Expansion of random wave phase in terms of eigenfunctions of phase correlation function

Yusup N. Isaev, Elena V. Zakharova

Research output: Contribution to journalArticle

Abstract

In numerical experiment the authors investigate a representation of the phase of random optical wave through the Karhunen-Loeve-Obukhov (KLO) functions obtained with the use of phase correlation function calculated from experimental data. For such KLO basis the averaged relative error of phase expansion is 5% for 10 basis functions in the expansion series, whereas for the KLO basis calculated with the Kolmogorov structure function of phase the error of phase expansion 5% has been obtained for 78 basis functions. When a propagation medium is close to Kolmogorov model it is possible to use this KLO basis obtained for a single section of distorted phase distribution for representation of whole phase distribution.

Original languageEnglish
Pages (from-to)168-173
Number of pages6
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume4538
DOIs
Publication statusPublished - 2002
Externally publishedYes

Fingerprint

Phase Correlation
Eigenvalues and eigenfunctions
Eigenfunctions
Correlation Function
eigenvectors
expansion
Basis Functions
series expansion
Structure-function
Relative Error
Series Expansion
propagation
Numerical Experiment
Experimental Data
Propagation
Experiments

Keywords

  • Adaptive optics
  • Atmospheric turbulence
  • Correlation function
  • Optimal basis
  • Wavefront expansion

ASJC Scopus subject areas

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

Cite this

@article{00170a08fbb2445a923af7b42ea97488,
title = "Expansion of random wave phase in terms of eigenfunctions of phase correlation function",
abstract = "In numerical experiment the authors investigate a representation of the phase of random optical wave through the Karhunen-Loeve-Obukhov (KLO) functions obtained with the use of phase correlation function calculated from experimental data. For such KLO basis the averaged relative error of phase expansion is 5{\%} for 10 basis functions in the expansion series, whereas for the KLO basis calculated with the Kolmogorov structure function of phase the error of phase expansion 5{\%} has been obtained for 78 basis functions. When a propagation medium is close to Kolmogorov model it is possible to use this KLO basis obtained for a single section of distorted phase distribution for representation of whole phase distribution.",
keywords = "Adaptive optics, Atmospheric turbulence, Correlation function, Optimal basis, Wavefront expansion",
author = "Isaev, {Yusup N.} and Zakharova, {Elena V.}",
year = "2002",
doi = "10.1117/12.454403",
language = "English",
volume = "4538",
pages = "168--173",
journal = "Proceedings of SPIE - The International Society for Optical Engineering",
issn = "0277-786X",
publisher = "SPIE",

}

TY - JOUR

T1 - Expansion of random wave phase in terms of eigenfunctions of phase correlation function

AU - Isaev, Yusup N.

AU - Zakharova, Elena V.

PY - 2002

Y1 - 2002

N2 - In numerical experiment the authors investigate a representation of the phase of random optical wave through the Karhunen-Loeve-Obukhov (KLO) functions obtained with the use of phase correlation function calculated from experimental data. For such KLO basis the averaged relative error of phase expansion is 5% for 10 basis functions in the expansion series, whereas for the KLO basis calculated with the Kolmogorov structure function of phase the error of phase expansion 5% has been obtained for 78 basis functions. When a propagation medium is close to Kolmogorov model it is possible to use this KLO basis obtained for a single section of distorted phase distribution for representation of whole phase distribution.

AB - In numerical experiment the authors investigate a representation of the phase of random optical wave through the Karhunen-Loeve-Obukhov (KLO) functions obtained with the use of phase correlation function calculated from experimental data. For such KLO basis the averaged relative error of phase expansion is 5% for 10 basis functions in the expansion series, whereas for the KLO basis calculated with the Kolmogorov structure function of phase the error of phase expansion 5% has been obtained for 78 basis functions. When a propagation medium is close to Kolmogorov model it is possible to use this KLO basis obtained for a single section of distorted phase distribution for representation of whole phase distribution.

KW - Adaptive optics

KW - Atmospheric turbulence

KW - Correlation function

KW - Optimal basis

KW - Wavefront expansion

UR - http://www.scopus.com/inward/record.url?scp=0036395329&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036395329&partnerID=8YFLogxK

U2 - 10.1117/12.454403

DO - 10.1117/12.454403

M3 - Article

VL - 4538

SP - 168

EP - 173

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

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

SN - 0277-786X

ER -