Representation of Karhunen-Loeve-Obukhov functions in bases of Walsh and Haar

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

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)507-514
Number of pages8
JournalProceedings of SPIE - The International Society for Optical Engineering
Publication statusPublished - 1997
Externally publishedYes


  • Adaptive system
  • Fast transform
  • Optimal basis
  • Wavefront

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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