In
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, ultra ...
, tilt is a deviation in the direction a beam of light propagates.
Overview
Tilt quantifies the
average
In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, ...
slope
In mathematics, the slope or gradient of a line is a number that describes both the ''direction'' and the ''steepness'' of the line. Slope is often denoted by the letter ''m''; there is no clear answer to the question why the letter ''m'' is used ...
in both the X and Y directions 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 fre ...
or
phase profile across the pupil of an optical system. In conjunction with
piston
A piston is a component of reciprocating engines, reciprocating pumps, gas compressors, hydraulic cylinders and pneumatic cylinders, among other similar mechanisms. It is the moving component that is contained by a cylinder and is made gas- ...
(the first
Zernike polynomial term), X and Y tilt can be modeled using the second and third Zernike polynomials:
:X-Tilt:
:Y-Tilt:
where
is the normalized radius with
and
is the azimuthal angle with
.
The
and
coefficients are typically expressed as a fraction of a chosen
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, tr ...
of light.
Piston and tilt 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 can ...
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.
Rapid optical tilts in both X and Y directions are termed jitter. Jitter can arise from three-dimensional mechanical vibration, and from rapidly varying 3D
refraction
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomen ...
in aerodynamic flowfields. Jitter may be compensated in an
adaptive optics
Adaptive optics (AO) is a technology used to improve the performance of optical systems by reducing the effect of incoming wavefront distortions by deforming a mirror in order to compensate for the distortion. It is used in astronomical tel ...
system by using a flat mirror mounted on a dynamic two-axis mount that allows small, rapid, computer-controlled changes in the mirror X and Y angles. This is often termed a "
fast steering mirror", or FSM. A
gimbal
A gimbal is a pivoted support that permits rotation of an object about an axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow an object mounted on the innermost gimbal to remain independent of ...
ed optical pointing system cannot mechanically track an object or stabilize a projected laser beam to much better than several hundred
microradians. Buffeting due to aerodynamic turbulence further degrades the pointing stability.
Light, however, has no appreciable momentum, and by reflecting from a computer-driven FSM, an image or laser beam can be stabilized to single microradians, or even a few hundred
nanoradians. This almost totally eliminates image blurring due to motion, and
far-field laser beam jitter. Limitations on the degree of line-of-sight stabilization arise from the limited dynamic range of the FSM tilt, and the highest frequency the mirror tilt angle can be changed. Most FSM's can be driven to several wavelengths of tilt, and at frequencies exceeding one
kilohertz
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one ...
.
As the FSM mirror is optically flat, FSM's need not be located at
pupil images. Two FSM's can be combined to create an anti-beamwalk pair, which stabilizes not only the beam pointing angle but the location of the beam center. Anti-beamwalk FSM's are positioned prior to a
deformable mirror (which must be located at a pupil image) to stabilize the position of the pupil image on the deformable mirror and minimize correction errors resulting from wavefront movement, or
shearing, on the deformable mirror faceplate.
References
*Malacara, D., ''Optical Shop Testing - Second Edition'', John Wiley and Sons, 1992, {{ISBN, 0-471-52232-5.
Geometrical optics