Abstract

One of the main limitations of utilizing optimal wavefront shaping in imaging and authentication applications is the slow speed of the optimization algorithms currently being used. To address this problem we develop a microgenetic optimization algorithm (μGA) for optimal wavefront shaping. We test the abilities of the μGA and make comparisons to previous algorithms (iterative and simple-genetic) by using each algorithm to optimize transmission through an opaque medium. From our experiments we find that the μGA is faster than both the iterative and simple-genetic algorithms and that both genetic algorithms are more resistant to noise and sample decoherence than the iterative algorithm.

© 2015 Optical Society of America

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References

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  4. Y. Guan, O. Katz, E. Small, J. Zhou, and Y. Silberberg, “Polarization control of multiply scattered light through random media by wavefront shaping,” Opt. Lett. 37, 4663–4665 (2012).
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  6. J. H. Park, C. Park, H. Yu, Y. H. Cho, and Y. Park, “Dynamic active wave plate using random nanoparticles,” Opt. Express 20, 17010–17016 (2012).
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  7. H. P. Paudel, C. Stockbridge, J. Mertz, and T. Bifano, “Focusing polychromatic light through strongly scattering media,” Opt. Express 21, 17299–17308 (2013).
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  8. F. van Beijnum, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Frequency bandwidth of light focused through turbid media,” Opt. Lett. 36, 373–375 (2011).
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    [Crossref]
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    [Crossref]
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  17. N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett. 109, 033903 (2012).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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  31. P. K. Senecal, “Numerical optimization using the gen4 micro-genetic algorithm code” (University of Wisconsin-Madison, 2000).
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  33. E. Elbeltagi, T. Hegazy, and D. Grierson, “Comparison among five evolutionary-based optimization algorithms,” Adv. Eng. Inf. 19, 43–53 (2005).
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  37. J. Holland, Adaptation in Natural and Artificial Systems (University of Michigan, 1975).
  38. R. Haupt and S. Haupt, Practical Genetic Algorithms, 2nd ed. (Wiley, 2004).
  39. B. L. Miller, B. L. Miller, D. E. Goldberg, and D. E. Goldberg, “Genetic algorithms, tournament selection, and the effects of noise,” Complex Syst. 9, 193–212 (1995).
  40. M. V. Butz, K. Sastry, and D. E. Goldberg, “Tournament selection in xcs,” in Proceedings of the Fifth Genetic and Evolutionary Computation Conference (Gecco-2003) (Association for Computing Machinery, 2002).
  41. J. E. Baker, “Reducing bias and inefficiency in the selection algorithm,” in Proceedings of the Second International Conference on Genetic Algorithms and Their Application (L. Erlbaum Associates, 1987), pp. 14–21.
  42. I. Loshchilov, M. Schoenauer, and M. Sebag, “Not all parents are equal for mo-cma-es,” in Evolutionary Multi-Criterion Optimization (Springer Verlag, 2011), pp. 31–45.
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  44. R. Gunawidjaja, T. Myint, and H. Eilers, “Temperature-dependent phase changes in multicolored ErxYbyZr1−x−yO2/Eu0.02Y1.98O3 core/shell nanoparticles,” J. Phys. Chem. C 117, 14427–14434 (2013).
    [Crossref]
  45. In order to compare the three algorithms in Fig. 4 we plot the enhancements as a function of normalized iteration, such that the max number of iterations is set to one. For the IA the total number of iterations is 131,072 and for both GAs the total number of iterations is 12,000.

2014 (6)

N. Bachelard, S. Gigan, X. Noblin, and P. Sebbah, “Adaptive pumping for spectral control of random lasers,” Nature 10, 426–431 (2014).

J. W. Tay, P. Lai, Y. Suzuki, and L. V. Wang, “Ultrasonically encoded wavefront shaping for focusing into random media,” Sci. Rep. 4, 3918 (2014).
[Crossref]

P. Lai, J. W. Tay, L. Wang, and L. V. Wang, “Optical focusing in scattering media with photoacoustic wavefront shaping (paws),” Proc. SPIE 8943, 894318 (2014).

B. R. Anderson, R. Gunawidjaja, and H. Eilers, “Effect of experimental parameters on optimal transmission of light through opaque media,” Phys. Rev. A 90, 053826 (2014).
[Crossref]

J. W. Tay, J. Liang, and L. V. Wang, “Amplitude-masked photoacoustic wavefront shaping and application in flowmetry,” Opt. Lett. 39, 5499–5502 (2014).
[Crossref]

T. Chaigne, J. Gateau, O. Katz, C. Boccara, S. Gigan, and E. Bossy, “Improving photoacoustic-guided optical focusing in scattering media by spectrally filtered detection,” Opt. Lett. 39, 6054–6057 (2014).
[Crossref]

2013 (4)

H. P. Paudel, C. Stockbridge, J. Mertz, and T. Bifano, “Focusing polychromatic light through strongly scattering media,” Opt. Express 21, 17299–17308 (2013).
[Crossref]

H. Yilmaz, W. L. Vos, and A. P. Mosk, “Optimal control of light propagation through multiple-scattering media in the presence of noise,” Biomed. Opt. Express 4, 1759–1768 (2013).
[Crossref]

R. Gunawidjaja, T. Myint, and H. Eilers, “Temperature-dependent phase changes in multicolored ErxYbyZr1−x−yO2/Eu0.02Y1.98O3 core/shell nanoparticles,” J. Phys. Chem. C 117, 14427–14434 (2013).
[Crossref]

M. Leonetti and C. Lopez, “Active subnanometer spectral control of a random laser,” Appl. Phys. Lett. 102, 071105 (2013).
[Crossref]

2012 (10)

M. Leonetti, C. Conti, and C. Lopez, “Random laser tailored by directional stimulated emission,” Phys. Rev. A 85, 043841 (2012).
[Crossref]

Y. M. Wang, B. Judkewitz, C. H. DiMarzio, and C. A. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett. 109, 033903 (2012).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (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, 4840–4849 (2012).
[Crossref]

C. Stockbridge, Y. Lu, J. Moore, S. Hoffman, R. Paxman, K. Toussaint, and T. Bifano, “Focusing through dynamic scattering media,” Opt. Express 20, 15086–15092 (2012).
[Crossref]

J. H. Park, C. Park, H. Yu, Y. H. Cho, and Y. Park, “Dynamic active wave plate using random nanoparticles,” Opt. Express 20, 17010–17016 (2012).
[Crossref]

J. H. Park, C. Park, H. Yu, Y. H. Cho, and Y. Park, “Active spectral filtering through turbid media,” Opt. Lett. 37, 3261–3263 (2012).
[Crossref]

E. Small, O. Katz, Y. Guan, and Y. Silberberg, “Spectral control of broadband light through random media by wavefront shaping,” Opt. Lett. 37, 3429–3431 (2012).
[Crossref]

Y. Guan, O. Katz, E. Small, J. Zhou, and Y. Silberberg, “Polarization control of multiply scattered light through random media by wavefront shaping,” Opt. Lett. 37, 4663–4665 (2012).
[Crossref]

2011 (4)

F. van Beijnum, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Frequency bandwidth of light focused through turbid media,” Opt. Lett. 36, 373–375 (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, 193905 (2011).
[Crossref]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[Crossref]

2010 (1)

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[Crossref]

2008 (1)

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

2007 (1)

2005 (1)

E. Elbeltagi, T. Hegazy, and D. Grierson, “Comparison among five evolutionary-based optimization algorithms,” Adv. Eng. Inf. 19, 43–53 (2005).

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, 182–197 (2002).

1995 (1)

B. L. Miller, B. L. Miller, D. E. Goldberg, and D. E. Goldberg, “Genetic algorithms, tournament selection, and the effects of noise,” Complex Syst. 9, 193–212 (1995).

1990 (1)

I. Freund, “Looking through walls and around corners,” Physica A 168, 49–65 (1990).
[Crossref]

1989 (1)

K. Krishnakumar, “Micro-genetic algorithms for stationary and stationary non-stationary function optimization,” Proc. SPIE 1196, 1196 (1989).

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, 182–197 (2002).

Akbulut, D.

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, 193905 (2011).
[Crossref]

Anderson, B. R.

B. R. Anderson, R. Gunawidjaja, and H. Eilers, “Effect of experimental parameters on optimal transmission of light through opaque media,” Phys. Rev. A 90, 053826 (2014).
[Crossref]

Andreasen, J.

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett. 109, 033903 (2012).
[Crossref]

Austin, D. R.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

Bachelard, N.

N. Bachelard, S. Gigan, X. Noblin, and P. Sebbah, “Adaptive pumping for spectral control of random lasers,” Nature 10, 426–431 (2014).

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett. 109, 033903 (2012).
[Crossref]

Back, T.

T. Back, Evolutionary Algorithms in Theory and Practice (Oxford University, 1996).

Baker, J. E.

J. E. Baker, “Reducing bias and inefficiency in the selection algorithm,” in Proceedings of the Second International Conference on Genetic Algorithms and Their Application (L. Erlbaum Associates, 1987), pp. 14–21.

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, 193905 (2011).
[Crossref]

Bifano, T.

Boccara, C.

Bondareff, P.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

Bossy, E.

Bromberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[Crossref]

Brown, A. N.

Butz, M. V.

M. V. Butz, K. Sastry, and D. E. Goldberg, “Tournament selection in xcs,” in Proceedings of the Fifth Genetic and Evolutionary Computation Conference (Gecco-2003) (Association for Computing Machinery, 2002).

Caravaca-Aguirre, A. M.

Chaigne, T.

Chatel, B.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

Cho, Y. H.

Conkey, D. B.

Conti, C.

M. Leonetti, C. Conti, and C. Lopez, “Random laser tailored by directional stimulated emission,” Phys. Rev. A 85, 043841 (2012).
[Crossref]

Deb, K.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: Nsga-ii,” IEEE Trans. Evol. Comput. 6, 182–197 (2002).

DiMarzio, C. H.

Y. M. Wang, B. Judkewitz, C. H. DiMarzio, and C. A. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

Eilers, H.

B. R. Anderson, R. Gunawidjaja, and H. Eilers, “Effect of experimental parameters on optimal transmission of light through opaque media,” Phys. Rev. A 90, 053826 (2014).
[Crossref]

R. Gunawidjaja, T. Myint, and H. Eilers, “Temperature-dependent phase changes in multicolored ErxYbyZr1−x−yO2/Eu0.02Y1.98O3 core/shell nanoparticles,” J. Phys. Chem. C 117, 14427–14434 (2013).
[Crossref]

Elbeltagi, E.

E. Elbeltagi, T. Hegazy, and D. Grierson, “Comparison among five evolutionary-based optimization algorithms,” Adv. Eng. Inf. 19, 43–53 (2005).

Fink, M.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

Freund, I.

I. Freund, “Looking through walls and around corners,” Physica A 168, 49–65 (1990).
[Crossref]

Gateau, J.

Gigan, S.

N. Bachelard, S. Gigan, X. Noblin, and P. Sebbah, “Adaptive pumping for spectral control of random lasers,” Nature 10, 426–431 (2014).

T. Chaigne, J. Gateau, O. Katz, C. Boccara, S. Gigan, and E. Bossy, “Improving photoacoustic-guided optical focusing in scattering media by spectrally filtered detection,” Opt. Lett. 39, 6054–6057 (2014).
[Crossref]

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett. 109, 033903 (2012).
[Crossref]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

S. Gigan and E. Bossy, “A photoacoustic transmission matrix for deep optical imaging,” in SPIE Newsroom (SPIE, 2014).

Goldberg, D.

D. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

Goldberg, D. E.

B. L. Miller, B. L. Miller, D. E. Goldberg, and D. E. Goldberg, “Genetic algorithms, tournament selection, and the effects of noise,” Complex Syst. 9, 193–212 (1995).

B. L. Miller, B. L. Miller, D. E. Goldberg, and D. E. Goldberg, “Genetic algorithms, tournament selection, and the effects of noise,” Complex Syst. 9, 193–212 (1995).

M. V. Butz, K. Sastry, and D. E. Goldberg, “Tournament selection in xcs,” in Proceedings of the Fifth Genetic and Evolutionary Computation Conference (Gecco-2003) (Association for Computing Machinery, 2002).

Grierson, D.

E. Elbeltagi, T. Hegazy, and D. Grierson, “Comparison among five evolutionary-based optimization algorithms,” Adv. Eng. Inf. 19, 43–53 (2005).

Guan, Y.

Gunawidjaja, R.

B. R. Anderson, R. Gunawidjaja, and H. Eilers, “Effect of experimental parameters on optimal transmission of light through opaque media,” Phys. Rev. A 90, 053826 (2014).
[Crossref]

R. Gunawidjaja, T. Myint, and H. Eilers, “Temperature-dependent phase changes in multicolored ErxYbyZr1−x−yO2/Eu0.02Y1.98O3 core/shell nanoparticles,” J. Phys. Chem. C 117, 14427–14434 (2013).
[Crossref]

Haupt, R.

R. Haupt and S. Haupt, Practical Genetic Algorithms, 2nd ed. (Wiley, 2004).

Haupt, S.

R. Haupt and S. Haupt, Practical Genetic Algorithms, 2nd ed. (Wiley, 2004).

Hegazy, T.

E. Elbeltagi, T. Hegazy, and D. Grierson, “Comparison among five evolutionary-based optimization algorithms,” Adv. Eng. Inf. 19, 43–53 (2005).

Hoffman, S.

Holland, J.

J. Holland, Adaptation in Natural and Artificial Systems (University of Michigan, 1975).

Judkewitz, B.

Y. M. Wang, B. Judkewitz, C. H. DiMarzio, and C. A. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

Katz, O.

Krishnakumar, K.

K. Krishnakumar, “Micro-genetic algorithms for stationary and stationary non-stationary function optimization,” Proc. SPIE 1196, 1196 (1989).

Lagendijk, A.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[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, 193905 (2011).
[Crossref]

F. van Beijnum, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Frequency bandwidth of light focused through turbid media,” Opt. Lett. 36, 373–375 (2011).
[Crossref]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[Crossref]

Lai, P.

J. W. Tay, P. Lai, Y. Suzuki, and L. V. Wang, “Ultrasonically encoded wavefront shaping for focusing into random media,” Sci. Rep. 4, 3918 (2014).
[Crossref]

P. Lai, J. W. Tay, L. Wang, and L. V. Wang, “Optical focusing in scattering media with photoacoustic wavefront shaping (paws),” Proc. SPIE 8943, 894318 (2014).

P. Lai, L. Wang, J. W. Tay, and L. V. Wang, “Nonlinear photoacoustic wavefront shaping (paws) for single speckle-grain optical focusing in scattering media,” arXiv:1402.0816v1 (2014).

Leonetti, M.

M. Leonetti and C. Lopez, “Active subnanometer spectral control of a random laser,” Appl. Phys. Lett. 102, 071105 (2013).
[Crossref]

M. Leonetti, C. Conti, and C. Lopez, “Random laser tailored by directional stimulated emission,” Phys. Rev. A 85, 043841 (2012).
[Crossref]

Lerosey, G.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

Liang, J.

Lopez, C.

M. Leonetti and C. Lopez, “Active subnanometer spectral control of a random laser,” Appl. Phys. Lett. 102, 071105 (2013).
[Crossref]

M. Leonetti, C. Conti, and C. Lopez, “Random laser tailored by directional stimulated emission,” Phys. Rev. A 85, 043841 (2012).
[Crossref]

Loshchilov, I.

I. Loshchilov, M. Schoenauer, and M. Sebag, “Not all parents are equal for mo-cma-es,” in Evolutionary Multi-Criterion Optimization (Springer Verlag, 2011), pp. 31–45.

Lu, Y.

McCabe, D. J.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

Mertz, J.

Meyarivan, T.

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

Mosk, A. P.

H. Yilmaz, W. L. Vos, and A. P. Mosk, “Optimal control of light propagation through multiple-scattering media in the presence of noise,” Biomed. Opt. Express 4, 1759–1768 (2013).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[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, 193905 (2011).
[Crossref]

F. van Beijnum, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Frequency bandwidth of light focused through turbid media,” Opt. Lett. 36, 373–375 (2011).
[Crossref]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[Crossref]

I. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
[Crossref]

Myint, T.

R. Gunawidjaja, T. Myint, and H. Eilers, “Temperature-dependent phase changes in multicolored ErxYbyZr1−x−yO2/Eu0.02Y1.98O3 core/shell nanoparticles,” J. Phys. Chem. C 117, 14427–14434 (2013).
[Crossref]

Noblin, X.

N. Bachelard, S. Gigan, X. Noblin, and P. Sebbah, “Adaptive pumping for spectral control of random lasers,” Nature 10, 426–431 (2014).

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J. Nocedal and S. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).

Park, C.

Park, J. H.

Park, Y.

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Paxman, R.

Piestun, R.

Pratap, A.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: Nsga-ii,” IEEE Trans. Evol. Comput. 6, 182–197 (2002).

Sastry, K.

M. V. Butz, K. Sastry, and D. E. Goldberg, “Tournament selection in xcs,” in Proceedings of the Fifth Genetic and Evolutionary Computation Conference (Gecco-2003) (Association for Computing Machinery, 2002).

Schoenauer, M.

I. Loshchilov, M. Schoenauer, and M. Sebag, “Not all parents are equal for mo-cma-es,” in Evolutionary Multi-Criterion Optimization (Springer Verlag, 2011), pp. 31–45.

Sebag, M.

I. Loshchilov, M. Schoenauer, and M. Sebag, “Not all parents are equal for mo-cma-es,” in Evolutionary Multi-Criterion Optimization (Springer Verlag, 2011), pp. 31–45.

Sebbah, P.

N. Bachelard, S. Gigan, X. Noblin, and P. Sebbah, “Adaptive pumping for spectral control of random lasers,” Nature 10, 426–431 (2014).

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett. 109, 033903 (2012).
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P. K. Senecal, “Numerical optimization using the gen4 micro-genetic algorithm code” (University of Wisconsin-Madison, 2000).

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J. W. Tay, P. Lai, Y. Suzuki, and L. V. Wang, “Ultrasonically encoded wavefront shaping for focusing into random media,” Sci. Rep. 4, 3918 (2014).
[Crossref]

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D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
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J. W. Tay, P. Lai, Y. Suzuki, and L. V. Wang, “Ultrasonically encoded wavefront shaping for focusing into random media,” Sci. Rep. 4, 3918 (2014).
[Crossref]

P. Lai, J. W. Tay, L. Wang, and L. V. Wang, “Optical focusing in scattering media with photoacoustic wavefront shaping (paws),” Proc. SPIE 8943, 894318 (2014).

J. W. Tay, J. Liang, and L. V. Wang, “Amplitude-masked photoacoustic wavefront shaping and application in flowmetry,” Opt. Lett. 39, 5499–5502 (2014).
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Toussaint, K.

van Beijnum, F.

van Putten, E. G.

F. van Beijnum, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Frequency bandwidth of light focused through turbid media,” Opt. Lett. 36, 373–375 (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, 193905 (2011).
[Crossref]

Vellekoop, I.

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

I. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
[Crossref]

Vellekoop, I. M.

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[Crossref]

Vos, W. L.

H. Yilmaz, W. L. Vos, and A. P. Mosk, “Optimal control of light propagation through multiple-scattering media in the presence of noise,” Biomed. Opt. Express 4, 1759–1768 (2013).
[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, 193905 (2011).
[Crossref]

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D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

Wang, L.

P. Lai, J. W. Tay, L. Wang, and L. V. Wang, “Optical focusing in scattering media with photoacoustic wavefront shaping (paws),” Proc. SPIE 8943, 894318 (2014).

P. Lai, L. Wang, J. W. Tay, and L. V. Wang, “Nonlinear photoacoustic wavefront shaping (paws) for single speckle-grain optical focusing in scattering media,” arXiv:1402.0816v1 (2014).

Wang, L. V.

P. Lai, J. W. Tay, L. Wang, and L. V. Wang, “Optical focusing in scattering media with photoacoustic wavefront shaping (paws),” Proc. SPIE 8943, 894318 (2014).

J. W. Tay, P. Lai, Y. Suzuki, and L. V. Wang, “Ultrasonically encoded wavefront shaping for focusing into random media,” Sci. Rep. 4, 3918 (2014).
[Crossref]

J. W. Tay, J. Liang, and L. V. Wang, “Amplitude-masked photoacoustic wavefront shaping and application in flowmetry,” Opt. Lett. 39, 5499–5502 (2014).
[Crossref]

P. Lai, L. Wang, J. W. Tay, and L. V. Wang, “Nonlinear photoacoustic wavefront shaping (paws) for single speckle-grain optical focusing in scattering media,” arXiv:1402.0816v1 (2014).

Wang, Y. M.

Y. M. Wang, B. Judkewitz, C. H. DiMarzio, and C. A. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
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J. Nocedal and S. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).

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Y. M. Wang, B. Judkewitz, C. H. DiMarzio, and C. A. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

Yilmaz, H.

Yu, H.

Zhou, J.

Adv. Eng. Inf. (1)

E. Elbeltagi, T. Hegazy, and D. Grierson, “Comparison among five evolutionary-based optimization algorithms,” Adv. Eng. Inf. 19, 43–53 (2005).

Appl. Phys. Lett. (1)

M. Leonetti and C. Lopez, “Active subnanometer spectral control of a random laser,” Appl. Phys. Lett. 102, 071105 (2013).
[Crossref]

Biomed. Opt. Express (1)

Complex Syst. (1)

B. L. Miller, B. L. Miller, D. E. Goldberg, and D. E. Goldberg, “Genetic algorithms, tournament selection, and the effects of noise,” Complex Syst. 9, 193–212 (1995).

IEEE Trans. Evol. Comput. (1)

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: Nsga-ii,” IEEE Trans. Evol. Comput. 6, 182–197 (2002).

J. Phys. Chem. C (1)

R. Gunawidjaja, T. Myint, and H. Eilers, “Temperature-dependent phase changes in multicolored ErxYbyZr1−x−yO2/Eu0.02Y1.98O3 core/shell nanoparticles,” J. Phys. Chem. C 117, 14427–14434 (2013).
[Crossref]

Nat. Commun. (2)

Y. M. Wang, B. Judkewitz, C. H. DiMarzio, and C. A. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

Nat. Photonics (3)

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[Crossref]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

Nature (1)

N. Bachelard, S. Gigan, X. Noblin, and P. Sebbah, “Adaptive pumping for spectral control of random lasers,” Nature 10, 426–431 (2014).

Opt. Commun. (1)

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

Opt. Express (4)

Opt. Lett. (7)

Phys. Rev. A (2)

B. R. Anderson, R. Gunawidjaja, and H. Eilers, “Effect of experimental parameters on optimal transmission of light through opaque media,” Phys. Rev. A 90, 053826 (2014).
[Crossref]

M. Leonetti, C. Conti, and C. Lopez, “Random laser tailored by directional stimulated emission,” Phys. Rev. A 85, 043841 (2012).
[Crossref]

Phys. Rev. Lett. (2)

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett. 109, 033903 (2012).
[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, 193905 (2011).
[Crossref]

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[Crossref]

Proc. SPIE (2)

K. Krishnakumar, “Micro-genetic algorithms for stationary and stationary non-stationary function optimization,” Proc. SPIE 1196, 1196 (1989).

P. Lai, J. W. Tay, L. Wang, and L. V. Wang, “Optical focusing in scattering media with photoacoustic wavefront shaping (paws),” Proc. SPIE 8943, 894318 (2014).

Sci. Rep. (1)

J. W. Tay, P. Lai, Y. Suzuki, and L. V. Wang, “Ultrasonically encoded wavefront shaping for focusing into random media,” Sci. Rep. 4, 3918 (2014).
[Crossref]

Other (13)

S. Gigan and E. Bossy, “A photoacoustic transmission matrix for deep optical imaging,” in SPIE Newsroom (SPIE, 2014).

P. Lai, L. Wang, J. W. Tay, and L. V. Wang, “Nonlinear photoacoustic wavefront shaping (paws) for single speckle-grain optical focusing in scattering media,” arXiv:1402.0816v1 (2014).

P. K. Senecal, “Numerical optimization using the gen4 micro-genetic algorithm code” (University of Wisconsin-Madison, 2000).

J. Nocedal and S. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).

E. Zitzler, K. Deb, L. Thiele, C. C. Coello, and D. Corne, eds., Evolutionary Multi-Criterion Optimization, Vol. 1993 of Lecture Notes in Computer Science (Springer, 2001).

T. Back, Evolutionary Algorithms in Theory and Practice (Oxford University, 1996).

D. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

J. Holland, Adaptation in Natural and Artificial Systems (University of Michigan, 1975).

R. Haupt and S. Haupt, Practical Genetic Algorithms, 2nd ed. (Wiley, 2004).

In order to compare the three algorithms in Fig. 4 we plot the enhancements as a function of normalized iteration, such that the max number of iterations is set to one. For the IA the total number of iterations is 131,072 and for both GAs the total number of iterations is 12,000.

M. V. Butz, K. Sastry, and D. E. Goldberg, “Tournament selection in xcs,” in Proceedings of the Fifth Genetic and Evolutionary Computation Conference (Gecco-2003) (Association for Computing Machinery, 2002).

J. E. Baker, “Reducing bias and inefficiency in the selection algorithm,” in Proceedings of the Second International Conference on Genetic Algorithms and Their Application (L. Erlbaum Associates, 1987), pp. 14–21.

I. Loshchilov, M. Schoenauer, and M. Sebag, “Not all parents are equal for mo-cma-es,” in Evolutionary Multi-Criterion Optimization (Springer Verlag, 2011), pp. 31–45.

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Figures (6)

Fig. 1.
Fig. 1. SEM images of ZrO 2 nanoparticles at magnifications of 20 000 × and 200000 × . The particles are found to be spherical with diameters ranging between 80 and 300 nm.
Fig. 2.
Fig. 2. Histogram of NP diameters measured from SEM measurements. The mean diameter is 195 ± 32 nm .
Fig. 3.
Fig. 3. Enhancement as a function of the number of iterations for the IA, SGA, and μGA, where the stop condition for the GAs is an enhancement of 55. The μGA is found to be the fastest algorithm, with the SGA only being slightly faster than the IA.
Fig. 4.
Fig. 4. Enhancement as a function of normalized iteration using a noisy laser, short persistence time sample, and 4096 bins. The IA only results in a small enhancement of 3.9, while the μGA obtains an enhancement of 66 and the SGA an enhancement of 138.5.
Fig. 5.
Fig. 5. Number of iterations required to reach an enhancement of η = 43 as a function of the total number of bins for the SGA and μGA. Bins with a side length greater than 16 px are not shown as they are found to be unable to optimize to the target enhancement within a reasonable time frame.
Fig. 6.
Fig. 6. Peak enhancement as a function of the number of SLM bins for the SGA and μGA with a stop condition of 12,500 iterations.

Equations (1)

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P i = f i j W f j ,

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