optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...

, piston is the

mean value There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the ''arithme ...

of a

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 freque ...

phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...

profile across the pupil of an optical system. The piston coefficient is typically expressed in

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...

s of light at a particular

. Its main use is in curve-fitting wavefronts with

Cartesian polynomials Cartesian means of or relating to the French philosopher René Descartes—from his Latinized name ''Cartesius''. It may refer to: Mathematics *Cartesian closed category, a closed category in category theory * Cartesian coordinate system, moder ...

Zernike polynomials In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike, winner of the 1953 Nobel Prize in Physics and the inventor of phase-contrast microscopy, th ...

. However, similar to a real engine piston moving up and down in its cylinder, optical piston values can be changed to

bias Bias is a disproportionate weight ''in favor of'' or ''against'' an idea or thing, usually in a way that is closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individual, a group, ...

the wavefront phase mean value as desired. As phase values can only vary from zero to 2π, then repeat in either direction (termed

phase wrapping Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase (also known as local phase or simply phase) of a ''comple ...

), changing the piston coefficient changes the zero phase value contour locations across the wavefront. This property is critical to the operation of phase-measuring interferometers, which give not only the magnitude but also the sign (

convexity Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytope ...

concavity In calculus, the second derivative, or the second order derivative, of a function is the derivative of the derivative of . Roughly speaking, the second derivative measures how the rate of change of a quantity is itself changing; for example, ...

) of a wavefront under test. Piston is physically created in the interferometer by

piezoelectric Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied Stress (mechanics), mechanical s ...

actuators An actuator is a component of a machine that is responsible for moving and controlling a mechanism or system, for example by opening a valve. In simple terms, it is a "mover". An actuator requires a control device (controlled by control signal) an ...

that translate the

Fizeau interferometer A Fizeau interferometerLawson, Peter R. "Principles of Long Baseline Stellar Interferometry." Course notes from the 1999 Michelson Summer School, held August 15–19, 1999. Edited by Peter R. Lawson. Published by National Aeronautics and Space Admi ...

reference surface along the optical axis by precise fractions of the test wavelength, usually by one quarter of a wavelength. This changes the interferometric fringe patterns and allows direct calculation of the exact wavefront error. Piston and

tilt Tilt may refer to: Music * Tilt (American band), a punk rock group, formed in 1992 * Tilt (British band), an electronic music group, formed in 1993 * Tilt (Polish band), a rock band, formed in 1979 Albums * ''Tilt'' (Cozy Powell album), 1981 * ...

are not actually true optical aberrations, as they do not represent or model

curvature In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonic ...

in the wavefront.

Defocus In optics, defocus is the aberration in optical systems, aberration in which an image is simply out of focus (optics), focus. This aberration is familiar to anyone who has used a camera, videocamera, microscope, telescope, or binoculars. Opti ...

is the lowest order true optical aberration. If piston and tilt are subtracted from an otherwise perfect wavefront, a perfect, aberration-free image is formed.

References

*Malacara, D., ''Optical Shop Testing - Second Edition'', John Wiley and Sons, 1992, . {{DEFAULTSORT:Piston (Optics) Physical optics