Abstract

Optical diffraction tomography (ODT) reconstructs a sample’s volumetric refractive index (RI) to create high-contrast, quantitative 3D visualizations of biological samples. However, standard implementations of ODT use interferometric systems, and so are sensitive to phase instabilities, complex mechanical design, and coherent noise. Furthermore, their reconstruction framework is typically limited to weakly scattering samples, and thus excludes a whole class of multiple-scattering samples. Here, we implement a new 3D RI microscopy technique that utilizes a computational multi-slice beam propagation method to invert the optical scattering process and reconstruct high-resolution (NA>1.0) 3D RI distributions of multiple-scattering samples. The method acquires intensity-only measurements from different illumination angles and then solves a nonlinear optimization problem to recover the sample’s 3D RI distribution. We experimentally demonstrate the reconstruction of samples with varying amounts of multiple-scattering: a 3T3 fibroblast cell, a cluster of C. elegans embryos, and a whole C. elegans worm, with lateral and axial resolutions of 240nm and 900nm, respectively. The results of this work lays groundwork for future studies into using optical wavelengths to probe 3D RI distributions of highly scattering biological organisms.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]

2018 (5)

D. Ancora, D. Di Battista, G. Giasafaki, S. E. Psycharakis, E. Liapis, J. Ripoll, and G. Zacharakis, “Optical projection tomography via phase retrieval algorithms,” Methods 136, 81–89 (2018).
[Crossref]

H.-Y. Liu, D. Liu, H. Mansour, P. T. Boufounos, L. Waller, and U. S. Kamilov, “SEAGLE: sparsity-driven image reconstruction under multiple scattering,” IEEE Trans. Comput. Imag. 4, 73–86 (2018).
[Crossref]

R. Ling, W. Tahir, H.-Y. Lin, H. Lee, and L. Tian, “High-throughput intensity diffraction tomography with a computational microscope,” Biomed. Opt. Express 9, 2130–2141 (2018).
[Crossref]

R. Eckert, Z. F. Phillips, and L. Waller, “Efficient illumination angle self-calibration in Fourier ptychography,” Appl. Opt. 57, 5434–5442 (2018).
[Crossref]

M. E. Kandel, M. Fanous, C. Best-Popescu, and G. Popescu, “Real-time halo correction in phase contrast imaging,” Biomed. Opt. Express 9, 623–635 (2018).
[Crossref]

2017 (5)

2016 (7)

W. J. Eldridge, A. Sheinfeld, M. T. Rinehart, and A. Wax, “Imaging deformation of adherent cells due to shear stress using quantitative phase imaging,” Opt. Lett. 41, 352–355 (2016).
[Crossref]

J. Jung, K. Kim, J. Yoon, and Y. Park, “Hyperspectral optical diffraction tomography,” Opt. Express 24, 2006–2012 (2016).
[Crossref]

M. Chen, L. Tian, and L. Waller, “3D differential phase contrast microscopy,” Biomed. Opt. Express 7, 3940–3950 (2016).
[Crossref]

R. Horstmeyer, J. Chung, X. Ou, G. Zheng, and C. Yang, “Diffraction tomography with Fourier ptychography,” Optica 3, 827–835 (2016).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2, 59–70 (2016).
[Crossref]

M. Schürmann, J. Scholze, P. Müller, J. Guck, and C. J. Chan, “Cell nuclei have lower refractive index and mass density than cytoplasm,” J. Biophoton. 9, 1068–1076 (2016).
[Crossref]

U. S. Kamilov, D. Liu, H. Mansour, and P. T. Boufounos, “A recursive Born approach to nonlinear inverse scattering,” IEEE Signal Process. Lett. 23, 1052–1056 (2016).
[Crossref]

2015 (3)

2014 (3)

S. Lee, K. Kim, A. Mubarok, A. Panduwirawan, K. Lee, S. Lee, H. Park, and Y. Park, “High-resolution 3-D refractive index tomography and 2-D synthetic aperture imaging of live phytoplankton,” J. Opt. Soc. Korea 18, 691–697 (2014).
[Crossref]

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

K. Kim, H. Yoon, M. Diez-Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by Plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19, 011005 (2014).
[Crossref]

2013 (2)

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[Crossref]

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

2012 (1)

2010 (1)

2009 (4)

2008 (1)

Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. USA 105, 13730–13735 (2008).
[Crossref]

2007 (1)

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

2006 (2)

2004 (1)

A. Rustom, R. Saffrich, I. Markovic, P. Walther, and H.-H. Gerdes, “Nanotubular highways for intercellular organelle transport,” Science 303, 1007–1010 (2004).
[Crossref]

2002 (3)

M. Okuda, K. Li, M. R. Beard, L. A. Showalter, F. Scholle, S. M. Lemon, and S. A. Weinman, “Mitochondrial injury, oxidative stress, and antioxidant gene expression are induced by hepatitis C virus core protein,” Gastroenterology 122, 366–375 (2002).
[Crossref]

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
[Crossref]

J. V. Small, T. Stradal, E. Vignal, and K. Rottner, “The lamellipodium: where motility begins,” Trends Cell Biol. 12, 112–120 (2002).
[Crossref]

2000 (1)

D. T. Ross, U. Scherf, M. B. Eisen, C. M. Perou, C. Rees, P. Spellman, V. Iyer, S. S. Jeffrey, M. Van de Rijn, and M. Waltham, “Systematic variation in gene expression patterns in human cancer cell lines,” Nat. Genet. 24, 227–235 (2000).
[Crossref]

1998 (1)

1995 (1)

R. Rizzuto, M. Brini, P. Pizzo, M. Murgia, and T. Pozzan, “Chimeric green fluorescent protein as a tool for visualizing subcellular organelles in living cells,” Curr. Biol. 5, 635–642 (1995).
[Crossref]

1994 (1)

1993 (1)

1992 (1)

1990 (1)

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335–1339 (1990).
[Crossref]

1986 (1)

J. G. White, E. Southgate, J. N. Thomson, and S. Brenner, “The structure of the nervous system of the nematode Caenorhabditis elegans,” Philos. Trans. R. Soc. B 314, 1–340 (1986).
[Crossref]

1983 (1)

J. E. Sulston, E. Schierenberg, J. G. White, and J. Thomson, “The embryonic cell lineage of the nematode Caenorhabditis elegans,” Dev. Biol. 100, 64–119 (1983).
[Crossref]

1981 (2)

1969 (1)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[Crossref]

Ancora, D.

D. Ancora, D. Di Battista, G. Giasafaki, S. E. Psycharakis, E. Liapis, J. Ripoll, and G. Zacharakis, “Optical projection tomography via phase retrieval algorithms,” Methods 136, 81–89 (2018).
[Crossref]

Babacan, S. D.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

Badizadegan, K.

Bailleul, J.

Beard, M. R.

M. Okuda, K. Li, M. R. Beard, L. A. Showalter, F. Scholle, S. M. Lemon, and S. A. Weinman, “Mitochondrial injury, oxidative stress, and antioxidant gene expression are induced by hepatitis C virus core protein,” Gastroenterology 122, 366–375 (2002).
[Crossref]

Belkebir, K.

Best-Popescu, C.

Boss, D.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Bostan, E.

E. Froustey, E. Bostan, S. Lefkimmiatis, and M. Unser, “Digital phase reconstruction via iterative solutions of transport-of-intensity equation,” in 13th Workshop on Information Optics (WIO) (IEEE, 2014), pp. 1–3.

Boufounos, P. T.

H.-Y. Liu, D. Liu, H. Mansour, P. T. Boufounos, L. Waller, and U. S. Kamilov, “SEAGLE: sparsity-driven image reconstruction under multiple scattering,” IEEE Trans. Comput. Imag. 4, 73–86 (2018).
[Crossref]

U. S. Kamilov, D. Liu, H. Mansour, and P. T. Boufounos, “A recursive Born approach to nonlinear inverse scattering,” IEEE Signal Process. Lett. 23, 1052–1056 (2016).
[Crossref]

Brenner, S.

J. G. White, E. Southgate, J. N. Thomson, and S. Brenner, “The structure of the nervous system of the nematode Caenorhabditis elegans,” Philos. Trans. R. Soc. B 314, 1–340 (1986).
[Crossref]

Brini, M.

R. Rizzuto, M. Brini, P. Pizzo, M. Murgia, and T. Pozzan, “Chimeric green fluorescent protein as a tool for visualizing subcellular organelles in living cells,” Curr. Biol. 5, 635–642 (1995).
[Crossref]

Bursac, N.

Carney, P. S.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

Chan, C. J.

M. Schürmann, J. Scholze, P. Müller, J. Guck, and C. J. Chan, “Cell nuclei have lower refractive index and mass density than cytoplasm,” J. Biophoton. 9, 1068–1076 (2016).
[Crossref]

Chaumet, P. C.

Chen, B.

Chen, M.

Cho, Y.-H.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[Crossref]

Choi, W.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009).
[Crossref]

Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. USA 105, 13730–13735 (2008).
[Crossref]

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

Chowdhury, S.

Chung, J.

Chung, Y.

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335–1339 (1990).
[Crossref]

Cotte, Y.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Dagli, N.

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335–1339 (1990).
[Crossref]

Dao, M.

K. Kim, H. Yoon, M. Diez-Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by Plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19, 011005 (2014).
[Crossref]

Dasari, R. R.

K. Kim, H. Yoon, M. Diez-Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by Plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19, 011005 (2014).
[Crossref]

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009).
[Crossref]

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

Y. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Diffraction phase and fluorescence microscopy,” Opt. Express 14, 8263–8268 (2006).
[Crossref]

Debailleul, M.

Depeursinge, C.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Devaney, A.

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K. Kim, H. Yoon, M. Diez-Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by Plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19, 011005 (2014).
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D. Ancora, D. Di Battista, G. Giasafaki, S. E. Psycharakis, E. Liapis, J. Ripoll, and G. Zacharakis, “Optical projection tomography via phase retrieval algorithms,” Methods 136, 81–89 (2018).
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Nat. Commun. (1)

T. H. Nguyen, M. E. Kandel, M. Rubessa, M. B. Wheeler, and G. Popescu, “Gradient light interference microscopy for 3D imaging of unlabeled specimens,” Nat. Commun. 8, 210 (2017).
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D. T. Ross, U. Scherf, M. B. Eisen, C. M. Perou, C. Rees, P. Spellman, V. Iyer, S. S. Jeffrey, M. Van de Rijn, and M. Waltham, “Systematic variation in gene expression patterns in human cancer cell lines,” Nat. Genet. 24, 227–235 (2000).
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T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

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[Crossref]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
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J. G. White, E. Southgate, J. N. Thomson, and S. Brenner, “The structure of the nervous system of the nematode Caenorhabditis elegans,” Philos. Trans. R. Soc. B 314, 1–340 (1986).
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Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. USA 105, 13730–13735 (2008).
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J. V. Small, T. Stradal, E. Vignal, and K. Rottner, “The lamellipodium: where motility begins,” Trends Cell Biol. 12, 112–120 (2002).
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E. Froustey, E. Bostan, S. Lefkimmiatis, and M. Unser, “Digital phase reconstruction via iterative solutions of transport-of-intensity equation,” in 13th Workshop on Information Optics (WIO) (IEEE, 2014), pp. 1–3.

Supplementary Material (8)

NameDescription
» Supplement 1       Supporting Information
» Visualization 1       Raw intensity measurements and Fourier spectrum
» Visualization 2       3T3 fibroblast 3D data reconstruction and visualization with axial flythrough
» Visualization 3       3T3 fibroblast 3D data reconstruction and visualization with tomographic rendering
» Visualization 4       Raw intensity measurements and Fourier spectrum
» Visualization 5       C. elegans embryo 3D data reconstruction and visualization with axial flythrough
» Visualization 6       C. elegans embryos 3D data reconstruction and visualization with tomographic rendering
» Visualization 7       Whole C. elegans worm 3D data reconstruction and visualization with planar translation and axial flythrough

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Figures (5)

Fig. 1.
Fig. 1. (a) Optical system design with illumination angle trajectories, comparing the raw position values outputted from the kinematic tilt mirror to that after algorithmic self-calibration. (b), (d), and (f) Raw intensity acquisitions and (c), (e), and (g) amplitudes of associated Fourier transforms, after illuminating the sample with varying angles.
Fig. 2.
Fig. 2. 3D reconstruction of refractive index (RI) for two 3 μm diameter polystyrene microspheres (n=1.598) in index-matched oil (n=1.552). (a) Lateral (x-y) slice, (b) axial (x-z) slice, taken along the horizontal dashed line in (a), and (c) 3D rendering of the reconstructed microspheres. (d) Cross-cut of the refractive index along the vertical dashed line in (a) matches well with expected values from the sample.
Fig. 3.
Fig. 3. Lateral cross-sections (gray-scale and RGB color-coded) through the 3D RI reconstruction volume at axial positions of (a) and (b) z=0.0μm, (c) and (d)z=1.05μm, and (e) and (f) z=2.10μm. (g) 3D rendering of the 3T3 cell RI.
Fig. 4.
Fig. 4. 3D RI reconstruction of a C. elegans embryo cluster. (a)–(c) Raw intensity acquisitions at varying illumination angles, along with their Fourier transform amplitudes. (d)–(f) Lateral slices through the 3D reconstruction volume at axial positions z=2.6,0,+2.6μm. (g) Axial slice taken at the location indicated by the dashed line in (e). (h)–(k) Lateral and axial slices in (d)–(g) are redisplayed in RGB-color to facilitate easy visual inspection of refractive index. (l) 3D tomographic rendering of the embryo cluster.
Fig. 5.
Fig. 5. 3D RI reconstruction of a whole C. elegans worm. (a) and (b) Lateral slices through the 3D reconstruction volume at axial positions z=0,4.9μm. Major components of the reproductive and digestive systems are labeled. (c) Axial slice through the pharynx. (d) and (e) Lateral slice zoom-ins of the worm’s head region at axial positions z=+2.42,+5.19μm. Zoom-ins of the ROIs ①, ②, and ③ are shown in (f), (j), and (n), respectively. RGB-colored slices of the ROIs ①, ②, and ③ are shown with defocus in (g)–(i), (k)–(m), and (o)–(q), respectively. (r)–(t) 3D tomographic renderings of the ROIs ①, ②, and ③.

Equations (10)

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

yk(r)=tk(r)·PΔz{yk1(r)},
E(r)=F1{p(k)·F{Pz^{yN(r)}}},
I(r)=|E(r)|2,
n^(r3D)=argminn(r3D)=1Lr|I(r)|G{n(r3D)}||2.
q0(r)=exp(jG{n(r3D)})·(|G{n(r3D)}|I(r))qN+1=Pz^{F1{p(k)¯·F{q0(r)}}}.
sk(r)=(j2πΔzλ)·tk(r)¯·PΔz{yk1(r)}¯·qk+1(r),
qk(r)=PΔz{tk(r)¯·qk+1(r)},
nk(r)nk(r)α·sk(r),
n(r3D)prox{n(r3D),β},
prox{f(r3D),γ}=argming(r3D){12f(r3D)g(r3D)22+γTV[g(r3D)]},