Simulation of a 10 Meter Aperture with 1' Field of View Using a Six Layer Atmosphere
In this simulation I have tested some idealized tomographic correction
techniques that aim to widen the compensated field of view of a
telescope. In this simulation I have used a 10 meter aperture to
image a 3x3 grid of stars spread over 1 square arcsecond. The
wavefronts from these stars traversed the six layer atmosphere that
Ellerbroek (JOSA A, 19, p 1803) used to model the Cerro Pachon
turbulence profile. This atmosphere has a Fried parameter of 16 cm at
.5 microns.
To select the wind velocities of the atmospheric layers I used the
wind model equation 3.20 in Hardy's book "Adaptive Optics for
Astronomical Telescopes". This model has a constant ground layer
component and a tropospheric component modulated in altitude by a
gaussian. I took 5 m/s as the ground layer wind speed and 20 m/s as
the tropospheric wind speed, with a tropospheric height of 10 km and
width of 5 km. These speeds were interpreted as the variance of a 2D
gaussian random variable, and a random wind vector was selected from
this distribution. For this particular simulation the random wind
velocity for the ground was vx=3.0, vy=2.7, and for the
troposphere was vx=20.8, vy=3.0. The tropospheric wind
velocity was then modulated by a gaussian with height 10 km and width
5 km to get the tropospheric contribution to the wind vector at the
height of each layer. The final wind vector was the sum of the
tropospheric and ground layer contributions.
This table summarizes the heights and relative statistical weights of
the layers in the model, along with the randomly chosen wind vectors
for this particular simulation.
| layer | altitude (km) | weight | vx (m/s) | vy (m/s) |
| 1 | 0.00 | .652 | 3.4 | 2.8 |
| 2 | 2.58 | .172 | 5.3 | 3.0 |
| 3 | 5.16 | .055 | 11.1 | 3.9 |
| 4 | 7.73 | .025 | 19.9 | 5.1 |
| 5 | 12.89 | .074 | 17.9 | 4.8 |
| 6 | 15.46 | .022 | 9.3 | 3.6 |
The simulation was carried out at three different wavelengths: 589 nm,
1 micron, and 2 microns, using both diffractive and geometric
propagation through the atmosphere. The remaining parameters of the
simulation are listed below:
10 meter aperture
r0 of .16 meters at .5 micron
Isoplanatic angle of 2.65 arcseconds at .5 microns
5 cm pixel scale in the wavefront
5 cm pixel scale in the turbulence layer
time step of duration 10 milliseconds
3x3 grid of sources 1 arcminute on edge
3 seconds (300 10 ms frames) of simulation time
Wavelengths of 589 nm, 1 micron, and 2 microns
To propagate the wavefronts from the 9 stars through the 6 layer
atmosphere at each of the 3 frequencies required about 2 minutes per
time step on a 2 Ghz Pentium 4. For purposes of comparing the results
at different frequencies, I chose all PSF's to be Nyquist sampled at
589 nm, thus oversampling the PSF's at 1 and 2 microns by factors of
order 2 and 4, respectively. This forced me to pad the 2 micron
wavefronts by a factor of 4 before performing the far field
propagation, and this step actually dominated the time required for
the simulation. The entire simulation required 10 hours. The
resulting wavefront data required 30 Gigabytes of storage
space.
The movies below show the amplitude in the pupil plane after diffractive
propagation of the wavefront through the atmosphere down to the aperture
Pupil Plane Amplitude
The wavefront data was processed in a number of different ways to form
the images below. The pupil plane amplitude shown below is that which
results from geometric propagation of the wavefront rather than
diffractive propagation. The reason the geometric phase is displayed
is because the near field diffractive propagator returns the phase
modulo 2 pi. The resulting pupil phase image thus includes many wraps
across the pupil. These wraps make the time dependent behavior of the
pupil plane phase difficult to interpret. The geometric propagator does
not induce these wraps.
Because the pupil plane phase is displayed on a color scale over its
full range, the movie itself looks the same at all three frequencies.
(The phase at two different wavelengths is just scaled by the ratio of
the wavelengths.) Because of this, only one movie is shown for each
processing technique.
Pupil Plane Phase and Focal Plane Amplitude
No Processing
Pupil plane phase MPEG
| 589 nm | 1 micron | 2 microns |
| focal plane amplitude |
MPEG |
MPEG |
MPEG |
Subtracting Central Wavefront Phase
Pupil plane phase MPEG
| 589 nm | 1 micron | 2 microns |
| focal plane amplitude |
MPEG |
MPEG |
MPEG |
Subtracting Average Wavefront Phase
Pupil plane phase MPEG
| 589 nm | 1 micron | 2 microns |
| focal plane amplitude |
MPEG |
MPEG |
MPEG |