The Atmosphere Reduces our Ability to See Distant Objects

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The Atmosphere Reduces our Ability to See Distant
Objects
Light Rays from Star
When light arrives at the atmosphere, it is
planar, i.e. all light from a single point
arrives at the same time. We call this a planar
wave front
We can focus light from a planar wave front into
nice sharp images
However, the atmosphere is very turbulent and has
lots of areas that are different temperatures and
densities
light takes a different amount of time to pass
through these different areas.
By the time it has reached the earths surface,
all the light from a single point no longer
reaches here at the same time and some of it lags
behind others. We no longer have a planar wave
front
The result is that we cannot focus the light in
this wave front into as sharp an image as we
could have without the effect of the
atmosphere. AO allows us to flatten the wave
front so we can focus the image sharply.
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How the Atmosphere Affects Light
Light Rays from Star
This column of the atmosphere affects each ray
that passes through it in the same manner
As does this column of the atmosphere
When the light from the same source is no longer
planar, we cannot focus it as well as if it were
still planar and our images are degraded.
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The Need for Adaptive Optics
The atmosphere slows down the passage of light,
compared to the vacuum of space, due to its
composition. We can think of the Atmosphere as
being divided into regions we will call voxels.
While the atmosphere as a whole is not uniform,
we will assume that within each voxel, the effect
of the atmosphere is uniform Each voxel will add
a different amount of delay to the rays that pass
through it, compared to its neighbors. The total
delay through the atmosphere for any ray is
likely to be different than its neighbors, since
it will travel through different voxels. The
result is that when the rays get to our
telescope, the wave front is no longer planar
since the path delays for each ray are
different. Adaptive Optics tries to develop a
model of the atmosphere so we can understand what
the atmosphere is doing to the light from the
objects we are trying to observe. We then use
that knowledge to undo what the atmosphere is
doing by making the wave front planar again.
Rays from a Guide Star
Atmosphere
Telescope
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Examples of the Effect of Atmospheric Turbulence
on Images
No correction for the Atmosphere (Earth bound)
No Atmosphere (Hubble)
With AO
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Rays from another nearby object
Lets say we have a star (guide start) that we
know is a nice point source and not a wide
galaxy. If we could measure the total delay
through the atmosphere, for the light from that
star, for each column of voxels, we could know
what the wave front was. If we had a nearby star
whose light went through the same columns as our
guide star it would have its wave front distorted
in the same manner. If we could apply a
correction to the rays in proportion to their
relative total delays so that those with lesser
delays were delayed more, we could flatten our
wave front and get a nice focus. We do this
We do this using a guide star a wave front
sensor and a deformable mirror. A guide star is
a relatively bright star in the sky that we can
observe. A wave front sensor is a device that
allows us to measure the difference in total path
delay of each ray from the guide star as the
light travels through the voxels in the
atmosphere. A deformable mirror is one which
compensates for the different path delays in the
atmosphere by adding different delays for each
ray to bring them all back to the same delay
before we try to look at them. This delay is the
sum of the delay due to in each voxel through
which the ray traverses. If we know the delay in
each voxel. We want to determine the path delay
due to individual voxels.
Rays from a Guide Star
Wave Front Sensor
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Wave Front Sensors
Rays from a Guide Star
A wave front sensor divides the light in the
telescope it into an array of regions. It then
determines the average path delay for each
region. This gives us an image of the wavefront
(that used to be flat) as it is being seen by the
telescope after having been distorted by the
atmosphere..
Wave Front Sensor
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Deformable Mirrors
Rays from a Guide Star
A deformable mirror can be made to change its
shape to change the path length of light
reflected off of it. We use these to use the
information from the wave front sensor to
compensate for the path difference it detected
and flatten the wave front.
Wave Front Sensor
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Using WFSs and DMs to Correct our Images
Rays from another nearby object
Rays from a Guide Star
This allows us to measure the wavefront
distortion of the atmosphere on a guide star and
correct for the atmospheric distortion for nearby
objects. However, as object get farther from the
guide star, they no longer pass through a common
path and the correction has less and less effect
as they get farther and farther from our guide
star. So, knowledge of the total distortion added
by a each column through the atmosphere needs to
be refined to knowledge of each voxel in the
atmosphere. If we have that knowledge we can
compensate for any path through the portion of
the atmosphere we have measured.
Wave Front Sensor
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Using Multiple Guide Stars to Model the Atmosphere
Rays from Guide Star 2
This voxel contributes the same path delay to
each ray that passes through it
Rays from Guide Star 1
However, since each of these rays passes through
a different set of voxels, their total path
delays are different (measured at the WFSs)
By measuring the actual total path delay of
enough rays from each guide star using different
WFSs for each, and knowing in which voxel the
rays intersected, we can estimate the effect of
each voxel.
WFS 2
WFS 1
The more rays we can measure from different guide
stars that pass through a given voxel, the more
accurate our estimate will be for the effect of
that voxel gt more guide stars The more voxels we
have, the more accurate our knowledge of the
atmosphere will be gt more sub apertures
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Rays from Our Science Object
Once we have obtained an estimate of the
atmosphere, we can predict the total path delay
for rays that come from a direction that we
havent measured directly, i.e., our science
object
Once we have the total path delays we expect from
our new direction, we can correct for them, thus
removing the effect of the atmosphere from our
image.
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Rays from a Guide Star
Once we have obtained an estimate of the
contribution of each voxel in the atmosphere
through which we are looking, we can calculate
the total path delay for rays that come from a
direction that we havent measured directly,
i.e., our science object Once we have the total
path delays we expect from our new direction, we
can correct for them with our deformable mirror,
thus removing the effect of the atmosphere from
our image.
Wave Front Sensor
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So How Do We Figure Out What the Contribution of
Each Voxel Is?
Rays from Guide Star 2
This voxel contributes the same path delay to
each ray that passes through it
Rays from Guide Star 1
However, since each of these rays passes through
a different set of voxels, their total path
delays are different (measured at the WFSs)
By measuring the actual total path delay of
enough rays from each guide star using different
WFSs for each, and knowing in which voxel the
rays intersected, we can estimate the effect of
each voxel.
WFS 2
WFS 1
The more rays we can measure from different guide
stars that pass through a given voxel, the more
accurate our estimate will be for the effect of
that voxel gt more guide stars The more voxels we
have, the more accurate our knowledge of the
atmosphere will be gt more sub apertures
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• The atmosphere is divided into voxels
• When two rays intersect, the voxel in which they
  intersect will deal with the back and forward
  propagation for those rays for that voxel.
• We model this with an array of voxel cells which
  will implement the algorithm for estimating the
  atmosphere

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Block Diagram of a SingleLAO Voxel Cell
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Iteration Algorithm for Estimating the Atmosphere

• Compare the measured value of each ray to the
  current predicted (forward propagated) value of
  the same ray
• Place the resultant error between our measured
  value and our predicted value for each ray on the
  Back Propagation bus for that ray
• Each voxel cell will take the error off the back
  propagation bus and load it into its error
  register for that ray
• The voxel cell will take all the ray errors for
  rays passing through it and will perform some
  form of averaging on them
• The average of the errors will then be multiplied
  by the Cn2 for the layer in which the Voxel lies
  (steps 2 5 accomplish the back propagation of
  the error)
• The resultant error value will be added to the
  current estimated value to create a new estimated
  value.
• All new estimated values for each voxel through
  which a ray passes will be summed. The result is
  a new predicted value (forward propagation).
• The new forward propagated, predicted value will
  be latched at the bottom of each ray, and we will
  repeat the sequence (starting at 1) until done.

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Assumptions

• Our analysis assumes that the differences in
  phase within a given voxel are lt Lamda / 4
• We ignore diffraction effects due to the
  atmosphere and only consider the change in phase
  of the light, i.e., we use geometrical optics.
• This is OK for good seeing locations and more or
  less vertical viewing, but less for viewing
  towards the azimuth or medium viewing