Abstract

Light microscopy on dynamic samples, for example neural activity in the brain, often requires imaging volumes that extend over several 100 µm in axial direction at a rate of at least several tens of Hertz. Here, we develop a tomography approach for scanning fluorescence microscopy which allows recording a volume image in a single frame scan. Volumes are imaged by simultaneously recording four independent projections at different angles using temporally multiplexed, tilted Bessel beams. From the resulting projections, three-dimensional images are reconstructed using inverse Radon transforms combined with convolutional neural networks (U-net).

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

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References

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2019 (1)

J. A. Calarco and A. D. Samuel, “Imaging whole nervous systems: insights into behavior from worms to fish,” Nat. Methods 16, 14 (2019).
[Crossref]

2018 (6)

S. Weisenburger and A. Vaziri, “A guide to emerging technologies for large-scale and whole-brain optical imaging of neuronal activity,” Ann. Rev. Neurosci. 41, 431–452 (2018).
[Crossref] [PubMed]

E. M. Hillman, V. Voleti, K. Patel, W. Li, H. Yu, C. Perez-Campos, S. E. Benezra, R. M. Bruno, and P. T. Galwaduge, “High-speed 3d imaging of cellular activity in the brain using axially-extended beams and light sheets,” Curr. Opin. Neurobiol. 50, 190–200 (2018).
[Crossref] [PubMed]

T. C. Nguyen, V. Bui, and G. Nehmetallah, “Computational optical tomography using 3-d deep convolutional neural networks,” Opt. Eng. 57, 043111 (2018).

D. Pelt, K. Batenburg, and J. Sethian, “Improving tomographic reconstruction from limited data using mixed-scale dense convolutional neural networks,” J. Imaging 4, 128 (2018).
[Crossref]

R. Lu, M. Tanimoto, M. Koyama, and N. Ji, “50 hz volumetric functional imaging with continuously adjustable depth of focus,” Biomed. Opt. Express 9, 1964–1976 (2018).
[Crossref] [PubMed]

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

2017 (2)

R. Lu, W. Sun, Y. Liang, A. Kerlin, J. Bierfeld, J. D. Seelig, D. E. Wilson, B. Scholl, B. Mohar, M. Tanimoto, and et al., “Video-rate volumetric functional imaging of the brain at synaptic resolution,” Nat. Neurosci. 20, 620 (2017).
[Crossref] [PubMed]

A. Song, A. S. Charles, S. A. Koay, J. L. Gauthier, S. Y. Thiberge, J. W. Pillow, and D. W. Tank, “Volumetric two-photon imaging of neurons using stereoscopy (vtwins),” Nat. Methods 14, 420 (2017).
[Crossref] [PubMed]

2016 (1)

Y. Yang, B. Yao, M. Lei, D. Dan, R. Li, M. Van Horn, X. Chen, Y. Li, and T. Ye, “Two-photon laser scanning stereomicroscopy for fast volumetric imaging,” PLOS ONE 11, e0168885 (2016).
[Crossref] [PubMed]

2015 (1)

P. J. Keller and M. B. Ahrens, “Visualizing whole-brain activity and development at the single-cell level using light-sheet microscopy,” Neuron 85, 462–483 (2015).
[Crossref] [PubMed]

2014 (1)

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).
[PubMed]

2013 (1)

2011 (2)

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8, 139 (2011).
[Crossref] [PubMed]

M. Rieckher, U. J. Birk, H. Meyer, J. Ripoll, and N. Tavernarakis, “Microscopic optical projection tomography in vivo,” PLOS ONE 6, e18963 (2011).
[Crossref] [PubMed]

2010 (2)

J. D. Seelig, M. E. Chiappe, G. K. Lott, A. Dutta, J. E. Osborne, M. B. Reiser, and V. Jayaraman, “Two-photon calcium imaging from head-fixed drosophila during optomotor walking behavior,” Nat. Methods 7, 535 (2010).
[Crossref] [PubMed]

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780 (2010).
[Crossref]

2007 (1)

2003 (1)

T. A. Pologruto, B. L. Sabatini, and K. Svoboda, “Scanimage: flexible software for operating laser scanning microscopes,” Biomed. Eng. Online 2, 13 (2003).
[Crossref] [PubMed]

2002 (1)

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3d microscopy and gene expression studies,” Science 296, 541–545 (2002).
[Crossref] [PubMed]

2000 (1)

X. F. Ma, M. Fukuhara, and T. Takeda, “Neural network ct image reconstruction method for small amount of projection data,” NUCL INSTRUM METH A 449, 366–377 (2000).
[Crossref]

Abdulkadir, A.

Ö. Çiçek, A. Abdulkadir, S. S. Lienkamp, T. Brox, and O. Ronneberger, “3d u-net: learning dense volumetric segmentation from sparse annotation,” in Med. Image. Comput. Comput. Assist. Interv., (Springer, 2016), pp. 424–432.

Ahlgren, U.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3d microscopy and gene expression studies,” Science 296, 541–545 (2002).
[Crossref] [PubMed]

Ahrens, M. B.

P. J. Keller and M. B. Ahrens, “Visualizing whole-brain activity and development at the single-cell level using light-sheet microscopy,” Neuron 85, 462–483 (2015).
[Crossref] [PubMed]

Akinwande, A. I.

A. Goy, G. Roghoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” arXiv preprint arXiv:1812.07380 (2018).

Amir, W.

Arisaka, K.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8, 139 (2011).
[Crossref] [PubMed]

Arthur, K.

A. Goy, G. Roghoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” arXiv preprint arXiv:1812.07380 (2018).

Baldock, R.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3d microscopy and gene expression studies,” Science 296, 541–545 (2002).
[Crossref] [PubMed]

Barbastathis, G.

A. Goy, G. Roghoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” arXiv preprint arXiv:1812.07380 (2018).

Batenburg, K.

D. Pelt, K. Batenburg, and J. Sethian, “Improving tomographic reconstruction from limited data using mixed-scale dense convolutional neural networks,” J. Imaging 4, 128 (2018).
[Crossref]

Benezra, S. E.

E. M. Hillman, V. Voleti, K. Patel, W. Li, H. Yu, C. Perez-Campos, S. E. Benezra, R. M. Bruno, and P. T. Galwaduge, “High-speed 3d imaging of cellular activity in the brain using axially-extended beams and light sheets,” Curr. Opin. Neurobiol. 50, 190–200 (2018).
[Crossref] [PubMed]

Bierfeld, J.

R. Lu, W. Sun, Y. Liang, A. Kerlin, J. Bierfeld, J. D. Seelig, D. E. Wilson, B. Scholl, B. Mohar, M. Tanimoto, and et al., “Video-rate volumetric functional imaging of the brain at synaptic resolution,” Nat. Neurosci. 20, 620 (2017).
[Crossref] [PubMed]

Birk, U. J.

M. Rieckher, U. J. Birk, H. Meyer, J. Ripoll, and N. Tavernarakis, “Microscopic optical projection tomography in vivo,” PLOS ONE 6, e18963 (2011).
[Crossref] [PubMed]

Boothe, T.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Borden, P.

A. Kazemipour, O. Novak, D. Flickinger, J. S. Marvin, J. King, P. Borden, S. Druckmann, K. Svoboda, L. L. Looger, and K. Podgorski, “Kilohertz frame-rate two-photon tomography,” bioRxiv p. 357269 (2018).

Broaddus, C.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Brox, T.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” in Med. Image. Comput. Comput. Assist. Interv., (Springer, 2015), pp. 234–241.

Ö. Çiçek, A. Abdulkadir, S. S. Lienkamp, T. Brox, and O. Ronneberger, “3d u-net: learning dense volumetric segmentation from sparse annotation,” in Med. Image. Comput. Comput. Assist. Interv., (Springer, 2016), pp. 424–432.

Bruno, R. M.

E. M. Hillman, V. Voleti, K. Patel, W. Li, H. Yu, C. Perez-Campos, S. E. Benezra, R. M. Bruno, and P. T. Galwaduge, “High-speed 3d imaging of cellular activity in the brain using axially-extended beams and light sheets,” Curr. Opin. Neurobiol. 50, 190–200 (2018).
[Crossref] [PubMed]

Bui, V.

T. C. Nguyen, V. Bui, and G. Nehmetallah, “Computational optical tomography using 3-d deep convolutional neural networks,” Opt. Eng. 57, 043111 (2018).

Calarco, J. A.

J. A. Calarco and A. D. Samuel, “Imaging whole nervous systems: insights into behavior from worms to fish,” Nat. Methods 16, 14 (2019).
[Crossref]

Carriles, R.

Castonguay, A.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).
[PubMed]

Charles, A. S.

A. Song, A. S. Charles, S. A. Koay, J. L. Gauthier, S. Y. Thiberge, J. W. Pillow, and D. W. Tank, “Volumetric two-photon imaging of neurons using stereoscopy (vtwins),” Nat. Methods 14, 420 (2017).
[Crossref] [PubMed]

Chen, X.

Y. Yang, B. Yao, M. Lei, D. Dan, R. Li, M. Van Horn, X. Chen, Y. Li, and T. Ye, “Two-photon laser scanning stereomicroscopy for fast volumetric imaging,” PLOS ONE 11, e0168885 (2016).
[Crossref] [PubMed]

Cheng, A.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8, 139 (2011).
[Crossref] [PubMed]

Chiappe, M. E.

J. D. Seelig, M. E. Chiappe, G. K. Lott, A. Dutta, J. E. Osborne, M. B. Reiser, and V. Jayaraman, “Two-photon calcium imaging from head-fixed drosophila during optomotor walking behavior,” Nat. Methods 7, 535 (2010).
[Crossref] [PubMed]

Çiçek, Ö.

Ö. Çiçek, A. Abdulkadir, S. S. Lienkamp, T. Brox, and O. Ronneberger, “3d u-net: learning dense volumetric segmentation from sparse annotation,” in Med. Image. Comput. Comput. Assist. Interv., (Springer, 2016), pp. 424–432.

Cottet, M.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).
[PubMed]

Culley, S.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Dan, D.

Y. Yang, B. Yao, M. Lei, D. Dan, R. Li, M. Van Horn, X. Chen, Y. Li, and T. Ye, “Two-photon laser scanning stereomicroscopy for fast volumetric imaging,” PLOS ONE 11, e0168885 (2016).
[Crossref] [PubMed]

Davidson, D.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3d microscopy and gene expression studies,” Science 296, 541–545 (2002).
[Crossref] [PubMed]

De Koninck, Y.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).
[PubMed]

G. Thériault, Y. De Koninck, and N. McCarthy, “Extended depth of field microscopy for rapid volumetric two-photon imaging,” Opt. Express 21, 10095–10104 (2013).
[Crossref] [PubMed]

Dholakia, K.

J. Nylk and K. Dholakia, “Light-sheet fluorescence microscopy with structured light,” in Neurophotonics and Biomedical Spectroscopy, (Elsevier, 2019), pp. 477–501.
[Crossref]

Dibrov, A.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Druckmann, S.

A. Kazemipour, O. Novak, D. Flickinger, J. S. Marvin, J. King, P. Borden, S. Druckmann, K. Svoboda, L. L. Looger, and K. Podgorski, “Kilohertz frame-rate two-photon tomography,” bioRxiv p. 357269 (2018).

Durfee, C. G.

Dutta, A.

J. D. Seelig, M. E. Chiappe, G. K. Lott, A. Dutta, J. E. Osborne, M. B. Reiser, and V. Jayaraman, “Two-photon calcium imaging from head-fixed drosophila during optomotor walking behavior,” Nat. Methods 7, 535 (2010).
[Crossref] [PubMed]

Fahrbach, F. O.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780 (2010).
[Crossref]

Feeman, T. G.

T. G. Feeman, The mathematics of medical imaging (Springer, 2010).
[Crossref]

Fischer, P.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” in Med. Image. Comput. Comput. Assist. Interv., (Springer, 2015), pp. 234–241.

Flickinger, D.

A. Kazemipour, O. Novak, D. Flickinger, J. S. Marvin, J. King, P. Borden, S. Druckmann, K. Svoboda, L. L. Looger, and K. Podgorski, “Kilohertz frame-rate two-photon tomography,” bioRxiv p. 357269 (2018).

Fukuhara, M.

X. F. Ma, M. Fukuhara, and T. Takeda, “Neural network ct image reconstruction method for small amount of projection data,” NUCL INSTRUM METH A 449, 366–377 (2000).
[Crossref]

Galwaduge, P. T.

E. M. Hillman, V. Voleti, K. Patel, W. Li, H. Yu, C. Perez-Campos, S. E. Benezra, R. M. Bruno, and P. T. Galwaduge, “High-speed 3d imaging of cellular activity in the brain using axially-extended beams and light sheets,” Curr. Opin. Neurobiol. 50, 190–200 (2018).
[Crossref] [PubMed]

Gauthier, J. L.

A. Song, A. S. Charles, S. A. Koay, J. L. Gauthier, S. Y. Thiberge, J. W. Pillow, and D. W. Tank, “Volumetric two-photon imaging of neurons using stereoscopy (vtwins),” Nat. Methods 14, 420 (2017).
[Crossref] [PubMed]

Golshani, P.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8, 139 (2011).
[Crossref] [PubMed]

Gonçalves, J. T.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8, 139 (2011).
[Crossref] [PubMed]

Goy, A.

A. Goy, G. Roghoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” arXiv preprint arXiv:1812.07380 (2018).

Hecksher-Sørensen, J.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3d microscopy and gene expression studies,” Science 296, 541–545 (2002).
[Crossref] [PubMed]

Henriques, R.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Hill, B.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3d microscopy and gene expression studies,” Science 296, 541–545 (2002).
[Crossref] [PubMed]

Hillman, E. M.

E. M. Hillman, V. Voleti, K. Patel, W. Li, H. Yu, C. Perez-Campos, S. E. Benezra, R. M. Bruno, and P. T. Galwaduge, “High-speed 3d imaging of cellular activity in the brain using axially-extended beams and light sheets,” Curr. Opin. Neurobiol. 50, 190–200 (2018).
[Crossref] [PubMed]

Hoover, E. E.

Jain, A.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Jayaraman, V.

J. D. Seelig, M. E. Chiappe, G. K. Lott, A. Dutta, J. E. Osborne, M. B. Reiser, and V. Jayaraman, “Two-photon calcium imaging from head-fixed drosophila during optomotor walking behavior,” Nat. Methods 7, 535 (2010).
[Crossref] [PubMed]

Ji, N.

Jug, F.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Kazemipour, A.

A. Kazemipour, O. Novak, D. Flickinger, J. S. Marvin, J. King, P. Borden, S. Druckmann, K. Svoboda, L. L. Looger, and K. Podgorski, “Kilohertz frame-rate two-photon tomography,” bioRxiv p. 357269 (2018).

Keller, P. J.

P. J. Keller and M. B. Ahrens, “Visualizing whole-brain activity and development at the single-cell level using light-sheet microscopy,” Neuron 85, 462–483 (2015).
[Crossref] [PubMed]

Kerlin, A.

R. Lu, W. Sun, Y. Liang, A. Kerlin, J. Bierfeld, J. D. Seelig, D. E. Wilson, B. Scholl, B. Mohar, M. Tanimoto, and et al., “Video-rate volumetric functional imaging of the brain at synaptic resolution,” Nat. Neurosci. 20, 620 (2017).
[Crossref] [PubMed]

King, J.

A. Kazemipour, O. Novak, D. Flickinger, J. S. Marvin, J. King, P. Borden, S. Druckmann, K. Svoboda, L. L. Looger, and K. Podgorski, “Kilohertz frame-rate two-photon tomography,” bioRxiv p. 357269 (2018).

Koay, S. A.

A. Song, A. S. Charles, S. A. Koay, J. L. Gauthier, S. Y. Thiberge, J. W. Pillow, and D. W. Tank, “Volumetric two-photon imaging of neurons using stereoscopy (vtwins),” Nat. Methods 14, 420 (2017).
[Crossref] [PubMed]

Koyama, M.

Lei, M.

Y. Yang, B. Yao, M. Lei, D. Dan, R. Li, M. Van Horn, X. Chen, Y. Li, and T. Ye, “Two-photon laser scanning stereomicroscopy for fast volumetric imaging,” PLOS ONE 11, e0168885 (2016).
[Crossref] [PubMed]

Li, R.

Y. Yang, B. Yao, M. Lei, D. Dan, R. Li, M. Van Horn, X. Chen, Y. Li, and T. Ye, “Two-photon laser scanning stereomicroscopy for fast volumetric imaging,” PLOS ONE 11, e0168885 (2016).
[Crossref] [PubMed]

Li, S.

A. Goy, G. Roghoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” arXiv preprint arXiv:1812.07380 (2018).

Li, W.

E. M. Hillman, V. Voleti, K. Patel, W. Li, H. Yu, C. Perez-Campos, S. E. Benezra, R. M. Bruno, and P. T. Galwaduge, “High-speed 3d imaging of cellular activity in the brain using axially-extended beams and light sheets,” Curr. Opin. Neurobiol. 50, 190–200 (2018).
[Crossref] [PubMed]

Li, Y.

Y. Yang, B. Yao, M. Lei, D. Dan, R. Li, M. Van Horn, X. Chen, Y. Li, and T. Ye, “Two-photon laser scanning stereomicroscopy for fast volumetric imaging,” PLOS ONE 11, e0168885 (2016).
[Crossref] [PubMed]

Liang, Y.

R. Lu, W. Sun, Y. Liang, A. Kerlin, J. Bierfeld, J. D. Seelig, D. E. Wilson, B. Scholl, B. Mohar, M. Tanimoto, and et al., “Video-rate volumetric functional imaging of the brain at synaptic resolution,” Nat. Neurosci. 20, 620 (2017).
[Crossref] [PubMed]

Lienkamp, S. S.

Ö. Çiçek, A. Abdulkadir, S. S. Lienkamp, T. Brox, and O. Ronneberger, “3d u-net: learning dense volumetric segmentation from sparse annotation,” in Med. Image. Comput. Comput. Assist. Interv., (Springer, 2016), pp. 424–432.

Looger, L. L.

A. Kazemipour, O. Novak, D. Flickinger, J. S. Marvin, J. King, P. Borden, S. Druckmann, K. Svoboda, L. L. Looger, and K. Podgorski, “Kilohertz frame-rate two-photon tomography,” bioRxiv p. 357269 (2018).

Lott, G. K.

J. D. Seelig, M. E. Chiappe, G. K. Lott, A. Dutta, J. E. Osborne, M. B. Reiser, and V. Jayaraman, “Two-photon calcium imaging from head-fixed drosophila during optomotor walking behavior,” Nat. Methods 7, 535 (2010).
[Crossref] [PubMed]

Lu, R.

R. Lu, M. Tanimoto, M. Koyama, and N. Ji, “50 hz volumetric functional imaging with continuously adjustable depth of focus,” Biomed. Opt. Express 9, 1964–1976 (2018).
[Crossref] [PubMed]

R. Lu, W. Sun, Y. Liang, A. Kerlin, J. Bierfeld, J. D. Seelig, D. E. Wilson, B. Scholl, B. Mohar, M. Tanimoto, and et al., “Video-rate volumetric functional imaging of the brain at synaptic resolution,” Nat. Neurosci. 20, 620 (2017).
[Crossref] [PubMed]

Ma, X. F.

X. F. Ma, M. Fukuhara, and T. Takeda, “Neural network ct image reconstruction method for small amount of projection data,” NUCL INSTRUM METH A 449, 366–377 (2000).
[Crossref]

Marvin, J. S.

A. Kazemipour, O. Novak, D. Flickinger, J. S. Marvin, J. King, P. Borden, S. Druckmann, K. Svoboda, L. L. Looger, and K. Podgorski, “Kilohertz frame-rate two-photon tomography,” bioRxiv p. 357269 (2018).

McCarthy, N.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).
[PubMed]

G. Thériault, Y. De Koninck, and N. McCarthy, “Extended depth of field microscopy for rapid volumetric two-photon imaging,” Opt. Express 21, 10095–10104 (2013).
[Crossref] [PubMed]

Meyer, H.

M. Rieckher, U. J. Birk, H. Meyer, J. Ripoll, and N. Tavernarakis, “Microscopic optical projection tomography in vivo,” PLOS ONE 6, e18963 (2011).
[Crossref] [PubMed]

Mohar, B.

R. Lu, W. Sun, Y. Liang, A. Kerlin, J. Bierfeld, J. D. Seelig, D. E. Wilson, B. Scholl, B. Mohar, M. Tanimoto, and et al., “Video-rate volumetric functional imaging of the brain at synaptic resolution,” Nat. Neurosci. 20, 620 (2017).
[Crossref] [PubMed]

Müller, A.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Myers, E. W.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Nehmetallah, G.

T. C. Nguyen, V. Bui, and G. Nehmetallah, “Computational optical tomography using 3-d deep convolutional neural networks,” Opt. Eng. 57, 043111 (2018).

Nguyen, T. C.

T. C. Nguyen, V. Bui, and G. Nehmetallah, “Computational optical tomography using 3-d deep convolutional neural networks,” Opt. Eng. 57, 043111 (2018).

Norden, C.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Novak, O.

A. Kazemipour, O. Novak, D. Flickinger, J. S. Marvin, J. King, P. Borden, S. Druckmann, K. Svoboda, L. L. Looger, and K. Podgorski, “Kilohertz frame-rate two-photon tomography,” bioRxiv p. 357269 (2018).

Nylk, J.

J. Nylk and K. Dholakia, “Light-sheet fluorescence microscopy with structured light,” in Neurophotonics and Biomedical Spectroscopy, (Elsevier, 2019), pp. 477–501.
[Crossref]

Osborne, J. E.

J. D. Seelig, M. E. Chiappe, G. K. Lott, A. Dutta, J. E. Osborne, M. B. Reiser, and V. Jayaraman, “Two-photon calcium imaging from head-fixed drosophila during optomotor walking behavior,” Nat. Methods 7, 535 (2010).
[Crossref] [PubMed]

Patel, K.

E. M. Hillman, V. Voleti, K. Patel, W. Li, H. Yu, C. Perez-Campos, S. E. Benezra, R. M. Bruno, and P. T. Galwaduge, “High-speed 3d imaging of cellular activity in the brain using axially-extended beams and light sheets,” Curr. Opin. Neurobiol. 50, 190–200 (2018).
[Crossref] [PubMed]

Payer, C.

F. Thaler, C. Payer, and D. Štern, “Volumetric reconstruction from a limited number of digitally reconstructed radiographs using cnns,” in Proc. of the OAGM Workshop, (2018), pp. 13–19.

Pelt, D.

D. Pelt, K. Batenburg, and J. Sethian, “Improving tomographic reconstruction from limited data using mixed-scale dense convolutional neural networks,” J. Imaging 4, 128 (2018).
[Crossref]

Perez-Campos, C.

E. M. Hillman, V. Voleti, K. Patel, W. Li, H. Yu, C. Perez-Campos, S. E. Benezra, R. M. Bruno, and P. T. Galwaduge, “High-speed 3d imaging of cellular activity in the brain using axially-extended beams and light sheets,” Curr. Opin. Neurobiol. 50, 190–200 (2018).
[Crossref] [PubMed]

Perry, P.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3d microscopy and gene expression studies,” Science 296, 541–545 (2002).
[Crossref] [PubMed]

Pillow, J. W.

A. Song, A. S. Charles, S. A. Koay, J. L. Gauthier, S. Y. Thiberge, J. W. Pillow, and D. W. Tank, “Volumetric two-photon imaging of neurons using stereoscopy (vtwins),” Nat. Methods 14, 420 (2017).
[Crossref] [PubMed]

Planchon, T. A.

Podgorski, K.

A. Kazemipour, O. Novak, D. Flickinger, J. S. Marvin, J. King, P. Borden, S. Druckmann, K. Svoboda, L. L. Looger, and K. Podgorski, “Kilohertz frame-rate two-photon tomography,” bioRxiv p. 357269 (2018).

Pologruto, T. A.

T. A. Pologruto, B. L. Sabatini, and K. Svoboda, “Scanimage: flexible software for operating laser scanning microscopes,” Biomed. Eng. Online 2, 13 (2003).
[Crossref] [PubMed]

Portera-Cailliau, C.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8, 139 (2011).
[Crossref] [PubMed]

Reiser, M. B.

J. D. Seelig, M. E. Chiappe, G. K. Lott, A. Dutta, J. E. Osborne, M. B. Reiser, and V. Jayaraman, “Two-photon calcium imaging from head-fixed drosophila during optomotor walking behavior,” Nat. Methods 7, 535 (2010).
[Crossref] [PubMed]

Rieckher, M.

M. Rieckher, U. J. Birk, H. Meyer, J. Ripoll, and N. Tavernarakis, “Microscopic optical projection tomography in vivo,” PLOS ONE 6, e18963 (2011).
[Crossref] [PubMed]

Rink, J.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Ripoll, J.

M. Rieckher, U. J. Birk, H. Meyer, J. Ripoll, and N. Tavernarakis, “Microscopic optical projection tomography in vivo,” PLOS ONE 6, e18963 (2011).
[Crossref] [PubMed]

Rocha-Martins, M.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Roghoobur, G.

A. Goy, G. Roghoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” arXiv preprint arXiv:1812.07380 (2018).

Rohrbach, A.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780 (2010).
[Crossref]

Ronneberger, O.

Ö. Çiçek, A. Abdulkadir, S. S. Lienkamp, T. Brox, and O. Ronneberger, “3d u-net: learning dense volumetric segmentation from sparse annotation,” in Med. Image. Comput. Comput. Assist. Interv., (Springer, 2016), pp. 424–432.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” in Med. Image. Comput. Comput. Assist. Interv., (Springer, 2015), pp. 234–241.

Ross, A.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3d microscopy and gene expression studies,” Science 296, 541–545 (2002).
[Crossref] [PubMed]

Royer, L.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Sabatini, B. L.

T. A. Pologruto, B. L. Sabatini, and K. Svoboda, “Scanimage: flexible software for operating laser scanning microscopes,” Biomed. Eng. Online 2, 13 (2003).
[Crossref] [PubMed]

Samuel, A. D.

J. A. Calarco and A. D. Samuel, “Imaging whole nervous systems: insights into behavior from worms to fish,” Nat. Methods 16, 14 (2019).
[Crossref]

Schmidt, D.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Schmidt, U.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Scholl, B.

R. Lu, W. Sun, Y. Liang, A. Kerlin, J. Bierfeld, J. D. Seelig, D. E. Wilson, B. Scholl, B. Mohar, M. Tanimoto, and et al., “Video-rate volumetric functional imaging of the brain at synaptic resolution,” Nat. Neurosci. 20, 620 (2017).
[Crossref] [PubMed]

Seelig, J. D.

R. Lu, W. Sun, Y. Liang, A. Kerlin, J. Bierfeld, J. D. Seelig, D. E. Wilson, B. Scholl, B. Mohar, M. Tanimoto, and et al., “Video-rate volumetric functional imaging of the brain at synaptic resolution,” Nat. Neurosci. 20, 620 (2017).
[Crossref] [PubMed]

J. D. Seelig, M. E. Chiappe, G. K. Lott, A. Dutta, J. E. Osborne, M. B. Reiser, and V. Jayaraman, “Two-photon calcium imaging from head-fixed drosophila during optomotor walking behavior,” Nat. Methods 7, 535 (2010).
[Crossref] [PubMed]

Segovia-Miranda, F.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Sethian, J.

D. Pelt, K. Batenburg, and J. Sethian, “Improving tomographic reconstruction from limited data using mixed-scale dense convolutional neural networks,” J. Imaging 4, 128 (2018).
[Crossref]

Sharpe, J.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3d microscopy and gene expression studies,” Science 296, 541–545 (2002).
[Crossref] [PubMed]

Simon, P.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780 (2010).
[Crossref]

Solimena, M.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090 (2018).
[Crossref] [PubMed]

Song, A.

A. Song, A. S. Charles, S. A. Koay, J. L. Gauthier, S. Y. Thiberge, J. W. Pillow, and D. W. Tank, “Volumetric two-photon imaging of neurons using stereoscopy (vtwins),” Nat. Methods 14, 420 (2017).
[Crossref] [PubMed]

Squier, J. A.

Štern, D.

F. Thaler, C. Payer, and D. Štern, “Volumetric reconstruction from a limited number of digitally reconstructed radiographs using cnns,” in Proc. of the OAGM Workshop, (2018), pp. 13–19.

Sun, W.

R. Lu, W. Sun, Y. Liang, A. Kerlin, J. Bierfeld, J. D. Seelig, D. E. Wilson, B. Scholl, B. Mohar, M. Tanimoto, and et al., “Video-rate volumetric functional imaging of the brain at synaptic resolution,” Nat. Neurosci. 20, 620 (2017).
[Crossref] [PubMed]

Svoboda, K.

T. A. Pologruto, B. L. Sabatini, and K. Svoboda, “Scanimage: flexible software for operating laser scanning microscopes,” Biomed. Eng. Online 2, 13 (2003).
[Crossref] [PubMed]

A. Kazemipour, O. Novak, D. Flickinger, J. S. Marvin, J. King, P. Borden, S. Druckmann, K. Svoboda, L. L. Looger, and K. Podgorski, “Kilohertz frame-rate two-photon tomography,” bioRxiv p. 357269 (2018).

Takeda, T.

X. F. Ma, M. Fukuhara, and T. Takeda, “Neural network ct image reconstruction method for small amount of projection data,” NUCL INSTRUM METH A 449, 366–377 (2000).
[Crossref]

Tanimoto, M.

R. Lu, M. Tanimoto, M. Koyama, and N. Ji, “50 hz volumetric functional imaging with continuously adjustable depth of focus,” Biomed. Opt. Express 9, 1964–1976 (2018).
[Crossref] [PubMed]

R. Lu, W. Sun, Y. Liang, A. Kerlin, J. Bierfeld, J. D. Seelig, D. E. Wilson, B. Scholl, B. Mohar, M. Tanimoto, and et al., “Video-rate volumetric functional imaging of the brain at synaptic resolution,” Nat. Neurosci. 20, 620 (2017).
[Crossref] [PubMed]

Tank, D. W.

A. Song, A. S. Charles, S. A. Koay, J. L. Gauthier, S. Y. Thiberge, J. W. Pillow, and D. W. Tank, “Volumetric two-photon imaging of neurons using stereoscopy (vtwins),” Nat. Methods 14, 420 (2017).
[Crossref] [PubMed]

Tavernarakis, N.

M. Rieckher, U. J. Birk, H. Meyer, J. Ripoll, and N. Tavernarakis, “Microscopic optical projection tomography in vivo,” PLOS ONE 6, e18963 (2011).
[Crossref] [PubMed]

Thaler, F.

F. Thaler, C. Payer, and D. Štern, “Volumetric reconstruction from a limited number of digitally reconstructed radiographs using cnns,” in Proc. of the OAGM Workshop, (2018), pp. 13–19.

Thériault, G.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).
[PubMed]

G. Thériault, Y. De Koninck, and N. McCarthy, “Extended depth of field microscopy for rapid volumetric two-photon imaging,” Opt. Express 21, 10095–10104 (2013).
[Crossref] [PubMed]

Thiberge, S. Y.

A. Song, A. S. Charles, S. A. Koay, J. L. Gauthier, S. Y. Thiberge, J. W. Pillow, and D. W. Tank, “Volumetric two-photon imaging of neurons using stereoscopy (vtwins),” Nat. Methods 14, 420 (2017).
[Crossref] [PubMed]

Tomancak, P.

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Figures (9)

Fig. 1
Fig. 1 (a) Schematic of the experimental setup. A laser beam is split into four temporally offset beams using beam splitters (BS). Each beam is converted into a Bessel beam with independently adjusted beam parameters. The Bessel beams excite the volume from four different sides. Inset: Fluorescence emission is detected in four temporally separated channels. (b) Workflow for volumetric reconstruction: four projections are recorded from a three dimensional (3D) sample and back projection is applied to obtain its 3D tomographic reconstruction. Then, a U-net is applied to correct distortions in the reconstructed sample. (c) Illustration of 3D tomography with different viewing angles. Left side: projections parallel to the xy plane allow a perfect reconstruction of a sphere of diameter D. Right side: projections at an oblique angle θ produce a reconstructed sphere elongated in the z axis by a factor of 1/sin(θ). This is corrected for by using convolutional networks. Projection images are obtained by bidirectional raster scanning of tilted Bessel beams across the sample (see Methods for details).
Fig. 2
Fig. 2 Calibration procedure for a single Bessel beam. (a) A volumetric sample of 1µm diameter beads in Agarose recorded with a Bessel beam with 1µm step size in the axial direction (z-axis), resulting in a Bessel beam z-stack. (b) For segmenting different beams, we applied a Gaussian filter with standard deviation of 5 pixels, thresholded the image with its mean value and binarized it. Segmented beams are colored randomly for visualization. (c) Using Principal Component Analysis (PCA) we computed the center of each beam and the directional vector at its center. These vectors are used in linear regression to compute the directional vector field for each the Bessel beam z-stack. Viewing angles were selected for best visibility of the vector fields.
Fig. 3
Fig. 3 Directional vector fields of each Bessel beam measured and computed from a volumetric sample of 1µm diameter beads. Top row: sample recorded with a Gaussian beam (left side) and projections of the volume in the xy, xz and yz planes, respectively (right side). Second row to bottom row: volumetric samples recorded by the four Bessel beams (left side) and plane projections (center). The extrapolated vector field for each beam (right side) is shown in plane projections. The elevation angle is centered around angle 166.75+/-2.75 degrees, see Table 1 and Fig. 8 for more details and quantification of vector fields. Viewing angles were selected for best visibility of the vector fields and projections, respectively.
Fig. 4
Fig. 4 Tomographic reconstruction of 1 µm diameter beads. (a) Top row: projections for each Bessel beam of a volumetric sample. The white frames indicate the overlap between the four Bessel beam projections and any bead within this area is visible in all projections. Center row: cropped projections corresponding to the overlapping area (white frames). Bottom row: cropped projections after applying a Gaussian filter with standard deviation of 5 pixels to improve bead visibility. (b) Reconstruction of the beads (using only back projection, no convolutional networks) in green, compared to the volume recorded with the Gaussian beam (ground truth). A single frame required for reconstruction was recorded at the same time in each channel with 512 × 512 pixels at 30 Hz. As described in the results section, the tomographic reconstruction only shows regions in which all four beams intersect. Due to the offsets between the different projections, some of the beads near the borders of the reference volume are therefore not reconstructed.
Fig. 5
Fig. 5 U-net architecture and simulated data. (a) U-net: each step in the network is composed of 3D convolution, batch normalization and max pooling in 3D in the encoding part while the decoding part is composed of 3D convolution, batch normalization and up sampling in 3D. (b) Simulated data used for training the network. The simulated 3D samples consist of ellipsoids of different sizes and serve as the output of the network. Four projections are generated from each simulated sample volume with addition of shot noise (bottom part). These four projections are produced using the calibration vector fields obtained experimentally. Applying back projection to these four projections yields a volume image. The black region in the reconstructed volume results from the cropping of the projections due to the offset between the different Bessel beam projections. This reconstructed volume serves as the input of the network, while the original volumes serves as the output.
Fig. 6
Fig. 6 Tomography on pollen grain sample. (a) Four projections recorded from a 3D sample of pollen grains. (b) Plane projections of the volumetric reconstructions. Top row: back projections show poor resolution in the z axis since the object approaches the beam length. The second row shows the reconstruction after applying the U-net. The third row additionally applies a mask recorded with the Gaussian beam (see text for details). The bottom row shows the reference Gaussian stack. The dimensions of the images are indicated for each image in the bottom row. A single frame required for reconstruction was recorded at the same time in each channel with 512 × 512 pixels at 30 Hz.
Fig. 7
Fig. 7 Simulated reconstruction error of 3D tomography depends on number of projections for the given isolated sample. (a) A homogeneous cube that contains a homogeneous sphere with higher density and its projection in the xy, xz and yz planes (for visualization). (b) Mean Square Error (MSE) between the simulated 3D sample and the reconstructed sample using back projection as a function of the number of recorded projections using a constant elevation angle of 170 degrees. (c) Projections of the reconstructed sample considering 1, 2, 3, 4, and 10 projections, respectively.
Fig. 8
Fig. 8 2D normalized distribution of the elevation (horizontal axis) and azimuth (vertical axis) angles for each Bessel beam. The distribution is computed from the interpolation equation (4), using a total of N = 106 vectors. See Table 1 for mean values of the distributions.
Fig. 9
Fig. 9 Pictures of the setup. (a) Top view of beam path before entering the resonant scanner and after the delay lines. Four independent Bessel beams are generated with four axicons and combined with polarizing beams splitters (PBS) and a reflecting prism (to combine all four beams) as shown schematically in Figure 1. Delay lines are not shown. Red lines schematically illustrate the beam paths and the number of parallel lines illustrate the number of combined beams. Rotation mounts contain half-wave plates and are not shown in the schematic in Fig. 1. (b) View of microscope with beam path illustrated between the scanner and the microscope objective, passing through scan lens and tube lens and reflected with a mirror into the objective. (c) Picture of the four Bessel beams at the back aperture of the objective with the laser tuned to 680 nm. A 1 inch diameter alignment disk was placed in the back aperture for taking the picture. The diameter of the back aperture is 20 mm. The back focal plane of the objective (Nikon MRP07220 -CFI-75 LWD 16x/ 0.80/ 3,00 water dipping) is at 42.6mm from the specimen surface. The collimation of each beam was iteratively adjusted to obtain four beams with similar focal length. This results in the four rings having different diameters, which is due to the different initial collimations of the beams resulting from the 1 m additional path lengths of each beam.

Tables (1)

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Table 1 Variation of elevation and azimuth angle of Bessel beam vector fields

Equations (8)

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[ f ] ( x c , s ^ , ) = / 2 / 2 f ( x c + t s ^ ) d t .
I ( ν , μ ) = [ f ] ( ν , μ ) = / 2 / 2 f ( x c ( ν , μ ) + t s ^ ( ν , μ ) ) d t .
S ( i ) { s ^ ( i , b ) ( ν c ( i , b ) , μ c ( i , b ) , z c ( i , b ) ) / b = 0 , 1 , , ( N b ( i ) 1 ) } ,
s ^ ( i ) ( ν , μ , z ) A s ( i ) ( ν , μ , z ) T + B s ( i ) ,
( i ) = 1 N b ( i ) b N b ( i ) ( i , b ) .
x c ( i ) ( ν , μ , z ) A c ( i ) ( ν , μ , z ) T + B c ( i ) .
[ ( 1 ) I ( i ) ] ( ν , μ , t ) = { I ( i ) ( ν , μ , c z ) t s ^ ( i ) ( ν , μ , c z ) if t [ ( i ) 2 , ( i ) 2 ] 0 otherwise
R ( ν , μ , t ) = i [ ( 1 ) I ( i ) ] ( ν , μ , t ) .

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