Adaptive Optics Model Anita Enmark Lund Observatory

Outline Adaptive Optics Model Current Work Generalization Model Improvment Parallelization

Euro50 Model Overview SCAO on a NGS DM 3169 Actuators

Adaptive Optics Model Test Vehicle for AO Design together with ELT Atmosphere Controller Reconstruction Wavefront sensor Deformable mirror SCAO / NGS Geometrical or Fresnel Propagation SVD Various influence functions and geometries DM1: 2 nd order systems for every actuator Delay/non-linearities from WFS Geometrical or physical model of SH-WFS

Current Work Generalization Improved adaptive optics model Parallelization

Generalization and improvment Adaptive optics model tested for VTT Improved model (atmosphere, noise etc)

Movie of VTT model with modes 1,2 (tip/tilt) and set to zero

Parallelization Simulation environment for first order model Beowulf cluster with Matlab+MatlabWS Memory capacity limiting factor Full matrix with DM influence function 6GB for 3169 actuators 64 bit Matlab needed– more primary memory Parts of code too slow Simple first order model takes many days/sec Network too slow Currently evaluating other simulation environments Cluster – LUNARC, Lund Shared memory - Galway, Ireland

ODE Multirate Solvers for Systems with Mixed Dynamics 1 million State Variables Fast SubsystemSlow Subsystem Modern work on multi-rate solvers (eg. Anne Kværnø et al) Andrus: Mixed 4th order Runge-Kutta Simpler multirate solvers with extra/interpolation Execution time reduction 5-10x

Integated Model Bottle Neck Atmosphere Controller Reconstruction Wavefront sensor Deformable mirror

Main drivers for execution time: One image for each subaperture -> For every subaperture: exponential and 2D IFFT Must give FOV as close to nominal as possible -> interpolation of wavefront Shack-Hartman Wavefont Sensor Model

Every subaperture is propagated to the image plane with Fraunhofer propagation. The image of the subaperture wavefront in angular coordinates is then where u(x,y) is the complex amplitude of the wavefront in the spatial coordinate system (x,y) and is the wavefront phase. denotes the inverse Fourier transform. Image formation 2 => exponential and IFFT

A large local tilt (for example wind residuals) in the wavefront gives a subaperture PSF far away from the center. A large FOV is needed. Fourier transforms: Higher resolution in one domain gives larger format in the other domain Dense sampling in the spatial domain gives a large band width Dense sampling of the wavefront gives a large FOV The characteristics of the atmosphere gives the number of samples for the wavefront, but in order to simulate a given FOV for the SH-WFS a denser grid can be necessary => interpolation Field of View

Good News: Both have outer loops with an independent variable=> Suitable for parallelization. Bad News: Matlabs parallel computing tools not good for our needs. MatlabWS not ported to shared memory machine. New C-code needed. More good news: The bottle necks are within the same Matlab subfunction, only a limited part of the model must be coded in C. This gives fast execution, but keeps good structure. Model groves with more sensors – can be parallelized Impact on AO-model

Tilted wavefront CCD detector 4x4 pixels/subaperture C mex-function result Matlab-function result C mex-function result Matlab-function result CCD detector 15x15 subapertures Status for C-code development in cooperation with Michael Browne National University of Ireland, Galway

Test results for one call to WFS Matlab on one CPU machine ~ 100 sec Sequential C-code on the same machine ~ 14 sec Sequential C-code on Itanium machine ~ 4 sec Expected for multi-processor Itanium ~ 0.5 sec

Integrated Modeling Conclusions A full Euro50 model with AO in place Generalization work in progress AO model improved Parallelization in progress – faster network and more memory needed – under test First tests promising

Full first order model simulation Atmosphere correction