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. 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. For many purposes, such a wavefront can be
considered planar. Wavefront aberrations
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 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 References
Further reading = Textbooks=
Concepts of Modern Physics, A. Beiser, Physics, McGraw-Hill, 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, 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, C.B. Parker, 1994, ISBN 0-07-051400-3
= Journals= François Roddier, Claude Roddier.
"Wavefront reconstruction using iterative Fourier transforms". Applied
Optics 30: 1325–1327. Bibcode:1991ApOpt..30.1325R.
doi:10.1364/AO.30.001325. ISSN 0003-6935. PMID 20700283.
Claude Roddier, François Roddier. "Wave-front reconstruction from
defocused images and the testing of ground-based optical telescopes".
Journal of the Optical Society of America A 10: 2277–2287.
Bibcode:1993OSAJ...10.2277R. doi:10.1364/JOSAA.10.002277.
Wavefront tip/tilt estimation from defocused images
External links LightPipes - Free Unix wavefront
propagation software