Abstract

Random scattering of light by a turbid layer prevents conventional imaging of objects hidden behind it. Angular correlations in the scattered light, created by the so-called optical memory effect, have been shown to enable computational image retrieval of hidden sources. However, basic memory-effect imaging contains no spatial (x) information, as only angular (k-space) measurements are made. Here, we use windowed Fourier transforms to record scattered-light images in the full {x,k} phase space. The result is the ability to discriminate size and depth of individual sources that are hidden behind a thin scattering layer.

© 2014 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2014 (1)

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(10), 784–790 (2014).
[Crossref]

2012 (4)

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[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(8), 549–553 (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]

D. V. Dylov, L. Waller, and J. W. Fleischer, “Nonlinear restoration of diffused images via seeded instability,” IEEE J. Sel. Top. Quantum Electron. 18(2), 916–925 (2012).
[Crossref]

2010 (5)

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4(5), 323–328 (2010).
[Crossref]

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7(2), 141–147 (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]

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]

I. M. Vellekoop and C. M. Aegerter, “Scattered light fluorescence microscopy: imaging through turbid layers,” Opt. Lett. 35(8), 1245–1247 (2010).
[Crossref] [PubMed]

2008 (1)

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 (1)

1990 (1)

I. Freund, “Looking through walls and around corners,” Physica A: Statistical Mechanics and its Applications 168(1), 49–65 (1990).
[Crossref]

1989 (1)

L. Cohen, “Time-frequency distributions – a review,” Proc. IEEE 77(7), 941–981 (1989).
[Crossref]

1988 (2)

S. C. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[Crossref] [PubMed]

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

1982 (1)

1978 (2)

M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25(1), 26–30 (1978).
[Crossref]

A. Yariv, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. 14(9), 650–660 (1978).
[Crossref]

1974 (1)

1970 (1)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

1966 (1)

Aegerter, C. M.

Bastiaans, M. J.

M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25(1), 26–30 (1978).
[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]

Betzig, E.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7(2), 141–147 (2010).
[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]

Bridges, W. B.

Brown, W. P.

Brunner, P. T.

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(10), 100601 (2010).
[Crossref] [PubMed]

Cohen, L.

L. Cohen, “Time-frequency distributions – a review,” Proc. IEEE 77(7), 941–981 (1989).
[Crossref]

Dylov, D. V.

D. V. Dylov, L. Waller, and J. W. Fleischer, “Nonlinear restoration of diffused images via seeded instability,” IEEE J. Sel. Top. Quantum Electron. 18(2), 916–925 (2012).
[Crossref]

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4(5), 323–328 (2010).
[Crossref]

Feld, M. S.

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]

Feng, S.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Feng, S. C.

S. C. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[Crossref] [PubMed]

Fienup, J. R.

Fink, M.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[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(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]

Fleischer, J. W.

D. V. Dylov, L. Waller, and J. W. Fleischer, “Nonlinear restoration of diffused images via seeded instability,” IEEE J. Sel. Top. Quantum Electron. 18(2), 916–925 (2012).
[Crossref]

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[Crossref]

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4(5), 323–328 (2010).
[Crossref]

Freund, I.

I. Freund, “Looking through walls and around corners,” Physica A: Statistical Mechanics and its Applications 168(1), 49–65 (1990).
[Crossref]

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[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(10), 784–790 (2014).
[Crossref]

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]

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(10), 784–790 (2014).
[Crossref]

Ji, N.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7(2), 141–147 (2010).
[Crossref] [PubMed]

Kane, C.

S. C. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 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(10), 784–790 (2014).
[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(8), 549–553 (2012).
[Crossref]

Labeyrie, A.

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

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

Lazzara, S. P.

Lee, P. A.

S. C. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[Crossref] [PubMed]

Leith, E. N.

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(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]

Milkie, D. E.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7(2), 141–147 (2010).
[Crossref] [PubMed]

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

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

Nussmeier, T. A.

O’Meara, T. R.

Popoff, S.

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]

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(10), 100601 (2010).
[Crossref] [PubMed]

Psaltis, D.

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]

Rosenbluh, M.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Sanguinet, J. A.

Silberberg, Y.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

Situ, G.

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[Crossref]

Small, E.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

Stone, A. D.

S. C. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[Crossref] [PubMed]

Upatnieks, J.

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

Vellekoop, I. M.

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

Waller, L.

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[Crossref]

D. V. Dylov, L. Waller, and J. W. Fleischer, “Nonlinear restoration of diffused images via seeded instability,” IEEE J. Sel. Top. Quantum Electron. 18(2), 916–925 (2012).
[Crossref]

Yang, C.

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]

Yaqoob, Z.

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]

Yariv, A.

A. Yariv, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. 14(9), 650–660 (1978).
[Crossref]

Appl. Opt. (2)

Astron. Astrophys. (1)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

IEEE J. Quantum Electron. (1)

A. Yariv, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. 14(9), 650–660 (1978).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

D. V. Dylov, L. Waller, and J. W. Fleischer, “Nonlinear restoration of diffused images via seeded instability,” IEEE J. Sel. Top. Quantum Electron. 18(2), 916–925 (2012).
[Crossref]

J. Opt. Soc. Am. (1)

Nat Commun (1)

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]

Nat. Methods (1)

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7(2), 141–147 (2010).
[Crossref] [PubMed]

Nat. Photonics (5)

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]

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4(5), 323–328 (2010).
[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(8), 549–553 (2012).
[Crossref]

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(10), 784–790 (2014).
[Crossref]

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[Crossref]

Nature (1)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref] [PubMed]

Opt. Commun. (1)

M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25(1), 26–30 (1978).
[Crossref]

Opt. Lett. (2)

Phys. Rev. Lett. (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. C. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[Crossref] [PubMed]

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Physica A: Statistical Mechanics and its Applications (1)

I. Freund, “Looking through walls and around corners,” Physica A: Statistical Mechanics and its Applications 168(1), 49–65 (1990).
[Crossref]

Proc. IEEE (1)

L. Cohen, “Time-frequency distributions – a review,” Proc. IEEE 77(7), 941–981 (1989).
[Crossref]

Other (2)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (New York: Cambridge University Press, 2002).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2010).

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Figures (5)

Fig. 1
Fig. 1 Experimental setup and phase-space measurement of scattered light. (a) Schematic of experimental setup. A ground glass diffuser is illuminated by a coherent laser beam for speckle imaging or, in image retrieval experiments, by the incoherent, de-magnified image of an individual cutout shape (“P” or “U”) illuminated by a bandpass-filtered lamp. The diffuser surface is imaged by a microscope objective (obj: 50x, 0.9 NA) and tube lens (TL: f = 120 mm) onto a LCOS spatial light modulator (SLM, Holoeye LCR-2500) configured for amplitude modulation. The field reflected from the SLM is imaged onto the x-space CCD sensor and optically Fourier transformed onto the k-space CCD. Pol: linear polarizer. PBS: polarizing beam splitter. (b) Top: x-space CCD image of the 64 μm-wide square window illuminated with a collimated laser. Bottom: k-space CCD image showing the far-field intensity of the square window. (c) Top: x-space image of a windowed region of the scattered light from the diffuser. Bottom: k-space image of the far-field random speckle produced by the scattered light.
Fig. 2
Fig. 2 Correlations in scattered light. (a) Composite speckle images from a point source moved between two positions (red and green) laterally separated by 200μm. (b) Grayscale values from simulated cross-correlation along the vertical axis (k-axis) as a function of source position (xo-axis). Blue circles show the cross-correlation peaks measured in experiment. (c) Composite average speckle images from the square window moved between two positions (red and green) on the diffuser surface separated by 500μm. (d) Red and blue pseudo-colored grayscale values from the simulated average spectrogram distribution, P S ( x,k ) , as a function of angle along the vertical axis (k-axis) and window position (xs-axis) for z1 = 1mm (blue) and z2 = 1.4mm (red). Thin lines are PS for unscattered, fully spatially coherent light. Experimental data for z ≈1mm are plotted as blue circles with bars representing the angular spread of the measured distribution.
Fig. 3
Fig. 3 Image retrieval from angular correlations. (a) Top and bottom: CCD image of k-space intensity, Ik, of scattered light for two different source shapes at different distances. (b) I k I k of CCD images, as in (a), taken over non-overlapping scattering regions. (c) Computationally recovered images from autocorrelations in (b). (d) Ground-truth images taken of sources.
Fig. 4
Fig. 4 Phase-space measurement of spatio-angular correlations. (a) x-space image of incoherent source hidden behind the diffuser and outline of phase-space window at four positions. (b) Pseudo-colored CCD images taken through windows in (a) of two different sources (“P”, red, top panels; “U”, blue, bottom panels) at two different distances. Dashed white line is the kx-axis. (c-d) PS of scattered light acquired by scanning the phase-space window along one spatial axis (x). The vertical axis is the line profile of intensity (kx) measured from CCD images (dashed line in (b)), and the horizontal axis is the position of the window. (e) Position of peak of the angular spectra along the kx-axis in (c) and (d) with linear fits to determine slopes. Error bars are the experimentally measured uncertainty of the peak contributed by variability of the diffuser.
Fig. 5
Fig. 5 Depth and size of hidden source. (a) Image taken directly of “P”- (top) and “U”-(bottom) shaped source for comparison with recovered image. (b) Recovered image data from Fig. 3(c) with pixel size calibration by source depth measured in Fig. 4(e). (c) Line profiles taken through the images as shown in (a) and (b).

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