Representation of Karhunen-Loeve-Obukhov functions based on Walsh and Haar

Yusup N. Isaev; Viktor A. Banakh; Elena V. Zakharova

doi:10.1117/12.290167

17 October 1997 Representation of Karhunen-Loeve-Obukhov functions based on Walsh and Haar

Yusup N. Isaev, Viktor A. Banakh, Elena V. Zakharova

Proceedings Volume 3126, Adaptive Optics and Applications; (1997) https://doi.org/10.1117/12.290167
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

Authors obtained the analytical relations allowing one to realize a transformation in expansions of optical wave phase from the Haar and Walsh bases, which are characterized by a simplicity of engineering realization in compensating devices of adaptive optics systems (AOS), to the statistically optimal Karhunen-Loeve-Obukhov basis describing the most completely and accurately the criteria of AOS approximation to ideal diffraction-limited system. The relations obtained and use of the fast Walsh and Haar transform algorithms allow one to approach the real time in wavefront reconstruction. Moreover, the analytical relations obtained allows an influence of the outer scale of turbulence to be taken into account. Results of numerical calculations of the transformation matrix are presented.

Citation Download Citation

Yusup N. Isaev, Viktor A. Banakh, and Elena V. Zakharova "Representation of Karhunen-Loeve-Obukhov functions based on Walsh and Haar", Proc. SPIE 3126, Adaptive Optics and Applications, (17 October 1997); https://doi.org/10.1117/12.290167

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