Abstract

We present a theoretical investigation of an optical microscope design that achieves wide-field, multiphoton fluorescence microscopy with finer axial resolution than confocal microscopy. Our technique creates a thin plane of excitation light at the sample using height-staggered microlens arrays (HSMAs), wherein the height staggering of microlenses generate temporal focusing to suppress out-of-focus excitation, and the dense spacing of microlenses enables the implementation of structured illumination technique to eliminate residual out-of-focus signal. We use physical optics-based numerical simulations to demonstrate that our proposed technique can achieve diffraction-limited three-dimensional imaging through a simple optical design.

© 2013 OSA

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References

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  1. J. B. Pawley, Handbook of Biological Confocal Microscopy, 3rd ed. (Springer, 2006).
    [CrossRef]
  2. W. Denk, J. Strickler, and W. Webb, “2-photon laser scanning fluorescence microscopy,” Science248, 73–76 (1990).
    [CrossRef] [PubMed]
  3. J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305, 1007–1009 (2004).
    [CrossRef] [PubMed]
  4. D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express13, 1468–1476 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  8. I. Akira, T. Takeo, I. Katsumi, S. Yumiko, K. Yasuhito, M. Kenta, A. Michio, and U. Isao, “High-speed confocal fluorescence microscopy using a nipkow scanner with microlenses for 3-d imaging of single fluorescent molecule in real time,” Bioimaging4, 57–62 (1996-06).
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    [CrossRef]
  10. V. Andresen, A. Egner, and S. Hell, “Time-multiplexed multifocal multiphoton microscope,” Opt. Lett.26, 75–77 (2001).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  13. C. Ventalon and J. Mertz, “Quasi-confocal fluorescence sectioning with dynamic speckle illumination,” Opt. Lett.30, 3350–3352 (2005).
    [CrossRef]
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    [CrossRef]
  15. J. Jahns and K.-H. Brenner, Microoptics: from Technology to Applications, vol. v. 97 (Springer, 2004).
  16. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Cambridge University Press, 1997).
  17. D. Lim, K. K. Chu, and J. Mertz, “Wide-field fluorescence sectioning with hybrid speckle and uniform-illumination microscopy,” Opt. Lett.33, 1819–21 (2008).
    [CrossRef] [PubMed]
  18. D. Lim, T. N. Ford, K. K. Chu, and J. Mertz, “Optically sectioned in vivo imaging with speckle illumination hilo microscopy,” J. Biomed. Opt.16, 016014 (2011).
    [CrossRef] [PubMed]
  19. R. Heintzmann and P. A. Benedetti, “High-resolution image reconstruction in fluorescence microscopy with patterned excitation,” Appl. Opt.45, 5037–5045 (2006).
    [CrossRef] [PubMed]
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2011 (2)

J.-Y. Yu, C.-H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C.-L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16, 116009 (2011).
[CrossRef] [PubMed]

D. Lim, T. N. Ford, K. K. Chu, and J. Mertz, “Optically sectioned in vivo imaging with speckle illumination hilo microscopy,” J. Biomed. Opt.16, 016014 (2011).
[CrossRef] [PubMed]

2010 (1)

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. K. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods7, 637–U55 (2010).
[CrossRef] [PubMed]

2008 (1)

2006 (1)

2005 (2)

2004 (2)

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305, 1007–1009 (2004).
[CrossRef] [PubMed]

B. Masters, P. So, C. Buehler, N. Barry, J. Sutin, W. Mantulin, and E. Gratton, “Mitigating thermal mechanical damage potential during two-photon dermal imaging,” J. Biomed. Opt.9, 1265–1270 (2004).
[CrossRef] [PubMed]

2001 (1)

2000 (1)

1998 (1)

1997 (1)

1990 (1)

W. Denk, J. Strickler, and W. Webb, “2-photon laser scanning fluorescence microscopy,” Science248, 73–76 (1990).
[CrossRef] [PubMed]

Akira, I.

I. Akira, T. Takeo, I. Katsumi, S. Yumiko, K. Yasuhito, M. Kenta, A. Michio, and U. Isao, “High-speed confocal fluorescence microscopy using a nipkow scanner with microlenses for 3-d imaging of single fluorescent molecule in real time,” Bioimaging4, 57–62 (1996-06).

Andresen, V.

Bao, Z.

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. K. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods7, 637–U55 (2010).
[CrossRef] [PubMed]

Barry, N.

B. Masters, P. So, C. Buehler, N. Barry, J. Sutin, W. Mantulin, and E. Gratton, “Mitigating thermal mechanical damage potential during two-photon dermal imaging,” J. Biomed. Opt.9, 1265–1270 (2004).
[CrossRef] [PubMed]

Benedetti, P. A.

Bewersdorf, J.

Blake, G. A.

J.-Y. Yu, C.-H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C.-L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16, 116009 (2011).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Cambridge University Press, 1997).

Brenner, K.-H.

J. Jahns and K.-H. Brenner, Microoptics: from Technology to Applications, vol. v. 97 (Springer, 2004).

Buehler, C.

B. Masters, P. So, C. Buehler, N. Barry, J. Sutin, W. Mantulin, and E. Gratton, “Mitigating thermal mechanical damage potential during two-photon dermal imaging,” J. Biomed. Opt.9, 1265–1270 (2004).
[CrossRef] [PubMed]

Chen, Y.

J.-Y. Yu, C.-H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C.-L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16, 116009 (2011).
[CrossRef] [PubMed]

Chu, K. K.

D. Lim, T. N. Ford, K. K. Chu, and J. Mertz, “Optically sectioned in vivo imaging with speckle illumination hilo microscopy,” J. Biomed. Opt.16, 016014 (2011).
[CrossRef] [PubMed]

D. Lim, K. K. Chu, and J. Mertz, “Wide-field fluorescence sectioning with hybrid speckle and uniform-illumination microscopy,” Opt. Lett.33, 1819–21 (2008).
[CrossRef] [PubMed]

Del Bene, F.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305, 1007–1009 (2004).
[CrossRef] [PubMed]

Denk, W.

W. Denk, J. Strickler, and W. Webb, “2-photon laser scanning fluorescence microscopy,” Science248, 73–76 (1990).
[CrossRef] [PubMed]

Egner, A.

Ford, T. N.

D. Lim, T. N. Ford, K. K. Chu, and J. Mertz, “Optically sectioned in vivo imaging with speckle illumination hilo microscopy,” J. Biomed. Opt.16, 016014 (2011).
[CrossRef] [PubMed]

Gratton, E.

B. Masters, P. So, C. Buehler, N. Barry, J. Sutin, W. Mantulin, and E. Gratton, “Mitigating thermal mechanical damage potential during two-photon dermal imaging,” J. Biomed. Opt.9, 1265–1270 (2004).
[CrossRef] [PubMed]

Guo, C.-L.

J.-Y. Yu, C.-H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C.-L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16, 116009 (2011).
[CrossRef] [PubMed]

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

Heintzmann, R.

Hell, S.

Holland, D. B.

J.-Y. Yu, C.-H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C.-L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16, 116009 (2011).
[CrossRef] [PubMed]

Huisken, J.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305, 1007–1009 (2004).
[CrossRef] [PubMed]

Isao, U.

I. Akira, T. Takeo, I. Katsumi, S. Yumiko, K. Yasuhito, M. Kenta, A. Michio, and U. Isao, “High-speed confocal fluorescence microscopy using a nipkow scanner with microlenses for 3-d imaging of single fluorescent molecule in real time,” Bioimaging4, 57–62 (1996-06).

Jahns, J.

J. Jahns and K.-H. Brenner, Microoptics: from Technology to Applications, vol. v. 97 (Springer, 2004).

Juskaitis, R.

Katsumi, I.

I. Akira, T. Takeo, I. Katsumi, S. Yumiko, K. Yasuhito, M. Kenta, A. Michio, and U. Isao, “High-speed confocal fluorescence microscopy using a nipkow scanner with microlenses for 3-d imaging of single fluorescent molecule in real time,” Bioimaging4, 57–62 (1996-06).

Keller, P. J.

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. K. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods7, 637–U55 (2010).
[CrossRef] [PubMed]

Kenta, M.

I. Akira, T. Takeo, I. Katsumi, S. Yumiko, K. Yasuhito, M. Kenta, A. Michio, and U. Isao, “High-speed confocal fluorescence microscopy using a nipkow scanner with microlenses for 3-d imaging of single fluorescent molecule in real time,” Bioimaging4, 57–62 (1996-06).

Khairy, K.

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. K. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods7, 637–U55 (2010).
[CrossRef] [PubMed]

Kuo, C.-H.

J.-Y. Yu, C.-H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C.-L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16, 116009 (2011).
[CrossRef] [PubMed]

Lim, D.

D. Lim, T. N. Ford, K. K. Chu, and J. Mertz, “Optically sectioned in vivo imaging with speckle illumination hilo microscopy,” J. Biomed. Opt.16, 016014 (2011).
[CrossRef] [PubMed]

D. Lim, K. K. Chu, and J. Mertz, “Wide-field fluorescence sectioning with hybrid speckle and uniform-illumination microscopy,” Opt. Lett.33, 1819–21 (2008).
[CrossRef] [PubMed]

Mantulin, W.

B. Masters, P. So, C. Buehler, N. Barry, J. Sutin, W. Mantulin, and E. Gratton, “Mitigating thermal mechanical damage potential during two-photon dermal imaging,” J. Biomed. Opt.9, 1265–1270 (2004).
[CrossRef] [PubMed]

Masters, B.

B. Masters, P. So, C. Buehler, N. Barry, J. Sutin, W. Mantulin, and E. Gratton, “Mitigating thermal mechanical damage potential during two-photon dermal imaging,” J. Biomed. Opt.9, 1265–1270 (2004).
[CrossRef] [PubMed]

Mertz, J.

Michio, A.

I. Akira, T. Takeo, I. Katsumi, S. Yumiko, K. Yasuhito, M. Kenta, A. Michio, and U. Isao, “High-speed confocal fluorescence microscopy using a nipkow scanner with microlenses for 3-d imaging of single fluorescent molecule in real time,” Bioimaging4, 57–62 (1996-06).

Neil, M.

Oron, D.

Ouyang, M.

J.-Y. Yu, C.-H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C.-L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16, 116009 (2011).
[CrossRef] [PubMed]

Pawley, J. B.

J. B. Pawley, Handbook of Biological Confocal Microscopy, 3rd ed. (Springer, 2006).
[CrossRef]

Pick, R.

Santella, A.

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. K. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods7, 637–U55 (2010).
[CrossRef] [PubMed]

Schmidt, A. D.

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. K. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods7, 637–U55 (2010).
[CrossRef] [PubMed]

Silberberg, Y.

So, P.

B. Masters, P. So, C. Buehler, N. Barry, J. Sutin, W. Mantulin, and E. Gratton, “Mitigating thermal mechanical damage potential during two-photon dermal imaging,” J. Biomed. Opt.9, 1265–1270 (2004).
[CrossRef] [PubMed]

Stelzer, E.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305, 1007–1009 (2004).
[CrossRef] [PubMed]

Stelzer, E. H. K.

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. K. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods7, 637–U55 (2010).
[CrossRef] [PubMed]

Strickler, J.

W. Denk, J. Strickler, and W. Webb, “2-photon laser scanning fluorescence microscopy,” Science248, 73–76 (1990).
[CrossRef] [PubMed]

Sutin, J.

B. Masters, P. So, C. Buehler, N. Barry, J. Sutin, W. Mantulin, and E. Gratton, “Mitigating thermal mechanical damage potential during two-photon dermal imaging,” J. Biomed. Opt.9, 1265–1270 (2004).
[CrossRef] [PubMed]

Swoger, J.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305, 1007–1009 (2004).
[CrossRef] [PubMed]

Takeo, T.

I. Akira, T. Takeo, I. Katsumi, S. Yumiko, K. Yasuhito, M. Kenta, A. Michio, and U. Isao, “High-speed confocal fluorescence microscopy using a nipkow scanner with microlenses for 3-d imaging of single fluorescent molecule in real time,” Bioimaging4, 57–62 (1996-06).

Tal, E.

Ventalon, C.

Webb, W.

W. Denk, J. Strickler, and W. Webb, “2-photon laser scanning fluorescence microscopy,” Science248, 73–76 (1990).
[CrossRef] [PubMed]

Wilson, T.

Wittbrodt, J.

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. K. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods7, 637–U55 (2010).
[CrossRef] [PubMed]

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305, 1007–1009 (2004).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Cambridge University Press, 1997).

Yasuhito, K.

I. Akira, T. Takeo, I. Katsumi, S. Yumiko, K. Yasuhito, M. Kenta, A. Michio, and U. Isao, “High-speed confocal fluorescence microscopy using a nipkow scanner with microlenses for 3-d imaging of single fluorescent molecule in real time,” Bioimaging4, 57–62 (1996-06).

Yu, J.-Y.

J.-Y. Yu, C.-H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C.-L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16, 116009 (2011).
[CrossRef] [PubMed]

Yumiko, S.

I. Akira, T. Takeo, I. Katsumi, S. Yumiko, K. Yasuhito, M. Kenta, A. Michio, and U. Isao, “High-speed confocal fluorescence microscopy using a nipkow scanner with microlenses for 3-d imaging of single fluorescent molecule in real time,” Bioimaging4, 57–62 (1996-06).

Zadoyan, R.

J.-Y. Yu, C.-H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C.-L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16, 116009 (2011).
[CrossRef] [PubMed]

Appl. Opt. (1)

Bioimaging (1)

I. Akira, T. Takeo, I. Katsumi, S. Yumiko, K. Yasuhito, M. Kenta, A. Michio, and U. Isao, “High-speed confocal fluorescence microscopy using a nipkow scanner with microlenses for 3-d imaging of single fluorescent molecule in real time,” Bioimaging4, 57–62 (1996-06).

J. Biomed. Opt. (3)

B. Masters, P. So, C. Buehler, N. Barry, J. Sutin, W. Mantulin, and E. Gratton, “Mitigating thermal mechanical damage potential during two-photon dermal imaging,” J. Biomed. Opt.9, 1265–1270 (2004).
[CrossRef] [PubMed]

J.-Y. Yu, C.-H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C.-L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16, 116009 (2011).
[CrossRef] [PubMed]

D. Lim, T. N. Ford, K. K. Chu, and J. Mertz, “Optically sectioned in vivo imaging with speckle illumination hilo microscopy,” J. Biomed. Opt.16, 016014 (2011).
[CrossRef] [PubMed]

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

Nat. Methods (1)

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. K. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods7, 637–U55 (2010).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (5)

Science (2)

W. Denk, J. Strickler, and W. Webb, “2-photon laser scanning fluorescence microscopy,” Science248, 73–76 (1990).
[CrossRef] [PubMed]

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305, 1007–1009 (2004).
[CrossRef] [PubMed]

Other (5)

T. Wilson, Confocal Microscopy (Academic Press, 1990).

J. B. Pawley, Handbook of Biological Confocal Microscopy, 3rd ed. (Springer, 2006).
[CrossRef]

J. Jahns and K.-H. Brenner, Microoptics: from Technology to Applications, vol. v. 97 (Springer, 2004).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Cambridge University Press, 1997).

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

Supplementary Material (1)

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Figures (8)

Fig. 1
Fig. 1

(a) Setup of MASI-PPMP. L1 is the microscope objective lens. L2 and L3 are tube lenses of focal length fT. XY stage performs the lateral translations for SIM. The specimen plane is defined as the focal plane of the objective lens L1. (b) Illustration of a spiral HSMA used in this study.

Fig. 2
Fig. 2

(a) Left panel: the intensity distribution ISP at several depths from the focal plane. dfoci is the distance between adjacent foci. The intensity profiles indicated by the yellow line segments are plotted in the right panel. The full widths at half maximum of the intensity peaks are similar to those of conventional 2PE (≈ 0.36λ0/NA). (b) Fluorescence signal S(z) of various (Nt, Δt) sets. (c) Upper panel: definition of in-focus signal (Sin) and out-of-focus signal (Sout). zHM is the position where half-maximum excitation occurs in 2PE (≈ 0.375λ0); Lower panel: Sout /Sin as a function of Nt.

Fig. 3
Fig. 3

S(z) of MA-PPMP (i.e., without SIM post-processing, red), CFM (green) and MASI-PPMP (blue) in linear and log scales. The S(z) of confocal microscopy is simulated as the diameter of the confocal pinhole equal to 1 Airy unit×M, where M is the magnification of the microscopy system. The log-scale plot shows that the optical sectioning of MASI-PPMP is better than CFM. The wavelengths of both the emitted fluorescence and the excitation light of CFM are set to be ∼ 0.56λ0.

Fig. 4
Fig. 4

Image analysis of conventional epifluorescence microscopy (Epi), CFM, MA-PPMP (i.e., without SIM post-processing), and MASI-PPMP. (a) The object. (b) The sectioned images obtained by various techniques at the corresponding depth of the virtual slice. The intensity profiles indicated by the yellow line segments are plotted in (c). (d) 3D-view reconstructed from the z-stacked images of Epi and MASI-PPMP.

Fig. 5
Fig. 5

A model of two adjacent microlenses. d: aperture of the microlenses. f : focal length of the microlens. df : the diameter of the focal spot. Δh: height difference between two microlenses.

Fig. 6
Fig. 6

Sout /Sin curves of distinct time-delay steps arranged in various patterns: jumping-sprial (left), raster (middle), and diagonal (right) geometry.

Fig. 7
Fig. 7

A static frame of Media 1: the time-dependent ESP near the specimen plane (top: Re(ESP); bottom: |ESP|2). The geometrical arrangement of the distinct time-delay steps used for this simulation is a spiral pattern (Fig. 1(b) of main article) with Nt = 49 and dfoci ≈ 0.4λ0. Both plots are normalized to their maximal values.

Fig. 8
Fig. 8

(a) The time-integrated intensity I at a particular position is numerically obtained by taking into account the contributions of foci within distance rtot. The dark area with an array of bright spots indicates the calculated intensity distribution. The faded grid patterns shows the locations of microlenses when projected to the specimen plane of the microscope. (b) The convergence of I for 100 randomly picked positions (upper panel: log scale; lower panel: linear scale). Each curve represents I/Iend as a function of rtot (see text) at a particular position. The analysis has been repeated 10 times; all results show similar convergence. (c) The area for the inf-HSMA model is valid can be determined by rinf and the size of the whole FOV of the microscope.

Equations (17)

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

d λ 0 Δ h max ,
Δ t tot ( N t 1 ) × Δ t = Δ h max ( n 1 ) c ,
E ( r , z , t ) = j e ( k j k 0 ) 2 2 σ k 2 E k j ( r , z ) e i ω j t ,
E k j ( r , z ) k j 0 α cos θ sin θ J 0 ( k j r sin θ ) e i k j z cos θ d θ ,
E S P ( r , z , t ) = m E P S F ( r r m , z , t Δ t m ) ,
I S P ( r , z ) = | E S P ( r , z , t ) | 2 n p d t ,
S ( z ) = I S P ( r , z ) d 2 r .
I I M ( r ) = I S P ( r , z ) f ( r , z ) I S Y S ( r + M r , M 2 z ) d 2 r d z ,
I I M ( r ; z f ) = I S P ( r , z f ) I S Y S ( r + M r , M 2 z f ) d 2 r .
I S I M = i = 1 9 j = 1 9 ( I I M i I I M j ) 2 .
d B d for z Δ h .
d f = 1.22 λ 0 × f # ,
d 1.22 λ 0 × f d λ 0 × Δ h d ,
d λ 0 Δ h .
d λ 0 Δ h max .
N t ( d 0 d f s ) 2 280.
Δ h max = ( N t 1 ) c Δ t ( n 1 ) ,

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