Wavefront

In physics, the wavefront of a time-varying wave field is the set (locus) of all points having the same phase. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal frequency (otherwise the phase is not well defined). Wavefronts usually move with time. For waves propagating in a unidimensional medium, the wavefronts are usually single points; they are curves in a two dimensional medium, and surfaces in a three-dimensional one. are planes. For a sinusoidal plane wave, the wavefronts are planes perpendicular to the direction of propagation, that move in that direction together with the wave. For a sinusoidal spherical wave, the wavefronts are spherical surfaces that expand with it. If the speed of propagation is different at different points of a wavefront, the shape and/or orientation of the wavefronts may change by refraction. In particular, lenses can change the shape of optical wavefronts from planar to spherical, or vice versa. In classical physics, the diffraction phenomenon is described by the Huygens–Fresnel principle treating each point in a propagating wavefront as a source of a secondary spherical waves. The characteristic wave bending pattern is most pronounced when a wave from a coherent source (such as a laser) encounters a slit/aperture that is comparable in size to the wavelength.…

In physics, the wavefront of a time-varying wave field is the set (locus) of all points having the same phase. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal frequency (otherwise the phase is not well defined). Wavefronts usually move with time. For waves propagating in a unidimensional medium, the wavefronts are usually single points; they are curves in a two dimensional medium, and surfaces in a three-dimensional one. are planes.]] For a sinusoidal plane wave, the wavefronts are planes perpendicular to the direction of propagation, that move in that direction together with the wave. For a sinusoidal spherical wave, the wavefronts are spherical surfaces that expand with it. If the speed of propagation is different at different points of a wavefront, the shape and/or orientation of the wavefronts may change by refraction. In particular, lenses can change the shape of optical wavefronts from planar to spherical, or vice versa. In classical physics, the diffraction phenomenon is described by the Huygens–Fresnel principle treating each point in a propagating wavefront as a source of a secondary spherical waves. The characteristic wave bending pattern is most pronounced when a wave from a coherent source (such as a laser) encounters a slit/aperture that is comparable in size to the wavelength. This is due to the addition, or interference, of secondary waves emanated from each point on the wavefront on a wave propagation blocking element like the slit/aperture. If there are multiple, closely spaced openings (e.g., a diffraction grating), a complex pattern of varying intensity can result. ==Simple wavefronts and propagation== Optical systems can be described with Maxwell's equations, and linear propagating waves such as sound or electron beams have similar wave equations. However, given the above simplifications, Huygens' principle provides a quick method to predict the propagation of a wavefront through, for example, free space. The construction is as follows: Let every point on the wavefront be considered a new point source. By calculating the total effect from every point source, the resulting field at new points can be computed. Computational algorithms are often based on this approach. Specific cases for simple wavefronts can be computed directly. For example, a spherical wavefront will remain spherical as the energy of the wave is carried away equally in all directions. Such directions of energy flow, which are always perpendicular to the wavefront, are called rays creating multiple wavefronts. The simplest form of a wavefront is the plane wave, where the rays are parallel to one another. The light from this type of wave is referred to as collimated light. The plane wavefront is a good model for a surface-section of a very large spherical wavefront; for instance, sunlight strikes the earth with a spherical wavefront that has a radius of about 150 million kilometers (1 AU). For many purposes, such a wavefront can be considered planar over distances of the diameter of Earth. In an isotropic medium, wavefronts travel with the same speed in all directions. ==Wavefront aberrations== Methods using wavefront measurements or predictions can be considered an advanced approach to lens optics, where a single focal distance may not exist due to lens thickness or imperfections. For manufacturing reasons, a perfect lens has a spherical (or toroidal) surface shape though, theoretically, the ideal surface would be aspheric. Shortcomings such as these in an optical system cause what are called optical aberrations. The best-known aberrations include spherical aberration and coma. However, there may be more complex sources of aberrations such as in a large telescope due to spatial variations in the index of refraction of the atmosphere. The deviation of a wavefront in an optical system from a desired perfect planar wavefront is called the wavefront aberration. Wavefront aberrations are usually described as either a sampled image or a collection of two-dimensional polynomial terms. Minimization of these aberrations is considered desirable for many applications in optical systems. ==See also== Huygens–Fresnel principle Wavefront sensor Adaptive optics Deformable mirror Wave field synthesis Hamilton–Jacobi equation ==References== ==Further reading== ===Textbooks and books=== Concepts of Modern Physics (4th Edition), A. Beiser, Physics, McGraw-Hill (International), 1987, Physics with Modern Applications, L. H. Greenberg, Holt-Saunders International W. B. Saunders and Co, 1978, Principles of Physics, J. B. Marion, W. F. Hornyak, Holt-Saunders International Saunders College, 1984, Introduction to Electrodynamics (3rd Edition), D. J. Griffiths, Pearson Education, Dorling Kindersley, 2007, Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers, Y. B. Band, John Wiley & Sons, 2010, The Light Fantastic – Introduction to Classic and Quantum Optics, I. R. Kenyon, Oxford University Press, 2008, McGraw Hill Encyclopaedia of Physics (2nd Edition), C. B. Parker, 1994, ===Journals=== Wavefront tip/tilt estimation from defocused images ==External links== AO Tutorial: Wave-front Sensors Wavefront sensing: Establishments Research groups and companies with interests in wavefront sensing and adaptive optics.

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