Abstract

A numerical simulator of a turbulence phase screen based on turbulence power spectrum density is described in this paper. The low-frequency adding technique used in the fast-Fourier-transform-based method is extended to the whole frequency domain. The frequency range and spatial coordinates are no longer limited by the spatial sampling, so that the phase screens can be applied in the multibeam time-dependent scenario. Several spectrums can be applied in this simulator. The structure function, modulation transfer function, and variance of the Zernike coefficient are calculated with the Kolmogorov model for validation. The simulation results have shown good agreement with the theoretical results.

© 2014 Optical Society of America

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References

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2013

2012

P. A. Konyaev, “Computer simulation of adaptive optics for laser systems in atmospheric applications,” Optoelectron. Instrum. Data Process. 48, 119–125 (2012).
[CrossRef]

2010

S. M. Ammons, L. Johnson, E. A. Laag, R. Kupke, D. T. Gavel, B. J. Bauman, and C. E. Max, “Integrated laboratory demonstrations of multi-object adaptive optics on a simulated 10 meter telescope at visible wavelengths,” Publ. Astron. Soc. Pac. 122, 573–589 (2010).
[CrossRef]

M. Carbillet and A. Riccardi, “Numerical modeling of atmospherically perturbed phase screens: new solutions for classical fast Fourier transform and Zernike methods,” Appl. Opt. 49, G47–G52 (2010).
[CrossRef]

2009

2006

2002

2000

1999

1995

V. P. Lukin, F. Yu, P. A. Konyaev, and B. V. Fortes, “Numerical model of atmospheric adaptive optical system,” Atmos. Ocean. Opt. 8, 210–222 (1995).

L. C. Andrews, R. L. Phillips, and P. T. Yu, “Optical scintillations and fade statistics for a satellite-communication system,” Appl. Opt. 34, 7742–7751 (1995).
[CrossRef]

1992

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

1990

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, 1174–1180 (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. 10, 129–160 (1976).
[CrossRef]

R. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
[CrossRef]

1967

1966

Ammons, S. M.

S. M. Ammons, L. Johnson, E. A. Laag, R. Kupke, D. T. Gavel, B. J. Bauman, and C. E. Max, “Integrated laboratory demonstrations of multi-object adaptive optics on a simulated 10 meter telescope at visible wavelengths,” Publ. Astron. Soc. Pac. 122, 573–589 (2010).
[CrossRef]

Andrews, L. C.

Bauman, B. J.

S. M. Ammons, L. Johnson, E. A. Laag, R. Kupke, D. T. Gavel, B. J. Bauman, and C. E. Max, “Integrated laboratory demonstrations of multi-object adaptive optics on a simulated 10 meter telescope at visible wavelengths,” Publ. Astron. Soc. Pac. 122, 573–589 (2010).
[CrossRef]

Burckel, W. P.

Carbillet, M.

Dudorov, V. V.

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. 10, 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. 10, 129–160 (1976).
[CrossRef]

Fortes, B. V.

V. P. Lukin, F. Yu, P. A. Konyaev, and B. V. Fortes, “Numerical model of atmospheric adaptive optical system,” Atmos. Ocean. Opt. 8, 210–222 (1995).

V. P. Lukin and B. V. Fortes, Adaptive Beaming and Imaging in the Turbulent Atmosphere (SPIE, 2002).

Frehlich, R.

Fried, D. L.

Gavel, D. T.

S. M. Ammons, L. Johnson, E. A. Laag, R. Kupke, D. T. Gavel, B. J. Bauman, and C. E. Max, “Integrated laboratory demonstrations of multi-object adaptive optics on a simulated 10 meter telescope at visible wavelengths,” Publ. Astron. Soc. Pac. 122, 573–589 (2010).
[CrossRef]

Glindemann, A.

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

Gray, R. N.

Harding, C. M.

Hardy, J. W.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University, 1998).

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]

Johnson, L.

S. M. Ammons, L. Johnson, E. A. Laag, R. Kupke, D. T. Gavel, B. J. Bauman, and C. E. Max, “Integrated laboratory demonstrations of multi-object adaptive optics on a simulated 10 meter telescope at visible wavelengths,” Publ. Astron. Soc. Pac. 122, 573–589 (2010).
[CrossRef]

Johnston, R. A.

Kolosov, V. V.

Konyaev, P. A.

P. A. Konyaev, “Computer simulation of adaptive optics for laser systems in atmospheric applications,” Optoelectron. Instrum. Data Process. 48, 119–125 (2012).
[CrossRef]

V. P. Lukin, F. Yu, P. A. Konyaev, and B. V. Fortes, “Numerical model of atmospheric adaptive optical system,” Atmos. Ocean. Opt. 8, 210–222 (1995).

Kupke, R.

S. M. Ammons, L. Johnson, E. A. Laag, R. Kupke, D. T. Gavel, B. J. Bauman, and C. E. Max, “Integrated laboratory demonstrations of multi-object adaptive optics on a simulated 10 meter telescope at visible wavelengths,” Publ. Astron. Soc. Pac. 122, 573–589 (2010).
[CrossRef]

Laag, E. A.

S. M. Ammons, L. Johnson, E. A. Laag, R. Kupke, D. T. Gavel, B. J. Bauman, and C. E. Max, “Integrated laboratory demonstrations of multi-object adaptive optics on a simulated 10 meter telescope at visible wavelengths,” Publ. Astron. Soc. Pac. 122, 573–589 (2010).
[CrossRef]

Lane, R. G.

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

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

Li, S.-S.

Li, X.-Y.

Lukin, V. P.

V. P. Lukin, F. Yu, P. A. Konyaev, and B. V. Fortes, “Numerical model of atmospheric adaptive optical system,” Atmos. Ocean. Opt. 8, 210–222 (1995).

V. P. Lukin and B. V. Fortes, Adaptive Beaming and Imaging in the Turbulent Atmosphere (SPIE, 2002).

Max, C. E.

S. M. Ammons, L. Johnson, E. A. Laag, R. Kupke, D. T. Gavel, B. J. Bauman, and C. E. Max, “Integrated laboratory demonstrations of multi-object adaptive optics on a simulated 10 meter telescope at visible wavelengths,” Publ. Astron. Soc. Pac. 122, 573–589 (2010).
[CrossRef]

McGlamery, B. L.

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. 10, 129–160 (1976).
[CrossRef]

Noll, R.

Phillips, R. L.

Riccardi, A.

Roddier, N.

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

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]

Tyson, R. K.

Vorontsov, M. A.

Wu, H.-L.

Yan, H.-X.

Yu, F.

V. P. Lukin, F. Yu, P. A. Konyaev, and B. V. Fortes, “Numerical model of atmospheric adaptive optical system,” Atmos. Ocean. Opt. 8, 210–222 (1995).

Yu, P. T.

Appl. Opt.

Appl. Phys.

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

Atmos. Ocean. Opt.

V. P. Lukin, F. Yu, P. A. Konyaev, and B. V. Fortes, “Numerical model of atmospheric adaptive optical system,” Atmos. Ocean. Opt. 8, 210–222 (1995).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

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

Opt. Express

Optoelectron. Instrum. Data Process.

P. A. Konyaev, “Computer simulation of adaptive optics for laser systems in atmospheric applications,” Optoelectron. Instrum. Data Process. 48, 119–125 (2012).
[CrossRef]

Proc. SPIE

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]

Publ. Astron. Soc. Pac.

S. M. Ammons, L. Johnson, E. A. Laag, R. Kupke, D. T. Gavel, B. J. Bauman, and C. E. Max, “Integrated laboratory demonstrations of multi-object adaptive optics on a simulated 10 meter telescope at visible wavelengths,” Publ. Astron. Soc. Pac. 122, 573–589 (2010).
[CrossRef]

Waves Random Media

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

Other

V. P. Lukin and B. V. Fortes, Adaptive Beaming and Imaging in the Turbulent Atmosphere (SPIE, 2002).

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University, 1998).

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Figures (9)

Fig. 1.
Fig. 1.

Schematic diagram of multiguide stars scenario.

Fig. 2.
Fig. 2.

Unequal sampling in one-dimensional frequency domain.

Fig. 3.
Fig. 3.

Comparison of (a) Kolmogorov and (b) von Karman phase screens.

Fig. 4.
Fig. 4.

Comparison of (a) von Karman and (b) modified von Karman phase screens.

Fig. 5.
Fig. 5.

Phase screen examples for multibeam time-dependent scenario. (b) is the 10m×10m area circled by a rectangle in (a). Both have the same sampling grid number 512×512. (c)–(e) are the screens moving left different distances, 2 m more each time. The color bars of (c)–(e) are reset to increase the contrast.

Fig. 6.
Fig. 6.

Comparison of phase structure functions. The solid line is the theoretical structure function, and the other three ones are calculated with 300 simulations for each curve.

Fig. 7.
Fig. 7.

Simulation results of (a) long-exposure image and (b) MTF. The long exposure is represented by the average of 1000 independent realizations.

Fig. 8.
Fig. 8.

Comparison of simulation and theory of the Zernike coefficient variances.

Fig. 9.
Fig. 9.

Diagram of PSD versus frequency and the logarithm of PSD versus the logarithm of frequency.

Tables (1)

Tables Icon

Table 1. Phase Screen Simulation Parameters

Equations (37)

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SΔϕ(fx,fy)=limTxTy1TxTy|F(fx,fy)|2,
F(fx,fy)=Δϕ(x,y)ei(xfx+yfy)dxdy,
SΔϕ(fx,fy)=F(fx,fy)·F*(fx,fy)dfxdfy.
Δϕ(x,y)=dfxdfyh(fx,fy)SΔϕ(fx,fy)dfxdfy×exp[i(xfx+yfy)],
Δϕ(xm,yn)=mNxnNyh(fxm,fyn)·SΔϕ(fxm,fyn)ΔfxΔfy×exp[2πi(mΔx·mΔfx+nΔy·nΔfy)]×ΔfxΔfy,
{fxmin=Δfx=1/Gxfymin=Δfy=1/Gy.
Δϕ(x,y)=mnh(fxm,fyn)·SΔϕ(fxm,fyn)×exp[2πi(x·fxm+y·fyn)]·ΔfxmΔfyn,
SΔϕK(fx,fy)=0.023·r05/3·(fx2+fy2)11/6,
SΔϕV(fx,fy)=0.023·r05/3·(fx2+fy2+1/L02)11/6,
SΔϕMV(fx,fy)=0.023·r05/3·(fx2+fy2+1/L02)11/6×exp[(2πfx)2+(2πfy)2(5.92/l0)2],
{fn=fmin·αn0.5Δfn=fmin·αn1·(α1)α=(fmax/fmin)1/N,
σratioVK=(1+fmin2L02)5/6(1+fmax2L02)5/6.
σratioMVK=ξ5/6ebξ|fmin2+afmax2+a+b5/6·Γ(16)·[G(fmax2+a|16,1b)G(fmin2+a|16,1b)]a5/6eab+b5/6·Γ(16)·[1G(a|16,1b)],
Dϕ(r)=6.88(r/r0)5/3,
τ(ρ)LE=τ0(ρ)exp[12D(λlρ)],
τ0={2π[cos1(λlρd)(λlρd)1(λlρd)2];λlρd0;λlρ>d,
aj2=2.246(n+1)Γ(n5/6)Γ2(17/6)Γ(n+23/6)(Dr0)3/5,
S(f)f11/3.
x=ln(f),
Δx=x¯n+1x¯n=xn+1xn,
{f¯n+1=α·f¯nΔfn+1=α·Δfn,
fmax=fmin·αN,
α=(fmax/fmin)1/N.
n=1NΔfn=fmaxfmin.
Δfn=fmin·αn1·(α1).
x¯n+1xn=xnx¯n.
fn2=f¯n·f¯n+1.
fn=fmin·αn0.5.
P=SΔϕ(fx,fy)dfxdfy.
P=0.023·2π·r0-5/3×f1f2(fr2+1/L02)-11/6exp[-(2πfr5.92/l0)2]dfr,
{a=(1L0)2;b=(2πl05.92)2;c=0.023·2π·r05/3;ξ=fr2+a;;
P=ceabf12+af22+aξ11/6exp(bξ)dξ.
y=g(x|α,β)=1βαΓ(α)xα1ex/β,
P=65ceab·[ξ5/6ebξ|f12+af22+a+bf12+af22+aξ5/6ebξdξ].
{5/6=α1b=1/β.
P=65ceab×[ξ5/6ebξ|f12+af22+a+b5/6Γ(16)f12+af22+ag(x|16,1b)dξ].
σratioMV=ξ5/6ebξ|fmin2+afmax2+a+b5/6·Γ(16)·[G(fmax2+a|16,1b)G(fmin2+a|16,1b)]a5/6eab+b5/6·Γ(16)·[1G(a|16,1b)],

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