The UH AO System
The concept of wavefront curvature sensing and compensation
Curvature wavefront sensing.
What does a wavefront sensor do?
The object of the wavefront sensor is to measure the deviations
of the wavefront surface from a plane.
Small temperature variations in the earth atmosphere cause the light entering
different parts of a telescope pupil to travel at slightly different speed, producing variations in the optical path.
This causes images of astronomical images to become blurred.
If we can measure these path length differences across the telescope
pupil, we can correct them in real time using a flexible mirror, and
hence sharpen the astronomical images.
Since the atmosphere is constantly moving the wavefront sensor must be
able to measure a new wavefront several hundred times a second.
Wavefront measurement techniques
In the laboratory optical wavefronts are most often measured by devices
which compare the target wavefront with a reference wavefront which is
known to be flat. Such devices measure the wavefront directly.
Unfortunately for astronomical wavefront sensors there is usually no
convenient way to provide a wavefront reference.
For astronomical wavefront sensing four techniques have been used
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Shearing interferometer.
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A special version of the shearing interferometer, which works by comparing
two copies of the wavefront shifted by a small amount relative to each other.
This type of sensor measures the gradient (or slope) of the wavefront.
By using a grating to perform the shear, the interferometer can be rendered
achromatic. Alternatively this wavefront sensor can be viewed as an a
special form of the knife edge test, known to opticians for centuries.
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The Hartmann wavefront sensor.
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The Shack-Hartmann sensor, a particular form of the Hartmann sensor is
by far the most popular AO wavefront sensor to date.
This type of sensor also measures the gradient (slope) of the wavefront.
The sensor works by splitting the wavefront into many sub-regions.
Each sub-region of the wavefront forms an independent image.
Shifts in the positions of these sub-images can be shown to be
proportional to the mean wavefront gradient over each sub-pupil.
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The curvature wavefront sensor.
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This wavefront sensor works by comparing the illumination patterns
in two extra-focal images. As will be explained below, the signal
from this sensor is proportional to the Laplacian (slope of the slope),
of the wavefront inside the wavefront, and proportional to the
wavefront radial gradient (slope) on the edges of the wavefront.
This sensor, like the shearing interferometer is based on a technique
which has been used qualitatively by opticians for centuries.
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The phase diversity wavefront sensor.
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This sensor can be viewed as a generalization of the curvature sensor,
it can only be used with monochromatic light.
Typically the illumination in the image plane is compared with the
illumination in a second image plane where the wavefront has been
disturbed by a precisely known phase function. In practice the
easiest way to do this is to look at an in focus image and a slightly out
of focus image. Unlike the curvature sensor, the extra-focus distance
is very small, typically inside the caustic zone (the region where
a geometric ray trace of the system would show rays crossing over each
other). The benefit of this is a higher SNR in the measured signal.
The main problem is that retrieving the wavefront requires complex non-linear
calculations.
The curvature wavefront sensor.
The curvature wavefront sensor is based upon the measurement of the illumination intensity in two planes.
The figure below shows how it works.
Two planes, the "before pupil plane" and the "after pupil plane" are shown on this diagram: they are the two planes that are imaged by the curvature sensor. The choice of the correct distance of these planes from the pupil plane is critical to the proper operation of the curvature sensor.
For an incoming wavefront as the one in the figure, with a bump on it, one of the images shows a lack of illumination as the other shows an excess of light at the very position of this bump. The contrast between the two images (the difference of intensities divided by their sum) give an "image" of the curvature of the incoming wavefront. In addition, the values of this fonction on the edge of the pupil yields the slope of the wavefront and therefore, all the information needed to rebuild the incoming wavefront is available.
Olivier Guyon guyon@ifa.hawaii.edu