My name is Daniela Saxenhuber and I am currently finishing my PhD in Industrial Mathematics at the Johannes Kepler University in Linz, Austria. The focus of my research is the development of fast algorithms for atmospheric tomography in Adaptive Optics systems for the European Extremely Large Telescope (E-ELT) currently under construction in the Atacama Desert.
Why Adaptive Optics?
Images from ground based telescopes suffer from turbulence in the atmosphere, which lead to serious image degradation. Adaptive Optics (AO) is a technique for the correction of the phase of the incoming light where one aims to compensate in real-time for the rapidly changing optical distortions in the atmosphere by deforming a mirror. The correction is based on the reconstruction of the turbulence in the atmosphere from measurements in the direction of one or several guide stars. A guide star is any star in the sky bright enough to be used as a sensor (Natural Guide Star) or an artificially generated light source using a laser (Laser Guide Star).
Figure 1: Adaptive optics of the E-ELT use powerful lasers to generate artificial guide stars, source: ESO
The 4-year project, “Mathematical algorithms and software for ELT adaptive optics” from 2009 to 2013, was part of the Austria’s contributions to the accession to ESO. The aim of this in-kind project was the development of algorithms and software for the correction of degraded images due to atmospheric turbulence for adaptive optics (AO) faster than the traditional approach taken until now. This correction process is based on the reconstruction of the refractive index of the atmosphere from noisy measurements of the incoming wave-front which has been implemented, up to now, with a matrix-vector multiplication. The challenging goal of this project was to invent a new and different approach to this problem while, at the same time, reducing the computing load on the computer that performs the computation.
The algorithms developed provide excellent quality and enormous savings with speed up factors of up to 1000 in computing power required to perform the wave-front reconstruction on future AO systems for the European ELT. One prominent example is eXtreme Adaptive Optics (XAO) which aims at high contrast imaging in one single guide star direction. Such a system needs the reconstruction of the wave-front 3000 times per second on a grid of 10000 to 100000 unknowns. Even for the extreme case of XAO, the algorithms developed, such as e.g. the Cumulative Reconstructor with preprocessing (P-CuRe), make the control of such systems manageable with computers of reasonable size and cost.
Three institutes, all based in Linz, have contributed to this project: the Industrial Mathematics Institute of the Johannes Kepler University Linz, the Johann Radon Institute for Computational and Applied Mathematics (RICAM) and MathConsult GmbH.