Wavefront

In physics, a wavefront is a specific set of points within a time-varying wave field. These points all share the same phase. Phase describes a specific stage in a wave's cycle. This concept is most useful for fields that vary sinusoidally in time. This means the field changes following a smooth, repeating pattern with a single frequency. Without this consistent frequency, the phase is not well defined.

Wavefronts generally move through space as time passes. Their geometric shape depends on the dimensions of the medium. In a unidimensional medium, a wavefront is typically a single point. In a two-dimensional medium, wavefronts appear as curves. In a three-dimensional medium, they exist as surfaces.

There are different types of simple wavefronts, such as plane waves and spherical waves. A plane wave consists of flat wavefronts that move together in one direction. The light from such a wave is called collimated light. A spherical wave consists of spherical surfaces that expand outward. This expansion happens because the wave carries energy equally in all directions. The paths of this energy flow are called rays. These rays are always perpendicular to the wavefront.

Sunlight provides a massive example of a spherical wavefront. It strikes the Earth with a radius of about 150 million kilometers, also known as 1 AU. Because this radius is so large, the wavefront can be treated as a plane over distances equal to Earth's diameter. The shape of a wavefront can also change through refraction. Refraction occurs if the speed of propagation differs at different points on the wavefront. For example, lenses can change optical wavefronts from planar to spherical or vice versa.

Classical physics explains wave bending through the Huygens–Fresnel principle. This principle treats every point on a propagating wavefront as a source of secondary spherical waves. When a coherent source, like a laser, hits a small slit or aperture, a bending pattern appears. This happens because secondary waves from each point interfere with one another. If there are multiple closely spaced openings, such as a diffraction grating, a complex pattern of varying intensity results. Scientists use Huygens' principle as a quick way to predict how wavefronts move through free space.

Sometimes, wavefronts do not maintain their ideal shapes. This deviation from a perfect planar wavefront is called a wavefront aberration. These errors can be caused by lens thickness or manufacturing imperfections. For instance, a lens might have a spherical surface, even though an aspheric surface would be ideal. These shortcomings create optical aberrations like coma or spherical aberration. Large telescopes also face aberrations due to spatial variations in the atmosphere's index of refraction.

To manage these errors, scientists use devices called wavefront sensors. These tools measure wavefront aberrations to describe the optical quality of a system. One common type is the Shack–Hartmann wavefront sensor, which uses a lenslet array. Other types include the pyramid wavefront sensor and the wavefront curvature sensor, also known as the Roddier test. These sensors are vital for adaptive optics and optical metrology. They are even used to measure aberrations in the human eye. In medical uses, a weak laser can reflect off the retina to sample the wavefront.