Abstract

A relative displacement between the grid points of optical fields and those of phase screens may occur in the simulation of light propagation through the turbulent atmosphere. A statistical interpolator is proposed to solve this problem in this paper. It is evaluated by the phase structure function and numerical experiments of light propagation through atmospheric turbulence with/without adaptive optics (AO) and it is also compared with the well-known linear interpolator under the same condition. Results of the phase structure function show that the statistical interpolator is more accurate in comparison with the linear one, especially in the high frequency region. More importantly, the long-exposure results of light propagation through the turbulent atmosphere with/without AO also show that the statistical interpolator is more accurate and reliable than the linear one.

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  1. J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
    [CrossRef]
  2. H.-X. Yan, S.-S. Li, D.-L. Zhang, and S. Chen, “Numerical simulation of an adaptive optics system with laser propagation in the atmosphere,” Appl. Opt. 39(18), 3023–3031 (2000).
    [CrossRef]
  3. L. C. Andrews, R. L. Philips, R. J. Sasiela, and R. R. Parenti, “Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects,” Opt. Eng. 45(7), 076001–1 (2006).
    [CrossRef]
  4. F. Dios, J. Recolons, A. Rodríguez, and O. Batet, “Temporal analysis of laser beam propagation in the atmosphere using computer-generated long phase screens,” Opt. Express 16(3), 2206–2220 (2008).
    [CrossRef] [PubMed]
  5. H.-X Yan, Han-Ling Wu, Shu-Shan Li and She Chen, “Cone effect in astronomical adaptive optics system investigated by a pure numerical simulation,” Proc. SPIE 5903, 5903OU1–12 (2005).
  6. E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2220, 372–383 (1994).
    [CrossRef]
  7. V. Sriram and D. Kearney, “An ultra fast Kolmogorov phase screen generator suitable for parallel implementation,” Opt. Express 15(21), 13709–13714 (2007).
    [CrossRef] [PubMed]
  8. A. Beghi, A. Cenedese, and A. Masiero, “Stochastic realization approach to the efficient simulation of phase screens,” J. Opt. Soc. Am. A 25(2), 515–525 (2008).
    [CrossRef]
  9. H. Jakobsson, “Simulations of time series of atmospherically distorted wave fronts,” Appl. Opt. 35(9), 1561–1565 (1996).
    [CrossRef] [PubMed]
  10. H.-X. Yan, S.-S. Li, and S. Chen, “Numerical simulation investigations of the dynamic control process and frequency response characteristics in an adaptive optics system,” Proc. SPIE 4494, 156–166 (2002).
    [CrossRef]
  11. B. M. Welsh, “Fourier-series-based atmospheric phase screen generator for simulating anisoplanatic geometries and temporal evolution,” Proc. SPIE 3125, 327–338 (1997).
    [CrossRef]
  12. G. Sedmak, “Performance analysis of and compensation for aspect-ratio effects of fast-fourier-transform-based simulations of large atmospheric wave fronts,” Appl. Opt. 37(21), 4605–4613 (1998).
    [CrossRef]
  13. M. C. Roggemann, B. M. Welsh, D. Montera, and T. A. Rhoadamer, “Method for simulating atmospheric turbulence phase effects for multiple time slices and anisoplanatic conditions,” Appl. Opt. 34(20), 4037–4051 (1995).
    [CrossRef] [PubMed]
  14. H.-X. Yan, S. Chen, and S.-S. Li, “Turbulent phase screens generated by covariance approach and their application in numerical simulation of atmospheric propagation of laser beam,” Proc. SPIE 6346, 634628 (2006).
    [CrossRef]
  15. 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] [PubMed]
  16. D. L. Fried and T. Clark, “Extruding Kolmogorov-type phase screen ribbons,” J. Opt. Soc. Am. A 25(2), 463–468 (2008).
    [CrossRef]
  17. C. S. Gardner, B. M. Welsh, and L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78(11), 1721–1743 (1990).
    [CrossRef]
  18. B. Formwalt and S. Cain, “Optimized phase screen modeling for optical turbulence,” Appl. Opt. 45(22), 5657–5668 (2006).
    [CrossRef] [PubMed]
  19. R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of Kolmogorov phase screen,” Waves Random Media 2(3), 209–224 (1992).
    [CrossRef]
  20. 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]
  21. L. C. Andrews, and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE Press, Washington, 2005).
  22. R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic Press, Boston, 1997).

2008

2007

2006

L. C. Andrews, R. L. Philips, R. J. Sasiela, and R. R. Parenti, “Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects,” Opt. Eng. 45(7), 076001–1 (2006).
[CrossRef]

H.-X. Yan, S. Chen, and S.-S. Li, “Turbulent phase screens generated by covariance approach and their application in numerical simulation of atmospheric propagation of laser beam,” Proc. SPIE 6346, 634628 (2006).
[CrossRef]

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] [PubMed]

B. Formwalt and S. Cain, “Optimized phase screen modeling for optical turbulence,” Appl. Opt. 45(22), 5657–5668 (2006).
[CrossRef] [PubMed]

2002

H.-X. Yan, S.-S. Li, and S. Chen, “Numerical simulation investigations of the dynamic control process and frequency response characteristics in an adaptive optics system,” Proc. SPIE 4494, 156–166 (2002).
[CrossRef]

2000

1999

1998

1997

B. M. Welsh, “Fourier-series-based atmospheric phase screen generator for simulating anisoplanatic geometries and temporal evolution,” Proc. SPIE 3125, 327–338 (1997).
[CrossRef]

1996

1995

1994

E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2220, 372–383 (1994).
[CrossRef]

1992

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

1990

C. S. Gardner, B. M. Welsh, and L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78(11), 1721–1743 (1990).
[CrossRef]

1976

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[CrossRef]

Andrews, L. C.

L. C. Andrews, R. L. Philips, R. J. Sasiela, and R. R. Parenti, “Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects,” Opt. Eng. 45(7), 076001–1 (2006).
[CrossRef]

Assémat, F.

Batet, O.

Beghi, A.

Cain, S.

Cenedese, A.

Chen, S.

H.-X. Yan, S. Chen, and S.-S. Li, “Turbulent phase screens generated by covariance approach and their application in numerical simulation of atmospheric propagation of laser beam,” Proc. SPIE 6346, 634628 (2006).
[CrossRef]

H.-X. Yan, S.-S. Li, and S. Chen, “Numerical simulation investigations of the dynamic control process and frequency response characteristics in an adaptive optics system,” Proc. SPIE 4494, 156–166 (2002).
[CrossRef]

H.-X. Yan, S.-S. Li, D.-L. Zhang, and S. Chen, “Numerical simulation of an adaptive optics system with laser propagation in the atmosphere,” Appl. Opt. 39(18), 3023–3031 (2000).
[CrossRef]

Clark, T.

Dainty, J. C.

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

Dios, F.

Feit, M. D.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[CrossRef]

Fleck, J. A.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[CrossRef]

Formwalt, B.

Fried, D. L.

Gardner, C. S.

C. S. Gardner, B. M. Welsh, and L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78(11), 1721–1743 (1990).
[CrossRef]

Gavel, D. T.

E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2220, 372–383 (1994).
[CrossRef]

Gendron, E.

Glindemann, A.

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

Harding, C. M.

Jakobsson, H.

Johansson, E. M.

E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2220, 372–383 (1994).
[CrossRef]

Johnston, R. A.

Kearney, D.

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]

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

Li, S.-S.

H.-X. Yan, S. Chen, and S.-S. Li, “Turbulent phase screens generated by covariance approach and their application in numerical simulation of atmospheric propagation of laser beam,” Proc. SPIE 6346, 634628 (2006).
[CrossRef]

H.-X. Yan, S.-S. Li, and S. Chen, “Numerical simulation investigations of the dynamic control process and frequency response characteristics in an adaptive optics system,” Proc. SPIE 4494, 156–166 (2002).
[CrossRef]

H.-X. Yan, S.-S. Li, D.-L. Zhang, and S. Chen, “Numerical simulation of an adaptive optics system with laser propagation in the atmosphere,” Appl. Opt. 39(18), 3023–3031 (2000).
[CrossRef]

Masiero, A.

Montera, D.

Morris, J. R.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[CrossRef]

Parenti, R. R.

L. C. Andrews, R. L. Philips, R. J. Sasiela, and R. R. Parenti, “Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects,” Opt. Eng. 45(7), 076001–1 (2006).
[CrossRef]

Philips, R. L.

L. C. Andrews, R. L. Philips, R. J. Sasiela, and R. R. Parenti, “Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects,” Opt. Eng. 45(7), 076001–1 (2006).
[CrossRef]

Recolons, J.

Rhoadamer, T. A.

Rodríguez, A.

Roggemann, M. C.

Sasiela, R. J.

L. C. Andrews, R. L. Philips, R. J. Sasiela, and R. R. Parenti, “Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects,” Opt. Eng. 45(7), 076001–1 (2006).
[CrossRef]

Sedmak, G.

Sriram, V.

Thompson, L. A.

C. S. Gardner, B. M. Welsh, and L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78(11), 1721–1743 (1990).
[CrossRef]

Welsh, B. M.

B. M. Welsh, “Fourier-series-based atmospheric phase screen generator for simulating anisoplanatic geometries and temporal evolution,” Proc. SPIE 3125, 327–338 (1997).
[CrossRef]

M. C. Roggemann, B. M. Welsh, D. Montera, and T. A. Rhoadamer, “Method for simulating atmospheric turbulence phase effects for multiple time slices and anisoplanatic conditions,” Appl. Opt. 34(20), 4037–4051 (1995).
[CrossRef] [PubMed]

C. S. Gardner, B. M. Welsh, and L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78(11), 1721–1743 (1990).
[CrossRef]

Wilson, R. W.

Yan, H.-X.

H.-X. Yan, S. Chen, and S.-S. Li, “Turbulent phase screens generated by covariance approach and their application in numerical simulation of atmospheric propagation of laser beam,” Proc. SPIE 6346, 634628 (2006).
[CrossRef]

H.-X. Yan, S.-S. Li, and S. Chen, “Numerical simulation investigations of the dynamic control process and frequency response characteristics in an adaptive optics system,” Proc. SPIE 4494, 156–166 (2002).
[CrossRef]

H.-X. Yan, S.-S. Li, D.-L. Zhang, and S. Chen, “Numerical simulation of an adaptive optics system with laser propagation in the atmosphere,” Appl. Opt. 39(18), 3023–3031 (2000).
[CrossRef]

Zhang, D.-L.

Appl. Opt.

Appl. Phys. (Berl.)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

L. C. Andrews, R. L. Philips, R. J. Sasiela, and R. R. Parenti, “Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects,” Opt. Eng. 45(7), 076001–1 (2006).
[CrossRef]

Opt. Express

Proc. IEEE

C. S. Gardner, B. M. Welsh, and L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78(11), 1721–1743 (1990).
[CrossRef]

Proc. SPIE

H.-X. Yan, S. Chen, and S.-S. Li, “Turbulent phase screens generated by covariance approach and their application in numerical simulation of atmospheric propagation of laser beam,” Proc. SPIE 6346, 634628 (2006).
[CrossRef]

H.-X. Yan, S.-S. Li, and S. Chen, “Numerical simulation investigations of the dynamic control process and frequency response characteristics in an adaptive optics system,” Proc. SPIE 4494, 156–166 (2002).
[CrossRef]

B. M. Welsh, “Fourier-series-based atmospheric phase screen generator for simulating anisoplanatic geometries and temporal evolution,” Proc. SPIE 3125, 327–338 (1997).
[CrossRef]

E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2220, 372–383 (1994).
[CrossRef]

Waves Random Media

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

Other

H.-X Yan, Han-Ling Wu, Shu-Shan Li and She Chen, “Cone effect in astronomical adaptive optics system investigated by a pure numerical simulation,” Proc. SPIE 5903, 5903OU1–12 (2005).

L. C. Andrews, and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE Press, Washington, 2005).

R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic Press, Boston, 1997).

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Figures (9)

Fig. 1
Fig. 1

Schematic illustration of the one-dimensional relative displacement. (a) At the initial time t = t0, the grid points of an optical field are in one-to-one correspondence with those of a phase screen. (b) At the time t = t1, the grid points of the optical field are still in one-to-one correspondence with those of the phase screen because the phase screen shifts by one grid spacing. (c) At the time t = t2, a relative displacement between the grid points of the optical field and those of the phase screen occurs because the phase screen shifts by non-integer multiples of the grid spacing.

Fig. 2
Fig. 2

Schematic illustration of the two-dimensional relative displacement. (a) The propagation geometry in the simulation of an astronomical telescope with a laser guide star adaptive optics system. (b) The grid points of a LGS optical field is among those of the phase screen and the grid spacing of the LGS optical field is smaller than that of the phase screen or the object optical field due to the finite altitude of LGS.

Fig. 3
Fig. 3

Graphical depiction of interpolation. The grid spacing is r. (a) One-dimensional interpolation of the first kind of scenario, r1 and r2 are the distances between P1 and P, P2 and P, respectively. (b) Two-dimensional interpolation of the second kind of scenario. uand v are the distances from a point P to the line P1P4 , P3P4 , respectively.

Fig. 4
Fig. 4

The relative error of the phase structure functions for different interpolation methods. (a) h = 0.3, (b) h = 0.5, (c) h = 0.7.

Fig. 5
Fig. 5

Relative error of the phase structure function for different interpolation methods at (a) l = 1.0, (b) l = 1.2, (c) l = 1.6, (d) l = 2.3.

Fig. 6
Fig. 6

The relative error of the phase structure function for different interpolation methods at (a) (m, n) = (0.1, 0.1), (b) (m, n) = (0.5, 0.5), (c) (m, n) = (0.8, 0.2), (d) (m, n) = (0.9, 0.8).

Fig. 7
Fig. 7

Generation of the low-resolution screen (hollow points) by extracting a point every pixel from the high-resolution screen (dark points).

Fig. 8
Fig. 8

Relative error of the long-exposure Strehl ratio from the first approach (the standard value) and that from the second approach which uses the linear interpolation given by Eq. (2) or the one-dimensional statistical interpolation given by Eq. (3). (a) Open-loop; (b) Closed-loop.

Fig. 9
Fig. 9

Relative error of the long-exposure Strehl ratio from the first approach (the standard value) and that from the second approach which uses the linear interpolator given by Eq. (2) or the two-dimensional statistical interpolator given by Eq. (6). (a) Open-loop; (b) Closed-loop.

Equations (16)

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Dφ(r)=E{(φ(R+r)φ(R))2}=6.88(r/r0)5/3
P=vr(1ur)P1+uvr2P2+ur(1vr)P3+(1ur)(1vr)P4
D0=E{(P1P2)2}=6.88(r/r0)5/3
D1=E{(PP1)2}=6.88(r1/r0)5/3
D2=E{(PP2)2}=6.88(r2/r0)5/3
P=aP1+bP2+R
{E{(P-P1)2}=(1-a)2D0+σ2=D1E{(P-P2)2}=a2D0+σ2=D2
{a=(D0D1+D2)/2D0σ2=D2(D0D1+D2)2/4D0
(αχ)(βχ)=12[(αχ)2+(βχ)2(αβ)2]
P=aP1+bP2+cP3+dP4+R
{E{(P-P1)2}=D1E{(P-P2)2}=D2E{(P-P3)2}=D3E{(P-P4)2}=D4
E{(P1P2)2}=E{(P2P3)2}=E{(P3P4)2}=E{(P4P1)2}=D0
E{(P1P3)2}=E{(P2P4)2}=D5
{(a1)2D0+b2D5+c2D0+b(a1)D5+c(a1)(2D0D5)+bcD5+σ2=D1(9.1)a2D0+(b1)2D5+c2D0+a(b1)D5+ac(2D0D5)+c(b1)D5+σ2=D2(9.2)a2D0+b2D5+(c1)2D0+abD5+a(c1)(2D0D5)+b(c1)D5+σ2=D3(9.3)a2D0+b2D5+c2D0+abD5+ac(2D0D5)+bcD5+σ2=D4(9.4)
{a=2D0D5+4D0D34D0D1D52+D4D53D3D5+D2D5+D1D54D5(2D0D5)b=2D0D5+4D0D44D0D2D52+D3D53D4D5+D2D5+D1D54D5(2D0D5)c=2D0D5+4D0D14D0D3D52+D3D53D1D5+D2D5+D4D54D5(2D0D5)d=2D0D5+4D0D24D0D4D52+D4D53D2D5+D3D5+D1D54D5(2D0D5)
Error(r)=1Dϕsimulation(r)/Dϕbase(r)

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