Tilt (optics)
Encyclopedia
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. In conjunction with piston
(the first Zernike polynomial
term), X and Y tilt can be modeled using the second and third Zernike polynomials:
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
of light.
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.
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 aerodynamic flowfields. Jitter may be compensated in an adaptive optics
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
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.
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.
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...
, tilt is a deviation in the direction a beam of light propagates. Tilt quantifies the average
Average
In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set. Average is one form of central tendency. Not all central tendencies should be considered definitions of average....
slope
Slope
In mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline....
in both the X and Y directions 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. In conjunction with piston
Piston (optics)
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 wavelengths of light at a particular wavelength...
(the first Zernike polynomial
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...
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 wavelengthWavelength
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...
of light.
Piston and tilt are not actually true optical aberrations
Aberration in optical systems
Aberrations are departures of the performance of an optical system from the predictions of paraxial optics. Aberration leads to blurring of the image produced by an image-forming optical system. It occurs when light from one point of an object after transmission through the system does not converge...
, 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.
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
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...
in aerodynamic flowfields. Jitter may be compensated in an adaptive optics
Adaptive optics
Adaptive optics is a technology used to improve the performance of optical systems by reducing the effect of wavefront distortions. It is used in astronomical telescopes and laser communication systems to remove the effects of atmospheric distortion, and in retinal imaging systems to reduce the...
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
Gimbal
A gimbal is a pivoted support that allows the rotation of an object about a single axis. A set of two gimbals, one mounted on the other with pivot axes orthogonal, may be used to allow an object mounted on the innermost gimbal to remain immobile regardless of the motion of its support...
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.
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
Deformable mirror
Deformable mirror represents the most convenient tool for wavefront control and correction of optical aberrations. Deformable mirrors are used in combination with wavefront sensors and real-time control systems in adaptive optics...
(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
Shearing Interferometer
The shearing interferometer is an extremely simple means to observe interference and to use this phenomenon to test the collimation of light beams, especially from laser sources which have a coherence length which is usually a lot longer than the thickness of the shear plate so that the basic...
, on the deformable mirror faceplate.