating the source as a dipole (not the monopole assumed by Huygens) will cancel waves propagating in the reverse direction, making Huygens' construction quantitatively correct. In 2021, Forrest L. Anderson showed that treating the wavelets as Dirac delta functions, summing and differentiating the summation is sufficient to cancel reverse propagating waves.