Abstract

A simple method for evaluating the wavefront compensation error of diffractive liquid-crystal wavefront correctors (DLCWFCs) for atmospheric turbulence correction is reported. A simple formula which describes the relationship between pixel number, DLCWFC aperture, quantization level, and atmospheric coherence length was derived based on the calculated atmospheric turbulence wavefronts using Kolmogorov atmospheric turbulence theory. It was found that the pixel number across the DLCWFC aperture is a linear function of the telescope aperture and the quantization level, and it is an exponential function of the atmosphere coherence length. These results are useful for people using DLCWFCs in atmospheric turbulence correction for large-aperture telescopes.

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  16. M. Loktev, G. Vdovin, N. Klimov, and S. Kotova, “Liquid crystal wavefront corrector with modal response based on spreading of the electric field in a dielectric material,” Opt. Express 15(6), 2770–2778 (2007).
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2008 (1)

2007 (2)

Z. Cao, Q. Mu, L. Hu, Y. Liu, and L. Xuan, “Diffractive characteristics of the liquid crystal spatial light modulator,” Chin. Phys. 16(6), 1665–1671 (2007).
[CrossRef]

M. Loktev, G. Vdovin, N. Klimov, and S. Kotova, “Liquid crystal wavefront corrector with modal response based on spreading of the electric field in a dielectric material,” Opt. Express 15(6), 2770–2778 (2007).
[CrossRef] [PubMed]

2006 (1)

Y. Liu, Z. Cao, D. Li, Q. Mu, L. Hu, X. Lu, and L. Xuan, “Correction for large aberration with phase-only liquid-crystal wavefront corrector,” Opt. Eng. 45(12), 128001 (2006).
[CrossRef]

2005 (2)

2002 (1)

2000 (1)

1997 (2)

G. D. Love, “Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator,” Appl. Opt. 36(7), 1517–1520 (1997).
[CrossRef] [PubMed]

L. N. Thibos and A. Bradley, “Use of liquid-crystal adaptive-optics to alter the refractive state of the eye,” Optom. Vis. Sci. 74(7), 581–587 (1997).
[CrossRef] [PubMed]

1990 (1)

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

1977 (1)

R. Hudgin, “Wave-front compensation error due to finite corrector-element size,” J. Opt. Am. 67(3), 393–395 (1977).
[CrossRef]

1976 (1)

Baker, J.

Bradley, A.

L. N. Thibos and A. Bradley, “Use of liquid-crystal adaptive-optics to alter the refractive state of the eye,” Optom. Vis. Sci. 74(7), 581–587 (1997).
[CrossRef] [PubMed]

Browne, S.

Cao, Z.

Carrion, B.

Dayton, D.

Gallegos, J.

Gonglewski, J.

Hartman, M.

Heimann, N.

Hu, L.

Hudgin, R.

R. Hudgin, “Wave-front compensation error due to finite corrector-element size,” J. Opt. Am. 67(3), 393–395 (1977).
[CrossRef]

Jin, L.

Kervin, P.

Klimov, N.

Kotova, S.

Li, D.

Liu, Y.

Loktev, M.

Love, G. D.

Lu, X.

Y. Liu, Z. Cao, D. Li, Q. Mu, L. Hu, X. Lu, and L. Xuan, “Correction for large aberration with phase-only liquid-crystal wavefront corrector,” Opt. Eng. 45(12), 128001 (2006).
[CrossRef]

Martin, J.

McDermott, S.

Mu, Q.

Noll, R. J.

Phillips, J.

Pohle, R.

Restaino, S.

Roddier, N.

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

Rogers, S.

Shilko, M.

Smith, C.

Snodgress, J.

Thibos, L. N.

L. N. Thibos and A. Bradley, “Use of liquid-crystal adaptive-optics to alter the refractive state of the eye,” Optom. Vis. Sci. 74(7), 581–587 (1997).
[CrossRef] [PubMed]

Thiel, D.

Vdovin, G.

Xuan, L.

Appl. Opt. (1)

Chin. Phys. (1)

Z. Cao, Q. Mu, L. Hu, Y. Liu, and L. Xuan, “Diffractive characteristics of the liquid crystal spatial light modulator,” Chin. Phys. 16(6), 1665–1671 (2007).
[CrossRef]

J. Opt. Am. (1)

R. Hudgin, “Wave-front compensation error due to finite corrector-element size,” J. Opt. Am. 67(3), 393–395 (1977).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (2)

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

Y. Liu, Z. Cao, D. Li, Q. Mu, L. Hu, X. Lu, and L. Xuan, “Correction for large aberration with phase-only liquid-crystal wavefront corrector,” Opt. Eng. 45(12), 128001 (2006).
[CrossRef]

Opt. Express (6)

Optom. Vis. Sci. (1)

L. N. Thibos and A. Bradley, “Use of liquid-crystal adaptive-optics to alter the refractive state of the eye,” Optom. Vis. Sci. 74(7), 581–587 (1997).
[CrossRef] [PubMed]

Other (3)

F. Roddier, Adaptive Optics in Astronomy (Cambridge University Press, 1999), pp. 13–15.

R. K. Tyson, Principles of adaptive optics (Second Edition Academic Press 1997), pp.71.

G. D. Love, “Liquid crystal adaptive optics,” in: Adaptive optics engineering handbook (R. K. Tyson, CRC, 1999)

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Figures (7)

Fig. 1
Fig. 1

Wavefront RMS error as a function of quantization level

Fig. 2
Fig. 2

The field of DLCWFC. The circle represents wavefront of atmospheric turbulence and P1…PN are the pixel numbers of the DLCWFC.

Fig. 3
Fig. 3

<PN> as a function of telescope aperture D, ■ represents calculated data for r0 = 10 cm and N = 16. The solid curve represents fitted data.

Fig. 4
Fig. 4

<PN> as a function of quantization level N, ▲ represents calculated data for D = 2 m and r0 = 10 cm. The solid curve represents fitted data.

Fig. 5
Fig. 5

<PN> as a function of atmosphere coherence length r0 , line is fitted curve. ■, ●, and ★ represent computed data with N = 16 and D = 4 m, N = 8 and D = 4 m, and N = 8 and D = 2 m, respectively.

Fig. 6
Fig. 6

Diffraction efficiency as a function of quantization level.

Fig. 7
Fig. 7

<PN> as functions of atmosphere coherence length r0 and telescope aperture D for N = 8.

Equations (11)

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

f=α(rsr0)5/3,
ΔW=λ23N,
Zevenj=2(n+1)Rnm(ρ)cos(mθ),m0Zoddj=2(n+1)Rnm(ρ)sin(mθ),m0,Zj=(n+1)Rn0(ρ),m=0,
Rnm(ρ)=s=0(nm)2(1)s(ns)!s![(n+m)2s]![(nm)2s]!rn2s.
D(r)=6.88(rr0)5/3.
ajaj={KzzδmmΓ[(n+n5/3)/2](D/r0)5/3Γ[(nn+17/3)/2]Γ[(nn+17/3)/2]Γ[(n+n+23/3)/2] jj=even0,                                                                                                         jj=odd,
ϕt=j=1JajZj.
mod(ϕt)=f(N,D,r0,PN),
PN=A+Br06/5,
B=a+bN+cD+dND,
PN=6.25N+(151.5D23N+0.91ND)r06/5,

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