Abstract

High resolution optical microscopy is essential in neuroscience but suffers from scattering in biological tissues and therefore grants access to superficial brain layers only. Recently developed techniques use scattered photons for imaging by exploiting angular correlations in transmitted light and could potentially increase imaging depths. But those correlations (‘angular memory effect’) are of a very short range and should theoretically be only present behind and not inside scattering media. From measurements on neural tissues and complementary simulations, we find that strong forward scattering in biological tissues can enhance the memory effect range and thus the possible field-of-view by more than an order of magnitude compared to isotropic scattering for ∼1 mm thick tissue layers.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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2014 (5)

2013 (4)

M. Mesradi, A. Genoux, V. Cuplov, D. AbiHaidar, S. Jan, I. Buvat, and F. Pain, “Experimental and analytical comparative study of optical coefficient of fresh and frozen rat tissues,” J. Biomed. Opt. 18, 117010 (2013).
[Crossref] [PubMed]

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

M. Nixon, O. Katz, E. Small, Y. Bromberg, A. A. Friesem, Y. Silberberg, and N. Davidson, “Real-time wavefront shaping through scattering media by all-optical feedback,” Nat. Photonics 7, 919–924 (2013).
[Crossref]

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

2012 (4)

N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” Proc. Natl. Acad. Sci. U. S. A. 109, 22–27 (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] [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, 549–553 (2012).
[Crossref]

J. Tang, R. N. Germain, and M. Cui, “Superpenetration optical microscopy by iterative multiphoton adaptive compensation technique,” Proc. Natl. Acad. Sci. U. S. A. 109, 8434–8439 (2012).
[Crossref] [PubMed]

2011 (2)

I. Nishidate, S. Kawauchi, S. Sato, M. Ishihara, M. Kikuchi, and M. Sato, “In vivo determination of absorption and scattering properties in rat cerebral cortex using single reflectance fiber probe with two sourcecollector geometries,” Proc. SPIE 8087, 80872P (2011).
[Crossref]

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt. 16, 106014 (2011).
[Crossref] [PubMed]

2010 (4)

I. M. Vellekoop and C. M. Aegerter, “Scattered light fluorescence microscopy: imaging through turbid layers,” Optics Letters 35, 1245 (2010).
[Crossref] [PubMed]

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7, 603–614 (2010).
[Crossref] [PubMed]

D. A. Dombeck, C. D. Harvey, L. Tian, L. L. Looger, and D. W. Tank, “Functional imaging of hippocampal place cells at cellular resolution during virtual navigation,” Nature Neuroscience 13, 1433–1440 (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, 100601 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

I. M. Vellekoop and A. P. Mosk, “Universal Optimal Transmission of Light Through Disordered Materials,” Phys. Rev. Lett. 101, 120601 (2008).
[Crossref] [PubMed]

2004 (1)

A. S. Marathay and J. F. McCalmont, “On the usual approximation used in the Rayleigh-Sommerfeld diffraction theory,” Journal of the Optical Society of America A 21, 510 (2004).
[Crossref]

2003 (1)

C. Dunsby and P. M. W. French, “Techniques for depth-resolved imaging through turbid media including coherence-gated imaging,” Journal of Physics D: Applied Physics 36, R207–R227 (2003).
[Crossref]

2002 (1)

A. N. Yaroslavsky, P. C. Schulze, I. V. Yaroslavsky, R. Schober, F. Ulrich, and H.-J. Schwarzmaier, “Optical properties of selected native and coagulated human brain tissues in vitro in the visible and near infrared spectral range,” Physics in Medicine and Biology 47, 2059–2073 (2002).
[Crossref] [PubMed]

2001 (2)

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” Journal of neuroscience methods 111, 29–37 (2001).
[Crossref] [PubMed]

E. Beaurepaire, M. Oheim, and J. Mertz, “Ultra-deep two-photon fluorescence excitation in turbid media,” Optics Communications 188, 25–29 (2001).
[Crossref]

2000 (1)

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131 (2000).
[Crossref] [PubMed]

1998 (1)

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, “Fluctuations and stimulus-induced changes in blood flow observed in individual capillaries in layers 2 through 4 of rat neocortex,” Proc. Natl. Acad. Sci. U. S. A. 95, 15741–15746 (1998).
[Crossref] [PubMed]

1990 (1)

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE Journal of Quantum Electronics 26, 2166–2185 (1990).
[Crossref]

1989 (1)

R. Berkovits, M. Kaveh, and S. Feng, “Memory effect of waves in disordered systems: A real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[Crossref]

1988 (1)

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

AbiHaidar, D.

M. Mesradi, A. Genoux, V. Cuplov, D. AbiHaidar, S. Jan, I. Buvat, and F. Pain, “Experimental and analytical comparative study of optical coefficient of fresh and frozen rat tissues,” J. Biomed. Opt. 18, 117010 (2013).
[Crossref] [PubMed]

Aegerter, C. M.

I. M. Vellekoop and C. M. Aegerter, “Scattered light fluorescence microscopy: imaging through turbid layers,” Optics Letters 35, 1245 (2010).
[Crossref] [PubMed]

Akkermans, E.

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University Press, Cambridge, 2010), Chap. 12.

Asher, S. E.

T. J. Coutts, X. Li, T. M. Barnes, B. M. Keyes, C. L. Perkins, S. E. Asher, S. B. Zhang, S.-H. Wei, and S. Limpijumnong, “Synthesis and Characterization of Nitrogen-Doped ZnO Films Grown by MOCVD,” in “Zinc oxide bulk, thin films and nanostructures: processing, properties, and applications,” (Elsevier, 2006), pp. 43–83.

Barnes, T. M.

T. J. Coutts, X. Li, T. M. Barnes, B. M. Keyes, C. L. Perkins, S. E. Asher, S. B. Zhang, S.-H. Wei, and S. Limpijumnong, “Synthesis and Characterization of Nitrogen-Doped ZnO Films Grown by MOCVD,” in “Zinc oxide bulk, thin films and nanostructures: processing, properties, and applications,” (Elsevier, 2006), pp. 43–83.

Beaurepaire, E.

E. Beaurepaire, M. Oheim, and J. Mertz, “Ultra-deep two-photon fluorescence excitation in turbid media,” Optics Communications 188, 25–29 (2001).
[Crossref]

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” Journal of neuroscience methods 111, 29–37 (2001).
[Crossref] [PubMed]

Berkovits, R.

R. Berkovits, M. Kaveh, and S. Feng, “Memory effect of waves in disordered systems: A real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[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, 232–234 (2012).
[Crossref] [PubMed]

Betzig, E.

N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” Proc. Natl. Acad. Sci. U. S. A. 109, 22–27 (2012).
[Crossref]

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] [PubMed]

Boccara, A. C.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Booth, M. J.

M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light: Science & Applications 3, e165 (2014).
[Crossref]

Bossy, E.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

Brocker, C.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131 (2000).
[Crossref] [PubMed]

Bromberg, Y.

M. Nixon, O. Katz, E. Small, Y. Bromberg, A. A. Friesem, Y. Silberberg, and N. Davidson, “Real-time wavefront shaping through scattering media by all-optical feedback,” Nat. Photonics 7, 919–924 (2013).
[Crossref]

Buvat, I.

M. Mesradi, A. Genoux, V. Cuplov, D. AbiHaidar, S. Jan, I. Buvat, and F. Pain, “Experimental and analytical comparative study of optical coefficient of fresh and frozen rat tissues,” J. Biomed. Opt. 18, 117010 (2013).
[Crossref] [PubMed]

Canpolat, M.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131 (2000).
[Crossref] [PubMed]

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] [PubMed]

Chaigne, T.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

Chaigneau, E.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” Journal of neuroscience methods 111, 29–37 (2001).
[Crossref] [PubMed]

Charpak, S.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” Journal of neuroscience methods 111, 29–37 (2001).
[Crossref] [PubMed]

Cheong, W. F.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE Journal of Quantum Electronics 26, 2166–2185 (1990).
[Crossref]

Clark, C. G.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

Coutts, T. J.

T. J. Coutts, X. Li, T. M. Barnes, B. M. Keyes, C. L. Perkins, S. E. Asher, S. B. Zhang, S.-H. Wei, and S. Limpijumnong, “Synthesis and Characterization of Nitrogen-Doped ZnO Films Grown by MOCVD,” in “Zinc oxide bulk, thin films and nanostructures: processing, properties, and applications,” (Elsevier, 2006), pp. 43–83.

Cui, M.

L. Kong and M. Cui, “In vivo fluorescence microscopy via iterative multi-photon adaptive compensation technique,” Opt. Express 22, 23786 (2014).
[Crossref] [PubMed]

J. Tang, R. N. Germain, and M. Cui, “Superpenetration optical microscopy by iterative multiphoton adaptive compensation technique,” Proc. Natl. Acad. Sci. U. S. A. 109, 8434–8439 (2012).
[Crossref] [PubMed]

Cuplov, V.

M. Mesradi, A. Genoux, V. Cuplov, D. AbiHaidar, S. Jan, I. Buvat, and F. Pain, “Experimental and analytical comparative study of optical coefficient of fresh and frozen rat tissues,” J. Biomed. Opt. 18, 117010 (2013).
[Crossref] [PubMed]

Davidson, N.

M. Nixon, O. Katz, E. Small, Y. Bromberg, A. A. Friesem, Y. Silberberg, and N. Davidson, “Real-time wavefront shaping through scattering media by all-optical feedback,” Nat. Photonics 7, 919–924 (2013).
[Crossref]

Denk, W.

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, “Fluctuations and stimulus-induced changes in blood flow observed in individual capillaries in layers 2 through 4 of rat neocortex,” Proc. Natl. Acad. Sci. U. S. A. 95, 15741–15746 (1998).
[Crossref] [PubMed]

Dombeck, D. A.

D. A. Dombeck, C. D. Harvey, L. Tian, L. L. Looger, and D. W. Tank, “Functional imaging of hippocampal place cells at cellular resolution during virtual navigation,” Nature Neuroscience 13, 1433–1440 (2010).
[Crossref] [PubMed]

Dunsby, C.

C. Dunsby and P. M. W. French, “Techniques for depth-resolved imaging through turbid media including coherence-gated imaging,” Journal of Physics D: Applied Physics 36, R207–R227 (2003).
[Crossref]

Durst, M. E.

Esponda-Ramos, O.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131 (2000).
[Crossref] [PubMed]

Feng, S.

R. Berkovits, M. Kaveh, and S. Feng, “Memory effect of waves in disordered systems: A real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[Crossref]

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

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).
[Crossref]

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Fleischer, J. W.

French, P. M. W.

C. Dunsby and P. M. W. French, “Techniques for depth-resolved imaging through turbid media including coherence-gated imaging,” Journal of Physics D: Applied Physics 36, R207–R227 (2003).
[Crossref]

Freyer, J. P.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131 (2000).
[Crossref] [PubMed]

Friesem, A. A.

M. Nixon, O. Katz, E. Small, Y. Bromberg, A. A. Friesem, Y. Silberberg, and N. Davidson, “Real-time wavefront shaping through scattering media by all-optical feedback,” Nat. Photonics 7, 919–924 (2013).
[Crossref]

Genoux, A.

M. Mesradi, A. Genoux, V. Cuplov, D. AbiHaidar, S. Jan, I. Buvat, and F. Pain, “Experimental and analytical comparative study of optical coefficient of fresh and frozen rat tissues,” J. Biomed. Opt. 18, 117010 (2013).
[Crossref] [PubMed]

Germain, R. N.

J. Tang, R. N. Germain, and M. Cui, “Superpenetration optical microscopy by iterative multiphoton adaptive compensation technique,” Proc. Natl. Acad. Sci. U. S. A. 109, 8434–8439 (2012).
[Crossref] [PubMed]

Gigan, S.

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).
[Crossref]

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Harvey, C. D.

D. A. Dombeck, C. D. Harvey, L. Tian, L. L. Looger, and D. W. Tank, “Functional imaging of hippocampal place cells at cellular resolution during virtual navigation,” Nature Neuroscience 13, 1433–1440 (2010).
[Crossref] [PubMed]

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).
[Crossref]

Helmchen, F.

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, “Fluctuations and stimulus-induced changes in blood flow observed in individual capillaries in layers 2 through 4 of rat neocortex,” Proc. Natl. Acad. Sci. U. S. A. 95, 15741–15746 (1998).
[Crossref] [PubMed]

Horstmeyer, R.

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, and C. Yang, “Translation correlations in anisotropically scattering media,” arXiv:1411.7157 (2014).

Horton, N. G.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt. 16, 106014 (2011).
[Crossref] [PubMed]

Ishihara, M.

I. Nishidate, S. Kawauchi, S. Sato, M. Ishihara, M. Kikuchi, and M. Sato, “In vivo determination of absorption and scattering properties in rat cerebral cortex using single reflectance fiber probe with two sourcecollector geometries,” Proc. SPIE 8087, 80872P (2011).
[Crossref]

Jan, S.

M. Mesradi, A. Genoux, V. Cuplov, D. AbiHaidar, S. Jan, I. Buvat, and F. Pain, “Experimental and analytical comparative study of optical coefficient of fresh and frozen rat tissues,” J. Biomed. Opt. 18, 117010 (2013).
[Crossref] [PubMed]

Ji, N.

N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” Proc. Natl. Acad. Sci. U. S. A. 109, 22–27 (2012).
[Crossref]

Johnson, T. M.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131 (2000).
[Crossref] [PubMed]

Judkewitz, B.

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, and C. Yang, “Translation correlations in anisotropically scattering media,” arXiv:1411.7157 (2014).

Kane, C.

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

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).
[Crossref]

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

M. Nixon, O. Katz, E. Small, Y. Bromberg, A. A. Friesem, Y. Silberberg, and N. Davidson, “Real-time wavefront shaping through scattering media by all-optical feedback,” Nat. Photonics 7, 919–924 (2013).
[Crossref]

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).
[Crossref]

Kaveh, M.

R. Berkovits, M. Kaveh, and S. Feng, “Memory effect of waves in disordered systems: A real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[Crossref]

Kawauchi, S.

I. Nishidate, S. Kawauchi, S. Sato, M. Ishihara, M. Kikuchi, and M. Sato, “In vivo determination of absorption and scattering properties in rat cerebral cortex using single reflectance fiber probe with two sourcecollector geometries,” Proc. SPIE 8087, 80872P (2011).
[Crossref]

Keyes, B. M.

T. J. Coutts, X. Li, T. M. Barnes, B. M. Keyes, C. L. Perkins, S. E. Asher, S. B. Zhang, S.-H. Wei, and S. Limpijumnong, “Synthesis and Characterization of Nitrogen-Doped ZnO Films Grown by MOCVD,” in “Zinc oxide bulk, thin films and nanostructures: processing, properties, and applications,” (Elsevier, 2006), pp. 43–83.

Kikuchi, M.

I. Nishidate, S. Kawauchi, S. Sato, M. Ishihara, M. Kikuchi, and M. Sato, “In vivo determination of absorption and scattering properties in rat cerebral cortex using single reflectance fiber probe with two sourcecollector geometries,” Proc. SPIE 8087, 80872P (2011).
[Crossref]

Kleinfeld, D.

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, “Fluctuations and stimulus-induced changes in blood flow observed in individual capillaries in layers 2 through 4 of rat neocortex,” Proc. Natl. Acad. Sci. U. S. A. 95, 15741–15746 (1998).
[Crossref] [PubMed]

Kobat, D.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt. 16, 106014 (2011).
[Crossref] [PubMed]

D. Kobat, M. E. Durst, N. Nishimura, A. W. Wong, C. B. Schaffer, and C. Xu, “Deep tissue multiphoton microscopy using longer wavelength excitation,” Opt. Express 17, 13354 (2009).
[Crossref] [PubMed]

Kong, L.

Lagendijk, A.

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] [PubMed]

Lee, P.

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

Lerosey, G.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Li, X.

T. J. Coutts, X. Li, T. M. Barnes, B. M. Keyes, C. L. Perkins, S. E. Asher, S. B. Zhang, S.-H. Wei, and S. Limpijumnong, “Synthesis and Characterization of Nitrogen-Doped ZnO Films Grown by MOCVD,” in “Zinc oxide bulk, thin films and nanostructures: processing, properties, and applications,” (Elsevier, 2006), pp. 43–83.

Limpijumnong, S.

T. J. Coutts, X. Li, T. M. Barnes, B. M. Keyes, C. L. Perkins, S. E. Asher, S. B. Zhang, S.-H. Wei, and S. Limpijumnong, “Synthesis and Characterization of Nitrogen-Doped ZnO Films Grown by MOCVD,” in “Zinc oxide bulk, thin films and nanostructures: processing, properties, and applications,” (Elsevier, 2006), pp. 43–83.

Looger, L. L.

D. A. Dombeck, C. D. Harvey, L. Tian, L. L. Looger, and D. W. Tank, “Functional imaging of hippocampal place cells at cellular resolution during virtual navigation,” Nature Neuroscience 13, 1433–1440 (2010).
[Crossref] [PubMed]

Marathay, A. S.

A. S. Marathay and J. F. McCalmont, “On the usual approximation used in the Rayleigh-Sommerfeld diffraction theory,” Journal of the Optical Society of America A 21, 510 (2004).
[Crossref]

Matanock, A.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131 (2000).
[Crossref] [PubMed]

McCalmont, J. F.

A. S. Marathay and J. F. McCalmont, “On the usual approximation used in the Rayleigh-Sommerfeld diffraction theory,” Journal of the Optical Society of America A 21, 510 (2004).
[Crossref]

Mertz, J.

E. Beaurepaire, M. Oheim, and J. Mertz, “Ultra-deep two-photon fluorescence excitation in turbid media,” Optics Communications 188, 25–29 (2001).
[Crossref]

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” Journal of neuroscience methods 111, 29–37 (2001).
[Crossref] [PubMed]

Mesradi, M.

M. Mesradi, A. Genoux, V. Cuplov, D. AbiHaidar, S. Jan, I. Buvat, and F. Pain, “Experimental and analytical comparative study of optical coefficient of fresh and frozen rat tissues,” J. Biomed. Opt. 18, 117010 (2013).
[Crossref] [PubMed]

Mitra, P. P.

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, “Fluctuations and stimulus-induced changes in blood flow observed in individual capillaries in layers 2 through 4 of rat neocortex,” Proc. Natl. Acad. Sci. U. S. A. 95, 15741–15746 (1998).
[Crossref] [PubMed]

Montambaux, G.

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University Press, Cambridge, 2010), Chap. 12.

Mosk, A. P.

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] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Universal Optimal Transmission of Light Through Disordered Materials,” Phys. Rev. Lett. 101, 120601 (2008).
[Crossref] [PubMed]

Mourant, J. R.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131 (2000).
[Crossref] [PubMed]

Nishidate, I.

I. Nishidate, S. Kawauchi, S. Sato, M. Ishihara, M. Kikuchi, and M. Sato, “In vivo determination of absorption and scattering properties in rat cerebral cortex using single reflectance fiber probe with two sourcecollector geometries,” Proc. SPIE 8087, 80872P (2011).
[Crossref]

Nishimura, N.

Nixon, M.

M. Nixon, O. Katz, E. Small, Y. Bromberg, A. A. Friesem, Y. Silberberg, and N. Davidson, “Real-time wavefront shaping through scattering media by all-optical feedback,” Nat. Photonics 7, 919–924 (2013).
[Crossref]

Ntziachristos, V.

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7, 603–614 (2010).
[Crossref] [PubMed]

Oheim, M.

E. Beaurepaire, M. Oheim, and J. Mertz, “Ultra-deep two-photon fluorescence excitation in turbid media,” Optics Communications 188, 25–29 (2001).
[Crossref]

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” Journal of neuroscience methods 111, 29–37 (2001).
[Crossref] [PubMed]

Pain, F.

M. Mesradi, A. Genoux, V. Cuplov, D. AbiHaidar, S. Jan, I. Buvat, and F. Pain, “Experimental and analytical comparative study of optical coefficient of fresh and frozen rat tissues,” J. Biomed. Opt. 18, 117010 (2013).
[Crossref] [PubMed]

Perkins, C. L.

T. J. Coutts, X. Li, T. M. Barnes, B. M. Keyes, C. L. Perkins, S. E. Asher, S. B. Zhang, S.-H. Wei, and S. Limpijumnong, “Synthesis and Characterization of Nitrogen-Doped ZnO Films Grown by MOCVD,” in “Zinc oxide bulk, thin films and nanostructures: processing, properties, and applications,” (Elsevier, 2006), pp. 43–83.

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Prahl, S. A.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE Journal of Quantum Electronics 26, 2166–2185 (1990).
[Crossref]

Psaltis, D.

Pu, Y.

Sato, M.

I. Nishidate, S. Kawauchi, S. Sato, M. Ishihara, M. Kikuchi, and M. Sato, “In vivo determination of absorption and scattering properties in rat cerebral cortex using single reflectance fiber probe with two sourcecollector geometries,” Proc. SPIE 8087, 80872P (2011).
[Crossref]

Sato, S.

I. Nishidate, S. Kawauchi, S. Sato, M. Ishihara, M. Kikuchi, and M. Sato, “In vivo determination of absorption and scattering properties in rat cerebral cortex using single reflectance fiber probe with two sourcecollector geometries,” Proc. SPIE 8087, 80872P (2011).
[Crossref]

Sato, T. R.

N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” Proc. Natl. Acad. Sci. U. S. A. 109, 22–27 (2012).
[Crossref]

Schaffer, C. B.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

D. Kobat, M. E. Durst, N. Nishimura, A. W. Wong, C. B. Schaffer, and C. Xu, “Deep tissue multiphoton microscopy using longer wavelength excitation,” Opt. Express 17, 13354 (2009).
[Crossref] [PubMed]

Schober, R.

A. N. Yaroslavsky, P. C. Schulze, I. V. Yaroslavsky, R. Schober, F. Ulrich, and H.-J. Schwarzmaier, “Optical properties of selected native and coagulated human brain tissues in vitro in the visible and near infrared spectral range,” Physics in Medicine and Biology 47, 2059–2073 (2002).
[Crossref] [PubMed]

Schulze, P. C.

A. N. Yaroslavsky, P. C. Schulze, I. V. Yaroslavsky, R. Schober, F. Ulrich, and H.-J. Schwarzmaier, “Optical properties of selected native and coagulated human brain tissues in vitro in the visible and near infrared spectral range,” Physics in Medicine and Biology 47, 2059–2073 (2002).
[Crossref] [PubMed]

Schwarzmaier, H.-J.

A. N. Yaroslavsky, P. C. Schulze, I. V. Yaroslavsky, R. Schober, F. Ulrich, and H.-J. Schwarzmaier, “Optical properties of selected native and coagulated human brain tissues in vitro in the visible and near infrared spectral range,” Physics in Medicine and Biology 47, 2059–2073 (2002).
[Crossref] [PubMed]

Silberberg, Y.

M. Nixon, O. Katz, E. Small, Y. Bromberg, A. A. Friesem, Y. Silberberg, and N. Davidson, “Real-time wavefront shaping through scattering media by all-optical feedback,” Nat. Photonics 7, 919–924 (2013).
[Crossref]

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).
[Crossref]

Small, E.

M. Nixon, O. Katz, E. Small, Y. Bromberg, A. A. Friesem, Y. Silberberg, and N. Davidson, “Real-time wavefront shaping through scattering media by all-optical feedback,” Nat. Photonics 7, 919–924 (2013).
[Crossref]

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).
[Crossref]

Stetter, K.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131 (2000).
[Crossref] [PubMed]

Stone, A.

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

Takasaki, K. T.

Tang, J.

J. Tang, R. N. Germain, and M. Cui, “Superpenetration optical microscopy by iterative multiphoton adaptive compensation technique,” Proc. Natl. Acad. Sci. U. S. A. 109, 8434–8439 (2012).
[Crossref] [PubMed]

Tank, D. W.

D. A. Dombeck, C. D. Harvey, L. Tian, L. L. Looger, and D. W. Tank, “Functional imaging of hippocampal place cells at cellular resolution during virtual navigation,” Nature Neuroscience 13, 1433–1440 (2010).
[Crossref] [PubMed]

Tian, L.

D. A. Dombeck, C. D. Harvey, L. Tian, L. L. Looger, and D. W. Tank, “Functional imaging of hippocampal place cells at cellular resolution during virtual navigation,” Nature Neuroscience 13, 1433–1440 (2010).
[Crossref] [PubMed]

Ulrich, F.

A. N. Yaroslavsky, P. C. Schulze, I. V. Yaroslavsky, R. Schober, F. Ulrich, and H.-J. Schwarzmaier, “Optical properties of selected native and coagulated human brain tissues in vitro in the visible and near infrared spectral range,” Physics in Medicine and Biology 47, 2059–2073 (2002).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Vellekoop, I. M.

I. M. Vellekoop and C. M. Aegerter, “Scattered light fluorescence microscopy: imaging through turbid layers,” Optics Letters 35, 1245 (2010).
[Crossref] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Universal Optimal Transmission of Light Through Disordered Materials,” Phys. Rev. Lett. 101, 120601 (2008).
[Crossref] [PubMed]

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, and C. Yang, “Translation correlations in anisotropically scattering media,” arXiv:1411.7157 (2014).

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).
[Crossref] [PubMed]

Wang, K.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

Wei, S.-H.

T. J. Coutts, X. Li, T. M. Barnes, B. M. Keyes, C. L. Perkins, S. E. Asher, S. B. Zhang, S.-H. Wei, and S. Limpijumnong, “Synthesis and Characterization of Nitrogen-Doped ZnO Films Grown by MOCVD,” in “Zinc oxide bulk, thin films and nanostructures: processing, properties, and applications,” (Elsevier, 2006), pp. 43–83.

Welch, A. J.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE Journal of Quantum Electronics 26, 2166–2185 (1990).
[Crossref]

Wise, F. W.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

Wong, A. W.

Xu, C.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt. 16, 106014 (2011).
[Crossref] [PubMed]

D. Kobat, M. E. Durst, N. Nishimura, A. W. Wong, C. B. Schaffer, and C. Xu, “Deep tissue multiphoton microscopy using longer wavelength excitation,” Opt. Express 17, 13354 (2009).
[Crossref] [PubMed]

Yang, C.

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, and C. Yang, “Translation correlations in anisotropically scattering media,” arXiv:1411.7157 (2014).

Yang, X.

Yaroslavsky, A. N.

A. N. Yaroslavsky, P. C. Schulze, I. V. Yaroslavsky, R. Schober, F. Ulrich, and H.-J. Schwarzmaier, “Optical properties of selected native and coagulated human brain tissues in vitro in the visible and near infrared spectral range,” Physics in Medicine and Biology 47, 2059–2073 (2002).
[Crossref] [PubMed]

Yaroslavsky, I. V.

A. N. Yaroslavsky, P. C. Schulze, I. V. Yaroslavsky, R. Schober, F. Ulrich, and H.-J. Schwarzmaier, “Optical properties of selected native and coagulated human brain tissues in vitro in the visible and near infrared spectral range,” Physics in Medicine and Biology 47, 2059–2073 (2002).
[Crossref] [PubMed]

Zhang, S. B.

T. J. Coutts, X. Li, T. M. Barnes, B. M. Keyes, C. L. Perkins, S. E. Asher, S. B. Zhang, S.-H. Wei, and S. Limpijumnong, “Synthesis and Characterization of Nitrogen-Doped ZnO Films Grown by MOCVD,” in “Zinc oxide bulk, thin films and nanostructures: processing, properties, and applications,” (Elsevier, 2006), pp. 43–83.

IEEE Journal of Quantum Electronics (1)

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE Journal of Quantum Electronics 26, 2166–2185 (1990).
[Crossref]

J. Biomed. Opt. (3)

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt. 16, 106014 (2011).
[Crossref] [PubMed]

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131 (2000).
[Crossref] [PubMed]

M. Mesradi, A. Genoux, V. Cuplov, D. AbiHaidar, S. Jan, I. Buvat, and F. Pain, “Experimental and analytical comparative study of optical coefficient of fresh and frozen rat tissues,” J. Biomed. Opt. 18, 117010 (2013).
[Crossref] [PubMed]

Journal of neuroscience methods (1)

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” Journal of neuroscience methods 111, 29–37 (2001).
[Crossref] [PubMed]

Journal of Physics D: Applied Physics (1)

C. Dunsby and P. M. W. French, “Techniques for depth-resolved imaging through turbid media including coherence-gated imaging,” Journal of Physics D: Applied Physics 36, R207–R227 (2003).
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Journal of the Optical Society of America A (1)

A. S. Marathay and J. F. McCalmont, “On the usual approximation used in the Rayleigh-Sommerfeld diffraction theory,” Journal of the Optical Society of America A 21, 510 (2004).
[Crossref]

Light: Science & Applications (1)

M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light: Science & Applications 3, e165 (2014).
[Crossref]

Nat. Methods (1)

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7, 603–614 (2010).
[Crossref] [PubMed]

Nat. Photonics (5)

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

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).
[Crossref]

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Nature (1)

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Figures (5)

Fig. 1
Fig. 1

Experimental setup to measure the optical ME: a 532 nm laser beam is focused on the axis of a mirror (M1) mounted on a rotation stage. This spot is imaged onto the sample through an objective (O1) with focal length f1 = 4.5 cm and a lens (L2) with focal length f2 = 50 cm. This results in a circular sample illumination area with 2.3 mm diameter. The scattered light is captured by a CCD with 1024 × 1280 pixels where one pixel measures 5.3 × 5.3μm2. An optional diaphragm can be inserted in front of the sample to reduce the beam size.

Fig. 2
Fig. 2

(a) to (c) show speckle patterns excerpts from rat cortex samples at three different angles. Axes denote pixels from CCD camera, intensity in arbitrary units. Horizontal shift and decorrelation are visible when following the circled speckle. (d) Calculated correlations against offset for images (a) to (c) with 0 deg as the reference image.

Fig. 3
Fig. 3

Measured angular correlation functions for (a) zinc oxide layer and ground glass diffuser as references, (b) chicken breast slices with thicknesses L from 0.85 mm to 2.73 mm and (c) Wistar cortex slices from first series (L from 0.4 mm to 1.6 mm). Solid lines are fits with Eq. (1) with the effective thickness Leff as a free parameter. Resulting Leff values from fitted curves are given in Table 2 and are significantly smaller than the actual sample thickness L for biological tissues. Dashed lines are predicted correlation curves from multiple scattering theory using the actual thicknesses L. They are shown as insets in panels (b) and (c) because of the smaller angular scale. Error bars (standard deviations over multiple measurements) are omitted if smaller than the marker size. (d) Ratio between experimental and theoretical (isotropic scattering) ME range for different sample thicknesses L in multiples of l*. Thickness values have an uncertainty of ∼ 20% from variations in the TMFP. Simulated values (for g ≈ 0.97) are shown as black circles. We get a simulated ratio of 1.08 for L = 50l* outside the horizontal axis range.

Fig. 4
Fig. 4

(a) Influence of the beam size on the ME for a 400 μm thick Wistar cortex sample. The angular correlation function remains the same for spot sizes from 0.7 mm to 2.3 mm. (b) Accessing the “near field” by placing a diaphragm (diameter, 0.7 mm) immediately behind the sample’s exit plane. The speckle pattern is then formed by interfering light from a limited area only. This allows us to access the ME in the diaphragm plane itself. While the correlation function remains the same, the interference pattern changes and the speckle size increases by a factor of ~ 3.6. The emerging plateau is an artifact from larger background correlations for a smaller number of speckles per image. Measurements were performed on a 1600 μm thick Wistar cortex sample.

Fig. 5
Fig. 5

(a) 2D cross-section of the light intensity in a simulation with five phase masks (dashed white lines), incident angle of 3 deg. (b) Cross-section of the path difference λΦ(x,y)/2π from a random phase mask. The resulting scattering angle θs is determined by the phase mask gradient. (c) Simulated angular correlation curves in the weak forward scattering regime. The sample consists of two phase masks with a distance of 100λ and g-factors from 0.7–0.98.

Tables (2)

Tables Icon

Table 1 Scattering properties of in-vivo and ex-vivo cortex tissues at different wavelengths. Values are obtained from references in the last column and values in parenthesis are deduced from the experimental data with (a) g = 0.88 at 532 nm and g = 0.9 for λ > 775 nm [23], (b) by extrapolating the fit in [24] up to 800 nm and (c) by neglecting water absorption.

Tables Icon

Table 2 Effective thickness Leff from fits to Eq. (1) and ME range for ZnO, chicken breast and rat cortex tissues. Uncertainties in the sample thickness L are about 50 μm for tissues and 8 μm for ZnO while error ranges for Leff are taken from fitting uncertainties. The theoretical ME range Δ ϕ 1 / 5 theo was calculated from Eq. (2).

Equations (4)

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

C ( Δ ϕ ) = ( k | Δ ϕ | L sinh ( k | Δ ϕ | L ) ) 2
Δ ϕ 1 / 5 theo 2.369 k 1 L 1 .
g = 4 π p ( θ ) cos θ d Ω .
θ s ( x , y ) = arctan ( λ 2 π | Φ ( x , y ) | )

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