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 journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)507-514
Number of pages8
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume3126
DOIs
Publication statusPublished - 1997
Externally publishedYes

Fingerprint

Adaptive optics
adaptive optics
Adaptive Optics
Wavefronts
Wavefront Reconstruction
Turbulence
Transformation Matrix
Diffraction
turbulence
engineering
Numerical Calculation
expansion
Simplicity
approximation
diffraction
Transform
Engineering
Approximation

Keywords

  • 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

Cite this

Representation of Karhunen-Loeve-Obukhov functions in bases of Walsh and Haar. / Isaev, Yusup N.; Banakh, Viktor A.; Zakharova, Elena V.

In: Proceedings of SPIE - The International Society for Optical Engineering, Vol. 3126, 1997, p. 507-514.

Research output: Contribution to journalArticle

@article{64ac275d60494c80a8dae0446523bdbe,
title = "Representation of Karhunen-Loeve-Obukhov functions in bases of Walsh and Haar",
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.",
keywords = "Adaptive system, Fast transform, Optimal basis, Wavefront",
author = "Isaev, {Yusup N.} and Banakh, {Viktor A.} and Zakharova, {Elena V.}",
year = "1997",
doi = "10.1117/12.290167",
language = "English",
volume = "3126",
pages = "507--514",
journal = "Proceedings of SPIE - The International Society for Optical Engineering",
issn = "0277-786X",
publisher = "SPIE",

}

TY - JOUR

T1 - Representation of Karhunen-Loeve-Obukhov functions in bases of Walsh and Haar

AU - Isaev, Yusup N.

AU - Banakh, Viktor A.

AU - Zakharova, Elena V.

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

KW - Adaptive system

KW - Fast transform

KW - Optimal basis

KW - Wavefront

UR - http://www.scopus.com/inward/record.url?scp=0031289037&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031289037&partnerID=8YFLogxK

U2 - 10.1117/12.290167

DO - 10.1117/12.290167

M3 - Article

VL - 3126

SP - 507

EP - 514

JO - Proceedings of SPIE - The International Society for Optical Engineering

JF - Proceedings of SPIE - The International Society for Optical Engineering

SN - 0277-786X

ER -