Abstract

Focusing light inside scattering media by optical phase conjugation has been intensively investigated due to its potential applications, such as in deep tissue imaging. However, no existing physical models explain the impact of the various factors on the focusing performance inside a dynamic scattering medium. Here, we establish an angular-spectrum model to trace the field propagation during the entire optical phase conjugation process in the presence of scattering media. By incorporating fast decorrelation components, the model enables us to investigate the competition between the guide star and fast tissue motions for photon tagging. Other factors affecting the focusing performance are also analyzed via the model. As a proof of concept, we experimentally verify our model in the case of focusing light through dynamic scattering media. This angular-spectrum model allows analysis of a series of scattering events in highly scattering media and benefits related applications.

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

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References

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2018 (3)

Z. Yu, J. Huangfu, F. Zhao, M. Xia, X. Wu, X. Niu, D. Li, P. Lai, and D. Wang, “Time-reversed magnetically controlled perturbation (TRMCP) optical focusing inside scattering media,” Sci. Rep. 8, 2927 (2018).
[Crossref]

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[Crossref]

W. Zhao, Y. Sun, Y. Wang, L. Qiu, R. Shao, and H. Cui, “Three-dimensional super-resolution correlation-differential confocal microscopy with nanometer axial focusing accuracy,” Opt. Express 26, 15759–15768 (2018).
[Crossref]

2017 (8)

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, “Generalized optical memory effect,” Optica 4, 886–892 (2017).
[Crossref]

Y. Shen, Y. Liu, C. Ma, and L. V. Wang, “Sub-Nyquist sampling boosts targeted light transport through opaque scattering media,” Optica 4, 97–102 (2017).
[Crossref]

J. Yang, L. Gong, X. Xu, P. Hai, Y. Shen, Y. Suzuki, and L. V. Wang, “Motionless volumetric photoacoustic microscopy with spatially invariant resolution,” Nat. Commun. 8, 780 (2017).
[Crossref]

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

H. Ruan, T. Haber, Y. Liu, J. Brake, J. Kim, J. M. Berlin, and C. Yang, “Focusing light inside scattering media with magnetic-particle-guided wavefront shaping,” Optica 4, 1337–1343 (2017).
[Crossref]

Y. Liu, C. Ma, Y. Shen, J. Shi, and L. V. Wang, “Focusing light inside dynamic scattering media with millisecond digital optical phase conjugation,” Optica 4, 280–288 (2017).
[Crossref]

A. Boniface, M. Mounaix, B. Blochet, R. Piestun, and S. Gigan, “Transmission-matrix-based point-spread-function engineering through a complex medium,” Optica 4, 54–59 (2017).
[Crossref]

J. Yang, Y. Shen, Y. Liu, A. S. Hemphill, and L. V. Wang, “Focusing light through scattering media by polarization modulation based generalized digital optical phase conjugation,” Appl. Phys. Lett. 111, 201108 (2017).
[Crossref]

2016 (3)

2015 (8)

M. Jang, H. Ruan, I. M. Vellekoop, B. Judkewitz, E. Chung, and C. Yang, “Relation between speckle decorrelation and optical phase conjugation (OPC)-based turbidity suppression through dynamic scattering media: a study on in vivo mouse skin,” Biomed. Opt. Express 6, 72–85(2015).
[Crossref]

Y. Liu, P. Lai, C. Ma, X. Xu, A. A. Grabar, and L. V. Wang, “Optical focusing deep inside dynamic scattering media with near-infrared time-reversed ultrasonically encoded (TRUE) light,” Nat. Commun. 6, 5904 (2015).
[Crossref]

C. Ma, F. Zhou, Y. Liu, and L. V. Wang, “Single-exposure optical focusing inside scattering media using binarized time-reversed adapted perturbation,” Optica 2, 869–876 (2015).
[Crossref]

J. Park, J.-H. Park, H. Yu, and Y. Park, “Focusing through turbid media by polarization modulation,” Opt. Lett. 40, 1667–1670 (2015).
[Crossref]

N. Kotagiri, G. P. Sudlow, W. J. Akers, and S. Achilefu, “Breaking the depth dependency of phototherapy with Cerenkov radiation and low-radiance-responsive nanophotosensitizers,” Nat. Nanotechnol. 10, 370–379 (2015).
[Crossref]

J. Yoon, M. Lee, K. Lee, N. Kim, J. M. Kim, J. Park, H. Yu, C. Choi, W. D. Heo, and Y. Park, “Optogenetic control of cell signaling pathway through scattering skull using wavefront shaping,” Sci. Rep. 5, 13289 (2015).
[Crossref]

P. Lai, L. Wang, J. W. Tay, and L. V. Wang, “Photoacoustically guided wavefront shaping for enhanced optical focusing in scattering media,” Nat. Photonics 9, 126–132 (2015).
[Crossref]

D. Wang, E. H. Zhou, J. Brake, H. Ruan, M. Jang, and C. Yang, “Focusing through dynamic tissue with millisecond digital optical phase conjugation,” Optica 2, 728–735 (2015).
[Crossref]

2014 (2)

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

P. Lai, X. Xu, and L. V. Wang, “Dependence of optical scattering from Intralipid in gelatin-gel based tissue-mimicking phantoms on mixing temperature and time,” J. Biomed. Opt. 19, 035002 (2014).
[Crossref]

2013 (2)

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
[Crossref]

B. Judkewitz, Y. M. Wang, R. Horstmeyer, A. Mathy, and C. Yang, “Speckle-scale focusing in the diffusive regime with time reversal of variance-encoded light (TROVE),” Nat. Photonics 7, 300–305 (2013).
[Crossref]

2012 (8)

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).
[Crossref]

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).
[Crossref]

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20, 10583–10590 (2012).
[Crossref]

S. Tripathi, R. Paxman, T. Bifano, and K. C. Toussaint, “Vector transmission matrix for the polarization behavior of light propagation in highly scattering media,” Opt. Express 20, 16067–16076 (2012).
[Crossref]

D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express 20, 1733–1740 (2012).
[Crossref]

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).
[Crossref]

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

K. Si, R. Fiolka, and M. Cui, “Breaking the spatial resolution barrier via iterative sound-light interaction in deep tissue microscopy,” Sci. Rep. 2, 748 (2012).
[Crossref]

2011 (3)

D. Akbulut, T. J. Huisman, E. G. van Putten, W. L. Vos, and A. P. Mosk, “Focusing light through random photonic media by binary amplitude modulation,” Opt. Express 19, 4017–4029 (2011).
[Crossref]

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5, 154–157 (2011).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

2010 (3)

2007 (1)

1995 (1)

1989 (1)

1988 (2)

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).
[Crossref]

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[Crossref]

1968 (1)

1954 (1)

C. J. Bouwkamp, “Diffraction Theory,” Rep. Prog. Phys. 17, 35–100 (1954).
[Crossref]

Achilefu, S.

N. Kotagiri, G. P. Sudlow, W. J. Akers, and S. Achilefu, “Breaking the depth dependency of phototherapy with Cerenkov radiation and low-radiance-responsive nanophotosensitizers,” Nat. Nanotechnol. 10, 370–379 (2015).
[Crossref]

Akbulut, D.

Akers, W. J.

N. Kotagiri, G. P. Sudlow, W. J. Akers, and S. Achilefu, “Breaking the depth dependency of phototherapy with Cerenkov radiation and low-radiance-responsive nanophotosensitizers,” Nat. Nanotechnol. 10, 370–379 (2015).
[Crossref]

Alfano, R. R.

Andreoli, D.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

Berlin, J. M.

Bertolotti, J.

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).
[Crossref]

Bifano, T.

Blochet, B.

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).
[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]

Bolin, F. P.

Boniface, A.

Bouwkamp, C. J.

C. J. Bouwkamp, “Diffraction Theory,” Rep. Prog. Phys. 17, 35–100 (1954).
[Crossref]

Brake, J.

Caravaca-Aguirre, A. M.

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Choi, C.

J. Yoon, M. Lee, K. Lee, N. Kim, J. M. Kim, J. Park, H. Yu, C. Choi, W. D. Heo, and Y. Park, “Optogenetic control of cell signaling pathway through scattering skull using wavefront shaping,” Sci. Rep. 5, 13289 (2015).
[Crossref]

Choi, W.

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Choi, Y.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Chung, E.

Conkey, D. B.

Cox, M. E.

J. W. Goodman and M. E. Cox, Introduction to Fourier Optics (McGraw-Hill, 1968).

Cui, H.

Cui, M.

K. Si, R. Fiolka, and M. Cui, “Breaking the spatial resolution barrier via iterative sound-light interaction in deep tissue microscopy,” Sci. Rep. 2, 748 (2012).
[Crossref]

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).
[Crossref]

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

M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18, 3444–3455 (2010).
[Crossref]

Dasari, R. R.

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Defienne, H.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

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).
[Crossref]

Fang-Yen, C.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Farahi, S.

Feld, M. S.

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
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Supplementary Material (1)

NameDescription
» Supplement 1       Detailed description of the angular-spectrum method, the single-shot focusing-through DOPC experimental system, and the preparation of the dynamic scattering medium.

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Figures (5)

Fig. 1.
Fig. 1. Angular-spectrum model for DOPC. (a) Modulation at the guide star and hologram recording. (b) Conjugated-light playback and focusing inside the scattering medium. (c) Light modulated by the guide star propagates through a scattering medium layer by layer. (d) Light propagates back through the scattering medium layer by layer, and focuses at the position of the guide star.
Fig. 2.
Fig. 2. Characterizing the relationship between the transport mean free path and the refractive index disturbance. (a) Normalized (Norm.) intensity distributions of the scattered light at depths of 0.5, 0.7, and 1.2 mm in k space. (b) IDC/IAC as a function of depth. (c) Transport mean free path l as a function of the refractive index disturbance ndev.
Fig. 3.
Fig. 3. Model implementation for focusing inside a scattering medium by DOPC. (a) Light field propagation in the recording process. (b) Light field propagation in the playback process. (c) PBR as a function of the SNR of the hologram measurement. (d) PBRs as a function of the guide star’s size with the SNRs of 100, 200, and 300. (e) PBRs for five Zernike modes of different orders as a function of the aberrations in the playback beam due to the manufacturing and alignment errors of the SLM. Scale bar, 100 μm.
Fig. 4.
Fig. 4. Focusing inside the dynamic scattering medium by DOPC. (a) Modeling a dynamic scattering medium by adding fast movement in the space between the layers p and p+1. (b) Simulated speckle correlation coefficient as a function of time t. (c) DOPC foci with different system latencies tlat. Scale bar, 100 μm. (d) PBR of the DOPC focus as a function of the system latency tlat.
Fig. 5.
Fig. 5. Verification of the angular-spectrum model by focusing through a dynamic scattering medium. (a) Recording process. (b) Playback process. (c) Comparison of the speckle correlation coefficient as a function of time t between the simulation and experiment. (d) Comparison of the PBR of the DOPC focus as a function of system latency between the simulation and experiment. Error bars indicate the standard deviation over 10 datasets.

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