Abstract

We introduce a new multi-objective genetic algorithm for wavefront shaping and realize controllable multi-point light focusing through scattering medium. Different from previous single-objective optimization genetic algorithms, our algorithm named Non-dominated Sorting Genetic Algorithm II based on hybrid optimization scheme (NSGA2-H) can make all focus points have uniform intensity while ensuring that their enhancement is as high as possible. We demonstrate the characteristics of NSGA2-H through simulations and experiments in amplitude optimization, analyze its optimization mechanisms and show its powerful optical control capability in uniform intensity focusing and even in customizable intensity focusing. This research will be expected to further promote future practical applications based on multi-point focusing of wavefront shaping, especially in optical trapping and optogenetics.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  25. T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2014).
    [Crossref]
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    [Crossref]
  28. M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18(4), 3444 (2010).
    [Crossref]
  29. I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101(8), 081108 (2012).
    [Crossref]
  30. D. Wang, E. H. Zhou, J. Brake, H. Ruan, M. Jang, and C. Yang, “Focusing through dynamic tissue with millisecond digital optical phase conjugation,” Optica 2(8), 728 (2015).
    [Crossref]
  31. Y. Shen, Y. Liu, C. Ma, and L. V. Wang, “Focusing light through scattering media by full-polarization digital optical phase conjugation,” Opt. Lett. 41(6), 1130 (2016).
    [Crossref]
  32. Y. Shen, Y. Liu, C. Ma, and L. V. Wang, “Focusing light through biological tissue and tissue-mimicking phantoms up to 9.6 cm in thickness with digital optical phase conjugation,” J. Biomed. Opt. 21(8), 085001 (2016).
    [Crossref]
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    [Crossref]
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    [Crossref]
  35. H. He, Y. Guan, and J. Zhou, “Image restoration through thin turbid layers by correlation with a known object,” Opt. Express 21(10), 12539 (2013).
    [Crossref]
  36. L. Wan, Z. Chen, H. Huang, and J. Pu, “Focusing light into desired patterns through turbid media by feedback-based wavefront shaping,” Appl. Phys. B: Lasers Opt. 122(7), 204 (2016).
    [Crossref]
  37. B. R. Anderson, R. Gunawidjaja, and H. Eilers, “Initial tamper tests of novel tamper-indicating optical physical unclonable functions,” Appl. Opt. 56(10), 2863 (2017).
    [Crossref]
  38. T. Peng, R. Li, S. An, X. Yu, M. Zhou, C. Bai, Y. Liang, M. Lei, C. Zhang, B. Yao, and P. Zhang, “Real-time optical manipulation of particles through turbid media,” Opt. Express 27(4), 4858 (2019).
    [Crossref]
  39. A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
    [Crossref]
  40. E. G. Bekele and J. W. Nicklow, “Multi-objective automatic calibration of SWAT using NSGA-II,” J. Hydrol. 341(3-4), 165–176 (2007).
    [Crossref]
  41. G. Vilcot and J.-C. Billaut, “A tabu search and a genetic algorithm for solving a bicriteria general job shop scheduling problem,” Eur. J. Oper. Res. 190(2), 398–411 (2008).
    [Crossref]
  42. S. Kannan, S. Baskar, J. D. McCalley, and P. Murugan, “Application of NSGA-II Algorithm to Generation Expansion Planning,” IEEE Trans. Power Syst. 24(1), 454–461 (2009).
    [Crossref]
  43. S. Honda, T. Igarashi, and Y. Narita, “Multi-objective optimization of curvilinear fiber shapes for laminated composite plates by using NSGA-II,” Composites, Part B 45(1), 1071–1078 (2013).
    [Crossref]
  44. K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
    [Crossref]
  45. I. M. Vellekoop, “Feedback-based wavefront shaping,” Opt. Express 23(9), 12189 (2015).
    [Crossref]

2019 (6)

Z. Cao, X. Zhang, G. Osnabrugge, J. Li, I. M. Vellekoop, and A. M. J. Koonen, “Reconfigurable beam system for non-line-of-sight free-space optical communication,” Light: Sci. Appl. 8(1), 69 (2019).
[Crossref]

Z. Wu, J. Luo, Y. Feng, X. Guo, Y. Shen, and Z. Li, “Controlling 1550-nm light through a multimode fiber using a Hadamard encoding algorithm,” Opt. Express 27(4), 5570 (2019).
[Crossref]

G. Osnabrugge, L. V. Amitonova, and I. M. Vellekoop, “Blind focusing through strongly scattering media using wavefront shaping with nonlinear feedback,” Opt. Express 27(8), 11673 (2019).
[Crossref]

Z. Fayyaz, N. Mohammadian, M. Reza Rahimi Tabar, R. Manwar, and K. Avanaki, “A comparative study of optimization algorithms for wavefront shaping,” J. Innovative Opt. Health Sci. 12(04), 1942002 (2019).
[Crossref]

D. Wu, J. Luo, Z. Li, and Y. Shen, “A thorough study on genetic algorithms in feedback-based wavefront shaping,” J. Innovative Opt. Health Sci. 12(04), 1942004 (2019).
[Crossref]

T. Peng, R. Li, S. An, X. Yu, M. Zhou, C. Bai, Y. Liang, M. Lei, C. Zhang, B. Yao, and P. Zhang, “Real-time optical manipulation of particles through turbid media,” Opt. Express 27(4), 4858 (2019).
[Crossref]

2018 (4)

Y. Wu, X. Zhang, and H. Yan, “Focusing light through scattering media using the harmony search algorithm for phase optimization of wavefront shaping,” Optik 158, 558–564 (2018).
[Crossref]

Z. Fayyaz, N. Mohammadian, F. Salimi, A. Fatima, M. R. R. Tabar, and M. R. N. Avanaki, “Simulated annealing optimization in wavefront shaping controlled transmission,” Appl. Opt. 57(21), 6233 (2018).
[Crossref]

L. Fang, X. Zhang, H. Zuo, and L. Pang, “Focusing light through random scattering media by four-element division algorithm,” Opt. Commun. 407, 301–310 (2018).
[Crossref]

L. Fang, H. Zuo, Z. Yang, X. Zhang, L. Pang, W. Li, Y. He, X. Yang, and Y. Wang, “Particle swarm optimization to focus coherent light through disordered media,” Appl. Phys. B: Lasers Opt. 124(8), 155 (2018).
[Crossref]

2017 (5)

H. Ruan, J. Brake, J. E. Robinson, Y. Liu, M. Jang, C. Xiao, C. Zhou, V. Gradinaru, and C. Yang, “Deep tissue optical focusing and optogenetic modulation with time-reversed ultrasonically encoded light,” Sci. Adv. 3(12), eaao5520 (2017).
[Crossref]

R. Li, T. Peng, Y. Liang, Y. Yang, B. Yao, X. Yu, J. Min, M. Lei, S. Yan, C. Zhang, and T. Ye, “Interleaved segment correction achieves higher improvement factors in using genetic algorithm to optimize light focusing through scattering media,” J. Opt. 19(10), 105602 (2017).
[Crossref]

H. Yu, K. Lee, and Y. Park, “Ultrahigh enhancement of light focusing through disordered media controlled by mega-pixel modes,” Opt. Express 25(7), 8036 (2017).
[Crossref]

Y. Liu, C. Ma, Y. Shen, J. Shi, and L. V. Wang, “Focusing light inside dynamic scattering media with millisecond digital optical phase conjugation,” Optica 4(2), 280 (2017).
[Crossref]

B. R. Anderson, R. Gunawidjaja, and H. Eilers, “Initial tamper tests of novel tamper-indicating optical physical unclonable functions,” Appl. Opt. 56(10), 2863 (2017).
[Crossref]

2016 (3)

L. Wan, Z. Chen, H. Huang, and J. Pu, “Focusing light into desired patterns through turbid media by feedback-based wavefront shaping,” Appl. Phys. B: Lasers Opt. 122(7), 204 (2016).
[Crossref]

Y. Shen, Y. Liu, C. Ma, and L. V. Wang, “Focusing light through scattering media by full-polarization digital optical phase conjugation,” Opt. Lett. 41(6), 1130 (2016).
[Crossref]

Y. Shen, Y. Liu, C. Ma, and L. V. Wang, “Focusing light through biological tissue and tissue-mimicking phantoms up to 9.6 cm in thickness with digital optical phase conjugation,” J. Biomed. Opt. 21(8), 085001 (2016).
[Crossref]

2015 (5)

2014 (2)

S. A. Goorden, M. Horstmann, A. P. Mosk, B. Škorić, and P. W. H. Pinkse, “Quantum-secure authentication of a physical unclonable key,” Optica 1(6), 421 (2014).
[Crossref]

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2014).
[Crossref]

2013 (2)

S. Honda, T. Igarashi, and Y. Narita, “Multi-objective optimization of curvilinear fiber shapes for laminated composite plates by using NSGA-II,” Composites, Part B 45(1), 1071–1078 (2013).
[Crossref]

H. He, Y. Guan, and J. Zhou, “Image restoration through thin turbid layers by correlation with a known object,” Opt. Express 21(10), 12539 (2013).
[Crossref]

2012 (5)

D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express 20(2), 1733 (2012).
[Crossref]

I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101(8), 081108 (2012).
[Crossref]

D. B. Conkey and R. Piestun, “Color image projection through a strongly scattering wall,” Opt. Express 20(25), 27312 (2012).
[Crossref]

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref]

D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, “Genetic algorithm optimization for focusing through turbid media in noisy environments,” Opt. Express 20(5), 4840 (2012).
[Crossref]

2011 (3)

D. Akbulut, T. J. Huisman, E. G. van Putten, W. L. Vos, and A. P. Mosk, “Focusing light through random photonic media by binary amplitude modulation,” Opt. Express 19(5), 4017 (2011).
[Crossref]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering Lens Resolves Sub-100 nm Structures with Visible Light,” Phys. Rev. Lett. 106(19), 193905 (2011).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the Diffraction Limit Using Multiple Light Scattering in a Highly Disordered Medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
[Crossref]

2010 (3)

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18(4), 3444 (2010).
[Crossref]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

2009 (1)

S. Kannan, S. Baskar, J. D. McCalley, and P. Murugan, “Application of NSGA-II Algorithm to Generation Expansion Planning,” IEEE Trans. Power Syst. 24(1), 454–461 (2009).
[Crossref]

2008 (2)

G. Vilcot and J.-C. Billaut, “A tabu search and a genetic algorithm for solving a bicriteria general job shop scheduling problem,” Eur. J. Oper. Res. 190(2), 398–411 (2008).
[Crossref]

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008).
[Crossref]

2007 (2)

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309 (2007).
[Crossref]

E. G. Bekele and J. W. Nicklow, “Multi-objective automatic calibration of SWAT using NSGA-II,” J. Hydrol. 341(3-4), 165–176 (2007).
[Crossref]

2006 (1)

A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
[Crossref]

2002 (1)

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[Crossref]

Agarwal, S.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[Crossref]

Akbulut, D.

D. Akbulut, T. J. Huisman, E. G. van Putten, W. L. Vos, and A. P. Mosk, “Focusing light through random photonic media by binary amplitude modulation,” Opt. Express 19(5), 4017 (2011).
[Crossref]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering Lens Resolves Sub-100 nm Structures with Visible Light,” Phys. Rev. Lett. 106(19), 193905 (2011).
[Crossref]

Amitonova, L. V.

An, S.

Anderson, B. R.

Avanaki, K.

Z. Fayyaz, N. Mohammadian, M. Reza Rahimi Tabar, R. Manwar, and K. Avanaki, “A comparative study of optimization algorithms for wavefront shaping,” J. Innovative Opt. Health Sci. 12(04), 1942002 (2019).
[Crossref]

Avanaki, M. R. N.

Bai, C.

Baskar, S.

S. Kannan, S. Baskar, J. D. McCalley, and P. Murugan, “Application of NSGA-II Algorithm to Generation Expansion Planning,” IEEE Trans. Power Syst. 24(1), 454–461 (2009).
[Crossref]

Bekele, E. G.

E. G. Bekele and J. W. Nicklow, “Multi-objective automatic calibration of SWAT using NSGA-II,” J. Hydrol. 341(3-4), 165–176 (2007).
[Crossref]

Bertolotti, J.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering Lens Resolves Sub-100 nm Structures with Visible Light,” Phys. Rev. Lett. 106(19), 193905 (2011).
[Crossref]

Billaut, J.-C.

G. Vilcot and J.-C. Billaut, “A tabu search and a genetic algorithm for solving a bicriteria general job shop scheduling problem,” Eur. J. Oper. Res. 190(2), 398–411 (2008).
[Crossref]

Boccara, A. C.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2014).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Bodington, D.

Bossy, E.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2014).
[Crossref]

Brake, J.

H. Ruan, J. Brake, J. E. Robinson, Y. Liu, M. Jang, C. Xiao, C. Zhou, V. Gradinaru, and C. Yang, “Deep tissue optical focusing and optogenetic modulation with time-reversed ultrasonically encoded light,” Sci. Adv. 3(12), eaao5520 (2017).
[Crossref]

D. Wang, E. H. Zhou, J. Brake, H. Ruan, M. Jang, and C. Yang, “Focusing through dynamic tissue with millisecond digital optical phase conjugation,” Optica 2(8), 728 (2015).
[Crossref]

Brown, A. N.

Cai, Z.

Cao, Z.

Z. Cao, X. Zhang, G. Osnabrugge, J. Li, I. M. Vellekoop, and A. M. J. Koonen, “Reconfigurable beam system for non-line-of-sight free-space optical communication,” Light: Sci. Appl. 8(1), 69 (2019).
[Crossref]

Caravaca-Aguirre, A. M.

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Chaigne, T.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2014).
[Crossref]

Chen, Z.

L. Wan, Z. Chen, H. Huang, and J. Pu, “Focusing light into desired patterns through turbid media by feedback-based wavefront shaping,” Appl. Phys. B: Lasers Opt. 122(7), 204 (2016).
[Crossref]

Choi, W.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the Diffraction Limit Using Multiple Light Scattering in a Highly Disordered Medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
[Crossref]

Choi, Y.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the Diffraction Limit Using Multiple Light Scattering in a Highly Disordered Medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
[Crossref]

Cižmár, T.

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A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
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I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101(8), 081108 (2012).
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M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18(4), 3444 (2010).
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Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
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Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the Diffraction Limit Using Multiple Light Scattering in a Highly Disordered Medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
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K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
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T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
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L. Fang, H. Zuo, Z. Yang, X. Zhang, L. Pang, W. Li, Y. He, X. Yang, and Y. Wang, “Particle swarm optimization to focus coherent light through disordered media,” Appl. Phys. B: Lasers Opt. 124(8), 155 (2018).
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L. Fang, X. Zhang, H. Zuo, and L. Pang, “Focusing light through random scattering media by four-element division algorithm,” Opt. Commun. 407, 301–310 (2018).
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Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
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Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the Diffraction Limit Using Multiple Light Scattering in a Highly Disordered Medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
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Fayyaz, Z.

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Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the Diffraction Limit Using Multiple Light Scattering in a Highly Disordered Medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
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T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2014).
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T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2014).
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S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104(10), 100601 (2010).
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Gradinaru, V.

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Guo, X.

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He, Y.

L. Fang, H. Zuo, Z. Yang, X. Zhang, L. Pang, W. Li, Y. He, X. Yang, and Y. Wang, “Particle swarm optimization to focus coherent light through disordered media,” Appl. Phys. B: Lasers Opt. 124(8), 155 (2018).
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Huang, H.

L. Wan, Z. Chen, H. Huang, and J. Pu, “Focusing light into desired patterns through turbid media by feedback-based wavefront shaping,” Appl. Phys. B: Lasers Opt. 122(7), 204 (2016).
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Igarashi, T.

S. Honda, T. Igarashi, and Y. Narita, “Multi-objective optimization of curvilinear fiber shapes for laminated composite plates by using NSGA-II,” Composites, Part B 45(1), 1071–1078 (2013).
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H. Ruan, J. Brake, J. E. Robinson, Y. Liu, M. Jang, C. Xiao, C. Zhou, V. Gradinaru, and C. Yang, “Deep tissue optical focusing and optogenetic modulation with time-reversed ultrasonically encoded light,” Sci. Adv. 3(12), eaao5520 (2017).
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D. Wang, E. H. Zhou, J. Brake, H. Ruan, M. Jang, and C. Yang, “Focusing through dynamic tissue with millisecond digital optical phase conjugation,” Optica 2(8), 728 (2015).
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Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the Diffraction Limit Using Multiple Light Scattering in a Highly Disordered Medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
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S. Kannan, S. Baskar, J. D. McCalley, and P. Murugan, “Application of NSGA-II Algorithm to Generation Expansion Planning,” IEEE Trans. Power Syst. 24(1), 454–461 (2009).
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T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2014).
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Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
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A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
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Z. Cao, X. Zhang, G. Osnabrugge, J. Li, I. M. Vellekoop, and A. M. J. Koonen, “Reconfigurable beam system for non-line-of-sight free-space optical communication,” Light: Sci. Appl. 8(1), 69 (2019).
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E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering Lens Resolves Sub-100 nm Structures with Visible Light,” Phys. Rev. Lett. 106(19), 193905 (2011).
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Lee, K. J.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref]

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R. Li, T. Peng, Y. Liang, Y. Yang, B. Yao, X. Yu, J. Min, M. Lei, S. Yan, C. Zhang, and T. Ye, “Interleaved segment correction achieves higher improvement factors in using genetic algorithm to optimize light focusing through scattering media,” J. Opt. 19(10), 105602 (2017).
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S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104(10), 100601 (2010).
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Z. Cao, X. Zhang, G. Osnabrugge, J. Li, I. M. Vellekoop, and A. M. J. Koonen, “Reconfigurable beam system for non-line-of-sight free-space optical communication,” Light: Sci. Appl. 8(1), 69 (2019).
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T. Peng, R. Li, S. An, X. Yu, M. Zhou, C. Bai, Y. Liang, M. Lei, C. Zhang, B. Yao, and P. Zhang, “Real-time optical manipulation of particles through turbid media,” Opt. Express 27(4), 4858 (2019).
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R. Li, T. Peng, Y. Liang, Y. Yang, B. Yao, X. Yu, J. Min, M. Lei, S. Yan, C. Zhang, and T. Ye, “Interleaved segment correction achieves higher improvement factors in using genetic algorithm to optimize light focusing through scattering media,” J. Opt. 19(10), 105602 (2017).
[Crossref]

Li, W.

L. Fang, H. Zuo, Z. Yang, X. Zhang, L. Pang, W. Li, Y. He, X. Yang, and Y. Wang, “Particle swarm optimization to focus coherent light through disordered media,” Appl. Phys. B: Lasers Opt. 124(8), 155 (2018).
[Crossref]

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D. Wu, J. Luo, Z. Li, and Y. Shen, “A thorough study on genetic algorithms in feedback-based wavefront shaping,” J. Innovative Opt. Health Sci. 12(04), 1942004 (2019).
[Crossref]

Z. Wu, J. Luo, Y. Feng, X. Guo, Y. Shen, and Z. Li, “Controlling 1550-nm light through a multimode fiber using a Hadamard encoding algorithm,” Opt. Express 27(4), 5570 (2019).
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T. Peng, R. Li, S. An, X. Yu, M. Zhou, C. Bai, Y. Liang, M. Lei, C. Zhang, B. Yao, and P. Zhang, “Real-time optical manipulation of particles through turbid media,” Opt. Express 27(4), 4858 (2019).
[Crossref]

R. Li, T. Peng, Y. Liang, Y. Yang, B. Yao, X. Yu, J. Min, M. Lei, S. Yan, C. Zhang, and T. Ye, “Interleaved segment correction achieves higher improvement factors in using genetic algorithm to optimize light focusing through scattering media,” J. Opt. 19(10), 105602 (2017).
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H. Ruan, J. Brake, J. E. Robinson, Y. Liu, M. Jang, C. Xiao, C. Zhou, V. Gradinaru, and C. Yang, “Deep tissue optical focusing and optogenetic modulation with time-reversed ultrasonically encoded light,” Sci. Adv. 3(12), eaao5520 (2017).
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Y. Liu, C. Ma, Y. Shen, J. Shi, and L. V. Wang, “Focusing light inside dynamic scattering media with millisecond digital optical phase conjugation,” Optica 4(2), 280 (2017).
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Y. Shen, Y. Liu, C. Ma, and L. V. Wang, “Focusing light through scattering media by full-polarization digital optical phase conjugation,” Opt. Lett. 41(6), 1130 (2016).
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Y. Shen, Y. Liu, C. Ma, and L. V. Wang, “Focusing light through biological tissue and tissue-mimicking phantoms up to 9.6 cm in thickness with digital optical phase conjugation,” J. Biomed. Opt. 21(8), 085001 (2016).
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D. Wu, J. Luo, Z. Li, and Y. Shen, “A thorough study on genetic algorithms in feedback-based wavefront shaping,” J. Innovative Opt. Health Sci. 12(04), 1942004 (2019).
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Z. Wu, J. Luo, Y. Feng, X. Guo, Y. Shen, and Z. Li, “Controlling 1550-nm light through a multimode fiber using a Hadamard encoding algorithm,” Opt. Express 27(4), 5570 (2019).
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Ma, C.

Manwar, R.

Z. Fayyaz, N. Mohammadian, M. Reza Rahimi Tabar, R. Manwar, and K. Avanaki, “A comparative study of optimization algorithms for wavefront shaping,” J. Innovative Opt. Health Sci. 12(04), 1942002 (2019).
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T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
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S. Kannan, S. Baskar, J. D. McCalley, and P. Murugan, “Application of NSGA-II Algorithm to Generation Expansion Planning,” IEEE Trans. Power Syst. 24(1), 454–461 (2009).
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K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
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R. Li, T. Peng, Y. Liang, Y. Yang, B. Yao, X. Yu, J. Min, M. Lei, S. Yan, C. Zhang, and T. Ye, “Interleaved segment correction achieves higher improvement factors in using genetic algorithm to optimize light focusing through scattering media,” J. Opt. 19(10), 105602 (2017).
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Z. Fayyaz, N. Mohammadian, M. Reza Rahimi Tabar, R. Manwar, and K. Avanaki, “A comparative study of optimization algorithms for wavefront shaping,” J. Innovative Opt. Health Sci. 12(04), 1942002 (2019).
[Crossref]

Z. Fayyaz, N. Mohammadian, F. Salimi, A. Fatima, M. R. R. Tabar, and M. R. N. Avanaki, “Simulated annealing optimization in wavefront shaping controlled transmission,” Appl. Opt. 57(21), 6233 (2018).
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Murugan, P.

S. Kannan, S. Baskar, J. D. McCalley, and P. Murugan, “Application of NSGA-II Algorithm to Generation Expansion Planning,” IEEE Trans. Power Syst. 24(1), 454–461 (2009).
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S. Honda, T. Igarashi, and Y. Narita, “Multi-objective optimization of curvilinear fiber shapes for laminated composite plates by using NSGA-II,” Composites, Part B 45(1), 1071–1078 (2013).
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G. Osnabrugge, L. V. Amitonova, and I. M. Vellekoop, “Blind focusing through strongly scattering media using wavefront shaping with nonlinear feedback,” Opt. Express 27(8), 11673 (2019).
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L. Fang, H. Zuo, Z. Yang, X. Zhang, L. Pang, W. Li, Y. He, X. Yang, and Y. Wang, “Particle swarm optimization to focus coherent light through disordered media,” Appl. Phys. B: Lasers Opt. 124(8), 155 (2018).
[Crossref]

L. Fang, X. Zhang, H. Zuo, and L. Pang, “Focusing light through random scattering media by four-element division algorithm,” Opt. Commun. 407, 301–310 (2018).
[Crossref]

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Peng, T.

T. Peng, R. Li, S. An, X. Yu, M. Zhou, C. Bai, Y. Liang, M. Lei, C. Zhang, B. Yao, and P. Zhang, “Real-time optical manipulation of particles through turbid media,” Opt. Express 27(4), 4858 (2019).
[Crossref]

R. Li, T. Peng, Y. Liang, Y. Yang, B. Yao, X. Yu, J. Min, M. Lei, S. Yan, C. Zhang, and T. Ye, “Interleaved segment correction achieves higher improvement factors in using genetic algorithm to optimize light focusing through scattering media,” J. Opt. 19(10), 105602 (2017).
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Pinkse, P. W. H.

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104(10), 100601 (2010).
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K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
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Pu, J.

L. Wan, Z. Chen, H. Huang, and J. Pu, “Focusing light into desired patterns through turbid media by feedback-based wavefront shaping,” Appl. Phys. B: Lasers Opt. 122(7), 204 (2016).
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Reza Rahimi Tabar, M.

Z. Fayyaz, N. Mohammadian, M. Reza Rahimi Tabar, R. Manwar, and K. Avanaki, “A comparative study of optimization algorithms for wavefront shaping,” J. Innovative Opt. Health Sci. 12(04), 1942002 (2019).
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H. Ruan, J. Brake, J. E. Robinson, Y. Liu, M. Jang, C. Xiao, C. Zhou, V. Gradinaru, and C. Yang, “Deep tissue optical focusing and optogenetic modulation with time-reversed ultrasonically encoded light,” Sci. Adv. 3(12), eaao5520 (2017).
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H. Ruan, J. Brake, J. E. Robinson, Y. Liu, M. Jang, C. Xiao, C. Zhou, V. Gradinaru, and C. Yang, “Deep tissue optical focusing and optogenetic modulation with time-reversed ultrasonically encoded light,” Sci. Adv. 3(12), eaao5520 (2017).
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D. Wang, E. H. Zhou, J. Brake, H. Ruan, M. Jang, and C. Yang, “Focusing through dynamic tissue with millisecond digital optical phase conjugation,” Optica 2(8), 728 (2015).
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Shen, Y.

Z. Wu, J. Luo, Y. Feng, X. Guo, Y. Shen, and Z. Li, “Controlling 1550-nm light through a multimode fiber using a Hadamard encoding algorithm,” Opt. Express 27(4), 5570 (2019).
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Y. Liu, C. Ma, Y. Shen, J. Shi, and L. V. Wang, “Focusing light inside dynamic scattering media with millisecond digital optical phase conjugation,” Optica 4(2), 280 (2017).
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Y. Shen, Y. Liu, C. Ma, and L. V. Wang, “Focusing light through scattering media by full-polarization digital optical phase conjugation,” Opt. Lett. 41(6), 1130 (2016).
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Y. Shen, Y. Liu, C. Ma, and L. V. Wang, “Focusing light through biological tissue and tissue-mimicking phantoms up to 9.6 cm in thickness with digital optical phase conjugation,” J. Biomed. Opt. 21(8), 085001 (2016).
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Z. Cao, X. Zhang, G. Osnabrugge, J. Li, I. M. Vellekoop, and A. M. J. Koonen, “Reconfigurable beam system for non-line-of-sight free-space optical communication,” Light: Sci. Appl. 8(1), 69 (2019).
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I. M. Vellekoop, “Feedback-based wavefront shaping,” Opt. Express 23(9), 12189 (2015).
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I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101(8), 081108 (2012).
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I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008).
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I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309 (2007).
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E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering Lens Resolves Sub-100 nm Structures with Visible Light,” Phys. Rev. Lett. 106(19), 193905 (2011).
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Wang, F.

Wang, L. V.

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L. Fang, H. Zuo, Z. Yang, X. Zhang, L. Pang, W. Li, Y. He, X. Yang, and Y. Wang, “Particle swarm optimization to focus coherent light through disordered media,” Appl. Phys. B: Lasers Opt. 124(8), 155 (2018).
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H. Ruan, J. Brake, J. E. Robinson, Y. Liu, M. Jang, C. Xiao, C. Zhou, V. Gradinaru, and C. Yang, “Deep tissue optical focusing and optogenetic modulation with time-reversed ultrasonically encoded light,” Sci. Adv. 3(12), eaao5520 (2017).
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Yang, X.

L. Fang, H. Zuo, Z. Yang, X. Zhang, L. Pang, W. Li, Y. He, X. Yang, and Y. Wang, “Particle swarm optimization to focus coherent light through disordered media,” Appl. Phys. B: Lasers Opt. 124(8), 155 (2018).
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R. Li, T. Peng, Y. Liang, Y. Yang, B. Yao, X. Yu, J. Min, M. Lei, S. Yan, C. Zhang, and T. Ye, “Interleaved segment correction achieves higher improvement factors in using genetic algorithm to optimize light focusing through scattering media,” J. Opt. 19(10), 105602 (2017).
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Yang, Z.

L. Fang, H. Zuo, Z. Yang, X. Zhang, L. Pang, W. Li, Y. He, X. Yang, and Y. Wang, “Particle swarm optimization to focus coherent light through disordered media,” Appl. Phys. B: Lasers Opt. 124(8), 155 (2018).
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T. Peng, R. Li, S. An, X. Yu, M. Zhou, C. Bai, Y. Liang, M. Lei, C. Zhang, B. Yao, and P. Zhang, “Real-time optical manipulation of particles through turbid media,” Opt. Express 27(4), 4858 (2019).
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R. Li, T. Peng, Y. Liang, Y. Yang, B. Yao, X. Yu, J. Min, M. Lei, S. Yan, C. Zhang, and T. Ye, “Interleaved segment correction achieves higher improvement factors in using genetic algorithm to optimize light focusing through scattering media,” J. Opt. 19(10), 105602 (2017).
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Ye, T.

R. Li, T. Peng, Y. Liang, Y. Yang, B. Yao, X. Yu, J. Min, M. Lei, S. Yan, C. Zhang, and T. Ye, “Interleaved segment correction achieves higher improvement factors in using genetic algorithm to optimize light focusing through scattering media,” J. Opt. 19(10), 105602 (2017).
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Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref]

Yu, H.

Yu, X.

T. Peng, R. Li, S. An, X. Yu, M. Zhou, C. Bai, Y. Liang, M. Lei, C. Zhang, B. Yao, and P. Zhang, “Real-time optical manipulation of particles through turbid media,” Opt. Express 27(4), 4858 (2019).
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R. Li, T. Peng, Y. Liang, Y. Yang, B. Yao, X. Yu, J. Min, M. Lei, S. Yan, C. Zhang, and T. Ye, “Interleaved segment correction achieves higher improvement factors in using genetic algorithm to optimize light focusing through scattering media,” J. Opt. 19(10), 105602 (2017).
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T. Peng, R. Li, S. An, X. Yu, M. Zhou, C. Bai, Y. Liang, M. Lei, C. Zhang, B. Yao, and P. Zhang, “Real-time optical manipulation of particles through turbid media,” Opt. Express 27(4), 4858 (2019).
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Z. Cao, X. Zhang, G. Osnabrugge, J. Li, I. M. Vellekoop, and A. M. J. Koonen, “Reconfigurable beam system for non-line-of-sight free-space optical communication,” Light: Sci. Appl. 8(1), 69 (2019).
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L. Fang, H. Zuo, Z. Yang, X. Zhang, L. Pang, W. Li, Y. He, X. Yang, and Y. Wang, “Particle swarm optimization to focus coherent light through disordered media,” Appl. Phys. B: Lasers Opt. 124(8), 155 (2018).
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H. Ruan, J. Brake, J. E. Robinson, Y. Liu, M. Jang, C. Xiao, C. Zhou, V. Gradinaru, and C. Yang, “Deep tissue optical focusing and optogenetic modulation with time-reversed ultrasonically encoded light,” Sci. Adv. 3(12), eaao5520 (2017).
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Zhou, J.

Zhou, M.

Zhuang, H.

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L. Fang, H. Zuo, Z. Yang, X. Zhang, L. Pang, W. Li, Y. He, X. Yang, and Y. Wang, “Particle swarm optimization to focus coherent light through disordered media,” Appl. Phys. B: Lasers Opt. 124(8), 155 (2018).
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Appl. Phys. B: Lasers Opt. (2)

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L. Fang, H. Zuo, Z. Yang, X. Zhang, L. Pang, W. Li, Y. He, X. Yang, and Y. Wang, “Particle swarm optimization to focus coherent light through disordered media,” Appl. Phys. B: Lasers Opt. 124(8), 155 (2018).
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I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101(8), 081108 (2012).
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J. Biomed. Opt. (1)

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Z. Cao, X. Zhang, G. Osnabrugge, J. Li, I. M. Vellekoop, and A. M. J. Koonen, “Reconfigurable beam system for non-line-of-sight free-space optical communication,” Light: Sci. Appl. 8(1), 69 (2019).
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I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008).
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Z. Wu, J. Luo, Y. Feng, X. Guo, Y. Shen, and Z. Li, “Controlling 1550-nm light through a multimode fiber using a Hadamard encoding algorithm,” Opt. Express 27(4), 5570 (2019).
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T. Peng, R. Li, S. An, X. Yu, M. Zhou, C. Bai, Y. Liang, M. Lei, C. Zhang, B. Yao, and P. Zhang, “Real-time optical manipulation of particles through turbid media,” Opt. Express 27(4), 4858 (2019).
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I. M. Vellekoop, “Feedback-based wavefront shaping,” Opt. Express 23(9), 12189 (2015).
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H. Ruan, J. Brake, J. E. Robinson, Y. Liu, M. Jang, C. Xiao, C. Zhou, V. Gradinaru, and C. Yang, “Deep tissue optical focusing and optogenetic modulation with time-reversed ultrasonically encoded light,” Sci. Adv. 3(12), eaao5520 (2017).
[Crossref]

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Figures (9)

Fig. 1.
Fig. 1. Principle of multi-point focusing of wavefront shaping.
Fig. 2.
Fig. 2. The flowchart of NSGA2-H.
Fig. 3.
Fig. 3. Experimental setup for multi-point focusing. OL1, OL2, OL3: objective lenses. A: aperture. P: linear polarizer. DMD: digital micromirror device. L1, L2: lenses. SF: spatial filter. S: scattering sample. CCD: charge coupled device. DAQ: data acquisition card. PC: personal computer.
Fig. 4.
Fig. 4. Effects of mixing factor H on 5-point focusing in amplitude optimization. (a) Pareto-optimal fronts. (b) Evolution curves of enhancement. (c) Evolution curves of coefficient of variation. Mixing factor H in the simulation and experiment are marked as Hs and He, respectively. (d)–(f) are the simulation results corresponding to Hs = 120, 160, 200, respectively. (g)–(i) are the experimental results corresponding to He = 120, 160, 200, respectively. Scale bar: 500 µm.
Fig. 5.
Fig. 5. Comparison of AM and GM discriminants on 10-point focusing in amplitude optimization. (a) Pareto-optimal fronts. (b) Evolution curves of enhancement. (c) Evolution curves of coefficient of variation. AM discriminant in the simulation and experiment are marked as AMs and AMe, respectively. GM discriminant in the simulation and experiment are marked as GMs and GMe, respectively. (d) and (e) are the simulation results corresponding to AMs and GMs, respectively. (f) and (g) are the experimental results corresponding to AMe and GMe, respectively. Scale bar: 500 µm.
Fig. 6.
Fig. 6. Experimental results of uniform intensity and customizable intensity focusing. (a) Speckles before optimization. (b) Uniform intensity focusing of 20-point after optimization. (c) Customizable intensity focusing of 9-point after optimization. (d) A bar chart of intensity of 9 focus points from (c). Scale bar: 500 µm.
Fig. 7.
Fig. 7. The simulation results of NSGA2, NSGA2-H and GA with AM discriminant.
Fig. 8.
Fig. 8. The simulation results of NSGA2, NSGA2-H and GA with GM discriminant.
Fig. 9.
Fig. 9. Comparison of ${f_{AM}}$ and ${f_{GM}}$ on two-point focusing

Tables (1)

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Table 1. Appropriate values of H for different numbers of focus points

Equations (7)

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f 1 = m = 1 M I m / m = 1 M I m I r e f I r e f ,
f 2 = σ M / σ M 1 M m = 1 M I m 1 M m = 1 M I m × 100 % ,
f 1 = m = 1 M I m M M / m = 1 M I m M M I r e f I r e f ,
η = α ( N 1 ) + 1 ,
f A M f G M ,
m = 1 M I m / m = 1 M I m I r e f I r e f m = 1 M I m M M / m = 1 M I m M M I r e f I r e f ,
m = 1 M I m / m = 1 M I m M M m = 1 M I m M .

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