Abstract

We show that Raman line-shapes can be extracted directly from congested coherent anti-Stokes Raman scattering (CARS) spectra, by using a numerical method to retrieve the phase-information hidden in measured CARS spectra. The proposed method utilizes the maximum entropy (ME) model to fit the CARS spectra and to further extract the imaginary part of the Raman susceptibility providing the Raman line-shape similar to the spontaneous Raman scattering spectrum. It circumvents the challenges arising with experimentally determining the real and imaginary parts of the susceptibility independently. Another important advantage of this method is that no a priori information regarding the vibrational resonances is required in the analysis. This permits, for the first time, the quantitative analysis of CARS spectra and microscopy images without any knowledge of e.g. sample composition or Raman response.

© 2006 Optical Society of America

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  1. G. R. Holtom, B. D. Thrall, B. Chin, and D. Colson, "Achieving molecular selectivity in imaging using multiphoton Raman spectroscopy techniques," Traffic 2, 781-788 (2001).
    [CrossRef] [PubMed]
  2. J. X. Cheng and X. S. Xie, "Coherent Anti-Stokes Raman Scattering Microscopy: Instrumentation, Theory, and Applications," J. Phys. Chem. B 108, 827-840 (2004).
    [CrossRef]
  3. A. Volkmer, "Vibrational imaging and microspectroscopies based on coherent anti-Stokes Raman scattering microscopy," J. Phys. D: Appl. Phys. 38, R59-R81 (2005).
    [CrossRef]
  4. G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, and T. M. Jovin, "Studying single living cells and chromosomes by confocal Raman microspectroscopy," Nature 347, 301-303 (1990).
    [CrossRef] [PubMed]
  5. H. van Manen, Y. M. Kraan, D. Roos, and C. Otto, "Single-cell Raman and fluorescence microscopy reveal the association of lipid bodies with phagosomes in leukocytes," Proc. Natl. Acad. Sci. USA 102, 10159-10164 (2005).
    [CrossRef] [PubMed]
  6. M. Müller and J. M. Schins, "Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy," J. Phys. Chem. B 106, 3715-3723 (2002).
    [CrossRef]
  7. G. W. H. Wurpel, J. M. Schins, and M. Müller, "Chemical specificity in 3D imaging with multiplex CARS microscopy," Opt. Lett. 27, 1093-1095 (2002).
    [CrossRef]
  8. J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, "Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles," J. Phys. Chem. B 106, 8493-8498 (2002).
    [CrossRef]
  9. M. Müller, J. M. Schins, and G. W. H. Wurpel, "Shot-noise limited detection sensitivity in multiplex CARS microscopy," SPIE 5323, 195-204 (2004).
    [CrossRef]
  10. G. W. H. Wurpel, J. M. Schins, and M. Müller, "Direct measurement of chain order in single lipid mono- and bilayers with multiplex CARS," J. Phys. Chem. B 108, 3400-3403 (2004).
    [CrossRef]
  11. S. A. Akhmanov, A. F. Bunkin, S. G. Ivanov, and N. I. Koroteev, "Polarization active Raman spectroscopy and coherent Raman elipsometry," Sov. Phys. JETP 47, 667-678 (1978).
  12. J. Cheng, L. D. Book, and X. S. Xie, "Polarization coherent anti-Stokes Raman scattering microscopy," Opt. Lett. 26, 1341-1343 (2001).
    [CrossRef]
  13. A. Volkmer, L. D. Book, and X. S. Xie, "Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay," Appl. Phys. Lett. 80, 1505-1507 (2002).
    [CrossRef]
  14. D. Oron, N. Dudovich, D. Yelihn, and Y. Silberberg, "Quantum control of coherent anti-Stokes Raman processes," Phys. Rev. A 65, 4340814 (2002).
    [CrossRef]
  15. D. Oron, N. Dudovich, and Y. Silberberg, "Femtosecond Phase-and-Polarization Control for Background-Free Coherent Anti-Stokes Raman Spectroscopy," Phys. Rev. Lett. 90, 213902 (2003).
    [CrossRef] [PubMed]
  16. A. Volkmer, J. Cheng, and X. S. Xie, "Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy," Phys. Rev. Lett. 87, 23901 (2001).
    [CrossRef]
  17. 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. B 105, 1277-1280 (2001).
    [CrossRef]
  18. H. A. Rinia, M. Bonn, and M. Müller, "Quantitative multiplex CARS spectroscopy in congested spectral regions," J. Phys. Chem. B 110, 4472-4479 (2006).
    [CrossRef] [PubMed]
  19. F. Y. Yueh and E. J. Beiting, "Simultaneous N2, CO, and H2 multiplex CARS measurements in combustion environments using a single dye laser," Appl. Opt. 27, 3233-3243 (1988).
    [CrossRef] [PubMed]
  20. C. F. Kaminski and P. Ewart, "Multiplex H2 coherent anti-Stokes Raman scattering thermometry with a modeless laser," Appl. Opt. 36, 731-734 (1997).
    [CrossRef] [PubMed]
  21. C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, "Vibrational bands of luminescent zinc(II)-octaethyl-porphyrin using a polarization-sensitive 'microscopic' multiplex CARS technique," J. Raman Spectrosc. 32, 495-501 (2001).
    [CrossRef]
  22. D. Oron, N. Dudovich, and Y. Silberberg, "Single-pulse phase-contrast nonlinear Raman spectroscopy," Phys. Rev. Lett. 89, 27300 (2002).
    [CrossRef]
  23. S. Lim, A. G. Caster, and S. R. Leone, "Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy," Phys. Rev. A 72, 41803 (2005).
    [CrossRef]
  24. 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]
  25. D.L. Marks, C. Vinegoni, J.S. Bredfeldt and S.A. Boppart, "Interferometric differentiation between resonant coherent anti-Stokes Raman scattering and nonresonant four-wave-mixing processes," Appl. Phys. Lett. 85, 5787-5789 (2004).
    [CrossRef]
  26. E. M. Vartiainen, "Phase retrieval approach for coherent anti-Stokes Raman scattering spectrum analysis," J. Opt. Soc. Am. B 9, 1209-1214 (1992).
    [CrossRef]
  27. E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, "Phase retrieval in optical spectroscopy: resolving optical constants from power spectra," Appl. Spectrosc. 50, 1283-1289 (1996).
    [CrossRef]
  28. R. A. MacPhail, H. L. Strauss, R. G. Snyder, and C. A. Elliger, "Carbon-hydrogen stretching modes and the structure of n-alkyl chains. 2. Long, all-trans chains," J. Phys. Chem. 88, 334-341 (1984).
    [CrossRef]
  29. R. Mendelsohn and D. J. Moore, "Vibrational spectroscopic studies of lipid domains in biomembranes and model systems," Chem. Phys. Lipids 96, 141-157 (1998).
    [CrossRef]
  30. K. T. Yue, C. L. Martin, D. Chen, P. Nelson, D. L. Sloan, and R. Callender, "Raman spectroscopy of oxidized and reduced nicotinamide adenine dinucleotides," Biochem 25, 4941-4947 (1986).
    [CrossRef]
  31. L. Rimai, T. Cole, J. L. Parsons, J. T. Hickmott, Jr., and E. B. Carew, "Studies of Raman spectra of water solutions of Adenosine tri-, di-, and monophosphate and some related compounds," Biophys. J. 9, 320-329 (1969).
    [CrossRef] [PubMed]
  32. R. H. Jenkins, R. Tuma, J. T. Juuti, D. H. Bamford and J. J. Thomas, "A novel Raman spectrophotometric method for quantitative measurement of nucleoside triphosphate hydrolysis," Biospectroscopy 5, 3-8 (1999).
    [CrossRef] [PubMed]

2006 (2)

H. A. Rinia, M. Bonn, and M. Müller, "Quantitative multiplex CARS spectroscopy in congested spectral regions," J. Phys. Chem. B 110, 4472-4479 (2006).
[CrossRef] [PubMed]

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]

2005 (3)

S. Lim, A. G. Caster, and S. R. Leone, "Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy," Phys. Rev. A 72, 41803 (2005).
[CrossRef]

A. Volkmer, "Vibrational imaging and microspectroscopies based on coherent anti-Stokes Raman scattering microscopy," J. Phys. D: Appl. Phys. 38, R59-R81 (2005).
[CrossRef]

H. van Manen, Y. M. Kraan, D. Roos, and C. Otto, "Single-cell Raman and fluorescence microscopy reveal the association of lipid bodies with phagosomes in leukocytes," Proc. Natl. Acad. Sci. USA 102, 10159-10164 (2005).
[CrossRef] [PubMed]

2004 (4)

M. Müller, J. M. Schins, and G. W. H. Wurpel, "Shot-noise limited detection sensitivity in multiplex CARS microscopy," SPIE 5323, 195-204 (2004).
[CrossRef]

G. W. H. Wurpel, J. M. Schins, and M. Müller, "Direct measurement of chain order in single lipid mono- and bilayers with multiplex CARS," J. Phys. Chem. B 108, 3400-3403 (2004).
[CrossRef]

J. X. Cheng and X. S. Xie, "Coherent Anti-Stokes Raman Scattering Microscopy: Instrumentation, Theory, and Applications," J. Phys. Chem. B 108, 827-840 (2004).
[CrossRef]

D.L. Marks, C. Vinegoni, J.S. Bredfeldt and S.A. Boppart, "Interferometric differentiation between resonant coherent anti-Stokes Raman scattering and nonresonant four-wave-mixing processes," Appl. Phys. Lett. 85, 5787-5789 (2004).
[CrossRef]

2003 (1)

D. Oron, N. Dudovich, and Y. Silberberg, "Femtosecond Phase-and-Polarization Control for Background-Free Coherent Anti-Stokes Raman Spectroscopy," Phys. Rev. Lett. 90, 213902 (2003).
[CrossRef] [PubMed]

2002 (6)

A. Volkmer, L. D. Book, and X. S. Xie, "Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay," Appl. Phys. Lett. 80, 1505-1507 (2002).
[CrossRef]

D. Oron, N. Dudovich, D. Yelihn, and Y. Silberberg, "Quantum control of coherent anti-Stokes Raman processes," Phys. Rev. A 65, 4340814 (2002).
[CrossRef]

M. Müller and J. M. Schins, "Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy," J. Phys. Chem. B 106, 3715-3723 (2002).
[CrossRef]

J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, "Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles," J. Phys. Chem. B 106, 8493-8498 (2002).
[CrossRef]

D. Oron, N. Dudovich, and Y. Silberberg, "Single-pulse phase-contrast nonlinear Raman spectroscopy," Phys. Rev. Lett. 89, 27300 (2002).
[CrossRef]

G. W. H. Wurpel, J. M. Schins, and M. Müller, "Chemical specificity in 3D imaging with multiplex CARS microscopy," Opt. Lett. 27, 1093-1095 (2002).
[CrossRef]

2001 (5)

J. Cheng, L. D. Book, and X. S. Xie, "Polarization coherent anti-Stokes Raman scattering microscopy," Opt. Lett. 26, 1341-1343 (2001).
[CrossRef]

G. R. Holtom, B. D. Thrall, B. Chin, and D. Colson, "Achieving molecular selectivity in imaging using multiphoton Raman spectroscopy techniques," Traffic 2, 781-788 (2001).
[CrossRef] [PubMed]

A. Volkmer, J. Cheng, and X. S. Xie, "Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy," Phys. Rev. Lett. 87, 23901 (2001).
[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. B 105, 1277-1280 (2001).
[CrossRef]

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, "Vibrational bands of luminescent zinc(II)-octaethyl-porphyrin using a polarization-sensitive 'microscopic' multiplex CARS technique," J. Raman Spectrosc. 32, 495-501 (2001).
[CrossRef]

1999 (1)

R. H. Jenkins, R. Tuma, J. T. Juuti, D. H. Bamford and J. J. Thomas, "A novel Raman spectrophotometric method for quantitative measurement of nucleoside triphosphate hydrolysis," Biospectroscopy 5, 3-8 (1999).
[CrossRef] [PubMed]

1998 (1)

R. Mendelsohn and D. J. Moore, "Vibrational spectroscopic studies of lipid domains in biomembranes and model systems," Chem. Phys. Lipids 96, 141-157 (1998).
[CrossRef]

1997 (1)

1996 (1)

1992 (1)

1990 (1)

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, and T. M. Jovin, "Studying single living cells and chromosomes by confocal Raman microspectroscopy," Nature 347, 301-303 (1990).
[CrossRef] [PubMed]

1988 (1)

1986 (1)

K. T. Yue, C. L. Martin, D. Chen, P. Nelson, D. L. Sloan, and R. Callender, "Raman spectroscopy of oxidized and reduced nicotinamide adenine dinucleotides," Biochem 25, 4941-4947 (1986).
[CrossRef]

1984 (1)

R. A. MacPhail, H. L. Strauss, R. G. Snyder, and C. A. Elliger, "Carbon-hydrogen stretching modes and the structure of n-alkyl chains. 2. Long, all-trans chains," J. Phys. Chem. 88, 334-341 (1984).
[CrossRef]

1978 (1)

S. A. Akhmanov, A. F. Bunkin, S. G. Ivanov, and N. I. Koroteev, "Polarization active Raman spectroscopy and coherent Raman elipsometry," Sov. Phys. JETP 47, 667-678 (1978).

1969 (1)

L. Rimai, T. Cole, J. L. Parsons, J. T. Hickmott, Jr., and E. B. Carew, "Studies of Raman spectra of water solutions of Adenosine tri-, di-, and monophosphate and some related compounds," Biophys. J. 9, 320-329 (1969).
[CrossRef] [PubMed]

Akhmanov, S. A.

S. A. Akhmanov, A. F. Bunkin, S. G. Ivanov, and N. I. Koroteev, "Polarization active Raman spectroscopy and coherent Raman elipsometry," Sov. Phys. JETP 47, 667-678 (1978).

Arndt-Jovin, D. J.

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, and T. M. Jovin, "Studying single living cells and chromosomes by confocal Raman microspectroscopy," Nature 347, 301-303 (1990).
[CrossRef] [PubMed]

Asakura, T.

Bamford, D. H.

R. H. Jenkins, R. Tuma, J. T. Juuti, D. H. Bamford and J. J. Thomas, "A novel Raman spectrophotometric method for quantitative measurement of nucleoside triphosphate hydrolysis," Biospectroscopy 5, 3-8 (1999).
[CrossRef] [PubMed]

Beiting, E. J.

Bonn, M.

H. A. Rinia, M. Bonn, and M. Müller, "Quantitative multiplex CARS spectroscopy in congested spectral regions," J. Phys. Chem. B 110, 4472-4479 (2006).
[CrossRef] [PubMed]

Book, L. D.

A. Volkmer, L. D. Book, and X. S. Xie, "Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay," Appl. Phys. Lett. 80, 1505-1507 (2002).
[CrossRef]

J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, "Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles," J. Phys. Chem. B 106, 8493-8498 (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. B 105, 1277-1280 (2001).
[CrossRef]

J. Cheng, L. D. Book, and X. S. Xie, "Polarization coherent anti-Stokes Raman scattering microscopy," Opt. Lett. 26, 1341-1343 (2001).
[CrossRef]

Boppart, S.A.

D.L. Marks, C. Vinegoni, J.S. Bredfeldt and S.A. Boppart, "Interferometric differentiation between resonant coherent anti-Stokes Raman scattering and nonresonant four-wave-mixing processes," Appl. Phys. Lett. 85, 5787-5789 (2004).
[CrossRef]

Bredfeldt, J.S.

D.L. Marks, C. Vinegoni, J.S. Bredfeldt and S.A. Boppart, "Interferometric differentiation between resonant coherent anti-Stokes Raman scattering and nonresonant four-wave-mixing processes," Appl. Phys. Lett. 85, 5787-5789 (2004).
[CrossRef]

Bunkin, A. F.

S. A. Akhmanov, A. F. Bunkin, S. G. Ivanov, and N. I. Koroteev, "Polarization active Raman spectroscopy and coherent Raman elipsometry," Sov. Phys. JETP 47, 667-678 (1978).

Callender, R.

K. T. Yue, C. L. Martin, D. Chen, P. Nelson, D. L. Sloan, and R. Callender, "Raman spectroscopy of oxidized and reduced nicotinamide adenine dinucleotides," Biochem 25, 4941-4947 (1986).
[CrossRef]

Carew, E. B.

L. Rimai, T. Cole, J. L. Parsons, J. T. Hickmott, Jr., and E. B. Carew, "Studies of Raman spectra of water solutions of Adenosine tri-, di-, and monophosphate and some related compounds," Biophys. J. 9, 320-329 (1969).
[CrossRef] [PubMed]

Caster, A. G.

S. Lim, A. G. Caster, and S. R. Leone, "Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy," Phys. Rev. A 72, 41803 (2005).
[CrossRef]

Chen, D.

K. T. Yue, C. L. Martin, D. Chen, P. Nelson, D. L. Sloan, and R. Callender, "Raman spectroscopy of oxidized and reduced nicotinamide adenine dinucleotides," Biochem 25, 4941-4947 (1986).
[CrossRef]

Cheng, J.

J. Cheng, L. D. Book, and X. S. Xie, "Polarization coherent anti-Stokes Raman scattering microscopy," Opt. Lett. 26, 1341-1343 (2001).
[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. B 105, 1277-1280 (2001).
[CrossRef]

A. Volkmer, J. Cheng, and X. S. Xie, "Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy," Phys. Rev. Lett. 87, 23901 (2001).
[CrossRef]

Cheng, J. X.

J. X. Cheng and X. S. Xie, "Coherent Anti-Stokes Raman Scattering Microscopy: Instrumentation, Theory, and Applications," J. Phys. Chem. B 108, 827-840 (2004).
[CrossRef]

J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, "Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles," J. Phys. Chem. B 106, 8493-8498 (2002).
[CrossRef]

Chin, B.

G. R. Holtom, B. D. Thrall, B. Chin, and D. Colson, "Achieving molecular selectivity in imaging using multiphoton Raman spectroscopy techniques," Traffic 2, 781-788 (2001).
[CrossRef] [PubMed]

Cole, T.

L. Rimai, T. Cole, J. L. Parsons, J. T. Hickmott, Jr., and E. B. Carew, "Studies of Raman spectra of water solutions of Adenosine tri-, di-, and monophosphate and some related compounds," Biophys. J. 9, 320-329 (1969).
[CrossRef] [PubMed]

Colson, D.

G. R. Holtom, B. D. Thrall, B. Chin, and D. Colson, "Achieving molecular selectivity in imaging using multiphoton Raman spectroscopy techniques," Traffic 2, 781-788 (2001).
[CrossRef] [PubMed]

de Mul, F. F. M.

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, and T. M. Jovin, "Studying single living cells and chromosomes by confocal Raman microspectroscopy," Nature 347, 301-303 (1990).
[CrossRef] [PubMed]

Dudovich, N.

D. Oron, N. Dudovich, and Y. Silberberg, "Femtosecond Phase-and-Polarization Control for Background-Free Coherent Anti-Stokes Raman Spectroscopy," Phys. Rev. Lett. 90, 213902 (2003).
[CrossRef] [PubMed]

D. Oron, N. Dudovich, D. Yelihn, and Y. Silberberg, "Quantum control of coherent anti-Stokes Raman processes," Phys. Rev. A 65, 4340814 (2002).
[CrossRef]

D. Oron, N. Dudovich, and Y. Silberberg, "Single-pulse phase-contrast nonlinear Raman spectroscopy," Phys. Rev. Lett. 89, 27300 (2002).
[CrossRef]

Elliger, C. A.

R. A. MacPhail, H. L. Strauss, R. G. Snyder, and C. A. Elliger, "Carbon-hydrogen stretching modes and the structure of n-alkyl chains. 2. Long, all-trans chains," J. Phys. Chem. 88, 334-341 (1984).
[CrossRef]

Evans, C. L.

Ewart, P.

Greve, J.

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, "Vibrational bands of luminescent zinc(II)-octaethyl-porphyrin using a polarization-sensitive 'microscopic' multiplex CARS technique," J. Raman Spectrosc. 32, 495-501 (2001).
[CrossRef]

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, and T. M. Jovin, "Studying single living cells and chromosomes by confocal Raman microspectroscopy," Nature 347, 301-303 (1990).
[CrossRef] [PubMed]

Hickmott, J. T.

L. Rimai, T. Cole, J. L. Parsons, J. T. Hickmott, Jr., and E. B. Carew, "Studies of Raman spectra of water solutions of Adenosine tri-, di-, and monophosphate and some related compounds," Biophys. J. 9, 320-329 (1969).
[CrossRef] [PubMed]

Holtom, G. R.

G. R. Holtom, B. D. Thrall, B. Chin, and D. Colson, "Achieving molecular selectivity in imaging using multiphoton Raman spectroscopy techniques," Traffic 2, 781-788 (2001).
[CrossRef] [PubMed]

Ivanov, S. G.

S. A. Akhmanov, A. F. Bunkin, S. G. Ivanov, and N. I. Koroteev, "Polarization active Raman spectroscopy and coherent Raman elipsometry," Sov. Phys. JETP 47, 667-678 (1978).

Jenkins, R. H.

R. H. Jenkins, R. Tuma, J. T. Juuti, D. H. Bamford and J. J. Thomas, "A novel Raman spectrophotometric method for quantitative measurement of nucleoside triphosphate hydrolysis," Biospectroscopy 5, 3-8 (1999).
[CrossRef] [PubMed]

Jovin, T. M.

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, and T. M. Jovin, "Studying single living cells and chromosomes by confocal Raman microspectroscopy," Nature 347, 301-303 (1990).
[CrossRef] [PubMed]

Juuti, J. T.

R. H. Jenkins, R. Tuma, J. T. Juuti, D. H. Bamford and J. J. Thomas, "A novel Raman spectrophotometric method for quantitative measurement of nucleoside triphosphate hydrolysis," Biospectroscopy 5, 3-8 (1999).
[CrossRef] [PubMed]

Kaminski, C. F.

Koroteev, N. I.

S. A. Akhmanov, A. F. Bunkin, S. G. Ivanov, and N. I. Koroteev, "Polarization active Raman spectroscopy and coherent Raman elipsometry," Sov. Phys. JETP 47, 667-678 (1978).

Kraan, Y. M.

H. van Manen, Y. M. Kraan, D. Roos, and C. Otto, "Single-cell Raman and fluorescence microscopy reveal the association of lipid bodies with phagosomes in leukocytes," Proc. Natl. Acad. Sci. USA 102, 10159-10164 (2005).
[CrossRef] [PubMed]

Kruglik, S. G.

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, "Vibrational bands of luminescent zinc(II)-octaethyl-porphyrin using a polarization-sensitive 'microscopic' multiplex CARS technique," J. Raman Spectrosc. 32, 495-501 (2001).
[CrossRef]

Leone, S. R.

S. Lim, A. G. Caster, and S. R. Leone, "Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy," Phys. Rev. A 72, 41803 (2005).
[CrossRef]

Lim, S.

S. Lim, A. G. Caster, and S. R. Leone, "Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy," Phys. Rev. A 72, 41803 (2005).
[CrossRef]

MacPhail, R. A.

R. A. MacPhail, H. L. Strauss, R. G. Snyder, and C. A. Elliger, "Carbon-hydrogen stretching modes and the structure of n-alkyl chains. 2. Long, all-trans chains," J. Phys. Chem. 88, 334-341 (1984).
[CrossRef]

Marks, D.L.

D.L. Marks, C. Vinegoni, J.S. Bredfeldt and S.A. Boppart, "Interferometric differentiation between resonant coherent anti-Stokes Raman scattering and nonresonant four-wave-mixing processes," Appl. Phys. Lett. 85, 5787-5789 (2004).
[CrossRef]

Martin, C. L.

K. T. Yue, C. L. Martin, D. Chen, P. Nelson, D. L. Sloan, and R. Callender, "Raman spectroscopy of oxidized and reduced nicotinamide adenine dinucleotides," Biochem 25, 4941-4947 (1986).
[CrossRef]

Mendelsohn, R.

R. Mendelsohn and D. J. Moore, "Vibrational spectroscopic studies of lipid domains in biomembranes and model systems," Chem. Phys. Lipids 96, 141-157 (1998).
[CrossRef]

Moore, D. J.

R. Mendelsohn and D. J. Moore, "Vibrational spectroscopic studies of lipid domains in biomembranes and model systems," Chem. Phys. Lipids 96, 141-157 (1998).
[CrossRef]

Müller, M.

H. A. Rinia, M. Bonn, and M. Müller, "Quantitative multiplex CARS spectroscopy in congested spectral regions," J. Phys. Chem. B 110, 4472-4479 (2006).
[CrossRef] [PubMed]

G. W. H. Wurpel, J. M. Schins, and M. Müller, "Direct measurement of chain order in single lipid mono- and bilayers with multiplex CARS," J. Phys. Chem. B 108, 3400-3403 (2004).
[CrossRef]

M. Müller, J. M. Schins, and G. W. H. Wurpel, "Shot-noise limited detection sensitivity in multiplex CARS microscopy," SPIE 5323, 195-204 (2004).
[CrossRef]

M. Müller and J. M. Schins, "Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy," J. Phys. Chem. B 106, 3715-3723 (2002).
[CrossRef]

G. W. H. Wurpel, J. M. Schins, and M. Müller, "Chemical specificity in 3D imaging with multiplex CARS microscopy," Opt. Lett. 27, 1093-1095 (2002).
[CrossRef]

Nelson, P.

K. T. Yue, C. L. Martin, D. Chen, P. Nelson, D. L. Sloan, and R. Callender, "Raman spectroscopy of oxidized and reduced nicotinamide adenine dinucleotides," Biochem 25, 4941-4947 (1986).
[CrossRef]

Oron, D.

D. Oron, N. Dudovich, and Y. Silberberg, "Femtosecond Phase-and-Polarization Control for Background-Free Coherent Anti-Stokes Raman Spectroscopy," Phys. Rev. Lett. 90, 213902 (2003).
[CrossRef] [PubMed]

D. Oron, N. Dudovich, D. Yelihn, and Y. Silberberg, "Quantum control of coherent anti-Stokes Raman processes," Phys. Rev. A 65, 4340814 (2002).
[CrossRef]

D. Oron, N. Dudovich, and Y. Silberberg, "Single-pulse phase-contrast nonlinear Raman spectroscopy," Phys. Rev. Lett. 89, 27300 (2002).
[CrossRef]

Otto, C.

H. van Manen, Y. M. Kraan, D. Roos, and C. Otto, "Single-cell Raman and fluorescence microscopy reveal the association of lipid bodies with phagosomes in leukocytes," Proc. Natl. Acad. Sci. USA 102, 10159-10164 (2005).
[CrossRef] [PubMed]

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, "Vibrational bands of luminescent zinc(II)-octaethyl-porphyrin using a polarization-sensitive 'microscopic' multiplex CARS technique," J. Raman Spectrosc. 32, 495-501 (2001).
[CrossRef]

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, and T. M. Jovin, "Studying single living cells and chromosomes by confocal Raman microspectroscopy," Nature 347, 301-303 (1990).
[CrossRef] [PubMed]

Parsons, J. L.

L. Rimai, T. Cole, J. L. Parsons, J. T. Hickmott, Jr., and E. B. Carew, "Studies of Raman spectra of water solutions of Adenosine tri-, di-, and monophosphate and some related compounds," Biophys. J. 9, 320-329 (1969).
[CrossRef] [PubMed]

Peiponen, K.-E.

Potma, E. O.

Puppels, G. J.

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, and T. M. Jovin, "Studying single living cells and chromosomes by confocal Raman microspectroscopy," Nature 347, 301-303 (1990).
[CrossRef] [PubMed]

Rimai, L.

L. Rimai, T. Cole, J. L. Parsons, J. T. Hickmott, Jr., and E. B. Carew, "Studies of Raman spectra of water solutions of Adenosine tri-, di-, and monophosphate and some related compounds," Biophys. J. 9, 320-329 (1969).
[CrossRef] [PubMed]

Rinia, H. A.

H. A. Rinia, M. Bonn, and M. Müller, "Quantitative multiplex CARS spectroscopy in congested spectral regions," J. Phys. Chem. B 110, 4472-4479 (2006).
[CrossRef] [PubMed]

Robert-Nicoud, M.

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, and T. M. Jovin, "Studying single living cells and chromosomes by confocal Raman microspectroscopy," Nature 347, 301-303 (1990).
[CrossRef] [PubMed]

Roos, D.

H. van Manen, Y. M. Kraan, D. Roos, and C. Otto, "Single-cell Raman and fluorescence microscopy reveal the association of lipid bodies with phagosomes in leukocytes," Proc. Natl. Acad. Sci. USA 102, 10159-10164 (2005).
[CrossRef] [PubMed]

Schins, J. M.

G. W. H. Wurpel, J. M. Schins, and M. Müller, "Direct measurement of chain order in single lipid mono- and bilayers with multiplex CARS," J. Phys. Chem. B 108, 3400-3403 (2004).
[CrossRef]

M. Müller, J. M. Schins, and G. W. H. Wurpel, "Shot-noise limited detection sensitivity in multiplex CARS microscopy," SPIE 5323, 195-204 (2004).
[CrossRef]

M. Müller and J. M. Schins, "Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy," J. Phys. Chem. B 106, 3715-3723 (2002).
[CrossRef]

G. W. H. Wurpel, J. M. Schins, and M. Müller, "Chemical specificity in 3D imaging with multiplex CARS microscopy," Opt. Lett. 27, 1093-1095 (2002).
[CrossRef]

Silberberg, Y.

D. Oron, N. Dudovich, and Y. Silberberg, "Femtosecond Phase-and-Polarization Control for Background-Free Coherent Anti-Stokes Raman Spectroscopy," Phys. Rev. Lett. 90, 213902 (2003).
[CrossRef] [PubMed]

D. Oron, N. Dudovich, D. Yelihn, and Y. Silberberg, "Quantum control of coherent anti-Stokes Raman processes," Phys. Rev. A 65, 4340814 (2002).
[CrossRef]

D. Oron, N. Dudovich, and Y. Silberberg, "Single-pulse phase-contrast nonlinear Raman spectroscopy," Phys. Rev. Lett. 89, 27300 (2002).
[CrossRef]

Sloan, D. L.

K. T. Yue, C. L. Martin, D. Chen, P. Nelson, D. L. Sloan, and R. Callender, "Raman spectroscopy of oxidized and reduced nicotinamide adenine dinucleotides," Biochem 25, 4941-4947 (1986).
[CrossRef]

Snyder, R. G.

R. A. MacPhail, H. L. Strauss, R. G. Snyder, and C. A. Elliger, "Carbon-hydrogen stretching modes and the structure of n-alkyl chains. 2. Long, all-trans chains," J. Phys. Chem. 88, 334-341 (1984).
[CrossRef]

Strauss, H. L.

R. A. MacPhail, H. L. Strauss, R. G. Snyder, and C. A. Elliger, "Carbon-hydrogen stretching modes and the structure of n-alkyl chains. 2. Long, all-trans chains," J. Phys. Chem. 88, 334-341 (1984).
[CrossRef]

Thomas, J. J.

R. H. Jenkins, R. Tuma, J. T. Juuti, D. H. Bamford and J. J. Thomas, "A novel Raman spectrophotometric method for quantitative measurement of nucleoside triphosphate hydrolysis," Biospectroscopy 5, 3-8 (1999).
[CrossRef] [PubMed]

Thrall, B. D.

G. R. Holtom, B. D. Thrall, B. Chin, and D. Colson, "Achieving molecular selectivity in imaging using multiphoton Raman spectroscopy techniques," Traffic 2, 781-788 (2001).
[CrossRef] [PubMed]

Tuma, R.

R. H. Jenkins, R. Tuma, J. T. Juuti, D. H. Bamford and J. J. Thomas, "A novel Raman spectrophotometric method for quantitative measurement of nucleoside triphosphate hydrolysis," Biospectroscopy 5, 3-8 (1999).
[CrossRef] [PubMed]

van Manen, H.

H. van Manen, Y. M. Kraan, D. Roos, and C. Otto, "Single-cell Raman and fluorescence microscopy reveal the association of lipid bodies with phagosomes in leukocytes," Proc. Natl. Acad. Sci. USA 102, 10159-10164 (2005).
[CrossRef] [PubMed]

Vartiainen, E. M.

Vinegoni, C.

D.L. Marks, C. Vinegoni, J.S. Bredfeldt and S.A. Boppart, "Interferometric differentiation between resonant coherent anti-Stokes Raman scattering and nonresonant four-wave-mixing processes," Appl. Phys. Lett. 85, 5787-5789 (2004).
[CrossRef]

Volkmer, A.

A. Volkmer, "Vibrational imaging and microspectroscopies based on coherent anti-Stokes Raman scattering microscopy," J. Phys. D: Appl. Phys. 38, R59-R81 (2005).
[CrossRef]

J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, "Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles," J. Phys. Chem. B 106, 8493-8498 (2002).
[CrossRef]

A. Volkmer, L. D. Book, and X. S. Xie, "Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay," Appl. Phys. Lett. 80, 1505-1507 (2002).
[CrossRef]

A. Volkmer, J. Cheng, and X. S. Xie, "Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy," Phys. Rev. Lett. 87, 23901 (2001).
[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. B 105, 1277-1280 (2001).
[CrossRef]

Voroshilov, A.

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, "Vibrational bands of luminescent zinc(II)-octaethyl-porphyrin using a polarization-sensitive 'microscopic' multiplex CARS technique," J. Raman Spectrosc. 32, 495-501 (2001).
[CrossRef]

Wurpel, G. W. H.

M. Müller, J. M. Schins, and G. W. H. Wurpel, "Shot-noise limited detection sensitivity in multiplex CARS microscopy," SPIE 5323, 195-204 (2004).
[CrossRef]

G. W. H. Wurpel, J. M. Schins, and M. Müller, "Direct measurement of chain order in single lipid mono- and bilayers with multiplex CARS," J. Phys. Chem. B 108, 3400-3403 (2004).
[CrossRef]

G. W. H. Wurpel, J. M. Schins, and M. Müller, "Chemical specificity in 3D imaging with multiplex CARS microscopy," Opt. Lett. 27, 1093-1095 (2002).
[CrossRef]

Xie, X. S.

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]

J. X. Cheng and X. S. Xie, "Coherent Anti-Stokes Raman Scattering Microscopy: Instrumentation, Theory, and Applications," J. Phys. Chem. B 108, 827-840 (2004).
[CrossRef]

J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, "Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles," J. Phys. Chem. B 106, 8493-8498 (2002).
[CrossRef]

A. Volkmer, L. D. Book, and X. S. Xie, "Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay," Appl. Phys. Lett. 80, 1505-1507 (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. B 105, 1277-1280 (2001).
[CrossRef]

A. Volkmer, J. Cheng, and X. S. Xie, "Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy," Phys. Rev. Lett. 87, 23901 (2001).
[CrossRef]

J. Cheng, L. D. Book, and X. S. Xie, "Polarization coherent anti-Stokes Raman scattering microscopy," Opt. Lett. 26, 1341-1343 (2001).
[CrossRef]

Yelihn, D.

D. Oron, N. Dudovich, D. Yelihn, and Y. Silberberg, "Quantum control of coherent anti-Stokes Raman processes," Phys. Rev. A 65, 4340814 (2002).
[CrossRef]

Yue, K. T.

K. T. Yue, C. L. Martin, D. Chen, P. Nelson, D. L. Sloan, and R. Callender, "Raman spectroscopy of oxidized and reduced nicotinamide adenine dinucleotides," Biochem 25, 4941-4947 (1986).
[CrossRef]

Yueh, F. Y.

Appl. Opt. (2)

Appl. Phys. Lett. (2)

D.L. Marks, C. Vinegoni, J.S. Bredfeldt and S.A. Boppart, "Interferometric differentiation between resonant coherent anti-Stokes Raman scattering and nonresonant four-wave-mixing processes," Appl. Phys. Lett. 85, 5787-5789 (2004).
[CrossRef]

A. Volkmer, L. D. Book, and X. S. Xie, "Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay," Appl. Phys. Lett. 80, 1505-1507 (2002).
[CrossRef]

Appl. Spectrosc. (1)

Biochem (1)

K. T. Yue, C. L. Martin, D. Chen, P. Nelson, D. L. Sloan, and R. Callender, "Raman spectroscopy of oxidized and reduced nicotinamide adenine dinucleotides," Biochem 25, 4941-4947 (1986).
[CrossRef]

Biophys. J. (1)

L. Rimai, T. Cole, J. L. Parsons, J. T. Hickmott, Jr., and E. B. Carew, "Studies of Raman spectra of water solutions of Adenosine tri-, di-, and monophosphate and some related compounds," Biophys. J. 9, 320-329 (1969).
[CrossRef] [PubMed]

Biospectroscopy (1)

R. H. Jenkins, R. Tuma, J. T. Juuti, D. H. Bamford and J. J. Thomas, "A novel Raman spectrophotometric method for quantitative measurement of nucleoside triphosphate hydrolysis," Biospectroscopy 5, 3-8 (1999).
[CrossRef] [PubMed]

Chem. Phys. Lipids (1)

R. Mendelsohn and D. J. Moore, "Vibrational spectroscopic studies of lipid domains in biomembranes and model systems," Chem. Phys. Lipids 96, 141-157 (1998).
[CrossRef]

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

J. Phys. Chem. (1)

R. A. MacPhail, H. L. Strauss, R. G. Snyder, and C. A. Elliger, "Carbon-hydrogen stretching modes and the structure of n-alkyl chains. 2. Long, all-trans chains," J. Phys. Chem. 88, 334-341 (1984).
[CrossRef]

J. Phys. Chem. B (6)

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. B 105, 1277-1280 (2001).
[CrossRef]

H. A. Rinia, M. Bonn, and M. Müller, "Quantitative multiplex CARS spectroscopy in congested spectral regions," J. Phys. Chem. B 110, 4472-4479 (2006).
[CrossRef] [PubMed]

J. X. Cheng and X. S. Xie, "Coherent Anti-Stokes Raman Scattering Microscopy: Instrumentation, Theory, and Applications," J. Phys. Chem. B 108, 827-840 (2004).
[CrossRef]

M. Müller and J. M. Schins, "Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy," J. Phys. Chem. B 106, 3715-3723 (2002).
[CrossRef]

J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, "Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles," J. Phys. Chem. B 106, 8493-8498 (2002).
[CrossRef]

G. W. H. Wurpel, J. M. Schins, and M. Müller, "Direct measurement of chain order in single lipid mono- and bilayers with multiplex CARS," J. Phys. Chem. B 108, 3400-3403 (2004).
[CrossRef]

J. Phys. D: Appl. Phys. (1)

A. Volkmer, "Vibrational imaging and microspectroscopies based on coherent anti-Stokes Raman scattering microscopy," J. Phys. D: Appl. Phys. 38, R59-R81 (2005).
[CrossRef]

J. Raman Spectrosc. (1)

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, "Vibrational bands of luminescent zinc(II)-octaethyl-porphyrin using a polarization-sensitive 'microscopic' multiplex CARS technique," J. Raman Spectrosc. 32, 495-501 (2001).
[CrossRef]

Nature (1)

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, and T. M. Jovin, "Studying single living cells and chromosomes by confocal Raman microspectroscopy," Nature 347, 301-303 (1990).
[CrossRef] [PubMed]

Opt. Lett. (3)

Phys. Rev. A (2)

S. Lim, A. G. Caster, and S. R. Leone, "Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy," Phys. Rev. A 72, 41803 (2005).
[CrossRef]

D. Oron, N. Dudovich, D. Yelihn, and Y. Silberberg, "Quantum control of coherent anti-Stokes Raman processes," Phys. Rev. A 65, 4340814 (2002).
[CrossRef]

Phys. Rev. Lett. (3)

D. Oron, N. Dudovich, and Y. Silberberg, "Femtosecond Phase-and-Polarization Control for Background-Free Coherent Anti-Stokes Raman Spectroscopy," Phys. Rev. Lett. 90, 213902 (2003).
[CrossRef] [PubMed]

A. Volkmer, J. Cheng, and X. S. Xie, "Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy," Phys. Rev. Lett. 87, 23901 (2001).
[CrossRef]

D. Oron, N. Dudovich, and Y. Silberberg, "Single-pulse phase-contrast nonlinear Raman spectroscopy," Phys. Rev. Lett. 89, 27300 (2002).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

H. van Manen, Y. M. Kraan, D. Roos, and C. Otto, "Single-cell Raman and fluorescence microscopy reveal the association of lipid bodies with phagosomes in leukocytes," Proc. Natl. Acad. Sci. USA 102, 10159-10164 (2005).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

S. A. Akhmanov, A. F. Bunkin, S. G. Ivanov, and N. I. Koroteev, "Polarization active Raman spectroscopy and coherent Raman elipsometry," Sov. Phys. JETP 47, 667-678 (1978).

SPIE (1)

M. Müller, J. M. Schins, and G. W. H. Wurpel, "Shot-noise limited detection sensitivity in multiplex CARS microscopy," SPIE 5323, 195-204 (2004).
[CrossRef]

Traffic (1)

G. R. Holtom, B. D. Thrall, B. Chin, and D. Colson, "Achieving molecular selectivity in imaging using multiphoton Raman spectroscopy techniques," Traffic 2, 781-788 (2001).
[CrossRef] [PubMed]

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Figures (1)

Fig. 1.
Fig. 1.

The CARS line-shapes in the vicinity of vibrational resonances of DMPC (a) and ADP/AMP/ATP (b). The corresponding ME phases, ψ(ω), (solid lines) and the estimated background phase, -φ est (a)), (dotted lines) of DMPC (c) and ADP/AMP/ATP (d). The Raman line-shapes obtained from CARS spectra (blue lines) and the corresponding spontaneous Raman scattering spectra (red lines) of DMPC (e) and ADP/AMP/ATP (f).

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

I CARS ( ω as ) P ( 3 ) ( ω as ) 2 = E pu 2 E pr 2 E S ( ω as ) 2 χ 1111 ( 3 ) ω as ω pu −ω S ω pr 2
χ 1111 ( 3 ) ( ω as ) = χ NR ( 3 ) + χ R ( 3 ) ( ω as )
χ R ( 3 ) ( ω as ) = j A j Ω j ( ω pu ω S ) i Γ j
S ( ω as ) = χ NR ( 3 ) + χ R ( 3 ) ( ω as ) 2 ω NR ( 3 ) 2 = χ nr + χ r ( ω as ) 2 = χ nr 2 + 2 χ nr Re [ χ r ( ω as ) ] + χ r ( ω as ) 2
I Raman ( ω ) Im [ χ R ( 3 ) ( ω ) ] = j A j Γ j ( Ω j ω ) 2 + Γ j 2
S ( ν ) = β 1 + k = 1 M a k exp ( 2 π i ) 2 = β A M ( ν ) 2
ν = ω as ω min ω max ω min
[ C 0 C 1 * C M * C 1 C 0 C M 1 * C M C M 1 C 0 ] [ 1 a 1 a M ] = [ β 2 0 0 ]
C m = L 1 j = 0 L 1 S ( ν j ) exp ( 2 π i m ν j )
χ nr + χ r ( ν ) = S ( ν ) exp [ i θ ( ν ) ] β exp [ i θ ( ν ) ] A M ( ν ) = β exp [ i θ ( ν ) i ψ ( ν ) ] A M ( ν ) exp [ i ψ ( ν ) ] = β exp [ ( ν ) ] A M * ( ν )
θ ( ν ) = tan 1 [ Im χ r ( ν ) χ nr + Re χ r ( ν ) ] 0
θ ( ν ) θ est ( ν ) = φ est ( ν ) + ψ ( ν )
Im = [ χ r ( ν ) ] S ( ν ) sin θ est ( ν )

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