Nonstationary turbulence simulation with an efficient multiscale approach

This paper considers the problem of simulating the turbulence effect on ground telescope observations. The approach presented here is an evolution of a recently proposed approach [3]. The main contributions with respect to [3] are: First, the Haar transform at the basis of the multiscale model in [3] is shown to be equivalent to a local PCA representation. This equivalence allows to reduce the computational complexity of the simulation algorithm by neglecting the components in the signal with lower energy. Furthermore, the simulation of nonstationary turbulence is obtained by properly changing the values of the multiscale model: Such change is eased by the invariance of the PCA spatial basis with respect to the change of turbulence statistical characteristics. The proposed approach is validated by means of some simulations.

[1]  A. Benveniste,et al.  Multiscale system theory , 1990, 29th IEEE Conference on Decision and Control.

[2]  Tim Clark,et al.  Extruding Kolmogorov-type phase screen ribbons. , 2008, Journal of the Optical Society of America. A, Optics, image science, and vision.

[3]  Michel Tallon,et al.  Fast minimum variance wavefront reconstruction for extremely large telescopes. , 2010, Journal of the Optical Society of America. A, Optics, image science, and vision.

[4]  Benjamin L. McGlamery,et al.  Computer Simulation Studies Of Compensation Of Turbulence Degraded Images , 1976, Other Conferences.

[5]  Gian Antonio Susto,et al.  A Predictive Maintenance System for Silicon Epitaxial Deposition , 2011, 2011 IEEE International Conference on Automation Science and Engineering.

[6]  Alan S. Willsky,et al.  Multiscale Autoregressive Models and Wavelets , 1999, IEEE Trans. Inf. Theory.

[7]  Benoit Noetinger,et al.  The FFT Moving Average (FFT-MA) Generator: An Efficient Numerical Method for Generating and Conditioning Gaussian Simulations , 2000 .

[8]  Eric Gendron,et al.  Method for simulating infinitely long and non stationary phase screens with optimized memory storage. , 2006, Optics express.

[9]  Francois Roddier,et al.  Adaptive Optics in Astronomy: Imaging through the atmosphere , 2004 .

[10]  Alan S. Willsky,et al.  A canonical correlations approach to multiscale stochastic realization , 2001, IEEE Trans. Autom. Control..

[11]  Alan S. Willsky,et al.  Computationally Efficient Stochastic Realization for Internal Multiscale Autoregressive Models , 2001, Multidimens. Syst. Signal Process..

[12]  R. Lane,et al.  Simulation of a Kolmogorov phase screen , 1992 .

[13]  Andrea Masiero,et al.  Stochastic realization approach to the efficient simulation of phase screens. , 2008 .

[14]  Rodolphe Conan.  Modélisation des effets de l'échelle externe de cohérence spatiale du front d'onde pour l'observation à haute résolution angulaire en astronomie : application à l'optique adaptative, à l'interférométrie et aux très grands télescopes , 2000 .

[15]  Andrea Masiero,et al.  A multiscale stochastic approach for phase screens synthesis , 2011, Proceedings of the 2011 American Control Conference.

[16]  W. Clem Karl,et al.  Multiscale representations of Markov random fields , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[17]  Gian Antonio Susto,et al.  A predictive maintenance system based on regularization methods for ion-implantation , 2012, 2012 SEMI Advanced Semiconductor Manufacturing Conference.

[18]  F. Roddier.  V The Effects of Atmospheric Turbulence in Optical Astronomy , 1981 .