Adaptive-optics systems are used to correct images of objects.
These systems work by measuring the phase distortion on a
downpropagating wave called a beacon and applying the negative of that
phase to a deformable mirror. If this is done well, then the
image of the beacon is close to diffraction limited; and if a
laser beam is projected along the corrected path, it will have
propagation characteristics approaching those of a wave propagating
in vacuum. It is not possible to make a perfect correction; one
of the major error sources is due to the fact that the rays of
the object to be imaged or the laser beam to be propagated are
along a path displaced from that of the beacon. A measurement of
this degradation is the Strehl ratio, which is the ratio of the
intensity of the actual beam on axis to that of a
diffraction-limited beam.
© Optical Society of America, 1992.
This displacement can have several causes. The receiving and the
transmitting apertures may be displaced from each other owing to
misalignment or vignetting of the beams. The paths can be
separated in angle, for instance, when the object to be imaged is
different from the beacon. The correction is applied with a time
delay after the measurements. In this time the turbulence is
displaced by winds and slewing of the telescope. The paths may be
separated because the beacon and the imaging wavelengths differ,
in which case refraction operates differently on the two waves.
All the effects are typically present simultaneously.
These anisoplanatisms have been treated separately in the
past[#!1!#,#!2!#,#!3!#,#!4!#,#!5!#,#!6!#,#!7!#]; however, they are all manifestations of
the same effect. ...A better analytic approximation that
applies in the range of operation of a typical adaptive-optics
system is developed here. This is applied to obtain expressions
for the various types of anisoplanatism discussed above.
In Section ![[*]](/file/18224/World_Of_Computer_Software-02-387-Vol-3of3.iso/j/josaa.zip/JOSAA.TEX/crossref.png)
the general formula for the Strehl ratio with
any type of anisoplanatism is derived. Gegenbauer polynomials
provide a convenient way to keep track of the series terms and to
cancel terms that lead to numerical difficulties if the integral
is evaluated numerically. In Sections – the
general formula is applied to obtain the Strehl ratio for various
types of anisoplanatism. The cases considered are parallel path
displacements, angular offsets, time-delay-induced offsets, and
offsets that are due to refractive effects that vary with
wavelength. The Strehl ratio in the presence of several effects
is examined in Section . It is shown that, depending on
the direction of the relative displacements, one can get a
cancellation of the displacements so that the Strehl ratio is high
or an enhancement so that the Strehl ratio is less than the
product of the Strehl ratios of the individual terms.