Abstract

We report on synthetic aperture microscopy through a highly turbid medium. We first recorded a transmission matrix for the turbid medium with an angular basis of 20,000 complex images covering 0.6 NA. This effectively converts the medium into a lens of the same NA. Distorted images of a target object are then taken at 500 different angles of illumination covering 0.6 NA. For each of the distorted images, the original object image is reconstructed from the transmission matrix by the recently developed turbid lens imaging (TLI) technique. All 500 reconstructed images are synthesized to enhance the NA to 1.2 and thereby generate an object image with twice the enhanced spatial resolution of the individual images. Our method of applying aperture synthesis for TLI makes it possible to enhance the resolving power without increasing the number of transmission matrix elements. This relieves the demand for data acquisition and processing that has impeded the practicality of TLI.

© 2011 Optical Society of America

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  1. N. Ji, D. E. Milkie, and E. Betzig, Nat. Methods 7, 141 (2009).
    [CrossRef] [PubMed]
  2. I. M. Vellekoop and A. P. Mosk, Opt. Lett. 32, 2309 (2007).
    [CrossRef] [PubMed]
  3. E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, Phys. Rev. Lett. 106, 193905 (2011).
    [CrossRef] [PubMed]
  4. B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Nat. Photon. 5, 360 (2011).
    [CrossRef]
  5. J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
    [CrossRef] [PubMed]
  6. Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
    [CrossRef]
  7. X. A. Xu, H. L. Liu, and L. V. Wang, Nat. Photon. 5, 154 (2011).
    [CrossRef]
  8. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
    [CrossRef] [PubMed]
  9. Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
    [CrossRef] [PubMed]
  10. T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, Opt. Lett. 30, 1165 (2005).
    [CrossRef] [PubMed]
  11. S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
    [CrossRef] [PubMed]
  12. M. Kim, Y. Choi, C. Fang-Yen, Y. J. Sung, R. R. Dasari, M. S. Feld, and W. Choi, Opt. Lett. 36, 148 (2011).
    [CrossRef] [PubMed]

2011 (6)

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, Phys. Rev. Lett. 106, 193905 (2011).
[CrossRef] [PubMed]

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Nat. Photon. 5, 360 (2011).
[CrossRef]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (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, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef] [PubMed]

X. A. Xu, H. L. Liu, and L. V. Wang, Nat. Photon. 5, 154 (2011).
[CrossRef]

M. Kim, Y. Choi, C. Fang-Yen, Y. J. Sung, R. R. Dasari, M. S. Feld, and W. Choi, Opt. Lett. 36, 148 (2011).
[CrossRef] [PubMed]

2010 (1)

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef] [PubMed]

2009 (1)

N. Ji, D. E. Milkie, and E. Betzig, Nat. Methods 7, 141 (2009).
[CrossRef] [PubMed]

2008 (1)

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

2007 (1)

2006 (1)

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

2005 (1)

Akbulut, D.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, Phys. Rev. Lett. 106, 193905 (2011).
[CrossRef] [PubMed]

Alexandrov, S. A.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Aulbach, J.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Nat. Photon. 5, 360 (2011).
[CrossRef]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef] [PubMed]

Bertolotti, J.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, Phys. Rev. Lett. 106, 193905 (2011).
[CrossRef] [PubMed]

Betzig, E.

N. Ji, D. E. Milkie, and E. Betzig, Nat. Methods 7, 141 (2009).
[CrossRef] [PubMed]

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef] [PubMed]

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef] [PubMed]

Choi, W.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef] [PubMed]

M. Kim, Y. Choi, C. Fang-Yen, Y. J. Sung, R. R. Dasari, M. S. Feld, and W. Choi, Opt. Lett. 36, 148 (2011).
[CrossRef] [PubMed]

Choi, Y.

M. Kim, Y. Choi, C. Fang-Yen, Y. J. Sung, R. R. Dasari, M. S. Feld, and W. Choi, Opt. Lett. 36, 148 (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, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef] [PubMed]

Dasari, R. R.

Fang-Yen, C.

M. Kim, Y. Choi, C. Fang-Yen, Y. J. Sung, R. R. Dasari, M. S. Feld, and W. Choi, Opt. Lett. 36, 148 (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, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef] [PubMed]

Feld, M. S.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef] [PubMed]

M. Kim, Y. Choi, C. Fang-Yen, Y. J. Sung, R. R. Dasari, M. S. Feld, and W. Choi, Opt. Lett. 36, 148 (2011).
[CrossRef] [PubMed]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, Opt. Lett. 30, 1165 (2005).
[CrossRef] [PubMed]

Fink, M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef] [PubMed]

Gigan, S.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef] [PubMed]

Gjonaj, B.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef] [PubMed]

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Nat. Photon. 5, 360 (2011).
[CrossRef]

Gutzler, T.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Hillman, T. R.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Ikeda, T.

Ji, N.

N. Ji, D. E. Milkie, and E. Betzig, Nat. Methods 7, 141 (2009).
[CrossRef] [PubMed]

Johnson, P. M.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Nat. Photon. 5, 360 (2011).
[CrossRef]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef] [PubMed]

Kang, P.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef] [PubMed]

Kim, M.

Kuipers, L.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Nat. Photon. 5, 360 (2011).
[CrossRef]

Lagendijk, A.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Nat. Photon. 5, 360 (2011).
[CrossRef]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef] [PubMed]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, Phys. Rev. Lett. 106, 193905 (2011).
[CrossRef] [PubMed]

Lee, K. J.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef] [PubMed]

Lerosey, G.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef] [PubMed]

Liu, H. L.

X. A. Xu, H. L. Liu, and L. V. Wang, Nat. Photon. 5, 154 (2011).
[CrossRef]

Milkie, D. E.

N. Ji, D. E. Milkie, and E. Betzig, Nat. Methods 7, 141 (2009).
[CrossRef] [PubMed]

Mosk, A. P.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, Phys. Rev. Lett. 106, 193905 (2011).
[CrossRef] [PubMed]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef] [PubMed]

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Nat. Photon. 5, 360 (2011).
[CrossRef]

I. M. Vellekoop and A. P. Mosk, Opt. Lett. 32, 2309 (2007).
[CrossRef] [PubMed]

Popescu, G.

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef] [PubMed]

Psaltis, D.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

Sampson, D. D.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Sung, Y. J.

van Putten, E. G.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, Phys. Rev. Lett. 106, 193905 (2011).
[CrossRef] [PubMed]

Vellekoop, I. M.

Vos, W. L.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, Phys. Rev. Lett. 106, 193905 (2011).
[CrossRef] [PubMed]

Wang, L. V.

X. A. Xu, H. L. Liu, and L. V. Wang, Nat. Photon. 5, 154 (2011).
[CrossRef]

Xu, X. A.

X. A. Xu, H. L. Liu, and L. V. Wang, Nat. Photon. 5, 154 (2011).
[CrossRef]

Yang, C.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

Yang, T. D.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef] [PubMed]

Yaqoob, Z.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

Nat. Methods (1)

N. Ji, D. E. Milkie, and E. Betzig, Nat. Methods 7, 141 (2009).
[CrossRef] [PubMed]

Nat. Photon. (3)

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Nat. Photon. 5, 360 (2011).
[CrossRef]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

X. A. Xu, H. L. Liu, and L. V. Wang, Nat. Photon. 5, 154 (2011).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (5)

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, Phys. Rev. Lett. 106, 193905 (2011).
[CrossRef] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef] [PubMed]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef] [PubMed]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef] [PubMed]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Supplementary Material (2)

» Media 1: MOV (3649 KB)     
» Media 2: PDF (261 KB)     

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Figures (3)

Fig. 1
Fig. 1

Experimental setup and transmission matrix. (a) Schematics of experimental setup. BS: beam splitter, C: condenser lens, OL: objective lens, SLM: spatial light modulator, SP: sample plane, IP: image plane. SLM and Galvanometer mirrors are placed at conjugate planes of the sample plane. (b) Conceptual scanning trajectory of illumination beam in k-space of the sample plane. (c) Phase images of measured transmission matrix elements. Scale bar: 10 μm . Color bar: phase in radians. (d) Zoom of white box in (c).

Fig. 2
Fig. 2

Process of aperture synthesis. (a) USAF target-like pattern written on the SLM. The numbers represent scaling factors for the structures. The structure marked with 1 has line spacing of 760 nm . (b) 0 ° illumination. The SLM is depicted as transmission geometry for convenience although it is working as a reflective type. The blue dashed lines represent conjugated image planes. (c) Distorted sample image for (b). Scale bar: 10 μm . (d) Illumination at an angle of 36.8 ° . (e) Distorted image for (d). (f)–(g) Amplitudes of restored angular spectra of (c) and (e), respectively. Red and blue circles represent 0.6 NA. Scale bar: 1 μm 1 . (h) Amplitude of synthesized angular spectrum of 500 images. White circle represents 1.2 NA. Red and blue circles are the shifted apertures of (f) and (g). All angular spectra are represented in log scale for better visibility.

Fig. 3
Fig. 3

Resolution enhancement after the aperture synthesis. (a) Reconstructed image from the angular spectrum in Fig. 2f. (b) Synthesized image with 500 reconstructed images. Scale bar: 10 μm . (c)–(d) Section profiles along the dashed lines in (a) and (b), respectively. All images are represented in amplitude. Media 1 shows the synthetic process and Media 2 the results of incoherent synthesis.

Equations (2)

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E d ( x , y ; k x i , k y i ) = k x , k y A ( k x , k y ; k x i , k y i ) E trans ( x , y ; k x , k y ) ,
A O ( k x , k y ) = A ( k x + k x i , k y + k y i ; k x i , k y i ) ,

Metrics