## Multiscale stochastic approach for phase screens synthesis |

Applied Optics, Vol. 50, Issue 21, pp. 4124-4133 (2011)

http://dx.doi.org/10.1364/AO.50.004124

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### Abstract

Simulating the turbulence effect on ground telescope observations is of fundamental importance for the design and test of suitable control algorithms for adaptive optics systems. In this paper we propose a multiscale approach for efficiently synthesizing turbulent phases at very high resolution. First, the turbulence is simulated at low resolution, taking advantage of a previously developed method for generating phase screens [ J. Opt. Soc. Am. A 25, 515 (2008)]. Then, high-resolution phase screens are obtained as the output of a multiscale linear stochastic system. The multiscale approach significantly improves the computational efficiency of turbulence simulation with respect to recently developed methods [ Opt. Express 14, 988 (2006)] [ J. Opt. Soc. Am. A 25, 515 (2008)] [ J. Opt. Soc. Am. A 25, 463 (2008)]. Furthermore, the proposed procedure ensures good accuracy in reproducing the statistical characteristics of the turbulent phase.

© 2011 Optical Society of America

**OCIS Codes**

(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

(350.5030) Other areas of optics : Phase

**ToC Category:**

Atmospheric and Oceanic Optics: Wave-front Sensing

**History**

Original Manuscript: February 1, 2011

Revised Manuscript: June 5, 2011

Manuscript Accepted: June 6, 2011

Published: July 19, 2011

**Citation**

Alessandro Beghi, Angelo Cenedese, and Andrea Masiero, "Multiscale stochastic approach for phase screens synthesis," Appl. Opt. **50**, 4124-4133 (2011)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-50-21-4124

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### References

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- Imposing F(θi)(h)=F(ce,i)(h), the solution is restricted to be symmetric. However, there might exist a shorter nonsymmetric sequence of coefficients leading to the same covariances {ce,i(−di),…,ce,i(di)}.
- To be more precise, let m¯ and n¯ be the dimensions of a single phase screen (if the wind velocity is parallel to u, then typically m¯=m and n¯≪n) and assume m0≪m and n0≪n; then the number of operations computed by the algorithm to generate an m¯×n¯ phase screen are approximately 64d¯2m¯n¯. When iteratively generating an m×n screen, with n≫n¯, dividing it in approximately n/n¯ phase screens, there is an extra computational load due to the extra computations to ensure the continuity between successive phase screens. Anyway, such extra computational load is usually a minor term in the overall complexity (lower than 10% in our simulations). Similar considerations can be repeated for the memory requirements.
- Wavelets different from the Haar transform have better multiscale prediction ability but worse complexity and memory requirements.

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