wavefront

A wavefront is a surface of constant phase in a propagating wave. All points on a given wavefront oscillate in step, and as the wave advances, the surface moves in the direction normal to the surface. In three-dimensional space, common wavefront shapes are planes (for plane waves in a uniform medium) and spheres (emitted from a point source in an unbounded medium). In media with spatially varying refractive index or with boundaries, wavefronts can become curved or distorted, and the propagation directions (rays) are everywhere normal to the local wavefront.

In geometrical optics, wavefronts are linked to rays through the principle that a ray is perpendicular to successive wavefronts. Huygens’ principle treats every point on a wavefront as a secondary source of wavelets, with the envelope of these wavelets forming the new wavefront. The evolution of wavefronts is described by the eikonal equation in the high-frequency limit and by Fermat’s principle, which leads to Snell’s law at interfaces. In a homogeneous medium with refractive index n, the wavefront advances along its normal at speed v = c/n, so after time t the wavefront has moved a distance (c/n) t along the normal.

Wavefront concepts are used to diagnose and correct optical aberrations. Wavefront sensors, such as Shack–Hartmann sensors, estimate the shape of a wavefront to enable adaptive optics in astronomy and microscopy, as well as beam shaping in laser systems. The idea also extends to acoustics and quantum matter waves, where analogous wavefronts describe phase patterns.