Wavefront

For other uses, see Wavefront (disambiguation).

In physics, a wavefront is the locus of points characterized by propagation of position of the same phase: a propagation of a line in 1d, a curve in 2d or a surface for a wave in 3d. Since infrared, optical, x-ray and gamma-ray frequencies are so high, the temporal component of electromagnetic waves is usually ignored at these wavelengths, and it is only the phase of the spatial oscillation that is described. Additionally, most optical systems and detectors are indifferent to polarization, so this property of the wave is also usually ignored. At radio wavelengths, the polarization becomes more important, and receivers are usually phase-sensitive. Many audio detectors are also phase-sensitive.

The wavefronts of a plane wave are planes.

File:Lens and wavefronts.gif

A lens can be used to change the shape of wavefronts. Here, plane wavefronts become spherical after going through the lens.

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.

Wavefront aberrations

Main article: Optical aberration

Methods utilizing 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. Note also that 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.

Wavefront sensor and reconstruction techniques

A wavefront sensor is a device which measures the wavefront aberration in a coherent signal to describe the optical quality or lack thereof in an optical system. A very common method is to use a Shack-Hartmann lenslet array. There are many applications that include adaptive optics, optical metrology and even the measurement of the aberrations in the eye itself. In this approach, a weak laser source is directed into the eye and the reflection off the retina is sampled and processed.

Alternative wavefront sensing techniques to the Shack-Hartmann system are emerging. 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.

Another application of software reconstruction of the phase is the control of telescopes through the use of adaptive optics. A common method is the Roddier test, also called wavefront curvature sensing. It yields good correction, but needs an already good system as a starting point.

See also

• Huygens' principle
• Wavefront sensor
• Adaptive optics
• Deformable mirror

Further reading

Textbooks

• Concepts of Modern Physics (4th Edition), A. Beiser, Physics, McGraw-Hill (International), 1987, ISBN 0-07-100144-1
• Physics with Modern Applications, L.H. Greenberg, Holt-Saunders International W.B. Saunders and Co, 1978, ISBN 0-7216-4247-0
• Principles of Physics, J.B. Marion, W.F. Hornyak, Holt-Saunders International Saunders College, 1984, ISBN 4-8337-0195-2
• Introduction to Electrodynamics (3rd Edition), D.J. Griffiths, Pearson Education, Dorling Kindersley, 2007, ISBN 81-7758-293-3
• Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers, Y.B. Band, John Wiley & Sons, 2010, ISBN 978-0-471-89931-0
• The Light Fantastic – Introduction to Classic and Quantum Optics, I.R. Kenyon, Oxford University Press, 2008, ISBN 978-0-19-856646-5
• McGraw Hill Encyclopaedia of Physics (2nd Edition), C.B. Parker, 1994, ISBN 0-07-051400-3

Journals

• Wavefront tip/tilt estimation from defocused images

External links

• LightPipes - Free Unix wavefront propagation software