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Wavefront

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For other uses, seeWavefront (disambiguation).

In physics, thewavefrontof a time-varyingwavefieldis the set (locus) of allpointshaving the samephase.[1]The term is generally meaningful only for fields that, at each point, varysinusoidallyin time with a single temporal frequency (otherwise the phase is not well defined).

Wavefronts usually move with time. For waves propagating in aunidimensionalmedium, the wavefronts are usually single points; they arecurvesin a two dimensional medium, andsurfacesin a three-dimensional one.

The wavefronts of aplane waveareplanes.
Wavefronts change shape after going through a lens.

For asinusoidal plane wave,the wavefronts are planes perpendicular to the direction of propagation, that move in that direction together with the wave. For asinusoidal 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 byrefraction.In particular,lensescan change the shape of optical wavefronts from planar to spherical, or vice versa.

Inclassical physics,the diffraction phenomenon is described by theHuygens–Fresnel principlethat treats each point in a propagating wavefront as a collection of individual sphericalwavelets.[2]The characteristic bending pattern is most pronounced when a wave from acoherentsource (such as a laser) encounters a slit/aperture that is comparable in size to itswavelength,as shown in the inserted image. This is due to the addition, orinterference,of different points on the wavefront (or, equivalently, each wavelet) that travel by paths of different lengths to the registering surface. If there are multiple,closely spaced openings(e.g., adiffraction grating), a complex pattern of varying intensity can result.

Simple wavefronts and propagation[edit]

Optical systems can be described withMaxwell's equations,and linear propagating waves such as sound or electron beams have similar wave equations. However, given the above simplifications,Huygens' principleprovides 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 newpoint 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 calledrayscreating multiple wavefronts.[3]

Rays and wavefronts

The simplest form of a wavefront is theplane wave,where the rays areparallelto one another. The light from this type of wave is referred to ascollimatedlight. 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 (1AU). 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[edit]

Main article:Optical aberration

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 beaspheric.Shortcomings such as these in an optical system cause what are calledoptical aberrations.The best-known aberrations includespherical aberrationandcoma.[4]

However, there may be more complex sources of aberrations such as in a large telescope due to spatial variations in theindex of refractionof the atmosphere. The deviation of a wavefront in an optical system from a desired perfect planar wavefront is called thewavefront 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.

Wavefront sensor and reconstruction techniques[edit]

Awavefront sensoris a device which measures the wavefront aberration in a coherent signal to describe the optical quality or lack thereof in an optical system. There are many applications that includeadaptive optics,optical metrology and even the measurement of theaberrationsin theeyeitself. In this approach, a weak laser source is directed into the eye and the reflection off theretinais sampled and processed. Another application of software reconstruction of the phase is the control of telescopes through the use of adaptive optics.

Mathematical techniques like phase imaging or curvature sensing are also capable of providing wavefront estimations. These algorithms compute wavefront images from conventional brightfield images at different focal planes without the need for specialised wavefront optics. While Shack-Hartmann lenslet arrays are limited in lateral resolution to the size of the lenslet array, techniques such as these are only limited by the resolution of digital images used to compute the wavefront measurements. That said, those wavefront sensors suffer from linearity issues and so are much less robust than the original SHWFS, in term of phase measurement.

There are several types of wavefront sensors, including:

Although an amplitude splittinginterferometersuch as theMichelson interferometercould be called a wavefront sensor, the term is normally applied to instruments that do not require an unaberrated reference beam to interfere with.

See also[edit]

References[edit]

  1. ^Essential Principles of Physics,P. M. Whelan, M. J. Hodgeson, 2nd Edition, 1978, John Murray,ISBN0-7195-3382-1
  2. ^Wireless Communications: Principles and Practice, Prentice Hall communications engineering and emerging technologies series, T. S. Rappaport, Prentice Hall, 2002 pg 126
  3. ^University Physics – With Modern Physics(12th Edition), H. D. Young, R. A. Freedman (Original edition), Addison-Wesley (Pearson International), 1st Edition: 1949, 12th Edition: 2008,ISBN0-321-50130-6,ISBN978-0-321-50130-1
  4. ^Encyclopaedia of Physics (2nd Edition),R.G. Lerner,G.L. Trigg, VHC publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1, ISBN (VHC Inc.) 0-89573-752-3

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