Representation of phase of distorted optical wave through the orthonormal bases including the outer scale of turbulence. Numerical experiment

Yusup N. Isaev, Elena V. Zakharova

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2 Citations (Scopus)

Abstract

It is usual in the problems of adaptive optics that the phase of optical wave is expanded into an orthogonal basis for a convenience of analysis. Zernike polynomials are popular for this expansion because they have simple analytical expression and their first modes coincide with the classical aberrations. However, if the power spectrum of distortions is known, its egienfunctions named Karhunen-Loeve-Obukhov (KLO) functions are a natural choice for such basis. Authors have derived the KLO functions represented through the Zernike polynomials and developed the effective method to expand distorted phase through the orthonormal bases. Usually, in investigations the Kolmogorov model of turbulence is used. However, the nature experimental data do not agree always with this model. But the range of validity for the Kolmogorov model can be extended introducing in it the outer scale of turbulence. Authors developed the algorithm to obtain analytically the KLO functions allowing for the outer scale of turbulence (von Karman model). The results of numerical experiment for representation of a random phase in different bases for various atmospheric conditions are presented.

Original languageEnglish
Pages (from-to)215-220
Number of pages6
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume4167
DOIs
Publication statusPublished - 2001

Fingerprint

Orthonormal basis
Turbulence
turbulence
Numerical Experiment
Zernike Polynomials
polynomials
Experiments
Polynomials
Orthogonal Basis
Adaptive optics
Adaptive Optics
meteorology
Power spectrum
Aberrations
Aberration
adaptive optics
Power Spectrum
Model
Expand
power spectra

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

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abstract = "It is usual in the problems of adaptive optics that the phase of optical wave is expanded into an orthogonal basis for a convenience of analysis. Zernike polynomials are popular for this expansion because they have simple analytical expression and their first modes coincide with the classical aberrations. However, if the power spectrum of distortions is known, its egienfunctions named Karhunen-Loeve-Obukhov (KLO) functions are a natural choice for such basis. Authors have derived the KLO functions represented through the Zernike polynomials and developed the effective method to expand distorted phase through the orthonormal bases. Usually, in investigations the Kolmogorov model of turbulence is used. However, the nature experimental data do not agree always with this model. But the range of validity for the Kolmogorov model can be extended introducing in it the outer scale of turbulence. Authors developed the algorithm to obtain analytically the KLO functions allowing for the outer scale of turbulence (von Karman model). The results of numerical experiment for representation of a random phase in different bases for various atmospheric conditions are presented.",
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AU - Isaev, Yusup N.

AU - Zakharova, Elena V.

PY - 2001

Y1 - 2001

N2 - It is usual in the problems of adaptive optics that the phase of optical wave is expanded into an orthogonal basis for a convenience of analysis. Zernike polynomials are popular for this expansion because they have simple analytical expression and their first modes coincide with the classical aberrations. However, if the power spectrum of distortions is known, its egienfunctions named Karhunen-Loeve-Obukhov (KLO) functions are a natural choice for such basis. Authors have derived the KLO functions represented through the Zernike polynomials and developed the effective method to expand distorted phase through the orthonormal bases. Usually, in investigations the Kolmogorov model of turbulence is used. However, the nature experimental data do not agree always with this model. But the range of validity for the Kolmogorov model can be extended introducing in it the outer scale of turbulence. Authors developed the algorithm to obtain analytically the KLO functions allowing for the outer scale of turbulence (von Karman model). The results of numerical experiment for representation of a random phase in different bases for various atmospheric conditions are presented.

AB - It is usual in the problems of adaptive optics that the phase of optical wave is expanded into an orthogonal basis for a convenience of analysis. Zernike polynomials are popular for this expansion because they have simple analytical expression and their first modes coincide with the classical aberrations. However, if the power spectrum of distortions is known, its egienfunctions named Karhunen-Loeve-Obukhov (KLO) functions are a natural choice for such basis. Authors have derived the KLO functions represented through the Zernike polynomials and developed the effective method to expand distorted phase through the orthonormal bases. Usually, in investigations the Kolmogorov model of turbulence is used. However, the nature experimental data do not agree always with this model. But the range of validity for the Kolmogorov model can be extended introducing in it the outer scale of turbulence. Authors developed the algorithm to obtain analytically the KLO functions allowing for the outer scale of turbulence (von Karman model). The results of numerical experiment for representation of a random phase in different bases for various atmospheric conditions are presented.

KW - Adaptive optics

KW - Atmospheric turbulence

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KW - Optimal basis

KW - Wavefront expansion

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