Abstract

We present a novel method to measure the interaction matrix of liquid-crystal adaptive optics systems, by applying least squares method to mitigate the impact of measurement noise. Experimental results showed a dramatic gain in the accuracy of interaction matrix, and a considerable improvement in image resolution with open loop adaptive optics correction.

© 2014 Optical Society of America

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References

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  1. K. Bauchert, S. Serati, and A. Furman, “Advances in liquid crystal spatial light modulators,” Optical Pattern Recognition Xiii 4734, 35–43 (2002).
    [Crossref]
  2. J. Gourlay, G. D. Love, P. M. Birch, R. M. Sharples, and A. Purvis, “A real-time closed-loop liquid crystal adaptive optics system: First results,” Opt. Commun. 137(1-3), 17–21 (1997).
    [Crossref]
  3. D. Dayton, J. Gonglewski, S. Restaino, J. Martin, J. Phillips, M. Hartman, P. Kervin, J. Snodgress, S. Browne, N. Heimann, M. Shilko, R. Pohle, B. Carrion, C. Smith, and D. Thiel, “Demonstration of new technology MEMS and liquid crystal adaptive optics on bright astronomical objects and satellites,” Opt. Express 10(25), 1508–1519 (2002).
    [Crossref] [PubMed]
  4. Z. L. Cao, Q. Q. Mu, L. F. Hu, D. Y. Li, Z. H. Peng, Y. G. Liu, and L. Xuan, “Preliminary use of nematic liquid crystal adaptive optics with a 2.16-meter reflecting telescope,” Opt. Express 17(4), 2530–2537 (2009).
    [Crossref] [PubMed]
  5. T. Shirai, “Liquid-crystal adaptive optics based on feedback interferometry for high-resolution retinal imaging,” Appl. Opt. 41(19), 4013–4023 (2002).
    [Crossref] [PubMed]
  6. N. N. Kong, C. Li, M. L. Xia, D. Y. Li, Y. Qi, and L. Xuan, “Optimization of the open-loop liquid crystal adaptive optics retinal imaging system,” J. Biomed. Opt. 17(2), 026001 (2012).
    [Crossref] [PubMed]
  7. K. Takeno and T. Shirai, “Chromatic aberration free liquid crystal adaptive optics for flood illuminated retinal camera,” Opt. Commun. 285(12), 2967–2971 (2012).
    [Crossref]
  8. Q. Q. Mu, Z. L. Cao, D. Y. Li, L. Hu, and L. Xuan, “Open-loop correction of horizontal turbulence: system design and result,” Appl. Opt. 47(23), 4297–4301 (2008).
    [Crossref] [PubMed]
  9. M. Kasper, E. Fedrigo, D. P. Looze, H. Bonnet, L. Ivanescu, and S. Oberti, “Fast calibration of high-order adaptive optics systems,” J. Opt. Soc. Am. A 21(6), 1004–1008 (2004).
    [Crossref] [PubMed]
  10. S. Meimon, T. Fusco, and C. Petit, “The Slope-Oriented Hadamard scheme for in-lab or on-sky interaction matrix calibration,” in Second International Conference on Adaptive Optics for Extremely Large Telescopes. Online at http://ao4elt2. lesia. obspm. fr , id. 65(2011), p. 65.
  11. X. Y. Zhang, C. Arcidiacono, A. R. Conrad, T. M. Herbst, W. Gaessler, T. Bertram, R. Ragazzoni, L. Schreiber, E. Diolaiti, M. Kuerster, P. Bizenberger, D. Meschke, H. W. Rix, C. H. Rao, L. Mohr, F. Briegel, F. Kittmann, J. Berwein, and J. Trowitzsch, “Calibrating the interaction matrix for the LINC-NIRVANA high layer wavefront sensor,” Opt. Express 20(7), 8078–8092 (2012).
    [PubMed]
  12. Q. Q. Mu, Z. L. Cao, Z. H. Peng, Y. G. Liu, L. F. Hu, X. H. Lu, and L. Xuan, “Modal interaction matrix measurement for liquid-crystal corrector: precision evaluation,” Opt. Express 17(11), 9330–9336 (2009).
    [Crossref] [PubMed]
  13. V. V. Michel, Filtering and System Identification: A Least Squares Approach (Cambridge University Press, 2007), pp. 111-112.

2012 (3)

N. N. Kong, C. Li, M. L. Xia, D. Y. Li, Y. Qi, and L. Xuan, “Optimization of the open-loop liquid crystal adaptive optics retinal imaging system,” J. Biomed. Opt. 17(2), 026001 (2012).
[Crossref] [PubMed]

K. Takeno and T. Shirai, “Chromatic aberration free liquid crystal adaptive optics for flood illuminated retinal camera,” Opt. Commun. 285(12), 2967–2971 (2012).
[Crossref]

X. Y. Zhang, C. Arcidiacono, A. R. Conrad, T. M. Herbst, W. Gaessler, T. Bertram, R. Ragazzoni, L. Schreiber, E. Diolaiti, M. Kuerster, P. Bizenberger, D. Meschke, H. W. Rix, C. H. Rao, L. Mohr, F. Briegel, F. Kittmann, J. Berwein, and J. Trowitzsch, “Calibrating the interaction matrix for the LINC-NIRVANA high layer wavefront sensor,” Opt. Express 20(7), 8078–8092 (2012).
[PubMed]

2009 (2)

2008 (1)

2004 (1)

2002 (3)

1997 (1)

J. Gourlay, G. D. Love, P. M. Birch, R. M. Sharples, and A. Purvis, “A real-time closed-loop liquid crystal adaptive optics system: First results,” Opt. Commun. 137(1-3), 17–21 (1997).
[Crossref]

Arcidiacono, C.

Bauchert, K.

K. Bauchert, S. Serati, and A. Furman, “Advances in liquid crystal spatial light modulators,” Optical Pattern Recognition Xiii 4734, 35–43 (2002).
[Crossref]

Bertram, T.

Berwein, J.

Birch, P. M.

J. Gourlay, G. D. Love, P. M. Birch, R. M. Sharples, and A. Purvis, “A real-time closed-loop liquid crystal adaptive optics system: First results,” Opt. Commun. 137(1-3), 17–21 (1997).
[Crossref]

Bizenberger, P.

Bonnet, H.

Briegel, F.

Browne, S.

Cao, Z. L.

Carrion, B.

Conrad, A. R.

Dayton, D.

Diolaiti, E.

Fedrigo, E.

Furman, A.

K. Bauchert, S. Serati, and A. Furman, “Advances in liquid crystal spatial light modulators,” Optical Pattern Recognition Xiii 4734, 35–43 (2002).
[Crossref]

Gaessler, W.

Gonglewski, J.

Gourlay, J.

J. Gourlay, G. D. Love, P. M. Birch, R. M. Sharples, and A. Purvis, “A real-time closed-loop liquid crystal adaptive optics system: First results,” Opt. Commun. 137(1-3), 17–21 (1997).
[Crossref]

Hartman, M.

Heimann, N.

Herbst, T. M.

Hu, L.

Hu, L. F.

Ivanescu, L.

Kasper, M.

Kervin, P.

Kittmann, F.

Kong, N. N.

N. N. Kong, C. Li, M. L. Xia, D. Y. Li, Y. Qi, and L. Xuan, “Optimization of the open-loop liquid crystal adaptive optics retinal imaging system,” J. Biomed. Opt. 17(2), 026001 (2012).
[Crossref] [PubMed]

Kuerster, M.

Li, C.

N. N. Kong, C. Li, M. L. Xia, D. Y. Li, Y. Qi, and L. Xuan, “Optimization of the open-loop liquid crystal adaptive optics retinal imaging system,” J. Biomed. Opt. 17(2), 026001 (2012).
[Crossref] [PubMed]

Li, D. Y.

Liu, Y. G.

Looze, D. P.

Love, G. D.

J. Gourlay, G. D. Love, P. M. Birch, R. M. Sharples, and A. Purvis, “A real-time closed-loop liquid crystal adaptive optics system: First results,” Opt. Commun. 137(1-3), 17–21 (1997).
[Crossref]

Lu, X. H.

Martin, J.

Meschke, D.

Mohr, L.

Mu, Q. Q.

Oberti, S.

Peng, Z. H.

Phillips, J.

Pohle, R.

Purvis, A.

J. Gourlay, G. D. Love, P. M. Birch, R. M. Sharples, and A. Purvis, “A real-time closed-loop liquid crystal adaptive optics system: First results,” Opt. Commun. 137(1-3), 17–21 (1997).
[Crossref]

Qi, Y.

N. N. Kong, C. Li, M. L. Xia, D. Y. Li, Y. Qi, and L. Xuan, “Optimization of the open-loop liquid crystal adaptive optics retinal imaging system,” J. Biomed. Opt. 17(2), 026001 (2012).
[Crossref] [PubMed]

Ragazzoni, R.

Rao, C. H.

Restaino, S.

Rix, H. W.

Schreiber, L.

Serati, S.

K. Bauchert, S. Serati, and A. Furman, “Advances in liquid crystal spatial light modulators,” Optical Pattern Recognition Xiii 4734, 35–43 (2002).
[Crossref]

Sharples, R. M.

J. Gourlay, G. D. Love, P. M. Birch, R. M. Sharples, and A. Purvis, “A real-time closed-loop liquid crystal adaptive optics system: First results,” Opt. Commun. 137(1-3), 17–21 (1997).
[Crossref]

Shilko, M.

Shirai, T.

K. Takeno and T. Shirai, “Chromatic aberration free liquid crystal adaptive optics for flood illuminated retinal camera,” Opt. Commun. 285(12), 2967–2971 (2012).
[Crossref]

T. Shirai, “Liquid-crystal adaptive optics based on feedback interferometry for high-resolution retinal imaging,” Appl. Opt. 41(19), 4013–4023 (2002).
[Crossref] [PubMed]

Smith, C.

Snodgress, J.

Takeno, K.

K. Takeno and T. Shirai, “Chromatic aberration free liquid crystal adaptive optics for flood illuminated retinal camera,” Opt. Commun. 285(12), 2967–2971 (2012).
[Crossref]

Thiel, D.

Trowitzsch, J.

Xia, M. L.

N. N. Kong, C. Li, M. L. Xia, D. Y. Li, Y. Qi, and L. Xuan, “Optimization of the open-loop liquid crystal adaptive optics retinal imaging system,” J. Biomed. Opt. 17(2), 026001 (2012).
[Crossref] [PubMed]

Xuan, L.

Zhang, X. Y.

Appl. Opt. (2)

J. Biomed. Opt. (1)

N. N. Kong, C. Li, M. L. Xia, D. Y. Li, Y. Qi, and L. Xuan, “Optimization of the open-loop liquid crystal adaptive optics retinal imaging system,” J. Biomed. Opt. 17(2), 026001 (2012).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

K. Takeno and T. Shirai, “Chromatic aberration free liquid crystal adaptive optics for flood illuminated retinal camera,” Opt. Commun. 285(12), 2967–2971 (2012).
[Crossref]

J. Gourlay, G. D. Love, P. M. Birch, R. M. Sharples, and A. Purvis, “A real-time closed-loop liquid crystal adaptive optics system: First results,” Opt. Commun. 137(1-3), 17–21 (1997).
[Crossref]

Opt. Express (4)

Optical Pattern Recognition Xiii (1)

K. Bauchert, S. Serati, and A. Furman, “Advances in liquid crystal spatial light modulators,” Optical Pattern Recognition Xiii 4734, 35–43 (2002).
[Crossref]

Other (2)

S. Meimon, T. Fusco, and C. Petit, “The Slope-Oriented Hadamard scheme for in-lab or on-sky interaction matrix calibration,” in Second International Conference on Adaptive Optics for Extremely Large Telescopes. Online at http://ao4elt2. lesia. obspm. fr , id. 65(2011), p. 65.

V. V. Michel, Filtering and System Identification: A Least Squares Approach (Cambridge University Press, 2007), pp. 111-112.

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Figures (7)

Fig. 1
Fig. 1 LC adaptive optics compensation setup in lab.

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Fig. 2
Fig. 2 Slopes reconstruct error of identity matrix method and least squares method.

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Fig. 3
Fig. 3 Zernike coefficients reconstruct error of identity matrix method and least squares method.

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Fig. 4
Fig. 4 (a) RatioS and (b) RatioC in 1000 trials with same conditions, only differ in the Zernike coefficients applied to LC corrector.

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Fig. 5
Fig. 5 Fiber bundle images: (a) before AO correction; (b) after correction with interaction matrix measured with identity matrix method; (c) after correction with interaction matrix measured with least squares method.

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Fig. 6
Fig. 6 Radially averaged power spectrum of images shown in Fig. 5: (a) before AO correction; (b) after correction with interaction matrix measured with identity matrix method; (c) after correction with interaction matrix measured with least squares method.

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Fig. 7
Fig. 7 Radially averaged power spectrum ratio between Fig. 5(c) (image after correction with interaction matrix measured with least squares method) and Fig. 5(b) (image after correction with interaction matrix measured with identity matrix method).

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Equations (12)

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

V S = M I * V Z + V N .
V Z = M C * V S .
M C = ( M I T * M I ) −1 * M I T .
{ V S1 = M I * [ 1 0 ⋯ 0 ] T + V N1 V S2 = M I * [ 0 1 ⋯ 0 ] T + V N2 ⋮ V Sm = M I * [ 0 0 ⋯ 1 ] T + V Nm .
M S = M I + M N .
{ V S1 = M I * V Z1 + V N1 V S2 = M I * V Z2 + V N2 ⋮ V SK = M I * V ZK + V NK .
M S = M I * M Z + M N .
M ˜ I = M S * M Z T * ( M Z * M Z T ) −1 = M I + M N * M Z T * ( M Z * M Z T ) −1 .
E S = V S − M I * V Z .
E Z = V Z − M C * V S = V Z − ( M I T * M I ) −1 * M I T * V S .
Rati o S = E S2 T * E S2 /( E S1 T * E S1 ) .
Rati o Z = E Z2 T * E Z2 /( E Z1 T * E Z1 ) .

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