Abstract

Computer generated holograms (CGHs) are widely used in optical tweezers, which will be employed in various research fields. We previously proposed an efficient generation method of CGH movies based on frame interpolation using coherent neural networks (CNNs) to reduce the high calculation cost of three-dimensional CGHs. At the same time, however, we also found that the quality observed in the interpolated CGH images needed to be improved even further so that the method could be accepted for general use. We report a successful error reduction in interpolated images by developing a new learning method of CNNs. We reduce the error by combining locally connected correlation learning and steepest descent learning in a sequential manner.

© 2008 Optical Society of America

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References

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  1. D. G. Grier, “A revolution in optical manipulation,” Nature (London) 424, 810-816 (2003).
    [CrossRef]
  2. J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multifunctional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77-82 (2000).
    [CrossRef]
  3. M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608-610 (1999).
    [CrossRef]
  4. E. Schonbrun, R. Piestun, P. Jordan, J. Cooper, K. Wulff, J. Courtial, and M. Padgett, “3D interferometric optical tweezers using a single spatial light modulator,” Opt. Express 13, 3777-3786 (2005).
    [CrossRef] [PubMed]
  5. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169-175 (2002).
    [CrossRef]
  6. P. J. Rodorigo, V. R. Daria, and J. Gluckstad, “Four-dimensional optical manipulation of colloidal particles,” Appl. Phys. Lett. 86, 074103 (2005).
    [CrossRef]
  7. A. Hirose, T. Higo, and K. Tanizawa, “Efficient generation of holographic movies with frame interpolation using a coherent neural network,” IEICE Electron. Express 3(19), 417-423 (2006).
    [CrossRef]
  8. A. Hirose, T. Higo, and K. Tanizawa, “Holographic three-dimensional movie generation with frame interpolation using coherent neural networks,” in Proceeding of IEEE/WCCI 2006 World Congress on Computational Intelligence (IEEE, 2006), pp. 1219-1224.
  9. S. Kawata and A. Hirose, “Coherent optical neural network that learns desirable phase values in the frequency domain by use of multiple optical-path differences,” Opt. Lett. 28, 2524-2526 (2003).
    [CrossRef] [PubMed]
  10. A. Hirose, Complex-Valued Neural Networks (Springer-Verlag, 2006).
    [CrossRef]
  11. A. Hirose and R. Eckmiller, “Coherent optical neural networks that have optical-frequency-controlled behavior and generalization ability in the frequency domain,” Appl. Opt. 35, 836-843 (1996).
    [CrossRef] [PubMed]

2006 (1)

A. Hirose, T. Higo, and K. Tanizawa, “Efficient generation of holographic movies with frame interpolation using a coherent neural network,” IEICE Electron. Express 3(19), 417-423 (2006).
[CrossRef]

2005 (2)

2003 (2)

2002 (1)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169-175 (2002).
[CrossRef]

2000 (1)

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multifunctional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77-82 (2000).
[CrossRef]

1999 (1)

1996 (1)

Cooper, J.

Courtial, J.

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Daria, V. R.

P. J. Rodorigo, V. R. Daria, and J. Gluckstad, “Four-dimensional optical manipulation of colloidal particles,” Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef]

Eckmiller, R.

Gluckstad, J.

P. J. Rodorigo, V. R. Daria, and J. Gluckstad, “Four-dimensional optical manipulation of colloidal particles,” Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature (London) 424, 810-816 (2003).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Haist, T.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multifunctional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77-82 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608-610 (1999).
[CrossRef]

Higo, T.

A. Hirose, T. Higo, and K. Tanizawa, “Efficient generation of holographic movies with frame interpolation using a coherent neural network,” IEICE Electron. Express 3(19), 417-423 (2006).
[CrossRef]

A. Hirose, T. Higo, and K. Tanizawa, “Holographic three-dimensional movie generation with frame interpolation using coherent neural networks,” in Proceeding of IEEE/WCCI 2006 World Congress on Computational Intelligence (IEEE, 2006), pp. 1219-1224.

Hirose, A.

A. Hirose, T. Higo, and K. Tanizawa, “Efficient generation of holographic movies with frame interpolation using a coherent neural network,” IEICE Electron. Express 3(19), 417-423 (2006).
[CrossRef]

S. Kawata and A. Hirose, “Coherent optical neural network that learns desirable phase values in the frequency domain by use of multiple optical-path differences,” Opt. Lett. 28, 2524-2526 (2003).
[CrossRef] [PubMed]

A. Hirose and R. Eckmiller, “Coherent optical neural networks that have optical-frequency-controlled behavior and generalization ability in the frequency domain,” Appl. Opt. 35, 836-843 (1996).
[CrossRef] [PubMed]

A. Hirose, Complex-Valued Neural Networks (Springer-Verlag, 2006).
[CrossRef]

A. Hirose, T. Higo, and K. Tanizawa, “Holographic three-dimensional movie generation with frame interpolation using coherent neural networks,” in Proceeding of IEEE/WCCI 2006 World Congress on Computational Intelligence (IEEE, 2006), pp. 1219-1224.

Jordan, P.

Kawata, S.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Liesener, J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multifunctional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77-82 (2000).
[CrossRef]

Padgett, M.

Piestun, R.

Reicherter, M.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multifunctional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77-82 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608-610 (1999).
[CrossRef]

Rodorigo, P. J.

P. J. Rodorigo, V. R. Daria, and J. Gluckstad, “Four-dimensional optical manipulation of colloidal particles,” Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef]

Schonbrun, E.

Tanizawa, K.

A. Hirose, T. Higo, and K. Tanizawa, “Efficient generation of holographic movies with frame interpolation using a coherent neural network,” IEICE Electron. Express 3(19), 417-423 (2006).
[CrossRef]

A. Hirose, T. Higo, and K. Tanizawa, “Holographic three-dimensional movie generation with frame interpolation using coherent neural networks,” in Proceeding of IEEE/WCCI 2006 World Congress on Computational Intelligence (IEEE, 2006), pp. 1219-1224.

Tiziani, H. J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multifunctional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77-82 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608-610 (1999).
[CrossRef]

Wagemann, E. U.

Wulff, K.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

P. J. Rodorigo, V. R. Daria, and J. Gluckstad, “Four-dimensional optical manipulation of colloidal particles,” Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef]

IEICE Electron. Express (1)

A. Hirose, T. Higo, and K. Tanizawa, “Efficient generation of holographic movies with frame interpolation using a coherent neural network,” IEICE Electron. Express 3(19), 417-423 (2006).
[CrossRef]

Nature (London) (1)

D. G. Grier, “A revolution in optical manipulation,” Nature (London) 424, 810-816 (2003).
[CrossRef]

Opt. Commun. (2)

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multifunctional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77-82 (2000).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Other (2)

A. Hirose, Complex-Valued Neural Networks (Springer-Verlag, 2006).
[CrossRef]

A. Hirose, T. Higo, and K. Tanizawa, “Holographic three-dimensional movie generation with frame interpolation using coherent neural networks,” in Proceeding of IEEE/WCCI 2006 World Congress on Computational Intelligence (IEEE, 2006), pp. 1219-1224.

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Figures (13)

Fig. 1
Fig. 1

Self-homodyne neural circuit.

Fig. 2
Fig. 2

Correspondence between CNN and CGH.

Fig. 3
Fig. 3

Schematic diagram of interpolation using CNN.

Fig. 4
Fig. 4

Structure of neural network with lateral connections to be used in Method 1.

Fig. 5
Fig. 5

Structure of previous neural network, which is used also in Method 2.

Fig. 6
Fig. 6

Comparison of error in generated holograms between different learning methods.

Fig. 7
Fig. 7

Error values E v for teacher data at seven learning frequency points versus learning iteration number in (a) Method 1 and (b) Method 2.

Fig. 8
Fig. 8

Comparison of final iteration E v in different methods.

Fig. 9
Fig. 9

Comparison of learning-point diagrams (top, holograms; bottom, movie frames).

Fig. 10
Fig. 10

Comparison of interpolated diagrams (top, holograms; bottom, movie frames).

Fig. 11
Fig. 11

Comparison of sharpness of reconstructed images.

Fig. 12
Fig. 12

Illustration of experimental setup.

Fig. 13
Fig. 13

Appearance of reconstructed holographic images on the screen.

Equations (11)

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y n = g ( u n ) = tan h ( B | u n | ) exp ( i arg ( u n ) ) ,
u n = m h ( | w n m , h | exp ( i 2 π f τ n m , h ) x m ) .
μ d | w n m , h | d t = | w n m , h | + | y ^ n | | x m | cos ( β ^ n α m θ n m , h ) ,
μ d τ n m , h d t = 1 2 π f | y ^ n | | x m | | w n m , h | sin ( β ^ n α m 2 π f τ n m , h ) .
μ d | w n m , h | d t = ( γ | x m | cos θ n m , h rot | y n | | y ^ n | sin ( β n β ^ n ) | x m | | u n | sin θ n m , h rot ) ,
μ d τ n m , h d t = 1 2 π f ( γ | x m | sin θ n m , h rot + | y n | | y ^ n | sin ( β n β ^ n ) | x m | | u n | cos θ n m , h rot ) .
γ = B ( 1 | y n | 2 ) ( | y n | | y ^ n | cos ( β n β ^ n ) ) ,
θ n m , h rot = β n α m 2 π f τ n m , h ,
d n = s n l n .
E v = 1 s i z e n ( β ^ arg ( u ^ n ) ) 2 ,
E b = 1 s i z e k = 1 s i z e ( L L ^ ) 2 ,

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