Abstract

Structured illumination microscopy can achieve super-resolution in fluorescence imaging. The sample is illuminated with periodic light patterns, and a series of images are acquired for different pattern positions, also called phases. From these a super-resolution image can be computed. However, for an artefact-free reconstruction it is important that the pattern phases be known with very high precision. If the necessary precision cannot be guaranteed experimentally, the phase information has to be retrieved a posteriori from the acquired data. We present a fast and robust algorithm that iteratively determines these phases with a precision of typically below λ/100. Our method, which is based on cross-correlations, allows optimisation of pattern phase even when the pattern itself is too fine for detection, in which case most other methods inevitably fail. We analyse the performance of this method using simulated data from a synthetic 2D sample as well as experimental single-slice data from a 3D sample and compare it with another previously published approach.

© 2013 OSA

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2012 (2)

E. H. Rego, L. Shao, J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution” PNAS109, E135–E143 (2012).
[CrossRef]

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nature Photon.6, 312–315 (2012).
[CrossRef]

2011 (1)

G. Best, R. Amberger, D. Baddeley, T. Ach, S. Dithmar, R. Heintzmann, and C. Cremer, “Structured illumination microscopy of autofluorescent aggregations in human tissue,” Micron42, 330–335 (2011).
[CrossRef]

2009 (2)

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. Methods6, 339–342 (2009).
[CrossRef] [PubMed]

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase-shift estimation in sinusoidally illuminated images for lateral superresolution,” JOSA A26, 413–424 (2009).
[CrossRef] [PubMed]

2008 (3)

R. Fiolka, M. Beck, and A. Stemmer, “Structured illumination in total internal reflection fluorescence microscopy using a spatial light modulator,” Opt. Lett.33, 1629–1631 (2008).
[CrossRef] [PubMed]

L. Hirvonen, O. Mandula, K. Wicker, and R. Heintzmann, “Structured illumination microscopy using photo-switchable fluorescent proteins,” Proc. SPIE6861, 68610L (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, 4957–4970 (2008).
[CrossRef] [PubMed]

2006 (3)

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J.91, 4258–4272 (2006).
[CrossRef] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313, 1642–1645 (2006).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3, 793–796 (2006).
[CrossRef] [PubMed]

2005 (2)

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” PNAS102, 17565–17569 (2005).
[CrossRef] [PubMed]

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” PNAS102, 13081–13086 (2005).
[CrossRef] [PubMed]

2002 (1)

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy - a concept for optical resolution improvement,” JOSA A19, 1599–1609” (2002).
[CrossRef] [PubMed]

2000 (1)

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

1999 (2)

T. A. Klar and S. W. Hell, “Subdiffraction resolution in far-field fluorescence microscopy,” Opt. Lett.24, 954–956 (1999).
[CrossRef]

R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE3568, 185–196 (1999).
[CrossRef]

1994 (1)

1955 (1)

R. Penrose, “A generalized inverse for matrices,” Proc. Cambridge Philos. Soc.51, 406–413 (1955).
[CrossRef]

1873 (1)

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosk. Anat.9, 413–468 (1873).
[CrossRef]

Abbe, E.

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosk. Anat.9, 413–468 (1873).
[CrossRef]

Ach, T.

G. Best, R. Amberger, D. Baddeley, T. Ach, S. Dithmar, R. Heintzmann, and C. Cremer, “Structured illumination microscopy of autofluorescent aggregations in human tissue,” Micron42, 330–335 (2011).
[CrossRef]

Agard, D. A.

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, 4957–4970 (2008).
[CrossRef] [PubMed]

Allain, M.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nature Photon.6, 312–315 (2012).
[CrossRef]

Amberger, R.

G. Best, R. Amberger, D. Baddeley, T. Ach, S. Dithmar, R. Heintzmann, and C. Cremer, “Structured illumination microscopy of autofluorescent aggregations in human tissue,” Micron42, 330–335 (2011).
[CrossRef]

Baddeley, D.

G. Best, R. Amberger, D. Baddeley, T. Ach, S. Dithmar, R. Heintzmann, and C. Cremer, “Structured illumination microscopy of autofluorescent aggregations in human tissue,” Micron42, 330–335 (2011).
[CrossRef]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3, 793–796 (2006).
[CrossRef] [PubMed]

Beck, M.

Belkebir, K.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nature Photon.6, 312–315 (2012).
[CrossRef]

Best, G.

G. Best, R. Amberger, D. Baddeley, T. Ach, S. Dithmar, R. Heintzmann, and C. Cremer, “Structured illumination microscopy of autofluorescent aggregations in human tissue,” Micron42, 330–335 (2011).
[CrossRef]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313, 1642–1645 (2006).
[CrossRef] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313, 1642–1645 (2006).
[CrossRef] [PubMed]

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, 4957–4970 (2008).
[CrossRef] [PubMed]

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, 4957–4970 (2008).
[CrossRef] [PubMed]

Caulfield, H. J.

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. Methods6, 339–342 (2009).
[CrossRef] [PubMed]

Cremer, C.

G. Best, R. Amberger, D. Baddeley, T. Ach, S. Dithmar, R. Heintzmann, and C. Cremer, “Structured illumination microscopy of autofluorescent aggregations in human tissue,” Micron42, 330–335 (2011).
[CrossRef]

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy - a concept for optical resolution improvement,” JOSA A19, 1599–1609” (2002).
[CrossRef] [PubMed]

R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE3568, 185–196 (1999).
[CrossRef]

Davidson, M. W.

E. H. Rego, L. Shao, J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution” PNAS109, E135–E143 (2012).
[CrossRef]

E. Betzig, G. H. Patterson, R. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313, 1642–1645 (2006).
[CrossRef] [PubMed]

Dithmar, S.

G. Best, R. Amberger, D. Baddeley, T. Ach, S. Dithmar, R. Heintzmann, and C. Cremer, “Structured illumination microscopy of autofluorescent aggregations in human tissue,” Micron42, 330–335 (2011).
[CrossRef]

Eggeling, C.

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” PNAS102, 17565–17569 (2005).
[CrossRef] [PubMed]

Fienup, J. R.

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase-shift estimation in sinusoidally illuminated images for lateral superresolution,” JOSA A26, 413–424 (2009).
[CrossRef] [PubMed]

Fiolka, R.

Frohn, J. T.

J. T. Frohn, “Super-resolution fluorescence microscopy by structured light illumination,” Ph.D. thesis, Eidgenössische Technische Hochschule Zürich, Switzerland (2000).

Girard, J.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nature Photon.6, 312–315 (2012).
[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, 4258–4272 (2006).
[CrossRef] [PubMed]

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, 4957–4970 (2008).
[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. Methods6, 339–342 (2009).
[CrossRef] [PubMed]

Gustafsson, M. G. L.

E. H. Rego, L. Shao, J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution” PNAS109, E135–E143 (2012).
[CrossRef]

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. Methods6, 339–342 (2009).
[CrossRef] [PubMed]

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, 4957–4970 (2008).
[CrossRef] [PubMed]

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” PNAS102, 13081–13086 (2005).
[CrossRef] [PubMed]

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

Heintzmann, R.

G. Best, R. Amberger, D. Baddeley, T. Ach, S. Dithmar, R. Heintzmann, and C. Cremer, “Structured illumination microscopy of autofluorescent aggregations in human tissue,” Micron42, 330–335 (2011).
[CrossRef]

L. Hirvonen, O. Mandula, K. Wicker, and R. Heintzmann, “Structured illumination microscopy using photo-switchable fluorescent proteins,” Proc. SPIE6861, 68610L (2008).
[CrossRef]

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy - a concept for optical resolution improvement,” JOSA A19, 1599–1609” (2002).
[CrossRef] [PubMed]

R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE3568, 185–196 (1999).
[CrossRef]

Hell, S. W.

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” PNAS102, 17565–17569 (2005).
[CrossRef] [PubMed]

T. A. Klar and S. W. Hell, “Subdiffraction resolution in far-field fluorescence microscopy,” Opt. Lett.24, 954–956 (1999).
[CrossRef]

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313, 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, 4258–4272 (2006).
[CrossRef] [PubMed]

Hirvonen, L.

L. Hirvonen, O. Mandula, K. Wicker, and R. Heintzmann, “Structured illumination microscopy using photo-switchable fluorescent proteins,” Proc. SPIE6861, 68610L (2008).
[CrossRef]

Hofmann, M.

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” PNAS102, 17565–17569 (2005).
[CrossRef] [PubMed]

Jakobs, S.

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” PNAS102, 17565–17569 (2005).
[CrossRef] [PubMed]

Johansson, G. A.

E. H. Rego, L. Shao, J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution” PNAS109, E135–E143 (2012).
[CrossRef]

Jovin, T. M.

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy - a concept for optical resolution improvement,” JOSA A19, 1599–1609” (2002).
[CrossRef] [PubMed]

Kamps-Hughes, N.

E. H. Rego, L. Shao, J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution” PNAS109, E135–E143 (2012).
[CrossRef]

Klar, T. A.

Kner, P.

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. Methods6, 339–342 (2009).
[CrossRef] [PubMed]

Le Moal, E.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nature Photon.6, 312–315 (2012).
[CrossRef]

Lindwasser, W.

E. Betzig, G. H. Patterson, R. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313, 1642–1645 (2006).
[CrossRef] [PubMed]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, R. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313, 1642–1645 (2006).
[CrossRef] [PubMed]

Macklin, J.

E. H. Rego, L. Shao, J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution” PNAS109, E135–E143 (2012).
[CrossRef]

Mandula, O.

L. Hirvonen, O. Mandula, K. Wicker, and R. Heintzmann, “Structured illumination microscopy using photo-switchable fluorescent proteins,” Proc. SPIE6861, 68610L (2008).
[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, 4258–4272 (2006).
[CrossRef] [PubMed]

Mudry, E.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nature Photon.6, 312–315 (2012).
[CrossRef]

Nicoletti, C.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nature Photon.6, 312–315 (2012).
[CrossRef]

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313, 1642–1645 (2006).
[CrossRef] [PubMed]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313, 1642–1645 (2006).
[CrossRef] [PubMed]

Penrose, R.

R. Penrose, “A generalized inverse for matrices,” Proc. Cambridge Philos. Soc.51, 406–413 (1955).
[CrossRef]

Rego, E. H.

E. H. Rego, L. Shao, J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution” PNAS109, E135–E143 (2012).
[CrossRef]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3, 793–796 (2006).
[CrossRef] [PubMed]

Savatier, J.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nature Photon.6, 312–315 (2012).
[CrossRef]

Sedat, J. W.

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, 4957–4970 (2008).
[CrossRef] [PubMed]

Sentenac, A.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nature Photon.6, 312–315 (2012).
[CrossRef]

Shao, L.

E. H. Rego, L. Shao, J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution” PNAS109, E135–E143 (2012).
[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, 4957–4970 (2008).
[CrossRef] [PubMed]

Shroff, S. A.

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase-shift estimation in sinusoidally illuminated images for lateral superresolution,” JOSA A26, 413–424 (2009).
[CrossRef] [PubMed]

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313, 1642–1645 (2006).
[CrossRef] [PubMed]

Stemmer, A.

Wang, C. J. R.

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, 4957–4970 (2008).
[CrossRef] [PubMed]

Wicker, K.

L. Hirvonen, O. Mandula, K. Wicker, and R. Heintzmann, “Structured illumination microscopy using photo-switchable fluorescent proteins,” Proc. SPIE6861, 68610L (2008).
[CrossRef]

K. Wicker, “Increasing resolution and light efficiency in fluorescence microscopy,” Ph.D. thesis, King’s College London, U.K. (2010).

Williams, D. R.

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase-shift estimation in sinusoidally illuminated images for lateral superresolution,” JOSA A26, 413–424 (2009).
[CrossRef] [PubMed]

Winoto, L.

E. H. Rego, L. Shao, J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution” PNAS109, E135–E143 (2012).
[CrossRef]

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. Methods6, 339–342 (2009).
[CrossRef] [PubMed]

Yaroslavsky, L. P.

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3, 793–796 (2006).
[CrossRef] [PubMed]

Appl. Opt. (1)

Arch. Mikrosk. Anat. (1)

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosk. Anat.9, 413–468 (1873).
[CrossRef]

Biophys. J. (2)

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J.91, 4258–4272 (2006).
[CrossRef] [PubMed]

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, 4957–4970 (2008).
[CrossRef] [PubMed]

J. Microsc. (1)

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

JOSA A (2)

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy - a concept for optical resolution improvement,” JOSA A19, 1599–1609” (2002).
[CrossRef] [PubMed]

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase-shift estimation in sinusoidally illuminated images for lateral superresolution,” JOSA A26, 413–424 (2009).
[CrossRef] [PubMed]

Micron (1)

G. Best, R. Amberger, D. Baddeley, T. Ach, S. Dithmar, R. Heintzmann, and C. Cremer, “Structured illumination microscopy of autofluorescent aggregations in human tissue,” Micron42, 330–335 (2011).
[CrossRef]

Nat. Methods (2)

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. Methods6, 339–342 (2009).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3, 793–796 (2006).
[CrossRef] [PubMed]

Nature Photon. (1)

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nature Photon.6, 312–315 (2012).
[CrossRef]

Opt. Lett. (2)

PNAS (3)

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” PNAS102, 17565–17569 (2005).
[CrossRef] [PubMed]

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” PNAS102, 13081–13086 (2005).
[CrossRef] [PubMed]

E. H. Rego, L. Shao, J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution” PNAS109, E135–E143 (2012).
[CrossRef]

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R. Penrose, “A generalized inverse for matrices,” Proc. Cambridge Philos. Soc.51, 406–413 (1955).
[CrossRef]

Proc. SPIE (2)

L. Hirvonen, O. Mandula, K. Wicker, and R. Heintzmann, “Structured illumination microscopy using photo-switchable fluorescent proteins,” Proc. SPIE6861, 68610L (2008).
[CrossRef]

R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE3568, 185–196 (1999).
[CrossRef]

Science (1)

E. Betzig, G. H. Patterson, R. Sougrat, W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313, 1642–1645 (2006).
[CrossRef] [PubMed]

Other (3)

J. T. Frohn, “Super-resolution fluorescence microscopy by structured light illumination,” Ph.D. thesis, Eidgenössische Technische Hochschule Zürich, Switzerland (2000).

K. Wicker, “Increasing resolution and light efficiency in fluorescence microscopy,” Ph.D. thesis, King’s College London, U.K. (2010).

M. Schmidt, “minfunc.m,” http://www.di.ens.fr/~mschmidt/Software/minFunc.html (2012).

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Figures (7)

Fig. 1
Fig. 1

Synthetic sample used in simulations. (a) shows the sample (with a close-up of the blue box to the left), (b) its Fourier transform.

Fig. 2
Fig. 2

Performance of the phase optimisation algorithms. Shown is the average phase error over the photon level in the brightest pixel of each set of three raw images (expectation value). Our correlation-based method is shown in blue, the phase-of-peak method in red. Shaded areas show the standard deviation around the average phase error. (a) shows the results obtained for the coarser of the two patterns at (210 nm)−1. While both methods yield similar results for high signal-to-noise ratios, correlation-based optimisation exhibits higher accuracy for lower photon levels. (b) For a finer pattern at (185 nm)−1, i.e. with a spatial frequency close to that of the OTF support, the phase-of-peak method fails to determine the correct pattern phases, while the correlation-based method performs nearly as well as for the coarser grating.

Fig. 3
Fig. 3

Results of a SIM reconstruction without phase optimisation (simulation). (a) shows a Wiener-filter deconvolved wide-field image, (b) its Fourier transform. Even without phase optimisation, the reconstructed SIM image (c) shows a clear resolution improvement. However, without phase optimisation its Fourier transform (d) exhibits residual information from an incomplete separation of components. This leads to artefacts in the reconstructed image (c), visible e.g. as jagged 3lines in the close-up in the blue box.

Fig. 4
Fig. 4

Results of SIM reconstructions using different phase optimisations (simulation). For the given high pattern frequency the phase-of-peak method fails to determine the correct pattern phases. As a result, components are not well-separated at all, clearly visible in the Fourier image (b). The reconstructed SIM image (a) is in fact much worse than when no phase optimisation was applied. Our correlations-based optimisation yields a good separation of Fourier components (d), leading to a reconstructed image void of artefacts (c).

Fig. 5
Fig. 5

Results of a SIM reconstruction without phase optimisation. (a) shows a deconvolved wide-field reconstruction, (b) its Fourier transform. The SIM reconstruction using wrong phases (i.e. assuming the phases {0°, 40°, 240°}) (c) suffers from grainy, honeycomb-like artefacts. Its Fourier transform (d) exhibits residual peaks (marked by blue circles) stemming from poor separation of components.

Fig. 6
Fig. 6

Results of a SIM reconstruction using different phase optimisations. (a) shows a reconstruction using the phase-of-peak method, (b) its Fourier transform. While this method improves the separation of components over the uncorrected case, some unwanted residual information remains visible in the Fourier image (b), and the reconstructed image (a) still exhibits some unwanted graininess. This is particularly obvious when comparing it to the image reconstructed using our correlation-based optimisation (c). Here the graininess is reduced, and unwanted information is no longer visible in the Fourier transformed image (d).

Fig. 7
Fig. 7

Component recombination using weighted averaging. (a) In 3D the recombination of components can be done using the correct 3D weights. This way, the missing cone around the kz-axis is filled by information from the ±1st order components. (b) When using the 2D sum projections of the OTFs as weights for combining 2D components, component will contribute most strongly around their central frequency, where they contain no missing cone information. Their strong contribution suppresses the contribution of components that could otherwise fill the missing cone. (c) Attenuating the 2D OTFs around their central frequency increases the contribution of other components, allowing the missing cone to be filled.

Equations (15)

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D ( r ) = m { [ S ( r ) J m ( r x y ) ] h m ( r ) }
D ˜ ( k ) = m { e ι m ϕ S ˜ ( k m p ) h ˜ m ( k ) } = m e ι m ϕ C ˜ m ( k ) , C ˜ m ( k ) : = S ˜ ( k m p ) h ˜ m ( k ) ,
D ˜ n ( k ) = m e ι m ϕ n C ˜ m ( k ) ,
D ˜ ( k ) = M C ˜ ( k ) , M n , m = e ι m ϕ n ,
C ˜ ( k ) = M 1 D ˜ ( k ) .
S ˜ ( k ) = q , m { h ˜ m * ( k + m p q ) C ˜ q , m ( k + m p q ) } q , m { | h ˜ m ( k + m p q ) | 2 } + w A ˜ ( k )
D ˜ n ( k ) = e ι ϕ n C ˜ 1 ( k ) + C ˜ 0 ( k ) + e ι ϕ n C ˜ + 1 ( k ) = c 2 e ι ϕ n S ˜ ( k + p ) h ˜ ( k ) + S ˜ ( k ) h ˜ ( k ) + c 2 e ι ϕ n S ˜ ( k p ) h ˜ ( k ) .
ϕ n arg { D ˜ n ( p ) } = arg { c 2 e ι ϕ n S ˜ ( 2 p ) h ˜ ( p ) + S ˜ ( p ) h ˜ ( p ) + c 2 e ι ϕ n S ˜ ( 0 ) h ˜ ( p ) } ,
ϕ n arg { e ι ϕ n S ˜ ( 0 ) h ˜ ( p ) } .
𝒞 i , j ( l ) = [ C ˜ i ( k ) w C ˜ j ( k l p ) ] | k = 0
g ( M ) = j + l i 0 | 𝒞 i , j ( l ) | 1 / 2 ,
𝒟 i , j ( l ) = [ D ˜ i ( k ) w D ˜ j ( k l p ) ] | k = 0 .
𝒞 ( l ) = M 1 𝒟 ( l ) ( M 1 ) .
𝒟 i , j ( l ) = { [ D ˜ i ( k ) w D ˜ j ( k l p ) ] | k = 0 δ i j σ 2 , l = 0 [ D ˜ i ( k ) w D ˜ j ( k l p ) ] | k = 0 , l 0 ,
S ˜ ( k k x ) = q , m { g ˜ ( k x y + m p q ) h ˜ m * ( k x y + m p q ) C ˜ q , m ( k x y + m p q ) } q , m { | h ˜ m ( k x y + m p q ) | 2 g ˜ ( k x y + m p q ) } + w A ˜ ( k x y )

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