Abstract

We report on the development of a superresolution four-wave mixing microscope with spatial resolution approaching 130 nm which represents better than twice the diffraction limit at 800 nm while retaining the ability to acquire materials- and chemical- specific contrast. The resolution enhancement is achieved by narrowing the microscope’s excitation volume in the focal plane through the combined use of a Toraldo-style pupil phase filter with the multiplicative nature of four-wave mixing.

© 2012 OSA

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  1. W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am. A56(11), 1463–1472 (1966).
    [CrossRef]
  2. M. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett.22(24), 1905–1907 (1997).
    [CrossRef] [PubMed]
  3. M. A. Neil, A. Squire, R. Juškaitis, P. I. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc.197(1), 1–4 (2000).
    [CrossRef] [PubMed]
  4. M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc.198(2), 82–87 (2000).
    [CrossRef] [PubMed]
  5. G. T. Francia, “Super-gain antennas and optical resolving power,” Nuovo Cim.9(S3), 426–438 (1952).
    [CrossRef]
  6. M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett.88(16), 163901 (2002).
    [CrossRef] [PubMed]
  7. R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods5(6), 539–544 (2008).
    [CrossRef] [PubMed]
  8. W. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. A62(1), 55–59 (1972).
    [CrossRef]
  9. I. Cox and C. Sheppard, “Information capacity and resolution in an optical system,” J. Opt. Soc. Am. A3(8), 1152–1158 (1986).
    [CrossRef]
  10. 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]
  11. 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]
  12. E. O. Potma and X. Xie, “CARS microscopy for biology and medicine,” Opt. Photonics News15(11), 40–45 (2004).
    [CrossRef]
  13. X. Nan, J. X. Cheng, and X. S. Xie, “Vibrational imaging of lipid droplets in live fibroblast cells with coherent anti-Stokes Raman scattering microscopy,” J. Lipid Res.44(11), 2202–2208 (2003).
    [CrossRef] [PubMed]
  14. C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A.102(46), 16807–16812 (2005).
    [CrossRef] [PubMed]
  15. Y. Jung, L. Tong, A. Tanaudommongkon, J.-X. Cheng, and C. Yang, “In vitro and in vivo nonlinear optical imaging of silicon nanowires,” Nano Lett.9(6), 2440–2444 (2009).
    [CrossRef] [PubMed]
  16. T. Ichimura, N. Hayazawa, M. Hashimoto, Y. Inouye, and S. Kawata, “Tip-enhanced coherent anti-stokes Raman scattering for vibrational nanoimaging,” Phys. Rev. Lett.92(22), 220801 (2004).
    [CrossRef] [PubMed]
  17. M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett.98(2), 026104 (2007).
    [CrossRef] [PubMed]
  18. L. Cheng and D. Y. Kim, “Differential imaging in coherent anti-Stokes Raman scattering microscopy with Laguerre- Gaussian excitation beams,” Opt. Express15(16), 10123–10134 (2007).
    [CrossRef] [PubMed]
  19. V. Raghunathan and E. O. Potma, “Multiplicative and subtractive focal volume engineering in coherent Raman microscopy,” J. Opt. Soc. Am. A27(11), 2365–2374 (2010).
    [CrossRef] [PubMed]
  20. V. V. Krishnamachari and E. O. Potma, “Focus-engineered coherent anti-Stokes Raman scattering microscopy: a numerical investigation,” J. Opt. Soc. Am. A24(4), 1138–1147 (2007).
    [CrossRef] [PubMed]
  21. W. P. Beeker, P. Groß, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express17(25), 22632–22638 (2009).
    [CrossRef] [PubMed]
  22. M. R. Beversluis and S. J. Stranick, “Enhanced contrast coherent anti-Stokes Raman scattering microscopy using annular phase masks,” Appl. Phys. Lett.93(23), 231115 (2008).
    [CrossRef]
  23. H. Kim, C. A. Michaels, G. W. Bryant, and S. J. Stranick, “Comparison of the sensitivity and image contrast in spontaneous Raman and coherent Stokes Raman scattering microscopy of geometry-controlled samples,” J. Biomed. Opt.16(2), 021107 (2011).
    [CrossRef] [PubMed]
  24. Certain commercial equipment, instruments, or materials are identified in this paper to specify adequately the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.
  25. E. Wolf, “Electromagnetic diffraction in optical systems: I An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 349–357 (1959).
    [CrossRef]
  26. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
    [CrossRef]
  27. Recall that in FWM three incident fields combine to generate a fourth field, thus two conventional and one phase filtered. Also of note, we do not account for the relative phase of the fields (intensity only) which will become increasingly important as the sample systems become microscopically complex/extended.
  28. A two-dimensional (2D) spatial filtering of a 100 nm feature was carried out with the 2D filter function or kernel consisting of a spatially calibrated PSF.
  29. E. O. Potma, D. J. Jones, J.-X. Cheng, X. S. Xie, and J. Ye, “High-sensitivity coherent anti-Stokes Raman scattering microscopy with two tightly synchronized picosecond lasers,” Opt. Lett.27(13), 1168–1170 (2002).
    [CrossRef] [PubMed]

2011

H. Kim, C. A. Michaels, G. W. Bryant, and S. J. Stranick, “Comparison of the sensitivity and image contrast in spontaneous Raman and coherent Stokes Raman scattering microscopy of geometry-controlled samples,” J. Biomed. Opt.16(2), 021107 (2011).
[CrossRef] [PubMed]

2010

2009

W. P. Beeker, P. Groß, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express17(25), 22632–22638 (2009).
[CrossRef] [PubMed]

Y. Jung, L. Tong, A. Tanaudommongkon, J.-X. Cheng, and C. Yang, “In vitro and in vivo nonlinear optical imaging of silicon nanowires,” Nano Lett.9(6), 2440–2444 (2009).
[CrossRef] [PubMed]

2008

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods5(6), 539–544 (2008).
[CrossRef] [PubMed]

M. R. Beversluis and S. J. Stranick, “Enhanced contrast coherent anti-Stokes Raman scattering microscopy using annular phase masks,” Appl. Phys. Lett.93(23), 231115 (2008).
[CrossRef]

2007

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

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A.102(46), 16807–16812 (2005).
[CrossRef] [PubMed]

2004

T. Ichimura, N. Hayazawa, M. Hashimoto, Y. Inouye, and S. Kawata, “Tip-enhanced coherent anti-stokes Raman scattering for vibrational nanoimaging,” Phys. Rev. Lett.92(22), 220801 (2004).
[CrossRef] [PubMed]

E. O. Potma and X. Xie, “CARS microscopy for biology and medicine,” Opt. Photonics News15(11), 40–45 (2004).
[CrossRef]

2003

X. Nan, J. X. Cheng, and X. S. Xie, “Vibrational imaging of lipid droplets in live fibroblast cells with coherent anti-Stokes Raman scattering microscopy,” J. Lipid Res.44(11), 2202–2208 (2003).
[CrossRef] [PubMed]

2002

2000

M. A. Neil, A. Squire, R. Juškaitis, P. I. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc.197(1), 1–4 (2000).
[CrossRef] [PubMed]

M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc.198(2), 82–87 (2000).
[CrossRef] [PubMed]

1997

1986

1972

W. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. A62(1), 55–59 (1972).
[CrossRef]

1966

W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am. A56(11), 1463–1472 (1966).
[CrossRef]

1959

E. Wolf, “Electromagnetic diffraction in optical systems: I An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 349–357 (1959).
[CrossRef]

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

1952

G. T. Francia, “Super-gain antennas and optical resolving power,” Nuovo Cim.9(S3), 426–438 (1952).
[CrossRef]

Bastiaens, P. I.

M. A. Neil, A. Squire, R. Juškaitis, P. I. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc.197(1), 1–4 (2000).
[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]

Beeker, W. P.

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]

Beversluis, M. R.

M. R. Beversluis and S. J. Stranick, “Enhanced contrast coherent anti-Stokes Raman scattering microscopy using annular phase masks,” Appl. Phys. Lett.93(23), 231115 (2008).
[CrossRef]

Boller, K.-J.

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]

Bryant, G. W.

H. Kim, C. A. Michaels, G. W. Bryant, and S. J. Stranick, “Comparison of the sensitivity and image contrast in spontaneous Raman and coherent Stokes Raman scattering microscopy of geometry-controlled samples,” J. Biomed. Opt.16(2), 021107 (2011).
[CrossRef] [PubMed]

Cheng, J. X.

X. Nan, J. X. Cheng, and X. S. Xie, “Vibrational imaging of lipid droplets in live fibroblast cells with coherent anti-Stokes Raman scattering microscopy,” J. Lipid Res.44(11), 2202–2208 (2003).
[CrossRef] [PubMed]

Cheng, J.-X.

Y. Jung, L. Tong, A. Tanaudommongkon, J.-X. Cheng, and C. Yang, “In vitro and in vivo nonlinear optical imaging of silicon nanowires,” Nano Lett.9(6), 2440–2444 (2009).
[CrossRef] [PubMed]

E. O. Potma, D. J. Jones, J.-X. Cheng, X. S. Xie, and J. Ye, “High-sensitivity coherent anti-Stokes Raman scattering microscopy with two tightly synchronized picosecond lasers,” Opt. Lett.27(13), 1168–1170 (2002).
[CrossRef] [PubMed]

Cheng, L.

Cleff, C.

Côté, D.

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A.102(46), 16807–16812 (2005).
[CrossRef] [PubMed]

Cox, I.

Danckwerts, M.

M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett.98(2), 026104 (2007).
[CrossRef] [PubMed]

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]

Dyba, M.

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett.88(16), 163901 (2002).
[CrossRef] [PubMed]

Egner, A.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods5(6), 539–544 (2008).
[CrossRef] [PubMed]

Engelhardt, J.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods5(6), 539–544 (2008).
[CrossRef] [PubMed]

Evans, C. L.

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A.102(46), 16807–16812 (2005).
[CrossRef] [PubMed]

Fallnich, C.

Francia, G. T.

G. T. Francia, “Super-gain antennas and optical resolving power,” Nuovo Cim.9(S3), 426–438 (1952).
[CrossRef]

Groß, P.

Gustafsson, M. G.

M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc.198(2), 82–87 (2000).
[CrossRef] [PubMed]

Hashimoto, M.

T. Ichimura, N. Hayazawa, M. Hashimoto, Y. Inouye, and S. Kawata, “Tip-enhanced coherent anti-stokes Raman scattering for vibrational nanoimaging,” Phys. Rev. Lett.92(22), 220801 (2004).
[CrossRef] [PubMed]

Hayazawa, N.

T. Ichimura, N. Hayazawa, M. Hashimoto, Y. Inouye, and S. Kawata, “Tip-enhanced coherent anti-stokes Raman scattering for vibrational nanoimaging,” Phys. Rev. Lett.92(22), 220801 (2004).
[CrossRef] [PubMed]

Hell, S. W.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods5(6), 539–544 (2008).
[CrossRef] [PubMed]

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett.88(16), 163901 (2002).
[CrossRef] [PubMed]

Herek, J. L.

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]

Ichimura, T.

T. Ichimura, N. Hayazawa, M. Hashimoto, Y. Inouye, and S. Kawata, “Tip-enhanced coherent anti-stokes Raman scattering for vibrational nanoimaging,” Phys. Rev. Lett.92(22), 220801 (2004).
[CrossRef] [PubMed]

Inouye, Y.

T. Ichimura, N. Hayazawa, M. Hashimoto, Y. Inouye, and S. Kawata, “Tip-enhanced coherent anti-stokes Raman scattering for vibrational nanoimaging,” Phys. Rev. Lett.92(22), 220801 (2004).
[CrossRef] [PubMed]

Jakobs, S.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods5(6), 539–544 (2008).
[CrossRef] [PubMed]

Jones, D. J.

Jung, Y.

Y. Jung, L. Tong, A. Tanaudommongkon, J.-X. Cheng, and C. Yang, “In vitro and in vivo nonlinear optical imaging of silicon nanowires,” Nano Lett.9(6), 2440–2444 (2009).
[CrossRef] [PubMed]

Juskaitis, R.

Juškaitis, R.

M. A. Neil, A. Squire, R. Juškaitis, P. I. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc.197(1), 1–4 (2000).
[CrossRef] [PubMed]

Kawata, S.

T. Ichimura, N. Hayazawa, M. Hashimoto, Y. Inouye, and S. Kawata, “Tip-enhanced coherent anti-stokes Raman scattering for vibrational nanoimaging,” Phys. Rev. Lett.92(22), 220801 (2004).
[CrossRef] [PubMed]

Kim, D. Y.

Kim, H.

H. Kim, C. A. Michaels, G. W. Bryant, and S. J. Stranick, “Comparison of the sensitivity and image contrast in spontaneous Raman and coherent Stokes Raman scattering microscopy of geometry-controlled samples,” J. Biomed. Opt.16(2), 021107 (2011).
[CrossRef] [PubMed]

Krishnamachari, V. V.

Lee, C. J.

Lin, C. P.

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A.102(46), 16807–16812 (2005).
[CrossRef] [PubMed]

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]

Lukosz, W.

W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am. A56(11), 1463–1472 (1966).
[CrossRef]

Michaels, C. A.

H. Kim, C. A. Michaels, G. W. Bryant, and S. J. Stranick, “Comparison of the sensitivity and image contrast in spontaneous Raman and coherent Stokes Raman scattering microscopy of geometry-controlled samples,” J. Biomed. Opt.16(2), 021107 (2011).
[CrossRef] [PubMed]

Nan, X.

X. Nan, J. X. Cheng, and X. S. Xie, “Vibrational imaging of lipid droplets in live fibroblast cells with coherent anti-Stokes Raman scattering microscopy,” J. Lipid Res.44(11), 2202–2208 (2003).
[CrossRef] [PubMed]

Neil, M. A.

M. A. Neil, A. Squire, R. Juškaitis, P. I. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc.197(1), 1–4 (2000).
[CrossRef] [PubMed]

M. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett.22(24), 1905–1907 (1997).
[CrossRef] [PubMed]

Novotny, L.

M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett.98(2), 026104 (2007).
[CrossRef] [PubMed]

Offerhaus, H. L.

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]

Potma, E. O.

Puoris’haag, M.

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A.102(46), 16807–16812 (2005).
[CrossRef] [PubMed]

Raghunathan, V.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

Richardson, W.

W. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. A62(1), 55–59 (1972).
[CrossRef]

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]

Schmidt, R.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods5(6), 539–544 (2008).
[CrossRef] [PubMed]

Sheppard, C.

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]

Squire, A.

M. A. Neil, A. Squire, R. Juškaitis, P. I. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc.197(1), 1–4 (2000).
[CrossRef] [PubMed]

Stranick, S. J.

H. Kim, C. A. Michaels, G. W. Bryant, and S. J. Stranick, “Comparison of the sensitivity and image contrast in spontaneous Raman and coherent Stokes Raman scattering microscopy of geometry-controlled samples,” J. Biomed. Opt.16(2), 021107 (2011).
[CrossRef] [PubMed]

M. R. Beversluis and S. J. Stranick, “Enhanced contrast coherent anti-Stokes Raman scattering microscopy using annular phase masks,” Appl. Phys. Lett.93(23), 231115 (2008).
[CrossRef]

Tanaudommongkon, A.

Y. Jung, L. Tong, A. Tanaudommongkon, J.-X. Cheng, and C. Yang, “In vitro and in vivo nonlinear optical imaging of silicon nanowires,” Nano Lett.9(6), 2440–2444 (2009).
[CrossRef] [PubMed]

Tong, L.

Y. Jung, L. Tong, A. Tanaudommongkon, J.-X. Cheng, and C. Yang, “In vitro and in vivo nonlinear optical imaging of silicon nanowires,” Nano Lett.9(6), 2440–2444 (2009).
[CrossRef] [PubMed]

Wilson, T.

M. A. Neil, A. Squire, R. Juškaitis, P. I. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc.197(1), 1–4 (2000).
[CrossRef] [PubMed]

M. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett.22(24), 1905–1907 (1997).
[CrossRef] [PubMed]

Wolf, E.

E. Wolf, “Electromagnetic diffraction in optical systems: I An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 349–357 (1959).
[CrossRef]

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

Wurm, C. A.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods5(6), 539–544 (2008).
[CrossRef] [PubMed]

Xie, X.

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Other

Certain commercial equipment, instruments, or materials are identified in this paper to specify adequately the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

Recall that in FWM three incident fields combine to generate a fourth field, thus two conventional and one phase filtered. Also of note, we do not account for the relative phase of the fields (intensity only) which will become increasingly important as the sample systems become microscopically complex/extended.

A two-dimensional (2D) spatial filtering of a 100 nm feature was carried out with the 2D filter function or kernel consisting of a spatially calibrated PSF.

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Figures (6)

Fig. 1
Fig. 1

(A) Energy diagram for coherent anti-Stoke Raman scattering (CARS). P and S stand for pump and Stokes beams. Ω is the vibrational energy. g is the vibrational ground state; e, excitation state; g’, virtual ground state; e’, virtual excitation state, respectively. (B) P, the focal fields calculated for the flat wave front; S, focal fields for the π-stepped annular (≈0.42 of beam diameter) phase mask; CARS, the product of the squared P and S. Insets in P and S are the illustrations for each wavefront. (C) A cartoon shows how a spatial light modulator (SLM) controls the PSF of microscope. PC; personal computer, OL; objective lens, SiNW; silicon nanowire, BS; beam splitter.

Fig. 2
Fig. 2

A schematic diagram of the super-resolution, four-wave mixing microscope. SL; SychroLock, BE; beam expander, CL0 – CL4; convex lenses, TS; a manual xy directional translation stage, BS; beam splitter, SS; piezo-driven xy image scanning stages, NPBS; non-polarizing beam splitter, BF; bandpass filter, CCD; charge coupled device, APD; avalanche photodiode, SLM; spatial light modulator, WS; wavefront sensor.

Fig. 3
Fig. 3

Geometry of the annular phase masks used in programming the SLM. () A background mask which corrects the wavefront distortion in the optical system along with the series of annular masks used to generate the Toraldo phase filters. (B) A series of focal distributions (xy) resulting from application of the associated phase masks in (A) recorded by epi-two photon luminescence imaging of an isolated gold nanoparticle with 785 nm excitation. (C) shows a series of focal field calculations for the each of the annular phase masks in (A). The dimension is indicated by the λ: the wavelength of the incident beam. (D) xz focal field distributions resulting from application of the associated phase masks and recorded in a similar manner as the xy fields. (E) A series of xz focal field calculations.

Fig. 4
Fig. 4

(A) FWM microscopy images of Si nanowires on glass taken with 754 nm and 785 nm excitation beams. The arrow indicates the direction of the polarization and the dotted line indicates the region where the xz scans were recorded. (B) Shows the FWM PSF (xz) that results from two conventional beams. FWM PSF images that result from phase filtering with annular masks are shown in (C) for d = 0.14, (D) for d = 0.28, (E) for d = 0.42, (F) for d = 0.56, (G) for d = 0.70 and (H) for d = 0.83.

Fig. 5
Fig. 5

The FWM images of an isolated nanowire using conventional (A) and engineered PSFs corresponding to phase filters with annular diameters of (B) d = 0.14, (C) d = 0.28, (D) d = 0.35, (E) d = 0.42 and (F) d = 0.56. Insets in the lower-left corners correspond to simulated images using the calculated PSF for each phase filter. (G) The line profiles for the white dotted lines noted as (1, 2) in (A) and (D) are the average of three adjacent line scans: there was a mean variation of ~5% from line to line. (H) Simulated cross sections from the calculated images (inset) of a 100 nm feature using a conventional FWM PSF (black) and a SR-PSF (red). Note: The color scales are normalized, and the total signal strength relative to the conventional PSF case (maximum) is down a factor of 3.2 (minimum) for the d = 0.35 case.

Fig. 6
Fig. 6

(A) A Raman spectrum of polystyrene beads. CARS images tuned to (B) 1000 cm−1 and (C) 900 cm−1. The contrast gap in (B) corresponds to a region when the phases of the laser pulses are temporally mismatched. (D) Identical 20 µm x 20 µm regions of dispersed 0.30 µm diameter polystyrene beads imaged with CARS and (E) SR-CARS. CARS Images were taken using 728 nm pump (≈2 mW) and 785 nm Stokes (≈4 mW) beams; 0.35 d0 sized annular mask was used to record the image in (E). The dotted rectangle denotes the subportion of the images (D) and (E) shown in 3D rendering in (F) and (G) respectively.

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