Abstract

Standard FFT-based turbulent phase screen generation method has very large errors due to the undersampling of the low frequency components. Subharmonic methods are the main low frequency components compensating methods to improve the accuracy, but the residual errors are still large. In this paper I propose a new low frequency components compensating method, which is based on the correlation matrix phase screen generation methods. Using this method, the low frequency components can be compensated accurately, both of the accuracy and speed are superior to those of the subharmonic methods.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. L. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” Proc. SPIE 74, 225–233 (1976).
  2. B. J. Herman and L. A. Strugala, “Method for inclusion of low-frequency contributions in numerical representation of atmospheric turbulence,” Proc. SPIE 1221, 183–192 (1990).
    [CrossRef]
  3. R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2(3), 209–224 (1992).
    [CrossRef]
  4. E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2200, 372–383 (1994).
    [CrossRef]
  5. G. Sedmak, “Implementation of fast-Fourier-transform-based simulations of extra-large atmospheric phase and scintillation screens,” Appl. Opt. 43(23), 4527–4538 (2004).
    [CrossRef] [PubMed]
  6. J. Recolons and F. Dios, “Accurate calculation of phase screens for the modelling of laser beam propagation through atmospheric turbulence,” Proc. SPIE 5891, 589107, 589107-12 (2005).
    [CrossRef]
  7. N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29(10), 1174–1180 (1990).
    [CrossRef]
  8. K. A. Winick, “Atmospheric turbulence-induced signal fades on optical heterodyne communication links,” Appl. Opt. 25(11), 1817–1825 (1986).
    [CrossRef] [PubMed]
  9. C. M. Harding, R. A. Johnston, and R. G. Lane, “Fast simulation of a kolmogorov phase screen,” Appl. Opt. 38(11), 2161–2170 (1999).
    [CrossRef] [PubMed]
  10. F. Assémat, R. W. Wilson, and E. Gendron, “Method for simulating infinitely long and non stationary phase screens with optimized memory storage,” Opt. Express 14(3), 988–999 (2006).
    [CrossRef]

2006 (1)

2005 (1)

J. Recolons and F. Dios, “Accurate calculation of phase screens for the modelling of laser beam propagation through atmospheric turbulence,” Proc. SPIE 5891, 589107, 589107-12 (2005).
[CrossRef]

2004 (1)

1999 (1)

1994 (1)

E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2200, 372–383 (1994).
[CrossRef]

1992 (1)

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2(3), 209–224 (1992).
[CrossRef]

1990 (2)

B. J. Herman and L. A. Strugala, “Method for inclusion of low-frequency contributions in numerical representation of atmospheric turbulence,” Proc. SPIE 1221, 183–192 (1990).
[CrossRef]

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29(10), 1174–1180 (1990).
[CrossRef]

1986 (1)

1976 (1)

B. L. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” Proc. SPIE 74, 225–233 (1976).

Assémat, F.

Dainty, J. C.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2(3), 209–224 (1992).
[CrossRef]

Dios, F.

J. Recolons and F. Dios, “Accurate calculation of phase screens for the modelling of laser beam propagation through atmospheric turbulence,” Proc. SPIE 5891, 589107, 589107-12 (2005).
[CrossRef]

Gavel, D. T.

E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2200, 372–383 (1994).
[CrossRef]

Gendron, E.

Glindemann, A.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2(3), 209–224 (1992).
[CrossRef]

Harding, C. M.

Herman, B. J.

B. J. Herman and L. A. Strugala, “Method for inclusion of low-frequency contributions in numerical representation of atmospheric turbulence,” Proc. SPIE 1221, 183–192 (1990).
[CrossRef]

Johansson, E. M.

E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2200, 372–383 (1994).
[CrossRef]

Johnston, R. A.

Lane, R. G.

C. M. Harding, R. A. Johnston, and R. G. Lane, “Fast simulation of a kolmogorov phase screen,” Appl. Opt. 38(11), 2161–2170 (1999).
[CrossRef] [PubMed]

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2(3), 209–224 (1992).
[CrossRef]

McGlamery, B. L.

B. L. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” Proc. SPIE 74, 225–233 (1976).

Recolons, J.

J. Recolons and F. Dios, “Accurate calculation of phase screens for the modelling of laser beam propagation through atmospheric turbulence,” Proc. SPIE 5891, 589107, 589107-12 (2005).
[CrossRef]

Roddier, N.

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29(10), 1174–1180 (1990).
[CrossRef]

Sedmak, G.

Strugala, L. A.

B. J. Herman and L. A. Strugala, “Method for inclusion of low-frequency contributions in numerical representation of atmospheric turbulence,” Proc. SPIE 1221, 183–192 (1990).
[CrossRef]

Wilson, R. W.

Winick, K. A.

Appl. Opt. (3)

Opt. Eng. (1)

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29(10), 1174–1180 (1990).
[CrossRef]

Opt. Express (1)

Proc. SPIE (4)

B. L. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” Proc. SPIE 74, 225–233 (1976).

B. J. Herman and L. A. Strugala, “Method for inclusion of low-frequency contributions in numerical representation of atmospheric turbulence,” Proc. SPIE 1221, 183–192 (1990).
[CrossRef]

E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2200, 372–383 (1994).
[CrossRef]

J. Recolons and F. Dios, “Accurate calculation of phase screens for the modelling of laser beam propagation through atmospheric turbulence,” Proc. SPIE 5891, 589107, 589107-12 (2005).
[CrossRef]

Waves Random Media (1)

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2(3), 209–224 (1992).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Errors induced by the negative eigenvalues of matrix Blow,low as a function of L0/Dy.

Fig. 2
Fig. 2

Phase structure functions of the final compensated phase screen, the initial FFT-based phase screen and the low frequency compensating phase screen. Square screen, Dx = Dy = 1 m, Nx = Ny = 256, Nlx = Nly = 9, Nzx = Nzy = 3, L0 = 3 m, averaged over 105 screens.

Fig. 3
Fig. 3

Relative errors of the phase structure functions on the edge line of the final compensated phase screen. (a) Square screen, Dx = Dy = 1 m, Nx = Ny = 256 and Nzx = Nzy = 3, averaged over 5 × 106 screens. (b) Rectangular screen. Solid line: Dx = 32 m, Dy = 1 m, Nx = 2048, Ny = 64, Nlx = 257, Nly = 9, Nzx = 97, Nzy = 3. Dashed line: Dx = 128 m, Dy = 1 m, Nx = 8192, Ny = 64, Nlx = 513, Nly = 5, Nzx = 385, Nzy = 3, averaged over 106 screens.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

φ FFT (m,n)= m ' = N x /2 N x /21 n ' = N y /2 N y /21 h( m ' , n ' ) Φ n ( m ' , n ' ) exp[i2π( m ' m N x + n ' n N y )]
Φ n ( m ' , n ' )=0.490 r 0 5/3 [ ( m ' Δ k x ) 2 + ( n ' Δ k y ) 2 + (2π/ L 0 ) 2 ] 11/6 Δ k x Δ k y
Φ n ( m ' , n ' )=0for| m ' |( N zx 1)/2and| n ' |( N zy 1)/2
N zx = N zy =3
{ N zx =3 N x / N y +1 N zy =3
ϕ= ϕ FFT + ϕ low
B ϕ (r)=<ϕ( s 1 )ϕ( s 2 )>=<[ ϕ FFT ( s 1 )+ ϕ low ( s 1 )][ ϕ FFT ( s 2 )+ ϕ low ( s 2 )]> = B ϕ FFT (r)+ B ϕ low (r)
B ϕ (r)= ( L 0 / r 0 ) 5/3 Γ(11/6) 2 5/6 π 8/3 [ 24 5 Γ(6/5)] 5/6 ( 2πr L 0 ) 5/6 K 5/6 ( 2πr L 0 )
B ϕ FFT ( m 2 + n 2 Δ)= m ' = N x /2 N x /21 n ' = N y /2 N y /21 Φ n ( m ' , n ' ) exp[i2π( m ' m N x + n ' n N y )]
B ϕ low ( m 2 + n 2 Δ)= B ϕ ( m 2 + n 2 Δ) B ϕ FFT ( m 2 + n 2 Δ)
B φ low,low [( m 1 1) N ly + n 1 ,( m 2 1) N ly + n 2 ]= B φ low [ ( m 1 m 2 ) 2 + ( n 1 n 2 ) 2 qΔ]
ψ low,low =URe( L )X
B ϕ low,low actual ( p 1 , p 2 )=< ψ low,low ( p 1 ) ψ low,low T ( p 2 )>= j=1 N lx N ly U( p 1 ,j) [Re( λ j )] 2 U(j, p 2 )
D ϕ low,low actual ( p 1 , p 2 )=< [ ϕ low,low ( m 1 , n 1 ) ϕ low,low ( m 2 , n 2 )] 2 > = B ϕ low,low actual ( p 1 , p 1 )+ B ϕ low,low actual ( p 2 , p 2 )2 B ϕ low,low actual ( p 1 , p 2 )
D ϕ low,low exp ( p 1 , p 2 )=2[ B ϕ low,low (1,1) B ϕ low,low ( p 1 , p 2 )]
D ϕ exp (r)= ( L 0 r 0 ) 5/3 2 1/6 Γ(11/6) π 8/3 [ 24 5 Γ( 6 5 ) ] 5/6 [ Γ(6/5) 2 1/6 ( 2πr L 0 ) 5/6 K 5/6 ( 2πr L 0 ) ]
ERRSVD=max(| D ϕ low,low actual D ϕ low,low exp |/ D ϕ exp )

Metrics