Abstract

We model the effect of depth dependent spherical aberration caused by a refractive index mismatch between the mounting and immersion mediums in a 3D structured illumination microscope (SIM). We first derive a forward model that takes into account the effect of the depth varying aberrations on both the illumination and the detection processes. From the model, we demonstrate that depth dependent spherical aberration leads to loss of signal only due to its effect on the detection response of the system, while its effect on illumination leads to phase shifts between orders that can be handled computationally in the reconstruction process. Further, by using the model, we provide guidelines for optical corrections of aberrations with different complexities, and explain how the proposed corrections simplify the forward model. Finally, we show that it is possible to correct both illumination and detection aberrations using a deformable mirror only on the detection path of the microscope.

© 2012 OSA

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  1. M. Gustafsson, A. Agard, and J. Sedat, “Doubling of lateral resolution of wide-field fluorescence microscopy using structured illumination,” Proc. SPIE 3919, 14–150 (2001).
  2. P. Kner, B. Chhun, E. Griffis, L. Winoto, and M. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Meth. 6, 339–342 (2009).
    [CrossRef]
  3. M. Gustafsson, L. Shao, P. Carlton, C. Wang, I. Golubovskaya, W. Cande, D. Agard, and J. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
    [CrossRef] [PubMed]
  4. M. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102, 13081–13086 (2005).
    [CrossRef] [PubMed]
  5. L. Schermelleh, P. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. Cardoso, D. Agard, M. Gustafsson, H. Leonhardt, and J. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
    [CrossRef] [PubMed]
  6. M. Trammell, N. Mahoney, D. Agard, and R. Vale, “Mob4 plays a role in spindle focusing in Drosophila S2 cells,” J. Cell Sci. 121, 1284–1292 (2008).
    [CrossRef] [PubMed]
  7. C. Wang, P. Carlton, I. Golubovskaya, and W. Cande, “Interlock formation and coiling of meiotic chromosome axes during synapsis,” Genetics 183, 905–915 (2009).
    [CrossRef] [PubMed]
  8. J. Fitzgibbon, K. Bell, E. King, and K. Oparka, “Super-resolution imaging of Plasmodesmata using three-dimensional structured illumination microscopy,” Plant Phys. 153, 1453 –1463 (2010).
    [CrossRef]
  9. S. Gibson and F. Lanni, “Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy,” J. Opt. Soc. Am. A 8, 1601–1613 (1991).
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  10. B. Hanser, M. Gustafsson, D. Agard, and J. Sedat, “Phase-retrieved pupil functions in wide-field fluorescent microscopy,” J. Microsc. 216, 32–48 (2004).
    [CrossRef] [PubMed]
  11. Z. Kam, P. Kner, D. Agard, and J. Sedat, ”Modelling the application of adaptive optics to wide-field microscope live imaging,” J. Microsc. 226, 33–42 (2007).
    [CrossRef] [PubMed]
  12. P. Kner, J. Sedat, and D. Agard, “Applying adaptive optics to three-dimensional wide-field microscopy,” Proc. SPIE 6888, 688–809 (2008).
  13. C. Preza and J. Conchello, “Image estimation account for point-spread function depth variation in three-dimensional fluorescence microscopy,” Proc. SPIE 4964, 1–8 (2003).
  14. C. Preza and J. Conchello, “Depth-variant maximum likelihood restoration for three-dimensional fluorescence microscopy,” J. Opt. Soc. Am. A 21, 1593–1601 (2004).
    [CrossRef]
  15. M. Arigovindan, J. Shaevitz, J. McGowan, J. Sedat, and D. Agard, “A parallel product-convolution approach for representing the depth varying point spread functions in 3D widefield microscopy based on principal component analysis,” Opt Express 18, 6461–6476 (2010).
    [CrossRef] [PubMed]
  16. D. Débarre, E. Botcherby, T. Watanabe, S. Srinivas, M. Booth, and T. Wilson, “Image-based adaptive optics for two-photon microscopy,” Opt. Lett. 34, 2495–2497 (2009).
    [CrossRef] [PubMed]
  17. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, 2004).
  18. S. Wiersma, P. Torok, T. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. B 14, 1482–1490 (1997).
    [CrossRef]

2010 (2)

J. Fitzgibbon, K. Bell, E. King, and K. Oparka, “Super-resolution imaging of Plasmodesmata using three-dimensional structured illumination microscopy,” Plant Phys. 153, 1453 –1463 (2010).
[CrossRef]

M. Arigovindan, J. Shaevitz, J. McGowan, J. Sedat, and D. Agard, “A parallel product-convolution approach for representing the depth varying point spread functions in 3D widefield microscopy based on principal component analysis,” Opt Express 18, 6461–6476 (2010).
[CrossRef] [PubMed]

2009 (3)

D. Débarre, E. Botcherby, T. Watanabe, S. Srinivas, M. Booth, and T. Wilson, “Image-based adaptive optics for two-photon microscopy,” Opt. Lett. 34, 2495–2497 (2009).
[CrossRef] [PubMed]

C. Wang, P. Carlton, I. Golubovskaya, and W. Cande, “Interlock formation and coiling of meiotic chromosome axes during synapsis,” Genetics 183, 905–915 (2009).
[CrossRef] [PubMed]

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

2008 (4)

M. Gustafsson, L. Shao, P. Carlton, C. Wang, I. Golubovskaya, W. Cande, D. Agard, and J. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

L. Schermelleh, P. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. Cardoso, D. Agard, M. Gustafsson, H. Leonhardt, and J. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef] [PubMed]

M. Trammell, N. Mahoney, D. Agard, and R. Vale, “Mob4 plays a role in spindle focusing in Drosophila S2 cells,” J. Cell Sci. 121, 1284–1292 (2008).
[CrossRef] [PubMed]

P. Kner, J. Sedat, and D. Agard, “Applying adaptive optics to three-dimensional wide-field microscopy,” Proc. SPIE 6888, 688–809 (2008).

2007 (1)

Z. Kam, P. Kner, D. Agard, and J. Sedat, ”Modelling the application of adaptive optics to wide-field microscope live imaging,” J. Microsc. 226, 33–42 (2007).
[CrossRef] [PubMed]

2005 (1)

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

2004 (2)

B. Hanser, M. Gustafsson, D. Agard, and J. Sedat, “Phase-retrieved pupil functions in wide-field fluorescent microscopy,” J. Microsc. 216, 32–48 (2004).
[CrossRef] [PubMed]

C. Preza and J. Conchello, “Depth-variant maximum likelihood restoration for three-dimensional fluorescence microscopy,” J. Opt. Soc. Am. A 21, 1593–1601 (2004).
[CrossRef]

2003 (1)

C. Preza and J. Conchello, “Image estimation account for point-spread function depth variation in three-dimensional fluorescence microscopy,” Proc. SPIE 4964, 1–8 (2003).

2001 (1)

M. Gustafsson, A. Agard, and J. Sedat, “Doubling of lateral resolution of wide-field fluorescence microscopy using structured illumination,” Proc. SPIE 3919, 14–150 (2001).

1997 (1)

S. Wiersma, P. Torok, T. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. B 14, 1482–1490 (1997).
[CrossRef]

1991 (1)

Agard, A.

M. Gustafsson, A. Agard, and J. Sedat, “Doubling of lateral resolution of wide-field fluorescence microscopy using structured illumination,” Proc. SPIE 3919, 14–150 (2001).

Agard, D.

M. Arigovindan, J. Shaevitz, J. McGowan, J. Sedat, and D. Agard, “A parallel product-convolution approach for representing the depth varying point spread functions in 3D widefield microscopy based on principal component analysis,” Opt Express 18, 6461–6476 (2010).
[CrossRef] [PubMed]

P. Kner, J. Sedat, and D. Agard, “Applying adaptive optics to three-dimensional wide-field microscopy,” Proc. SPIE 6888, 688–809 (2008).

M. Gustafsson, L. Shao, P. Carlton, C. Wang, I. Golubovskaya, W. Cande, D. Agard, and J. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

L. Schermelleh, P. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. Cardoso, D. Agard, M. Gustafsson, H. Leonhardt, and J. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef] [PubMed]

M. Trammell, N. Mahoney, D. Agard, and R. Vale, “Mob4 plays a role in spindle focusing in Drosophila S2 cells,” J. Cell Sci. 121, 1284–1292 (2008).
[CrossRef] [PubMed]

Z. Kam, P. Kner, D. Agard, and J. Sedat, ”Modelling the application of adaptive optics to wide-field microscope live imaging,” J. Microsc. 226, 33–42 (2007).
[CrossRef] [PubMed]

B. Hanser, M. Gustafsson, D. Agard, and J. Sedat, “Phase-retrieved pupil functions in wide-field fluorescent microscopy,” J. Microsc. 216, 32–48 (2004).
[CrossRef] [PubMed]

Arigovindan, M.

M. Arigovindan, J. Shaevitz, J. McGowan, J. Sedat, and D. Agard, “A parallel product-convolution approach for representing the depth varying point spread functions in 3D widefield microscopy based on principal component analysis,” Opt Express 18, 6461–6476 (2010).
[CrossRef] [PubMed]

Bell, K.

J. Fitzgibbon, K. Bell, E. King, and K. Oparka, “Super-resolution imaging of Plasmodesmata using three-dimensional structured illumination microscopy,” Plant Phys. 153, 1453 –1463 (2010).
[CrossRef]

Booth, M.

Botcherby, E.

Burke, B.

L. Schermelleh, P. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. Cardoso, D. Agard, M. Gustafsson, H. Leonhardt, and J. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef] [PubMed]

Cande, W.

C. Wang, P. Carlton, I. Golubovskaya, and W. Cande, “Interlock formation and coiling of meiotic chromosome axes during synapsis,” Genetics 183, 905–915 (2009).
[CrossRef] [PubMed]

M. Gustafsson, L. Shao, P. Carlton, C. Wang, I. Golubovskaya, W. Cande, D. Agard, and J. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

Cardoso, M.

L. Schermelleh, P. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. Cardoso, D. Agard, M. Gustafsson, H. Leonhardt, and J. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef] [PubMed]

Carlton, P.

C. Wang, P. Carlton, I. Golubovskaya, and W. Cande, “Interlock formation and coiling of meiotic chromosome axes during synapsis,” Genetics 183, 905–915 (2009).
[CrossRef] [PubMed]

L. Schermelleh, P. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. Cardoso, D. Agard, M. Gustafsson, H. Leonhardt, and J. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef] [PubMed]

M. Gustafsson, L. Shao, P. Carlton, C. Wang, I. Golubovskaya, W. Cande, D. Agard, and J. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

Chhun, B.

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

Conchello, J.

C. Preza and J. Conchello, “Depth-variant maximum likelihood restoration for three-dimensional fluorescence microscopy,” J. Opt. Soc. Am. A 21, 1593–1601 (2004).
[CrossRef]

C. Preza and J. Conchello, “Image estimation account for point-spread function depth variation in three-dimensional fluorescence microscopy,” Proc. SPIE 4964, 1–8 (2003).

Débarre, D.

Fitzgibbon, J.

J. Fitzgibbon, K. Bell, E. King, and K. Oparka, “Super-resolution imaging of Plasmodesmata using three-dimensional structured illumination microscopy,” Plant Phys. 153, 1453 –1463 (2010).
[CrossRef]

Gibson, S.

Golubovskaya, I.

C. Wang, P. Carlton, I. Golubovskaya, and W. Cande, “Interlock formation and coiling of meiotic chromosome axes during synapsis,” Genetics 183, 905–915 (2009).
[CrossRef] [PubMed]

M. Gustafsson, L. Shao, P. Carlton, C. Wang, I. Golubovskaya, W. Cande, D. Agard, and J. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, 2004).

Griffis, E.

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

Gustafsson, M.

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

M. Gustafsson, L. Shao, P. Carlton, C. Wang, I. Golubovskaya, W. Cande, D. Agard, and J. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

L. Schermelleh, P. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. Cardoso, D. Agard, M. Gustafsson, H. Leonhardt, and J. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef] [PubMed]

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

B. Hanser, M. Gustafsson, D. Agard, and J. Sedat, “Phase-retrieved pupil functions in wide-field fluorescent microscopy,” J. Microsc. 216, 32–48 (2004).
[CrossRef] [PubMed]

M. Gustafsson, A. Agard, and J. Sedat, “Doubling of lateral resolution of wide-field fluorescence microscopy using structured illumination,” Proc. SPIE 3919, 14–150 (2001).

Haase, S.

L. Schermelleh, P. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. Cardoso, D. Agard, M. Gustafsson, H. Leonhardt, and J. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef] [PubMed]

Hanser, B.

B. Hanser, M. Gustafsson, D. Agard, and J. Sedat, “Phase-retrieved pupil functions in wide-field fluorescent microscopy,” J. Microsc. 216, 32–48 (2004).
[CrossRef] [PubMed]

Kam, Z.

Z. Kam, P. Kner, D. Agard, and J. Sedat, ”Modelling the application of adaptive optics to wide-field microscope live imaging,” J. Microsc. 226, 33–42 (2007).
[CrossRef] [PubMed]

King, E.

J. Fitzgibbon, K. Bell, E. King, and K. Oparka, “Super-resolution imaging of Plasmodesmata using three-dimensional structured illumination microscopy,” Plant Phys. 153, 1453 –1463 (2010).
[CrossRef]

Kner, P.

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

L. Schermelleh, P. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. Cardoso, D. Agard, M. Gustafsson, H. Leonhardt, and J. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef] [PubMed]

P. Kner, J. Sedat, and D. Agard, “Applying adaptive optics to three-dimensional wide-field microscopy,” Proc. SPIE 6888, 688–809 (2008).

Z. Kam, P. Kner, D. Agard, and J. Sedat, ”Modelling the application of adaptive optics to wide-field microscope live imaging,” J. Microsc. 226, 33–42 (2007).
[CrossRef] [PubMed]

Lanni, F.

Leonhardt, H.

L. Schermelleh, P. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. Cardoso, D. Agard, M. Gustafsson, H. Leonhardt, and J. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef] [PubMed]

Mahoney, N.

M. Trammell, N. Mahoney, D. Agard, and R. Vale, “Mob4 plays a role in spindle focusing in Drosophila S2 cells,” J. Cell Sci. 121, 1284–1292 (2008).
[CrossRef] [PubMed]

McGowan, J.

M. Arigovindan, J. Shaevitz, J. McGowan, J. Sedat, and D. Agard, “A parallel product-convolution approach for representing the depth varying point spread functions in 3D widefield microscopy based on principal component analysis,” Opt Express 18, 6461–6476 (2010).
[CrossRef] [PubMed]

Oparka, K.

J. Fitzgibbon, K. Bell, E. King, and K. Oparka, “Super-resolution imaging of Plasmodesmata using three-dimensional structured illumination microscopy,” Plant Phys. 153, 1453 –1463 (2010).
[CrossRef]

Preza, C.

C. Preza and J. Conchello, “Depth-variant maximum likelihood restoration for three-dimensional fluorescence microscopy,” J. Opt. Soc. Am. A 21, 1593–1601 (2004).
[CrossRef]

C. Preza and J. Conchello, “Image estimation account for point-spread function depth variation in three-dimensional fluorescence microscopy,” Proc. SPIE 4964, 1–8 (2003).

Schermelleh, L.

L. Schermelleh, P. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. Cardoso, D. Agard, M. Gustafsson, H. Leonhardt, and J. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef] [PubMed]

Sedat, J.

M. Arigovindan, J. Shaevitz, J. McGowan, J. Sedat, and D. Agard, “A parallel product-convolution approach for representing the depth varying point spread functions in 3D widefield microscopy based on principal component analysis,” Opt Express 18, 6461–6476 (2010).
[CrossRef] [PubMed]

P. Kner, J. Sedat, and D. Agard, “Applying adaptive optics to three-dimensional wide-field microscopy,” Proc. SPIE 6888, 688–809 (2008).

M. Gustafsson, L. Shao, P. Carlton, C. Wang, I. Golubovskaya, W. Cande, D. Agard, and J. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

L. Schermelleh, P. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. Cardoso, D. Agard, M. Gustafsson, H. Leonhardt, and J. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef] [PubMed]

Z. Kam, P. Kner, D. Agard, and J. Sedat, ”Modelling the application of adaptive optics to wide-field microscope live imaging,” J. Microsc. 226, 33–42 (2007).
[CrossRef] [PubMed]

B. Hanser, M. Gustafsson, D. Agard, and J. Sedat, “Phase-retrieved pupil functions in wide-field fluorescent microscopy,” J. Microsc. 216, 32–48 (2004).
[CrossRef] [PubMed]

M. Gustafsson, A. Agard, and J. Sedat, “Doubling of lateral resolution of wide-field fluorescence microscopy using structured illumination,” Proc. SPIE 3919, 14–150 (2001).

Shaevitz, J.

M. Arigovindan, J. Shaevitz, J. McGowan, J. Sedat, and D. Agard, “A parallel product-convolution approach for representing the depth varying point spread functions in 3D widefield microscopy based on principal component analysis,” Opt Express 18, 6461–6476 (2010).
[CrossRef] [PubMed]

Shao, L.

M. Gustafsson, L. Shao, P. Carlton, C. Wang, I. Golubovskaya, W. Cande, D. Agard, and J. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

L. Schermelleh, P. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. Cardoso, D. Agard, M. Gustafsson, H. Leonhardt, and J. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef] [PubMed]

Srinivas, S.

Torok, P.

S. Wiersma, P. Torok, T. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. B 14, 1482–1490 (1997).
[CrossRef]

Trammell, M.

M. Trammell, N. Mahoney, D. Agard, and R. Vale, “Mob4 plays a role in spindle focusing in Drosophila S2 cells,” J. Cell Sci. 121, 1284–1292 (2008).
[CrossRef] [PubMed]

Vale, R.

M. Trammell, N. Mahoney, D. Agard, and R. Vale, “Mob4 plays a role in spindle focusing in Drosophila S2 cells,” J. Cell Sci. 121, 1284–1292 (2008).
[CrossRef] [PubMed]

Varga, P.

S. Wiersma, P. Torok, T. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. B 14, 1482–1490 (1997).
[CrossRef]

Visser, T.

S. Wiersma, P. Torok, T. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. B 14, 1482–1490 (1997).
[CrossRef]

Wang, C.

C. Wang, P. Carlton, I. Golubovskaya, and W. Cande, “Interlock formation and coiling of meiotic chromosome axes during synapsis,” Genetics 183, 905–915 (2009).
[CrossRef] [PubMed]

M. Gustafsson, L. Shao, P. Carlton, C. Wang, I. Golubovskaya, W. Cande, D. Agard, and J. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

Watanabe, T.

Wiersma, S.

S. Wiersma, P. Torok, T. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. B 14, 1482–1490 (1997).
[CrossRef]

Wilson, T.

Winoto, L.

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

L. Schermelleh, P. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. Cardoso, D. Agard, M. Gustafsson, H. Leonhardt, and J. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef] [PubMed]

Biophys. J. (1)

M. Gustafsson, L. Shao, P. Carlton, C. Wang, I. Golubovskaya, W. Cande, D. Agard, and J. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

Genetics (1)

C. Wang, P. Carlton, I. Golubovskaya, and W. Cande, “Interlock formation and coiling of meiotic chromosome axes during synapsis,” Genetics 183, 905–915 (2009).
[CrossRef] [PubMed]

J. Cell Sci. (1)

M. Trammell, N. Mahoney, D. Agard, and R. Vale, “Mob4 plays a role in spindle focusing in Drosophila S2 cells,” J. Cell Sci. 121, 1284–1292 (2008).
[CrossRef] [PubMed]

J. Microsc. (2)

B. Hanser, M. Gustafsson, D. Agard, and J. Sedat, “Phase-retrieved pupil functions in wide-field fluorescent microscopy,” J. Microsc. 216, 32–48 (2004).
[CrossRef] [PubMed]

Z. Kam, P. Kner, D. Agard, and J. Sedat, ”Modelling the application of adaptive optics to wide-field microscope live imaging,” J. Microsc. 226, 33–42 (2007).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (2)

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

S. Wiersma, P. Torok, T. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. B 14, 1482–1490 (1997).
[CrossRef]

Nat. Meth. (1)

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

Opt Express (1)

M. Arigovindan, J. Shaevitz, J. McGowan, J. Sedat, and D. Agard, “A parallel product-convolution approach for representing the depth varying point spread functions in 3D widefield microscopy based on principal component analysis,” Opt Express 18, 6461–6476 (2010).
[CrossRef] [PubMed]

Opt. Lett. (1)

Plant Phys. (1)

J. Fitzgibbon, K. Bell, E. King, and K. Oparka, “Super-resolution imaging of Plasmodesmata using three-dimensional structured illumination microscopy,” Plant Phys. 153, 1453 –1463 (2010).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

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

Proc. SPIE (3)

M. Gustafsson, A. Agard, and J. Sedat, “Doubling of lateral resolution of wide-field fluorescence microscopy using structured illumination,” Proc. SPIE 3919, 14–150 (2001).

P. Kner, J. Sedat, and D. Agard, “Applying adaptive optics to three-dimensional wide-field microscopy,” Proc. SPIE 6888, 688–809 (2008).

C. Preza and J. Conchello, “Image estimation account for point-spread function depth variation in three-dimensional fluorescence microscopy,” Proc. SPIE 4964, 1–8 (2003).

Science (1)

L. Schermelleh, P. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Burke, M. Cardoso, D. Agard, M. Gustafsson, H. Leonhardt, and J. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef] [PubMed]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, 2004).

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Figures (2)

Fig. 1
Fig. 1

3D structured illumination microscope. (a) optical set-up; (b) simplified schematic.

Fig. 2
Fig. 2

Flow diagram of SIM imaging model with depth dependent spherical aberration.

Equations (66)

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A ( X , Y ) = 1 , for X 2 + Y 2 < N A / λ = 0 , otherwise ,
T ( X , Y , z , z ) = A ( X , Y ) exp ( j 2 π Q ( X , Y ) ) exp [ j 2 π ( z n obj N ( X , Y , n obj ) z n imm N ( X , Y , n imm ) ) ] ,
N ( X , Y , n ) = 1 λ 1 ( λ X / n ) 2 ( λ Y / n ) 2 ,
W B F ( X , Y , z ) = z S a ( X , Y , z ) T ( X , Y , z , z ) d z .
R ( x , y , z ) = | x y 1 [ W B F ( X , Y , z ) ] | 2 = z g ( x , y , z , z ) x y S ( x , y , z ) d z ,
g ( x , y , z , z ) = | x y 1 [ T ( X , Y , z , z ) ] | 2 , S ( x , y , z ) = | S a ( x , y , z ) | 2 ,
g ( x , y , z , z ) = g ( x , y , z z , 0 ) ,
R ( x , y , z ) = g 0 ( x , y , z ) S ( x , y , z ) ,
h ( x , y , z , z ) = g ( x , y , z + a z , z ) ,
R ( x , y , z ) = z h ( x , y , z a z , z ) x y S ( x , y , z ) d z
v k + = [ X k Y k Z k ] T , v k = [ X k Y k Z k ] T ,
E B F , k ( X , Y ) = u k + δ ( X X k , Y Y k ) exp ( j ϕ k + + j ϕ s ) + u k δ ( X + X k , Y + Y k ) exp ( j ϕ k j ϕ s ) + u 0 k exp ( j ϕ k 0 ) .
L ^ ( X , Y , z , z ) = E k ( X , Y , z , z ) X , Y E ¯ k ( X , Y , z , z ) ,
L ( x , y , z , z ) = 3 + 4 m 0 k cos ( 2 π ( X k x + Y k y ) + φ k ϕ s ) × cos ( 2 π f z ( z a f z ) + ϕ k z ) + 2 m 1 k cos ( 2 π ( 2 X k x + 2 Y k y ) + 2 φ k 2 ϕ s ) ,
a f = f z / f z
f z = n obj λ [ 1 1 ( λ X k / n obj ) 2 ( λ Y k / n obj ) 2 ]
f z = n imm λ [ 1 1 ( λ X k / n imm ) 2 ( λ Y k / n imm ) 2 ]
m 0 k = u 0 k , u k + = u 0 k , u k ; m 1 k = u k , u k +
φ k = ( 1 / 2 ) ( ϕ k ϕ k + + 2 π Q ( X k , Y k ) 2 π Q ( X k , Y k ) )
φ k z = ( 1 / 2 ) ( ϕ k + ϕ k + + 2 π Q ( X k , Y k ) + 2 π Q ( X k , Y k ) ) ϕ k 0 2 π Q ( 0 , 0 ) .
F I ( x , y , z , z ) = L ( x , y , z , z ) S ( x , y , z ) ,
P z ( z ) = 2 π f z ( a a f ) z
R ( x , y , z ) = D V C ( S ( x , y , z ) , h ( x , y , z , z ) ) , + D V C ( S k ( x , y , z ) cos ( P z ( z ) ) , h ( x , y , z , z ) cos ( 2 π f z z φ k z ) ) , D V C ( S k ( x , y , z ) sin ( P z ( z ) ) , h ( x , y , z , z ) sin ( 2 π f z z φ k z ) ) , + D V C ( S k 2 ( x , y , z ) , h ( x , y , z , z ) ) ,
S k ( x , y , z ) = cos ( 2 π ( X k x + Y k y ) + φ k ϕ s ) S ( x , y , z ) S k 2 ( x , y , z ) = cos ( 2 π ( 2 X k x + 2 Y k y ) + 2 φ k 2 ϕ s ) S ( x , y , z ) ,
R ( x , y , z ) = 3 h ( x , y , z ) S ( x , y , z ) + 4 m 0 k h c ( x , y , z ) [ S k ( x , y , z ) ] + 2 m 1 k h ( x , y , z ) S k 2 ( x , y , z ) ,
R ( x , y , z ) = 3 h ( x , y , z ) S ( x , y , z ) + 4 m 0 k h c ( x , y , z ) [ cos ( P z ( z ) ) S k ( x , y , z ) ] 4 m 0 k h s ( x , y , z ) [ sin ( P z ( z ) ) S k ( x , y , z ) ] + 2 m 1 k h ( x , y , z ) S k 2 ( x , y , z ) ,
M 1 ( ) = h c ( x , y , z ) ( ) ,
M 2 ( ) = h c ( x , y , z ) [ cos ( P z ( z ) ) ( ) ] h s ( x , y , z ) [ sin ( P z ( z ) ) ( ) ] ,
T a o ( X , Y , z , z ) = A ( X , Y ) exp ( j 2 π Q ( X , Y ) ) exp ( j 2 π N ( X , Y , n obj ) n obj ( z z ) )
D M 2 ( X , Y , z ) = z ( n imm N ( X , Y , n imm ) n obj N ( X , Y , n obj ) ) .
D M 2 ( X , Y , z ) = z ( n imm N ( X , Y , n imm ) 1 a ˜ n obj N ( X , Y , n obj ) ) ,
T a o ( X , Y , z , z ) = A ( X , Y ) exp ( j 2 π Q ( X , Y ) ) exp ( j 2 π N ( X , Y , n obj ) n obj ( z 1 a ˜ z ) ) .
R ( x , y , z ) = z | x y 1 [ T a o ( X , Y , z , z ) ] | 2 S ( x , y , z ) d z
R ( x , y , z ) = z h a o ( x , y , 1 a ˜ z z ) S ( x , y , z ) d z ,
h a o ( x , y , z ) = | x y 1 [ A ( X , Y ) exp ( j 2 π Q ( X , Y ) ) exp ( j 2 π N ( X , Y , n obj ) n obj z ) ] | 2
R ( x , y , z ) = 3 h a o ( x , y , z ) S ( x , y , z ) + 4 m 0 k h a o , c ( x , y , z ) [ cos ( P z ( z ) ) S k ( x , y , z ) ] 4 m 0 k h a o , s ( x , y , z ) [ sin ( P z ( z ) ) S k ( x , y , z ) ] + 2 m 1 k h a o ( x , y , z ) S k 2 ( x , y , z )
R ( x , y , z ) = 3 h a o ( x , y , z ) S ( x , y , z ) + 4 m 0 k h a o , c ( x , y , z ) [ S k ( x , y , z ) ] + 2 m 1 k h a o ( x , y , z ) S k 2 ( x , y , z ) ,
D M i ( X , Y , z ) = δ ( X , Y ) ( f ^ z z )
T ill ( X , Y , z , z ) = A ( X , Y ) exp ( j 2 π f ^ z δ ( X , Y ) z ) exp ( j 2 π Q ( X , Y ) ) exp [ j 2 π ( z n obj N ( X , Y , n obj ) z n imm N ( X , Y , n imm ) ) ] ,
P z ( z ) = 2 π ( f z + f ^ z ) ( a ( f z / ( f z + f ^ z ) ) ) z .
R ( x , y , z ) = D V C ( S ( x , y , z ) , h ( x , y , z , z ) ) , + D V C ( S k ( x , y , z ) , h ( x , y , z , z ) cos ( 2 π ( f z / a ) z φ k z ) ) , + D V C ( S k 2 ( x , y , z ) , h ( x , y , z , z ) ) ,
E k ( X , Y , z , z ) = u k + δ ( X X k , Y Y k ) exp ( j 2 π λ S k n obj z ) exp ( j 2 π λ S k n imm z ) a + u 0 k δ ( X , Y ) exp ( j 2 π λ n obj z ) exp ( j 2 π λ n imm z ) b + u k δ ( X + X k , Y + Y k ) exp ( j 2 π λ S k n obj z ) exp ( j 2 π λ S k n imm z ) c
S k = 1 ( λ X k / n obj ) 2 ( λ Y k / n obj ) 2
S k = 1 ( λ X k / n imm ) 2 ( λ Y k / n imm ) 2
a = exp ( j ϕ s + ϕ k + + j 2 π Q ( X k , Y k ) )
b = exp ( j ϕ k 0 + j 2 π Q ( 0 , 0 ) )
c = exp ( j ϕ s + j ϕ k + j 2 π Q ( X k , Y k ) )
E k ( X , Y , z , z ) = u k + δ ( X X k , Y Y k ) p ( z , z ) a + u 0 k δ ( X , Y ) p 0 ( z , z ) b + u k δ ( X + X k , Y + Y k ) p ( z , z ) c
p ( z , z ) = exp ( j 2 π λ S k n obj z ) exp ( j 2 π λ S k n imm z ) , p 0 ( z , z ) = exp ( j 2 π λ n obj z ) exp ( j 2 π λ n imm z ) .
L ^ ( X , Y , z , z ) = 3 + δ ( X X k , Y Y k ) [ m 0 k a ¯ b p ¯ ( z , z ) p 0 ( z , z ) + m 0 k b ¯ c p ( z , z ) p ¯ 0 ( z , z ) ] + δ ( X + X k , Y + Y k ) [ m 0 k a b ¯ p ( z , z ) p ¯ 0 ( z , z ) + m 0 k b c p ¯ ( z , z ) p 0 ( z , z ) ] + δ ( X 2 X k , Y 2 Y k ) m 1 k a ¯ c + δ ( X + 2 X k , Y + 2 Y k ) m 1 k a c ¯ ,
m 0 k = u 0 k , u k + = u 0 k , u k ; m 1 k = u k , u k +
L ^ ( X , Y , z , z ) = 3 + δ ( X X k , Y Y k ) [ m 0 k a ¯ b exp ( j 2 π ( f z z f z z ) ) + m 0 k b ¯ c exp ( j 2 π ( f z z f z z ) ) ] + δ ( X + X k , Y + Y k ) [ m 0 k a b ¯ exp ( j 2 π ( f z z f z z ) ) + m 0 k b c ¯ exp ( j 2 π ( f z z = f z z ) ) ] + δ ( X 2 X k , Y 2 Y k ) m 1 k a ¯ c + δ ( X + 2 X k , Y + 2 Y k ) m 1 k a c ¯ ,
f z = n obj λ [ 1 S k ] = n obj λ [ 1 1 ( λ X k / n obj ) 2 ( λ Y k / n obj ) 2 ]
f z = n imm λ [ 1 S k ] = n imm λ [ 1 1 ( λ X k / n imm ) 2 ( λ Y k / n imm ) 2 ]
L ( x , y , z , z ) = 3 + 2 m 0 k cos ( 2 π ( X k x + Y k y + f z z f z z ) ψ a + ψ b ) + 2 m 0 k cos ( 2 π ( X k x + Y k y f z z + f z z ) + ψ c ψ b ) + 2 m 1 k cos ( 2 π ( 2 X k x + 2 Y k y ) ψ a + ψ c ) ,
L ( x , y , z , z ) = 3 + 4 m 0 k cos ( 2 π ( X k x + Y k y ) + ( ψ c ψ a ) / 2 ) × cos ( 2 π ( f z z f z z ) + ( ψ c + ψ a ) / 2 ψ b ) + 2 m 1 k cos ( 2 π ( 2 X k x + 2 Y k y ) + ψ c ψ a ) ,
L ( x , y , z , z ) = 3 + 4 m 0 k cos ( 2 π ( X k x + Y k y ) + φ k ϕ s ) cos ( 2 π ( f z z f z z ) + φ k z ) + 2 m 1 k cos ( 2 π ( 2 X k x + 2 Y k y ) + 2 φ k 2 ϕ s ) ,
φ k = ( 1 / 2 ) ( ϕ k ϕ k + + 2 π Q ( X k , Y k ) 2 π Q ( X k , Y k ) ) φ k z = ( 1 / 2 ) ( ϕ k + ϕ k + + 2 π Q ( X k , Y k ) + 2 π Q ( X k , Y k ) ) ϕ k 0 2 π Q ( 0 , 0 ) .
R ( x , y , z ) = z h ( x , y , z a z , z ) x y F I ( x , y , z , z ) d z = z h ( x , y , z a z , z ) x y [ L ( x , y , z , z ) S ( x , y , z ) ] d z = 3 z h ( x , y , z a z , z ) x y S ( x , y , z ) d z + 4 m 0 k z h ( x , y , z a z , z ) x y [ cos ( 2 π ( f z z f z z ) + φ k z ) C k ( x , y ) S ( x , y , z ) ] d z R 2 ( x , y , z ) + 2 m k 2 z h ( x , y , z a z , z ) x y [ C k 2 ( x , y ) S ( x , y , z ) ] d z ,
C k ( x , y ) = cos ( 2 π ( X k x + Y k y ) + φ k ϕ s ) ; C k 2 ( x , y ) = cos ( 2 π ( 2 X k x + 2 Y k y ) + 2 φ k 2 ϕ s )
cos ( 2 π ( f z z f z z ) + φ k z ) = cos ( 2 π ( f z ( z a f z ) ) φ k z ) = cos ( 2 π ( f z ( z a z ) ) φ k z + 2 π f z ( a a f ) z ) = cos ( 2 π ( f z ( z a z ) ) φ k z ) cos ( 2 π f z ( a a f ) z ) sin ( 2 π ( f z ( z a z ) ) φ k z ) sin ( 2 π f z ( a a f ) z ) ,
R 2 ( x , y , z ) = z h c ( x , y , z a z , z ) x y [ cos ( 2 π f z ( a a f ) z ) C k ( x , y ) S ( x , y , z ) ] + h s ( x , y , z a z , z ) x y [ sin ( 2 π f z ( a a f ) z ) C k ( x , y ) S ( x , y , z ) d z , ]
h c ( x , y , z a z , z ) = h ( x , y , z a z , z ) cos ( 2 π f z ( z a z ) φ k z ) , h s ( x , y , z a z , z ) = h ( x , y , z a z , z ) sin ( 2 π f z ( z a z ) φ k z ) .
G ( x , y , z ) = z h ( x , y , z a z , z ) x y S ( x , y , z ) d z + z h c ( x , y , z a z , z ) x y [ cos ( P z ( z ) ) cos ( P ( x , y ) ) S ( x , y , z ) ] d z z h z ( x , y , z a z , z ) x y [ sin ( P z ( z ) ) cos ( P ( x , y ) ) S ( x , y , z ) ] d z + z h ( x , y , z a z , z ) x y [ cos ( 2 P ( x , y ) ) S ( x , y , z ) ] d z ,
M ¯ 1 , z 0 ( x , y , z ) = M 1 ( δ ( x , y , z z 0 ) ) = h c ( x , y , z ) , M ¯ 2 , z 0 ( x , y , z ) = M 2 ( δ ( x , y , z z 0 ) ) = cos ( P z ( z 0 ) h c ( x , y , z ) sin ( P z ( z 0 ) ) h s ( x , y , z )
M ¯ 2 , z 0 ( x , y , z ) = h ( x , y , z ) cos ( 2 π f z z φ k z + P z ( z 0 ) ) .

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