Abstract

We demonstrate a motion-free intensity diffraction tomography technique that enables the direct inversion of 3D phase and absorption from intensity-only measurements for weakly scattering samples. We derive a novel linear forward model featuring slice-wise phase and absorption transfer functions using angled illumination. This new framework facilitates flexible and efficient data acquisition, enabling arbitrary sampling of the illumination angles. The reconstruction algorithm performs 3D synthetic aperture using a robust computation and memory efficient slice-wise deconvolution to achieve resolution up to the incoherent limit. We demonstrate our technique with thick biological samples having both sparse 3D structures and dense cell clusters. We further investigate the limitation of our technique when imaging strongly scattering samples. Imaging performance and the influence of multiple scattering is evaluated using a 3D sample consisting of stacked phase and absorption resolution targets. This computational microscopy system is directly built on a standard commercial microscope with a simple LED array source add-on, and promises broad applications by leveraging the ubiquitous microscopy platforms with minimal hardware modifications.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Diffraction tomography with Fourier ptychography

Roarke Horstmeyer, Jaebum Chung, Xiaoze Ou, Guoan Zheng, and Changhuei Yang
Optica 3(8) 827-835 (2016)

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    [Crossref] [PubMed]
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2018 (1)

J. M. Soto, J. A. Rodrigo, and T. Alieva, “Optical diffraction tomography with fully and partially coherent illumination in high numerical aperture label-free microscopy,” Applied Optics 57(1), A205–A214 (2018).
[Crossref]

2017 (5)

T. H. Nguyen, M. E. Kandel, M. Rubessa, M. B. Wheeler, and G. Popescu, “Gradient light interference microscopy for 3D imaging of unlabeled specimens,” Nature Communications 8(1), 210 (2017).
[Crossref] [PubMed]

K. Kim and Y. Park, “Tomographic active optical trapping of arbitrarily shaped objects by exploiting 3D refractive index maps,” Nature Communications 8, 15340 (2017).
[Crossref] [PubMed]

J. M. Soto, J. A. Rodrigo, and T. Alieva, “Label-free quantitative 3D tomographic imaging for partially coherent light microscopy,” Optics Express 25(14), 15699–15712 (2017).
[Crossref] [PubMed]

J. A. Rodrigo, J. M. Soto, and T. Alieva, “Fast label-free microscopy technique for 3D dynamic quantitative imaging of living cells,” Biomedical Optics Express 8(12), 5507–5517 (2017).
[Crossref]

B. Simon, M. Debailleul, M. Houkal, C. Ecoffet, J. Bailleul, J. Lambert, A. Spangenberg, H. Liu, O. Soppera, and O. Haeberlé, “Tomographic diffractive microscopy with isotropic resolution,” Optica 4(4), 460–463 (2017).
[Crossref]

2016 (4)

2015 (9)

S. Shin, K. Kim, J. Yoon, and Y. Park, “Active illumination using a digital micromirror device for quantitative phase imaging,” Optics Letters 40(22), 5407–5410 (2015).
[Crossref] [PubMed]

M. H. Jenkins and T. K. Gaylord, “Three-dimensional quantitative phase imaging via tomographic deconvolution phase microscopy,” Applied Optics 54(31), 9213–9227 (2015).
[Crossref] [PubMed]

M. Habaza, B. Gilboa, Y. Roichman, and N. T. Shaked, “Tomographic phase microscopy with 180 rotation of live cells in suspension by holographic optical tweezers,” Optics Letters 40(8), 1881–1884 (2015).
[Crossref] [PubMed]

S. Wäldchen, J. Lehmann, T. Klein, S. Van De Linde, and M. Sauer, “Light-induced cell damage in live-cell super-resolution microscopy,” Scientific Reports 5, 15348 (2015).
[Crossref] [PubMed]

L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an LED array microscope,” Optica 2(2), 104–111 (2015).
[Crossref]

K. Kim, J. Yoon, and Y. Park, “Simultaneous 3D visualization and position tracking of optically trapped particles using optical diffraction tomography,” Optica 2(4), 343–346 (2015).
[Crossref]

L. Tian and L. Waller, “Quantitative differential phase contrast imaging in an LED array microscope,” Opt. Express 23(9), 11394–11403 (2015).
[Crossref] [PubMed]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2(10), 904–911 (2015).
[Crossref]

2014 (6)

L. Tian, J. Wang, and L. Waller, “3D differential phase-contrast microscopy with computational illumination using an LED array,” Opt. Lett. 39(5), 1326–1329 (2014).
[Crossref] [PubMed]

L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier ptychography with an LED array microscope,” Biomed. Opt. Express 5(7), 2376–2389 (2014).
[Crossref] [PubMed]

P. Bon, S. Aknoun, S. Monneret, and B. Wattellier, “Enhanced 3D spatial resolution in quantitative phase microscopy using spatially incoherent illumination,” Optics Express 22(7), 8654–8671 (2014).
[Crossref] [PubMed]

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

Y. Kim, H. Shim, K. Kim, H. Park, J. H. Heo, J. Yoon, C. Choi, S. Jang, and Y. Park, “Common-path diffraction optical tomography for investigation of three-dimensional structures and dynamics of biological cells,” Optics Express 22(9), 10398–10407 (2014).
[Crossref] [PubMed]

A. Kuś, M. Dudek, B. Kemper, M. Kujawińska, and A. Vollmer, “Tomographic phase microscopy of living three-dimensional cell cultures,” Journal of Biomedical Optics 19(4), 046009 (2014).
[Crossref]

2013 (3)

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

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier Ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

K. Lee, H.-D. Kim, K. Kim, Y. Kim, T. R. Hillman, B. Min, and Y. Park, “Synthetic Fourier transform light scattering,” Optics Express 21(19), 22453–22463 (2013).
[Crossref] [PubMed]

2011 (1)

G. Zheng, C. Kolner, and C. Yang, “Microscopy refocusing and dark-field imaging by using a simple LED array,” Optics Letters 36(20), 3987–3989 (2011).
[Crossref] [PubMed]

2009 (2)

2008 (1)

N. Lue, W. Choi, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Synthetic aperture tomographic phase microscopy for 3D imaging of live cells in translational motion,” Optics Express 16(20), 16240–16246 (2008).
[Crossref] [PubMed]

2007 (2)

R. Hoebe, C. Van Oven, T. J. Gadella, P. Dhonukshe, C. Van Noorden, and E. Manders, “Controlled light-exposure microscopy reduces photobleaching and phototoxicity in fluorescence live-cell imaging,” Nature Biotechnology 25(2), 249–253 (2007).
[Crossref] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

2006 (2)

2005 (2)

2003 (1)

D. J. Stephens and V. J. Allan, “Light microscopy techniques for live cell imaging,” Science 300(5616), 82–86 (2003).
[Crossref] [PubMed]

2002 (2)

1998 (1)

B. Chen and J. J. Stamnes, “Validity of diffraction tomography based on the first Born and the first Rytov approximations,” Applied Optics 37(14), 2996–3006 (1998).
[Crossref]

1994 (1)

1993 (1)

1985 (1)

1984 (1)

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49(1), 6–10 (1984).
[Crossref]

1983 (1)

M. Azimi and A. Kak, “Distortion in diffraction tomography caused by multiple scattering,” IEEE Trans. Med. Imaging 2(4), 176–195 (1983).
[Crossref] [PubMed]

1969 (1)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1(4), 153–156 (1969).
[Crossref]

Adams, A.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Transactions on Graphics 25(3), 924–934 (2006).
[Crossref]

Aknoun, S.

P. Bon, S. Aknoun, S. Monneret, and B. Wattellier, “Enhanced 3D spatial resolution in quantitative phase microscopy using spatially incoherent illumination,” Optics Express 22(7), 8654–8671 (2014).
[Crossref] [PubMed]

Alieva, T.

J. M. Soto, J. A. Rodrigo, and T. Alieva, “Optical diffraction tomography with fully and partially coherent illumination in high numerical aperture label-free microscopy,” Applied Optics 57(1), A205–A214 (2018).
[Crossref]

J. A. Rodrigo, J. M. Soto, and T. Alieva, “Fast label-free microscopy technique for 3D dynamic quantitative imaging of living cells,” Biomedical Optics Express 8(12), 5507–5517 (2017).
[Crossref]

J. M. Soto, J. A. Rodrigo, and T. Alieva, “Label-free quantitative 3D tomographic imaging for partially coherent light microscopy,” Optics Express 25(14), 15699–15712 (2017).
[Crossref] [PubMed]

Allain, M.

Allan, V. J.

D. J. Stephens and V. J. Allan, “Light microscopy techniques for live cell imaging,” Science 300(5616), 82–86 (2003).
[Crossref] [PubMed]

Anastasio, M. A.

Azimi, M.

M. Azimi and A. Kak, “Distortion in diffraction tomography caused by multiple scattering,” IEEE Trans. Med. Imaging 2(4), 176–195 (1983).
[Crossref] [PubMed]

Babacan, S.

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

Badizadegan, K.

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(1), 266–277 (2009).
[Crossref] [PubMed]

N. Lue, W. Choi, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Synthetic aperture tomographic phase microscopy for 3D imaging of live cells in translational motion,” Optics Express 16(20), 16240–16246 (2008).
[Crossref] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

Bailleul, J.

Belkebir, K.

Bertero, M.

M. Bertero and P. Boccacci, Introduction to inverse problems in imaging (Taylor & Francis, 1998).
[Crossref]

Boccacci, P.

M. Bertero and P. Boccacci, Introduction to inverse problems in imaging (Taylor & Francis, 1998).
[Crossref]

Bon, P.

P. Bon, S. Aknoun, S. Monneret, and B. Wattellier, “Enhanced 3D spatial resolution in quantitative phase microscopy using spatially incoherent illumination,” Optics Express 22(7), 8654–8671 (2014).
[Crossref] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999), 7th ed.
[Crossref]

Boss, D.

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

Carney, P.

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

Charrière, F.

Chaumet, P. C.

Chen, B.

B. Chen and J. J. Stamnes, “Validity of diffraction tomography based on the first Born and the first Rytov approximations,” Applied Optics 37(14), 2996–3006 (1998).
[Crossref]

Chen, M.

Choi, C.

Y. Kim, H. Shim, K. Kim, H. Park, J. H. Heo, J. Yoon, C. Choi, S. Jang, and Y. Park, “Common-path diffraction optical tomography for investigation of three-dimensional structures and dynamics of biological cells,” Optics Express 22(9), 10398–10407 (2014).
[Crossref] [PubMed]

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(1), 266–277 (2009).
[Crossref] [PubMed]

N. Lue, W. Choi, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Synthetic aperture tomographic phase microscopy for 3D imaging of live cells in translational motion,” Optics Express 16(20), 16240–16246 (2008).
[Crossref] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

Chung, J.

Colomb, T.

Cotte, Y.

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

Cuche, E.

Dasari, R. R.

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(1), 266–277 (2009).
[Crossref] [PubMed]

N. Lue, W. Choi, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Synthetic aperture tomographic phase microscopy for 3D imaging of live cells in translational motion,” Optics Express 16(20), 16240–16246 (2008).
[Crossref] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

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,” Nature Photonics 7, 113–117 (2013).
[Crossref]

F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31(2), 178–180 (2006).
[Crossref] [PubMed]

Devaney, A. J.

Dhonukshe, P.

R. Hoebe, C. Van Oven, T. J. Gadella, P. Dhonukshe, C. Van Noorden, and E. Manders, “Controlled light-exposure microscopy reduces photobleaching and phototoxicity in fluorescence live-cell imaging,” Nature Biotechnology 25(2), 249–253 (2007).
[Crossref] [PubMed]

Dudek, M.

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Figures (4)

Fig. 1
Fig. 1 Intensity diffraction tomography from angled illumination. (a) The setup consists of a standard microscope with an LED array that allows flexible patterning of illumination angles. (b) Images are taken by varying the illumination angle. Each intensity spectrum of the raw data exhibits two shifted circles, whose shift is set by the illumination angle. (c) Corresponding phase (imaginary part) and amplitude (real part) transfer functions (TF) for the same set of illumination angles are visualized at various sample depths. (d) The slice-wise deconvolution algorithm outputs two 3D stacks, corresponding to the phase and absorption reconstruction.
Fig. 2
Fig. 2 Phase and absorption reconstruction of a stained spirogyra sample. (a) The full field of view (FOV) brightfield image with the on-axis LED illumination (10×, 0.25NA). The sample contains both highly absorbing features (e.g. chloroplasts) and “phase” features (e.g. filaments). (b) A dense algae cluster is successfully resolved in the phase reconstruction. (c) Phase reconstruction of spiral structures on a single spirogyra, further demonstrating the axial sectioning capability of our technique. (d) Unstained filaments are resolved with high contrast in the phase reconstruction whereas the absorption does not provide much contrast.
Fig. 3
Fig. 3 Reconstruction of unstained MCF-7 cancer cells. (a) The full FOV PhC image (40×, 0.65NA). (b) Phase reconstructions on a few cell regions, demonstrating its versatility and robustness in reconstructing both thin and thick samples. (c) Phase reconstruction of a dense cell cluster across multiple slices. The comparison with the physically scanned PhC images demonstrates that our IDT technique provides similar lateral resolution and axial sectioning capability. (d) Phase reconstruction of the cell clusters using symmetric and pseudorandom illumination patterns. Our IDT framework allows flexibly designing the illumination pattern and the number of LEDs used. The reconstruction algorithm produces high quality phase recovery as the number of images used is reduced, and remains robust even when the number of images is much fewer than the number of unknowns.
Fig. 4
Fig. 4 Imaging of strongly scattering phase and absorption targets. (a) The sample consists of a phase target placed above an absorption target. Experiments are taken at: (A) near the phase target plane, (B) in between the phase and absorption targets, and (C) near the absorption target. (b) The brightfield image with on-axis LED illumination (10×, 0.25NA). (c) The reconstruction of phase patterns with 50nm, 100nm, and 200nm in height at the three focal positions. The reconstruction shows under-estimation of the phase due to multiple scattering. The reconstruction of the taller pattern contains larger error, because of the stronger multiple scattering. The recovered resolution when the target is near focus in (A) matches with the theory, and degrades as increasing the defocus. Nevertheless, the recovered phase values are consistent at all focal positions. (d) Simulation shows that the unaccounted multiple scattering indeed results in under-estimation of the phase; the amount of reconstruction error matches well with the experiment. (e) The reconstruction of the absorption target at the three focal positions. Similar to the phase target, the recovered resolution agrees with the theory when the target is near focus in (C), while degrades with large defocus.

Equations (8)

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f ( r ) = f i ( r ) + f i ( r ) V ( r ) G ( r r ) d 3 r ,
I ( x , 0 | u i ) = | f ( x , 0 | u i ) * h ( x ) | 2 ,
f s ( x , 0 | u i ) = i k 0 2 2 S ( u i ) 1 { Δ ˜ ( u + u i , z ) e i ( η ( u ) + η i ) z η ( u ) } d z ,
I ˜ ( u , 0 | u i ) S ( u i ) | P ( u i ) | 2 δ ( u ) + [ H Re ( u , z | u i ) Δ ˜ Re ( u , z ) + H Im ( u , z | u i ) Δ ˜ Im ( u , z ) ] d z ,
H Re ( u , z | u i ) = i k 0 2 2 S ( u i ) { P * ( u i ) e i [ η i + η ( u u i ) ] z η ( u u i ) P ( u u i ) P ( u i ) e i [ η i + η ( u + u i ) ] z η ( u + u i ) P * ( u u i ) } ,
H Im ( u , z | u i ) = k 0 2 2 S ( u i ) { P * ( u i ) e i [ η i + η ( u u i ) ] z η ( u u i ) P ( u u i ) + P ( u i ) e i [ η i + η ( u + u i ) ] z η ( u + u i ) P * ( u u i ) } .
Δ Re [ m ] = 1 { 1 A { ( l | Im [ l , m ] | 2 + β ) ( l Re * [ l , m ] g ˜ [ l ] ) ( l Re * [ l , m ] Im [ l , m ] ) ( l Im * [ l , m ] g ˜ [ l ] ) } } ,
Δ Im [ m ] = 1 { 1 A { ( l | Re [ l , m ] | 2 + α ) ( l Im * [ l , m ] g ˜ [ l ] ) ( l Re [ l , m ] Im * [ l , m ] ) ( l Re * [ l , m ] g ˜ [ l ] ) } } ,