Image Processing Reference
In-Depth Information
Low-Order Wavefront Compensation
wavefront through to the final image plane. The critical elements are the tip-tilt mir-
ror and the deformable mirror. The tip-tilt mirror provides the correction for the
high-amplitude, low-spatial-frequency stabilization, and the deformable mirror
provides high-spatial-frequency correction, typically at lower amplitudes.
Ideally, the optical figure of the wavefront compensation device exactly com-
plements the aberrated beam, resulting in a flat wavefront. Unfortunately, this is
rarely the case, and some residual error almost always exists. While it is desirable to
have complete wavefront compensation, this requires the compensation system to
reduce the fitting error to zero at each point in the restored wavefront. Most wave-
front compensation systems provide only partial compensation of the wavefront;
that is, some residual fitting error remains. This residual error usually results from
the granularity of the wavefront sensor, having an insufficient number of degrees of
freedom in the wavefront compensator, or inadequate bandwidth in the system to
keep up with the temporal changes.
Clearly, the amount of residual fitting error in a system is directly dependent on
the choice of components for the system. As an example, the segmented mirror
corrector shown in Fig. 4.2 relies on each segment of the mirror to move in tip-tilt,
and piston to provide a uniform surface for compensating the wavefront. Even
when everything lines up well, the mirror is at best continuous piecewise; that is,
abrupt transitions that do not match the wavefront occur from one mirror segment
to the other. This type of mirror is able to restore much of the wavefront; however,
the wavefront will still contain considerable irregularities. This is described as a
spatial fitting error; it depends directly on how well the correction element matches
the aberrated wavefront profile. Clearly, for the segmented mirror system to pro-
vide better correction, the size of each segment must be reduced.
An additional source of fitting error appears when considering how fast the ab-
errations change in the optical system. The chain of events for a correction system
requires that the wavefront be sensed and analyzed, and then the prescription
passed on to the correction element. In most adaptive optics systems, this occurs
over a very short period of time. However, a time delay occurs between the sensing
and correction of the wavefront. As a result, the correction prescription has aged
and may no longer be a perfect fit for the wavefront entering the correction surface
when the wavefront arrives. This temporal fitting error will be present in almost
Figure 4.2 Demonstration of the fitting of a wavefront using segmented mirrors
through to a continuous facesheet mirror. Clearly, the fitting error for smoothly vary-
ing wavefronts will be greater for segmented mirrors.
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