Piston (optics)
Encyclopedia
In optics
, piston is the mean value of a wavefront
or phase
profile across the pupil of an optical system. The piston coefficient is typically expressed in wavelength
s of light at a particular wavelength
. Its main use is in curve-fitting wavefronts with Cartesian polynomials or Zernike polynomials
.
However, similar to a real V8 engine piston moving up and down in its cylinder, optical piston values can be changed to bias 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), 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 or concavity) of a wavefront under test. Piston is physically created in the interferometer by piezoelectric actuators that translate the Fizeau interferometer
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
are not actually true optical aberrations, as they do not represent or model curvature
in the wavefront. Defocus 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.
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
, piston is the mean value of a wavefront
Wavefront
In physics, a wavefront is the locus of points having the same phase. 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...
or phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
profile across the pupil of an optical system. The piston coefficient is typically expressed in wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
s of light at a particular wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
. Its main use is in curve-fitting wavefronts with Cartesian polynomials or Zernike polynomials
Zernike polynomials
In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after Frits Zernike, they play an important role in beam optics.-Definitions:There are even and odd Zernike polynomials...
.
However, similar to a real V8 engine piston moving up and down in its cylinder, optical piston values can be changed to bias 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), 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 or concavity) of a wavefront under test. Piston is physically created in the interferometer by piezoelectric actuators that translate the Fizeau interferometer
Fizeau interferometer
A Fizeau interferometer is similar to a Fabry–Pérot interferometer in that they both consist of two reflecting surfaces. In a Fizeau interferometer, however, the two surfaces are usually much less than totally reflecting , so that secondary reflections don't contribute greatly to the fringe...
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 (optics)
In optics, tilt is a deviation in the direction a beam of light propagates. Tilt quantifies the average slope in both the X and Y directions of a wavefront or phase profile across the pupil of an optical system...
are not actually true optical aberrations, as they do not represent or model curvature
Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...
in the wavefront. Defocus 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.