Abstract

We describe a two-beam interference structured illumination fluorescence microscope. The novelty of the presented system lies in its simplicity. A programmable spatial light modulator (ferroelectric LCoS) in an intermediate image plane enables precise and rapid control of the excitation pattern in the specimen. The contrast of the projected light pattern is strongly influenced by the polarization state of the light entering the high NA objective. To achieve high contrast, we use a segmented polarizer. Furthermore, a mask with six holes blocks unwanted components in the spatial frequency spectrum of the illumination grating. Both these passive components serve their purpose in a simpler and almost as efficient way as active components. We demonstrate a lateral resolution of 114.2 ± 9.5 nm at a frame rate of 7.6 fps per reconstructed 2D slice.

© 2014 Optical Society of America

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References

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2013 (1)

2012 (2)

E. H. Rego, L. Shao, J. J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution,” Proc. Natl. Acad. Sci. U.S.A. 109(3), E135–E143 (2012).
[Crossref] [PubMed]

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. U.S.A. 109(14), 5311–5315 (2012).
[Crossref] [PubMed]

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] [PubMed]

2009 (3)

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[Crossref] [PubMed]

A. Martínez-García, I. Moreno, M. M. Sánchez-López, and P. García-Martínez, “Operational modes of a ferroelectric LCoS modulator for displaying binary polarization, amplitude, and phase diffraction gratings,” Appl. Opt. 48(15), 2903–2914 (2009).
[Crossref] [PubMed]

R. Heintzmann and M. G. L. Gustafsson, “Subdiffraction resolution in continuous samples,” Nat. Photonics 3(7), 362–364 (2009).
[Crossref]

2006 (4)

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 103(31), 11440–11445 (2006).
[Crossref] [PubMed]

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] [PubMed]

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] [PubMed]

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] [PubMed]

2005 (1)

2000 (1)

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] [PubMed]

1999 (1)

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

1994 (1)

Andrei, M. A.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 103(31), 11440–11445 (2006).
[Crossref] [PubMed]

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] [PubMed]

Best, G.

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] [PubMed]

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] [PubMed]

Chhun, B. B.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[Crossref] [PubMed]

Cremer, C.

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

Davidson, M. W.

E. H. Rego, L. Shao, J. J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution,” Proc. Natl. Acad. Sci. U.S.A. 109(3), E135–E143 (2012).
[Crossref] [PubMed]

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. U.S.A. 109(14), 5311–5315 (2012).
[Crossref] [PubMed]

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] [PubMed]

Donnert, G.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 103(31), 11440–11445 (2006).
[Crossref] [PubMed]

Eggeling, C.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 103(31), 11440–11445 (2006).
[Crossref] [PubMed]

Fiolka, R.

K. Wicker, O. Mandula, G. Best, R. Fiolka, and R. Heintzmann, “Phase optimisation for structured illumination microscopy,” Opt. Express 21(2), 2032–2049 (2013).
[Crossref] [PubMed]

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. U.S.A. 109(14), 5311–5315 (2012).
[Crossref] [PubMed]

García-Martínez, P.

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] [PubMed]

Griffis, E. R.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[Crossref] [PubMed]

Gustafsson, M. G.

E. H. Rego, L. Shao, J. J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution,” Proc. Natl. Acad. Sci. U.S.A. 109(3), E135–E143 (2012).
[Crossref] [PubMed]

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. U.S.A. 109(14), 5311–5315 (2012).
[Crossref] [PubMed]

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] [PubMed]

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[Crossref] [PubMed]

R. Heintzmann and M. G. L. Gustafsson, “Subdiffraction resolution in continuous samples,” Nat. Photonics 3(7), 362–364 (2009).
[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] [PubMed]

Heintzmann, R.

K. Wicker, O. Mandula, G. Best, R. Fiolka, and R. Heintzmann, “Phase optimisation for structured illumination microscopy,” Opt. Express 21(2), 2032–2049 (2013).
[Crossref] [PubMed]

R. Heintzmann and M. G. L. Gustafsson, “Subdiffraction resolution in continuous samples,” Nat. Photonics 3(7), 362–364 (2009).
[Crossref]

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

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

Hell, S. W.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 103(31), 11440–11445 (2006).
[Crossref] [PubMed]

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (1994).
[Crossref] [PubMed]

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] [PubMed]

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] [PubMed]

Jahn, R.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 103(31), 11440–11445 (2006).
[Crossref] [PubMed]

Johansson, G. A.

E. H. Rego, L. Shao, J. J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution,” Proc. Natl. Acad. Sci. U.S.A. 109(3), E135–E143 (2012).
[Crossref] [PubMed]

Jovin, T.

Kamps-Hughes, N.

E. H. Rego, L. Shao, J. J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution,” Proc. Natl. Acad. Sci. U.S.A. 109(3), E135–E143 (2012).
[Crossref] [PubMed]

Keller, J.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 103(31), 11440–11445 (2006).
[Crossref] [PubMed]

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] [PubMed]

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[Crossref] [PubMed]

Lidke, K.

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] [PubMed]

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] [PubMed]

Lührmann, R.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 103(31), 11440–11445 (2006).
[Crossref] [PubMed]

Macklin, J. J.

E. H. Rego, L. Shao, J. J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution,” Proc. Natl. Acad. Sci. U.S.A. 109(3), E135–E143 (2012).
[Crossref] [PubMed]

Mandula, O.

Martínez-García, A.

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] [PubMed]

Medda, R.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 103(31), 11440–11445 (2006).
[Crossref] [PubMed]

Moreno, I.

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] [PubMed]

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] [PubMed]

Rego, E. H.

E. H. Rego, L. Shao, J. J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution,” Proc. Natl. Acad. Sci. U.S.A. 109(3), E135–E143 (2012).
[Crossref] [PubMed]

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. U.S.A. 109(14), 5311–5315 (2012).
[Crossref] [PubMed]

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] [PubMed]

Rieger, B.

Rizzoli, S. O.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 103(31), 11440–11445 (2006).
[Crossref] [PubMed]

Rust, M. J.

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] [PubMed]

Sánchez-López, M. M.

Shao, 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. U.S.A. 109(14), 5311–5315 (2012).
[Crossref] [PubMed]

E. H. Rego, L. Shao, J. J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution,” Proc. Natl. Acad. Sci. U.S.A. 109(3), E135–E143 (2012).
[Crossref] [PubMed]

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] [PubMed]

Sougrat, R.

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] [PubMed]

Wichmann, J.

Wicker, K.

Winoto, L.

E. H. Rego, L. Shao, J. J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution,” Proc. Natl. Acad. Sci. U.S.A. 109(3), E135–E143 (2012).
[Crossref] [PubMed]

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[Crossref] [PubMed]

Zhuang, X.

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] [PubMed]

Appl. Opt. (1)

Biophys. J. (1)

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Nat. Methods (3)

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P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
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Nat. Photonics (1)

R. Heintzmann and M. G. L. Gustafsson, “Subdiffraction resolution in continuous samples,” Nat. Photonics 3(7), 362–364 (2009).
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Opt. Express (2)

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Science (1)

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).
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Figures (12)

Fig. 1
Fig. 1 The AOTF switches the illumination beam on and off. Mode cleaning and beam expansion is performed by the lenses L1 & L2 and a pinhole. The SLM is illuminated and the light is diffracted into different orders. L3, L4, the illumination tube lens and the objective project the grating from the SLM in the sample plane. A “pizza polarizer” and a mask accomplish a sinusoidal illumination grating of high contrast in the sample. Emitted light goes through the dichromatic reflector and is imaged with the detection tube lens to the sCMOS camera
Fig. 2
Fig. 2 Twelve circular segments of linear polarizers form one azimuthally polarizer – termed pizza polarizer. The position of the two first orders is shown for each grating direction in different colors.
Fig. 3
Fig. 3 Grating on a SLM. White and red pixels are on, black pixels are off. The red pixels are lattice points, which are connected by the lattice vectors a θ and a Η . The grating direction θ is only defined by a θ . The grating constant has to be calculated with both lattice vectors. Five equidistant phase steps (three-beam illumination) are provided by a horizontal shift (green). Three such phase steps (two-beam illumination) are done vertically (cyan).
Fig. 4
Fig. 4 All three Fourier tranforms of the gratings in one RGB image. The yellow circles represent the holes in the mask. The triplet is useless if unwanted orders are in the circle. Gamma correction of 0.30 is applied for a better visibility.
Fig. 5
Fig. 5 Grating on the SLM based on Fiolka's approach. White and red pixels are on, black pixels are off. The red pixels are lattice points, which are connected by the lattice vectors a θ and a Η . The grating direction is still only defined by a θ . The second lattice vector a Η does not have to be horizontal anymore.
Fig. 6
Fig. 6 Illumination orders close to the pupil plane after the order selection mask with and without the mask. Left: Unwanted orders are present. Right: The used mask blocks unwanted orders except the first orders.
Fig. 7
Fig. 7 110 nm bead with different brightness resulting from the high illumination grating contrast (left: maximum, right: minimum). The gray values are non-linear (gamma = 0.4).
Fig. 8
Fig. 8 Comparison of wide-field (a) and SIM (b) with a 110 nm bead sample
Fig. 9
Fig. 9 Wide-field (blue dotted) and SIM (green) profile along the yellow line from Fig. 8 beginning at the left bottom.
Fig. 10
Fig. 10 Average point spread function of wide-field (left) and SIM (right) from Fig. 8
Fig. 11
Fig. 11 Six different grating directions filtered by a mask in a pupil plane. All unwanted orders are blocked.
Fig. 12
Fig. 12 Electronic circuit to synchronize SLM,Camera and AOTF with an Arduino.

Tables (2)

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Table 1 Grating Parameters of Three Different gratings Separated by ~60°

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Table 2 Grating Parameters of Six Different Gratings Separated by ~30°

Equations (13)

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P={ a H ; a θ } with a H =( h 0 ) and a θ =( θ x θ y )
h{ 1,2,, h max } θ x { 1,2,, θ x max } θ y { θ y max , θ y max +1,, θ y max 1, θ y max }
θ( P )=θ( a θ )={ π 2 for θ x =0 arctan( θ y θ x )[ 0;π ] for θ x 0
g( P )=g( a H , a θ )=hsin( θ )
α( T )={ | θ( P 1 )θ( P 2 ) |;| θ( P 1 )θ( P 3 ) |;| θ( P 2 )θ( P 3 ) | } Δα( T )=max{ α( T ) 60 o }< 5 o
g( T )={ g( P 1 );g( P 2 );g( P 3 ) }
g ¯ ( T )= max( g( T ) )+min( g( T ) ) 2
Δg( T )= max{ g ¯ ( T )g( T ) } g ¯ ( T ) <2%
P={ a H ; a θ } with a H =( h x h y ) and a θ =( θ x θ y )
θ( P )=θ( a θ )={ π 2 for θ x =0 arctan( θ y θ x )[ 0;π ] for θ x 0
g( P )= h x 2 + h y 2 | sin( θ( a θ )θ( a H ) ) |= h x θ y h y θ x h x 2 + h y 2
If: h x =0: h y mod7=0 Else: ( lcm( | h x |,| θ x | ) θ y θ x h y h x )mod7=0
If: h y =0: h x mod7=0 Else: ( lcm( | h y |,| θ y | ) θ x θ y h x h y )mod7=0

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