Abstract

Realizing both high temporal and spatial resolution across a large volume is a key challenge for 3D fluorescent imaging. Towards achieving this objective, we introduce an interferometric multifocus microscopy (iMFM) system, a combination of multifocus microscopy (MFM) with two opposing objective lenses. We show that the proposed iMFM is capable of simultaneously producing multiple focal plane interferometry that provides axial super-resolution and hence isotropic 3D resolution with a single exposure. We design and simulate the iMFM microscope by employing two special diffractive optical elements. The point spread function of this new iMFM microscope is simulated and the image formation model is given. For reconstruction, we use the Richardson-Lucy deconvolution algorithm with total variation regularization for 3D extended object recovery, and a maximum likelihood estimator (MLE) for single molecule tracking. A method for determining an initial axial position of the molecule is also proposed to improve the convergence of the MLE. We demonstrate both theoretically and numerically that isotropic 3D nanoscopic localization accuracy is achievable with an axial imaging range of 2um when tracking a fluorescent molecule in three dimensions and that the diffraction limited axial resolution can be improved by 3–4 times in the single shot wide-field 3D extended object recovery. We believe that iMFM will be a useful tool in 3D dynamic event imaging that requires both high temporal and spatial resolution.

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

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2018 (1)

2017 (3)

W. Wang and G. Situ, “Interferometric rotating point spread function and its application in localization based super resolution imaging,” Sci. Rep. 7(1), 5882 (2017).
[Crossref] [PubMed]

B. Hajj, L. Oudjedi, J. B. Fiche, M. Dahan, and M. Nollmann, “Highly efficient multicolor multifocus microscopy by optimal design of diffraction binary gratings,” Sci. Rep. 12(7), 5284 (2017).
[Crossref]

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An Open-Source Software for Deconvolution Microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

2015 (1)

2014 (4)

J. Chen, Z. Zhang, L. Li, B. Chen, A. Revyakin, B. Hajj, W. Legant, M. Dahan, T. Lionnet, E. Betzig, R. Tjian, and Z. Liu, “Single-molecule dynamics of enhanceosome assembly in embryonic stem cells,” Cell,  156(6), 1274–1285 (2014).
[Crossref] [PubMed]

J. Wisniewski, B. Hajj, J. Chen, G. Mizuguchi, H. Xiao, D. Wei, M. Dahan, and C. Wu, “Imaging the fate of histone Cse4 reveals de novo replacement in S phase and subsequent stable residence at centromeres,” eLife 3, e02203 (2014).
[Crossref] [PubMed]

B. Hajj, J. Wisniewski, M. El Beheiry, J. Chen, A. Revyakin, C. Wu, and M. Dahan, “Whole-cell, multicolor superresolution imaging using volumetric multifocus microscopy,” Proc. Natl. Acad. Sci. U.S.A. 111(49), 17480–17485 (2014).
[Crossref] [PubMed]

A. Tahmasbi, S. Ram, J. Chao, A. V. Abraham, F. W. Tang, E. S. Ward, and R. J. Ober, “Designing the focal plane spacing for multifocal plane microscopy,” Opt. Express 22(14), 16706–16721 (2014).
[Crossref] [PubMed]

2013 (1)

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

2012 (1)

S. Ram, D. Kim, R. J. Ober, and E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intracellular transferrin transport at epithelial cell barriers,” Biophys. J. 103, 1594–1603 (2012).
[Crossref] [PubMed]

2011 (1)

D. Aquino, A. Schonle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (5)

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
[Crossref] [PubMed]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

S. Ram, P. Prabhat, E. S. Ward, and R. J. Ober, “Improved single particle localization accuracy with dual objective multifocal plane microscopy,” Opt. Express 17(8), 6881–6898 (2009).
[Crossref] [PubMed]

S. W. Hell, R. Schmidt, and A. Egner, “Diffraction-unlimited three-dimensional optical nanoscopy with opposing lenses,” Nat. Photonics 3, 381–387 (2009).
[Crossref]

M. J. Mlodzianoski, M. F. Juette, G. L. Beane, and J. Bewersdorf, “Experimental characterization of 3D localization techniques for particle-tracking and super-resolution microscopy,” Opt. Express 17, 8264–8277 (2009).
[Crossref] [PubMed]

2008 (2)

C. V. Middendorff, A. Egner, C. Geisler, S. W. Hell, and A. Schönle, “Isotropic 3D Nanoscopy based on single emitter switching,” Opt. Express 16(25), 20774–20788 (2008).
[Crossref]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[Crossref] [PubMed]

2007 (1)

P. Prabhat, Z. Gan, J. Chao, S. Ram, C. Vaccaro, S. Gibbons, R. J. Ober, and E. S. Ward, “Elucidation of intracellular recycling pathways leading to exocytosis of the Fc receptor, FcRn, by using multifocal plane microscopy,” Proc. Natl. Acad. Sci. U.S.A. 104, 5889–5894 (2007).
[Crossref] [PubMed]

2006 (2)

J. Bewersdorf, R. Schmidt, and S. W. Hell, “Comparison of I5M and 4Pi-microscopy,” J. Microsc. 222(2), 105–117 (2006).
[Crossref] [PubMed]

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69(4), 260–266 (2006).
[Crossref] [PubMed]

2005 (1)

2004 (2)

R.J. Ober, S. Ram, and S.E. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86, 1185–1200 (2004).
[Crossref] [PubMed]

P. Prabhat, S. Ram, E. S. Ward, and R. J. Ober, “Simultaneous imaging of different focal planes in fluorescence microscopy for the study of cellular dynamics in three dimensions,” IEEE Trans. Nanobioscience 3(4), 237–242 (2004).
[Crossref]

2001 (2)

M. Nagorni and S. W. Hell, “Coherent use of opposing lenses for axial resolution increase in fluorescence microscopy. I. Comparative study of concepts,” J. Opt. Soc. Am. A 18(1), 36–48 (2001).
[Crossref]

T. Kues, R. Peters, and U. Kubitscheck, “Visualization and tracking of single protein molecules in the cell nucleus,” Biophys. J. 80, 2954–2967 (2001).
[Crossref] [PubMed]

2000 (1)

U. Kubitscheck, O. Kuckmann, T. Kues, and R. Peters, “Imaging and tracking single GFP molecules in solution,” Biophys. J. 78, 2170–2179 (2000).
[Crossref] [PubMed]

1999 (1)

1995 (2)

M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Sevenfold improvement of axial resolution in 3D wide-field microscopy using two objective-lenses,” Proc. SPIE 2412, 147–156 (1995).
[Crossref]

J. N. Mait, “Understanding diffractive optic design in the scalar domain,” J. Opt. Soc. Am. A 12, 2145–2158 (1995).
[Crossref]

1993 (1)

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366, 44–48 (1993).
[Crossref] [PubMed]

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Abraham, A. V.

Abrahamsson, S.

S. Abrahamsson, M. McQuilken, S. B. Mehta, A. Verma, J. Larsch, R. Ilic, R. Heintzmann, C. I. Bargmann, A. S. Gladfelter, and R. Oldenbourg, “MultiFocus Polarization Microscope (MF-PolScope) for 3D polarization imaging of up to 25 focal planes simultaneously,” Opt. Express 23, 7734–7754 (2015).
[Crossref] [PubMed]

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Agard, D. A.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Sevenfold improvement of axial resolution in 3D wide-field microscopy using two objective-lenses,” Proc. SPIE 2412, 147–156 (1995).
[Crossref]

Aguet, F.

Aquino, D.

D. Aquino, A. Schonle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

Bailey, B.

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366, 44–48 (1993).
[Crossref] [PubMed]

Bargmann, C. I.

S. Abrahamsson, M. McQuilken, S. B. Mehta, A. Verma, J. Larsch, R. Ilic, R. Heintzmann, C. I. Bargmann, A. S. Gladfelter, and R. Oldenbourg, “MultiFocus Polarization Microscope (MF-PolScope) for 3D polarization imaging of up to 25 focal planes simultaneously,” Opt. Express 23, 7734–7754 (2015).
[Crossref] [PubMed]

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Beane, G. L.

Betzig, E.

J. Chen, Z. Zhang, L. Li, B. Chen, A. Revyakin, B. Hajj, W. Legant, M. Dahan, T. Lionnet, E. Betzig, R. Tjian, and Z. Liu, “Single-molecule dynamics of enhanceosome assembly in embryonic stem cells,” Cell,  156(6), 1274–1285 (2014).
[Crossref] [PubMed]

Bewersdorf, J.

Biteen, J. S.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Blanc-Feraud, L.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69(4), 260–266 (2006).
[Crossref] [PubMed]

Blanchard, P. M.

Chao, J.

A. Tahmasbi, S. Ram, J. Chao, A. V. Abraham, F. W. Tang, E. S. Ward, and R. J. Ober, “Designing the focal plane spacing for multifocal plane microscopy,” Opt. Express 22(14), 16706–16721 (2014).
[Crossref] [PubMed]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[Crossref] [PubMed]

P. Prabhat, Z. Gan, J. Chao, S. Ram, C. Vaccaro, S. Gibbons, R. J. Ober, and E. S. Ward, “Elucidation of intracellular recycling pathways leading to exocytosis of the Fc receptor, FcRn, by using multifocal plane microscopy,” Proc. Natl. Acad. Sci. U.S.A. 104, 5889–5894 (2007).
[Crossref] [PubMed]

Chen, B.

J. Chen, Z. Zhang, L. Li, B. Chen, A. Revyakin, B. Hajj, W. Legant, M. Dahan, T. Lionnet, E. Betzig, R. Tjian, and Z. Liu, “Single-molecule dynamics of enhanceosome assembly in embryonic stem cells,” Cell,  156(6), 1274–1285 (2014).
[Crossref] [PubMed]

Chen, J.

J. Chen, Z. Zhang, L. Li, B. Chen, A. Revyakin, B. Hajj, W. Legant, M. Dahan, T. Lionnet, E. Betzig, R. Tjian, and Z. Liu, “Single-molecule dynamics of enhanceosome assembly in embryonic stem cells,” Cell,  156(6), 1274–1285 (2014).
[Crossref] [PubMed]

J. Wisniewski, B. Hajj, J. Chen, G. Mizuguchi, H. Xiao, D. Wei, M. Dahan, and C. Wu, “Imaging the fate of histone Cse4 reveals de novo replacement in S phase and subsequent stable residence at centromeres,” eLife 3, e02203 (2014).
[Crossref] [PubMed]

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S. Yoo, P. Ruiz, X. Huang, K. He, M. Hereld, A. Selewa, M. Daddysman, N. Scherer, O. Cossairt, and A. K. Katsaggelos, “3D image reconstruction from multi-focus microscope: axial super-resolution and multiple-frame processing,” Proc. IEEE Int. Conf. Acoust. Speech, and Signal Processing, (2018).

X. Huang, A. Selewa, X. Wang, M. K. Daddysman, I. Gdor, R. Wilton, K. M. Kemner, S. Yoo, A. K. Katsaggelos, K. He, O. Cossairt, N. J. Ferrier, M. Hereld, and N. F. Scherer, “3D snapshot microscopy of extended objects,” https://arXiv:1802.01565 (2018).

Daddysman, M.

I. Gdor, X. Wang, M. Daddysman, Y. Yifat, R. Wilton, M. Hereld, M. F. Noirot-Gros, and N. F. Scherer, “Particle Tracking by Repetitive Phase-Shift Interferometric Super Resolution Microscopy,” Opt. Lett. 43, 2819–2822 (2018).
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Daddysman, M. K.

X. Huang, A. Selewa, X. Wang, M. K. Daddysman, I. Gdor, R. Wilton, K. M. Kemner, S. Yoo, A. K. Katsaggelos, K. He, O. Cossairt, N. J. Ferrier, M. Hereld, and N. F. Scherer, “3D snapshot microscopy of extended objects,” https://arXiv:1802.01565 (2018).

Dahan, M.

B. Hajj, L. Oudjedi, J. B. Fiche, M. Dahan, and M. Nollmann, “Highly efficient multicolor multifocus microscopy by optimal design of diffraction binary gratings,” Sci. Rep. 12(7), 5284 (2017).
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J. Wisniewski, B. Hajj, J. Chen, G. Mizuguchi, H. Xiao, D. Wei, M. Dahan, and C. Wu, “Imaging the fate of histone Cse4 reveals de novo replacement in S phase and subsequent stable residence at centromeres,” eLife 3, e02203 (2014).
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J. Chen, Z. Zhang, L. Li, B. Chen, A. Revyakin, B. Hajj, W. Legant, M. Dahan, T. Lionnet, E. Betzig, R. Tjian, and Z. Liu, “Single-molecule dynamics of enhanceosome assembly in embryonic stem cells,” Cell,  156(6), 1274–1285 (2014).
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B. Hajj, J. Wisniewski, M. El Beheiry, J. Chen, A. Revyakin, C. Wu, and M. Dahan, “Whole-cell, multicolor superresolution imaging using volumetric multifocus microscopy,” Proc. Natl. Acad. Sci. U.S.A. 111(49), 17480–17485 (2014).
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S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
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S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
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G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
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N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69(4), 260–266 (2006).
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B. Hajj, J. Wisniewski, M. El Beheiry, J. Chen, A. Revyakin, C. Wu, and M. Dahan, “Whole-cell, multicolor superresolution imaging using volumetric multifocus microscopy,” Proc. Natl. Acad. Sci. U.S.A. 111(49), 17480–17485 (2014).
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B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366, 44–48 (1993).
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B. Hajj, L. Oudjedi, J. B. Fiche, M. Dahan, and M. Nollmann, “Highly efficient multicolor multifocus microscopy by optimal design of diffraction binary gratings,” Sci. Rep. 12(7), 5284 (2017).
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D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An Open-Source Software for Deconvolution Microscopy,” Methods 115, 28–41 (2017).
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D. Aquino, A. Schonle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
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B. Hajj, L. Oudjedi, J. B. Fiche, M. Dahan, and M. Nollmann, “Highly efficient multicolor multifocus microscopy by optimal design of diffraction binary gratings,” Sci. Rep. 12(7), 5284 (2017).
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X. Huang, A. Selewa, X. Wang, M. K. Daddysman, I. Gdor, R. Wilton, K. M. Kemner, S. Yoo, A. K. Katsaggelos, K. He, O. Cossairt, N. J. Ferrier, M. Hereld, and N. F. Scherer, “3D snapshot microscopy of extended objects,” https://arXiv:1802.01565 (2018).

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D. Aquino, A. Schonle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
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S. W. Hell, R. Schmidt, and A. Egner, “Diffraction-unlimited three-dimensional optical nanoscopy with opposing lenses,” Nat. Photonics 3, 381–387 (2009).
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C. V. Middendorff, A. Egner, C. Geisler, S. W. Hell, and A. Schönle, “Isotropic 3D Nanoscopy based on single emitter switching,” Opt. Express 16(25), 20774–20788 (2008).
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S. Yoo, P. Ruiz, X. Huang, K. He, M. Hereld, A. Selewa, M. Daddysman, N. Scherer, O. Cossairt, and A. K. Katsaggelos, “3D image reconstruction from multi-focus microscope: axial super-resolution and multiple-frame processing,” Proc. IEEE Int. Conf. Acoust. Speech, and Signal Processing, (2018).

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G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009).
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S. Yoo, P. Ruiz, X. Huang, K. He, M. Hereld, A. Selewa, M. Daddysman, N. Scherer, O. Cossairt, and A. K. Katsaggelos, “3D image reconstruction from multi-focus microscope: axial super-resolution and multiple-frame processing,” Proc. IEEE Int. Conf. Acoust. Speech, and Signal Processing, (2018).

X. Huang, A. Selewa, X. Wang, M. K. Daddysman, I. Gdor, R. Wilton, K. M. Kemner, S. Yoo, A. K. Katsaggelos, K. He, O. Cossairt, N. J. Ferrier, M. Hereld, and N. F. Scherer, “3D snapshot microscopy of extended objects,” https://arXiv:1802.01565 (2018).

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S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
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[Crossref]

Wu, C.

B. Hajj, J. Wisniewski, M. El Beheiry, J. Chen, A. Revyakin, C. Wu, and M. Dahan, “Whole-cell, multicolor superresolution imaging using volumetric multifocus microscopy,” Proc. Natl. Acad. Sci. U.S.A. 111(49), 17480–17485 (2014).
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J. Wisniewski, B. Hajj, J. Chen, G. Mizuguchi, H. Xiao, D. Wei, M. Dahan, and C. Wu, “Imaging the fate of histone Cse4 reveals de novo replacement in S phase and subsequent stable residence at centromeres,” eLife 3, e02203 (2014).
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Xiao, H.

J. Wisniewski, B. Hajj, J. Chen, G. Mizuguchi, H. Xiao, D. Wei, M. Dahan, and C. Wu, “Imaging the fate of histone Cse4 reveals de novo replacement in S phase and subsequent stable residence at centromeres,” eLife 3, e02203 (2014).
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S. Yoo, P. Ruiz, X. Huang, K. He, M. Hereld, A. Selewa, M. Daddysman, N. Scherer, O. Cossairt, and A. K. Katsaggelos, “3D image reconstruction from multi-focus microscope: axial super-resolution and multiple-frame processing,” Proc. IEEE Int. Conf. Acoust. Speech, and Signal Processing, (2018).

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eLife (1)

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IEEE Trans. Nanobioscience (1)

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Figures (10)

Fig. 1
Fig. 1 Comparison between (a) I2M + MFM and (b) the proposed iMFM systems. Both systems consist of two opposing objectives, one beam splitter (BS) and one detector. However, in (a), an MFG is placed in the Fourier plane behind BS, prohibiting the correct interference to occur on the detector. In (b), two MFGs of opposite focal shifts are employed in the respective Fourier planes of dual objectives before BS, and are capable of producing multifocal interferometry detection on the BS, which is then imaged via a 4f system (lenses L3 and L4) onto the detector in a single exposure.
Fig. 2
Fig. 2 A representation of the designed MFG with a focal step of 250nm (a) and −250nm (b). The central 400 × 400 pixels of the MFG containing multiple grating unit cells are shown in the top right corner inset.
Fig. 3
Fig. 3 Comparison of the detection PSF of MFM and the proposed iMFM microscopes. (a) MFM and (b) iMFM monochromatic PSFs; (c) MFM and (d) iMFM polychromatic PSFs in the presence of chromatic aberration under 10nm bandwidth emission. For each PSF, xy (left), xz (middle left), yz (middle right) cuts and 1D axial profile or each tile’s PSF (right) are shown. Color indicates differently focused tiles.
Fig. 4
Fig. 4 Comparison of z-derivative between MFM and iMFM PSFs. (a) xz cuts of the square of z-derivative for MFM monochromatic PSF (left), MFM polychromatic PSF (middle left), iMFM monochromatic PSF (middle right) and iMFM polychromatic PSF (right), respectively. The z-derivative is higher for dual objective iMFM detection due to the steepened axial features of interferometric iMFM PSF. (b) xz cuts of combined z-derivative summed over 3 × 3 tiles in (a). The combination of 9 tiles leads to almost uniformly high information content along the optical axis. Note that for the visualization purpose, each tile is cropped and only shown 31 × 241 pixels with the pixel size of 80nm × 10nm in x and z directions.
Fig. 5
Fig. 5 (Left) Theoretical axial localization precision σz for the proposed iMFM aberrated (cyan) and unaberrated detection scheme (red) in comparison to MFM aberrated (green) and unaberrated detection scheme (blue). 2500 detected signal photons per objective lens and 10 background photons per pixel are considered for the calculation. (Right) Mean squared error of the z position determined during 50 simulated localizations per individual axial value (black for monochromatic MFM and purple for monochromatic iMFM, respectively) and corresponding theoretical predications (blue for monochromatic MFM and red for monochromatic iMFM, respectively).
Fig. 6
Fig. 6 An example of determining the initial axial position and range of a single point for the MLE localization algorithm in iMFM. It is clear that the bottom middle tile (outlined by red rectangle) is most in focus compared with other tiles. According to our MFG design (left), this tile focuses at the focal plane of 3Δz. Therefore, the initial axial position of a point is set to be 3Δz. Note that the out-of-focus versions of the point source in other tiles are severely contaminated by the background noise, and therefore are invisible. In the simulation, Ntot = 2500 total detected signal photons and b = 10 background photons per pixel are considered. For the visualization purpose, we cropped each tile image and only showed a ROI of 41 × 41 pixels for each tile in the simulated iMFM image.
Fig. 7
Fig. 7 Single molecule tracking by MFM and iMFM. (a) The ground truth trajectory of a single emitter, shown in 3D space along with its projections onto xy, xz and yz planes. (b) MFM and (c) iMFM reconstructed trajectories by MLE with proposed initial value estimations. color indicates time. (d) The histogram of lateral (left) and axial (right) localization error between ground truth (a) and MFM recovery (b). (e) The histogram of lateral (left) and axial (right) localization error between ground truth (a) and iMFM recovery (c). The standard deviation for MFM axial resolution is 48.37nm and standard deviation for iMFM is 12.12nm, resulting in a 4-fold improvement in axial localization precision.
Fig. 8
Fig. 8 Lateral (left and middle columns) and axial (right column) localization precision of the iMFM system using different filter’s (or emission) bandwidths, i.e., 10nm (cyan), 20nm (red), 40nm (blue), and 80nm (black). Both chromatic corrected iMFM (a) and chromatic aberrated iMFM (b) systems are considered. (c) The average localization over the axial imaging range is plotted as a function of the bandwidth for both iMFM systems.
Fig. 9
Fig. 9 Lateral (left) and axial (right) localization precision of the iMFM system with different focal plane spacing Δz. We consider three focal plane spacings: 100nm (red), 250nm (blue) and 400nm (black).
Fig. 10
Fig. 10 Snapshot axial super resolution of 3D extended object recovery by the proposed iMFM. (a) 3D synthetic object of the microtubules. (b) MFM snapshot recovery. (c) iMFM snapshot recovery. (d) Chromatically aberrated iMFM snapshot recovery in the presence of 10nm bandwidth emission. The 3D image is shown in one xy slice (first row), and two xz slices (second and third rows). The fourth row shows comparison of linecuts indicated by red line in the third row. The last row shows the comparison of kz kx spectra by Fourier transforming the reconstructions. The results clearly demonstrate that both aberrated and unaberrated iMFM can recover higher axial spatial frequencies beyond the detection cut-off of the single lens MFM.

Equations (24)

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E 1 i , MFM ( x , y ; 0 , 0 , z ; λ ) = { g 1 ( x g , y g ; λ ) f 1 ( x g , y g ; 0 , 0 , z ; λ ) } ,
E 2 i , MFM ( x , y ; 0 , 0 , z ; λ ) = { g 2 ( x g , y g ; λ ) f 2 ( x g , y g ; 0 , 0 , z ; λ ) } ,
p 1 ( x , y ; 0 , 0 , z ; λ ) = A λ 0 α sin θ cos θ exp ( i k z cos θ ) J 0 ( k ρ ( x , y ) sin θ ) d θ ,
p 2 ( x , y ; 0 , 0 , z ; λ ) = p 1 ( x , y ; 0 , 0 , z ; λ )
h iMFM mono ( x , y ; 0 , 0 , z ; λ ) = | E 1 , iMFM ( x , y ; 0 , 0 , z ; λ ) + E 2 , iMFM ( x , y ; 0 , 0 , z ; λ ) | 2 .
{ g 1 ( x g , y g ; λ ) } = m = M M n = N N w m , n ( λ ) exp ( i k z m , n λ λ c cos θ ) δ ( x m x 0 λ λ c , y n y 0 λ λ c ) ,
{ g 2 ( x g , y g ; λ ) } = m = M M n = N N w m , n ( λ ) exp ( i k z m , n λ λ c cos θ ) δ ( x m x 0 λ λ c , y n y 0 λ λ c ) ,
E 1 , iMFM ( x , y ; 0 , 0 , z ; λ ) ) = m = M M n = N N w m , n ( λ ) p 1 ( x m x 0 λ λ c , y n y 0 λ λ c ; 0 , 0 , z z m , n λ λ c ) ,
E 2 , iMFM ( x , y ; 0 , 0 , z ; λ ) ) = m = M M n = N N w m , n ( λ ) p 1 ( x m x 0 λ λ c , y n y 0 λ λ c ; 0 , 0 , z m , n λ λ c z ) ,
h iMFM mono ( x , y ; 0 , 0 , z ; λ ) = m = M M n = N N h m , n ( x , y ; 0 , 0 , z z m , n λ λ c ) ,
h m , n ( x , y ; 0 , 0 , z z m , n λ λ c ) = ( A w m , n ( λ ) λ ) 2 | 0 α { exp [ i k ( z z m , n λ λ c ) cos θ ] + exp [ i k ( z m , n λ λ c z ) cos θ ] } × sin θ cos θ J 0 [ ρ ( x m x 0 λ λ c , y n y 0 λ λ c ) sin θ ] d θ | 2 ,
h iMFM mono ( x , y ; 0 , 0 , z ; λ ) = m = M M n = N N λ c Δ λ / 2 λ c + Δ λ / 2 h m , n ( x , y ; 0 , 0 , z z m , n λ λ c ) d λ .
I ( x , y ) = P { z o ( x , y ; z ) * h iMFM ( x , y ; z ) d z + b } + n ^ ,
I = P { Ao + b } ,
arg min o p { I ( p ) log [ ( Ao + b ) ( p ) ] + ( Ao + b ) ( p ) } + λ TV ( o ) subject to o 0 ,
o k + 1 ( s ) = { [ A t ( I A o k + b ) ] ( s ) } o k ( s ) 1 λ TV d i v ( o k ( s ) | o k ( s ) | ) , o k + 1 ( s ) 0 ,
arg min θ p { I ( p ) log [ ( h iMFM ( θ ) + b ) ( p ) ] + ( h iMFM ( θ ) + b ) ( p ) }
F = [ F x x , F x y , F x z F y x , F y y , F y z F z x , F z y , F z z ] ,
F i j = m = M M n = N N p = 1 N p N m , n 2 N m , n h ^ m , n ( p ) + b h ^ m , n ( p ) i h ^ m , n ( p ) j ,
[ CRLB x CRLB y CRLB z ] = [ σ x 2 σ y 2 σ z 2 ] = Diag ( F 1 ) ,
I ( x , y ; x ^ 0 , y ^ 0 , z 0 ) = P [ N tot C p h ^ iMFM ( x x ^ 0 , y y ^ 0 ; z 0 ) d x d y + b ] ,
{ g ( x g , y g ; λ ) } = m = M M n = N N w m , n ( λ ) δ ( u m u 0 , v n v 0 ) ,
{ g 1 ( x g , y g ; λ ) } = { g ( x g Δ x , y g Δ y ; λ ) } = m = M M n = N N w m , n ( λ ) exp [ i 2 π ( m u 0 Δ x + n v 0 Δ y ) ] δ ( u m u 0 , v n v 0 ) ,
{ g 1 ( x g , y g ; λ ) } = m = M M n = N N w m , n ( λ ) exp ( i k z m , n λ λ c cos θ ) δ ( x m x 0 λ λ c , y n y 0 λ λ c ) ,

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