Abstract

With sub-micron spatial resolution and femtosecond temporal resolution, pump probe microscopy provides a powerful spectroscopic probe of complex electronic environments in bulk and nanoscale materials. However, the electronic structure of many materials systems are governed by compositional and morphological heterogeneities on length scales that lie below the diffraction limit. We have recently demonstrated Structured Pump Probe Microscopy (SPPM), which employs a patterned pump excitation field to provide spectroscopic interrogation of sub-diffraction limited sample volumes. Herein, we develop the imaging theory of SPPM in two dimensions to accompany the previously published experimental methodology. We show that regardless of pump and probe wavelengths, a nearly two-fold reduction in spectroscopic probe volume can be achieved. We also examine the limitations of the approach, with a detailed discussion of ringing in the point spread function that can reduce imaging performance.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]
  3. L. Huang and J.-X. Cheng, “Nonlinear Optical Microscopy of Single Nanostructures,” Annu. Rev. Mater. Res. 43(1), 213–236 (2013).
    [Crossref]
  4. D. y. Davydova, A. de la Cadena, D. Akimov, and B. Dietzek, “Transient absorption microscopy: advances in chemical imaging of photoinduced dynamics,” Laser Photonics Rev. 10(1), 62–81 (2016).
    [Crossref]
  5. 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).
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    [PubMed]
  7. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (2006).
    [Crossref] [PubMed]
  8. E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
    [Crossref] [PubMed]
  9. P. Wang, M. N. Slipchenko, J. Mitchell, C. Yang, E. O. Potma, X. Xu, and J. X. Cheng, “Far-field Imaging of Non-fluorescent Species with Sub-diffraction Resolution,” Nat. Photonics 7(6), 449–453 (2013).
    [Crossref] [PubMed]
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  15. R. Heintzmann and C. Cremer, “Laterally Modulated Excitation Microscopy- Improvement of resolution by using a diffraction grating,” Opt. Biopsies Microscopic Tech. 3568, 185–196 (1999).
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2016 (2)

D. y. Davydova, A. de la Cadena, D. Akimov, and B. Dietzek, “Transient absorption microscopy: advances in chemical imaging of photoinduced dynamics,” Laser Photonics Rev. 10(1), 62–81 (2016).
[Crossref]

E. S. Massaro, A. H. Hill, and E. M. Grumstrup, “Super-Resolution Structured Pump–Probe Microscopy,” ACS Photonics 3(4), 501–506 (2016).
[Crossref]

2015 (2)

E. A. Muller, B. Pollard, and M. B. Raschke, “Infrared Chemical Nano-Imaging: Accessing Structure, Coupling, and Dynamics on Molecular Length Scales,” J. Phys. Chem. Lett. 6(7), 1275–1284 (2015).
[Crossref] [PubMed]

E. M. Grumstrup, M. M. Gabriel, E. E. M. Cating, E. M. Van Goethem, and J. M. Papanikolas, “Pump–probe microscopy: Visualization and spectroscopy of ultrafast dynamics at the nanoscale,” Chem. Phys. 458, 30–40 (2015).
[Crossref]

2014 (2)

H. A. Bechtel, E. A. Muller, R. L. Olmon, M. C. Martin, and M. B. Raschke, “Ultrabroadband infrared nanospectroscopic imaging,” Proc. Natl. Acad. Sci. U.S.A. 111(20), 7191–7196 (2014).
[Crossref] [PubMed]

J. H. Park, S. W. Lee, E. S. Lee, and J. Y. Lee, “A method for super-resolved CARS microscopy with structured illumination in two dimensions,” Opt. Express 22(8), 9854–9870 (2014).
[Crossref] [PubMed]

2013 (4)

C.-Y. Chung, J. Hsu, S. Mukamel, and E. O. Potma, “Controlling stimulated coherent spectroscopy and microscopy by a position-dependent phase,” Phys. Rev. A 87(3), 033833 (2013).
[Crossref] [PubMed]

P. Wang, M. N. Slipchenko, J. Mitchell, C. Yang, E. O. Potma, X. Xu, and J. X. Cheng, “Far-field Imaging of Non-fluorescent Species with Sub-diffraction Resolution,” Nat. Photonics 7(6), 449–453 (2013).
[Crossref] [PubMed]

A. Jost and R. Heintzmann, “Superresolution Multidimensional Imaging with Structured Illumination Microscopy,” Annu. Rev. Mater. Res. 43(1), 261–282 (2013).
[Crossref]

L. Huang and J.-X. Cheng, “Nonlinear Optical Microscopy of Single Nanostructures,” Annu. Rev. Mater. Res. 43(1), 213–236 (2013).
[Crossref]

2010 (1)

2006 (2)

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (2006).
[Crossref] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

2005 (1)

M. G. 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]

2001 (1)

F. de Lange, A. Cambi, R. Huijbens, B. de Bakker, W. Rensen, M. Garcia-Parajo, N. van Hulst, and C. G. Figdor, “Cell biology beyond the diffraction limit: near-field scanning optical microscopy,” J. Cell Sci. 114(Pt 23), 4153–4160 (2001).
[PubMed]

1999 (2)

S. Mahajan, “Defects in semiconductors and their effects on devices,” Acta Mater. 48(1), 137–149 (1999).
[Crossref]

R. Heintzmann and C. Cremer, “Laterally Modulated Excitation Microscopy- Improvement of resolution by using a diffraction grating,” Opt. Biopsies Microscopic Tech. 3568, 185–196 (1999).
[Crossref]

1994 (1)

1981 (1)

H. Köhler, “On Abbe’s Theory of Image Formation in the Microscope,” Optica Acta 28(12), 1691–1701 (1981).
[Crossref]

Akimov, D.

D. y. Davydova, A. de la Cadena, D. Akimov, and B. Dietzek, “Transient absorption microscopy: advances in chemical imaging of photoinduced dynamics,” Laser Photonics Rev. 10(1), 62–81 (2016).
[Crossref]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (2006).
[Crossref] [PubMed]

Bechtel, H. A.

H. A. Bechtel, E. A. Muller, R. L. Olmon, M. C. Martin, and M. B. Raschke, “Ultrabroadband infrared nanospectroscopic imaging,” Proc. Natl. Acad. Sci. U.S.A. 111(20), 7191–7196 (2014).
[Crossref] [PubMed]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Cambi, A.

F. de Lange, A. Cambi, R. Huijbens, B. de Bakker, W. Rensen, M. Garcia-Parajo, N. van Hulst, and C. G. Figdor, “Cell biology beyond the diffraction limit: near-field scanning optical microscopy,” J. Cell Sci. 114(Pt 23), 4153–4160 (2001).
[PubMed]

Cating, E. E. M.

E. M. Grumstrup, M. M. Gabriel, E. E. M. Cating, E. M. Van Goethem, and J. M. Papanikolas, “Pump–probe microscopy: Visualization and spectroscopy of ultrafast dynamics at the nanoscale,” Chem. Phys. 458, 30–40 (2015).
[Crossref]

Cheng, J. X.

P. Wang, M. N. Slipchenko, J. Mitchell, C. Yang, E. O. Potma, X. Xu, and J. X. Cheng, “Far-field Imaging of Non-fluorescent Species with Sub-diffraction Resolution,” Nat. Photonics 7(6), 449–453 (2013).
[Crossref] [PubMed]

Cheng, J.-X.

L. Huang and J.-X. Cheng, “Nonlinear Optical Microscopy of Single Nanostructures,” Annu. Rev. Mater. Res. 43(1), 213–236 (2013).
[Crossref]

Chung, C.-Y.

C.-Y. Chung, J. Hsu, S. Mukamel, and E. O. Potma, “Controlling stimulated coherent spectroscopy and microscopy by a position-dependent phase,” Phys. Rev. A 87(3), 033833 (2013).
[Crossref] [PubMed]

Cremer, C.

R. Heintzmann and C. Cremer, “Laterally Modulated Excitation Microscopy- Improvement of resolution by using a diffraction grating,” Opt. Biopsies Microscopic Tech. 3568, 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,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Davydova, D. y.

D. y. Davydova, A. de la Cadena, D. Akimov, and B. Dietzek, “Transient absorption microscopy: advances in chemical imaging of photoinduced dynamics,” Laser Photonics Rev. 10(1), 62–81 (2016).
[Crossref]

de Bakker, B.

F. de Lange, A. Cambi, R. Huijbens, B. de Bakker, W. Rensen, M. Garcia-Parajo, N. van Hulst, and C. G. Figdor, “Cell biology beyond the diffraction limit: near-field scanning optical microscopy,” J. Cell Sci. 114(Pt 23), 4153–4160 (2001).
[PubMed]

de la Cadena, A.

D. y. Davydova, A. de la Cadena, D. Akimov, and B. Dietzek, “Transient absorption microscopy: advances in chemical imaging of photoinduced dynamics,” Laser Photonics Rev. 10(1), 62–81 (2016).
[Crossref]

de Lange, F.

F. de Lange, A. Cambi, R. Huijbens, B. de Bakker, W. Rensen, M. Garcia-Parajo, N. van Hulst, and C. G. Figdor, “Cell biology beyond the diffraction limit: near-field scanning optical microscopy,” J. Cell Sci. 114(Pt 23), 4153–4160 (2001).
[PubMed]

Dietzek, B.

D. y. Davydova, A. de la Cadena, D. Akimov, and B. Dietzek, “Transient absorption microscopy: advances in chemical imaging of photoinduced dynamics,” Laser Photonics Rev. 10(1), 62–81 (2016).
[Crossref]

Figdor, C. G.

F. de Lange, A. Cambi, R. Huijbens, B. de Bakker, W. Rensen, M. Garcia-Parajo, N. van Hulst, and C. G. Figdor, “Cell biology beyond the diffraction limit: near-field scanning optical microscopy,” J. Cell Sci. 114(Pt 23), 4153–4160 (2001).
[PubMed]

Gabriel, M. M.

E. M. Grumstrup, M. M. Gabriel, E. E. M. Cating, E. M. Van Goethem, and J. M. Papanikolas, “Pump–probe microscopy: Visualization and spectroscopy of ultrafast dynamics at the nanoscale,” Chem. Phys. 458, 30–40 (2015).
[Crossref]

Garcia-Parajo, M.

F. de Lange, A. Cambi, R. Huijbens, B. de Bakker, W. Rensen, M. Garcia-Parajo, N. van Hulst, and C. G. Figdor, “Cell biology beyond the diffraction limit: near-field scanning optical microscopy,” J. Cell Sci. 114(Pt 23), 4153–4160 (2001).
[PubMed]

Grumstrup, E. M.

E. S. Massaro, A. H. Hill, and E. M. Grumstrup, “Super-Resolution Structured Pump–Probe Microscopy,” ACS Photonics 3(4), 501–506 (2016).
[Crossref]

E. M. Grumstrup, M. M. Gabriel, E. E. M. Cating, E. M. Van Goethem, and J. M. Papanikolas, “Pump–probe microscopy: Visualization and spectroscopy of ultrafast dynamics at the nanoscale,” Chem. Phys. 458, 30–40 (2015).
[Crossref]

Gustafsson, M. G.

M. G. 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]

Hajek, K. M.

Heintzmann, R.

A. Jost and R. Heintzmann, “Superresolution Multidimensional Imaging with Structured Illumination Microscopy,” Annu. Rev. Mater. Res. 43(1), 261–282 (2013).
[Crossref]

R. Heintzmann and C. Cremer, “Laterally Modulated Excitation Microscopy- Improvement of resolution by using a diffraction grating,” Opt. Biopsies Microscopic Tech. 3568, 185–196 (1999).
[Crossref]

Hell, S. W.

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Hill, A. H.

E. S. Massaro, A. H. Hill, and E. M. Grumstrup, “Super-Resolution Structured Pump–Probe Microscopy,” ACS Photonics 3(4), 501–506 (2016).
[Crossref]

Hsu, J.

C.-Y. Chung, J. Hsu, S. Mukamel, and E. O. Potma, “Controlling stimulated coherent spectroscopy and microscopy by a position-dependent phase,” Phys. Rev. A 87(3), 033833 (2013).
[Crossref] [PubMed]

Huang, L.

L. Huang and J.-X. Cheng, “Nonlinear Optical Microscopy of Single Nanostructures,” Annu. Rev. Mater. Res. 43(1), 213–236 (2013).
[Crossref]

Huijbens, R.

F. de Lange, A. Cambi, R. Huijbens, B. de Bakker, W. Rensen, M. Garcia-Parajo, N. van Hulst, and C. G. Figdor, “Cell biology beyond the diffraction limit: near-field scanning optical microscopy,” J. Cell Sci. 114(Pt 23), 4153–4160 (2001).
[PubMed]

Jost, A.

A. Jost and R. Heintzmann, “Superresolution Multidimensional Imaging with Structured Illumination Microscopy,” Annu. Rev. Mater. Res. 43(1), 261–282 (2013).
[Crossref]

Köhler, H.

H. Köhler, “On Abbe’s Theory of Image Formation in the Microscope,” Optica Acta 28(12), 1691–1701 (1981).
[Crossref]

Lee, E. S.

Lee, J. Y.

Lee, S. W.

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Littleton, B.

Mahajan, S.

S. Mahajan, “Defects in semiconductors and their effects on devices,” Acta Mater. 48(1), 137–149 (1999).
[Crossref]

Martin, M. C.

H. A. Bechtel, E. A. Muller, R. L. Olmon, M. C. Martin, and M. B. Raschke, “Ultrabroadband infrared nanospectroscopic imaging,” Proc. Natl. Acad. Sci. U.S.A. 111(20), 7191–7196 (2014).
[Crossref] [PubMed]

Massaro, E. S.

E. S. Massaro, A. H. Hill, and E. M. Grumstrup, “Super-Resolution Structured Pump–Probe Microscopy,” ACS Photonics 3(4), 501–506 (2016).
[Crossref]

Mitchell, J.

P. Wang, M. N. Slipchenko, J. Mitchell, C. Yang, E. O. Potma, X. Xu, and J. X. Cheng, “Far-field Imaging of Non-fluorescent Species with Sub-diffraction Resolution,” Nat. Photonics 7(6), 449–453 (2013).
[Crossref] [PubMed]

Mukamel, S.

C.-Y. Chung, J. Hsu, S. Mukamel, and E. O. Potma, “Controlling stimulated coherent spectroscopy and microscopy by a position-dependent phase,” Phys. Rev. A 87(3), 033833 (2013).
[Crossref] [PubMed]

Muller, E. A.

E. A. Muller, B. Pollard, and M. B. Raschke, “Infrared Chemical Nano-Imaging: Accessing Structure, Coupling, and Dynamics on Molecular Length Scales,” J. Phys. Chem. Lett. 6(7), 1275–1284 (2015).
[Crossref] [PubMed]

H. A. Bechtel, E. A. Muller, R. L. Olmon, M. C. Martin, and M. B. Raschke, “Ultrabroadband infrared nanospectroscopic imaging,” Proc. Natl. Acad. Sci. U.S.A. 111(20), 7191–7196 (2014).
[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,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Olmon, R. L.

H. A. Bechtel, E. A. Muller, R. L. Olmon, M. C. Martin, and M. B. Raschke, “Ultrabroadband infrared nanospectroscopic imaging,” Proc. Natl. Acad. Sci. U.S.A. 111(20), 7191–7196 (2014).
[Crossref] [PubMed]

Papanikolas, J. M.

E. M. Grumstrup, M. M. Gabriel, E. E. M. Cating, E. M. Van Goethem, and J. M. Papanikolas, “Pump–probe microscopy: Visualization and spectroscopy of ultrafast dynamics at the nanoscale,” Chem. Phys. 458, 30–40 (2015).
[Crossref]

Park, J. H.

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Pollard, B.

E. A. Muller, B. Pollard, and M. B. Raschke, “Infrared Chemical Nano-Imaging: Accessing Structure, Coupling, and Dynamics on Molecular Length Scales,” J. Phys. Chem. Lett. 6(7), 1275–1284 (2015).
[Crossref] [PubMed]

Potma, E. O.

P. Wang, M. N. Slipchenko, J. Mitchell, C. Yang, E. O. Potma, X. Xu, and J. X. Cheng, “Far-field Imaging of Non-fluorescent Species with Sub-diffraction Resolution,” Nat. Photonics 7(6), 449–453 (2013).
[Crossref] [PubMed]

C.-Y. Chung, J. Hsu, S. Mukamel, and E. O. Potma, “Controlling stimulated coherent spectroscopy and microscopy by a position-dependent phase,” Phys. Rev. A 87(3), 033833 (2013).
[Crossref] [PubMed]

Raschke, M. B.

E. A. Muller, B. Pollard, and M. B. Raschke, “Infrared Chemical Nano-Imaging: Accessing Structure, Coupling, and Dynamics on Molecular Length Scales,” J. Phys. Chem. Lett. 6(7), 1275–1284 (2015).
[Crossref] [PubMed]

H. A. Bechtel, E. A. Muller, R. L. Olmon, M. C. Martin, and M. B. Raschke, “Ultrabroadband infrared nanospectroscopic imaging,” Proc. Natl. Acad. Sci. U.S.A. 111(20), 7191–7196 (2014).
[Crossref] [PubMed]

Rensen, W.

F. de Lange, A. Cambi, R. Huijbens, B. de Bakker, W. Rensen, M. Garcia-Parajo, N. van Hulst, and C. G. Figdor, “Cell biology beyond the diffraction limit: near-field scanning optical microscopy,” J. Cell Sci. 114(Pt 23), 4153–4160 (2001).
[PubMed]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (2006).
[Crossref] [PubMed]

Slipchenko, M. N.

P. Wang, M. N. Slipchenko, J. Mitchell, C. Yang, E. O. Potma, X. Xu, and J. X. Cheng, “Far-field Imaging of Non-fluorescent Species with Sub-diffraction Resolution,” Nat. Photonics 7(6), 449–453 (2013).
[Crossref] [PubMed]

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Timothy, J.

Turk, D.

Van Goethem, E. M.

E. M. Grumstrup, M. M. Gabriel, E. E. M. Cating, E. M. Van Goethem, and J. M. Papanikolas, “Pump–probe microscopy: Visualization and spectroscopy of ultrafast dynamics at the nanoscale,” Chem. Phys. 458, 30–40 (2015).
[Crossref]

van Hulst, N.

F. de Lange, A. Cambi, R. Huijbens, B. de Bakker, W. Rensen, M. Garcia-Parajo, N. van Hulst, and C. G. Figdor, “Cell biology beyond the diffraction limit: near-field scanning optical microscopy,” J. Cell Sci. 114(Pt 23), 4153–4160 (2001).
[PubMed]

Wang, P.

P. Wang, M. N. Slipchenko, J. Mitchell, C. Yang, E. O. Potma, X. Xu, and J. X. Cheng, “Far-field Imaging of Non-fluorescent Species with Sub-diffraction Resolution,” Nat. Photonics 7(6), 449–453 (2013).
[Crossref] [PubMed]

Wichmann, J.

Xu, X.

P. Wang, M. N. Slipchenko, J. Mitchell, C. Yang, E. O. Potma, X. Xu, and J. X. Cheng, “Far-field Imaging of Non-fluorescent Species with Sub-diffraction Resolution,” Nat. Photonics 7(6), 449–453 (2013).
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Figures (8)

Fig. 1
Fig. 1 (A) Experimental schematic of two-dimensional SPPM. The dotted line represents the input pulse train derived from a suitable ultrafast laser source. After a beamsplitter, the probe pulse is directed to a set of Galvanometer (GV) mirrors and coupled through a 4-f lens system onto the back aperture of the objective. The GV mirrors provide a reliable method for spatially overlapping the pump and probe pulses. The pump path is directed through an acousto-optic modulator (AOM), a translating delay stage, and toward an SLM, which is programmed to display a two dimensional grating pattern. The four 1st order diffractions are collected by a collimating lens (L1) in such a way that they are incident at the far outer edges of the objective aperture. (B) An expanded view of the optics needed to create a structured pump excitation field. The 5 diffraction orders from the SLM are labeled in the (x, y) directions where a value of one denotes the 1st order diffraction of the respective axes. The (0,0) diffraction order is blocked with a mask.
Fig. 2
Fig. 2 One-dimensional illustration of four component convolution in Eq. (5). (A) Coherent OTFs Hn are convolved, producing a triangle function for both pump (n = 1) and probe (n = 2). (B) Convolution of the pump and probe OTFs produced in step 1 resulting in the diffraction-limited effective OTF.
Fig. 3
Fig. 3 The structured excitation field employed in SPPM. (A, B) Sinusoidal fields propagating along the y- and x- axes, respectively, formed by the interference of two ± 1st order diffractions. (C) Two-dimensional excitation field produced from the mutual interference of all four diffraction orders. (D) Fourier Transform of the 2D excitation field in panel C showing the nine shifted delta functions in the kx-ky plane. The amplitude of each component is normalized to the component centered at k0.
Fig. 4
Fig. 4 Comparison of SPPM and DL OTF profiles along the kx axes. The diffraction-limited effective OTF (purple dots) is given by the triple convolution in Eq. (5). The effective SPPM OTF before normalization is shown as a black dashed line. The normalized effective OTF is shown by the solid black line.
Fig. 5
Fig. 5 (A) Profile comparison of the SPPM (green circles, 97 nm fwhm) and DL (red squares, 180 nm fwhm) effective PSFs with 400 nm pump and 540nm probe wavelengths. The black profile is the profile of the delta function used to determine the PSF of the imaging model. (B) Wavelength dependence of SPPM localization enhancement represented by the ratio of the SPPM PSF to the DL PSF at varying excitation and probe wavelengths through the visible spectrum.
Fig. 6
Fig. 6 Comparison of DL and SPPM imaging capabilities. (A) Shows the simulated test target (top) with a magnified region (bottom) designated by the white square. The remaining panels (B-G) are arranged so that the top and bottom rows correspond to the modeled wavelengths (labeled to the left of panels B and E). The three separate columns of panels B-G show DL (B, E), SPPM (C, F) imaging models and profile comparisons (D, G). Profile comparison are from location indicated by the red dashed line in the magnified region of panel A. The black (triangles) trace represents the original object while the blue (squares) and red (circles) traces are the DL and the SPPM models, respectively.
Fig. 7
Fig. 7 Evaluation of the vertical and diagonal features of the SPPM OTF. (A) The object described in panel A of Fig. 6 imaged using the SPPM model (560 nm pump, 800 nm probe). (B) The resulting PSF generated by the SPPM model. (C) The black and red traces correspond to the red and black dashed lines in panel A. The nine components are identical in the original image. However, the nine components that produce the red trace in panel C have been rotated 45°. (D) Profile comparison of the SPPM PSF along directions of the blue and green arrows in panel B.
Fig. 8
Fig. 8 Comparison of Δt = 0 ps images (left) and time-resolved kinetics (right) of modeled single pixel features using DL and SPPM approaches. Simulated pump wavelength is 560 nm and probe wavelength is 800 nm. The amplitude of the feature located to the left of the origin decays with a single exponential lifetime of 100 ps (red, solid line), whereas the feature to the right decays with a lifetime of 200 ps (green, solid line). (A) DL decay kinetics (blue circles) reflect an average of the fast and slow components with an object spacing of 175 nm. (B) The SPPM model recovers the distinct kinetics of the two objects (purple squares and triangles) when separated by 175 nm. (C) If the objects are unresolvable with SPPM, the recovered kinetics (orange triangles) reflect the average of fast and slow decays. For all panels, the kinetics are collected at the peak location(s) of the lineshape at Δt = 0 ps.

Equations (15)

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fwh m min = λ 2NA
I N (r)=o(r)( E(r)h(r) )
( Eh ) eff = | E 1 (r) h 1 | 2 | E 2 (r) h 2 | 2
I DL =o(r) | E 1 (r) h 1 | 2 | E 2 (r) h 2 | 2 =o(r) ( δ(r) h 1 ) 2 ( δ(r) h 2 ) 2 =o(r)( h 1 2 h 2 2 )
I ˜ DL (k)= O ˜ (k)[ H ˜ 1 (k) H ˜ 1 (k) H ˜ 2 (k) H ˜ 2 (k) ]
E 1 (r)=exp(i k x r+ φ x )+exp(i k x r φ x ) +exp(i k y r+ φ y )+exp(i k y r φ y )
I Str (r; φ x , φ y )=o(r) | exp(i k x r+ φ x )+exp(i k x r φ x ) +exp(i k y r+ φ y )+exp(i k y r φ y ) | 2 ( δ(r) h 2 ) 2 =o(r) | exp(i k x r+ φ x )+exp(i k x r φ x ) +exp(i k y r+ φ y )+exp(i k y r φ y ) | 2 h 2 2
I ˜ Str (k; φ x , φ y )= O ˜ (k)[ ( H ˜ 2 ' ( k ) ) 1 + ( 1 2 H ˜ 2 ' ( k+ k x + k y ) e i φ x i φ y ) 2 + ( 1 2 H ˜ 2 ' ( k k x k y ) e +i φ x +i φ y ) 3 + ( 1 2 H ˜ 2 ' ( k+ k x k y ) e i φ x +i φ y ) 4 + ( 1 2 H ˜ 2 ' ( k k x + k y ) e +i φ x i φ y ) 5 + ( 1 4 H ˜ 2 ' ( k2 k y ) e +i2 φ y ) 6 + ( 1 4 H ˜ 2 ' ( k+2 k y ) e i2 φ y ) 7 + ( 1 4 H ˜ 2 ' ( k2 k x ) e +i2 φ x ) 8 + ( 1 4 H ˜ 2 ' ( k+2 k x ) e i2 φ x ) 9 ] = n=1 9 a n Y ˜ n exp[ Φ n ]
I ˜ ideal (k)= O ˜ (k)[ H ˜ 2 ' ( k ) + H ˜ 2 ' ( k+ k x + k y ) + H ˜ 2 ' ( k k x k y ) + H ˜ 2 ' ( k+ k x k y ) + H ˜ 2 ' ( k k x + k y ) + H ˜ 2 ' ( k2 k y )+ H ˜ 2 ' ( k+2 k y ) + H ˜ 2 ' ( k2 k x )+ H ˜ 2 ' ( k+2 k x ) ] = n=1 9 Y ˜ n
I ˜ V =( I ˜ Str 1 (k) I ˜ Str 2 (k) I ˜ Str 9 (k) )
AP=( a 1 1 exp( Φ 1 1 ) a 9 1 exp( Φ 9 1 ) a 1 9 exp( Φ 1 9 ) a 9 9 exp( Φ 9 9 ) )
A P 1 I ˜ V =( Y ˜ 1 Y ˜ 2 Y ˜ 9 )
OT F SPPM =[ H ˜ 2 ' ( k ) + H ˜ 2 ' ( k+ k x + k y ) + H ˜ 2 ' ( k k x k y ) + H ˜ 2 ' ( k+ k x k y ) + H ˜ 2 ' ( k k x + k y ) + H ˜ 2 ' ( k2 k y ) + H ˜ 2 ' ( k+2 k y ) + H ˜ 2 ' ( k2 k x ) + H ˜ 2 ' ( k+2 k x ) ]
I SPPM (r)=Re[ F T 1 { ( n Y ˜ n )÷OT F SPPM } ]
K ˜ V =( K ˜ Str 1 K ˜ Str 2 K ˜ Str 9 )

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