Image Processing Reference
any system, no matter how much spatial resolution the system has. How these dif-
ferent errors recombine into the performance of the system is determined by Eq. 4.1
σσ σ +σ
2 are the various uncoupled wavefront variations. This will be discussed
again in Chapter 6.
4.3 Wavefront Correctors for Piston, and Tip and Tilt
Types of wavefront correctors come in a wide range based on a number of technol-
ogies. For high-order devices, the most popular are continuous face-sheet mirrors
driven by mechanical actuators or electrostatic force. Typically, these are charac-
terized by their ability to correct for many Zernike modes, but they have limited an-
gular range. Wavefront correctors used in beam-steering and image-stabilization
applications are not required to compensate for as many Zernike modes (usually
piston, and tip and tilt are required), but they can cover a much wider range. The
critical specifications for most applications are the operational bandwidth and the
angular range, while maintaining high-precision control. Fortunately, it is common
that applications requiring a large range of motion will tolerate lower bandwidth
and vice versa.
Low-order wavefront correctors can be constructed from mirrors and lenses,
liquid crystal materials, and other devices. Correctors that use lenses or mirrors re-
quire some form of actuator to drive the correcting element. Actuators are typically
divided into two types: force actuators and displacement actuators. An example of a
force actuator is a voice coil, driven by electromagnetics, while a piezoelectric
stack is an example of a displacement actuator.
A novel means of correcting the wavefront, requiring no moving parts, is a liq-
uid-crystal spatial-light modulator. These devices control the phase of the light di-
rectly, and by writing the correct pattern to the device, the desired tip-tilt or
higher-order aberration can be applied. Liquid-crystal devices are discussed again
in Chapter 8.
A temporal bandwidth of about 100 Hz is required to correct the wavefront tilt
induced by the atmosphere. The angular range of the mirror is governed by the qual-
ity of the astronomical seeing and ratio of the collector diameter to that of the active
mirror. The angular tilt variation (
2 ) induced by the atmosphere is (Hardy 1998)
where r 0 is the Fried parameter, D is the aperture, and
is the wavelength.