Abstract

Coherent anti-Stokes Raman scattering (CARS) microscopy is a third-order nonlinear optical technique which permits label-free, molecule-specific hyperspectral imaging. The interference between coherent resonant and non-resonant terms leads to well known distortions in the vibrational spectrum, requiring the use of retrieval algorithms. It also leads to spatial imaging distortions, largely due to the Gouy phase, when objects are smaller than the Rayleigh range. Here we consider that the focal position and spectral contributions to the nonlinear image formation are intrinsically coupled and cannot be corrected by conventional retrieval methods.

© 2013 OSA

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  1. A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett.824142–4145 (1999).
    [CrossRef]
  2. E. O. Potma and X. S. Xie, “CARS microscopy for biology and medicine,” Opt. Photon. News15, 40–45 (2004).
    [CrossRef]
  3. C. L. Evans and X. S. Xie, “Coherent anti-Stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Annu. Rev. Anal. Chem.1, 883–909 (2008).
    [CrossRef]
  4. J. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “An epi-detected coherent anti-Stokes Raman scattering (E-CARS) microscope with high spectral resolution and high sensitivity,” J. Phys. Chem. B105, 1277–1280 (2001).
    [CrossRef]
  5. L. Li, H. Wang, and J. Cheng, “Quantitative coherent anti-Stokes Raman scattering imaging of lipid distribution in coexisting domains”, Biophys. J.89, 3480–3490 (2005).
    [CrossRef] [PubMed]
  6. M. Müller and J. M. Schins, “Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy,” J. Phys. Chem.106, 3715–3723 (2002).
  7. S. H. Parekh, Y. J. Lee, K. A. Aamer, and M. T. Cicerone, “Label-free cellular imaging by broadband coherent anti-Stokes Raman scattering microscopy,” Biophys. J.99, 2695–2704 (2010).
    [CrossRef] [PubMed]
  8. A. F. Pegoraro, A. D. Slepkov, A. Ridsdale, D. J. Moffatt, and A. Stolow, “Hyperspectral multimodal CARS microscopy in the fingerprint region,” J. Biophotonics (2012)
    [CrossRef] [PubMed]
  9. C. Chung, J. Hsu, S. Mukamel, and E. O. Potma, “Controlling stimulated coherent spectroscopy and microscopy by a position-dependent phase,” Phys. Rev. A87, 033833 (2013).
    [CrossRef]
  10. S. Maeda, T. Kamisuki, and Y. Adachi, Advances in Non-linear Spectroscopy, R. J. H. Clark and R. E. Hester, eds. (John Wiley and Sons Ltd., 1988) p. 253.
  11. E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett.31, 241–243 (2006).
    [CrossRef] [PubMed]
  12. W. M. Tolles, J. W. Nibler, J. R. McDonald, and A. B. Harvey, “A Review of the Theory and Applications of Coherent Anti-Stokes Raman Spectroscopy (CARS),” Appl. Spectrosc.31253–271 (1971).
    [CrossRef]
  13. Y. Liu, Y. J. Lee, and M. T. Cicerone, “Broadband CARS spectral phase retrieval using a time-domain Kramers-Kronig transform,” Opt. Lett.34, 1363–1365 (2009).
    [CrossRef] [PubMed]
  14. E. M. Vartiainen, H. A. Rinia, M. Müller, and M. Bonn, “Direct extraction of Raman line-shapes from congested CARS spectra,” Opt. Express14, 3622–3630 (2006).
    [CrossRef] [PubMed]
  15. G. L. Eesley, Coherent Raman Spectroscopy(Pergamon Press, 1981).
  16. E. O. Potma, W. P. de Boeij, and D. A. Wiersma, “Nonlinear coherent four-wave mixing in optical microscopy,” J. Opt. Soc. Am. B17, 1678–1684, (2000).
    [CrossRef]
  17. J. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterization of coherent anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B19, 1363–1375 (2002).
    [CrossRef]
  18. N. Djaker, D. Gachet, N. Sandeau, PF. Lenne, and H. Rigneault, “Refractive effects in coherent anti-Stokes Raman scattering microscopy,” Appl. Opt.45, 7005–7011 (2006).
    [CrossRef] [PubMed]
  19. K. I. Popov, A. F. Pegoraro, A. Stolow, and L. Ramunno, “Image formation in CARS microscopy: effect of the Gouy phase shift,” Opt. Express19, 5902–5911 (2011).
    [CrossRef] [PubMed]
  20. D. Gachet, F. Billard, N. Sandeau, and H. Rigneault, “Coherent anti-Stokes Raman scattering (CARS) microscopy imaging at interfaces: evidence of interference effects,” Opt. Express1510408–10420 (2007).
    [CrossRef] [PubMed]
  21. D. Gachet, F. Billard, and H. Rigneault, “Focused field symmetries for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. A77061802(R) 1–4 (2008).
    [CrossRef]
  22. D. Gachet, S. Brustlein, and H. Rigneault, “Revisiting the Youngs double slit experiment for background-free nonlinear Raman spectroscopy and microscopy,” Phys. Rev. Lett.104213905 1–4 (2010).
  23. C. V. Stephenson, W. C. Coburn, and W. S. Wilcox, “The vibrational spectra and assignments of nitrobenzene, phenyl isocyanate, phenyl isothiocyanate, thionylaniline and anisole”, Spectrochim. Acta17, 933–946 (1961).
    [CrossRef]
  24. A. F. Pegoraro, A. Ridsdale, D. J. Moffatt, Y. Jia, J. P. Pezacki, and A. Stolow, “Optimally chirped multimodal CARS microscopy based on a single Ti:sapphire oscillator,” œ172984–2996 (2009).
  25. K. S. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Ant. Prop.14, 302–307 (1966).
    [CrossRef]
  26. M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media,” IEEE J. Quant. Electron.40, 175–182 (2004).
    [CrossRef]
  27. D. Vanderbilt and S. G. Louie, “A Monte Carlo simulated annealing approach to optimization over continuous variables,” J. Comput. Phys.56, 259–271 (1984).
    [CrossRef]

2013 (1)

C. Chung, J. Hsu, S. Mukamel, and E. O. Potma, “Controlling stimulated coherent spectroscopy and microscopy by a position-dependent phase,” Phys. Rev. A87, 033833 (2013).
[CrossRef]

2012 (1)

A. F. Pegoraro, A. D. Slepkov, A. Ridsdale, D. J. Moffatt, and A. Stolow, “Hyperspectral multimodal CARS microscopy in the fingerprint region,” J. Biophotonics (2012)
[CrossRef] [PubMed]

2011 (1)

2010 (2)

S. H. Parekh, Y. J. Lee, K. A. Aamer, and M. T. Cicerone, “Label-free cellular imaging by broadband coherent anti-Stokes Raman scattering microscopy,” Biophys. J.99, 2695–2704 (2010).
[CrossRef] [PubMed]

D. Gachet, S. Brustlein, and H. Rigneault, “Revisiting the Youngs double slit experiment for background-free nonlinear Raman spectroscopy and microscopy,” Phys. Rev. Lett.104213905 1–4 (2010).

2009 (2)

A. F. Pegoraro, A. Ridsdale, D. J. Moffatt, Y. Jia, J. P. Pezacki, and A. Stolow, “Optimally chirped multimodal CARS microscopy based on a single Ti:sapphire oscillator,” œ172984–2996 (2009).

Y. Liu, Y. J. Lee, and M. T. Cicerone, “Broadband CARS spectral phase retrieval using a time-domain Kramers-Kronig transform,” Opt. Lett.34, 1363–1365 (2009).
[CrossRef] [PubMed]

2008 (2)

C. L. Evans and X. S. Xie, “Coherent anti-Stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Annu. Rev. Anal. Chem.1, 883–909 (2008).
[CrossRef]

D. Gachet, F. Billard, and H. Rigneault, “Focused field symmetries for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. A77061802(R) 1–4 (2008).
[CrossRef]

2007 (1)

2006 (3)

2005 (1)

L. Li, H. Wang, and J. Cheng, “Quantitative coherent anti-Stokes Raman scattering imaging of lipid distribution in coexisting domains”, Biophys. J.89, 3480–3490 (2005).
[CrossRef] [PubMed]

2004 (2)

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

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media,” IEEE J. Quant. Electron.40, 175–182 (2004).
[CrossRef]

2002 (2)

M. Müller and J. M. Schins, “Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy,” J. Phys. Chem.106, 3715–3723 (2002).

J. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterization of coherent anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B19, 1363–1375 (2002).
[CrossRef]

2001 (1)

J. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “An epi-detected coherent anti-Stokes Raman scattering (E-CARS) microscope with high spectral resolution and high sensitivity,” J. Phys. Chem. B105, 1277–1280 (2001).
[CrossRef]

2000 (1)

1999 (1)

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett.824142–4145 (1999).
[CrossRef]

1984 (1)

D. Vanderbilt and S. G. Louie, “A Monte Carlo simulated annealing approach to optimization over continuous variables,” J. Comput. Phys.56, 259–271 (1984).
[CrossRef]

1971 (1)

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Ant. Prop.14, 302–307 (1966).
[CrossRef]

1961 (1)

C. V. Stephenson, W. C. Coburn, and W. S. Wilcox, “The vibrational spectra and assignments of nitrobenzene, phenyl isocyanate, phenyl isothiocyanate, thionylaniline and anisole”, Spectrochim. Acta17, 933–946 (1961).
[CrossRef]

Aamer, K. A.

S. H. Parekh, Y. J. Lee, K. A. Aamer, and M. T. Cicerone, “Label-free cellular imaging by broadband coherent anti-Stokes Raman scattering microscopy,” Biophys. J.99, 2695–2704 (2010).
[CrossRef] [PubMed]

Adachi, Y.

S. Maeda, T. Kamisuki, and Y. Adachi, Advances in Non-linear Spectroscopy, R. J. H. Clark and R. E. Hester, eds. (John Wiley and Sons Ltd., 1988) p. 253.

Billard, F.

D. Gachet, F. Billard, and H. Rigneault, “Focused field symmetries for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. A77061802(R) 1–4 (2008).
[CrossRef]

D. Gachet, F. Billard, N. Sandeau, and H. Rigneault, “Coherent anti-Stokes Raman scattering (CARS) microscopy imaging at interfaces: evidence of interference effects,” Opt. Express1510408–10420 (2007).
[CrossRef] [PubMed]

Bonn, M.

Book, L. D.

J. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “An epi-detected coherent anti-Stokes Raman scattering (E-CARS) microscope with high spectral resolution and high sensitivity,” J. Phys. Chem. B105, 1277–1280 (2001).
[CrossRef]

Brustlein, S.

D. Gachet, S. Brustlein, and H. Rigneault, “Revisiting the Youngs double slit experiment for background-free nonlinear Raman spectroscopy and microscopy,” Phys. Rev. Lett.104213905 1–4 (2010).

Cheng, J.

L. Li, H. Wang, and J. Cheng, “Quantitative coherent anti-Stokes Raman scattering imaging of lipid distribution in coexisting domains”, Biophys. J.89, 3480–3490 (2005).
[CrossRef] [PubMed]

J. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterization of coherent anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B19, 1363–1375 (2002).
[CrossRef]

J. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “An epi-detected coherent anti-Stokes Raman scattering (E-CARS) microscope with high spectral resolution and high sensitivity,” J. Phys. Chem. B105, 1277–1280 (2001).
[CrossRef]

Chung, C.

C. Chung, J. Hsu, S. Mukamel, and E. O. Potma, “Controlling stimulated coherent spectroscopy and microscopy by a position-dependent phase,” Phys. Rev. A87, 033833 (2013).
[CrossRef]

Cicerone, M. T.

S. H. Parekh, Y. J. Lee, K. A. Aamer, and M. T. Cicerone, “Label-free cellular imaging by broadband coherent anti-Stokes Raman scattering microscopy,” Biophys. J.99, 2695–2704 (2010).
[CrossRef] [PubMed]

Y. Liu, Y. J. Lee, and M. T. Cicerone, “Broadband CARS spectral phase retrieval using a time-domain Kramers-Kronig transform,” Opt. Lett.34, 1363–1365 (2009).
[CrossRef] [PubMed]

Coburn, W. C.

C. V. Stephenson, W. C. Coburn, and W. S. Wilcox, “The vibrational spectra and assignments of nitrobenzene, phenyl isocyanate, phenyl isothiocyanate, thionylaniline and anisole”, Spectrochim. Acta17, 933–946 (1961).
[CrossRef]

de Boeij, W. P.

Djaker, N.

Eesley, G. L.

G. L. Eesley, Coherent Raman Spectroscopy(Pergamon Press, 1981).

Evans, C. L.

C. L. Evans and X. S. Xie, “Coherent anti-Stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Annu. Rev. Anal. Chem.1, 883–909 (2008).
[CrossRef]

E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett.31, 241–243 (2006).
[CrossRef] [PubMed]

Freude, W.

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media,” IEEE J. Quant. Electron.40, 175–182 (2004).
[CrossRef]

Fujii, M.

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media,” IEEE J. Quant. Electron.40, 175–182 (2004).
[CrossRef]

Gachet, D.

D. Gachet, S. Brustlein, and H. Rigneault, “Revisiting the Youngs double slit experiment for background-free nonlinear Raman spectroscopy and microscopy,” Phys. Rev. Lett.104213905 1–4 (2010).

D. Gachet, F. Billard, and H. Rigneault, “Focused field symmetries for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. A77061802(R) 1–4 (2008).
[CrossRef]

D. Gachet, F. Billard, N. Sandeau, and H. Rigneault, “Coherent anti-Stokes Raman scattering (CARS) microscopy imaging at interfaces: evidence of interference effects,” Opt. Express1510408–10420 (2007).
[CrossRef] [PubMed]

N. Djaker, D. Gachet, N. Sandeau, PF. Lenne, and H. Rigneault, “Refractive effects in coherent anti-Stokes Raman scattering microscopy,” Appl. Opt.45, 7005–7011 (2006).
[CrossRef] [PubMed]

Harvey, A. B.

Holtom, G. R.

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett.824142–4145 (1999).
[CrossRef]

Hsu, J.

C. Chung, J. Hsu, S. Mukamel, and E. O. Potma, “Controlling stimulated coherent spectroscopy and microscopy by a position-dependent phase,” Phys. Rev. A87, 033833 (2013).
[CrossRef]

Jia, Y.

A. F. Pegoraro, A. Ridsdale, D. J. Moffatt, Y. Jia, J. P. Pezacki, and A. Stolow, “Optimally chirped multimodal CARS microscopy based on a single Ti:sapphire oscillator,” œ172984–2996 (2009).

Kamisuki, T.

S. Maeda, T. Kamisuki, and Y. Adachi, Advances in Non-linear Spectroscopy, R. J. H. Clark and R. E. Hester, eds. (John Wiley and Sons Ltd., 1988) p. 253.

Lee, Y. J.

S. H. Parekh, Y. J. Lee, K. A. Aamer, and M. T. Cicerone, “Label-free cellular imaging by broadband coherent anti-Stokes Raman scattering microscopy,” Biophys. J.99, 2695–2704 (2010).
[CrossRef] [PubMed]

Y. Liu, Y. J. Lee, and M. T. Cicerone, “Broadband CARS spectral phase retrieval using a time-domain Kramers-Kronig transform,” Opt. Lett.34, 1363–1365 (2009).
[CrossRef] [PubMed]

Lenne, PF.

Li, L.

L. Li, H. Wang, and J. Cheng, “Quantitative coherent anti-Stokes Raman scattering imaging of lipid distribution in coexisting domains”, Biophys. J.89, 3480–3490 (2005).
[CrossRef] [PubMed]

Liu, Y.

Louie, S. G.

D. Vanderbilt and S. G. Louie, “A Monte Carlo simulated annealing approach to optimization over continuous variables,” J. Comput. Phys.56, 259–271 (1984).
[CrossRef]

Maeda, S.

S. Maeda, T. Kamisuki, and Y. Adachi, Advances in Non-linear Spectroscopy, R. J. H. Clark and R. E. Hester, eds. (John Wiley and Sons Ltd., 1988) p. 253.

McDonald, J. R.

Moffatt, D. J.

A. F. Pegoraro, A. D. Slepkov, A. Ridsdale, D. J. Moffatt, and A. Stolow, “Hyperspectral multimodal CARS microscopy in the fingerprint region,” J. Biophotonics (2012)
[CrossRef] [PubMed]

A. F. Pegoraro, A. Ridsdale, D. J. Moffatt, Y. Jia, J. P. Pezacki, and A. Stolow, “Optimally chirped multimodal CARS microscopy based on a single Ti:sapphire oscillator,” œ172984–2996 (2009).

Mukamel, S.

C. Chung, J. Hsu, S. Mukamel, and E. O. Potma, “Controlling stimulated coherent spectroscopy and microscopy by a position-dependent phase,” Phys. Rev. A87, 033833 (2013).
[CrossRef]

Müller, M.

E. M. Vartiainen, H. A. Rinia, M. Müller, and M. Bonn, “Direct extraction of Raman line-shapes from congested CARS spectra,” Opt. Express14, 3622–3630 (2006).
[CrossRef] [PubMed]

M. Müller and J. M. Schins, “Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy,” J. Phys. Chem.106, 3715–3723 (2002).

Nibler, J. W.

Parekh, S. H.

S. H. Parekh, Y. J. Lee, K. A. Aamer, and M. T. Cicerone, “Label-free cellular imaging by broadband coherent anti-Stokes Raman scattering microscopy,” Biophys. J.99, 2695–2704 (2010).
[CrossRef] [PubMed]

Pegoraro, A. F.

A. F. Pegoraro, A. D. Slepkov, A. Ridsdale, D. J. Moffatt, and A. Stolow, “Hyperspectral multimodal CARS microscopy in the fingerprint region,” J. Biophotonics (2012)
[CrossRef] [PubMed]

K. I. Popov, A. F. Pegoraro, A. Stolow, and L. Ramunno, “Image formation in CARS microscopy: effect of the Gouy phase shift,” Opt. Express19, 5902–5911 (2011).
[CrossRef] [PubMed]

A. F. Pegoraro, A. Ridsdale, D. J. Moffatt, Y. Jia, J. P. Pezacki, and A. Stolow, “Optimally chirped multimodal CARS microscopy based on a single Ti:sapphire oscillator,” œ172984–2996 (2009).

Pezacki, J. P.

A. F. Pegoraro, A. Ridsdale, D. J. Moffatt, Y. Jia, J. P. Pezacki, and A. Stolow, “Optimally chirped multimodal CARS microscopy based on a single Ti:sapphire oscillator,” œ172984–2996 (2009).

Popov, K. I.

Potma, E. O.

C. Chung, J. Hsu, S. Mukamel, and E. O. Potma, “Controlling stimulated coherent spectroscopy and microscopy by a position-dependent phase,” Phys. Rev. A87, 033833 (2013).
[CrossRef]

E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett.31, 241–243 (2006).
[CrossRef] [PubMed]

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

E. O. Potma, W. P. de Boeij, and D. A. Wiersma, “Nonlinear coherent four-wave mixing in optical microscopy,” J. Opt. Soc. Am. B17, 1678–1684, (2000).
[CrossRef]

Ramunno, L.

Ridsdale, A.

A. F. Pegoraro, A. D. Slepkov, A. Ridsdale, D. J. Moffatt, and A. Stolow, “Hyperspectral multimodal CARS microscopy in the fingerprint region,” J. Biophotonics (2012)
[CrossRef] [PubMed]

A. F. Pegoraro, A. Ridsdale, D. J. Moffatt, Y. Jia, J. P. Pezacki, and A. Stolow, “Optimally chirped multimodal CARS microscopy based on a single Ti:sapphire oscillator,” œ172984–2996 (2009).

Rigneault, H.

D. Gachet, S. Brustlein, and H. Rigneault, “Revisiting the Youngs double slit experiment for background-free nonlinear Raman spectroscopy and microscopy,” Phys. Rev. Lett.104213905 1–4 (2010).

D. Gachet, F. Billard, and H. Rigneault, “Focused field symmetries for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. A77061802(R) 1–4 (2008).
[CrossRef]

D. Gachet, F. Billard, N. Sandeau, and H. Rigneault, “Coherent anti-Stokes Raman scattering (CARS) microscopy imaging at interfaces: evidence of interference effects,” Opt. Express1510408–10420 (2007).
[CrossRef] [PubMed]

N. Djaker, D. Gachet, N. Sandeau, PF. Lenne, and H. Rigneault, “Refractive effects in coherent anti-Stokes Raman scattering microscopy,” Appl. Opt.45, 7005–7011 (2006).
[CrossRef] [PubMed]

Rinia, H. A.

Russer, P.

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media,” IEEE J. Quant. Electron.40, 175–182 (2004).
[CrossRef]

Sakagami, I.

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media,” IEEE J. Quant. Electron.40, 175–182 (2004).
[CrossRef]

Sandeau, N.

Schins, J. M.

M. Müller and J. M. Schins, “Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy,” J. Phys. Chem.106, 3715–3723 (2002).

Slepkov, A. D.

A. F. Pegoraro, A. D. Slepkov, A. Ridsdale, D. J. Moffatt, and A. Stolow, “Hyperspectral multimodal CARS microscopy in the fingerprint region,” J. Biophotonics (2012)
[CrossRef] [PubMed]

Stephenson, C. V.

C. V. Stephenson, W. C. Coburn, and W. S. Wilcox, “The vibrational spectra and assignments of nitrobenzene, phenyl isocyanate, phenyl isothiocyanate, thionylaniline and anisole”, Spectrochim. Acta17, 933–946 (1961).
[CrossRef]

Stolow, A.

A. F. Pegoraro, A. D. Slepkov, A. Ridsdale, D. J. Moffatt, and A. Stolow, “Hyperspectral multimodal CARS microscopy in the fingerprint region,” J. Biophotonics (2012)
[CrossRef] [PubMed]

K. I. Popov, A. F. Pegoraro, A. Stolow, and L. Ramunno, “Image formation in CARS microscopy: effect of the Gouy phase shift,” Opt. Express19, 5902–5911 (2011).
[CrossRef] [PubMed]

A. F. Pegoraro, A. Ridsdale, D. J. Moffatt, Y. Jia, J. P. Pezacki, and A. Stolow, “Optimally chirped multimodal CARS microscopy based on a single Ti:sapphire oscillator,” œ172984–2996 (2009).

Tahara, M.

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media,” IEEE J. Quant. Electron.40, 175–182 (2004).
[CrossRef]

Tolles, W. M.

Vanderbilt, D.

D. Vanderbilt and S. G. Louie, “A Monte Carlo simulated annealing approach to optimization over continuous variables,” J. Comput. Phys.56, 259–271 (1984).
[CrossRef]

Vartiainen, E. M.

Volkmer, A.

J. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterization of coherent anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B19, 1363–1375 (2002).
[CrossRef]

J. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “An epi-detected coherent anti-Stokes Raman scattering (E-CARS) microscope with high spectral resolution and high sensitivity,” J. Phys. Chem. B105, 1277–1280 (2001).
[CrossRef]

Wang, H.

L. Li, H. Wang, and J. Cheng, “Quantitative coherent anti-Stokes Raman scattering imaging of lipid distribution in coexisting domains”, Biophys. J.89, 3480–3490 (2005).
[CrossRef] [PubMed]

Wiersma, D. A.

Wilcox, W. S.

C. V. Stephenson, W. C. Coburn, and W. S. Wilcox, “The vibrational spectra and assignments of nitrobenzene, phenyl isocyanate, phenyl isothiocyanate, thionylaniline and anisole”, Spectrochim. Acta17, 933–946 (1961).
[CrossRef]

Xie, X. S.

C. L. Evans and X. S. Xie, “Coherent anti-Stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Annu. Rev. Anal. Chem.1, 883–909 (2008).
[CrossRef]

E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett.31, 241–243 (2006).
[CrossRef] [PubMed]

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

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Figures (5)

Fig. 1
Fig. 1

CARS microscopy of small nitrobenzene droplets of various sizes in agarose gel medium, imaged at Raman shifts of 1580 cm−1. (a) A CARS image recorded at the best focus (z = 0 μm) for the highlighted droplet. (b) A CARS image of the identical droplets, but with the focus displaced to z = −1 μm with respect to that in panel (a). Importantly, the Raman retrieved Raman spectra associated with these focal positions are different, as seen in Fig. 2.

Fig. 2
Fig. 2

(a) Experimentally measured raw CARS spectra of the highlighted NB droplet of Fig. 1, located at the z = 0 μm best focus position (circles) and at displaced foci (z = −1 μm, crosses, and z = +1 μm, squares). (b) The Raman spectra, retrieved via a Kramers-Kronig algorithm, of the same droplet, overlaid with the spontaneous Raman spectrum of NB (solid line). The intrinsic spatial-spectral coupling can be seen from the z-dependence of the retrieved Raman spectrum, in this case, the peak maximum varying by ∼10 cm−1. (Color online)

Fig. 3
Fig. 3

Numerical (FDTD) simulations of spatial-spectral coupling in CARS microscopy. (a) CARS spectra of NB droplets in a uniform NRB, located at the z = 0 μm best focus position (solid line) and displaced along z (z = −1μm, dashed line, and z = +1μm, dotted line), centered at ΩR = 1600 cm−1. (b) The Raman spectra of NB droplets retrieved using a standard protocol which does not consider the Gouy phase. The shift in ΩR is 10 cm−1 (9 × 10−4ωP). (c) The CARS spectra are also affected by linear index mismatches for a resonant NB droplet located at the z = 0 μm best focus position, within a uniform NRB occupying the entire Rayleigh range. The case of linear index-matching with the NRB is shown as the solid CARS spectrum. Using the known linear refractive index difference between NB and agarose leads to the dashed line CARS spectrum. (d) The retrieved Raman spectra of the preceding case, accounting for the index mismatch. In this case, the shift in ΩR is 5.5 cm−1 (5 × 10−4ωP)

Fig. 4
Fig. 4

Retrieved Raman spectra of NB droplet, using a modified algorithm which takes into account the effect of the Gouy phase. The retrieved spectra are for a droplet located at best focus (solid line) and displaced to z = ±1 μm (dashed lines). These results show that including the intrinsic spatial-spectral coupling allows for accurate retrieval of the resonant Raman spectrum of sub-focal objects.

Fig. 5
Fig. 5

The propagation phase term in Eq 2. has a significant effect on the form of both the CARS and retrieved Raman spectra. (a) Generated CARS spectra by assuming the Lorentzian line shape of Eq. (4), using the modified form of Eq.(2), for various δϕ. (b) The Raman retrieved spectra of the CARS lineshapes from (a). Use of standard retrieval algorithms can lead to significant distortions due to spatial-spectral coupling. (Color online)

Equations (4)

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I CARS ( ω ) | χ ( 3 ) ( ω ) | 2 = | χ N R ( 3 ) + χ R ( 3 ) ( ω ) | 2 ,
I CARS ( ω ) | χ ( 3 ) ( ω ) | 2 = | χ N R ( 3 ) + χ R ( 3 ) ( ω ) e i δ ϕ | 2 ,
| χ ( 3 ) ( ω ) | 2 = | χ N R ( 3 ) + 1 V R V R χ R ( 3 ) ( ω , r ) e i δ ϕ ( r ) d 3 r | 2
χ R ( 3 ) ( ω ) = χ R 0 ( 3 ) Γ Ω R ω i Γ

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