Simulations of Servo, Fitting and Focal Anisoplanatism Errors at Palomar
Servo Error Simulation
Simulation of the servo error. A six layer Cerro Pachon atmospheric
model was chosen. The remaining parameters of the simulation were as
follows:
5.1 meter aperture
r0 of .15 meters at .5 micron
2.5 cm pixel scale in the wavefront
2.5 cm pixel scale in the turbulence layer
time step of duration 1 millisecond
1 second (1000 1 ms frames) of simulation time
Wavelength of 2.2 microns
The ground layer wind velocity was chosen from a 2d gaussian
distribution with width 5 m/s. The actual ground layer wind vector
for the results shown in the images below turned out to point up and
to the left at about 45 degrees. A tropospheric wind component was
also included, though its effects are not obvious in the
images.
A rather idealized correction was applied to the wavefront phase in
the pupil plane to mimic the effects of an adaptive optics system. At
each timestep the wavefront phase from a previous image was subtracted
from the current wavefront phase before propagating the current
wavefront to the focal plane. The delay between the current wavefront
and the one whose phase was subtracted plays the role of a servo
error. Simulations were performed for three different delays: 10 ms,
3 ms and 2 ms.
The image below show the three psfs that result from the above
simulations: 10 ms, 3 ms and 2 ms delays are shown from left to
right. These images were formed from 1 second of integrated data, and
are oversampled by a factor of 2. They are shown on a log stretch.
The Strehl ratios for the three psfs are 83%, 97%, and 98.7%. In all
three cases the random atmosphere used in the simulation was exactly
the same.
Fitting Error Simulation
Simulation of the fitting error. The atmospheric model and simulation
parameters are the same as were used for modelling the servo error,
except that a hundred 10 millisecond samples were generated in the
simulation.
To model the fitting error arising from the finite actuator size of a
deformable mirror in the adaptive optics system, the wavefront phase
in the pupil plane was transformed into spatial frequency space and
filtered to remove low frequency power. The filter chosen for these
simulations was a two dimensional top hat. The simulation was
repeated for three different cutoffs: 8, 16 and 32 cycles across the
aperture. This roughly mimics the correction possible with 16, 32
and 64 actuators across the aperture.
The images below are oversampled by a factor of 2, and result from
averaging 1 second of integrated data. They are shown on a log
stretch, and have been chopped to 10% of the full height of the
ideal psf. The Strehl ratios for the three images are 95%, 98.7%,
and 99.6%, respectively.
Focal Anisoplanatism Error
Cerro Pachon 6 layer turbulence profile, LGS at 92 km is pointed
directly at a star and the LGS wavefront phase in the pupil plane is
subtracted from that of the star. The resulting error arises solely
from focal anisoplanatism.
5.1 meter aperture
r0 of .15 meters at .5 micron
1 cm pixel scale in the wavefront
1 cm pixel scale in the turbulence layer
time step of duration 10 milliseconds
1 second (100 10 ms frames) of simulation time
Wavelength of 2.2 microns
From left to right:
The NGS phase corrected using the LGS phase
The NGS phase corrected using the high order LGS phase supplemented by
its own low order correction. The first three Zernike orders were
used to form the low order correction.
The corrected NGS psf - Strehl ratio 94%
