Abstract

A conventional lens has well-defined transfer function with which we can form an image of a target object. On the contrary, scattering media such as biological tissues, multimode optical fibers and layers of disordered nanoparticles have highly complex transfer function, which makes them impractical for the general imaging purpose. In recent studies, we presented a method of experimentally recording the transmission matrix of such media, which is a measure of the transfer function. In this review paper, we introduce two major applications of the transmission matrix: enhancing light energy delivery and imaging through scattering media. For the former, we identified the eigenchannels of the transmission matrix with large eigenvalues and then coupled light to those channels in order to enhance light energy delivery through the media. For the latter, we solved matrix inversion problem to reconstruct an object image from the distorted image by the scattering media. We showed the enlargement of the numerical aperture of imaging systems with the use of scattering media and demonstrated endoscopic imaging through a single multimode optical fiber working in both reflectance and fluorescence modes. Our approach will pave the way of using scattering media as unique optical elements for various biophotonics applications.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  39. Y. Choi, T. D. Yang, K. J. Lee, and W. Choi, “Full-field and single-shot quantitative phase microscopy using dynamic speckle illumination,” Opt. Lett. 36(13), 2465–2467 (2011).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  47. Y. Choi, T. R. Hillman, W. Choi, N. Lue, R. R. Dasari, P. T. C. So, W. Choi, and Z. Yaqoob, “Measurement of the Time-Resolved Reflection Matrix for Enhancing Light Energy Delivery into a Scattering Medium,” Phys. Rev. Lett. 111(24), 243901 (2013).
    [Crossref] [PubMed]

2014 (2)

D. Kim, J. Moon, M. Kim, T. D. Yang, J. Kim, E. Chung, and W. Choi, “Toward a miniature endomicroscope: pixelation-free and diffraction-limited imaging through a fiber bundle,” Opt. Lett. 39(7), 1921–1924 (2014).
[Crossref] [PubMed]

B. Gérardin, J. Laurent, A. Derode, C. Prada, and A. Aubry, “Full transmission and reflection of waves propagating through a maze of disorder,” Phys. Rev. Lett. 113(17), 173901 (2014).
[Crossref] [PubMed]

2013 (5)

M. Kim, W. Choi, C. Yoon, G. H. Kim, and W. Choi, “Relation between transmission eigenchannels and single-channel optimizing modes in a disordered medium,” Opt. Lett. 38(16), 2994–2996 (2013).
[Crossref] [PubMed]

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(4), 300–305 (2013).
[Crossref] [PubMed]

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “High-resolution, lensless endoscope based on digital scanning through a multimode optical fiber,” Biomed. Opt. Express 4(2), 260–270 (2013).
[Crossref] [PubMed]

A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express 21(10), 12881–12887 (2013).
[Crossref] [PubMed]

Y. Choi, T. R. Hillman, W. Choi, N. Lue, R. R. Dasari, P. T. C. So, W. Choi, and Z. Yaqoob, “Measurement of the Time-Resolved Reflection Matrix for Enhancing Light Energy Delivery into a Scattering Medium,” Phys. Rev. Lett. 111(24), 243901 (2013).
[Crossref] [PubMed]

2012 (11)

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(10), 10583–10590 (2012).
[Crossref] [PubMed]

D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express 20(2), 1733–1740 (2012).
[Crossref] [PubMed]

T. Cižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref] [PubMed]

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12(3), 635–639 (2012).
[Crossref] [PubMed]

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(5), 283–292 (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(7423), 232–234 (2012).
[Crossref] [PubMed]

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(8), 549–553 (2012).
[Crossref]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 581-585 (2012).
[Crossref]

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref] [PubMed]

W. Choi, Q. H. Park, and W. Choi, “Perfect transmission through Anderson localized systems mediated by a cluster of localized modes,” Opt. Express 20(18), 20721–20729 (2012).
[Crossref] [PubMed]

Z. Shi and A. Z. Genack, “Transmission eigenvalues and the bare conductance in the crossover to Anderson localization,” Phys. Rev. Lett. 108(4), 043901 (2012).
[Crossref] [PubMed]

2011 (6)

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

W. Choi, A. P. Mosk, Q. H. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83(13), 134207 (2011).
[Crossref]

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5(3), 154–157 (2011).
[Crossref] [PubMed]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
[Crossref] [PubMed]

Y. Choi, T. D. Yang, K. J. Lee, and W. Choi, “Full-field and single-shot quantitative phase microscopy using dynamic speckle illumination,” Opt. Lett. 36(13), 2465–2467 (2011).
[Crossref] [PubMed]

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] [PubMed]

2010 (3)

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref] [PubMed]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1(6), 81 (2010).
[Crossref] [PubMed]

B. Payne, J. Andreasen, H. Cao, and A. Yamilov, “Relation between transmission and energy stored in random media with gain,” Phys. Rev. B 82(10), 104204 (2010).
[Crossref]

2009 (1)

2008 (3)

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101(12), 120601 (2008).
[Crossref] [PubMed]

E. G. van Putten, I. M. Vellekoop, and A. P. Mosk, “Spatial amplitude and phase modulation using commercial twisted nematic LCDs,” Appl. Opt. 47(12), 2076–2081 (2008).
[Crossref] [PubMed]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2(2), 110–115 (2008).
[Crossref] [PubMed]

2007 (4)

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

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98(14), 143902 (2007).
[Crossref] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[Crossref] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

2005 (2)

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[Crossref] [PubMed]

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30(10), 1165–1167 (2005).
[Crossref] [PubMed]

2004 (1)

1999 (1)

J. G. Rivas, R. Sprik, C. M. Soukoulis, K. Busch, and A. Lagendijk, “Optical transmission through strong scattering and highly polydisperse media,” Europhys. Lett. 48(1), 22–28 (1999).
[Crossref]

1997 (2)

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69(3), 731–808 (1997).
[Crossref]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[Crossref]

1988 (1)

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random-media - an experimental-study,” J. Phys. (Paris) 49(1), 63–75 (1988).
[Crossref]

1987 (1)

J. B. Pendry, “Quasi-extended electron-states in strongly disordered-systems,” J. Phys. C: Solid State Phys. 20(5), 733–742 (1987).
[Crossref]

1984 (2)

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53(22), 2169–2172 (1984).
[Crossref]

O. N. Dorokhov, “On the coexistence of localized and extended electronic states in the metallic phase,” Solid State Commun. 51(6), 381–384 (1984).
[Crossref]

1968 (1)

1958 (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Akkermans, E.

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random-media - an experimental-study,” J. Phys. (Paris) 49(1), 63–75 (1988).
[Crossref]

Anderson, P. W.

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Andreasen, J.

B. Payne, J. Andreasen, H. Cao, and A. Yamilov, “Relation between transmission and energy stored in random media with gain,” Phys. Rev. B 82(10), 104204 (2010).
[Crossref]

Aubry, A.

B. Gérardin, J. Laurent, A. Derode, C. Prada, and A. Aubry, “Full transmission and reflection of waves propagating through a maze of disorder,” Phys. Rev. Lett. 113(17), 173901 (2014).
[Crossref] [PubMed]

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] [PubMed]

Badizadegan, K.

Y. Park, W. Choi, Z. Yaqoob, R. Dasari, K. Badizadegan, and M. S. Feld, “Speckle-field digital holographic microscopy,” Opt. Express 17(15), 12285–12292 (2009).
[Crossref] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[Crossref] [PubMed]

Bartolini, P.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[Crossref]

Beenakker, C. W. J.

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69(3), 731–808 (1997).
[Crossref]

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(7423), 232–234 (2012).
[Crossref] [PubMed]

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[Crossref] [PubMed]

Bianchi, S.

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12(3), 635–639 (2012).
[Crossref] [PubMed]

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(7423), 232–234 (2012).
[Crossref] [PubMed]

Boccara, A. C.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1(6), 81 (2010).
[Crossref] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref] [PubMed]

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] [PubMed]

Bromberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

Busch, K.

J. G. Rivas, R. Sprik, C. M. Soukoulis, K. Busch, and A. Lagendijk, “Optical transmission through strong scattering and highly polydisperse media,” Europhys. Lett. 48(1), 22–28 (1999).
[Crossref]

Cao, H.

B. Payne, J. Andreasen, H. Cao, and A. Yamilov, “Relation between transmission and energy stored in random media with gain,” Phys. Rev. B 82(10), 104204 (2010).
[Crossref]

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98(14), 143902 (2007).
[Crossref] [PubMed]

Caravaca-Aguirre, A. M.

Carminati, R.

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Z. Shi and A. Z. Genack, “Transmission eigenvalues and the bare conductance in the crossover to Anderson localization,” Phys. Rev. Lett. 108(4), 043901 (2012).
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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(8), 549–553 (2012).
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O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

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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(8), 549–553 (2012).
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O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
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Y. Choi, T. R. Hillman, W. Choi, N. Lue, R. R. Dasari, P. T. C. So, W. Choi, and Z. Yaqoob, “Measurement of the Time-Resolved Reflection Matrix for Enhancing Light Energy Delivery into a Scattering Medium,” Phys. Rev. Lett. 111(24), 243901 (2013).
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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(7423), 232–234 (2012).
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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(7423), 232–234 (2012).
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Figures (17)

Fig. 1
Fig. 1

Construction of a transmission matrix of a disordered medium and analysis of its eigenvalues. (a) Schematic of numerical simulation. The disordered medium is 130 μm wide in x-direction. The electric field is recorded at the output side of the medium indicated as a red dashed-dot line and then numerically Fourier transformed to obtain the field at the wave vector space, k out =( k x ' , k z ' ) . The lens represents numerical Fourier transform. The inset is the magnified image of the disordered medium. Black squares are the particles. (b) Comparison between FDTD computation and random matrix theory (RMT). Eigenvalue distribution of the transmission matrix sorted in descending order. Red curves are calculated from the FDTD method while blue dashed curves are obtained by RMT. Three different curves account for three different disordered media with thickness of 8, 12, and 16 μm, respectively, for the same np = 2.0. For each of the FDTD result and RMT, the uppermost curve is from the 8 μm sample, the middle one is from the 12 μm sample, and the curve at the very bottom is from the 16 μm sample (modified from Ref [17].).

Fig. 2
Fig. 2

Field distributions of eigenchannels inside medium. (a)-(c) Field distribution of a plane wave whose incident angle is 11.5°, open eigenchannel and closed eigenchannel, respectively. The incident field is subtracted on the left-hand side of the medium. Here, the amplitude normalized to the input wave. Scale bar: 10 μm. (d) Average intensity along the x direction as a function of the depth in the z direction. The disordered medium fills the space between 0 and 16 μm in depth. The intensity is normalized to that of a normally incident plane wave (modified from Ref [17].).

Fig. 3
Fig. 3

Internal field distribution. (a), (b) Intensity maps inside the random media of np = 1.6 and 2.5 respectively. Incident wave is a plane wave propagating in z-direction. Color bar of amplitude is in arbitrary unity. Scale bar is 5 μm. (c) and (d) are angular spectrum maps for (a) and (b), respectively. Horizontal and vertical axes are represented in terms of the wave number, k0, in free space. Color bar of amplitude is in arbitrary unit (modified from Ref [18].).

Fig. 4
Fig. 4

Internal field distribution of eigenchannels for the disordered medium of np = 2.5 (a)-(e): eigenchannels indices are 1, 11, 21, 31, and 291, respectively, and their transmittances are 80, 12, 2.3, 0.39, and 2.0 × 10-7% respectively. Color bar indicates natural logarithm of the amplitude. Aspect ratio is set to different between horizontal and vertical axes for better visibility. Both scales bars indicate 5 μm (modified from Ref [18].).

Fig. 5
Fig. 5

Experimental schematic for recording a transmission matrix and generating each transmission eigenchannel. The main frame of the setup is an off-axis interference microscope with scanning mirrors (GM, Cambridge Technology) installed in the sample beam path. The laser output from a He-Ne laser is split by a beam splitter (BS1), and one of the beams (sample beam) is sent to the sample and the other (reference beam) through free space. The two beams are recombined by another beam splitter (BS2) to form an interference image at the camera (RedLake M3, 500 fps). A spatial light modulator (SLM, Hamamatsu Photonics, X10468-06) that can generate an arbitrary wavefront is installed in the sample beam path. A disordered medium is placed between the input plane (IP) and the output plane (OP), and the transmitted image at the OP is delivered to the camera by an objective lens (Olympus UPLSAPO) and a tube lens (modified from Ref [20].).

Fig. 6
Fig. 6

Construction of a transmission matrix for a disordered medium. a, Phase maps of the recorded waves acquired in the absence of a disordered medium as a function of incident angle. Scale bar, 10 μm. b, Phase maps of the transmitted waves through a disordered medium as a function of incident angle. c, Amplitude part of a transmission matrix constructed from (a) and (b). Color bar, amplitude in arbitrary unit. (d), Phase part of the transmission matrix. The same color bar, which represents the phase in radians, applies to those phase maps in (a), (b) and (d) (modified from Ref [20].).

Fig. 7
Fig. 7

Comparison between the uncontrolled wave and the first eigenchannel. (a), (b), Transmitted images of the uncontrolled wave and the first eigenchannel through the disordered medium, respectively (modified from Ref [20].).

Fig. 8
Fig. 8

Measured transmittance of individual eigenchannels. Red circles: measured transmittance when the optical wave of each eigenchannel is generated and illuminated onto the disordered medium. Blue squares: corrected eigenvalues. Black line: mean transmittance of the medium measured under illumination by a plane wave. Green line: mean transmittance when the point optimization process is performed (modified from Ref [20].).

Fig. 9
Fig. 9

Reconstruction of 2-D object images. (a) The USAF target-like pattern used as an object. (b) The distorted image of the structure in (a) by the ZnO layer. (c) Angular spectrum of the object extracted by the projection operation. Corresponding phase components are also acquired. Scale bar: 0.5 mm−1. (d) The reconstructed target image by using the angular spectrum in (c). (e) An image of the emblem of Korea University positioned before the ZnO layer. (f) Reconstructed emblem image from the distorted image (modified from Ref [12].).

Fig. 10
Fig. 10

(a) Conventional imaging configuration. θ max is the maximum angle that the imaging setup can collect. (b) Scattering lens imaging configuration. Scattered wave whose angle θ r exceeding θ max can be captured with a disordered medium. (c) Imaging with high NA (1.0 NA), and (d) low NA (0.15 NA), respectively. Red arrows indicate invisible structures. Scale bar: 10 μm. (e) A distorted object image through a ZnO layer (T = 6%). The image is taken with low NA. (f) The object image recovered from the distorted image in (e) (modified from Ref [12].).

Fig. 11
Fig. 11

Experimental scheme for LMSF. The setup is based on an interferometric phase microscope. The interference between the reflected light from the object located at the opposite side of a single multimode fiber and the reference light is recorded by a camera. GM: 2-axis galvanometer scanning mirror. BS1, BS2 and BS3: beam splitters. OL: objective lens. IP: illumination plane of a multimode optical fiber. SP: sample plane (modified from Ref [21].).

Fig. 12
Fig. 12

Image reconstruction process. (a) Representative images of the measured TM following the scheme shown in (b). (b) Scheme of the separate setup for measuring a TM of the single fiber from SP to IP. (c) Reflected object images taken by the setup shown in Fig. 14 at different illumination angles ( θ x , θ y ) S . (d) Reconstructed object images by applying TLI method on the images in (c). (e) Averaging of all reconstructed images in (d) ([21]).

Fig. 13
Fig. 13

Scanning operation of LMSF. (a) The fiber end is translated to take images at different sites of the sample. Each image is reconstructed with the same TM measured at the initial position of the fiber. (b) Reconstructed images are stitched to extend the field of view. Scale bar: 100 μm ([21]).

Fig. 14
Fig. 14

Image of villi in a rat intestine tissue taken by LMSF. (a) A composite bright field image taken by a conventional transmission microscope. Scale bar, 100 μm. (b) A composite image by LMSF at the same site. (c) The same image as (b) but after numerical refocusing by 40 μm toward the fiber end. The arrows indicated by (A) point to the villus in focus at (c) while those indicated by (B) refer to the villus in focus at (b) ([21]).

Fig. 15
Fig. 15

Schematic for recording a TM and fluorescence endoscopy. The output beam from a He-Ne laser is divided into a sample and a reference beam using a beam splitter, BS1. Another beams splitter, BS2, recombines the two beams. OL1 and OL2, objective lenses (PLN 40 × , Olympus); DS, dichroic beam splitter (T647lpxr, Chroma); TL1, TL2, and TL3, tube lenses (LA1979-A, Thorlabs); LF, long wavelength fiber (FELH0650, Thorlabs); DG, diffraction grating (830 Grooves); D, aperture; PMT, photomultiplier tube (H5784-20, Hamamatsu); camera (M3, IDT, 500 fps); IP, input plane of the fiber bundle; SP, sample plane. x, y, and z are the spatial coordinates in SP. The magnification from the DMD to IP 1/111 and that from SP to the camera is 55.6 (modified from Ref [22].).

Fig. 16
Fig. 16

Transmission matrix recording and diffraction-limited focusing. (a) Representative maps of the binary speckle basis, i.e., the binary sequence S in the main text, displayed on the DMD. White (black) pixels indicate that mirrors are in an on (off) state. (b) Intensity maps at SP corresponding to the individual binary speckle basis in (a). x and y are the coordinates at SP, and p is the index of the speckle basis. Scale bar, 10 μm. (c) A binary input pattern on the DMD identified from the measured TM for focusing the laser beam at SP. (d) Output intensity image at SP when the binary pattern in (c) was displayed on the DMD. The inset figure is 3.33 times zoom-view and 10 times over saturated display of the focus. Scale bar, 5 μm (modified from Ref [22].).

Fig. 17
Fig. 17

Pixelation-free endoscopic imaging through fiber bundle. (a) and (c) Conventional transmission images of 2 μm fluorescence beads (Skyblue, Spherotech) and a cancer cell line (SNU-1074), respectively, recorded with an LED illumination through the fiber bundle. (b) and (d) Endoscopic fluorescence images of the same samples as in (a) and (c), respectively, recorded by our method. Scale bar, 20 μm (modified from Ref [22].).

Equations (6)

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

E out ( k x ) = t( k x , k x ) E in ( k x ).
t=Uτ V + ,
E OP (ξ,η) =T(ξ,η;x,y) E IP ( θ x , θ y ). 
E IP ( θ x , θ y ) =T (ξ,η;x,y) 1 E OP (ξ,η). 
O ip = j T ij S jp  ,
T ij = p O ip S pj 1  ,

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