Abstract

Wide-field fluorescence microscopy, while much faster than confocal microscopy, suffers from a lack of optical sectioning and poor axial resolution. 3D structured illumination microscopy (SIM) has been demonstrated to provide optical sectioning and to double the resolution limit both laterally and axially, but even with this the axial resolution is still worse than the lateral resolution of unmodified wide-field microscopy. Interferometric schemes using two high numerical aperture objectives, such as 4Pi confocal and I5M microscopy, have improved the axial resolution beyond that of the lateral, but at the cost of a significantly more complex optical setup. Here, we theoretically and numerically investigate a simpler dual-objective scheme which we propose can be easily added to an existing 3D-SIM microscope, providing lateral and axial resolutions in excess of 125 nm with conventional fluorophores and without the need for interferometric detection.

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References

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2016 (1)

M. Müller, V. Mönkemöller, S. Hennig, W. Hübner, and T. Huser, “Open-source image reconstruction of super-resolution structured illumination microscopy data in Image,” Nat. Commun. 7(1), 10980 (2016).
[Crossref]

2012 (2)

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. L. Gustafsson, “Time-lapse two-color 3d imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. 109(14), 5311–5315 (2012).
[Crossref]

L. Shao, L. Winoto, D. Agard, M. Gustafsson, and J. Sedat, “Interferometer-based structured-illumination microscopy utilizing complementary phase relationship through constructive and destructive image detection by two cameras,” J. Microsc. 246(3), 229–236 (2012).
[Crossref]

2011 (1)

L. Shao, P. Kner, E. H. Rego, and M. G. L. Gustafsson, “Super-resolution 3d microscopy of live whole cells using structured illumination,” Nat. Methods 8(12), 1044–1046 (2011).
[Crossref]

2010 (1)

C. B. Müller and J. Enderlein, “Image Scanning Microscopy,” Phys. Rev. Lett. 104(19), 198101 (2010).
[Crossref]

2008 (2)

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-Dimensional Resolution Doubling in Wide-Field Fluorescence Microscopy by Structured Illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref]

L. Shao, B. Isaac, S. Uzawa, D. A. Agard, J. W. Sedat, and M. G. L. Gustafsson, “I5s: Wide-Field Light Microscopy with 100-nm-Scale Resolution in Three Dimensions,” Biophys. J. 94(12), 4971–4983 (2008).
[Crossref]

2006 (4)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-High Resolution Imaging by Fluorescence Photoactivation Localization Microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref]

A. Sharonov and R. M. Hochstrasser, “Wide-field subdiffraction imaging by accumulated binding of diffusing probes,” Proc. Natl. Acad. Sci. 103(50), 18911–18916 (2006).
[Crossref]

2005 (2)

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U. S. A. 102(37), 13081–13086 (2005).
[Crossref]

K. A. Lidke, B. Rieger, T. M. Jovin, and R. Heintzmann, “Superresolution by localization of quantum dots using blinking statistics,” Opt. Express 13(18), 7052–7062 (2005).
[Crossref]

2003 (1)

R. Heintzmann, “Saturated patterned excitation microscopy with two-dimensional excitation patterns,” Micron 34(6-7), 283–291 (2003).
[Crossref]

2000 (3)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref]

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. 97(13), 7232–7236 (2000).
[Crossref]

G. E. Cragg and P. T. C. So, “Lateral resolution enhancement with standing evanescent waves,” Opt. Lett. 25(1), 46 (2000).
[Crossref]

1999 (2)

R. Heintzmann and C. G. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999).
[Crossref]

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “I5m: 3d widefield light microscopy with better than 100 nm axial resolution,” J. Microsc. 195(1), 10–16 (1999).
[Crossref]

1995 (1)

1994 (2)

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780 (1994).
[Crossref]

S. W. Hell, “Improvement of lateral resolution in far-field fluorescence light microscopy by using two-photon excitation with offset beams,” Opt. Commun. 106(1-3), 19–24 (1994).
[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(6450), 44–48 (1993).
[Crossref]

1992 (1)

1988 (1)

C. J. R. Sheppard, “Super-resolution in Confocal Imaging,” Optik 80, 83–84 (1988).

1967 (1)

Agard, D.

L. Shao, L. Winoto, D. Agard, M. Gustafsson, and J. Sedat, “Interferometer-based structured-illumination microscopy utilizing complementary phase relationship through constructive and destructive image detection by two cameras,” J. Microsc. 246(3), 229–236 (2012).
[Crossref]

Agard, D. A.

L. Shao, B. Isaac, S. Uzawa, D. A. Agard, J. W. Sedat, and M. G. L. Gustafsson, “I5s: Wide-Field Light Microscopy with 100-nm-Scale Resolution in Three Dimensions,” Biophys. J. 94(12), 4971–4983 (2008).
[Crossref]

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-Dimensional Resolution Doubling in Wide-Field Fluorescence Microscopy by Structured Illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref]

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “I5m: 3d widefield light microscopy with better than 100 nm axial resolution,” J. Microsc. 195(1), 10–16 (1999).
[Crossref]

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(6450), 44–48 (1993).
[Crossref]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

E. Betzig, “Proposed method for molecular optical imaging,” Opt. Lett. 20(3), 237 (1995).
[Crossref]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Cande, W. Z.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-Dimensional Resolution Doubling in Wide-Field Fluorescence Microscopy by Structured Illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref]

Carlton, P. M.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-Dimensional Resolution Doubling in Wide-Field Fluorescence Microscopy by Structured Illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref]

Cragg, G. E.

Cremer, C. G.

R. Heintzmann and C. G. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999).
[Crossref]

Davidson, M. W.

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. L. Gustafsson, “Time-lapse two-color 3d imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. 109(14), 5311–5315 (2012).
[Crossref]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Enderlein, J.

C. B. Müller and J. Enderlein, “Image Scanning Microscopy,” Phys. Rev. Lett. 104(19), 198101 (2010).
[Crossref]

Farkas, D. L.

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366(6450), 44–48 (1993).
[Crossref]

Fiolka, R.

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. L. Gustafsson, “Time-lapse two-color 3d imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. 109(14), 5311–5315 (2012).
[Crossref]

Frieden, B. R.

Frohn, J. T.

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. 97(13), 7232–7236 (2000).
[Crossref]

Girirajan, T. P. K.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-High Resolution Imaging by Fluorescence Photoactivation Localization Microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref]

Golubovskaya, I. N.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-Dimensional Resolution Doubling in Wide-Field Fluorescence Microscopy by Structured Illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref]

Gustafsson, M.

L. Shao, L. Winoto, D. Agard, M. Gustafsson, and J. Sedat, “Interferometer-based structured-illumination microscopy utilizing complementary phase relationship through constructive and destructive image detection by two cameras,” J. Microsc. 246(3), 229–236 (2012).
[Crossref]

Gustafsson, M. G.

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “I5m: 3d widefield light microscopy with better than 100 nm axial resolution,” J. Microsc. 195(1), 10–16 (1999).
[Crossref]

Gustafsson, M. G. L.

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. L. Gustafsson, “Time-lapse two-color 3d imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. 109(14), 5311–5315 (2012).
[Crossref]

L. Shao, P. Kner, E. H. Rego, and M. G. L. Gustafsson, “Super-resolution 3d microscopy of live whole cells using structured illumination,” Nat. Methods 8(12), 1044–1046 (2011).
[Crossref]

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-Dimensional Resolution Doubling in Wide-Field Fluorescence Microscopy by Structured Illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref]

L. Shao, B. Isaac, S. Uzawa, D. A. Agard, J. W. Sedat, and M. G. L. Gustafsson, “I5s: Wide-Field Light Microscopy with 100-nm-Scale Resolution in Three Dimensions,” Biophys. J. 94(12), 4971–4983 (2008).
[Crossref]

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U. S. A. 102(37), 13081–13086 (2005).
[Crossref]

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref]

Heintzmann, R.

K. A. Lidke, B. Rieger, T. M. Jovin, and R. Heintzmann, “Superresolution by localization of quantum dots using blinking statistics,” Opt. Express 13(18), 7052–7062 (2005).
[Crossref]

R. Heintzmann, “Saturated patterned excitation microscopy with two-dimensional excitation patterns,” Micron 34(6-7), 283–291 (2003).
[Crossref]

R. Heintzmann and C. G. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999).
[Crossref]

Hell, S.

Hell, S. W.

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780 (1994).
[Crossref]

S. W. Hell, “Improvement of lateral resolution in far-field fluorescence light microscopy by using two-photon excitation with offset beams,” Opt. Commun. 106(1-3), 19–24 (1994).
[Crossref]

Hennig, S.

M. Müller, V. Mönkemöller, S. Hennig, W. Hübner, and T. Huser, “Open-source image reconstruction of super-resolution structured illumination microscopy data in Image,” Nat. Commun. 7(1), 10980 (2016).
[Crossref]

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Hess, S. T.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-High Resolution Imaging by Fluorescence Photoactivation Localization Microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref]

Hochstrasser, R. M.

A. Sharonov and R. M. Hochstrasser, “Wide-field subdiffraction imaging by accumulated binding of diffusing probes,” Proc. Natl. Acad. Sci. 103(50), 18911–18916 (2006).
[Crossref]

Hübner, W.

M. Müller, V. Mönkemöller, S. Hennig, W. Hübner, and T. Huser, “Open-source image reconstruction of super-resolution structured illumination microscopy data in Image,” Nat. Commun. 7(1), 10980 (2016).
[Crossref]

Huser, T.

M. Müller, V. Mönkemöller, S. Hennig, W. Hübner, and T. Huser, “Open-source image reconstruction of super-resolution structured illumination microscopy data in Image,” Nat. Commun. 7(1), 10980 (2016).
[Crossref]

Isaac, B.

L. Shao, B. Isaac, S. Uzawa, D. A. Agard, J. W. Sedat, and M. G. L. Gustafsson, “I5s: Wide-Field Light Microscopy with 100-nm-Scale Resolution in Three Dimensions,” Biophys. J. 94(12), 4971–4983 (2008).
[Crossref]

Jovin, T. M.

Knapp, H. F.

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. 97(13), 7232–7236 (2000).
[Crossref]

Kner, P.

L. Shao, P. Kner, E. H. Rego, and M. G. L. Gustafsson, “Super-resolution 3d microscopy of live whole cells using structured illumination,” Nat. Methods 8(12), 1044–1046 (2011).
[Crossref]

Lanni, F.

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366(6450), 44–48 (1993).
[Crossref]

Lidke, K. A.

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Mason, M. D.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-High Resolution Imaging by Fluorescence Photoactivation Localization Microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref]

Mönkemöller, V.

M. Müller, V. Mönkemöller, S. Hennig, W. Hübner, and T. Huser, “Open-source image reconstruction of super-resolution structured illumination microscopy data in Image,” Nat. Commun. 7(1), 10980 (2016).
[Crossref]

Müller, C. B.

C. B. Müller and J. Enderlein, “Image Scanning Microscopy,” Phys. Rev. Lett. 104(19), 198101 (2010).
[Crossref]

Müller, M.

M. Müller, V. Mönkemöller, S. Hennig, W. Hübner, and T. Huser, “Open-source image reconstruction of super-resolution structured illumination microscopy data in Image,” Nat. Commun. 7(1), 10980 (2016).
[Crossref]

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Rego, E. H.

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. L. Gustafsson, “Time-lapse two-color 3d imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. 109(14), 5311–5315 (2012).
[Crossref]

L. Shao, P. Kner, E. H. Rego, and M. G. L. Gustafsson, “Super-resolution 3d microscopy of live whole cells using structured illumination,” Nat. Methods 8(12), 1044–1046 (2011).
[Crossref]

Rieger, B.

Rust, M. J.

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Supplementary Material (4)

NameDescription
» Code 1       Code for calculating OTFs for our four-beam SIM approach and others.
» Visualization 1       A 2D simulation of the effect of increasing the illumination pupil fraction for our four-beam SIM approach. As the pupil fraction increases, the holes in the OTF are filled in, at the expense of weaker strength in the sidebands compared to the centra
» Visualization 2       Simulated optical transfer functions for our four-beam SIM approach showing the effect of increasing primary objective numerical aperture (NA). Central slices are shown, displayed using the same co-ordinate system, logarithmic scaling and colourmap a
» Visualization 3       Simulated optical transfer functions for our four-beam SIM approach showing the effect of increasing primary objective numerical aperture (NA). Central slices are shown, displayed using the same co-ordinate system, logarithmic scaling and colourmap a

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Figures (4)

Fig. 1.
Fig. 1. Creating an illumination profile using four mutually coherent beams. (a) Fourier domain illumination electric field distribution formed by four coherent beams, with those present in 3D-SIM drawn in magenta and the additional beam considered in this work drawn in green. Here the angular separation is the maximum possible, namely the half-angle, $\alpha$, of the lens. (b) Real domain illumination intensity distribution resulting from the electric field distribution of (a). (c) Fourier domain illumination intensity distribution drawn as magenta and green spots (corresponding to those present in 3D-SIM and the new components considered in this work) with the overall support of the OTF drawn as a black line and each wide-field OTF contribution shown in the colour of the illumination component that produced it. These illumination components can be seen to lie on the edge of the support of the 4Pi OTF (cyan lines) for this case where the angular separation is $\alpha$. Note the holes within the support of the OTF near the off-axis green spots.
Fig. 2.
Fig. 2. Strategies for filling the holes in the OTF. (a) Overall effective OTF (support shown as black line) for illumination at 445 nm (purple spots) and 561 nm (yellow-green spots) with fluorescence detection at 610 nm (gray OTFs). Here the holes are filled due to the difference in $k$-vector length, but two new ones are created along $k_z$. These can easily be removed by apodisation at the cost of slightly reduced resolution. (b) The effect of multimode illumination with a pupil fraction of $1/3$. Considering the centre of each illumination image created by the grating leads to the Fourier domain illumination distribution shown as the magenta and green spots. Summing over all such point tetrads causes an axial broadening of this distribution, shown as the magenta and green lines. While no contributions from outside the 4Pi OTF exist, the shifting of contributions within this ensures a good overlap and hence no holes in the overall OTF support. (c) The effect of considering multiple orientations on the $k_x$$k_z$ coverage. With one orientation, a cut through the full 3D OTF support shows the holes suggested by the 2D geometrical consideration. However, with this 3D view it becomes clear that these holes are filled by contributions from the other orientations when three orientations are used to produce the full 3D OTF. (d) Schematic of the proposed experimental setup in which a conventional 3D-SIM microscope is augmented with a low numerical aperture, high working distance objective on the other side of the sample, paired with a tube lens and mirror to reflect just the central beam.
Fig. 3.
Fig. 3. Simulated modulation transfer functions (MTF) for wide-field microscopy techniques, assuming an aperture half-angle of 72.7°. Top rows show the central slice of the MTF, while bottom rows show the projection of the MTF (as would be seen by Fourier transforming a slice of a sub-diffraction bead). All panels follow the same co-ordinate systems. Central slices are shown on a logarithmic scale to enhance dim details. Visualization 3 shows a flythrough of these same MTFs. (a) Wide-field microscopy with uniform illumination. (b) I5M (incoherent illumination + interferometric detection). (c) 3D-SIM. (d) Our proposed dual-objective four-beam SIM (without interferometric detection). (e) Dual-objective six-beam SIM without interferometric detection. (f) I5S (dual-objective six-beam SIM + interferometric detection).
Fig. 4.
Fig. 4. Simulated imaging performance on a fibrous ground truth test image, shown as an $xz$ slice. All images are normalised to have the same minimum and maximum intensity. Cyan arrowheads point to closely-spaced fibre pairs that cannot be resolved using conventional 3D-SIM, but which are resolvable using our four-beam approach or I5S. (a) Ground truth. (b) 3D-SIM. (c) I5S (dual-objective six-beam SIM + interferometric detection). (d) Our proposed dual-objective four-beam SIM (without interferometric detection).