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 language | English |
|---|---|
| Pages (from-to) | 215-220 |
| Number of pages | 6 |
| Journal | Proceedings of SPIE - The International Society for Optical Engineering |
| Volume | 4167 |
| DOIs | |
| Publication status | Published - 2001 |
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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
Representation of phase of distorted optical wave through the orthonormal bases including the outer scale of turbulence. Numerical experiment. / Isaev, Yusup N.; Zakharova, Elena V.
In: Proceedings of SPIE - The International Society for Optical Engineering, Vol. 4167, 2001, p. 215-220.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Representation of phase of distorted optical wave through the orthonormal bases including the outer scale of turbulence. Numerical experiment
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
KW - Correlation function
KW - Optimal basis
KW - Wavefront expansion
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UR - http://www.scopus.com/inward/citedby.url?scp=0035050870&partnerID=8YFLogxK
U2 - 10.1117/12.413826
DO - 10.1117/12.413826
M3 - Article
VL - 4167
SP - 215
EP - 220
JO - Proceedings of SPIE - The International Society for Optical Engineering
JF - Proceedings of SPIE - The International Society for Optical Engineering
SN - 0277-786X
ER -