Abstract

We present a method to improve the isotropy of spatial resolution in a structured illumination microscopy (SIM) implemented for imaging non-fluorescent samples. To alleviate the problem of anisotropic resolution involved with the previous scheme of coherent SIM that employs the two orthogonal standing-wave illumination, referred to as the orthogonal SIM, we introduce a hexagonal-lattice illumination that incorporates three standing-wave fields simultaneously superimposed at the orientations equally divided in the lateral plane. A theoretical formulation is worked out rigorously for the coherent image formation with such a simultaneous multiple-beam illumination and an explicit Fourier-domain framework is derived for reconstructing an image with enhanced resolution. Using a computer-synthesized resolution target as a 2D coherent sample, we perform numerical simulations to examine the imaging characteristics of our three-angle SIM compared with the orthogonal SIM. The investigation on the 2D resolving power with the various test patterns of different periods and orientations reveal that the orientation-dependent undulation of lateral resolution can be reduced from 27% to 8% by using the three-angle SIM while the best resolution (0.54 times the resolution limit of conventional coherent imaging) in the directions of structured illumination is slightly deteriorated by 4.6% from that of the orthogonal SIM.

© 2014 Optical Society of America

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References

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  1. J. Pawley, Handbook of Biological Confocal Microscopy (Springer Science + Business Media, New York, 1989).
  2. M. Born and E. Wolf, Principles of Optics (Cambridge University, Cambridge, UK, 1959).
  3. 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]
  4. D. Wildanger, R. Medda, L. Kastrup, and S. W. Hell, “A compact STED microscope providing 3D nanoscale resolution,” J. Microsc.236(1), 35–43 (2009).
    [CrossRef] [PubMed]
  5. 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,” Science313(5793), 1642–1645 (2006).
    [CrossRef] [PubMed]
  6. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (2006).
    [CrossRef] [PubMed]
  7. R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: Improvement of resolution by using a diffraction grating,” Proc. SPIE3568, 185–196 (1999).
    [CrossRef]
  8. 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]
  9. J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A.97(13), 7232–7236 (2000).
    [CrossRef] [PubMed]
  10. R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy--a concept for optical resolution improvement,” J. Opt. Soc. Am. A19(8), 1599–1609 (2002).
    [CrossRef] [PubMed]
  11. M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A.102(37), 13081–13086 (2005).
    [CrossRef] [PubMed]
  12. R. Fiolka, M. Beck, and A. Stemmer, “Structured illumination in total internal reflection fluorescence microscopy using a spatial light modulator,” Opt. Lett.33(14), 1629–1631 (2008).
    [CrossRef] [PubMed]
  13. B.-J. Chang, L.-J. Chou, Y.-C. Chang, and S.-Y. Chiang, “Isotropic image in structured illumination microscopy patterned with a spatial light modulator,” Opt. Express17(17), 14710–14721 (2009).
    [CrossRef] [PubMed]
  14. 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(5), 339–342 (2009).
    [CrossRef] [PubMed]
  15. M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J.94(12), 4957–4970 (2008).
    [CrossRef] [PubMed]
  16. W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am.56(11), 1463–1471 (1966).
    [CrossRef]
  17. P. C. Sun and E. N. Leith, “Superresolution by spatial-temporal encoding methods,” Appl. Opt.31(23), 4857–4862 (1992).
    [CrossRef] [PubMed]
  18. A. Mudassar, A. R. Harvey, A. H. Greenaway, and J. D. C. Jones, “Resolution beyond classical limits with spatial frequency heterodyning,” Chin. Opt. Lett.4(3), 148–151 (2006).
  19. B. Littleton, K. Lai, D. Longstaff, V. Sarafis, P. Munroe, N. Heckenberg, and H. Rubinsztein-Dunlop, “Coherent super-resolution microscopy via laterally structured illumination,” Micron38(2), 150–157 (2007).
    [CrossRef] [PubMed]
  20. S. Chowdhury, A.-H. Dhalla, and J. Izatt, “Structured oblique illumination microscopy for enhanced resolution imaging of non-fluorescent, coherently scattering samples,” Biomed. Opt. Express3(8), 1841–1854 (2012).
    [CrossRef] [PubMed]
  21. M. Gu, Advanced Optical Imaging Theory, Springer Series in Optical Sciences (Springer, 2000).
  22. J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 6.

2012 (1)

2009 (3)

B.-J. Chang, L.-J. Chou, Y.-C. Chang, and S.-Y. Chiang, “Isotropic image in structured illumination microscopy patterned with a spatial light modulator,” Opt. Express17(17), 14710–14721 (2009).
[CrossRef] [PubMed]

D. Wildanger, R. Medda, L. Kastrup, and S. W. Hell, “A compact STED microscope providing 3D nanoscale resolution,” J. Microsc.236(1), 35–43 (2009).
[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. Methods6(5), 339–342 (2009).
[CrossRef] [PubMed]

2008 (2)

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J.94(12), 4957–4970 (2008).
[CrossRef] [PubMed]

R. Fiolka, M. Beck, and A. Stemmer, “Structured illumination in total internal reflection fluorescence microscopy using a spatial light modulator,” Opt. Lett.33(14), 1629–1631 (2008).
[CrossRef] [PubMed]

2007 (1)

B. Littleton, K. Lai, D. Longstaff, V. Sarafis, P. Munroe, N. Heckenberg, and H. Rubinsztein-Dunlop, “Coherent super-resolution microscopy via laterally structured illumination,” Micron38(2), 150–157 (2007).
[CrossRef] [PubMed]

2006 (3)

A. Mudassar, A. R. Harvey, A. H. Greenaway, and J. D. C. Jones, “Resolution beyond classical limits with spatial frequency heterodyning,” Chin. Opt. Lett.4(3), 148–151 (2006).

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,” Science313(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. Methods3(10), 793–796 (2006).
[CrossRef] [PubMed]

2005 (1)

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

2002 (1)

2000 (2)

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]

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

1999 (1)

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)

1992 (1)

1966 (1)

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(12), 4957–4970 (2008).
[CrossRef] [PubMed]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (2006).
[CrossRef] [PubMed]

Beck, M.

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,” Science313(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,” Science313(5793), 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(12), 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(12), 4957–4970 (2008).
[CrossRef] [PubMed]

Chang, B.-J.

Chang, Y.-C.

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(5), 339–342 (2009).
[CrossRef] [PubMed]

Chiang, S.-Y.

Chou, L.-J.

Chowdhury, S.

Cremer, C.

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy--a concept for optical resolution improvement,” J. Opt. Soc. Am. A19(8), 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. 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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Dhalla, A.-H.

Fiolka, R.

Frohn, J. T.

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A.97(13), 7232–7236 (2000).
[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(12), 4957–4970 (2008).
[CrossRef] [PubMed]

Greenaway, A. H.

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(5), 339–342 (2009).
[CrossRef] [PubMed]

Gustafsson, M. G. L.

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(5), 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(12), 4957–4970 (2008).
[CrossRef] [PubMed]

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

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]

Harvey, A. R.

Heckenberg, N.

B. Littleton, K. Lai, D. Longstaff, V. Sarafis, P. Munroe, N. Heckenberg, and H. Rubinsztein-Dunlop, “Coherent super-resolution microscopy via laterally structured illumination,” Micron38(2), 150–157 (2007).
[CrossRef] [PubMed]

Heintzmann, R.

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy--a concept for optical resolution improvement,” J. Opt. Soc. Am. A19(8), 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.

D. Wildanger, R. Medda, L. Kastrup, and S. W. Hell, “A compact STED microscope providing 3D nanoscale resolution,” J. Microsc.236(1), 35–43 (2009).
[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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Izatt, J.

Jones, J. D. C.

Jovin, T. M.

Kastrup, L.

D. Wildanger, R. Medda, L. Kastrup, and S. W. Hell, “A compact STED microscope providing 3D nanoscale resolution,” J. Microsc.236(1), 35–43 (2009).
[CrossRef] [PubMed]

Knapp, H. F.

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

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(5), 339–342 (2009).
[CrossRef] [PubMed]

Lai, K.

B. Littleton, K. Lai, D. Longstaff, V. Sarafis, P. Munroe, N. Heckenberg, and H. Rubinsztein-Dunlop, “Coherent super-resolution microscopy via laterally structured illumination,” Micron38(2), 150–157 (2007).
[CrossRef] [PubMed]

Leith, E. N.

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,” Science313(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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Littleton, B.

B. Littleton, K. Lai, D. Longstaff, V. Sarafis, P. Munroe, N. Heckenberg, and H. Rubinsztein-Dunlop, “Coherent super-resolution microscopy via laterally structured illumination,” Micron38(2), 150–157 (2007).
[CrossRef] [PubMed]

Longstaff, D.

B. Littleton, K. Lai, D. Longstaff, V. Sarafis, P. Munroe, N. Heckenberg, and H. Rubinsztein-Dunlop, “Coherent super-resolution microscopy via laterally structured illumination,” Micron38(2), 150–157 (2007).
[CrossRef] [PubMed]

Lukosz, W.

Medda, R.

D. Wildanger, R. Medda, L. Kastrup, and S. W. Hell, “A compact STED microscope providing 3D nanoscale resolution,” J. Microsc.236(1), 35–43 (2009).
[CrossRef] [PubMed]

Mudassar, A.

Munroe, P.

B. Littleton, K. Lai, D. Longstaff, V. Sarafis, P. Munroe, N. Heckenberg, and H. Rubinsztein-Dunlop, “Coherent super-resolution microscopy via laterally structured illumination,” Micron38(2), 150–157 (2007).
[CrossRef] [PubMed]

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,” Science313(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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Rubinsztein-Dunlop, H.

B. Littleton, K. Lai, D. Longstaff, V. Sarafis, P. Munroe, N. Heckenberg, and H. Rubinsztein-Dunlop, “Coherent super-resolution microscopy via laterally structured illumination,” Micron38(2), 150–157 (2007).
[CrossRef] [PubMed]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (2006).
[CrossRef] [PubMed]

Sarafis, V.

B. Littleton, K. Lai, D. Longstaff, V. Sarafis, P. Munroe, N. Heckenberg, and H. Rubinsztein-Dunlop, “Coherent super-resolution microscopy via laterally structured illumination,” Micron38(2), 150–157 (2007).
[CrossRef] [PubMed]

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(12), 4957–4970 (2008).
[CrossRef] [PubMed]

Shao, L.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J.94(12), 4957–4970 (2008).
[CrossRef] [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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Stemmer, A.

R. Fiolka, M. Beck, and A. Stemmer, “Structured illumination in total internal reflection fluorescence microscopy using a spatial light modulator,” Opt. Lett.33(14), 1629–1631 (2008).
[CrossRef] [PubMed]

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

Sun, P. C.

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(12), 4957–4970 (2008).
[CrossRef] [PubMed]

Wichmann, J.

Wildanger, D.

D. Wildanger, R. Medda, L. Kastrup, and S. W. Hell, “A compact STED microscope providing 3D nanoscale resolution,” J. Microsc.236(1), 35–43 (2009).
[CrossRef] [PubMed]

Winoto, L.

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(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. Methods3(10), 793–796 (2006).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biomed. Opt. Express (1)

Biophys. J. (1)

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J.94(12), 4957–4970 (2008).
[CrossRef] [PubMed]

Chin. Opt. Lett. (1)

J. Microsc. (2)

D. Wildanger, R. Medda, L. Kastrup, and S. W. Hell, “A compact STED microscope providing 3D nanoscale resolution,” J. Microsc.236(1), 35–43 (2009).
[CrossRef] [PubMed]

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]

J. Opt. Soc. Am. (1)

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

Micron (1)

B. Littleton, K. Lai, D. Longstaff, V. Sarafis, P. Munroe, N. Heckenberg, and H. Rubinsztein-Dunlop, “Coherent super-resolution microscopy via laterally structured illumination,” Micron38(2), 150–157 (2007).
[CrossRef] [PubMed]

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(5), 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(10), 793–796 (2006).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Proc. Natl. Acad. Sci. U.S.A. (2)

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

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

Proc. SPIE (1)

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, 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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Other (4)

J. Pawley, Handbook of Biological Confocal Microscopy (Springer Science + Business Media, New York, 1989).

M. Born and E. Wolf, Principles of Optics (Cambridge University, Cambridge, UK, 1959).

M. Gu, Advanced Optical Imaging Theory, Springer Series in Optical Sciences (Springer, 2000).

J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 6.

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Figures (8)

Fig. 1
Fig. 1

Extended coherent transfer functions (CTFs) with structured illuminations incorporating (a) two orthogonal standing-wave components (in the previous study) and (b) three-angle standing-wave fields (in the present method), respectively. For comparison, the 2D frequency support of a diffraction-limited coherent system is delineated with a dotted orange circle.

Fig. 2
Fig. 2

Structured illumination consisting of three-angle standing-wave field components (a-c) and the resulting amplitude distribution of hexagonal lattice-patterned field (d). The 2D grid points defining the displacement (phase) vectors (e) by which the structured illumination is laterally translated in the acquisition of a series of raw SIM image data.

Fig. 3
Fig. 3

References used in the numerical simulations. (a) Computer-synthesized resolution test target and its (b) coherent and (c) incoherent bright-field (BF) images. The black-and-white contrast in the test target represents a binary sample distribution with uniform-amplitude objects present only within white regions. Along the red circle drawn on the sector star pattern in (a), the radial bars have a cycle period equal to the diffraction limit of resolution. The gap at the bottom right of (a), sandwiched by blue arrows, also indicates the diffraction limit (296 nm).

Fig. 4
Fig. 4

Structured illumination (SI) spectral components acquired in the 3-angle SIM imaging for the resolution test target shown in Fig. 3(a). The SI components are in one-to-one correspondence with the extended-passband (EP) components representing the auto-correlation and 18 cross-correlation terms that account for an enhanced-resolution coherent imaging with the hypothetical CTF synthesized with six frequency-shifted CTFs. The Fourier image components are displayed in logarithmic scale with the horizontal and vertical axes normalized with the “intensity” cutoff frequency (the inverse of diffraction-limited resolution).

Fig. 5
Fig. 5

Reconstructed images of (a) the orthogonal SIM and (b) the 3-angle SIM obtained for the resolution test target shown in Fig. 3(a). Below the images are the corresponding spatial-frequency spectra for (c) the orthogonal SIM and (d) the 3-angle SIM, compared with (e) that of the conventional coherent BF image shown in Fig. 3(b). The image spectra (logarithmic scale) are displayed in false color with their horizontal and vertical axes normalized with the “intensity” cutoff frequency (the inverse of diffraction-limited resolution).

Fig. 6
Fig. 6

Auto-correlations of the extended coherent transfer functions (CTFs) for (a) the orthogonal SIM and (b) the 3-angle SIM, compared with (c) the auto-correlated CTF of a coherent bright-field (BF) imaging system. The frequency-cutoff boundaries of the functions are delineated with dotted orange lines. Below are the intensity distributions of the coherent images for a point amplitude object obtainable with the (a’) orthogonal SIM, (b’) 3-angle SIM, and (c’) coherent BF system. The auto-correlated functions (a-c) and point object images (a’-c’) are in logarithmic scale, which are displayed in false color with their plot axes normalized with the intensity cutoff frequency and the abbe’s diffraction limit of resolution, respectively.

Fig. 7
Fig. 7

Comparison of the bar pattern images obtained with the orthogonal SIM (on the left columns of (b-e)) and the 3-angle SIM (on the right columns of (b-e)). (a) The original bar patterns of the target (on the left column) and their coherent BF images (on the right column) are given for comparison, where the bar-pattern elements 10, 12, 14, and 20, corresponding to the cycle periods of 254 nm, 305 nm, 356 nm, and 508 nm, respectively, are investigated of different orientations specified by their line normals at (b) 0°, (c) 45°, (d) 60°, and (e) 90°. The magnified views of bar-pattern images shown in this figure were taken from the coherent BF image in Fig. 3(b) and the reconstructed images in Figs. 5(a) and 5(b) for the orthogonal SIM and the 3-angle SIM schemes, respectively. The corresponding line intensity profiles of bar-pattern images are extracted and grouped for (f’)-(i’) the orthogonal SIM and (f”)-(i”) the 3-angle SIM. For comparison, the profiles of the original bar patterns (dotted gray lines) and the line intensity distributions of the coherent BF images (blue lines) are displayed together. In each line plot, the distance is normalized to the diffraction limit of resolution (296 nm).

Fig. 8
Fig. 8

Line intensity profiles of the sector star pattern image along the circular arcs of different radii where the intersecting bars have different cycle periods as indicated in the figure. The results of the 3-angle SIM (red lines) and the orthogonal SIM (blue lines) are compared. For convenience, line intensity profiles of the original target patterns (dotted lines) and the coherent BF images (green lines) are displayed together.

Equations (10)

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E SI (r)=cos( 2π f s1 r+ ϕ s1 )+cos( 2π f s2 r+ ϕ s2 )+cos( 2π f s3 r+ ϕ s3 ),
C EP (f)=C(f f s1 )+C(f+ f s1 )+C(f f s2 )+C(f+ f s2 )+C(f f s3 )+C(f+ f s3 ) C 1 + C 1 + + C 2 + C 2 + + C 3 + C 3 + ,
d(r)= u i (r) u i * (r)= | [ s(r)E(r) ] h c (r) | 2 ,
D(f)= d ˜ (f)=F{ d(r) }=ac{ [ S(f) E ˜ (f) ]C(f) },
D BF (f)=ac{ S(f)C(f) }
D SI (f)=ac{ [ S(f) E ˜ SI (f) ]C(f) } ac{ [ S(f)( δ(f f s1 ) e +i ϕ s1 +δ(f+ f s1 ) e i ϕ s1 +δ(f f s2 ) e +i ϕ s2 +δ(f+ f s2 ) e i ϕ s2 +δ(f f s3 ) e +i ϕ s3 +δ(f+ f s3 ) e i ϕ s3 ) ]C(f) }
D SI (f)= [ ac{ S 1 + C(f) }+ac{ S 1 C(f) } +ac{ S 2 + C(f) }+ac{ S 2 C(f) } +ac{ S 3 + C(f) }+ac{ S 3 C(f) } ] 0 + [ S 1 C(f) S 1 + C(f) ] 1 exp[ +i2 ϕ s1 ]+ [ S 1 + C(f) S 1 C(f) ] 2 exp[ i2 ϕ s1 ] + [ S 2 C(f) S 2 + C(f) ] 3 exp[ +i2 ϕ s2 ]+ [ S 2 + C(f) S 2 C(f) ] 4 exp[ i2 ϕ s2 ] + [ S 3 C(f) S 3 + C(f) ] 5 exp[ +i2 ϕ s3 ]+ [ S 3 + C(f) S 3 C(f) ] 6 exp[ i2 ϕ s3 ] + [ S 1 C(f) S 2 C(f)+ S 2 + C(f) S 1 + C(f) ] 7 exp[ +i( ϕ s1 ϕ s2 ) ] + [ S 2 C(f) S 1 C(f)+ S 1 + C(f) S 2 + C(f) ] 8 exp[ i( ϕ s1 ϕ s2 ) ] + [ S 1 C(f) S 2 + C(f)+ S 2 C(f) S 1 + C(f) ] 9 exp[ +i( ϕ s1 + ϕ s2 ) ] + [ S 2 + C(f) S 1 C(f)+ S 1 + C(f) S 2 C(f) ] 10 exp[ i( ϕ s1 + ϕ s2 ) ] + [ S 2 C(f) S 3 C(f)+ S 3 + C(f) S 2 + C(f) ] 11 exp[ +i( ϕ s2 ϕ s3 ) ] + [ S 3 C(f) S 2 C(f)+ S 2 + C(f) S 3 + C(f) ] 12 exp[ i( ϕ s2 ϕ s3 ) ] + [ S 2 C(f) S 3 + C(f)+ S 3 C(f) S 2 + C(f) ] 13 exp[ +i( ϕ s2 + ϕ s3 ) ] + [ S 3 + C(f) S 2 C(f)+ S 2 + C(f) S 3 C(f) ] 14 exp[ i( ϕ s2 + ϕ s3 ) ] + [ S 3 C(f) S 1 C(f)+ S 1 + C(f) S 3 + C(f) ] 15 exp[ +i( ϕ s3 ϕ s1 ) ] + 16 [ S 1 C(f) S 3 C(f)+ S 3 + C(f) S 1 + C(f) ]exp[ i( ϕ s3 ϕ s1 ) ] + [ S 3 C(f) S 1 + C(f)+ S 1 C(f) S 3 + C(f) ] 17 exp[ +i( ϕ s3 + ϕ s1 ) ] + [ S 1 + C(f) S 3 C(f)+ S 3 + C(f) S 1 C(f) ] 18 exp[ i( ϕ s3 + ϕ s1 ) ] = n=0 18 T n (f) exp[i Φ n ],
D EP (f)= [ ac{ C 1 + S(f) }+ac{ C 1 S(f) } +ac{ C 2 + S(f) }+ac{ C 2 S(f) } +ac{ C 3 + S(f) }+ac{ C 3 S(f) } ] 0 + [ C 1 + S(f) C 1 S(f) ] 1 + [ C 1 S(f) C 1 + S(f) ] 2 + [ C 2 + S(f) C 2 S(f) ] 3 + [ C 2 S(f) C 2 + S(f) ] 4 + [ C 3 + S(f) C 3 S(f) ] 5 + [ C 3 S(f) C 3 + S(f) ] 6 + [ C 1 + S(f) C 2 + S(f)+ C 1 S(f) C 2 S(f) ] 7 + [ C 2 + S(f) C 1 + S(f)+ C 1 S(f) C 2 S(f) ] 8 + [ C 1 + S(f) C 2 S(f)+ C 2 + S(f) C 1 S(f) ] 9 + [ C 2 S(f) C 1 + S(f)+ C 1 S(f) C 2 + S(f) ] 10 + [ C 2 + S(f) C 3 + S(f)+ C 2 S(f) C 3 S(f) ] 11 + [ C 3 + S(f) C 2 + S(f)+ C 2 S(f) C 3 S(f) ] 12 + [ C 2 + S(f) C 3 S(f)+ C 3 + S(f) C 2 S(f) ] 13 + [ C 3 S(f) C 2 + S(f)+ C 2 S(f) C 3 + S(f) ] 14 + [ C 3 + S(f) C 1 + S(f)+ C 3 S(f) C 1 S(f) ] 15 + [ C 1 + S(f) C 3 + S(f)+ C 3 S(f) C 1 S(f) ] 16 + [ C 3 + S(f) C 1 S(f)+ C 1 + S(f) C 3 S(f) ] 17 + [ C 1 S(f) C 3 + S(f)+ C 3 S(f) C 1 + S(f) ] 18 = n=0 18 V n (f) ,
D EP (f)= n=0 12 T n (f[ f α f β ] | n ) ,
{0,2 f 1 ,+2 f 1 ,2 f 2 ,+2 f 2 ,2 f 3 ,+2 f 3 ,[ f 1 f 2 ],+[ f 1 f 2 ],[ f 1 + f 2 ],+[ f 1 + f 2 ], [ f 2 f 3 ],+[ f 2 f 3 ],[ f 2 + f 3 ],+[ f 2 + f 3 ],[ f 3 f 1 ],+[ f 3 f 1 ],[ f 3 + f 1 ],+[ f 3 + f 1 ]}.

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