Abstract

Structured illumination microscopy (SIM) is a powerful technique for obtaining super-resolved fluorescence maps of samples, but it is very sensitive to aberrations or misalignments affecting the excitation patterns. Here, we present a reconstruction algorithm that is able to process SIM data even if the illuminations are strongly distorted. The approach is an extension of the recent blind-SIM technique, which reconstructs simultaneously the sample and the excitation patterns without a priori information on the latter. Our algorithm was checked on synthetic and experimental data using distorted and nondistorted illuminations. The reconstructions were similar to that obtained by up-to-date SIM methods when the illuminations were periodic and remained artifact-free when the illuminations were strongly distorted.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013

2012

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

2009

S. A. Shroff, J. R. Fienup, and D. R. Williams, J. Opt. Soc. Am. A 26, 413 (2009).
[CrossRef]

P. Kner, B. B. Chhun, E. R. Griffis, and L. W. M. G. Gustafsson, Nat. Methods 6, 339 (2009).
[CrossRef]

2008

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, Science 320, 1332 (2008).
[CrossRef]

2006

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, Biophys. J. 91, 4258 (2006).
[CrossRef]

E. Betzig, G. H. Patterson, P. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, and J. Lippincott-Schwartz, Science 313, 1642 (2006).
[CrossRef]

M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
[CrossRef]

2005

M. Hofman, C. Eggeling, S. Jakobs, and S. W. Hell, Proc. Natl. Acad. Sci. USA 102, 17565 (2005).
[CrossRef]

A. Dubois, K. Belkebir, and M. Saillard, Inverse Probl. 21, S65 (2005).
[CrossRef]

2003

2001

K. Belkebir and A. G. Tijhuis, Inverse Probl. 17, 1671 (2001).
[CrossRef]

2000

M. Gustafsson, J. Microsc. 198, 82 (2000).
[CrossRef]

1999

T. A. Klar and S. W. Hell, Opt. Lett. 24, 954 (1999).
[CrossRef]

R. Heintzmann and C. Cremer, Proc. SPIE 3568, 185 (1999).
[CrossRef]

1993

Agard, D. A.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, Science 320, 1332 (2008).
[CrossRef]

Allain, M.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
[CrossRef]

Belkebir, K.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

A. Dubois, K. Belkebir, and M. Saillard, Inverse Probl. 21, S65 (2005).
[CrossRef]

K. Belkebir and A. Sentenac, J. Opt. Soc. Am. A 20, 1223 (2003).
[CrossRef]

K. Belkebir and A. G. Tijhuis, Inverse Probl. 17, 1671 (2001).
[CrossRef]

Best, G.

Betzig, E.

E. Betzig, G. H. Patterson, P. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, and J. Lippincott-Schwartz, Science 313, 1642 (2006).
[CrossRef]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, P. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, and J. Lippincott-Schwartz, Science 313, 1642 (2006).
[CrossRef]

Burke, B.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, Science 320, 1332 (2008).
[CrossRef]

Cardoso, M. C.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, Science 320, 1332 (2008).
[CrossRef]

Carlton, P. M.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, Science 320, 1332 (2008).
[CrossRef]

Chhun, B. B.

P. Kner, B. B. Chhun, E. R. Griffis, and L. W. M. G. Gustafsson, Nat. Methods 6, 339 (2009).
[CrossRef]

Cremer, C.

R. Heintzmann and C. Cremer, Proc. SPIE 3568, 185 (1999).
[CrossRef]

Davidson, M. W.

E. Betzig, G. H. Patterson, P. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, and J. Lippincott-Schwartz, Science 313, 1642 (2006).
[CrossRef]

Dubois, A.

A. Dubois, K. Belkebir, and M. Saillard, Inverse Probl. 21, S65 (2005).
[CrossRef]

Eggeling, C.

M. Hofman, C. Eggeling, S. Jakobs, and S. W. Hell, Proc. Natl. Acad. Sci. USA 102, 17565 (2005).
[CrossRef]

Fienup, J. R.

Fiolka, R.

Girard, J.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Girirajan, T. P. K.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, Biophys. J. 91, 4258 (2006).
[CrossRef]

Griffis, E. R.

P. Kner, B. B. Chhun, E. R. Griffis, and L. W. M. G. Gustafsson, Nat. Methods 6, 339 (2009).
[CrossRef]

Gustafsson, L. W. M. G.

P. Kner, B. B. Chhun, E. R. Griffis, and L. W. M. G. Gustafsson, Nat. Methods 6, 339 (2009).
[CrossRef]

Gustafsson, M.

M. Gustafsson, J. Microsc. 198, 82 (2000).
[CrossRef]

Gustafsson, M. G. L.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, Science 320, 1332 (2008).
[CrossRef]

Haase, S.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, Science 320, 1332 (2008).
[CrossRef]

Heintzmann, R.

Hell, S. W.

M. Hofman, C. Eggeling, S. Jakobs, and S. W. Hell, Proc. Natl. Acad. Sci. USA 102, 17565 (2005).
[CrossRef]

T. A. Klar and S. W. Hell, Opt. Lett. 24, 954 (1999).
[CrossRef]

Hess, S. T.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, Biophys. J. 91, 4258 (2006).
[CrossRef]

Hofman, M.

M. Hofman, C. Eggeling, S. Jakobs, and S. W. Hell, Proc. Natl. Acad. Sci. USA 102, 17565 (2005).
[CrossRef]

Hunt, B. R.

Jakobs, S.

M. Hofman, C. Eggeling, S. Jakobs, and S. W. Hell, Proc. Natl. Acad. Sci. USA 102, 17565 (2005).
[CrossRef]

Klar, T. A.

Kner, P.

P. Kner, B. B. Chhun, E. R. Griffis, and L. W. M. G. Gustafsson, Nat. Methods 6, 339 (2009).
[CrossRef]

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, Science 320, 1332 (2008).
[CrossRef]

Leonhardt, H.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, Science 320, 1332 (2008).
[CrossRef]

Lindwasser, W.

E. Betzig, G. H. Patterson, P. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, and J. Lippincott-Schwartz, Science 313, 1642 (2006).
[CrossRef]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, P. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, and J. Lippincott-Schwartz, Science 313, 1642 (2006).
[CrossRef]

Mandula, O.

Mason, M. D.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, Biophys. J. 91, 4258 (2006).
[CrossRef]

Moal, E. L.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Mudry, E.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Nadar, M. S.

Nicoletti, C.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Olenych, S.

E. Betzig, G. H. Patterson, P. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, and J. Lippincott-Schwartz, Science 313, 1642 (2006).
[CrossRef]

Patterson, G. H.

E. Betzig, G. H. Patterson, P. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, and J. Lippincott-Schwartz, Science 313, 1642 (2006).
[CrossRef]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
[CrossRef]

Saillard, M.

A. Dubois, K. Belkebir, and M. Saillard, Inverse Probl. 21, S65 (2005).
[CrossRef]

Savatier, J.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Schermelleh, L.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, Science 320, 1332 (2008).
[CrossRef]

Sedat, J. W.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, Science 320, 1332 (2008).
[CrossRef]

Sementilli, P. J.

Sentenac, A.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

K. Belkebir and A. Sentenac, J. Opt. Soc. Am. A 20, 1223 (2003).
[CrossRef]

Shao, L.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, Science 320, 1332 (2008).
[CrossRef]

Shroff, S. A.

Sougrat, P.

E. Betzig, G. H. Patterson, P. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, and J. Lippincott-Schwartz, Science 313, 1642 (2006).
[CrossRef]

Tijhuis, A. G.

K. Belkebir and A. G. Tijhuis, Inverse Probl. 17, 1671 (2001).
[CrossRef]

Wicker, K.

Williams, D. R.

Winoto, L.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, Science 320, 1332 (2008).
[CrossRef]

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
[CrossRef]

Biophys. J.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, Biophys. J. 91, 4258 (2006).
[CrossRef]

Inverse Probl.

K. Belkebir and A. G. Tijhuis, Inverse Probl. 17, 1671 (2001).
[CrossRef]

A. Dubois, K. Belkebir, and M. Saillard, Inverse Probl. 21, S65 (2005).
[CrossRef]

J. Microsc.

M. Gustafsson, J. Microsc. 198, 82 (2000).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Methods

P. Kner, B. B. Chhun, E. R. Griffis, and L. W. M. G. Gustafsson, Nat. Methods 6, 339 (2009).
[CrossRef]

M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
[CrossRef]

Nat. Photonics

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. Natl. Acad. Sci. USA

M. Hofman, C. Eggeling, S. Jakobs, and S. W. Hell, Proc. Natl. Acad. Sci. USA 102, 17565 (2005).
[CrossRef]

Proc. SPIE

R. Heintzmann and C. Cremer, Proc. SPIE 3568, 185 (1999).
[CrossRef]

Science

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, Science 320, 1332 (2008).
[CrossRef]

E. Betzig, G. H. Patterson, P. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, and J. Lippincott-Schwartz, Science 313, 1642 (2006).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Reconstructions of synthetic SIM images by several reconstruction methods. The blue circle delimitates the regions in which the arc-period of the radial modulation is above or below the Rayleigh criterion. (a) Fluorescence density of the radial sample, (b) reconstructed fluorescence map using the classical SIM algorithm [10], (c) reconstructed fluorescence map using a blind-SIM [12], and (d) reconstructed fluorescence map using a filtered blind-SIM.

Fig. 2.
Fig. 2.

Robustness of filtered blind-SIM and SIM algorithms with respect to pattern distortion. (a) One example of the distorted excitation pattern, (b) filtered blind-SIM estimation of the pattern displayed in (a), (c) filtered blind-SIM reconstruction of the sample, and (d) classical SIM reconstruction of the sample. The color scale indicates the normalized fluorophore density.

Fig. 3.
Fig. 3.

Experimental results on fixed cells with marked paxillin for nondistorted [(a)–(c)] and artificially distorted [(d)–(f)] SIM configurations. The images size is 1.6μm×3.6μm. (a) SIM image in the nondistorted case, (b) filtered blind-SIM image in the nondistorted case, (c) one example of the nondistorted illumination intensity, (d) SIM image obtained when the excitation patterns have been distorted by introducing a granular plastic sheet on the light path, (e) filtered blind-SIM in the distorted case, and (f) one example of the distorted illumination intensity.

Equations (9)

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

ζl=(Ilρ)*p,
ζl=A(Ilρ).
l=1LIlI0,
F(ξ,{Il})=l=1L1hl2+hL2
ξn=ξn1+αndn;ξandIl,n=Il,n1+βl,ndl,n;I,
dn=gn+γndn1,withγn=gn,gn1gn122,
gn;ξ=4l=1Lξn1Il,n1Ahl,n1,gl,n;I=2ξn12A(hl,n1hL,n1)
I˜l=I^˜lf˜l.
gl,n;I^=2ξn12A(hl,n1hL,n1)*fl.

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