Abstract

A modal interaction matrix (IM) measurement procedure is introduced for a liquid-crystal (LC) corrector for use in a phase-wrapping technique. Zernike modes are used to reconstruct the aberration wavefront and to drive the LC corrector. Usually the driving area is different from the active area. This difference induces a coupling effect on Zernike modes, which may have an impact on correction precision. In this paper the coupling effect is evaluated due to area difference and decentration, respectively. Then, a simulated turbulence wavefront is used to simulate the reconstruction process to evaluate its influence on reconstruction precision. We present simulation results that show that this method can be used to measure the IM with very high reconstruction precision under proper configuration. In order to maintain precision, the permissible eccentricity distance is also simulated with a result of no more than 5% of the LC corrector diameter.

© 2009 Optical Society of America

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References

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  1. Z. Hu and W. Jiang, "Optimum the matching problem of wavefront sensor and wavefront corrector," High Power Laser and Particle Beams (in Chinese) 8, 327-332 (1996).
  2. S. R. Restaino, D. M. Payne, J. T. Baker, J. R. Andrews, S. W. Teare, G. C. Gilbreath, D. Dayton, and J. Gonglewski, "Liquid-crystal technology for adaptive optics: an update," SPIE 5003, 187-192 (2003).
    [CrossRef]
  3. L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, "Phase-only liquid-crystal spatial light modulator for wavefront correction with high precision," Opt. Express 12, 6403-6409 (2004).
    [CrossRef] [PubMed]
  4. Q. Mu, Z. Cao, L. Hu, D. Li, and L. Xuan, "Adaptive-optics imaging system based on a high-resolution liquid crystal on silicon device," Opt. Express 14, 8013-8018 (2006).
    [CrossRef] [PubMed]
  5. K. A. Bauchert, S. A. Serati, and A. Furman, "Advances in liquid-crystal spatial light modulators," SPIE 4734, 35-43 (2002).
    [CrossRef]
  6. H. Huang, T. Inoue, and T. Hara, "An adaptive wavefront control system using a high-resolution liquid-crystal spatial light modulator," SPIE 5639, 129-137 (2004).
    [CrossRef]
  7. Q. Mu, Z. Cao, C. Li, B. Jiang, L. Hu, and L. Xuan, "Accommodation-based liquid-crystal adaptive optics system for large ocular aberration correction," Opt. Lett. 33, 2898-2900 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  10. J. Schwiegerling, "Scaling Zernike expansion coefficients to different pupil sizes," J. Opt. Soc. Am. A 19, 1937-1945 (2002).
    [CrossRef]
  11. L. Lundström and P. Unsbo, "Transformation of Zernike coefficients: scaled, translated, and rotated wavefronts with circular and elliptical pupils," J. Opt. Soc. Am. A 24, 569-577 (2007).
    [CrossRef]

2008 (1)

2007 (1)

2006 (1)

2004 (2)

L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, "Phase-only liquid-crystal spatial light modulator for wavefront correction with high precision," Opt. Express 12, 6403-6409 (2004).
[CrossRef] [PubMed]

H. Huang, T. Inoue, and T. Hara, "An adaptive wavefront control system using a high-resolution liquid-crystal spatial light modulator," SPIE 5639, 129-137 (2004).
[CrossRef]

2003 (1)

S. R. Restaino, D. M. Payne, J. T. Baker, J. R. Andrews, S. W. Teare, G. C. Gilbreath, D. Dayton, and J. Gonglewski, "Liquid-crystal technology for adaptive optics: an update," SPIE 5003, 187-192 (2003).
[CrossRef]

2002 (2)

K. A. Bauchert, S. A. Serati, and A. Furman, "Advances in liquid-crystal spatial light modulators," SPIE 4734, 35-43 (2002).
[CrossRef]

J. Schwiegerling, "Scaling Zernike expansion coefficients to different pupil sizes," J. Opt. Soc. Am. A 19, 1937-1945 (2002).
[CrossRef]

1997 (1)

1996 (1)

Z. Hu and W. Jiang, "Optimum the matching problem of wavefront sensor and wavefront corrector," High Power Laser and Particle Beams (in Chinese) 8, 327-332 (1996).

Andrews, J. R.

S. R. Restaino, D. M. Payne, J. T. Baker, J. R. Andrews, S. W. Teare, G. C. Gilbreath, D. Dayton, and J. Gonglewski, "Liquid-crystal technology for adaptive optics: an update," SPIE 5003, 187-192 (2003).
[CrossRef]

Baker, J. T.

S. R. Restaino, D. M. Payne, J. T. Baker, J. R. Andrews, S. W. Teare, G. C. Gilbreath, D. Dayton, and J. Gonglewski, "Liquid-crystal technology for adaptive optics: an update," SPIE 5003, 187-192 (2003).
[CrossRef]

Bauchert, K. A.

K. A. Bauchert, S. A. Serati, and A. Furman, "Advances in liquid-crystal spatial light modulators," SPIE 4734, 35-43 (2002).
[CrossRef]

Cao, Z.

Dayton, D.

S. R. Restaino, D. M. Payne, J. T. Baker, J. R. Andrews, S. W. Teare, G. C. Gilbreath, D. Dayton, and J. Gonglewski, "Liquid-crystal technology for adaptive optics: an update," SPIE 5003, 187-192 (2003).
[CrossRef]

Furman, A.

K. A. Bauchert, S. A. Serati, and A. Furman, "Advances in liquid-crystal spatial light modulators," SPIE 4734, 35-43 (2002).
[CrossRef]

Gilbreath, G. C.

S. R. Restaino, D. M. Payne, J. T. Baker, J. R. Andrews, S. W. Teare, G. C. Gilbreath, D. Dayton, and J. Gonglewski, "Liquid-crystal technology for adaptive optics: an update," SPIE 5003, 187-192 (2003).
[CrossRef]

Gonglewski, J.

S. R. Restaino, D. M. Payne, J. T. Baker, J. R. Andrews, S. W. Teare, G. C. Gilbreath, D. Dayton, and J. Gonglewski, "Liquid-crystal technology for adaptive optics: an update," SPIE 5003, 187-192 (2003).
[CrossRef]

Hara, T.

H. Huang, T. Inoue, and T. Hara, "An adaptive wavefront control system using a high-resolution liquid-crystal spatial light modulator," SPIE 5639, 129-137 (2004).
[CrossRef]

Hu, L.

Hu, Z.

Z. Hu and W. Jiang, "Optimum the matching problem of wavefront sensor and wavefront corrector," High Power Laser and Particle Beams (in Chinese) 8, 327-332 (1996).

Huang, H.

H. Huang, T. Inoue, and T. Hara, "An adaptive wavefront control system using a high-resolution liquid-crystal spatial light modulator," SPIE 5639, 129-137 (2004).
[CrossRef]

Inoue, T.

H. Huang, T. Inoue, and T. Hara, "An adaptive wavefront control system using a high-resolution liquid-crystal spatial light modulator," SPIE 5639, 129-137 (2004).
[CrossRef]

Jiang, B.

Jiang, W.

Z. Hu and W. Jiang, "Optimum the matching problem of wavefront sensor and wavefront corrector," High Power Laser and Particle Beams (in Chinese) 8, 327-332 (1996).

Li, C.

Li, D.

Liu, Y.

Love, G. D.

Lundström, L.

Mu, Q.

Payne, D. M.

S. R. Restaino, D. M. Payne, J. T. Baker, J. R. Andrews, S. W. Teare, G. C. Gilbreath, D. Dayton, and J. Gonglewski, "Liquid-crystal technology for adaptive optics: an update," SPIE 5003, 187-192 (2003).
[CrossRef]

Restaino, S. R.

S. R. Restaino, D. M. Payne, J. T. Baker, J. R. Andrews, S. W. Teare, G. C. Gilbreath, D. Dayton, and J. Gonglewski, "Liquid-crystal technology for adaptive optics: an update," SPIE 5003, 187-192 (2003).
[CrossRef]

Schwiegerling, J.

Serati, S. A.

K. A. Bauchert, S. A. Serati, and A. Furman, "Advances in liquid-crystal spatial light modulators," SPIE 4734, 35-43 (2002).
[CrossRef]

Teare, S. W.

S. R. Restaino, D. M. Payne, J. T. Baker, J. R. Andrews, S. W. Teare, G. C. Gilbreath, D. Dayton, and J. Gonglewski, "Liquid-crystal technology for adaptive optics: an update," SPIE 5003, 187-192 (2003).
[CrossRef]

Unsbo, P.

Xuan, L.

Appl. Opt. (1)

High Power Laser and Particle Beams (1)

Z. Hu and W. Jiang, "Optimum the matching problem of wavefront sensor and wavefront corrector," High Power Laser and Particle Beams (in Chinese) 8, 327-332 (1996).

J. Opt. Soc. Am. A (2)

Opt. Express (2)

Opt. Lett. (1)

SPIE (3)

K. A. Bauchert, S. A. Serati, and A. Furman, "Advances in liquid-crystal spatial light modulators," SPIE 4734, 35-43 (2002).
[CrossRef]

H. Huang, T. Inoue, and T. Hara, "An adaptive wavefront control system using a high-resolution liquid-crystal spatial light modulator," SPIE 5639, 129-137 (2004).
[CrossRef]

S. R. Restaino, D. M. Payne, J. T. Baker, J. R. Andrews, S. W. Teare, G. C. Gilbreath, D. Dayton, and J. Gonglewski, "Liquid-crystal technology for adaptive optics: an update," SPIE 5003, 187-192 (2003).
[CrossRef]

Other (1)

L. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," in Vision Science and its Applications, OSA Technical Digest (Optical Society of America, 2000), paper SuC1.

Supplementary Material (1)

» Media 1: MOV (336 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

Configuration of LC corrector.

Fig. 2.
Fig. 2.

IM coefficient profile.

Fig. 3.
Fig. 3.

Coupling relationship of all 35 polynomials.

Fig. 4.
Fig. 4.

Distribution of IM at decentration condition (Media 1).

Fig. 5
Fig. 5

The simulated turbulence map.

Fig. 6.
Fig. 6.

Rms error for different SF and K.

Fig. 7.
Fig. 7.

Relationship between rms error and K.

Fig. 8.
Fig. 8.

Rms error induced by decentration.

Equations (6)

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

Zi(r,θ)={NnmRnm(r)cos(mθ),m0NnmRnm(r)sin(mθ),m<0,
Rnm(m)=s=o(nm)/2(1)s(ns)!s![n+m)/2s]![nm/2s]!rn2s,
Zi(r2,θ2)=j=1NMi,jZj(r1,θ1),when0r2r1;0r11,
[c1cicN]=[M1,1M1,jM1,NMi,1Mi,jMi,NMN,1MN,jMN,N]1[a1ajaN]
error(r1,θ1)=i=1NciZj(r2,θ2)j=1NajZj(r1,θ1)when0r2r1;0r11,
RMS(K,SF)=K1 ×(0.0356+9302×e(SF/0.082)).

Metrics