Parallelized Simulation Code for Multiconjugate Adaptive Optics
A.J. Ahmadia
a
and B.L. Ellerbroek
b
a
Gemini Observatory, 670 N. A’ohoku Place, Hilo, HI 96720
b
AURA New Initiatives Offices, 950 N. Cherry Avenue, Tucson, AZ 85719
ABSTRACT
Advances in adaptive optics (AO) systems are necessary to achieve optical performance that is suitable for
future extremely large telescopes (ELTs). Accurate simulation of system performance during the design process is
essential. We detail the current implementation and near-term development plans for a coarse-grain parallel code for
simulations of multiconjugate adaptive optics (MCAO). Included is a summary of the simulation’s computationally
intensive mathematical subroutines and the associated scaling laws that quantify the size of the computational burden as
a function of the simulation parameters. The current state of three different approaches to parallelizing the original
serial code is outlined, and the timing results of all three approaches are demonstrated. The first approach, coarse-
grained parallelization of the atmospheric propagations, divides the tasks of propagating wavefronts through the
atmosphere among a group of processors. The second method of parallelization, fine-grained parallelization of the
individual wavefront propagations, is then introduced. Finally, a technique for computing the wavefront reconstructions
is analyzed. A parallel version of the block-symmetric Gauss-Seidel smoother, used in the conjugate-gradients
reconstructor with multigrid-solver preconditioning, has been implemented. The timing results demonstrate that this is
currently the fastest known full-featured, operational multiconjugate adaptive optics simulation.
Keywords: Adaptive optics, propagation simulations, parallel computing, Beowulf cluster
1. INTRODUCTION
Future advances in the theory and development of adaptive optics (AO) systems will be fundamental for
achieving the desired levels of image quality and optical performance from future giant astronomical telescopes with
aperture diameters of 30 meters or more
1,2,3
. An important aspect of developing these new adaptive optics technologies
and systems is the ability of the scientists and designers to accurately simulate system performance during the design
process to establish an optimized set of first-order design parameters, and develop error budgets for the impact of
implementation error sources and higher-order effects. The adaptive optics simulation code, previously introduced in
2001
4
, is a well-developed model for studying current and future adaptive optics systems. Such systems include
multiconjugate adaptive optics (MCAO), which employ multiple deformable mirrors (DM) and wavefront sensors
(WFS) to compensate for the effects of atmospheric turbulence across extended fields of view
5,6,7,8,9
.
In an effort to reduce execution times for complex adaptive optics systems, particularly for very high order
MCAO systems on future giant telescopes, we have introduced parallel code into the simulation. The sections of the
code that were the most CPU-intensive have been identified and parallelized. A combination of C and compiled Matlab
code has been used to implement a parallel solution using several mathematical and parallel packages. The code has
been tested against the original serial version for speed and verification of data. The serial code’s simple yet flexible
interface allowed a novice Matlab user to wield the full power of the simulation. During the parallelization process,
much of this simplicity and flexibility was maintained. The parallel design was crafted such that improvements in speed
will scale well from a small x86 cluster to large supercomputers.
The simulation code has four phases: (1) an interactive command menu that allows the programmer to input
the parameters of the simulation; (2) preprocessing to compute the full description of the adaptive optics system from
the specified parameters; (3) the actual simulation loop that evaluates the effects of the atmosphere, telescope, and
adaptive optics system on a set of wavefronts over a range of sequential time steps; and (4) postprocessing analysis of
the results. The parameters of the simulation allow for multiple atmospheric layers, geometrical or diffraction models
for optical propagation, the introduction of various types of measurement and correction error, and the ability to
simulate laser guide stars and multiconjugate adaptive optics systems.

Details about the methods and results are presented in the subsequent sections. Section 2 elaborates on the
simulation and its capabilities. Section 3 identifies the pieces of the simulation that are the most time-intensive, and
introduces the theoretical scaling for simulations of extremely large telescopes. Section 4 describes the basic
programming techniques used to add parallel code to the software. Sections 5 and 6 fully detail the decisions made and
the improvements in execution time obtained from parallelizing the code for the two major elements of the
simulation–the wavefront propagator and the reconstructor. Section 7 summarizes the findings.
1. SIMULATION DESCRIPTION
This section provides an overview of the serial simulation that has been previously introduced and described
4
.
Figure 1 illustrates the basic structure of the software and steps of the simulation.
Figure 1: Serial Simulation Overview
The software’s interactive menu allows the user to generate a custom scenario for simulation. The menu of choices
available to define the system include the atmospheric model, modes of performance evaluation, defining optical
surfaces, wavefront sensor and guide star parameters, deformable and tip-tilt mirror parameters, and the control
algorithm parameters. The user is also able to customize additional parameters that allow for multiple atmospheric
layers, flexible grid sizes, geometrical or diffraction models for optical propagation, the introduction of various types of
measurement and correction error, and the ability to simulate laser guide stars and MCAO systems.
Once the system has been defined, the simulation generates necessary data structures. These include mirror
figure errors, atmospheric phase screens, aperture masks, wavefront sensor subaperture locations, deformable mirror
actuator grid locations, and the corresponding mirror-to-sensor geometric influence matrix. Based upon the turbulence
profile and this influence matrix, a wavefront reconstruction matrix is computed to minimize field and aperture
averaged mean-square residual wavefront error over the user’s chosen directions for system performance evaluation.
Once the user has configured the simulation problem, the program enters a loop-driven model of the adaptive
optics system’s behavior in the time domain. Sequentially, the simulation propagates wavefronts from guide stars and
evaluation points down through the atmosphere and the telescope’s corrective mirrors using the chosen model for
Postprocessing
Update DM
commands
Reconstruct
wavefront
Compute WFS
measurements
Evaluate AO
performance
Generate
reconstructor
Generate
datastructures
Input
parameters
Parameter
files
Results
Reconstructor
files
Data
files
Simulation loop