Abstract

Observing the various anatomical and functional information that spans many spatiotemporal scales with high resolution provides deep understandings of the fundamentals of biological systems. Light-field microscopy (LFM) has recently emerged as a scanning-free, scalable method that allows for high-speed, volumetric imaging ranging from single-cell specimens to the mammalian brain. However, the prohibitive reconstruction artifacts and severe computational cost have thus far limited broader applications of LFM. To address the challenge, in this work, we report Fourier LFM (FLFM), a system that processes the light-field information through the Fourier domain. We established a complete theoretical and algorithmic framework that describes light propagation, image formation and system characterization of FLFM. Compared with conventional LFM, FLFM fundamentally mitigates the artifacts, allowing high-resolution imaging across a two- to three-fold extended depth. In addition, the system substantially reduces the reconstruction time by roughly two orders of magnitude. FLFM was validated by high-resolution, artifact-free imaging of various caliber and biological samples. Furthermore, we proposed a generic design principle for FLFM, as a highly scalable method to meet broader imaging needs across various spatial levels. We anticipate FLFM to be a particularly powerful tool for imaging diverse phenotypic and functional information, spanning broad molecular, cellular and tissue systems.

© 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)

2018 (2)

2017 (2)

T. Nöbauer, O. Skocek, A. J. Pernía-Andrade, L. Weilguny, F. M. Traub, M. I. Molodtsov, and A. Vaziri, “Video rate volumetric Ca2+ imaging across cortex using seeded iterative demixing (SID) microscopy,” Nat. Methods 14(8), 811–818 (2017).
[Crossref]

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref]

2016 (2)

2015 (1)

2014 (2)

N. Cohen, S. Yang, A. Andalman, M. Broxton, K. Deisseroth, M. Horowitz, and M. Levoy, “Enhancing the performance of the light field microscope using wavefront coding,” Opt. Express 22(1), 727–730 (2014).
[Crossref]

R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref]

2013 (1)

2009 (1)

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref]

2007 (1)

F. Dell’Acqua, G. Rizzo, P. Scifo, R. A. Clarke, G. Scotti, and F. Fazio, “A model-based deconvolution approach to solve fiber crossing in diffusion-weighted MR imaging,” IEEE Trans. Biomed. Eng. 54(3), 462–472 (2007).
[Crossref]

2006 (1)

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

1998 (1)

1908 (1)

G. Lippmann, “Epreuves reversibles, photographies integrales,” Comptes Rendus l’Académie des Sci. 444, 446–451 (1908).

Adams, A.

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

Adesnik, H.

Altshuller, Y.

Andalman, A.

Antipa, N.

Bai, L.

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref]

Barreiro, J. C.

Boyden, E. S.

R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref]

Broxton, M.

Chai, Y.

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref]

Chang, J.

I. Kauvar, J. Chang, and G. Wetzstein, “Aperture interference and the volumetric resolution of light field fluorescence microscopy,” in IEEE International Conference on Computational Photography (ICCP) (2017).

Clarke, R. A.

F. Dell’Acqua, G. Rizzo, P. Scifo, R. A. Clarke, G. Scotti, and F. Fazio, “A model-based deconvolution approach to solve fiber crossing in diffusion-weighted MR imaging,” IEEE Trans. Biomed. Eng. 54(3), 462–472 (2007).
[Crossref]

Cohen, N.

Cong, L.

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref]

Dai, Q.

Deisseroth, K.

Delen, N.

Dell’Acqua, F.

F. Dell’Acqua, G. Rizzo, P. Scifo, R. A. Clarke, G. Scotti, and F. Fazio, “A model-based deconvolution approach to solve fiber crossing in diffusion-weighted MR imaging,” IEEE Trans. Biomed. Eng. 54(3), 462–472 (2007).
[Crossref]

Du, J.

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref]

Fazio, F.

F. Dell’Acqua, G. Rizzo, P. Scifo, R. A. Clarke, G. Scotti, and F. Fazio, “A model-based deconvolution approach to solve fiber crossing in diffusion-weighted MR imaging,” IEEE Trans. Biomed. Eng. 54(3), 462–472 (2007).
[Crossref]

Footer, M.

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

French, J. B.

Frohman, M. A.

Garcia-Sucerquia, J.

Georgiev, T.

A. Lumsdaine and T. Georgiev, “The focused plenoptic camera,” in IEEE International Conference on Computational Photography (ICCP) (2009).

Gerlock, M.

Grosenick, L.

Gu, M.

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

Guo, C.

Hang, W.

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref]

Hoffmann, M.

R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref]

Hooker, B.

Horowitz, M.

Javidi, B.

Jia, S.

Kak, A. C.

A. C. Kak and M. Slaney, “3. Algorithms for Reconstruction with Nondiffracting Sources,” in Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001), pp. 49–112.

Kato, S.

R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref]

Kauvar, I.

I. Kauvar, J. Chang, and G. Wetzstein, “Aperture interference and the volumetric resolution of light field fluorescence microscopy,” in IEEE International Conference on Computational Photography (ICCP) (2017).

Kim-Holzapfel, D.

Levoy, M.

Li, H.

Li, W.

Lin, X.

Lippmann, G.

G. Lippmann, “Epreuves reversibles, photographies integrales,” Comptes Rendus l’Académie des Sci. 444, 446–451 (1908).

Liu, H.-Y.

Liu, W.

Llavador, A.

Lumsdaine, A.

A. Lumsdaine and T. Georgiev, “The focused plenoptic camera,” in IEEE International Conference on Computational Photography (ICCP) (2009).

Martínez-Corral, M.

McDowall, I.

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref]

Meng, Y.

Molodtsov, M. I.

T. Nöbauer, O. Skocek, A. J. Pernía-Andrade, L. Weilguny, F. M. Traub, M. I. Molodtsov, and A. Vaziri, “Video rate volumetric Ca2+ imaging across cortex using seeded iterative demixing (SID) microscopy,” Nat. Methods 14(8), 811–818 (2017).
[Crossref]

Ng, R.

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

Nöbauer, T.

M. A. Taylor, T. Nöbauer, A. Pernia-Andrade, F. Schlumm, and A. Vaziri, “Brain-wide 3D light-field imaging of neuronal activity with speckle-enhanced resolution,” Optica 5(4), 345–353 (2018).
[Crossref]

T. Nöbauer, O. Skocek, A. J. Pernía-Andrade, L. Weilguny, F. M. Traub, M. I. Molodtsov, and A. Vaziri, “Video rate volumetric Ca2+ imaging across cortex using seeded iterative demixing (SID) microscopy,” Nat. Methods 14(8), 811–818 (2017).
[Crossref]

Pak, N.

R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref]

Pégard, N. C.

Pernia-Andrade, A.

Pernía-Andrade, A. J.

T. Nöbauer, O. Skocek, A. J. Pernía-Andrade, L. Weilguny, F. M. Traub, M. I. Molodtsov, and A. Vaziri, “Video rate volumetric Ca2+ imaging across cortex using seeded iterative demixing (SID) microscopy,” Nat. Methods 14(8), 811–818 (2017).
[Crossref]

Prevedel, R.

R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref]

Raskar, R.

R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref]

Rizzo, G.

F. Dell’Acqua, G. Rizzo, P. Scifo, R. A. Clarke, G. Scotti, and F. Fazio, “A model-based deconvolution approach to solve fiber crossing in diffusion-weighted MR imaging,” IEEE Trans. Biomed. Eng. 54(3), 462–472 (2007).
[Crossref]

Saavedra, G.

Sanchez-Ortiga, E.

Schlumm, F.

Schrödel, T.

R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref]

Schroeder, B.

Scifo, P.

F. Dell’Acqua, G. Rizzo, P. Scifo, R. A. Clarke, G. Scotti, and F. Fazio, “A model-based deconvolution approach to solve fiber crossing in diffusion-weighted MR imaging,” IEEE Trans. Biomed. Eng. 54(3), 462–472 (2007).
[Crossref]

Scotti, G.

F. Dell’Acqua, G. Rizzo, P. Scifo, R. A. Clarke, G. Scotti, and F. Fazio, “A model-based deconvolution approach to solve fiber crossing in diffusion-weighted MR imaging,” IEEE Trans. Biomed. Eng. 54(3), 462–472 (2007).
[Crossref]

Scrofani, G.

Shang, C.

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref]

Skocek, O.

T. Nöbauer, O. Skocek, A. J. Pernía-Andrade, L. Weilguny, F. M. Traub, M. I. Molodtsov, and A. Vaziri, “Video rate volumetric Ca2+ imaging across cortex using seeded iterative demixing (SID) microscopy,” Nat. Methods 14(8), 811–818 (2017).
[Crossref]

Slaney, M.

A. C. Kak and M. Slaney, “3. Algorithms for Reconstruction with Nondiffracting Sources,” in Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001), pp. 49–112.

Sola-Pikabea, J.

Takamaru, K.-I.

Taylor, M. A.

Traub, F. M.

T. Nöbauer, O. Skocek, A. J. Pernía-Andrade, L. Weilguny, F. M. Traub, M. I. Molodtsov, and A. Vaziri, “Video rate volumetric Ca2+ imaging across cortex using seeded iterative demixing (SID) microscopy,” Nat. Methods 14(8), 811–818 (2017).
[Crossref]

Vaziri, A.

M. A. Taylor, T. Nöbauer, A. Pernia-Andrade, F. Schlumm, and A. Vaziri, “Brain-wide 3D light-field imaging of neuronal activity with speckle-enhanced resolution,” Optica 5(4), 345–353 (2018).
[Crossref]

T. Nöbauer, O. Skocek, A. J. Pernía-Andrade, L. Weilguny, F. M. Traub, M. I. Molodtsov, and A. Vaziri, “Video rate volumetric Ca2+ imaging across cortex using seeded iterative demixing (SID) microscopy,” Nat. Methods 14(8), 811–818 (2017).
[Crossref]

R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref]

Waller, L.

Wang, K.

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref]

Wang, Z.

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref]

Weilguny, L.

T. Nöbauer, O. Skocek, A. J. Pernía-Andrade, L. Weilguny, F. M. Traub, M. I. Molodtsov, and A. Vaziri, “Video rate volumetric Ca2+ imaging across cortex using seeded iterative demixing (SID) microscopy,” Nat. Methods 14(8), 811–818 (2017).
[Crossref]

Wen, Q.

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref]

Wetzstein, G.

R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref]

I. Kauvar, J. Chang, and G. Wetzstein, “Aperture interference and the volumetric resolution of light field fluorescence microscopy,” in IEEE International Conference on Computational Photography (ICCP) (2017).

Wu, J.

Yang, S.

Yang, W.

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref]

Yoon, Y.-G.

R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref]

Zhang, Z.

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref]

Zheng, G.

Zimmer, M.

R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref]

ACM Trans. Graph. (1)

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

Biomed. Opt. Express (3)

Comptes Rendus l’Académie des Sci. (1)

G. Lippmann, “Epreuves reversibles, photographies integrales,” Comptes Rendus l’Académie des Sci. 444, 446–451 (1908).

eLife (1)

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref]

IEEE Trans. Biomed. Eng. (1)

F. Dell’Acqua, G. Rizzo, P. Scifo, R. A. Clarke, G. Scotti, and F. Fazio, “A model-based deconvolution approach to solve fiber crossing in diffusion-weighted MR imaging,” IEEE Trans. Biomed. Eng. 54(3), 462–472 (2007).
[Crossref]

J. Microsc. (1)

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref]

J. Opt. Soc. Am. A (1)

Nat. Methods (2)

R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref]

T. Nöbauer, O. Skocek, A. J. Pernía-Andrade, L. Weilguny, F. M. Traub, M. I. Molodtsov, and A. Vaziri, “Video rate volumetric Ca2+ imaging across cortex using seeded iterative demixing (SID) microscopy,” Nat. Methods 14(8), 811–818 (2017).
[Crossref]

Opt. Express (3)

Optica (2)

Other (4)

I. Kauvar, J. Chang, and G. Wetzstein, “Aperture interference and the volumetric resolution of light field fluorescence microscopy,” in IEEE International Conference on Computational Photography (ICCP) (2017).

A. Lumsdaine and T. Georgiev, “The focused plenoptic camera,” in IEEE International Conference on Computational Photography (ICCP) (2009).

A. C. Kak and M. Slaney, “3. Algorithms for Reconstruction with Nondiffracting Sources,” in Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001), pp. 49–112.

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

Supplementary Material (4)

NameDescription
» Visualization 1       Tracking 200-nm fluorescent particles at a volume acquisition rate of 10 Hz. The corresponding images were shown in Fig. 2e.
» Visualization 2       Tracking 200-nm fluorescent particles at a volume acquisition rate of 26 Hz.
» Visualization 3       Tracking 200-nm fluorescent particles at a volume acquisition rate of 100 Hz.
» Visualization 4       Imaging mouse kidney tissue using FLFM. The video demonstrates a reconstructed volume of 67 µm × 67 µm ×20 µm in x, y and z, respectively. The corresponding images were shown in Fig. 4.

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Figures (16)

Fig. 1.
Fig. 1. Fourier light-field microscopy (FLFM). (a) A schematic of the experimental setup for FLFM. The objective lens (OL) and the tube lens (TL) form an image at the native image plane (NIP), which area is adjusted by an iris. The Fourier lens (FL) transforms the image at the NIP to the back focal plane of the FL, where the microlens array (MLA) is situated. The light-field information is recorded by the sCMOS camera at the back focal plane of the MLA. DM, dichroic mirror; M, mirror. The inset diagram illustrates image formation through the MLA for emitters at different axial positions, implying recording of both the spatial and angular information in an uncompromised manner. (b, c) 3D perspective view (b) and stack projection (c) of the simulated PSF through a 5×5 MLA (effective pitch = 89 µm in the object space) within an axial range from −40 µm to 40 µm. (d) The corresponding experimental PSF of the system across the same range, showing good agreement with the numerical model. The depth information in (c) and (d) is coded as shown in the color-scale bars.
Fig. 2.
Fig. 2. Characterization of FLFM and imaging caliber samples. (a) Left panel, 3D view of a reconstructed 200-nm fluorescent bead using the MATLAB function ‘isosurface’. Right panel, the reconstructed cross-sectional images and the corresponding profiles in x-y, y-z and x-z across the center of the bead, exhibiting FWHM values of 1.98 µm, 2.07 µm, and 4.39 µm in x, y, and z, respectively. (b) Wide-field (i) and raw FLFM (ii) images of 200-nm fluorescent beads located on the focal plane. The inset in (i) shows the zoomed-in image of the boxed region. A reconstructed axial stack of (ii) using wave-optics deconvolution (iii) and ray-optics integral (iv) models. (v) and (vi) show the zoomed-in images (left) and interpolated cross-sectional profiles (right) of the corresponding boxed regions in (iii) and (iv), respectively. FLFM with the wave-optics model has been shown to resolve two beads separated by 2.90 µm, confirmed by the inset in (i). (c) The reconstructed cross-sectional images (left panel) and profiles along the dashed lines (right panel) of a surface-stained 6-µm fluorescent bead using FLFM with the wave-optics (top row) and ray-optics (middle row) models. The hollow structure was clearly observed using the wave-optics model, while the ray-optics model failed to provide sufficient resolution. The same sample was also imaged using conventional LFM (bottom row) near the NIP, where strong artifacts prohibited proper visualization of lateral and axial structures. (d) Raw light-field (top) and reconstructed 3D FLFM (bottom) images of 200-nm fluorescent beads distributed in a volume. The reconstructed axial positions of four beads were identified at −28 µm, −22 µm, −9 µm and −5µm. The dashed lines in the raw image represent the edges of the square-shaped microlenses. (e) Top left, 3D reconstructed trajectories of 200-nm fluorescent beads suspended in water and axially separated by > 30 µm, tracked at a volume acquisition time of 100 ms (see Visualization 1). Top right, zoomed-in 3D trajectory of the corresponding boxed region in the left image. Bottom, the trajectories of the beads in x-y, x-z, and y-z. Different time-points are linearly color-coded from 0 to 4 s. The FLs of ${f_{\textrm{FL}}} = 75\textrm{ mm}$ (a, c, d) and ${f_{\textrm{FL}}} = 100\textrm{ mm}$ (b, e) were employed. Scale bars: 2 µm (a, b (i, v, vi)), 5 µm (c), 20 µm (b (ii), d), 10 µm (b (iii, iv), e).
Fig. 3.
Fig. 3. Imaging pollen grains using FLFM. (a,b) Raw light-field (a) and reconstructed 3D FLFM (b) images of a pollen grain stained with hematoxylin and phloxine B. The spines of the pollen oriented into three dimensions can be observed in (b). The depth information across a 50-µm range in (b) is color-coded according to the color scale bar. (c) Selected z-stack images. The insets show the zoomed-in FLFM (left) and wide-field (right) images at z = 2 µm of two spines (both are 12.03 × 12.03 µm), respectively. The results show sensitive axial discrimination and 3D resolution of the pollen structure using FLFM. (d) Corresponding cross-sectional profiles along the dashed line in (c) at z = 2 µm. The profiles exhibited two spines separated by ∼4 µm and their FWHM values of 1–2 µm resolved by FLFM. Scale bars: 20 µm (a), 10 µm (b, c).
Fig. 4.
Fig. 4. Imaging mouse kidney tissue using FLFM (see Visualization 4). (a,b) Raw light-field (a) and reconstructed 3D FLFM (b) images of a cryostat section of mouse kidney stained with Alexa Fluor 568 phalloidin using a 75-mm Fourier lens. The inset in (b) shows the cross-sectional view in x-z of the corresponding layer marked in (b). The color represents intensity levels in (b). (c, d) Axial-stack images of the reconstructed volume by FLFM (c) and by scanning wide-field microscopy (d). The arrows indicate the enhanced signals and sectioning capability of FLFM that reveal fine 3D structural changes. The grids in the images are the edges of the microlenses when acquiring the corresponding wide-field images through the MLA. (e) The cross-sectional profile along the axial dimension of the region as marked in (b), exhibiting a FWHM value of 4.75 µm. (f) The cross-sectional profile along the dashed line in (c), exhibiting resolved filaments at z=−1.5 µm separated by 3.3 µm. Scale bars: 20 µm.
Fig. 5.
Fig. 5. Experimental setup and light propagation for traditional LFM (top) and FLFM (bottom) using a 40×, 0.95NA objective lens. The insets on the right show the corresponding light-field images on the camera. NOP, native object plane; OL, objective lens; TL, tube lens; NIP, native image plane; FL, Fourier lens; CP, camera plane.
Fig. 6.
Fig. 6. x-z view of the PSFs across the central row of microlenses for FLFM (left panel) and traditional LFM (right panel). Numerical (top panel) and experimental (bottom panel) results show good agreement. The dashed lines represent the NIP and the redundantly aliased region can be observed in the PSF of traditional LFM. The experimental results show background noised due to less sufficient SNRs. Scale bars: 10 µm.
Fig. 7.
Fig. 7. Left to right, raw light-field data, reconstructed 3D image, cross-sectional images at the NIP and the corresponding profiles of the 200-nm fluorescent bead located on the native object plane using traditional LFM. Compared to the result in Fig. 2(a), severe reconstruction artifacts can be observed for traditional LFM near the NIP.
Fig. 8.
Fig. 8. Analysis of the lateral resolution of FLFM. The figure shows the model of light propagation, image formation and symbols to determine the lateral resolution.
Fig. 9.
Fig. 9. Numerical study of the FWHM values of the reconstructed images of a point emitter in all three dimensions, as a function of axial positions from −20 µm to 20 µm. 5 iterations were used for deconvolution, consistent with Fig. 2(a).
Fig. 10.
Fig. 10. Analysis of the axial resolution of FLFM. (a) Left, the model and symbols to determine the axial resolution. Right, symbols and indices of the corresponding microlenses. (b) Simulated light propagation and identification of axial distributions of the PSF after microlenses. Scale bar: 20 µm.
Fig. 11.
Fig. 11. Analysis of the axial resolution of FLFM by reconstructing two axially separated point emitters. Scale bars: 20 µm (left panel), 2 µm (middle panel).
Fig. 12.
Fig. 12. Analysis of the field of view (FOV) of FLFM. The figure shows the model and symbols to determine the FOV.
Fig. 13.
Fig. 13. Analysis of the depth of field (DOF) of FLFM. (a) Ray optics sketch of the model and symbols to determine the DOF based on axial diffraction of light. (b) Simulated light propagation and identification of axial distributions of the PSF after microlenses. (c) Ray optics sketch of the model and symbols to determine the DOF based on the translation of the light-field pattern at varying depths. Scale bars: 20 µm.
Fig. 14.
Fig. 14. Algorithm flow chart of FLFM.
Fig. 15.
Fig. 15. Analysis for the reconstruction of the surface-stained structure (diameter = 20 µm). (a) top row from left to right, the structure sampled with 5 slices, raw light-field image, reconstructed image of the surface-stained structure, cross-sectional images in x-z of the sampled structure, reconstructed image and the overlay, showing difference between the original and reconstructed structures due to the limited sampling step size and overlapping spatial information. (b) Same images with respect to (a) but with 11 slices. (c) Top rows are the same images with respect to (a) but with infinite slices (or sufficiently small step size to be exact), showing increasingly continuous structure and the enhanced stretching effect in the axial dimension (e.g. the 3rd image from the left in the top row of (c)) compared to (a) and (b). The bottom row of (c) demonstrates the agreement of the lateral patterns in x-y on the focal plane of the raw (bottom left), reconstructed (bottom middle) and overlay (bottom right) structures. The numerical results are consistent with our experimental observation in Fig. 2(c). Scale bars: 20 µm (c, left on the top row), 5 µm (c, right on the top row and the bottom row).
Fig. 16.
Fig. 16. Mitigating of the cross talk using a different FL (${f_{\textrm{FL}}} = 50$ mm). Top row from left to right, the densely sampled structure, raw light-field image, and reconstructed image of the surface-stained structure (diameter = 20 µm). Bottom row from left to right, overlay of the original (red) and reconstructed (green) x-z (left) and x-y (middle) sections. Bottom right, the reconstructed hollow structure of the microsphere. Scale bars: 20 µm (top middle), 5 µm (bottom middle).

Tables (1)

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Table 1. Design principle of FLFM.

Equations (5)

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U i ( x , p ) = M f o b j 2 λ 2 e x p [ i u 4 s i n 2 ( α 2 ) ] × 0 α P ( θ ) e x p [ i u s i n 2 ( θ / 2 ) 2 s i n 2 ( α / 2 ) ] J 0 [ s i n ( θ ) s i n ( α ) v ] s i n ( θ ) d θ
ϕ ( x ) = r e c t ( x / d M L A ) e x p ( i k 2 f M L A x 2 2 )
h ( x , p ) = F 1 { F [ O F T [ U i ( x , p ) ] Φ ( x ) ] × e x p [ i 2 π f M L A ( 1 λ ) 2 ( f x 2 + f y 2 ) ] }
O ( x ) = | h ( x , p ) | 2 g ( p ) d p
g ( k + 1 ) = d i a g [ d i a g ( H T H g ( k ) ) 1 ( H T O ) ] g ( k )

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