A user-friendly, object oriented,
AO simulation in Python
Andrew Reeves
Summary
• Another AO Simulation….?
• Python Programming Language
• Simulation code Overview
• Examples of current investigations
Why another Simulation?
• Written entirely in Python
• Object-Oriented Simulation “Toolkit”
• Easy to use
– Rapid development and testing of new,
complicated AO concepts
– Learning tool to explore AO systems
Python
• Interpreted, high-level, general purpose programming language.
• Portable, works “out of the box” on Windows, Mac OS, Linux
etc….
• Interpreter can be used interactively, with impressive interactive
tools (matplotlib, ipython)
• Object-oriented, but can be used as a functional language, or
just for scripting
• Enormous community support with packages available for
almost anything with usage growing very quickly
Python Syntax
Docstrings: Distinct from comments, these
are used to document code as the code is
written. Can be parsed by various tools to
create documentation, or when “
help(function)” is called.
Indentation: Code blocks are delimited
by the indentation level, no {}s are
required. Makes code very easy to read.
Python can be used to write ObjectOriented or functional code, or can be
used simply to write scripts.
Python data-structures
• Flexible data structures
– “lists”, “dictionarys” and “tuples”
– Can contain combinations of any type of data or object
– Can be dynamically expanded/shrunk as required
–
list1 = ["helloWorld", 1, 10.67, aoSimObject, (10,10)]
• NumPy Arrays
– Multi-dimensional arrays of fixed size and type
– Fast data access, with many fancy indexing techniques
–
array1 = numpy.array([1,2,3], [4,5,6]), slice = array1[1:2, :]
• No explicit pointer syntax, though NumPy Arrays will pass
pointers automatically and NumPy methods are available
which make this more user controllable.
Python performance
• Pure python isn’t very fast
– But……..
• Many libraries exist which wrap fast C algorithms in python
– especially for scientific purposes e.g. numPy, sciPy,
matplotlib, pyfftw
• Multi-processing is very easy
• Tools such as Cython exist to accelerate pure python by
converting to C and compiling.
• C-Python API makes writing extensions in C easy.
10000
Time solving 100
iterations of the
Laplace Equation for a
500x500 grid.
1500
Execution Time (s)
1000
100
29.3
29
Code is still highlevel, easy to
understand Python!
10
4.3
2.5
2.16
1
Pure Python
Matlab
C
Python +
NumPy
Python +
SciPy inline
Cython
http://wiki.scipy.org/PerformancePython#head-a3f4dd816378d3ba4cbdd3d23dc98529e8ad7087
The Python AO Simulation
• An AO simulation which uses many of pythons features to make it simple to
understand and easy to use and expand.
• AO components, such as WFSs, DMs, and reconstructors are modelled as selfcontained objects, which act in an way which corresponds to the real world
items.
• Objects can be run in the existing simulation framework, or used
independently.
• A base class for most component types is available which deals with boilerplate code. A new type of sub-system can be created quickly by inheriting the
base and adding the new, interesting methods.
• Using external libraries, acceptable performance can be achieved.
Simulation Class Diagram
Class name:
Example Class Attributes:
Example Class Methods:
Simulation
Configuration
WFSs
LGSs
Reconstructor
DMs
Science Cameras
aoinit()
makeIMat()
aoloop()
Simulation
Configuration
WFSs
LGSs
Reconstructor
DMs
Science Cameras
A
B
Class A contains
instances of Class B
A
B
Class B inherits from
Class A
aoinit()
makeIMat()
aoloop()
Reconstructor
Deformable
Mirrors
Science
Camera
Guide Star Position
wavelength
LGS
reconstructorMode
controlMatrix
actuators
dmShapes
fieldofView
Wavelength
pixels
wfsPhase()
makeFocalPlane()
frame()
loadCMat()
saveCMat()
Reconstruct()
makeIMat()
frame()
sciencePhase()
makeFocalPlane()
frame()
Atmosphere
Wave-Front
Sensor
wholeScrns
interpolatedScrns
windSpeed
loadScreens()
moveScreens()
randomScreens()
Laser Guide
Star
LGS Wavelength
LGS Height
lgsPhase()
makeLgsPsf()
ShackHartmann
MVM
SCAO
Learn &
Apply
Zernike
Piezo-stack
sub-apertures
pxlsPerSubap
cMatConditioning
cMatConditioning
learnFrames
dmShapes
nModes
dmShapes
nActuators
makeFocalPlane()
CalculateSlopes()
makeCMat()
Reconstruct()
getLearnSlopes()
Reconstruct()
makeDMShapes()
makeDMShapes()
Simulation Features
• Multiple Wave-Front Sensors
– Only Shack-Hartmann, but easy to create new
types.
– WFS objects stored in a python, so can be easily
accessed and examined.
Simulation Features
• Realistic Laser Guide Stars
– Physical propagation of up-link path includes tiptilt variations
LGS uplink PSF
Convolved WFS spots
Simulation Features
• Realistic Laser Guide Stars
– Elongation modelled by propagating multiple LGS
layers at different heights
8m Primary, 6” subap FOV
32x32 subaps
90km Sodium Layer, 10km
thickness
5 elongation layers, Uplink
turbulence
Simulation Features
• Using IPython console, can inspect and plot
simulation data and change simulation
parameters in real time
Simulation GUI, showing plotting of simulation data. Console can be used to inspect
data and change parameters in real-time
Simulation Features
• Multiprocessing for multiple WFSs
– Each WFS assigned to a core.
– Simple with python
• Physical or geometric light propagation for WFSs
and LGS.
• Variety of reconstructors implemented, including
Woofer-Tweeter, Learn and Apply, Artificial
Neural Network
• Simple configuration from Config file
Current Investigations
Artificial Neural Networks
• A potential tomographic reconstructor.
• There is evidence to suggest that ANNs are
robust against changing turbulence profiles.
• ANN must be ``trained’’ on a generic data set,
then can be used for any turbulence profile.
Artificial Neural Networks
• Easy to adapt the
simulation to use an ANN.
• Sub-class the
“Reconstructor” class, and
override the “reconstruct”
method
• Parent “Reconstructor”
takes care of all interfaces
and boiler-plate code
• Now simulation can use an
ANN instead of traditional
matrix based reconstructor
LGS Up-link Prediction
• Possible to predict LGS up-link path using
tomography?
• If each WFS views the path through
turbulence of other Lasers perhaps.
• Only possible if up-link path is not reciprocal
to path down….
Correlation of tip-tilt modes in up and down-link paths
through Kolmogorov turbulence
Correlation of tip-tilt
is small for a small
aperture concentric
with the telescope
aperture.
DLLT/D: Ratio of LGS launch
aperture size to telescope
diameter
(Wilson & Jenkins, 1996)
Correlation of tip-tilt modes in up and down-link paths
through Kolmogorov turbulence
Correlation of tip-tilt
is small for a small
aperture concentric
with the telescope
aperture.
DLLT/D: Ratio of LGS launch
aperture size to telescope
diameter
(Wilson & Jenkins, 1996)
art mann (SH) WFS, WFS dat a will be in t h
represent ing t he gradient s of t he measured
LGS Up-link Prediction
ny given sub-apert ure, we assume t he use o
t he• Iffollowing
ions.
can express
up-link and derivat
down-link
tip-tiltWe
uncorrelated,
slope measured
WFSsum
is a combination
d by then
an LGS
WFS asont he
of t he laser
of both effects
slopes and t he down-link t urbulence induced
˜s = ˜sl + ˜st
e ˜s is a vector represent ing t he slopes m
Measured
slope
Component
of slope due
to up-link
turbulence
Component
of slope due
to down-link
turbulence
LGS Up-link Prediction
α
β
• If 2 LGS, α and β, the WFS β observes
the up-link path of LGS α.
• Can prove that there is a linear
relationship between down-link only
slopes sαt, and sβt and the slopes
measured on a WFS sα and sβ.
H
• With sαt, and sβt can now reconstruct
on-phase correction as usual.
h
• Manuscript on the above in
preparation
0 … n
D
LGS Up-link Prediction
α
β
• If 2 LGS, α and β, the WFS β observes
the up-link path of LGS α.
• Can prove that there is a linear
relationship between down-link only
slopes sαt, and sβt and the slopes
measured on a WFS sα and sβ.
H
• With sαt, and sβt can now reconstruct
on-phase correction as usual.
h
• Manuscript on the above in
preparation
0 … n
D
• Can simulate this with realistic LGS
up-link turbulence using python AO
sim.
• LGS covariance on on-axis and 4 offaxis LGS for an 8x8 sub-aperture
system
• Note vertical and horizontal dark
lines of negative correlation.
LGS3
LGS1 LGS2
• Relies on covariance matrices
between off and on axis matrices.
NGS
• Since relationship between up-link
slopes and down-link turbulence
slopes is linear, can use Learn &
Apply algorithm (Vidal, Gendron &
Rousset, 2010)
LGS4
LGS Up-link Prediction
NGS
LGS1 LGS2
LGS3
LGS4
Simulation Parameters
• 512 phase points
across aperture
• 16x16 sub-aperture
system
• 17x17 actuator DM
• 4 off-axis LGS WFSs on
10” square
• LGS at height of 90km
• uses on-axis NGS for
“learn” step
• 5 Layer Profile (shown
right)
Results
• Algorithm improves
performance over no
tip-tilt correction.
• Not suited to high
resolution imaging
applications.
• Ground layer not
corrected well, NGS
could still be required
for Ground layer
correction
• Algorithm shows
promise to improve
GLAO performance for
low resolution
spectroscopy
applications
Summary
• Python is a great language for scientific applications,
including AO simulations.
• We have created a python AO simulation which can be run
stand-alone, or used as a toolkit to quickly develop new AO
ideas.
• Simulation already contains many useful features such as
multiple WFSs, realistic LGS and different reconstructors.
• Code is under heavy development to increase features and
performance.
• Simulation already being used to develop new, novel, ideas
for AO.