Abstract

Speckles commonly satisfy Rayleigh statistics. However, in many applications, non-Rayleigh speckles with customized intensity statistics are desirable. Here, we present a general method for customizing the intensity statistics of speckle patterns on a target plane. By judiciously modulating the phase front of a monochromatic laser beam, we experimentally generate speckle patterns with arbitrarily tailored intensity probability density functions. Relative to Rayleigh speckles, our customized speckles exhibit radically different topologies yet maintain the same spatial correlation length. The customized speckles are fully developed, ergodic, and stationary–with circular non-Gaussian statistics for the complex field. Propagating away from the target plane, the customized speckles revert back to Rayleigh speckles. This work provides a versatile framework for tailoring speckle patterns with varied applications in microscopy, imaging, and optical manipulation.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]

2017 (3)

S. Akbar, R. Fickler, M. J. Padgett, and R. W. Boyd, “Generation of caustics and rogue waves from nonlinear instability,” Phys. Rev. Lett. 119, 203901 (2017).
[Crossref]

C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. D. Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13, 497–502 (2017).
[Crossref]

M. Guillon, B. C. Forget, A. J. Foust, V. De Sars, M. Ritsch-Marte, and V. Emiliani, “Vortex-free phase profiles for uniform patterning with computer-generated holography,” Opt. Express 25, 12640–12652 (2017).
[Crossref]

2016 (8)

T. Chaigne, J. Gateau, M. Allain, O. Katz, S. Gigan, A. Sentenac, and E. Bossy, “Super-resolution photoacoustic fluctuation imaging with multiple speckle illumination,” Optica 3, 54–57 (2016).
[Crossref]

H. E. Kondakci, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, “Sub-thermal to super-thermal light statistics from a disordered lattice via deterministic control of excitation symmetry,” Optica 3, 477–482 (2016).
[Crossref]

K. Kuplicki and K. W. C. Chan, “High-order ghost imaging using non-Rayleigh speckle sources,” Opt. Express 24, 26766–26776 (2016).
[Crossref]

J. Bewerunge and S. U. Egelhaaf, “Experimental creation and characterization of random potential-energy landscapes exploiting speckle patterns,” Phys. Rev. A 93, 013806 (2016).
[Crossref]

C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016).
[Crossref]

E. Pinçe, S. K. Velu, A. Callegari, P. Elahi, S. Gigan, G. Volpe, and G. Volpe, “Disorder-mediated crowd control in an active matter system,” Nat. Commun. 7, 10907 (2016).
[Crossref]

S. Zhang, W. Wang, R. Yu, and X. Yang, “High-order correlation of non-Rayleigh speckle fields and its application in super-resolution imaging,” Laser Phys. 26, 055007 (2016).
[Crossref]

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122, 82 (2016).
[Crossref]

2015 (4)

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[Crossref]

J. P. Amaral, E. J. S. Fonseca, and A. J. Jesus-Silva, “Tailoring speckles with Weibull intensity statistics,” Phys. Rev. A 92, 063851 (2015).
[Crossref]

E.-F. Zhang, W.-T. Liu, and P.-X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17, 085602 (2015).
[Crossref]

J. Yoon, K. Lee, J. Park, and Y. Park, “Measuring optical transmission matrices by wavefront shaping,” Opt. Express 23, 10158–10167 (2015).
[Crossref]

2014 (3)

G. Volpe, L. Kurz, A. Callegari, G. Volpe, and S. Gigan, “Speckle optical tweezers: micromanipulation with random light fields,” Opt. Express 22, 18159–18167 (2014).
[Crossref]

G. Volpe, G. Volpe, and S. Gigan, “Brownian motion in a speckle light field: tunable anomalous diffusion and selective optical manipulation,” Sci. Rep. 4, 3936 (2014).
[Crossref]

Y. Bromberg and H. Cao, “Generating non-Rayleigh speckles with tailored intensity statistics,” Phys. Rev. Lett. 112, 213904 (2014).
[Crossref]

2013 (3)

2012 (2)

K. M. Douglass, S. Sukhov, and A. Dogariu, “Superdiffusion in optically controlled active media,” Nat. Photonics 6, 834–837 (2012).
[Crossref]

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys. 8, 398–403 (2012).
[Crossref]

2011 (1)

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

2010 (2)

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, 100601 (2010).
[Crossref]

S. Kubota and J. W. Goodman, “Very efficient speckle contrast reduction realized by moving diffuser device,” Appl. Opt. 49, 4385–4391 (2010).
[Crossref]

2006 (1)

C. Ventalon and J. Mertz, “Dynamic speckle illumination microscopy with translated versus randomized speckle patterns,” Opt. Lett. 14, 7198–7209 (2006).
[Crossref]

1999 (1)

1994 (1)

1984 (1)

E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng. 23, 234453 (1984).
[Crossref]

1983 (1)

B. M. Levine and J. C. Dainty, “Non-Gaussian image plane speckle: measurements from diffusers of known statistics,” Opt. Commun. 45, 252–257 (1983).
[Crossref]

1982 (1)

1981 (1)

E. Jakeman and J. G. McWhirter, “Non-Gaussian scattering by a random phase screen,” Appl. Phys. B 26, 125–131 (1981).
[Crossref]

1980 (2)

J. C. Dainty, “An introduction to ‘Gaussian’ speckle,” Proc. SPIE 243, 2–8 (1980).

J. Nocedal, “Updating quasi-Newton matrices with limited storage,” Math. Comp. 35, 773–782 (1980).
[Crossref]

1976 (1)

1975 (2)

J. W. Goodman, “Dependence of image speckle contrast on surface roughness,” Opt. Commun. 14, 324–327 (1975).
[Crossref]

H. Fujii and T. Asakura, “Statistical properties of image speckle patterns in partially coherent light,” Nouv. Rev. Opt. 6, 5–14 (1975).
[Crossref]

1974 (2)

H. M. Pedersen, “The roughness dependence of partially developed, monochromatic speckle patterns,” Opt. Commun. 12, 156–159 (1974).
[Crossref]

H. Fujii and T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[Crossref]

1972 (1)

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

1970 (1)

J. C. Dainty, “Some statistical properties of random speckle patterns in coherent and partially coherent illumination,” J. Mod. Opt. 17, 761–772 (1970).
[Crossref]

Abouraddy, A. F.

Akbar, S.

S. Akbar, R. Fickler, M. J. Padgett, and R. W. Boyd, “Generation of caustics and rogue waves from nonlinear instability,” Phys. Rev. Lett. 119, 203901 (2017).
[Crossref]

Allain, M.

Amaral, J. P.

J. P. Amaral, E. J. S. Fonseca, and A. J. Jesus-Silva, “Tailoring speckles with Weibull intensity statistics,” Phys. Rev. A 92, 063851 (2015).
[Crossref]

Asakura, T.

H. Fujii and T. Asakura, “Statistical properties of image speckle patterns in partially coherent light,” Nouv. Rev. Opt. 6, 5–14 (1975).
[Crossref]

H. Fujii and T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[Crossref]

Aspect, A.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys. 8, 398–403 (2012).
[Crossref]

Bechinger, C.

C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016).
[Crossref]

Bernard, A.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys. 8, 398–403 (2012).
[Crossref]

Bewerunge, J.

J. Bewerunge and S. U. Egelhaaf, “Experimental creation and characterization of random potential-energy landscapes exploiting speckle patterns,” Phys. Rev. A 93, 013806 (2016).
[Crossref]

Boccara, A. C.

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, 100601 (2010).
[Crossref]

Bossy, E.

Bouyer, P.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys. 8, 398–403 (2012).
[Crossref]

Boyd, R. W.

S. Akbar, R. Fickler, M. J. Padgett, and R. W. Boyd, “Generation of caustics and rogue waves from nonlinear instability,” Phys. Rev. Lett. 119, 203901 (2017).
[Crossref]

Bromberg, Y.

Y. Bromberg and H. Cao, “Generating non-Rayleigh speckles with tailored intensity statistics,” Phys. Rev. Lett. 112, 213904 (2014).
[Crossref]

Callegari, A.

E. Pinçe, S. K. Velu, A. Callegari, P. Elahi, S. Gigan, G. Volpe, and G. Volpe, “Disorder-mediated crowd control in an active matter system,” Nat. Commun. 7, 10907 (2016).
[Crossref]

G. Volpe, L. Kurz, A. Callegari, G. Volpe, and S. Gigan, “Speckle optical tweezers: micromanipulation with random light fields,” Opt. Express 22, 18159–18167 (2014).
[Crossref]

Cao, H.

C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. D. Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13, 497–502 (2017).
[Crossref]

Y. Bromberg and H. Cao, “Generating non-Rayleigh speckles with tailored intensity statistics,” Phys. Rev. Lett. 112, 213904 (2014).
[Crossref]

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, 100601 (2010).
[Crossref]

Chaigne, T.

Chan, K. W. C.

Cheinet, P.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys. 8, 398–403 (2012).
[Crossref]

Chen, P.-X.

E.-F. Zhang, W.-T. Liu, and P.-X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17, 085602 (2015).
[Crossref]

Cho, Y.-W.

Christodoulides, D. N.

Cižmár, T.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

Correia, R. R. B.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[Crossref]

Dainty, J. C.

B. M. Levine and J. C. Dainty, “Non-Gaussian image plane speckle: measurements from diffusers of known statistics,” Opt. Commun. 45, 252–257 (1983).
[Crossref]

J. C. Dainty, “An introduction to ‘Gaussian’ speckle,” Proc. SPIE 243, 2–8 (1980).

J. C. Dainty, “Some statistical properties of random speckle patterns in coherent and partially coherent illumination,” J. Mod. Opt. 17, 761–772 (1970).
[Crossref]

J. C. Dainty, Laser Speckle and Related Phenomena, Topics in Applied Physics (Springer, 2013).

De Sars, V.

Dholakia, K.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

Di Leonardo, R.

C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016).
[Crossref]

Dixit, S. N.

Dogariu, A.

K. M. Douglass, S. Sukhov, and A. Dogariu, “Superdiffusion in optically controlled active media,” Nat. Photonics 6, 834–837 (2012).
[Crossref]

Douglass, K. M.

K. M. Douglass, S. Sukhov, and A. Dogariu, “Superdiffusion in optically controlled active media,” Nat. Photonics 6, 834–837 (2012).
[Crossref]

Egelhaaf, S. U.

J. Bewerunge and S. U. Egelhaaf, “Experimental creation and characterization of random potential-energy landscapes exploiting speckle patterns,” Phys. Rev. A 93, 013806 (2016).
[Crossref]

Eimerl, D.

Elahi, P.

E. Pinçe, S. K. Velu, A. Callegari, P. Elahi, S. Gigan, G. Volpe, and G. Volpe, “Disorder-mediated crowd control in an active matter system,” Nat. Commun. 7, 10907 (2016).
[Crossref]

Emiliani, V.

Fickler, R.

S. Akbar, R. Fickler, M. J. Padgett, and R. W. Boyd, “Generation of caustics and rogue waves from nonlinear instability,” Phys. Rev. Lett. 119, 203901 (2017).
[Crossref]

Fink, 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, 100601 (2010).
[Crossref]

Fischer, R.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[Crossref]

Fonseca, E. J. S.

J. P. Amaral, E. J. S. Fonseca, and A. J. Jesus-Silva, “Tailoring speckles with Weibull intensity statistics,” Phys. Rev. A 92, 063851 (2015).
[Crossref]

Forget, B. C.

Foust, A. J.

Fujii, H.

H. Fujii and T. Asakura, “Statistical properties of image speckle patterns in partially coherent light,” Nouv. Rev. Opt. 6, 5–14 (1975).
[Crossref]

H. Fujii and T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[Crossref]

Gateau, J.

Gerchberg, R. W.

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

Gigan, S.

E. Pinçe, S. K. Velu, A. Callegari, P. Elahi, S. Gigan, G. Volpe, and G. Volpe, “Disorder-mediated crowd control in an active matter system,” Nat. Commun. 7, 10907 (2016).
[Crossref]

T. Chaigne, J. Gateau, M. Allain, O. Katz, S. Gigan, A. Sentenac, and E. Bossy, “Super-resolution photoacoustic fluctuation imaging with multiple speckle illumination,” Optica 3, 54–57 (2016).
[Crossref]

G. Volpe, L. Kurz, A. Callegari, G. Volpe, and S. Gigan, “Speckle optical tweezers: micromanipulation with random light fields,” Opt. Express 22, 18159–18167 (2014).
[Crossref]

G. Volpe, G. Volpe, and S. Gigan, “Brownian motion in a speckle light field: tunable anomalous diffusion and selective optical manipulation,” Sci. Rep. 4, 3936 (2014).
[Crossref]

J. Gateau, T. Chaigne, O. Katz, S. Gigan, and E. Bossy, “Improving visibility in photoacoustic imaging using dynamic speckle illumination,” Opt. Lett. 38, 5188–5191 (2013).
[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, 100601 (2010).
[Crossref]

Gilboa, D.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[Crossref]

Goetschy, A.

C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. D. Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13, 497–502 (2017).
[Crossref]

Goodman, J. W.

S. Kubota and J. W. Goodman, “Very efficient speckle contrast reduction realized by moving diffuser device,” Appl. Opt. 49, 4385–4391 (2010).
[Crossref]

J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145–1150 (1976).
[Crossref]

J. W. Goodman, “Dependence of image speckle contrast on surface roughness,” Opt. Commun. 14, 324–327 (1975).
[Crossref]

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).

Guillon, M.

Haist, T.

Hickman, J.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[Crossref]

Hsu, C. W.

C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. D. Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13, 497–502 (2017).
[Crossref]

Jakeman, E.

E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng. 23, 234453 (1984).
[Crossref]

E. Jakeman and J. G. McWhirter, “Non-Gaussian scattering by a random phase screen,” Appl. Phys. B 26, 125–131 (1981).
[Crossref]

Jendrzejewski, F.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys. 8, 398–403 (2012).
[Crossref]

Jesus-Silva, A. J.

J. P. Amaral, E. J. S. Fonseca, and A. J. Jesus-Silva, “Tailoring speckles with Weibull intensity statistics,” Phys. Rev. A 92, 063851 (2015).
[Crossref]

Josse, V.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys. 8, 398–403 (2012).
[Crossref]

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Kelly, D. P.

Kim, Y.-H.

Kondakci, H. E.

Kubota, S.

Kuplicki, K.

Kurz, L.

Lee, K.

Lerosey, G.

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, 100601 (2010).
[Crossref]

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B. M. Levine and J. C. Dainty, “Non-Gaussian image plane speckle: measurements from diffusers of known statistics,” Opt. Commun. 45, 252–257 (1983).
[Crossref]

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Li, H.

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122, 82 (2016).
[Crossref]

Li, X.

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122, 82 (2016).
[Crossref]

Liew, S. F.

C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. D. Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13, 497–502 (2017).
[Crossref]

Liu, W.-T.

E.-F. Zhang, W.-T. Liu, and P.-X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17, 085602 (2015).
[Crossref]

Löwen, H.

C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016).
[Crossref]

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E. Jakeman and J. G. McWhirter, “Non-Gaussian scattering by a random phase screen,” Appl. Phys. B 26, 125–131 (1981).
[Crossref]

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C. Ventalon and J. Mertz, “Dynamic speckle illumination microscopy with translated versus randomized speckle patterns,” Opt. Lett. 14, 7198–7209 (2006).
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F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys. 8, 398–403 (2012).
[Crossref]

Nie, Z.

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122, 82 (2016).
[Crossref]

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J. Nocedal, “Updating quasi-Newton matrices with limited storage,” Math. Comp. 35, 773–782 (1980).
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Oh, J.-E.

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S. Akbar, R. Fickler, M. J. Padgett, and R. W. Boyd, “Generation of caustics and rogue waves from nonlinear instability,” Phys. Rev. Lett. 119, 203901 (2017).
[Crossref]

Park, J.

Park, Y.

Pau, S.

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H. M. Pedersen, “The roughness dependence of partially developed, monochromatic speckle patterns,” Opt. Commun. 12, 156–159 (1974).
[Crossref]

Pezzé, L.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys. 8, 398–403 (2012).
[Crossref]

Pinçe, E.

E. Pinçe, S. K. Velu, A. Callegari, P. Elahi, S. Gigan, G. Volpe, and G. Volpe, “Disorder-mediated crowd control in an active matter system,” Nat. Commun. 7, 10907 (2016).
[Crossref]

Piraud, M.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys. 8, 398–403 (2012).
[Crossref]

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, 100601 (2010).
[Crossref]

Prado, S. D.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[Crossref]

Reicherter, M.

Reichhardt, C.

C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016).
[Crossref]

Ribeiro-Teixeira, A. C.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[Crossref]

Ritsch-Marte, M.

Saleh, B. E. A.

Sanchez-Palencia, L.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys. 8, 398–403 (2012).
[Crossref]

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

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Sentenac, A.

Sheridan, J. T.

Silberberg, Y.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[Crossref]

Stone, A. D.

C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. D. Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13, 497–502 (2017).
[Crossref]

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K. M. Douglass, S. Sukhov, and A. Dogariu, “Superdiffusion in optically controlled active media,” Nat. Photonics 6, 834–837 (2012).
[Crossref]

Szameit, A.

Tai, Y.

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122, 82 (2016).
[Crossref]

Tiziani, H. J.

Velu, S. K.

E. Pinçe, S. K. Velu, A. Callegari, P. Elahi, S. Gigan, G. Volpe, and G. Volpe, “Disorder-mediated crowd control in an active matter system,” Nat. Commun. 7, 10907 (2016).
[Crossref]

Ventalon, C.

C. Ventalon and J. Mertz, “Dynamic speckle illumination microscopy with translated versus randomized speckle patterns,” Opt. Lett. 14, 7198–7209 (2006).
[Crossref]

Vidal, I.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[Crossref]

Volpe, G.

C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016).
[Crossref]

C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016).
[Crossref]

E. Pinçe, S. K. Velu, A. Callegari, P. Elahi, S. Gigan, G. Volpe, and G. Volpe, “Disorder-mediated crowd control in an active matter system,” Nat. Commun. 7, 10907 (2016).
[Crossref]

E. Pinçe, S. K. Velu, A. Callegari, P. Elahi, S. Gigan, G. Volpe, and G. Volpe, “Disorder-mediated crowd control in an active matter system,” Nat. Commun. 7, 10907 (2016).
[Crossref]

G. Volpe, L. Kurz, A. Callegari, G. Volpe, and S. Gigan, “Speckle optical tweezers: micromanipulation with random light fields,” Opt. Express 22, 18159–18167 (2014).
[Crossref]

G. Volpe, L. Kurz, A. Callegari, G. Volpe, and S. Gigan, “Speckle optical tweezers: micromanipulation with random light fields,” Opt. Express 22, 18159–18167 (2014).
[Crossref]

G. Volpe, G. Volpe, and S. Gigan, “Brownian motion in a speckle light field: tunable anomalous diffusion and selective optical manipulation,” Sci. Rep. 4, 3936 (2014).
[Crossref]

G. Volpe, G. Volpe, and S. Gigan, “Brownian motion in a speckle light field: tunable anomalous diffusion and selective optical manipulation,” Sci. Rep. 4, 3936 (2014).
[Crossref]

Wagemann, E. U.

Wang, H.

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122, 82 (2016).
[Crossref]

Wang, J.

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122, 82 (2016).
[Crossref]

Wang, W.

S. Zhang, W. Wang, R. Yu, and X. Yang, “High-order correlation of non-Rayleigh speckle fields and its application in super-resolution imaging,” Laser Phys. 26, 055007 (2016).
[Crossref]

Yang, X.

S. Zhang, W. Wang, R. Yu, and X. Yang, “High-order correlation of non-Rayleigh speckle fields and its application in super-resolution imaging,” Laser Phys. 26, 055007 (2016).
[Crossref]

Yoon, J.

Yu, R.

S. Zhang, W. Wang, R. Yu, and X. Yang, “High-order correlation of non-Rayleigh speckle fields and its application in super-resolution imaging,” Laser Phys. 26, 055007 (2016).
[Crossref]

Zhang, E.-F.

E.-F. Zhang, W.-T. Liu, and P.-X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17, 085602 (2015).
[Crossref]

Zhang, S.

S. Zhang, W. Wang, R. Yu, and X. Yang, “High-order correlation of non-Rayleigh speckle fields and its application in super-resolution imaging,” Laser Phys. 26, 055007 (2016).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (2)

E. Jakeman and J. G. McWhirter, “Non-Gaussian scattering by a random phase screen,” Appl. Phys. B 26, 125–131 (1981).
[Crossref]

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122, 82 (2016).
[Crossref]

J. Mod. Opt. (1)

J. C. Dainty, “Some statistical properties of random speckle patterns in coherent and partially coherent illumination,” J. Mod. Opt. 17, 761–772 (1970).
[Crossref]

J. Opt. (1)

E.-F. Zhang, W.-T. Liu, and P.-X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17, 085602 (2015).
[Crossref]

J. Opt. Soc. Am. (2)

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

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

Laser Phys. (1)

S. Zhang, W. Wang, R. Yu, and X. Yang, “High-order correlation of non-Rayleigh speckle fields and its application in super-resolution imaging,” Laser Phys. 26, 055007 (2016).
[Crossref]

Math. Comp. (1)

J. Nocedal, “Updating quasi-Newton matrices with limited storage,” Math. Comp. 35, 773–782 (1980).
[Crossref]

Nat. Commun. (1)

E. Pinçe, S. K. Velu, A. Callegari, P. Elahi, S. Gigan, G. Volpe, and G. Volpe, “Disorder-mediated crowd control in an active matter system,” Nat. Commun. 7, 10907 (2016).
[Crossref]

Nat. Photonics (2)

K. M. Douglass, S. Sukhov, and A. Dogariu, “Superdiffusion in optically controlled active media,” Nat. Photonics 6, 834–837 (2012).
[Crossref]

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

Nat. Phys. (2)

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys. 8, 398–403 (2012).
[Crossref]

C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. D. Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13, 497–502 (2017).
[Crossref]

Nouv. Rev. Opt. (1)

H. Fujii and T. Asakura, “Statistical properties of image speckle patterns in partially coherent light,” Nouv. Rev. Opt. 6, 5–14 (1975).
[Crossref]

Opt. Commun. (4)

H. M. Pedersen, “The roughness dependence of partially developed, monochromatic speckle patterns,” Opt. Commun. 12, 156–159 (1974).
[Crossref]

B. M. Levine and J. C. Dainty, “Non-Gaussian image plane speckle: measurements from diffusers of known statistics,” Opt. Commun. 45, 252–257 (1983).
[Crossref]

J. W. Goodman, “Dependence of image speckle contrast on surface roughness,” Opt. Commun. 14, 324–327 (1975).
[Crossref]

H. Fujii and T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[Crossref]

Opt. Eng. (1)

E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng. 23, 234453 (1984).
[Crossref]

Opt. Express (4)

Opt. Lett. (4)

Optica (2)

Optik (1)

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

Phys. Rev. A (2)

J. Bewerunge and S. U. Egelhaaf, “Experimental creation and characterization of random potential-energy landscapes exploiting speckle patterns,” Phys. Rev. A 93, 013806 (2016).
[Crossref]

J. P. Amaral, E. J. S. Fonseca, and A. J. Jesus-Silva, “Tailoring speckles with Weibull intensity statistics,” Phys. Rev. A 92, 063851 (2015).
[Crossref]

Phys. Rev. Lett. (4)

S. Akbar, R. Fickler, M. J. Padgett, and R. W. Boyd, “Generation of caustics and rogue waves from nonlinear instability,” Phys. Rev. Lett. 119, 203901 (2017).
[Crossref]

Y. Bromberg and H. Cao, “Generating non-Rayleigh speckles with tailored intensity statistics,” Phys. Rev. Lett. 112, 213904 (2014).
[Crossref]

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[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, 100601 (2010).
[Crossref]

Proc. SPIE (1)

J. C. Dainty, “An introduction to ‘Gaussian’ speckle,” Proc. SPIE 243, 2–8 (1980).

Rev. Mod. Phys. (1)

C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016).
[Crossref]

Sci. Rep. (1)

G. Volpe, G. Volpe, and S. Gigan, “Brownian motion in a speckle light field: tunable anomalous diffusion and selective optical manipulation,” Sci. Rep. 4, 3936 (2014).
[Crossref]

Other (3)

J. C. Dainty, Laser Speckle and Related Phenomena, Topics in Applied Physics (Springer, 2013).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).

S. G. Johnson, “The NLopt nonlinear-optimization package,” 2011, http://ab-initio.mit.edu/nlopt . We use the low-storage BFGS algorithm, which converges to the target pattern within 10,000 iterations: with an error less than 10%. The intensity PDF of the obtained pattern is the same as that of the target pattern.

Supplementary Material (1)

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» Supplement 1       Supplementary Document

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Figures (4)

Fig. 1.
Fig. 1. (a) Rayleigh speckle pattern and (b–e) customized speckle patterns with distinct intensity statistics. In the top row, each pattern has a size of 504 μm by 504 μm, and the maximum intensity is normalized to 1. The associated PDF, shown in the lower row, is (b) uniform, (c) increasing linearly, (d) peaked at a non-zero intensity, and (e) bimodal, within a predefined range of intensity. The red solid curves are experimental data, whereas the blue dashed curves are from numerically generated target speckle patterns. Both are a result of spatial and ensemble averaging over 50 independent speckle patterns.
Fig. 2.
Fig. 2. Characteristics of customized speckle patterns. (a) The phase histogram of the speckle fields demonstrates that they are all fully developed speckles. (b) The spatial field correlation function, |CE(|Δr|)|2, and (c) the spatial intensity correlation function, CI(|Δr|), for the customized speckles, remain the same as in Rayleigh speckles. In panels (a–c), the four customized speckle patterns have constant (black), linearly increasing (red), unimodal (blue), and bimodal (green) PDFs, and the purple is for Rayleigh speckles. (d) Comparing |CE(|Δr|)|2 (black curve) to CI(|Δr|) (blue dashed curve), both averaged over the five curves in (b) and (c), respectively, to confirm that they have the same correlation width.
Fig. 3.
Fig. 3. Statistical properties of the customized speckle patterns with a bimodal intensity PDF. (a) The spatially averaged intensity PDF, PS(I), of 2500 speckle patterns verifies that the speckle patterns are stationary. (b) The ensemble-averaged intensity PDF, PE(I)–within the area of a single speckle grain — for each spatial position in a pattern confirms that the speckles are ergodic. (c) The complex-amplitude joint PDF for the speckle field, P(Re[E],Im[E]), displays circular non-Gaussian statistics. (d) The joint PDF for two intensities, P(I1,I2), at spatial positions separated by approximately one speckle grain size (twice the spatial intensity correlation width) are uncorrelated. The results in panels (c, d) are obtained from averaging over space and 100 speckle patterns; a digital low-pass Fourier filter is applied to remove noise.
Fig. 4.
Fig. 4. Evolution of customized speckle patterns upon axial propagation. The intensity PDF at the Fourier plane of the SLM (z=0) is (a) increasing linearly and (e) bimodal. The distance from the Fourier plane is (b, f) Rl/5, (c, g) (2/5)Rl, and (d, h) (10/7)Rl.

Tables (1)

Tables Icon

Table 1. Intensity Moments of Speckle Patterns with Different Intensity PDFs

Equations (2)

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P(I)dI=F(I˜)dI˜.
0IeIdI=I˜minI˜F(I˜)dI˜.

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