Atmospheric turbulence limits the resolving power of astronomical telescopes by distorting
the paths of light between distant objects of interest and the imaging camera at the telescope.
After many light-years of travel, passing through the turbulence in that last 100km of a
photon’s journey results in a blurred image in the telescope, no less than 1” (arc-second)
in width. To achieve higher resolutions, corresponding to smaller image widths, various
methods have been proposed with varying degrees of effectiveness and practicality.
Space telescopes avoid atmospheric turbulence completely and are limited in resolution
solely by the size of their mirror apertures. However, the design and maintenance cost of
space telescopes, which increases prohibitively with size, has limited the number of space
telescopes deployed for astronomical imaging purposes. Ground based telescopes can be
built larger and more cheaply, so atmospheric compensation schemes using adaptive optical
cancellation mirrors can be a cheaper substitute for space telescopes.
Adaptive optics is referred to here as the use of electronic control of optical component to
modify the phase of an incident ray within an optical system like an imaging telescope. Fast
adaptive optics systems operating in real-time can be used to correct the optical aberrations
introduced by atmospheric turbulence. To compensate those aberrations, they must first
be measured using a wavefront sensor. The wavefront estimate from the wavefront sensor
can then be applied, in a closed-loop system, to a deformable mirror to compensate the
incoming wavefront.
Many wavefront sensors have been proposed and are in used today in adaptive optics and
atmospheric turbulence measurement systems. Experimental results comparing the performance
of wavefront sensors have also been published. However, little detailed analyses
of the fundamental similarities and differences between the wavefront sensors have been
performed.
This study concentrates on fourmain types of wavefront sensors, namely the Shack-Hartmann,
pyramid, geometric, and the curvature wavefront sensors, and attempts to unify their description
within a common framework. The quad-cell is a wavefront slope detector and is
first examined as it lays the groundwork for analysing the Shack-Hartmann and pyramid
wavefront sensors.
The quad-cell slope detector is examined, and a new measure of performance based on the
Strehl ratio of the focal plane image is adopted. The quad-cell performance based on the
Strehl ratio is compared using simulations against the Cramer-Rao bound, an information
theoretic or statistical limit, and a polynomial approximation. The effects of quad-cell
modulation, its relationship to extended objects, and the effect on performance are also
examined briefly.
In the Shack-Hartmann and pyramid wavefront sensor, a strong duality in the imaging and
aperture planes exists, allowing for comparison of the performance of the two wavefront
sensors. Both sensors subdivide the input wavefront into smaller regions, and measure the
local slope. They are equivalent in every way except for the order in which the subdivision
and slope measurements were carried out. We show that this crucial difference leads to a
theoretically higher performance from the pyramid wavefront sensor. We also presented
simulations showing the trade-off between sensor precision and resolution.
The geometric wavefront sensor can be considered to be an improved curvature wavefront
sensor as it uses a more accurate algorithm based on geometric optics to estimate the wavefront.
The algorithm is relatively new and has not found application in operating adaptive
optics systems. Further analysis of the noise propagation in the algorithm, sensor resolution,
and precision is presented. We also made some observations on the implementation
of the geometric wavefront sensor based on image recovery through projections.
| Identifer | oai:union.ndltd.org:canterbury.ac.nz/oai:ir.canterbury.ac.nz:10092/1645 |
| Date | January 2008 |
| Creators | Chew, Theam Yong |
| Publisher | University of Canterbury. Electrical and Computer Engineering |
| Source Sets | University of Canterbury |
| Language | English |
| Detected Language | English |
| Type | Electronic thesis or dissertation, Text |
| Rights | Copyright Theam Yong Chew, http://library.canterbury.ac.nz/thesis/etheses_copyright.shtml |
| Relation | NZCU |
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