Abstract

Incoherently illuminated or luminescent objects give rise to a low-contrast speckle-like pattern when observed through a thin diffusive medium, as such a medium effectively convolves their shape with a speckle-like point spread function (PSF). This point spread function can be extracted in the presence of a reference object of known shape. Here it is shown that reference objects that are both spatially and spectrally separated from the object of interest can be used to obtain an approximation of the point spread function. The crucial observation, corroborated by analytical calculations, is that the spectrally shifted point spread function is strongly correlated to a spatially scaled one. With the approximate point spread function thus obtained, the speckle-like pattern is deconvolved to produce a clear and sharp image of the object on a speckle-like background of low intensity.

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

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2018 (4)

M. Hofer, C. Soeller, S. Brasselet, and J. Bertolotti, “Wide field fluorescence epi-microscopy behind a scattering medium enabled by speckle correlations,” Opt. Express 26, 9866–9881 (2018).

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8, 4585 (2018).

N. Antipa, G. Kuo, R. Heckel, B. Mildenhall, E. Bostan, R. Ng, and L. Waller, “DiffuserCam: lensless single-exposure 3D imaging,” Optica 5(1), 1–9 (2018).

S. Mukherjee, A. Vijayakumar, M. Kumar, and J. Rosen, “3D imaging through scatterers with interferenceless optical system,” Sci. Rep. 8, 1134 (2018).

2017 (7)

2016 (4)

E. Edrei and G. Scarcelli, “Optical imaging through dynamic turbid media using the Fourier-domain shower-curtain effect,” Optica 3, 71–74 (2016).

J. A. Newman, Q. Luo, and K. J. Webb, “Imaging Hidden Objects with Spatial Speckle Intensity Correlations over Object Position,” Phys. Rev. Lett. 116, 073902 (2016).

H. Zhuang, H. He, X. Xie, and J. Zhou, “High speed color imaging through scattering media with a large field of view,” Sci. Rep. 6, 32696 (2016).

E. Edrei and G. Scarcelli, “Memory-effect based deconvolution microscopy for super-resolution imaging through scattering media,” Sci. Rep. 6, 33558 (2016).

2015 (2)

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).

S. Schott, J. Bertolotti, J. F. Leger, L. Bourdieu, and S. Gigan, “Characterization of the angular memory effect of scattered light in biological tissues,” Opt. Express 23, 13505–13516 (2015).

2014 (5)

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).

K. T. Takasaki and J. W. Fleischer, “Phase-space measurement for depth-resolved memory-effect imaging,” Opt. Express 22, 31426–31433 (2014).

C. Ma, X. Xu, Y. Liu, and L. Wang, “Time-reversed adapted-perturbation (TRAP) optical focusing onto dynamic objects inside scattering media,” Nat. Photonics 8, 931–936 (2014).

J. A. Newman and K. J. Webb, “Imaging optical fields through heavily scattering media,” Phys. Rev. Lett. 113, 263903 (2014).

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).

2013 (1)

2012 (6)

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound pulse guided digital phase conjugation,” Nat. Photonics 6, 657–661 (2012).

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

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).

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).

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, 203901 (2012).

2010 (3)

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).

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).

C.-L. Hsieh, Y. Pu, R. Grange, G. Laporte, and D. Psaltis, “Imaging through turbid layers by scanning the phase conjugated second harmonic radiation from a nanoparticle,” Opt. Express 18, 20723–20731 (2010).

2007 (1)

1990 (1)

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

1988 (2)

I. Freund, M. Rosenbluh, and S. Feng, “Memory Effects in Propagation of Optical Waves through Disordered Media,” Phys. Rev. Lett. 61, 2328–2331 (1988).

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and Fluctuations of Coherent Wave Transmission through Disordered Media,” Phys. Rev. Lett. 61, 834–837 (1988).

1982 (1)

1950 (1)

H. G. Booker, J. A. Ratcliffe, and D. H. Shinn, “Diffraction from an irregular screen with applications to ionospheric problems,” Philos. Trans. R. Soc. Lond. A 242, 579–607 (1950).

Antipa, N.

Bertolotti, J.

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).

Boccara, A. C.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).

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).

Booker, H. G.

H. G. Booker, J. A. Ratcliffe, and D. H. Shinn, “Diffraction from an irregular screen with applications to ionospheric problems,” Philos. Trans. R. Soc. Lond. A 242, 579–607 (1950).

Bostan, E.

Bourdieu, L.

Brasselet, S.

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).

Chen, Y.

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).

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, 203901 (2012).

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, 203901 (2012).

Cua, M.

Cui, M.

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound pulse guided digital phase conjugation,” Nat. Photonics 6, 657–661 (2012).

Dang, C.

Dasari, R. R.

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, 203901 (2012).

DiMarzio, C. A.

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

Dong, J.

Edrei, E.

E. Edrei and G. Scarcelli, “Optical imaging through dynamic turbid media using the Fourier-domain shower-curtain effect,” Optica 3, 71–74 (2016).

E. Edrei and G. Scarcelli, “Memory-effect based deconvolution microscopy for super-resolution imaging through scattering media,” Sci. Rep. 6, 33558 (2016).

Fang-Yen, C.

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, 203901 (2012).

Feng, S.

I. Freund, M. Rosenbluh, and S. Feng, “Memory Effects in Propagation of Optical Waves through Disordered Media,” Phys. Rev. Lett. 61, 2328–2331 (1988).

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and Fluctuations of Coherent Wave Transmission through Disordered Media,” Phys. Rev. Lett. 61, 834–837 (1988).

Fienup, J. R.

Fink, M.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).

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).

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).

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).

Fiolka, R.

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound pulse guided digital phase conjugation,” Nat. Photonics 6, 657–661 (2012).

Fleischer, J. W.

French, R.

Freund, I.

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

I. Freund, M. Rosenbluh, and S. Feng, “Memory Effects in Propagation of Optical Waves through Disordered Media,” Phys. Rev. Lett. 61, 2328–2331 (1988).

Gigan, S.

R. French, S. Gigan, and O. L. Muskens, “Speckle-based hyperspectral imaging combining multiple scattering and compressive sensing in nanowire mats,” Opt. Lett. 42, 1820–1823 (2017).

T. Wu, J. Dong, X. Shao, and S. Gigan, “Imaging through a thin scattering layer and jointly retrieving the point-spread-function using phase-diversity,” Opt. Express 25, 27182–27194 (2017).

S. Schott, J. Bertolotti, J. F. Leger, L. Bourdieu, and S. Gigan, “Characterization of the angular memory effect of scattered light in biological tissues,” Opt. Express 23, 13505–13516 (2015).

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).

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).

Grange, R.

Guan, Y.

He, H.

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8, 4585 (2018).

X. Xu, X. Xie, H. He, H. Zhuang, J. Zhou, A. Thendiyammal, and A. P. Mosk, “Imaging objects through scattering layers and around corners by retrieval of the scattered point spread function,” Opt. Express 25, 32829–32840 (2017).

H. Zhuang, H. He, X. Xie, and J. Zhou, “High speed color imaging through scattering media with a large field of view,” Sci. Rep. 6, 32696 (2016).

H. He, Y. Guan, and J. Zhou, “Image restoration through thin turbid layers by correlation with a known object,” Opt. Express 21, 12539–12545 (2013).

Heckel, R.

Heidmann, P.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).

Hofer, M.

Horstmeyer, R.

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).

Hsieh, C.-L.

Judkewitz, B.

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).

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

Kane, C.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and Fluctuations of Coherent Wave Transmission through Disordered Media,” Phys. Rev. Lett. 61, 834–837 (1988).

Katz, O.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).

Kim, M.

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, 203901 (2012).

Kumar, M.

S. Mukherjee, A. Vijayakumar, M. Kumar, and J. Rosen, “3D imaging through scatterers with interferenceless optical system,” Sci. Rep. 8, 1134 (2018).

Kuo, G.

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).

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).

Laporte, G.

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, 203901 (2012).

Lee, P. A.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and Fluctuations of Coherent Wave Transmission through Disordered Media,” Phys. Rev. Lett. 61, 834–837 (1988).

Leger, J. F.

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).

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).

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).

Liang, H.

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8, 4585 (2018).

Liu, Y.

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8, 4585 (2018).

Y. Shi, Y. Liu, J. Wang, and T. Wu, “Non-invasive depth-resolved imaging through scattering layers via speckle correlations and parallax,” Appl. Phys. Lett. 110, 231101 (2017).

C. Ma, X. Xu, Y. Liu, and L. Wang, “Time-reversed adapted-perturbation (TRAP) optical focusing onto dynamic objects inside scattering media,” Nat. Photonics 8, 931–936 (2014).

Luo, Q.

J. A. Newman, Q. Luo, and K. J. Webb, “Imaging Hidden Objects with Spatial Speckle Intensity Correlations over Object Position,” Phys. Rev. Lett. 116, 073902 (2016).

Ma, C.

C. Ma, X. Xu, Y. Liu, and L. Wang, “Time-reversed adapted-perturbation (TRAP) optical focusing onto dynamic objects inside scattering media,” Nat. Photonics 8, 931–936 (2014).

Mildenhall, B.

Mosk, A. P.

X. Xu, X. Xie, H. He, H. Zhuang, J. Zhou, A. Thendiyammal, and A. P. Mosk, “Imaging objects through scattering layers and around corners by retrieval of the scattered point spread function,” Opt. Express 25, 32829–32840 (2017).

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).

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).

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309–2311 (2007).

Mukherjee, S.

S. Mukherjee, A. Vijayakumar, M. Kumar, and J. Rosen, “3D imaging through scatterers with interferenceless optical system,” Sci. Rep. 8, 1134 (2018).

Muskens, O. L.

Naik, D. N.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6, e16219 (2017).

Newman, J. A.

J. A. Newman, Q. Luo, and K. J. Webb, “Imaging Hidden Objects with Spatial Speckle Intensity Correlations over Object Position,” Phys. Rev. Lett. 116, 073902 (2016).

J. A. Newman and K. J. Webb, “Imaging optical fields through heavily scattering media,” Phys. Rev. Lett. 113, 263903 (2014).

Ng, R.

Osten, W.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6, e16219 (2017).

Papadopoulos, I. N.

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).

Pedrini, G.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6, e16219 (2017).

Popoff, S.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).

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).

Psaltis, D.

Pu, Y.

Ratcliffe, J. A.

H. G. Booker, J. A. Ratcliffe, and D. H. Shinn, “Diffraction from an irregular screen with applications to ionospheric problems,” Philos. Trans. R. Soc. Lond. A 242, 579–607 (1950).

Rosen, J.

S. Mukherjee, A. Vijayakumar, M. Kumar, and J. Rosen, “3D imaging through scatterers with interferenceless optical system,” Sci. Rep. 8, 1134 (2018).

Rosenbluh, M.

I. Freund, M. Rosenbluh, and S. Feng, “Memory Effects in Propagation of Optical Waves through Disordered Media,” Phys. Rev. Lett. 61, 2328–2331 (1988).

Sahoo, S.

Scarcelli, G.

E. Edrei and G. Scarcelli, “Optical imaging through dynamic turbid media using the Fourier-domain shower-curtain effect,” Optica 3, 71–74 (2016).

E. Edrei and G. Scarcelli, “Memory-effect based deconvolution microscopy for super-resolution imaging through scattering media,” Sci. Rep. 6, 33558 (2016).

Schott, S.

Shao, X.

Shi, Y.

Y. Shi, Y. Liu, J. Wang, and T. Wu, “Non-invasive depth-resolved imaging through scattering layers via speckle correlations and parallax,” Appl. Phys. Lett. 110, 231101 (2017).

Shinn, D. H.

H. G. Booker, J. A. Ratcliffe, and D. H. Shinn, “Diffraction from an irregular screen with applications to ionospheric problems,” Philos. Trans. R. Soc. Lond. A 242, 579–607 (1950).

Si, K.

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound pulse guided digital phase conjugation,” Nat. Photonics 6, 657–661 (2012).

Silberberg, Y.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).

Singh, A. K.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6, e16219 (2017).

Small, E.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).

Soeller, C.

Stone, A. D.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and Fluctuations of Coherent Wave Transmission through Disordered Media,” Phys. Rev. Lett. 61, 834–837 (1988).

Takasaki, K. T.

Takeda, M.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6, e16219 (2017).

Tang, D.

Thendiyammal, A.

van Putten, E. G.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).

Vellekoop, I. M.

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309–2311 (2007).

Vijayakumar, A.

S. Mukherjee, A. Vijayakumar, M. Kumar, and J. Rosen, “3D imaging through scatterers with interferenceless optical system,” Sci. Rep. 8, 1134 (2018).

Vos, W. L.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).

Waller, L.

Wang, J.

Y. Shi, Y. Liu, J. Wang, and T. Wu, “Non-invasive depth-resolved imaging through scattering layers via speckle correlations and parallax,” Appl. Phys. Lett. 110, 231101 (2017).

Wang, L.

C. Ma, X. Xu, Y. Liu, and L. Wang, “Time-reversed adapted-perturbation (TRAP) optical focusing onto dynamic objects inside scattering media,” Nat. Photonics 8, 931–936 (2014).

Wang, Y. M.

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

Webb, K. J.

J. A. Newman, Q. Luo, and K. J. Webb, “Imaging Hidden Objects with Spatial Speckle Intensity Correlations over Object Position,” Phys. Rev. Lett. 116, 073902 (2016).

J. A. Newman and K. J. Webb, “Imaging optical fields through heavily scattering media,” Phys. Rev. Lett. 113, 263903 (2014).

Wu, T.

Y. Shi, Y. Liu, J. Wang, and T. Wu, “Non-invasive depth-resolved imaging through scattering layers via speckle correlations and parallax,” Appl. Phys. Lett. 110, 231101 (2017).

T. Wu, J. Dong, X. Shao, and S. Gigan, “Imaging through a thin scattering layer and jointly retrieving the point-spread-function using phase-diversity,” Opt. Express 25, 27182–27194 (2017).

Xie, X.

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8, 4585 (2018).

X. Xu, X. Xie, H. He, H. Zhuang, J. Zhou, A. Thendiyammal, and A. P. Mosk, “Imaging objects through scattering layers and around corners by retrieval of the scattered point spread function,” Opt. Express 25, 32829–32840 (2017).

H. Zhuang, H. He, X. Xie, and J. Zhou, “High speed color imaging through scattering media with a large field of view,” Sci. Rep. 6, 32696 (2016).

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).

Xu, X.

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8, 4585 (2018).

X. Xu, X. Xie, H. He, H. Zhuang, J. Zhou, A. Thendiyammal, and A. P. Mosk, “Imaging objects through scattering layers and around corners by retrieval of the scattered point spread function,” Opt. Express 25, 32829–32840 (2017).

C. Ma, X. Xu, Y. Liu, and L. Wang, “Time-reversed adapted-perturbation (TRAP) optical focusing onto dynamic objects inside scattering media,” Nat. Photonics 8, 931–936 (2014).

Yang, C.

M. Cua, E. Zhou, and C. Yang, “Imaging moving targets through scattering media,” Opt. Express 25(12), 3935–3945 (2017).

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).

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

Yang, K.

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).

Yang, T. D.

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, 203901 (2012).

Yoon, C.

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, 203901 (2012).

Zhou, E.

Zhou, J.

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8, 4585 (2018).

X. Xu, X. Xie, H. He, H. Zhuang, J. Zhou, A. Thendiyammal, and A. P. Mosk, “Imaging objects through scattering layers and around corners by retrieval of the scattered point spread function,” Opt. Express 25, 32829–32840 (2017).

H. Zhuang, H. He, X. Xie, and J. Zhou, “High speed color imaging through scattering media with a large field of view,” Sci. Rep. 6, 32696 (2016).

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).

H. He, Y. Guan, and J. Zhou, “Image restoration through thin turbid layers by correlation with a known object,” Opt. Express 21, 12539–12545 (2013).

Zhuang, H.

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8, 4585 (2018).

X. Xu, X. Xie, H. He, H. Zhuang, J. Zhou, A. Thendiyammal, and A. P. Mosk, “Imaging objects through scattering layers and around corners by retrieval of the scattered point spread function,” Opt. Express 25, 32829–32840 (2017).

H. Zhuang, H. He, X. Xie, and J. Zhou, “High speed color imaging through scattering media with a large field of view,” Sci. Rep. 6, 32696 (2016).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

Y. Shi, Y. Liu, J. Wang, and T. Wu, “Non-invasive depth-resolved imaging through scattering layers via speckle correlations and parallax,” Appl. Phys. Lett. 110, 231101 (2017).

Light Sci. Appl. (1)

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6, e16219 (2017).

Nat. Commun. (2)

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

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).

Nat. Photonics (5)

C. Ma, X. Xu, Y. Liu, and L. Wang, “Time-reversed adapted-perturbation (TRAP) optical focusing onto dynamic objects inside scattering media,” Nat. Photonics 8, 931–936 (2014).

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).

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound pulse guided digital phase conjugation,” Nat. Photonics 6, 657–661 (2012).

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).

Nat. Phys. (1)

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).

Nature (1)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).

Opt. Express (8)

Opt. Lett. (2)

Optica (3)

Philos. Trans. R. Soc. Lond. A (1)

H. G. Booker, J. A. Ratcliffe, and D. H. Shinn, “Diffraction from an irregular screen with applications to ionospheric problems,” Philos. Trans. R. Soc. Lond. A 242, 579–607 (1950).

Phys. Rev. Lett. (7)

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).

J. A. Newman and K. J. Webb, “Imaging optical fields through heavily scattering media,” Phys. Rev. Lett. 113, 263903 (2014).

J. A. Newman, Q. Luo, and K. J. Webb, “Imaging Hidden Objects with Spatial Speckle Intensity Correlations over Object Position,” Phys. Rev. Lett. 116, 073902 (2016).

I. Freund, M. Rosenbluh, and S. Feng, “Memory Effects in Propagation of Optical Waves through Disordered Media,” Phys. Rev. Lett. 61, 2328–2331 (1988).

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and Fluctuations of Coherent Wave Transmission through Disordered Media,” Phys. Rev. Lett. 61, 834–837 (1988).

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).

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, 203901 (2012).

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

Sci. Rep. (4)

H. Zhuang, H. He, X. Xie, and J. Zhou, “High speed color imaging through scattering media with a large field of view,” Sci. Rep. 6, 32696 (2016).

E. Edrei and G. Scarcelli, “Memory-effect based deconvolution microscopy for super-resolution imaging through scattering media,” Sci. Rep. 6, 33558 (2016).

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8, 4585 (2018).

S. Mukherjee, A. Vijayakumar, M. Kumar, and J. Rosen, “3D imaging through scatterers with interferenceless optical system,” Sci. Rep. 8, 1134 (2018).

Other (4)

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

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice-Hall, Inc., 2006).

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Figures (7)

Fig. 1
Fig. 1 Experimental setup: Imaging objects at another depth by deconvolution with a scaled PSF. The reference object and the unknown object are inserted alternately.
Fig. 2
Fig. 2 Imaging objects at the same wavelength but different depth with PSF scaling. (a) is the reference object. The scalebar is 1.1 mm and applies to panels (a-f). (b) is the unknown object. (c) and (d) are the speckle patterns of the reference object and unknown object respectively. (e) is the retrieved PSF from (c) and (f) is the scaled PSF. (g) and (h) are the reconstruction using (e) and (f), respectively. The scale bar in (h) is 0.275 mm and applies to panels (g,h).
Fig. 3
Fig. 3 Setup to measure the PSF at different wavelengths.
Fig. 4
Fig. 4 (a) Normalized correlation between PSFs at different wavelengths as a function of the scaling factor m. The theoretical curves are the result of Eq. (13) and have been scaled vertically by a factor 0.5 for clarity. (b) Position of the maximum in the correlation function versus wavelength ratio. Open circles: Beam radius on the diffuser 1 mm defined by a round aperture. Closed squares: No aperture, measured 1/e2 beam radius w = 1.75 mm. The theory lines are the results of Eq. (14) with no adjustable parameters.
Fig. 5
Fig. 5 Experimental setup to demonstrate reconstruction imaging using spectral correlation and PSF scaling. The reference and unknown objects are illuminated alternately (when using a monochrome CCD) or simultaneously (when using a color CCD).
Fig. 6
Fig. 6 Imaging objects with separated-spectrum at the same depth. The spectrum of LED source (a) without and (e) with filters. (b) and (c) are the speckle patterns of the reference object and unknown object under illumination without filters, and (d) is the reconstructed result, without scaling the PSF. (f) and (g) are the speckle patterns of the reference object and unknown object under illumination with filter, and the reconstructed results are shown without (h) and with (i) PSF scaling. The scale bar in (b) is 1.1 mm and applies also to (c), (f) and (g). The scale bar in (d) is 0.275 mm and applies also to (h) and (i).
Fig. 7
Fig. 7 Single-shot imaging of spectrum-separated objects at different depth. (a) is the hybrid speckle pattern of the reference object and unknown object. The scale bar is 1.1 mm and applies to (a-d). (b) is the reference object’s speckle pattern separated from (a), and (c) is that of the unknown object separated from (a). (d) is another unknown object. (e) and (f) are the reconstructed object, using the spectral sensitivities of the pixels at the center wavelength of the light sources. The scale bar in (e) is 0.275 mm and applies to (e-h). (g) and (h) are reconstructed with the measured spectrally averaged sensitivity coefficients of the CCD filter.

Equations (14)

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

C( λ 1 / λ 2 ,m)= dx dyPS F λ1 (mx,my)PS F λ2 (x,y).
m total = m z ×m.
R= R 1 × I λ1 + R 2 × I λ2 G= G 1 × I λ1 + G 2 × I λ2 . B= B 1 × I λ1 + B 2 × I λ2
R= R λ1 ¯ I( λ 1 )d λ 1 + R λ2 ¯ I( λ 2 )d λ 2 G= G λ1 ¯ I( λ 1 )d λ 1 + G λ2 ¯ I( λ 2 )d λ 2 , B= B λ1 ¯ I( λ 1 )d λ 1 + B λ2 ¯ I( λ 2 )d λ 2
h(x,y,d)= h 0 exp(ik x 2 + y 2 2d ).
E d (x,y)= h 0 S t(x,y)exp(ik x 2 + y 2 2d ) exp(- x 2 + y 2 w 2 ).
E i ( x i , y i )= h 0 2 S dxdy t(x,y)exp (ik x 2 + y 2 2 d 0 +ik (x x i ) 2 + (y y i ) 2 2 d i - x 2 + y 2 w 2 ) = h 0 2 S exp(ik x i 2 + y i 2 2 d i ) dxdy t(x,y)exp (ik x 2 + y 2 2f +ik x x i +y y i 2 d i - x 2 + y 2 w 2 ).
I i ( ρ i ,λ)= I 0 d 2 ρ 1 d 2 ρ 2 t( ρ 1 ) t * ( ρ 2 )exp( πi λ ρ 1 2 ρ 2 2 f + 2πi λ ( ρ 1 ρ 2 ) ρ i d i ρ 1 2 + ρ 2 2 w 2 ).
C( λ 1 , λ 2 ,m)= C 0 d 2 ρ 1 d 2 ρ 2 d 2 ρ 3 d 2 ρ 4 t( ρ 1 ) t * ( ρ 2 )t( ρ 3 ) t * ( ρ 4 )exp( ρ 1 2 + ρ 2 2 + ρ 3 2 + ρ 4 2 w 2 ) exp( iπ ( ρ 1 2 ρ 2 2 )/ λ 1 +( ρ 3 2 + ρ 4 2 )/ λ 2 f )δ( ( ρ 1 ρ 2 )+(m λ 1 / λ 2 )( ρ 3 ρ 4 ) ).
t( ρ a ) t * ( ρ b )= e ( ρ a ρ b ) 2 /2 l c 2 .
t( ρ 1 ) t * ( ρ 2 )t( ρ 3 ) t * ( ρ 4 ) t( ρ 1 ) t * ( ρ 2 ) t( ρ 3 ) t * ( ρ 4 ) + t( ρ 1 ) t * ( ρ 4 ) t * ( ρ 2 )t( ρ 3 ) .
C(n,m)= C 0 d 2 ρ 1 d 2 ρ 2 d 2 ρ 3 d 2 ρ 4 exp( ρ 1 2 + ρ 2 2 + ρ 3 2 + ρ 4 2 w 2 ( ρ 1 ρ 4 ) 2 + ( ρ 2 ρ 3 ) 2 2 l c 2 ) exp( iπ ( ρ 1 2 ρ 2 2 )+( ρ 3 2 ρ 4 2 )/n λf )δ( ( ρ 1 ρ 2 )+(m/n)( ρ 3 ρ 4 ) ),
C(n,m) 2 n 2 ( f 2 λ 2 l c 2 +2 π 2 l c 4 w 2 ) f 2 λ 2 ( 2 l c 2 ( m 2 + n 2 )+ w 2 (mn) 2 )+ π 2 l c 2 w 2 ( 2 l c 2 ( m 2 +1)+ (m1) 2 w 2 ) .
m peak (n)= f 2 λ 2 n+ π 2 l c 2 w 2 f 2 λ 2 + π 2 l c 2 w 2 .

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