Stochastic realization approach to the efficient simulation of phase screens.

The phase screen method is a well-established approach to take into account the effects of atmospheric turbulence in astronomical seeing. This is of key importance in designing adaptive optics for new-generation telescopes, in particular in view of applications such as exoplanet detection or long-exposure spectroscopy. We present an innovative approach to simulate turbulent phase that is based on stochastic realization theory. The method shows appealing properties in terms of both accuracy in reconstructing the structure function and compactness of the representation.

[1]  H. Akaike.  Markovian Representation of Stochastic Processes by Canonical Variables , 1975 .

[2]  Β. L. HO,et al.  Editorial: Effective construction of linear state-variable models from input/output functions , 1966 .

[3]  David L. Fried,et al.  Statistics of a Geometric Representation of Wavefront Distortion: Errata , 1965 .

[4]  U. Desai,et al.  A realization approach to stochastic model reduction and balanced stochastic realizations , 1982, 1982 21st IEEE Conference on Decision and Control.

[5]  H. Zeiger,et al.  Approximate linear realizations of given dimension via Ho's algorithm , 1974 .

[6]  R. Noll.  Zernike polynomials and atmospheric turbulence , 1976 .

[7]  Daniel Enard,et al.  The Very Large Telescope project. , 1983 .

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

[9]  N. Hubin,et al.  New challenges for adaptive optics: extremely large telescopes , 2000, astro-ph/0004065.

[10]  H. Booker,et al.  Diffraction from an irregular screen with applications to ionospheric problems , 1950, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[11]  Marc S. Sarazin,et al.  The eye of the beholder: designing the OWL , 2003, SPIE Astronomical Telescopes + Instrumentation.

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

[13]  Andrei Tokovinin,et al.  From Differential Image Motion to Seeing , 2002 .

[14]  A. Kolmogorov.  Dissipation of energy in the locally isotropic turbulence , 1941, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[15]  Ichirou Yamaguchi,et al.  Spatial correlation of Zernike phase-expansion coefficients for atmospheric turbulence with finite outer scale. , 1995 .

[16]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[17]  H. Akaike.  Stochastic theory of minimal realization , 1974 .

[18]  Anders Lindquist,et al.  Canonical correlation analysis, approximate covariance extension, and identification of stationary time series , 1996, Autom..

[19]  Sun-Yuan Kung,et al.  A new identification and model reduction algorithm via singular value decomposition , 1978 .

[20]  D. Winker.  Effect of a finite outer scale on the Zernike decomposition of atmospheric optical turbulence , 1991 .

[21]  R. A. Silverman,et al.  Wave Propagation in a Turbulent Medium , 1961 .