Abstract

Benefitting from the development of commercial spatial light modulator (SLM), holographic optical tweezers (HOT) have emerged as a powerful tool for life science, material science and particle physics. The calculation of computer-generated holograms (CGH) for generating multi-focus arrays plays a key role in HOT for trapping of a bunch of particles in parallel. To realize dynamic 3D manipulation, we propose a new tilted-plane GS algorithm for fast generation of multiple foci. The multi-focal spots with a uniformity of 99% can be generated in a tilted plane. The computation time for a CGH with 512×512 pixels is less than 0.1 second. We demonstrated the power of the algorithm by simultaneously trapping and rotating silica beads with a 7×7 spots array in three dimensions. The presented algorithm is expected as a powerful kernel of HOT.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]

2020 (1)

Y. Liang, S. Yan, Z. Wang, R. Li, Y. Cai, M. He, B. Yao, and M. Lei, “Simultaneous optical trapping and imaging in the axial plane: a review of current progress,” Rep. Prog. Phys. 83(3), 032401 (2020).
[Crossref]

2019 (3)

H. Kim, M. Kim, W. Lee, and J. Ahn, “Gerchberg-Saxton algorithm for fast and efficient atom rearrangement in optical tweezer traps,” Opt. Express 27(3), 2184–2196 (2019).
[Crossref]

H. T. Chang, Y. T. Wang, and C. Y. Chen, “Angle multiplexing optical image encryption in the Fresnel transform domain using phase-only computer-generated hologram,” Photonics 7(1), 1 (2019).
[Crossref]

Y. Cai, Z. Wang, Y. Liang, F. Ren, B. Yao, M. Lei, and S. Yan, “Direct calculation of tightly focused field in an arbitrary plane,” Opt. Commun. 450, 329–334 (2019).
[Crossref]

2018 (1)

2015 (1)

2014 (3)

2013 (2)

E. H. Waller and G. V. Freymann, “Multi foci with diffraction limited resolution,” Opt. Express 21(18), 21708–21713 (2013).
[Crossref]

H. Chen, Y. Guo, Z. Chen, J. Hao, J. Xu, H. Wang, and J. Ding, “Holographic optical tweezers obtained by using the three-dimensional Gerchberg-Saxton algorithm,” J. Opt. 15(3), 035401 (2013).
[Crossref]

2011 (3)

2010 (2)

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181(8), 1444–1448 (2010).
[Crossref]

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12(11), 115707 (2010).
[Crossref]

2009 (1)

B. R. Boruah and M. A. A. Neil, “Focal field computation of an arbitrarily polarized beam using fast Fourier transforms,” Opt. Commun. 282(24), 4660–4667 (2009).
[Crossref]

2007 (2)

R. Di Leonardo, F. Ianni, and G. Ruocco, “Computer generation of optimal holograms for optical trap arrays,” Opt. Express 15(4), 1913–1922 (2007).
[Crossref]

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys. 3(7), 477–480 (2007).
[Crossref]

2006 (3)

2005 (1)

G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm,” New J. Phys. 7, 117 (2005).
[Crossref]

2004 (1)

2003 (2)

K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves,” J. Opt. Soc. Am. A 20(9), 1755–1762 (2003).
[Crossref]

K. Mangold, P. Leiderer, and C. Bechinger, “Phase transitions of colloidal monolayers in periodic pinning arrays,” Phys. Rev. Lett. 90(15), 158302 (2003).
[Crossref]

2002 (6)

M. Brunner and C. Bechinger, “Phase behavior of colloidal molecular crystals on triangular light lattices,” Phys. Rev. Lett. 88(24), 248302 (2002).
[Crossref]

P. T. Korda, M. B. Taylor, and D. G. Grier, “Kinetically locked-in colloidal transport in an array of optical tweezer,” Phys. Rev. Lett. 89(12), 128301 (2002).
[Crossref]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[Crossref]

R. L. Eriksen, V. R. Daria, and J. Gluckstad, “Fully dynamic multiple-beam optical tweezers,” Opt. Express 10(14), 597–602 (2002).
[Crossref]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[Crossref]

J. S. Liu and M. R. Taghizadeh, “Iterative algorithm for the design of diffractive phase elements for laser beam shaping,” Opt. Lett. 27(16), 1463–1465 (2002).
[Crossref]

2000 (1)

M. Johansson and J. Bengtsson, “Robust design method for highly efficient beam-shaping diffractive optical elements using an iterative-Fourier-transform algorithm with soft operations,” J. Mod. Opt. 47(8), 1385–1398 (2000).
[Crossref]

1999 (1)

1995 (1)

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-moleculemechanics of heavy-meromyosin and s1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68(4), 298S–303S (1995).

1992 (1)

J. Schmidhuber, “A fixed size storage O (n3) time complexity learning algorithm for fully recurrent continually running networks,” Neural Comput. 4(2), 243–248 (1992).
[Crossref]

1991 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35(2), 237–246 (1972).

Ahn, J.

Ameer-Beg, S. M.

Andilla, J.

Arlt, J.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[Crossref]

Bao, Y.

Bechinger, C.

K. Mangold, P. Leiderer, and C. Bechinger, “Phase transitions of colloidal monolayers in periodic pinning arrays,” Phys. Rev. Lett. 90(15), 158302 (2003).
[Crossref]

M. Brunner and C. Bechinger, “Phase behavior of colloidal molecular crystals on triangular light lattices,” Phys. Rev. Lett. 88(24), 248302 (2002).
[Crossref]

Bengtsson, J.

M. Johansson and J. Bengtsson, “Robust design method for highly efficient beam-shaping diffractive optical elements using an iterative-Fourier-transform algorithm with soft operations,” J. Mod. Opt. 47(8), 1385–1398 (2000).
[Crossref]

Bianchi, S.

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181(8), 1444–1448 (2010).
[Crossref]

Bianco, P. R.

Boruah, B. R.

B. R. Boruah and M. A. A. Neil, “Focal field computation of an arbitrarily polarized beam using fast Fourier transforms,” Opt. Commun. 282(24), 4660–4667 (2009).
[Crossref]

Brunner, M.

M. Brunner and C. Bechinger, “Phase behavior of colloidal molecular crystals on triangular light lattices,” Phys. Rev. Lett. 88(24), 248302 (2002).
[Crossref]

Burns, J. E.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-moleculemechanics of heavy-meromyosin and s1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68(4), 298S–303S (1995).

Cai, Y.

Y. Liang, S. Yan, Z. Wang, R. Li, Y. Cai, M. He, B. Yao, and M. Lei, “Simultaneous optical trapping and imaging in the axial plane: a review of current progress,” Rep. Prog. Phys. 83(3), 032401 (2020).
[Crossref]

Y. Cai, Z. Wang, Y. Liang, F. Ren, B. Yao, M. Lei, and S. Yan, “Direct calculation of tightly focused field in an arbitrary plane,” Opt. Commun. 450, 329–334 (2019).
[Crossref]

Y. Liang, Y. Cai, Z. Wang, M. Lei, Z. Cao, Y. Wang, M. Li, S. Yan, P. R. Bianco, and Y. Bao, “Aberration correction in holographic optical tweezers using a high-order optical vortex,” Appl. Opt. 57(13), 3618–3623 (2018).
[Crossref]

Cao, Z.

Chang, C.

C. Chang, J. Xia, and Y. Jiang, “Holographic image projection on tilted planes by phase-only computer generated hologram using fractional Fourier transformation,” J. Disp. Technol. 10(2), 107–113 (2014).
[Crossref]

Chang, H. T.

H. T. Chang, Y. T. Wang, and C. Y. Chen, “Angle multiplexing optical image encryption in the Fresnel transform domain using phase-only computer-generated hologram,” Photonics 7(1), 1 (2019).
[Crossref]

H. T. Chang, C. Y. Chen, J. S. Lin, and W. J. Li, “Image reconstruction by applying Fresnel transform on phase-only computer generated hologram at tilted planes,” Digital Holography and Three-Dimensional Imaging, Optical Society of America, DW2A, 11 (2015).

Charsooghi, M. A.

Chen, C. Y.

H. T. Chang, Y. T. Wang, and C. Y. Chen, “Angle multiplexing optical image encryption in the Fresnel transform domain using phase-only computer-generated hologram,” Photonics 7(1), 1 (2019).
[Crossref]

H. T. Chang, C. Y. Chen, J. S. Lin, and W. J. Li, “Image reconstruction by applying Fresnel transform on phase-only computer generated hologram at tilted planes,” Digital Holography and Three-Dimensional Imaging, Optical Society of America, DW2A, 11 (2015).

Chen, H.

H. Chen, Y. Guo, Z. Chen, J. Hao, J. Xu, H. Wang, and J. Ding, “Holographic optical tweezers obtained by using the three-dimensional Gerchberg-Saxton algorithm,” J. Opt. 15(3), 035401 (2013).
[Crossref]

Chen, Z.

H. Chen, Y. Guo, Z. Chen, J. Hao, J. Xu, H. Wang, and J. Ding, “Holographic optical tweezers obtained by using the three-dimensional Gerchberg-Saxton algorithm,” J. Opt. 15(3), 035401 (2013).
[Crossref]

Conkey, D. B.

Courtial, J.

G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm,” New J. Phys. 7, 117 (2005).
[Crossref]

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[Crossref]

Daria, V. R.

Dholakia, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[Crossref]

Di Leonardo, R.

M. Padgett and R. Di Leonardo, “Holographic optical tweezers and their relevance to lab on chip devices,” Lab Chip 11(7), 1196–1205 (2011).
[Crossref]

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181(8), 1444–1448 (2010).
[Crossref]

R. Di Leonardo, F. Ianni, and G. Ruocco, “Computer generation of optimal holograms for optical trap arrays,” Opt. Express 15(4), 1913–1922 (2007).
[Crossref]

Ding, J.

H. Chen, Y. Guo, Z. Chen, J. Hao, J. Xu, H. Wang, and J. Ding, “Holographic optical tweezers obtained by using the three-dimensional Gerchberg-Saxton algorithm,” J. Opt. 15(3), 035401 (2013).
[Crossref]

Eriksen, R. L.

Freymann, G. V.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35(2), 237–246 (1972).

Gibson, G.

Gilboa, B.

Girard, C.

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys. 3(7), 477–480 (2007).
[Crossref]

Gluckstad, J.

Grier, D. G.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[Crossref]

P. T. Korda, M. B. Taylor, and D. G. Grier, “Kinetically locked-in colloidal transport in an array of optical tweezer,” Phys. Rev. Lett. 89(12), 128301 (2002).
[Crossref]

Gu, M.

Guo, Y.

H. Chen, Y. Guo, Z. Chen, J. Hao, J. Xu, H. Wang, and J. Ding, “Holographic optical tweezers obtained by using the three-dimensional Gerchberg-Saxton algorithm,” J. Opt. 15(3), 035401 (2013).
[Crossref]

Habaza, M.

Haist, T.

Hao, J.

H. Chen, Y. Guo, Z. Chen, J. Hao, J. Xu, H. Wang, and J. Ding, “Holographic optical tweezers obtained by using the three-dimensional Gerchberg-Saxton algorithm,” J. Opt. 15(3), 035401 (2013).
[Crossref]

Hao, X.

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12(11), 115707 (2010).
[Crossref]

He, M.

Y. Liang, S. Yan, Z. Wang, R. Li, Y. Cai, M. He, B. Yao, and M. Lei, “Simultaneous optical trapping and imaging in the axial plane: a review of current progress,” Rep. Prog. Phys. 83(3), 032401 (2020).
[Crossref]

Henderson, R. K.

Ianni, F.

Jia, B.

Jiang, Y.

C. Chang, J. Xia, and Y. Jiang, “Holographic image projection on tilted planes by phase-only computer generated hologram using fractional Fourier transformation,” J. Disp. Technol. 10(2), 107–113 (2014).
[Crossref]

Johansson, M.

M. Johansson and J. Bengtsson, “Robust design method for highly efficient beam-shaping diffractive optical elements using an iterative-Fourier-transform algorithm with soft operations,” J. Mod. Opt. 47(8), 1385–1398 (2000).
[Crossref]

Jordan, P.

Kendrickjones, J.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-moleculemechanics of heavy-meromyosin and s1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68(4), 298S–303S (1995).

Khalesifard, H. R.

Kim, H.

Kim, M.

Kitamura, N.

Knight, R. D.

Korda, P. T.

P. T. Korda, M. B. Taylor, and D. G. Grier, “Kinetically locked-in colloidal transport in an array of optical tweezer,” Phys. Rev. Lett. 89(12), 128301 (2002).
[Crossref]

Koshioka, M.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[Crossref]

Krstajic, N.

Kuang, C.

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12(11), 115707 (2010).
[Crossref]

Lasser, T.

Leach, J.

Lee, W.

Lei, M.

Y. Liang, S. Yan, Z. Wang, R. Li, Y. Cai, M. He, B. Yao, and M. Lei, “Simultaneous optical trapping and imaging in the axial plane: a review of current progress,” Rep. Prog. Phys. 83(3), 032401 (2020).
[Crossref]

Y. Cai, Z. Wang, Y. Liang, F. Ren, B. Yao, M. Lei, and S. Yan, “Direct calculation of tightly focused field in an arbitrary plane,” Opt. Commun. 450, 329–334 (2019).
[Crossref]

Y. Liang, Y. Cai, Z. Wang, M. Lei, Z. Cao, Y. Wang, M. Li, S. Yan, P. R. Bianco, and Y. Bao, “Aberration correction in holographic optical tweezers using a high-order optical vortex,” Appl. Opt. 57(13), 3618–3623 (2018).
[Crossref]

Leiderer, P.

K. Mangold, P. Leiderer, and C. Bechinger, “Phase transitions of colloidal monolayers in periodic pinning arrays,” Phys. Rev. Lett. 90(15), 158302 (2003).
[Crossref]

Leitgeb, R. A.

Leutenegger, M.

Li, M.

Li, R.

Y. Liang, S. Yan, Z. Wang, R. Li, Y. Cai, M. He, B. Yao, and M. Lei, “Simultaneous optical trapping and imaging in the axial plane: a review of current progress,” Rep. Prog. Phys. 83(3), 032401 (2020).
[Crossref]

Li, W. J.

H. T. Chang, C. Y. Chen, J. S. Lin, and W. J. Li, “Image reconstruction by applying Fresnel transform on phase-only computer generated hologram at tilted planes,” Digital Holography and Three-Dimensional Imaging, Optical Society of America, DW2A, 11 (2015).

Liang, Y.

Y. Liang, S. Yan, Z. Wang, R. Li, Y. Cai, M. He, B. Yao, and M. Lei, “Simultaneous optical trapping and imaging in the axial plane: a review of current progress,” Rep. Prog. Phys. 83(3), 032401 (2020).
[Crossref]

Y. Cai, Z. Wang, Y. Liang, F. Ren, B. Yao, M. Lei, and S. Yan, “Direct calculation of tightly focused field in an arbitrary plane,” Opt. Commun. 450, 329–334 (2019).
[Crossref]

Y. Liang, Y. Cai, Z. Wang, M. Lei, Z. Cao, Y. Wang, M. Li, S. Yan, P. R. Bianco, and Y. Bao, “Aberration correction in holographic optical tweezers using a high-order optical vortex,” Appl. Opt. 57(13), 3618–3623 (2018).
[Crossref]

Lin, H.

Lin, J. S.

H. T. Chang, C. Y. Chen, J. S. Lin, and W. J. Li, “Image reconstruction by applying Fresnel transform on phase-only computer generated hologram at tilted planes,” Digital Holography and Three-Dimensional Imaging, Optical Society of America, DW2A, 11 (2015).

Liu, J. S.

Liu, X.

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12(11), 115707 (2010).
[Crossref]

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M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
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Montes-Usategui, M.

Neil, M. A. A.

B. R. Boruah and M. A. A. Neil, “Focal field computation of an arbitrarily polarized beam using fast Fourier transforms,” Opt. Commun. 282(24), 4660–4667 (2009).
[Crossref]

Padgett, M.

M. Padgett and R. Di Leonardo, “Holographic optical tweezers and their relevance to lab on chip devices,” Lab Chip 11(7), 1196–1205 (2011).
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Paterson, L.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
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Reihani, S. N. S.

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Y. Cai, Z. Wang, Y. Liang, F. Ren, B. Yao, M. Lei, and S. Yan, “Direct calculation of tightly focused field in an arbitrary plane,” Opt. Commun. 450, 329–334 (2019).
[Crossref]

Ren, H.

Righini, M.

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys. 3(7), 477–480 (2007).
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J. Schmidhuber, “A fixed size storage O (n3) time complexity learning algorithm for fully recurrent continually running networks,” Neural Comput. 4(2), 243–248 (1992).
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Shaked, N. T.

Sibbett, W.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
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Sinclair, G.

Smalyukh, I. I.

Sparrow, J. C.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-moleculemechanics of heavy-meromyosin and s1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68(4), 298S–303S (1995).

Taghizadeh, M. R.

Taylor, M. B.

P. T. Korda, M. B. Taylor, and D. G. Grier, “Kinetically locked-in colloidal transport in an array of optical tweezer,” Phys. Rev. Lett. 89(12), 128301 (2002).
[Crossref]

Tiziani, H. J.

Tregear, R. T.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-moleculemechanics of heavy-meromyosin and s1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68(4), 298S–303S (1995).

Trivedi, R. P.

Volke-Sepulveda, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[Crossref]

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Waller, E. H.

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H. Chen, Y. Guo, Z. Chen, J. Hao, J. Xu, H. Wang, and J. Ding, “Holographic optical tweezers obtained by using the three-dimensional Gerchberg-Saxton algorithm,” J. Opt. 15(3), 035401 (2013).
[Crossref]

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X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12(11), 115707 (2010).
[Crossref]

Wang, Y.

Wang, Y. T.

H. T. Chang, Y. T. Wang, and C. Y. Chen, “Angle multiplexing optical image encryption in the Fresnel transform domain using phase-only computer-generated hologram,” Photonics 7(1), 1 (2019).
[Crossref]

Wang, Z.

Y. Liang, S. Yan, Z. Wang, R. Li, Y. Cai, M. He, B. Yao, and M. Lei, “Simultaneous optical trapping and imaging in the axial plane: a review of current progress,” Rep. Prog. Phys. 83(3), 032401 (2020).
[Crossref]

Y. Cai, Z. Wang, Y. Liang, F. Ren, B. Yao, M. Lei, and S. Yan, “Direct calculation of tightly focused field in an arbitrary plane,” Opt. Commun. 450, 329–334 (2019).
[Crossref]

Y. Liang, Y. Cai, Z. Wang, M. Lei, Z. Cao, Y. Wang, M. Li, S. Yan, P. R. Bianco, and Y. Bao, “Aberration correction in holographic optical tweezers using a high-order optical vortex,” Appl. Opt. 57(13), 3618–3623 (2018).
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J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-moleculemechanics of heavy-meromyosin and s1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68(4), 298S–303S (1995).

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G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm,” New J. Phys. 7, 117 (2005).
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Xia, J.

C. Chang, J. Xia, and Y. Jiang, “Holographic image projection on tilted planes by phase-only computer generated hologram using fractional Fourier transformation,” J. Disp. Technol. 10(2), 107–113 (2014).
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H. Chen, Y. Guo, Z. Chen, J. Hao, J. Xu, H. Wang, and J. Ding, “Holographic optical tweezers obtained by using the three-dimensional Gerchberg-Saxton algorithm,” J. Opt. 15(3), 035401 (2013).
[Crossref]

Yan, S.

Y. Liang, S. Yan, Z. Wang, R. Li, Y. Cai, M. He, B. Yao, and M. Lei, “Simultaneous optical trapping and imaging in the axial plane: a review of current progress,” Rep. Prog. Phys. 83(3), 032401 (2020).
[Crossref]

Y. Cai, Z. Wang, Y. Liang, F. Ren, B. Yao, M. Lei, and S. Yan, “Direct calculation of tightly focused field in an arbitrary plane,” Opt. Commun. 450, 329–334 (2019).
[Crossref]

Y. Liang, Y. Cai, Z. Wang, M. Lei, Z. Cao, Y. Wang, M. Li, S. Yan, P. R. Bianco, and Y. Bao, “Aberration correction in holographic optical tweezers using a high-order optical vortex,” Appl. Opt. 57(13), 3618–3623 (2018).
[Crossref]

Yao, B.

Y. Liang, S. Yan, Z. Wang, R. Li, Y. Cai, M. He, B. Yao, and M. Lei, “Simultaneous optical trapping and imaging in the axial plane: a review of current progress,” Rep. Prog. Phys. 83(3), 032401 (2020).
[Crossref]

Y. Cai, Z. Wang, Y. Liang, F. Ren, B. Yao, M. Lei, and S. Yan, “Direct calculation of tightly focused field in an arbitrary plane,” Opt. Commun. 450, 329–334 (2019).
[Crossref]

Yao, E.

Zelenina, A. S.

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys. 3(7), 477–480 (2007).
[Crossref]

Appl. Opt. (1)

Biophys. J. (1)

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-moleculemechanics of heavy-meromyosin and s1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68(4), 298S–303S (1995).

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X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12(11), 115707 (2010).
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H. Chen, Y. Guo, Z. Chen, J. Hao, J. Xu, H. Wang, and J. Ding, “Holographic optical tweezers obtained by using the three-dimensional Gerchberg-Saxton algorithm,” J. Opt. 15(3), 035401 (2013).
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J. Opt. Soc. Am. A (1)

Lab Chip (1)

M. Padgett and R. Di Leonardo, “Holographic optical tweezers and their relevance to lab on chip devices,” Lab Chip 11(7), 1196–1205 (2011).
[Crossref]

Nat. Phys. (1)

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys. 3(7), 477–480 (2007).
[Crossref]

Neural Comput. (1)

J. Schmidhuber, “A fixed size storage O (n3) time complexity learning algorithm for fully recurrent continually running networks,” Neural Comput. 4(2), 243–248 (1992).
[Crossref]

New J. Phys. (1)

G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm,” New J. Phys. 7, 117 (2005).
[Crossref]

Opt. Commun. (3)

B. R. Boruah and M. A. A. Neil, “Focal field computation of an arbitrarily polarized beam using fast Fourier transforms,” Opt. Commun. 282(24), 4660–4667 (2009).
[Crossref]

Y. Cai, Z. Wang, Y. Liang, F. Ren, B. Yao, M. Lei, and S. Yan, “Direct calculation of tightly focused field in an arbitrary plane,” Opt. Commun. 450, 329–334 (2019).
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Optik (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35(2), 237–246 (1972).

Photonics (1)

H. T. Chang, Y. T. Wang, and C. Y. Chen, “Angle multiplexing optical image encryption in the Fresnel transform domain using phase-only computer-generated hologram,” Photonics 7(1), 1 (2019).
[Crossref]

Phys. Rev. Lett. (3)

P. T. Korda, M. B. Taylor, and D. G. Grier, “Kinetically locked-in colloidal transport in an array of optical tweezer,” Phys. Rev. Lett. 89(12), 128301 (2002).
[Crossref]

K. Mangold, P. Leiderer, and C. Bechinger, “Phase transitions of colloidal monolayers in periodic pinning arrays,” Phys. Rev. Lett. 90(15), 158302 (2003).
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Y. Liang, S. Yan, Z. Wang, R. Li, Y. Cai, M. He, B. Yao, and M. Lei, “Simultaneous optical trapping and imaging in the axial plane: a review of current progress,” Rep. Prog. Phys. 83(3), 032401 (2020).
[Crossref]

Science (1)

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[Crossref]

Other (1)

H. T. Chang, C. Y. Chen, J. S. Lin, and W. J. Li, “Image reconstruction by applying Fresnel transform on phase-only computer generated hologram at tilted planes,” Digital Holography and Three-Dimensional Imaging, Optical Society of America, DW2A, 11 (2015).

Supplementary Material (1)

NameDescription
» Visualization 1       Demonstration of trapping and rotating silica beads with 7×7 spots array in arbitrary tilted planes in three dimensions.

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Figures (6)

Fig. 1.
Fig. 1. (a) Schematic diagram of light propagation from SLM panel to the focal plane of the objective. (b) Definition of an arbitrary plane. The arbitrary plane is defined as a general plane in the focal volume, including not only the xy-plane, xz-plane, yz-plane, but also planes not parallel to any of the coordinate axes.
Fig. 2.
Fig. 2. The flow chart of the tilted-plane GS algorithm.
Fig. 3.
Fig. 3. The intensity distributions of the focal fields in the xz-plane resulting from the calculated holograms with (a) and without (b) introducing the weighting factor (WF). (c) The intensity profiles along the lines marked in (a) and (b).
Fig. 4.
Fig. 4. The intensity distributions of the focal fields in the xz-plane resulting from the holograms calculated by the multi-plane 3D GS algorithm (a) and the tilted-plane GS algorithm (b), respectively. The scale bar is 5µm.
Fig. 5.
Fig. 5. (a) Schematic of the home-built holographic optical tweezers. (b) Experimentally measured 3D intensity profile of the foci array. (c) The CGH for the foci array.
Fig. 6.
Fig. 6. The video frames extracted from Visualization 1. (a)-(e) The silica beads are instantaneously trapped in different tilted planes defined by the angles θ0 and ϕ0. (f)-(h) The trapped silica beads array is rotated around the normal of the (θ0, ϕ0) = (10°, 45°) plane. The same particle is marked by a black dotted circle. The scale bar is 4µm.

Equations (10)

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

E T ( x , y , z ) = C D E H ( k x , k y ) e i ( k x x + k y y + k z z ) d k x d k y k z
D = { ( k x , k y ) : ( k x ) 2 + ( k y ) 2 ( k sin θ m a x ) 2 }
( x y z ) = R T ( x y z ) = ( cos θ 0 cos ϕ 0 cos θ 0 sin ϕ 0 sin ϕ 0 sin ϕ 0 cos ϕ 0 0 sin θ 0 cos ϕ 0 sin θ 0 sin ϕ 0 cos θ 0 ) ( x y z )
( k x k y k z ) = R T ( k x k y k z )
D ± = { ( k x , k y ) | k x ( k x , k y , ± | k z | ) 2 + k y ( k x , k y , ± | k z | ) 2 < ( k sin θ m a x ) 2 k cos θ m a x < k z ( k x , k y , ± | k z | ) < k k x 2 + k y 2 < k }
E T ( x , y , 0 ) = C D ( χ + ( k ) E H + ( k ) + χ ( k ) E H ( k ) ) e i k x d 2 k | k z |
E T ( x , y , 0 ) = C D ( χ + ( k ) + χ ( k ) ) E H + ( k ) e i k x d 2 k | k z |
w j = w j 1 i = 1 M | A T , j ( x i , y i ) | | A T , j ( x i , y i ) | ( w 0 = 1 )
u = 1 I m a x I m i n I m a x + I m i n
φ = mod ( φ H + φ a b e r r , 2 π )

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