Abstract

We propose an approach, based on wavelet prism decomposition analysis, for correcting experimental artefacts in a coherent anti-Stokes Raman scattering (CARS) spectrum. This method allows estimating and eliminating a slowly varying modulation error function in the measured normalized CARS spectrum and yields a corrected CARS line-shape. The main advantage of the approach is that the spectral phase and amplitude corrections are avoided in the retrieved Raman line-shape spectrum, thus significantly simplifying the quantitative reconstruction of the sample’s Raman response from a normalized CARS spectrum in the presence of experimental artefacts. Moreover, the approach obviates the need for assumptions about the modulation error distribution and the chemical composition of the specimens under study. The method is quantitatively validated on normalized CARS spectra recorded for equimolar aqueous solutions of D-fructose, D-glucose, and their disaccharide combination sucrose.

© 2016 Optical Society of America

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References

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  1. C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, “Vibrational bands of luminescent zinc(II)-octaethylporphyrin using a polarization-sensitive “microscopic” multiplex CARS technique,” J. Raman Spectrosc. 32(6-7), 495–501 (2001).
    [Crossref]
  2. J. 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(34), 8493–8498 (2002).
    [Crossref]
  3. M. Müller and J. M. Schins, “Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy,” J. Phys. Chem. B 106(14), 3715–3723 (2002).
    [Crossref]
  4. H. A. Rinia, K. N. J. Burger, M. Bonn, and M. Müller, “Quantitative label-free imaging of lipid composition and packing of individual cellular lipid droplets using multiplex CARS microscopy,” Biophys. J. 95(10), 4908–4914 (2008).
    [Crossref] [PubMed]
  5. M. Okuno, H. Kano, P. Leproux, V. Couderc, J. P. R. Day, M. Bonn, and H. O. Hamaguchi, “Quantitative CARS molecular fingerprinting of single living cells with the use of the maximum entropy method,” Angew. Chem. Int. Ed. Engl. 49(38), 6773–6777 (2010).
    [Crossref] [PubMed]
  6. K. F. Domke, T. A. Riemer, G. Rago, A. N. Parvulescu, P. C. A. Bruijnincx, A. Enejder, B. M. Weckhuysen, and M. Bonn, “Tracing catalytic conversion on single zeolite crystals in 3D with nonlinear spectromicroscopy,” J. Am. Chem. Soc. 134(2), 1124–1129 (2012).
    [Crossref] [PubMed]
  7. C. H. Camp and M. T. Cicerone, “Chemically sensitive bioimaging with coherent Raman scattering,” Nat. Photonics 9(5), 295–305 (2015).
    [Crossref]
  8. E. M. Vartiainen, “Phase retrieval approach for coherent anti-Stokes Raman scattering spectrum analysis,” J. Opt. Soc. Am. B 9(8), 1209–1214 (1992).
    [Crossref]
  9. E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, “Phase retrieval in optical spectroscopy: resolving optical constants from power spectra,” Appl. Spectrosc. 50(10), 1283–1289 (1996).
    [Crossref]
  10. E. M. Vartiainen, H. A. Rinia, M. Müller, and M. Bonn, “Direct extraction of Raman line-shapes from congested CARS spectra,” Opt. Express 14(8), 3622–3630 (2006).
    [Crossref] [PubMed]
  11. Y. Liu, Y. J. Lee, and M. T. Cicerone, “Broadband CARS spectral phase retrieval using a time-domain Kramers-Kronig transform,” Opt. Lett. 34(9), 1363–1365 (2009).
    [Crossref] [PubMed]
  12. M. T. Cicerone, K. A. Aamer, Y. J. Lee, and E. Vartiainen, “Maximum entropy and time-domain Kramers-Kronig phase retrieval approaches are functionally equivalent for CARS microspectroscopy,” J. Raman Spectrosc. 43(5), 637–643 (2012).
    [Crossref]
  13. E. M. Vartiainen and K.-E. Peiponen, “Optical and terahertz spectra analysis by the maximum entropy method,” Rep. Prog. Phys. 76(6), 066401 (2013).
    [Crossref] [PubMed]
  14. A. Volkmer, “Vibrational imaging and microspectroscopies based on coherent anti-Stokes Raman scattering microscopy,” J. Phys. Appl. Phys. 38(5), R59–R81 (2005).
    [Crossref]
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    [Crossref]
  16. J. P. R. Day, K. F. Domke, G. Rago, H. Kano, H. O. Hamaguchi, E. M. Vartiainen, and M. Bonn, “Quantitative coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Phys. Chem. B 115(24), 7713–7725 (2011).
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    [Crossref]
  19. J. Li, L.-P. Choo-Smith, Z. Tang, and M. G. Sowa, “Background removal from polarized Raman spectra of tooth enamel using the wavelet transform,” J. Raman Spectrosc. 42(4), 580–585 (2011).
    [Crossref]
  20. C. H. Camp, Y. J. Lee, and M. T. Cicerone, “Quantitative, comparable coherent anti-Stokes Raman scattering (CARS) spectroscopy: correcting errors in phase retrieval,” J. Raman Spectrosc. 47(4), 408-415 (2015).
  21. J. S. Gomez, “Coherent Raman spectroscopy,” in: Modern Techniques in Raman Spectroscopy, J. J. Laserna, ed. (Wiley, 1996).
  22. M. A. Yuratich and D. C. Hanna, “Coherent anti-Stokes Raman spectroscopy (CARS): Selection rules, depolarization ratios and rotational structure,” Mol. Phys. 33(3), 671–682 (1977).
    [Crossref]
  23. R. Igarashi, Y. Adachi, and S. Maeda, “Resonance CARS and CSRS line shapes of Ni(II)‐octaethylporphyrin,” J. Chem. Phys. 72(8), 4308–4314 (1980).
    [Crossref]
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    [Crossref]
  28. S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11(7), 674–693 (1989).
    [Crossref]
  29. H. A. Rinia, M. Bonn, and M. Müller, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” J. Phys. Chem. B 110(9), 4472–4479 (2006).
    [Crossref] [PubMed]
  30. M. Mathlouthi and D. V. Luu, “Laser-Raman spectra of d-fructose in aqueous solution,” Carbohydr. Res. 78(2), 225–233 (1980).
    [Crossref]
  31. M. Mathlouthi and D. Vinh Luu, “Laser-Raman spectra of d-glucose and sucrose in aqueous solution,” Carbohydr. Res. 81(2), 203–212 (1980).
    [Crossref]
  32. S. Söderholm, Y. H. Roos, N. Meinander, and M. Hotokka, “Raman spectra of fructose and glucose in the amorphous and crystalline states,” J. Raman Spectrosc. 30(11), 1009–1018 (1999).
    [Crossref]
  33. P. L. Polavarapu, S. R. Chatterjee, and D. F. Michalska, “Infrared investigations of sucrose in aqueous solutions,” Carbohydr. Res. 137, 253–258 (1985).
    [Crossref]
  34. M. Kacuráková and M. Mathlouthi, “FTIR and laser-Raman spectra of oligosaccharides in water: characterization of the glycosidic bond,” Carbohydr. Res. 284(2), 145–157 (1996).
    [Crossref] [PubMed]

2015 (2)

C. H. Camp, Y. J. Lee, and M. T. Cicerone, “Quantitative, comparable coherent anti-Stokes Raman scattering (CARS) spectroscopy: correcting errors in phase retrieval,” J. Raman Spectrosc. 47(4), 408-415 (2015).

C. H. Camp and M. T. Cicerone, “Chemically sensitive bioimaging with coherent Raman scattering,” Nat. Photonics 9(5), 295–305 (2015).
[Crossref]

2013 (1)

E. M. Vartiainen and K.-E. Peiponen, “Optical and terahertz spectra analysis by the maximum entropy method,” Rep. Prog. Phys. 76(6), 066401 (2013).
[Crossref] [PubMed]

2012 (2)

M. T. Cicerone, K. A. Aamer, Y. J. Lee, and E. Vartiainen, “Maximum entropy and time-domain Kramers-Kronig phase retrieval approaches are functionally equivalent for CARS microspectroscopy,” J. Raman Spectrosc. 43(5), 637–643 (2012).
[Crossref]

K. F. Domke, T. A. Riemer, G. Rago, A. N. Parvulescu, P. C. A. Bruijnincx, A. Enejder, B. M. Weckhuysen, and M. Bonn, “Tracing catalytic conversion on single zeolite crystals in 3D with nonlinear spectromicroscopy,” J. Am. Chem. Soc. 134(2), 1124–1129 (2012).
[Crossref] [PubMed]

2011 (2)

J. P. R. Day, K. F. Domke, G. Rago, H. Kano, H. O. Hamaguchi, E. M. Vartiainen, and M. Bonn, “Quantitative coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Phys. Chem. B 115(24), 7713–7725 (2011).
[Crossref] [PubMed]

J. Li, L.-P. Choo-Smith, Z. Tang, and M. G. Sowa, “Background removal from polarized Raman spectra of tooth enamel using the wavelet transform,” J. Raman Spectrosc. 42(4), 580–585 (2011).
[Crossref]

2010 (1)

M. Okuno, H. Kano, P. Leproux, V. Couderc, J. P. R. Day, M. Bonn, and H. O. Hamaguchi, “Quantitative CARS molecular fingerprinting of single living cells with the use of the maximum entropy method,” Angew. Chem. Int. Ed. Engl. 49(38), 6773–6777 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

H. A. Rinia, K. N. J. Burger, M. Bonn, and M. Müller, “Quantitative label-free imaging of lipid composition and packing of individual cellular lipid droplets using multiplex CARS microscopy,” Biophys. J. 95(10), 4908–4914 (2008).
[Crossref] [PubMed]

2007 (2)

Y. Hu, T. Jiang, A. Shen, W. Li, X. Wang, and J. Hu, “A background elimination method based on wavelet transform for Raman spectra,” Chemom. Intell. Lab. Syst. 85(1), 94–101 (2007).
[Crossref]

M. Müller, H. A. Rinia, M. Bonn, E. M. Vartiainen, M. Lisker, and A. van Bel, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” Proc. SPIE 6442, 644206 (2007).
[Crossref]

2006 (2)

H. A. Rinia, M. Bonn, and M. Müller, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” J. Phys. Chem. B 110(9), 4472–4479 (2006).
[Crossref] [PubMed]

E. M. Vartiainen, H. A. Rinia, M. Müller, and M. Bonn, “Direct extraction of Raman line-shapes from congested CARS spectra,” Opt. Express 14(8), 3622–3630 (2006).
[Crossref] [PubMed]

2005 (1)

A. Volkmer, “Vibrational imaging and microspectroscopies based on coherent anti-Stokes Raman scattering microscopy,” J. Phys. Appl. Phys. 38(5), R59–R81 (2005).
[Crossref]

2002 (3)

H.-W. Tan and S. D. Brown, “Wavelet analysis applied to removing non-constant, varying spectroscopic background in multivariate calibration,” J. Chemometr. 16(5), 228–240 (2002).
[Crossref]

J. 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(34), 8493–8498 (2002).
[Crossref]

M. Müller and J. M. Schins, “Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy,” J. Phys. Chem. B 106(14), 3715–3723 (2002).
[Crossref]

2001 (1)

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, “Vibrational bands of luminescent zinc(II)-octaethylporphyrin using a polarization-sensitive “microscopic” multiplex CARS technique,” J. Raman Spectrosc. 32(6-7), 495–501 (2001).
[Crossref]

1999 (1)

S. Söderholm, Y. H. Roos, N. Meinander, and M. Hotokka, “Raman spectra of fructose and glucose in the amorphous and crystalline states,” J. Raman Spectrosc. 30(11), 1009–1018 (1999).
[Crossref]

1996 (2)

M. Kacuráková and M. Mathlouthi, “FTIR and laser-Raman spectra of oligosaccharides in water: characterization of the glycosidic bond,” Carbohydr. Res. 284(2), 145–157 (1996).
[Crossref] [PubMed]

E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, “Phase retrieval in optical spectroscopy: resolving optical constants from power spectra,” Appl. Spectrosc. 50(10), 1283–1289 (1996).
[Crossref]

1992 (1)

1989 (1)

S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11(7), 674–693 (1989).
[Crossref]

1985 (1)

P. L. Polavarapu, S. R. Chatterjee, and D. F. Michalska, “Infrared investigations of sucrose in aqueous solutions,” Carbohydr. Res. 137, 253–258 (1985).
[Crossref]

1980 (3)

M. Mathlouthi and D. V. Luu, “Laser-Raman spectra of d-fructose in aqueous solution,” Carbohydr. Res. 78(2), 225–233 (1980).
[Crossref]

M. Mathlouthi and D. Vinh Luu, “Laser-Raman spectra of d-glucose and sucrose in aqueous solution,” Carbohydr. Res. 81(2), 203–212 (1980).
[Crossref]

R. Igarashi, Y. Adachi, and S. Maeda, “Resonance CARS and CSRS line shapes of Ni(II)‐octaethylporphyrin,” J. Chem. Phys. 72(8), 4308–4314 (1980).
[Crossref]

1977 (1)

M. A. Yuratich and D. C. Hanna, “Coherent anti-Stokes Raman spectroscopy (CARS): Selection rules, depolarization ratios and rotational structure,” Mol. Phys. 33(3), 671–682 (1977).
[Crossref]

Aamer, K. A.

M. T. Cicerone, K. A. Aamer, Y. J. Lee, and E. Vartiainen, “Maximum entropy and time-domain Kramers-Kronig phase retrieval approaches are functionally equivalent for CARS microspectroscopy,” J. Raman Spectrosc. 43(5), 637–643 (2012).
[Crossref]

Adachi, Y.

R. Igarashi, Y. Adachi, and S. Maeda, “Resonance CARS and CSRS line shapes of Ni(II)‐octaethylporphyrin,” J. Chem. Phys. 72(8), 4308–4314 (1980).
[Crossref]

Asakura, T.

Bonn, M.

K. F. Domke, T. A. Riemer, G. Rago, A. N. Parvulescu, P. C. A. Bruijnincx, A. Enejder, B. M. Weckhuysen, and M. Bonn, “Tracing catalytic conversion on single zeolite crystals in 3D with nonlinear spectromicroscopy,” J. Am. Chem. Soc. 134(2), 1124–1129 (2012).
[Crossref] [PubMed]

J. P. R. Day, K. F. Domke, G. Rago, H. Kano, H. O. Hamaguchi, E. M. Vartiainen, and M. Bonn, “Quantitative coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Phys. Chem. B 115(24), 7713–7725 (2011).
[Crossref] [PubMed]

M. Okuno, H. Kano, P. Leproux, V. Couderc, J. P. R. Day, M. Bonn, and H. O. Hamaguchi, “Quantitative CARS molecular fingerprinting of single living cells with the use of the maximum entropy method,” Angew. Chem. Int. Ed. Engl. 49(38), 6773–6777 (2010).
[Crossref] [PubMed]

H. A. Rinia, K. N. J. Burger, M. Bonn, and M. Müller, “Quantitative label-free imaging of lipid composition and packing of individual cellular lipid droplets using multiplex CARS microscopy,” Biophys. J. 95(10), 4908–4914 (2008).
[Crossref] [PubMed]

M. Müller, H. A. Rinia, M. Bonn, E. M. Vartiainen, M. Lisker, and A. van Bel, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” Proc. SPIE 6442, 644206 (2007).
[Crossref]

E. M. Vartiainen, H. A. Rinia, M. Müller, and M. Bonn, “Direct extraction of Raman line-shapes from congested CARS spectra,” Opt. Express 14(8), 3622–3630 (2006).
[Crossref] [PubMed]

H. A. Rinia, M. Bonn, and M. Müller, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” J. Phys. Chem. B 110(9), 4472–4479 (2006).
[Crossref] [PubMed]

Book, L. D.

J. 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(34), 8493–8498 (2002).
[Crossref]

Brown, S. D.

H.-W. Tan and S. D. Brown, “Wavelet analysis applied to removing non-constant, varying spectroscopic background in multivariate calibration,” J. Chemometr. 16(5), 228–240 (2002).
[Crossref]

Bruijnincx, P. C. A.

K. F. Domke, T. A. Riemer, G. Rago, A. N. Parvulescu, P. C. A. Bruijnincx, A. Enejder, B. M. Weckhuysen, and M. Bonn, “Tracing catalytic conversion on single zeolite crystals in 3D with nonlinear spectromicroscopy,” J. Am. Chem. Soc. 134(2), 1124–1129 (2012).
[Crossref] [PubMed]

Burger, K. N. J.

H. A. Rinia, K. N. J. Burger, M. Bonn, and M. Müller, “Quantitative label-free imaging of lipid composition and packing of individual cellular lipid droplets using multiplex CARS microscopy,” Biophys. J. 95(10), 4908–4914 (2008).
[Crossref] [PubMed]

Camp, C. H.

C. H. Camp and M. T. Cicerone, “Chemically sensitive bioimaging with coherent Raman scattering,” Nat. Photonics 9(5), 295–305 (2015).
[Crossref]

C. H. Camp, Y. J. Lee, and M. T. Cicerone, “Quantitative, comparable coherent anti-Stokes Raman scattering (CARS) spectroscopy: correcting errors in phase retrieval,” J. Raman Spectrosc. 47(4), 408-415 (2015).

Chatterjee, S. R.

P. L. Polavarapu, S. R. Chatterjee, and D. F. Michalska, “Infrared investigations of sucrose in aqueous solutions,” Carbohydr. Res. 137, 253–258 (1985).
[Crossref]

Cheng, J.

J. 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(34), 8493–8498 (2002).
[Crossref]

Choo-Smith, L.-P.

J. Li, L.-P. Choo-Smith, Z. Tang, and M. G. Sowa, “Background removal from polarized Raman spectra of tooth enamel using the wavelet transform,” J. Raman Spectrosc. 42(4), 580–585 (2011).
[Crossref]

Cicerone, M. T.

C. H. Camp, Y. J. Lee, and M. T. Cicerone, “Quantitative, comparable coherent anti-Stokes Raman scattering (CARS) spectroscopy: correcting errors in phase retrieval,” J. Raman Spectrosc. 47(4), 408-415 (2015).

C. H. Camp and M. T. Cicerone, “Chemically sensitive bioimaging with coherent Raman scattering,” Nat. Photonics 9(5), 295–305 (2015).
[Crossref]

M. T. Cicerone, K. A. Aamer, Y. J. Lee, and E. Vartiainen, “Maximum entropy and time-domain Kramers-Kronig phase retrieval approaches are functionally equivalent for CARS microspectroscopy,” J. Raman Spectrosc. 43(5), 637–643 (2012).
[Crossref]

Y. Liu, Y. J. Lee, and M. T. Cicerone, “Broadband CARS spectral phase retrieval using a time-domain Kramers-Kronig transform,” Opt. Lett. 34(9), 1363–1365 (2009).
[Crossref] [PubMed]

Couderc, V.

M. Okuno, H. Kano, P. Leproux, V. Couderc, J. P. R. Day, M. Bonn, and H. O. Hamaguchi, “Quantitative CARS molecular fingerprinting of single living cells with the use of the maximum entropy method,” Angew. Chem. Int. Ed. Engl. 49(38), 6773–6777 (2010).
[Crossref] [PubMed]

Day, J. P. R.

J. P. R. Day, K. F. Domke, G. Rago, H. Kano, H. O. Hamaguchi, E. M. Vartiainen, and M. Bonn, “Quantitative coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Phys. Chem. B 115(24), 7713–7725 (2011).
[Crossref] [PubMed]

M. Okuno, H. Kano, P. Leproux, V. Couderc, J. P. R. Day, M. Bonn, and H. O. Hamaguchi, “Quantitative CARS molecular fingerprinting of single living cells with the use of the maximum entropy method,” Angew. Chem. Int. Ed. Engl. 49(38), 6773–6777 (2010).
[Crossref] [PubMed]

Domke, K. F.

K. F. Domke, T. A. Riemer, G. Rago, A. N. Parvulescu, P. C. A. Bruijnincx, A. Enejder, B. M. Weckhuysen, and M. Bonn, “Tracing catalytic conversion on single zeolite crystals in 3D with nonlinear spectromicroscopy,” J. Am. Chem. Soc. 134(2), 1124–1129 (2012).
[Crossref] [PubMed]

J. P. R. Day, K. F. Domke, G. Rago, H. Kano, H. O. Hamaguchi, E. M. Vartiainen, and M. Bonn, “Quantitative coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Phys. Chem. B 115(24), 7713–7725 (2011).
[Crossref] [PubMed]

Enejder, A.

K. F. Domke, T. A. Riemer, G. Rago, A. N. Parvulescu, P. C. A. Bruijnincx, A. Enejder, B. M. Weckhuysen, and M. Bonn, “Tracing catalytic conversion on single zeolite crystals in 3D with nonlinear spectromicroscopy,” J. Am. Chem. Soc. 134(2), 1124–1129 (2012).
[Crossref] [PubMed]

Greve, J.

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, “Vibrational bands of luminescent zinc(II)-octaethylporphyrin using a polarization-sensitive “microscopic” multiplex CARS technique,” J. Raman Spectrosc. 32(6-7), 495–501 (2001).
[Crossref]

Hamaguchi, H. O.

J. P. R. Day, K. F. Domke, G. Rago, H. Kano, H. O. Hamaguchi, E. M. Vartiainen, and M. Bonn, “Quantitative coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Phys. Chem. B 115(24), 7713–7725 (2011).
[Crossref] [PubMed]

M. Okuno, H. Kano, P. Leproux, V. Couderc, J. P. R. Day, M. Bonn, and H. O. Hamaguchi, “Quantitative CARS molecular fingerprinting of single living cells with the use of the maximum entropy method,” Angew. Chem. Int. Ed. Engl. 49(38), 6773–6777 (2010).
[Crossref] [PubMed]

Hanna, D. C.

M. A. Yuratich and D. C. Hanna, “Coherent anti-Stokes Raman spectroscopy (CARS): Selection rules, depolarization ratios and rotational structure,” Mol. Phys. 33(3), 671–682 (1977).
[Crossref]

Hotokka, M.

S. Söderholm, Y. H. Roos, N. Meinander, and M. Hotokka, “Raman spectra of fructose and glucose in the amorphous and crystalline states,” J. Raman Spectrosc. 30(11), 1009–1018 (1999).
[Crossref]

Hu, J.

Y. Hu, T. Jiang, A. Shen, W. Li, X. Wang, and J. Hu, “A background elimination method based on wavelet transform for Raman spectra,” Chemom. Intell. Lab. Syst. 85(1), 94–101 (2007).
[Crossref]

Hu, Y.

Y. Hu, T. Jiang, A. Shen, W. Li, X. Wang, and J. Hu, “A background elimination method based on wavelet transform for Raman spectra,” Chemom. Intell. Lab. Syst. 85(1), 94–101 (2007).
[Crossref]

Igarashi, R.

R. Igarashi, Y. Adachi, and S. Maeda, “Resonance CARS and CSRS line shapes of Ni(II)‐octaethylporphyrin,” J. Chem. Phys. 72(8), 4308–4314 (1980).
[Crossref]

Jiang, T.

Y. Hu, T. Jiang, A. Shen, W. Li, X. Wang, and J. Hu, “A background elimination method based on wavelet transform for Raman spectra,” Chemom. Intell. Lab. Syst. 85(1), 94–101 (2007).
[Crossref]

Kacuráková, M.

M. Kacuráková and M. Mathlouthi, “FTIR and laser-Raman spectra of oligosaccharides in water: characterization of the glycosidic bond,” Carbohydr. Res. 284(2), 145–157 (1996).
[Crossref] [PubMed]

Kano, H.

J. P. R. Day, K. F. Domke, G. Rago, H. Kano, H. O. Hamaguchi, E. M. Vartiainen, and M. Bonn, “Quantitative coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Phys. Chem. B 115(24), 7713–7725 (2011).
[Crossref] [PubMed]

M. Okuno, H. Kano, P. Leproux, V. Couderc, J. P. R. Day, M. Bonn, and H. O. Hamaguchi, “Quantitative CARS molecular fingerprinting of single living cells with the use of the maximum entropy method,” Angew. Chem. Int. Ed. Engl. 49(38), 6773–6777 (2010).
[Crossref] [PubMed]

Kruglik, S. G.

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, “Vibrational bands of luminescent zinc(II)-octaethylporphyrin using a polarization-sensitive “microscopic” multiplex CARS technique,” J. Raman Spectrosc. 32(6-7), 495–501 (2001).
[Crossref]

Lee, Y. J.

C. H. Camp, Y. J. Lee, and M. T. Cicerone, “Quantitative, comparable coherent anti-Stokes Raman scattering (CARS) spectroscopy: correcting errors in phase retrieval,” J. Raman Spectrosc. 47(4), 408-415 (2015).

M. T. Cicerone, K. A. Aamer, Y. J. Lee, and E. Vartiainen, “Maximum entropy and time-domain Kramers-Kronig phase retrieval approaches are functionally equivalent for CARS microspectroscopy,” J. Raman Spectrosc. 43(5), 637–643 (2012).
[Crossref]

Y. Liu, Y. J. Lee, and M. T. Cicerone, “Broadband CARS spectral phase retrieval using a time-domain Kramers-Kronig transform,” Opt. Lett. 34(9), 1363–1365 (2009).
[Crossref] [PubMed]

Leproux, P.

M. Okuno, H. Kano, P. Leproux, V. Couderc, J. P. R. Day, M. Bonn, and H. O. Hamaguchi, “Quantitative CARS molecular fingerprinting of single living cells with the use of the maximum entropy method,” Angew. Chem. Int. Ed. Engl. 49(38), 6773–6777 (2010).
[Crossref] [PubMed]

Li, J.

J. Li, L.-P. Choo-Smith, Z. Tang, and M. G. Sowa, “Background removal from polarized Raman spectra of tooth enamel using the wavelet transform,” J. Raman Spectrosc. 42(4), 580–585 (2011).
[Crossref]

Li, W.

Y. Hu, T. Jiang, A. Shen, W. Li, X. Wang, and J. Hu, “A background elimination method based on wavelet transform for Raman spectra,” Chemom. Intell. Lab. Syst. 85(1), 94–101 (2007).
[Crossref]

Lisker, M.

M. Müller, H. A. Rinia, M. Bonn, E. M. Vartiainen, M. Lisker, and A. van Bel, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” Proc. SPIE 6442, 644206 (2007).
[Crossref]

Liu, Y.

Luu, D. V.

M. Mathlouthi and D. V. Luu, “Laser-Raman spectra of d-fructose in aqueous solution,” Carbohydr. Res. 78(2), 225–233 (1980).
[Crossref]

Maeda, S.

R. Igarashi, Y. Adachi, and S. Maeda, “Resonance CARS and CSRS line shapes of Ni(II)‐octaethylporphyrin,” J. Chem. Phys. 72(8), 4308–4314 (1980).
[Crossref]

Mallat, S. G.

S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11(7), 674–693 (1989).
[Crossref]

Mathlouthi, M.

M. Kacuráková and M. Mathlouthi, “FTIR and laser-Raman spectra of oligosaccharides in water: characterization of the glycosidic bond,” Carbohydr. Res. 284(2), 145–157 (1996).
[Crossref] [PubMed]

M. Mathlouthi and D. Vinh Luu, “Laser-Raman spectra of d-glucose and sucrose in aqueous solution,” Carbohydr. Res. 81(2), 203–212 (1980).
[Crossref]

M. Mathlouthi and D. V. Luu, “Laser-Raman spectra of d-fructose in aqueous solution,” Carbohydr. Res. 78(2), 225–233 (1980).
[Crossref]

Meinander, N.

S. Söderholm, Y. H. Roos, N. Meinander, and M. Hotokka, “Raman spectra of fructose and glucose in the amorphous and crystalline states,” J. Raman Spectrosc. 30(11), 1009–1018 (1999).
[Crossref]

Michalska, D. F.

P. L. Polavarapu, S. R. Chatterjee, and D. F. Michalska, “Infrared investigations of sucrose in aqueous solutions,” Carbohydr. Res. 137, 253–258 (1985).
[Crossref]

Müller, M.

H. A. Rinia, K. N. J. Burger, M. Bonn, and M. Müller, “Quantitative label-free imaging of lipid composition and packing of individual cellular lipid droplets using multiplex CARS microscopy,” Biophys. J. 95(10), 4908–4914 (2008).
[Crossref] [PubMed]

M. Müller, H. A. Rinia, M. Bonn, E. M. Vartiainen, M. Lisker, and A. van Bel, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” Proc. SPIE 6442, 644206 (2007).
[Crossref]

H. A. Rinia, M. Bonn, and M. Müller, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” J. Phys. Chem. B 110(9), 4472–4479 (2006).
[Crossref] [PubMed]

E. M. Vartiainen, H. A. Rinia, M. Müller, and M. Bonn, “Direct extraction of Raman line-shapes from congested CARS spectra,” Opt. Express 14(8), 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. B 106(14), 3715–3723 (2002).
[Crossref]

Okuno, M.

M. Okuno, H. Kano, P. Leproux, V. Couderc, J. P. R. Day, M. Bonn, and H. O. Hamaguchi, “Quantitative CARS molecular fingerprinting of single living cells with the use of the maximum entropy method,” Angew. Chem. Int. Ed. Engl. 49(38), 6773–6777 (2010).
[Crossref] [PubMed]

Otto, C.

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, “Vibrational bands of luminescent zinc(II)-octaethylporphyrin using a polarization-sensitive “microscopic” multiplex CARS technique,” J. Raman Spectrosc. 32(6-7), 495–501 (2001).
[Crossref]

Parvulescu, A. N.

K. F. Domke, T. A. Riemer, G. Rago, A. N. Parvulescu, P. C. A. Bruijnincx, A. Enejder, B. M. Weckhuysen, and M. Bonn, “Tracing catalytic conversion on single zeolite crystals in 3D with nonlinear spectromicroscopy,” J. Am. Chem. Soc. 134(2), 1124–1129 (2012).
[Crossref] [PubMed]

Peiponen, K.-E.

E. M. Vartiainen and K.-E. Peiponen, “Optical and terahertz spectra analysis by the maximum entropy method,” Rep. Prog. Phys. 76(6), 066401 (2013).
[Crossref] [PubMed]

E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, “Phase retrieval in optical spectroscopy: resolving optical constants from power spectra,” Appl. Spectrosc. 50(10), 1283–1289 (1996).
[Crossref]

Polavarapu, P. L.

P. L. Polavarapu, S. R. Chatterjee, and D. F. Michalska, “Infrared investigations of sucrose in aqueous solutions,” Carbohydr. Res. 137, 253–258 (1985).
[Crossref]

Rago, G.

K. F. Domke, T. A. Riemer, G. Rago, A. N. Parvulescu, P. C. A. Bruijnincx, A. Enejder, B. M. Weckhuysen, and M. Bonn, “Tracing catalytic conversion on single zeolite crystals in 3D with nonlinear spectromicroscopy,” J. Am. Chem. Soc. 134(2), 1124–1129 (2012).
[Crossref] [PubMed]

J. P. R. Day, K. F. Domke, G. Rago, H. Kano, H. O. Hamaguchi, E. M. Vartiainen, and M. Bonn, “Quantitative coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Phys. Chem. B 115(24), 7713–7725 (2011).
[Crossref] [PubMed]

Riemer, T. A.

K. F. Domke, T. A. Riemer, G. Rago, A. N. Parvulescu, P. C. A. Bruijnincx, A. Enejder, B. M. Weckhuysen, and M. Bonn, “Tracing catalytic conversion on single zeolite crystals in 3D with nonlinear spectromicroscopy,” J. Am. Chem. Soc. 134(2), 1124–1129 (2012).
[Crossref] [PubMed]

Rinia, H. A.

H. A. Rinia, K. N. J. Burger, M. Bonn, and M. Müller, “Quantitative label-free imaging of lipid composition and packing of individual cellular lipid droplets using multiplex CARS microscopy,” Biophys. J. 95(10), 4908–4914 (2008).
[Crossref] [PubMed]

M. Müller, H. A. Rinia, M. Bonn, E. M. Vartiainen, M. Lisker, and A. van Bel, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” Proc. SPIE 6442, 644206 (2007).
[Crossref]

H. A. Rinia, M. Bonn, and M. Müller, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” J. Phys. Chem. B 110(9), 4472–4479 (2006).
[Crossref] [PubMed]

E. M. Vartiainen, H. A. Rinia, M. Müller, and M. Bonn, “Direct extraction of Raman line-shapes from congested CARS spectra,” Opt. Express 14(8), 3622–3630 (2006).
[Crossref] [PubMed]

Roos, Y. H.

S. Söderholm, Y. H. Roos, N. Meinander, and M. Hotokka, “Raman spectra of fructose and glucose in the amorphous and crystalline states,” J. Raman Spectrosc. 30(11), 1009–1018 (1999).
[Crossref]

Schins, J. M.

M. Müller and J. M. Schins, “Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy,” J. Phys. Chem. B 106(14), 3715–3723 (2002).
[Crossref]

Shen, A.

Y. Hu, T. Jiang, A. Shen, W. Li, X. Wang, and J. Hu, “A background elimination method based on wavelet transform for Raman spectra,” Chemom. Intell. Lab. Syst. 85(1), 94–101 (2007).
[Crossref]

Söderholm, S.

S. Söderholm, Y. H. Roos, N. Meinander, and M. Hotokka, “Raman spectra of fructose and glucose in the amorphous and crystalline states,” J. Raman Spectrosc. 30(11), 1009–1018 (1999).
[Crossref]

Sowa, M. G.

J. Li, L.-P. Choo-Smith, Z. Tang, and M. G. Sowa, “Background removal from polarized Raman spectra of tooth enamel using the wavelet transform,” J. Raman Spectrosc. 42(4), 580–585 (2011).
[Crossref]

Tan, H.-W.

H.-W. Tan and S. D. Brown, “Wavelet analysis applied to removing non-constant, varying spectroscopic background in multivariate calibration,” J. Chemometr. 16(5), 228–240 (2002).
[Crossref]

Tang, Z.

J. Li, L.-P. Choo-Smith, Z. Tang, and M. G. Sowa, “Background removal from polarized Raman spectra of tooth enamel using the wavelet transform,” J. Raman Spectrosc. 42(4), 580–585 (2011).
[Crossref]

van Bel, A.

M. Müller, H. A. Rinia, M. Bonn, E. M. Vartiainen, M. Lisker, and A. van Bel, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” Proc. SPIE 6442, 644206 (2007).
[Crossref]

Vartiainen, E.

M. T. Cicerone, K. A. Aamer, Y. J. Lee, and E. Vartiainen, “Maximum entropy and time-domain Kramers-Kronig phase retrieval approaches are functionally equivalent for CARS microspectroscopy,” J. Raman Spectrosc. 43(5), 637–643 (2012).
[Crossref]

Vartiainen, E. M.

E. M. Vartiainen and K.-E. Peiponen, “Optical and terahertz spectra analysis by the maximum entropy method,” Rep. Prog. Phys. 76(6), 066401 (2013).
[Crossref] [PubMed]

J. P. R. Day, K. F. Domke, G. Rago, H. Kano, H. O. Hamaguchi, E. M. Vartiainen, and M. Bonn, “Quantitative coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Phys. Chem. B 115(24), 7713–7725 (2011).
[Crossref] [PubMed]

M. Müller, H. A. Rinia, M. Bonn, E. M. Vartiainen, M. Lisker, and A. van Bel, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” Proc. SPIE 6442, 644206 (2007).
[Crossref]

E. M. Vartiainen, H. A. Rinia, M. Müller, and M. Bonn, “Direct extraction of Raman line-shapes from congested CARS spectra,” Opt. Express 14(8), 3622–3630 (2006).
[Crossref] [PubMed]

E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, “Phase retrieval in optical spectroscopy: resolving optical constants from power spectra,” Appl. Spectrosc. 50(10), 1283–1289 (1996).
[Crossref]

E. M. Vartiainen, “Phase retrieval approach for coherent anti-Stokes Raman scattering spectrum analysis,” J. Opt. Soc. Am. B 9(8), 1209–1214 (1992).
[Crossref]

Vinh Luu, D.

M. Mathlouthi and D. Vinh Luu, “Laser-Raman spectra of d-glucose and sucrose in aqueous solution,” Carbohydr. Res. 81(2), 203–212 (1980).
[Crossref]

Volkmer, A.

A. Volkmer, “Vibrational imaging and microspectroscopies based on coherent anti-Stokes Raman scattering microscopy,” J. Phys. Appl. Phys. 38(5), R59–R81 (2005).
[Crossref]

J. 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(34), 8493–8498 (2002).
[Crossref]

Voroshilov, A.

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, “Vibrational bands of luminescent zinc(II)-octaethylporphyrin using a polarization-sensitive “microscopic” multiplex CARS technique,” J. Raman Spectrosc. 32(6-7), 495–501 (2001).
[Crossref]

Wang, X.

Y. Hu, T. Jiang, A. Shen, W. Li, X. Wang, and J. Hu, “A background elimination method based on wavelet transform for Raman spectra,” Chemom. Intell. Lab. Syst. 85(1), 94–101 (2007).
[Crossref]

Weckhuysen, B. M.

K. F. Domke, T. A. Riemer, G. Rago, A. N. Parvulescu, P. C. A. Bruijnincx, A. Enejder, B. M. Weckhuysen, and M. Bonn, “Tracing catalytic conversion on single zeolite crystals in 3D with nonlinear spectromicroscopy,” J. Am. Chem. Soc. 134(2), 1124–1129 (2012).
[Crossref] [PubMed]

Xie, X. S.

J. 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(34), 8493–8498 (2002).
[Crossref]

Yuratich, M. A.

M. A. Yuratich and D. C. Hanna, “Coherent anti-Stokes Raman spectroscopy (CARS): Selection rules, depolarization ratios and rotational structure,” Mol. Phys. 33(3), 671–682 (1977).
[Crossref]

Angew. Chem. Int. Ed. Engl. (1)

M. Okuno, H. Kano, P. Leproux, V. Couderc, J. P. R. Day, M. Bonn, and H. O. Hamaguchi, “Quantitative CARS molecular fingerprinting of single living cells with the use of the maximum entropy method,” Angew. Chem. Int. Ed. Engl. 49(38), 6773–6777 (2010).
[Crossref] [PubMed]

Appl. Spectrosc. (1)

Biophys. J. (1)

H. A. Rinia, K. N. J. Burger, M. Bonn, and M. Müller, “Quantitative label-free imaging of lipid composition and packing of individual cellular lipid droplets using multiplex CARS microscopy,” Biophys. J. 95(10), 4908–4914 (2008).
[Crossref] [PubMed]

Carbohydr. Res. (4)

M. Mathlouthi and D. V. Luu, “Laser-Raman spectra of d-fructose in aqueous solution,” Carbohydr. Res. 78(2), 225–233 (1980).
[Crossref]

M. Mathlouthi and D. Vinh Luu, “Laser-Raman spectra of d-glucose and sucrose in aqueous solution,” Carbohydr. Res. 81(2), 203–212 (1980).
[Crossref]

P. L. Polavarapu, S. R. Chatterjee, and D. F. Michalska, “Infrared investigations of sucrose in aqueous solutions,” Carbohydr. Res. 137, 253–258 (1985).
[Crossref]

M. Kacuráková and M. Mathlouthi, “FTIR and laser-Raman spectra of oligosaccharides in water: characterization of the glycosidic bond,” Carbohydr. Res. 284(2), 145–157 (1996).
[Crossref] [PubMed]

Chemom. Intell. Lab. Syst. (1)

Y. Hu, T. Jiang, A. Shen, W. Li, X. Wang, and J. Hu, “A background elimination method based on wavelet transform for Raman spectra,” Chemom. Intell. Lab. Syst. 85(1), 94–101 (2007).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11(7), 674–693 (1989).
[Crossref]

J. Am. Chem. Soc. (1)

K. F. Domke, T. A. Riemer, G. Rago, A. N. Parvulescu, P. C. A. Bruijnincx, A. Enejder, B. M. Weckhuysen, and M. Bonn, “Tracing catalytic conversion on single zeolite crystals in 3D with nonlinear spectromicroscopy,” J. Am. Chem. Soc. 134(2), 1124–1129 (2012).
[Crossref] [PubMed]

J. Chem. Phys. (1)

R. Igarashi, Y. Adachi, and S. Maeda, “Resonance CARS and CSRS line shapes of Ni(II)‐octaethylporphyrin,” J. Chem. Phys. 72(8), 4308–4314 (1980).
[Crossref]

J. Chemometr. (1)

H.-W. Tan and S. D. Brown, “Wavelet analysis applied to removing non-constant, varying spectroscopic background in multivariate calibration,” J. Chemometr. 16(5), 228–240 (2002).
[Crossref]

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

J. Phys. Appl. Phys. (1)

A. Volkmer, “Vibrational imaging and microspectroscopies based on coherent anti-Stokes Raman scattering microscopy,” J. Phys. Appl. Phys. 38(5), R59–R81 (2005).
[Crossref]

J. Phys. Chem. B (4)

J. 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(34), 8493–8498 (2002).
[Crossref]

M. Müller and J. M. Schins, “Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy,” J. Phys. Chem. B 106(14), 3715–3723 (2002).
[Crossref]

J. P. R. Day, K. F. Domke, G. Rago, H. Kano, H. O. Hamaguchi, E. M. Vartiainen, and M. Bonn, “Quantitative coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Phys. Chem. B 115(24), 7713–7725 (2011).
[Crossref] [PubMed]

H. A. Rinia, M. Bonn, and M. Müller, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” J. Phys. Chem. B 110(9), 4472–4479 (2006).
[Crossref] [PubMed]

J. Raman Spectrosc. (5)

S. Söderholm, Y. H. Roos, N. Meinander, and M. Hotokka, “Raman spectra of fructose and glucose in the amorphous and crystalline states,” J. Raman Spectrosc. 30(11), 1009–1018 (1999).
[Crossref]

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, “Vibrational bands of luminescent zinc(II)-octaethylporphyrin using a polarization-sensitive “microscopic” multiplex CARS technique,” J. Raman Spectrosc. 32(6-7), 495–501 (2001).
[Crossref]

M. T. Cicerone, K. A. Aamer, Y. J. Lee, and E. Vartiainen, “Maximum entropy and time-domain Kramers-Kronig phase retrieval approaches are functionally equivalent for CARS microspectroscopy,” J. Raman Spectrosc. 43(5), 637–643 (2012).
[Crossref]

J. Li, L.-P. Choo-Smith, Z. Tang, and M. G. Sowa, “Background removal from polarized Raman spectra of tooth enamel using the wavelet transform,” J. Raman Spectrosc. 42(4), 580–585 (2011).
[Crossref]

C. H. Camp, Y. J. Lee, and M. T. Cicerone, “Quantitative, comparable coherent anti-Stokes Raman scattering (CARS) spectroscopy: correcting errors in phase retrieval,” J. Raman Spectrosc. 47(4), 408-415 (2015).

Mol. Phys. (1)

M. A. Yuratich and D. C. Hanna, “Coherent anti-Stokes Raman spectroscopy (CARS): Selection rules, depolarization ratios and rotational structure,” Mol. Phys. 33(3), 671–682 (1977).
[Crossref]

Nat. Photonics (1)

C. H. Camp and M. T. Cicerone, “Chemically sensitive bioimaging with coherent Raman scattering,” Nat. Photonics 9(5), 295–305 (2015).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (1)

M. Müller, H. A. Rinia, M. Bonn, E. M. Vartiainen, M. Lisker, and A. van Bel, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” Proc. SPIE 6442, 644206 (2007).
[Crossref]

Rep. Prog. Phys. (1)

E. M. Vartiainen and K.-E. Peiponen, “Optical and terahertz spectra analysis by the maximum entropy method,” Rep. Prog. Phys. 76(6), 066401 (2013).
[Crossref] [PubMed]

Other (5)

J. S. Gomez, “Coherent Raman spectroscopy,” in: Modern Techniques in Raman Spectroscopy, J. J. Laserna, ed. (Wiley, 1996).

P. H. Eilers and H. F. Boelens, “Baseline correction with asymmetric least squares smoothing,” Leiden Univ. Med. Cent. Rep. (2005).

S. Maeda, T. Kamisuki, and Y. Adachi, “Condensed phase CARS,” in Advances in Nonlinear Spectroscopy, R. J. H. Clark, R. E. Hester eds. (Wiley, 1988).

S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University Press, 1999), Chap. 9.

R. M. Rao and A. S. Bopardikar, Wavelet Transforms: Introduction to Theory and Applications (Prentice Hall, 1998).

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Figures (3)

Fig. 1
Fig. 1

Illustration of the principle of the WP method applied to the ln S exp (ν) spectrum of an aqueous solution of sucrose. (a) WP decomposition into discrete detail components, D jJ , and approximation, A J , for J=14. (b) Spectral contributions of noise, signal, modulation error function, and DC-offset constructed from the corresponding groups of detail and approximation components from the input ln S exp (ν) spectrum.

Fig. 2
Fig. 2

Experimental normalized CARS spectrum, S exp (ν), the WP-extracted slowly varying modulation error spectrum, ε(ν), and the error-corrected normalized CARS line shape, S(ν), for aqueous solutions of (a) sucrose, (b) fructose, and (c) glucose. D, E, F: The corresponding ME phase spectra, ϕ exp (ν) and ϕ(ν), as retrieved from the S exp (ν) and S(ν) spectra, respectively. g, h, i: The corresponding reconstructed Im [ χ R (3) (ν) ] exp and Im[ χ R (3) (ν) ] spectra in comparison with the spontaneous Raman spectra, I Raman (ν), of the same samples obtained by independent measurements.

Fig. 3
Fig. 3

Comparison of the reconstructed spectrum obtained for the sucrose sample, Im [ χ R (3) (ν) ] suc (dark gray curve), with the best fit (red curve) according to Eq. (16) within the spectral region from 1000 to 1200 cm−1. The linear spectral unmixing model consisting of the Im [ χ R (3) (ν) ] fruc (dashed blue curve) and Im [ χ R (3) (ν) ] gluc (dashed green curve) spectra obtained for the fructose and glucose samples, respectively, yields molar weights of C fruc =0.98 and C gluc =0.98 . Insert: Chemical structure of sucrose (α-D-glucopyranosyl-(1→2)-β-D-fructofuranoside).

Equations (16)

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

I CARS (ν) | d ν p d ν S d ν p' χ (3) (ν) E p ( ν p ) E S ( ν S ) E p' ( ν p' )δ( ν p + ν p' ν S ν) | 2 .
χ (3) (ν)= χ (3)nr + χ (3)r (ν),
S exp (ν)= I CARS sample (ν) I CARS ref (ν) .
S(ν)= | χ NR (3) + χ R (3) (ν) | 2 ,
Im[ χ R (3) (ν) ]= S(ν) sin( ϕ(ν) ϕ err (ν) ),
I Raman (ν)Im[ χ R (3) (ν) ].
S exp (ν)=ε(ν)S(ν).
ln S exp (ν)=lnS(ν)+lnε(ν).
ψ a,b (ν)= 1 a ψ( νb a ).
ψ j,k (ν)= 2 j/2 ψ( 2 j νk).
ln S exp (ν)= j= k= d(j,k) ψ j,k (ν),
d(j,k)= 2 j k 2 j (k+1) ln S exp (ν) ψ j,k (ν)
ln S exp (ν)= jJ D j (ν) + A J (ν).
ln S exp (ν)= [ ln S exp (ν) ] noise + [ ln S exp (ν) ] signal +lnε(ν)+ [ ln S exp (ν) ] DC .
S(ν)=exp{ [ ln S exp (ν) ] noise + [ ln S exp (ν) ] signal + [ ln S exp (ν) ] DC }.
Im [ χ R (3) (ν)] suc = C fruc Im [ χ R (3) (ν)] fruc + C gluc Im [ χ R (3) (ν)] gluc ,

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