Abstract

Fluorescence microscopy is widely used in biological imaging, however scattering from tissues strongly limits its applicability to a shallow depth. In this work we adapt a methodology inspired from stellar speckle interferometry, and exploit the optical memory effect to enable fluorescence microscopy through a turbid layer. We demonstrate efficient reconstruction of micrometer-size fluorescent objects behind a scattering medium in epi-microscopy, and study the specificities of this imaging modality (magnification, field of view, resolution) as compared to traditional microscopy. Using a modified phase retrieval algorithm to reconstruct fluorescent objects from speckle images, we demonstrate robust reconstructions even in relatively low signal to noise conditions. This modality is particularly appropriate for imaging in biological media, which are known to exhibit relatively large optical memory ranges compatible with tens of micrometers size field of views, and large spectral bandwidths compatible with emission fluorescence spectra of tens of nanometers widths.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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2017 (6)

N. Ji, “Adaptive optical fluorescence microscopy,” Nat. Methods 14(4), 374–380 (2017).
[Crossref] [PubMed]

J. Chang and G. Wetzstein, “Single-shot speckle correlation fluorescence microscopy in thick scattering tissue with image reconstruction priors,” J. Biophotonics 11(3), e201700224 (2017).
[PubMed]

D. Ancora, D. Di Battista, G. Giasafaki, S. Psycharakis, A. Zacharopoulos, and G. Zacharakis, “Optical Projection Tomography via Phase Retrieval Algorithms for Hidden Three Dimensional Imaging,” Proc. SPIE 10074, 1–7 (2017).

Y. Shi, Y. Liu, J. Wang, and T. Wu, “Non-invasive depth-resolved imaging through scattering layers via speckle correlations and parallax,” Appl. Phys. Lett. 110(23), 231101 (2017).
[Crossref]

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, “The generalized optical memory effect,” Optica 4(8), 886–892 (2017).
[Crossref]

T. Wu, J. Dong, X. Shao, and S. Gigan, “Imaging through a thin scattering layer and jointly retrieving the point-spread-function using phase-diversity,” Opt. Express 25(22), 27182–27194 (2017).
[Crossref] [PubMed]

2016 (5)

D. L. N. Kallepalli, A. M. Alshehri, D. T. Marquez, L. Andrzejewski, J. C. Scaiano, and R. Bhardwaj, “Ultra-high density optical data storage in common transparent plastics,” Sci. Rep. 6(1), 26163 (2016).
[Crossref] [PubMed]

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6(2), e16219 (2016).
[Crossref]

E. Edrei and G. Scarcelli, “Optical imaging through dynamic turbid media using the Fourier-domain shower-curtain effect,” Optica 3(1), 71–74 (2016).
[Crossref] [PubMed]

T. Wu, O. Katz, X. Shao, and S. Gigan, “Single-shot diffraction-limited imaging through scattering layers via bispectrum analysis,” Opt. Lett. 41(21), 5003–5006 (2016).
[Crossref] [PubMed]

E. Edrei and G. Scarcelli, “Memory-effect based deconvolution microscopy for super-resolution imaging through scattering media,” Sci. Rep. 6(1), 33558 (2016).
[Crossref] [PubMed]

2015 (2)

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11(8), 1–6 (2015).
[Crossref]

S. Schott, J. Bertolotti, J.-F. Léger, L. Bourdieu, and S. Gigan, “Characterization of the angular memory effect of scattered light in biological tissues,” Opt. Express 23(10), 13505–13516 (2015).
[Crossref] [PubMed]

2014 (5)

2013 (1)

2012 (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]

2011 (1)

2010 (2)

V. Ntziachristos, “Going deeper than microscopy: The optical imaging frontier in biology,” Nat. Methods 7(8), 603–614 (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]

2008 (1)

I. M. Vellekoop, “Controlling the propagation of light in disordered scattering media,” Nat. Photonics 8, 784–790 (2008).

2000 (1)

1999 (1)

J. Schmitt, “Optical Coherence Tomography (OCT): A Review,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1205–1215 (1999).
[Crossref]

1992 (1)

A. Lagendijk, M. P. Van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B Condens. Matter 45(2), 658–666 (1992).
[Crossref] [PubMed]

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

1990 (1)

I. Freund, “Looking through walls and around corners,” Phys. A Stat. Mech. its Appl. 168(1), 49–65 (1990).
[Crossref]

1988 (1)

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)

Alshehri, A. M.

D. L. N. Kallepalli, A. M. Alshehri, D. T. Marquez, L. Andrzejewski, J. C. Scaiano, and R. Bhardwaj, “Ultra-high density optical data storage in common transparent plastics,” Sci. Rep. 6(1), 26163 (2016).
[Crossref] [PubMed]

Ancora, D.

D. Ancora, D. Di Battista, G. Giasafaki, S. Psycharakis, A. Zacharopoulos, and G. Zacharakis, “Optical Projection Tomography via Phase Retrieval Algorithms for Hidden Three Dimensional Imaging,” Proc. SPIE 10074, 1–7 (2017).

Andersen, P. E.

Andrzejewski, L.

D. L. N. Kallepalli, A. M. Alshehri, D. T. Marquez, L. Andrzejewski, J. C. Scaiano, and R. Bhardwaj, “Ultra-high density optical data storage in common transparent plastics,” Sci. Rep. 6(1), 26163 (2016).
[Crossref] [PubMed]

Bertolotti, J.

S. Schott, J. Bertolotti, J.-F. Léger, L. Bourdieu, and S. Gigan, “Characterization of the angular memory effect of scattered light in biological tissues,” Opt. Express 23(10), 13505–13516 (2015).
[Crossref] [PubMed]

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]

Bhardwaj, R.

D. L. N. Kallepalli, A. M. Alshehri, D. T. Marquez, L. Andrzejewski, J. C. Scaiano, and R. Bhardwaj, “Ultra-high density optical data storage in common transparent plastics,” Sci. Rep. 6(1), 26163 (2016).
[Crossref] [PubMed]

Bifano, T.

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. 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.

Bourdieu, L.

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]

Chang, J.

J. Chang and G. Wetzstein, “Single-shot speckle correlation fluorescence microscopy in thick scattering tissue with image reconstruction priors,” J. Biophotonics 11(3), e201700224 (2017).
[PubMed]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Curry, N.

Das, B.

Di Battista, D.

D. Ancora, D. Di Battista, G. Giasafaki, S. Psycharakis, A. Zacharopoulos, and G. Zacharakis, “Optical Projection Tomography via Phase Retrieval Algorithms for Hidden Three Dimensional Imaging,” Proc. SPIE 10074, 1–7 (2017).

Dong, J.

Edrei, E.

E. Edrei and G. Scarcelli, “Optical imaging through dynamic turbid media using the Fourier-domain shower-curtain effect,” Optica 3(1), 71–74 (2016).
[Crossref] [PubMed]

E. Edrei and G. Scarcelli, “Memory-effect based deconvolution microscopy for super-resolution imaging through scattering media,” Sci. Rep. 6(1), 33558 (2016).
[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]

Fienup, J. R.

Fink, M.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive real-time 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]

Fleischer, J. W.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Freund, I.

I. Freund, “Looking through walls and around corners,” Phys. A Stat. Mech. its Appl. 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]

Giasafaki, G.

D. Ancora, D. Di Battista, G. Giasafaki, S. Psycharakis, A. Zacharopoulos, and G. Zacharakis, “Optical Projection Tomography via Phase Retrieval Algorithms for Hidden Three Dimensional Imaging,” Proc. SPIE 10074, 1–7 (2017).

Gigan, S.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Grésillon, S.

Guan, Y.

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Heidmann, P.

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

Horstmeyer, R.

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, “The generalized optical memory effect,” Optica 4(8), 886–892 (2017).
[Crossref]

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11(8), 1–6 (2015).
[Crossref]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Ji, N.

N. Ji, “Adaptive optical fluorescence microscopy,” Nat. Methods 14(4), 374–380 (2017).
[Crossref] [PubMed]

Judkewitz, B.

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, “The generalized optical memory effect,” Optica 4(8), 886–892 (2017).
[Crossref]

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11(8), 1–6 (2015).
[Crossref]

Kallepalli, D. L. N.

D. L. N. Kallepalli, A. M. Alshehri, D. T. Marquez, L. Andrzejewski, J. C. Scaiano, and R. Bhardwaj, “Ultra-high density optical data storage in common transparent plastics,” Sci. Rep. 6(1), 26163 (2016).
[Crossref] [PubMed]

Katz, O.

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]

A. Lagendijk, M. P. Van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B Condens. Matter 45(2), 658–666 (1992).
[Crossref] [PubMed]

A. Lagendijk, M. P. Van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B Condens. Matter 45(2), 658–666 (1992).
[Crossref] [PubMed]

Leclercq, M.

Léger, J.-F.

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]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Liu, Y.

Y. Shi, Y. Liu, J. Wang, and T. Wu, “Non-invasive depth-resolved imaging through scattering layers via speckle correlations and parallax,” Appl. Phys. Lett. 110(23), 231101 (2017).
[Crossref]

Marquez, D. T.

D. L. N. Kallepalli, A. M. Alshehri, D. T. Marquez, L. Andrzejewski, J. C. Scaiano, and R. Bhardwaj, “Ultra-high density optical data storage in common transparent plastics,” Sci. Rep. 6(1), 26163 (2016).
[Crossref] [PubMed]

Mertz, J.

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]

Naik, D. N.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6(2), e16219 (2016).
[Crossref]

Ntziachristos, V.

V. Ntziachristos, “Going deeper than microscopy: The optical imaging frontier in biology,” Nat. Methods 7(8), 603–614 (2010).
[Crossref] [PubMed]

Osnabrugge, G.

Osten, W.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6(2), e16219 (2016).
[Crossref]

Papadopoulos, I. N.

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, “The generalized optical memory effect,” Optica 4(8), 886–892 (2017).
[Crossref]

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11(8), 1–6 (2015).
[Crossref]

Paudel, H. P.

Pedrini, G.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6(2), e16219 (2016).
[Crossref]

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.

Psycharakis, S.

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Appl. Opt. (1)

Appl. Phys. Lett. (1)

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

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Proc. SPIE (1)

D. Ancora, D. Di Battista, G. Giasafaki, S. Psycharakis, A. Zacharopoulos, and G. Zacharakis, “Optical Projection Tomography via Phase Retrieval Algorithms for Hidden Three Dimensional Imaging,” Proc. SPIE 10074, 1–7 (2017).

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E. Edrei and G. Scarcelli, “Memory-effect based deconvolution microscopy for super-resolution imaging through scattering media,” Sci. Rep. 6(1), 33558 (2016).
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D. L. N. Kallepalli, A. M. Alshehri, D. T. Marquez, L. Andrzejewski, J. C. Scaiano, and R. Bhardwaj, “Ultra-high density optical data storage in common transparent plastics,” Sci. Rep. 6(1), 26163 (2016).
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Science (1)

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Figures (11)

Fig. 1
Fig. 1 (a) Regular inverted laser microscope in wide-field mode. cw:continuous wave light source, DM:dichroic mirror, TL:tube lens, FF:fuorescence filter. (b) Scheme of the excitation and fluorescence light emission with object-diffuser distance z and diffuser-focal plane distance z’. (c) Fluorescent object consisting of deposited 1 μm orange beads, imaged without diffuser (d) Normalized scattered light detected below the diffuser (distances z = 2 mm, z’ = 600 µm). (e) Windowed autocorrelation of (d). (f) Reconstructed object using the autocorrelation and ping-pong algorithm (see text). Scale bars are 200 µm in (c)-(e) and 50 µm in (f). The
Fig. 2
Fig. 2 Detailed flow chart of the ping-pong algorithm which consists of a modified hybrid input-output algorithm and the error reduction algorithm. The missing phase φG is desired to be retrieved with |H| as the Fourier domain modulus as the only available information
Fig. 3
Fig. 3 Fluorescent quantum dot square pattern imaged with a 10x/0.25 objective. In the absence of a diffuser, scale bar 100 μm (a) or in the presence of a diffuser at different distances (b)-(d). The second column shows the raw scattered light image detected at 600 μm below the diffuser, the third column shows a cropped and normalized scattered light and the most right column shows the reconstructed object. Scale bars from second to fourth column are: 300 μm, 200 μm and 50 μm. Excitation power on the diffuser was 25 mW with integration times of 10 to 30 s. The autocorrelation based ping-pong algorithm is used for all reconstructions.
Fig. 4
Fig. 4 Normalized scattered light image with the focal plane at three different distances from the diffuser, z’ = 150, 300 and 600 μm. (a) Scheme of excitation and emission of the fluorescent object. The dashed line represents the focal plane of the objective. (b) Object imaged without diffuser. (c), (e) and (g) show the normalized scattered light. Scale bars: 100 μm. (d), (f) and (h) show the reconstruction of the object. Scale bars: 40 μm (in the plane of scattered light detection, using the scattering lens magnification Mscatt, see text). The sampling of the total object size along the horizontal direction is 34 (c), 69 (e) and 138 (g) pixels on the camera. Excitation power on the diffuser was 1 mW, integration time was 1 s. The autocorrelation based ping-pong algorithm is used for all recontructions.
Fig. 5
Fig. 5 Fluorescent object reconstructions with different emission filter bandwidths. (a) Object imaged without diffuser. (b) Emission spectrum of orange red beads. Reconstruction with bandpass filter 632-1 nm (c), 590-10 nm (d), 692-40 nm (e) and a 550 long pass filter (creating a 60 nm bandpass detection accounting for the dichroic mirror used) (f). Scale bars are 300 μm in (a) and 40 μm in (c) to (f). Excitation power on the diffuser was 1 mW with integration times from (c)-(d) of 30 s, 1.5 s, 5 s and 0.2 s respectively. Fourier Domain Smoothing (see Appendix A1) and ping-pong algorithm were used for all reconstructions.
Fig. 6
Fig. 6 Reconstructed objects from simulated scattered light images. The normalized cross correlation (cc) values are calculated with respect to the original object and serve as a metric to assess the quality of reconstruction. The reconstructions shown are taken from simulations with SNR-image treatment (method + algorithm): (a) no noise (AC + HIO), (b) 8dB (FDS + PP), (c) 5dB (FDS + PP), (d) no noise (AC + HIO).
Fig. 7
Fig. 7 Performance comparison of a HIO algorithm with the ping-pong algorithm. The normalized cross correlation between the reconstruction and the original object is used a reconstruction quality metric. The mean value over 20 reconstructions is plotted as a blue circle (PP) and a red triangle (HIO) for signal-to-noise values of the scattered light image of 5, 8 and 15 dB, as well as for noise free (∞dB) and experimental data. Error bars indicate the mean deviation in both positive and negative direction. The square and cross sign indicate the maximum normalized cross correlation value reached for each of the reconstruction conditions. Additionally, the autocorrelation (AC) and Fourier domain smoothing (FDS) image treatment techniques are compared.
Fig. 8
Fig. 8 Examples for very good reconstruction results for varying signal-to-noise levels on the scattered light images (left row) (a)-(d) and experimental data (e). The combination of image treatment (AC or FDS) and phase retrieval algorithm (PP or HIO) is indicated in the top right corner of the object reconstruction.
Fig. 9
Fig. 9 (a) object, (b) generated speckle, (c) convolution of object with speckle, (d) FT of object, (e) FT of speckle, (f) FT(I) = FT(S)*FT(O), (g) smoothened speckle FT, (h) smoothened FT(I), (i) reconstruction of (h) with phase retrieval algorithm, (j) IFT of (h) with known phase of object, (k) smoothened FT(I) from experimental data, (l) reconstruction from (k).
Fig. 10
Fig. 10 Correlation of scattered light images recorded with the diffuser translated. The tilt angle is calculated from the translation distance d of the diffuser by arctan(d/z), where z is the distance between object and diffuser.
Fig. 11
Fig. 11 A simple (a) and a more complex object (b), its scattered light after the diffuser (center row) and the reconstruction (right row). (a) ‘F’ pattern fabricated by direct laser writing process with organic dyes fluorescent structures in a clear polymer. (b) Drop casted orange beads.

Equations (3)

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I=OS= O(x)S(xδx)dx .
II=[ OO ][ SS ]OO.
| H |=| F{ O } |= | F{ II } | .

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