1. A user-friendly, object oriented, AO simulation in Python
Andrew Reeves

2. Summary Another AO Simulation….? Python Programming Language
Simulation code Overview
Examples of current investigations

3. 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
Written in python – upcoming language used in many applications.
also uses accelerated libs
Not intended as “end to end” sim (though does include all bits if you want to)
Each modules an “object” which is self contained and can be fitted into different systems easily
(easy in python – lists and so forth)

4. 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

5. 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 Object-Oriented or functional code, or can be used simply to write scripts.

6. 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.

7. 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.

8. Time solving 100 iterations of the Laplace Equation for a 500x500 grid.
Code is still high-level, easy to understand Python!
Note that this is still the same code – just

9. 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 self-contained 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 boiler-plate 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.

10. Simulation Class Diagram
Configuration
WFSs
LGSs
Reconstructor
DMs
Science Cameras
aoinit()
makeIMat()
aoloop()
Class name:
Example Class Attributes:
Example Class Methods:

11. Simulation A B A B Atmosphere Wave-Front Sensor Reconstructor
Configuration
WFSs
LGSs
Reconstructor
DMs
Science Cameras
aoinit()
makeIMat()
aoloop()
Class A contains instances of Class B A B A
Class B inherits from Class A B
Atmosphere
wholeScrns
interpolatedScrns
windSpeed
loadScreens()
moveScreens()
randomScreens()
Wave-Front Sensor
Guide Star Position
wavelength
LGS
wfsPhase()
makeFocalPlane()
frame()
Reconstructor
reconstructorMode
controlMatrix
loadCMat()
saveCMat()
Reconstruct()
Deformable Mirrors
actuators
dmShapes
makeIMat()
frame()
Science Camera
fieldofView
Wavelength
pixels
sciencePhase()
makeFocalPlane()
frame()
Laser Guide Star
LGS Wavelength
LGS Height
lgsPhase()
makeLgsPsf()
Shack-Hartmann
sub-apertures
pxlsPerSubap
makeFocalPlane()
CalculateSlopes()
MVM
SCAO
cMatConditioning
makeCMat()
Reconstruct()
Learn & Apply
cMatConditioning
learnFrames
getLearnSlopes()
Reconstruct()
Zernike
dmShapes
nModes
makeDMShapes()
Piezo-stack
dmShapes
nActuators
makeDMShapes()

12. 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.

13. Simulation Features Realistic Laser Guide Stars
Physical propagation of up-link path includes tip-tilt variations
LGS uplink PSF
Convolved WFS spots

14. 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

15. Simulation Features
Using IPython console, can inspect and plot simulation data and change simulation parameters in real time

16. Simulation GUI, showing plotting of simulation data
Simulation GUI, showing plotting of simulation data. Console can be used to inspect data and change parameters in real-time

17. 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

18. Current Investigations

19. 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.

20. 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

21. 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….

22. 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)

23. 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)

24. LGS Up-link Prediction
If up-link and down-link tip-tilt uncorrelated, then slope measured on WFS is a combination of both effects
Measured slope
Component of slope due to down-link turbulence
Component of slope due to up-link turbulence

25. LGS Up-link Predictionα β D h H … n
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.
With sαt, and sβt can now reconstruct on-phase correction as usual.
Manuscript on the above in preparation

26. LGS Up-link Predictionα β D h H … n
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.
With sαt, and sβt can now reconstruct on-phase correction as usual.
Manuscript on the above in preparation

27. LGS Up-link Prediction
Since relationship between up-link slopes and down-link turbulence slopes is linear, can use Learn & Apply algorithm (Vidal, Gendron & Rousset, 2010)
Relies on covariance matrices between off and on axis matrices.
Can simulate this with realistic LGS up-link turbulence using python AO sim.
LGS covariance on on-axis and 4 off-axis LGS for an 8x8 sub-aperture system
Note vertical and horizontal dark lines of negative correlation.
NGS LGS1 LGS2 LGS3 LGS4
NGS LGS1 LGS2 LGS3 LGS4

28. 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)

29. 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

30. 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.