Abstract

Vibrational spectroscopic imaging is useful and important in biological and medical studies. Yet, vibrational imaging in the terahertz region (<300cm1) under biologically relevant conditions is currently unavailable, as none of the available methods possesses a sufficient sensitivity and high spatial resolution at the same time. Here, we develop a terahertz coherent anti-Stokes Raman scattering (THz-CARS) microscope with a high sensitivity and high spatial resolution that shows chemically selective imaging of biological tissues by using low-frequency collective modes of the corresponding constituents, filling the existing energy scale gap for vibrational imaging in the THz region. The observation of collective modes of biomacromolecules, such as collagen and non-collagenous proteins, may have significant implications for elucidating their corresponding biological functions, and the methodology presented may find wider applications in biomedical research.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2015 (4)

S. Kumar, T. Kamali, J. M. Levitte, O. Katz, B. Hermann, R. Werkmeister, B. Považay, W. Drexler, A. Unterhuber, and Y. Silberberg, Opt. Express 23, 13082 (2015).
[Crossref]

Y. Shen, D. V. Voronine, A. V. Sokolov, and M. O. Scully, Opt. Lett. 40, 1223 (2015).
[Crossref]

T. C. B. Harlang, Y. Liu, O. Gordivska, L. A. Fredin, C. S. Ponseca, P. Huang, P. Chábera, K. S. Kjaer, H. Mateos, J. Uhlig, R. Lomoth, R. Wallenberg, S. Styring, P. Persson, V. Sundström, and K. Wärnmark, Nat. Chem. 7, 883 (2015).
[Crossref]

J.-X. Cheng and X. S. Xie, Science 350, aaa8870 (2015).
[Crossref]

2014 (4)

C. H. Camp, Y. J. Lee, J. M. Hddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, Nat. Photonics 8, 627 (2014).
[Crossref]

G. Acbas, K. A. Niessen, E. H. Snell, and A. G. Markelz, Nat. Commun. 5, 3076 (2014).
[Crossref]

D. A. Turton, H. M. Senn, T. Harwood, A. J. Lapthorn, E. M. Ellis, and K. Wynne, Nat. Commun. 5, 3999 (2014).
[Crossref]

A. F. Pegoraro, A. D. Slepkov, A. Ridsdale, D. J. Moffatt, and A. Stolow, J. Biophoton. 7, 49 (2014).
[Crossref]

2011 (1)

2010 (1)

2002 (1)

N. Dudovich, D. Oron, and Y. Silberberg, Nature 418, 512 (2002).
[Crossref]

1994 (1)

H. Tsuda and J. Arends, J. Dent. Res. 73, 1703 (1994).
[Crossref]

1987 (1)

C. V. Berney, V. Renugopalakrishnan, and R. S. Bhatnagar, Biophys. J. 52, 343 (1987).
[Crossref]

1985 (2)

K.-C. Chou, Biophys. J. 48, 289 (1985).
[Crossref]

B. Brooks and M. Karplus, Proc. Natl. Acad. Sci. USA 82, 4995 (1985).
[Crossref]

1983 (1)

A. L. Dendramis, J. W. Poser, and E. W. Schwinn, Biochim. Biophys. Acta 742, 525 (1983).
[Crossref]

1982 (1)

D. G. A. Nelson and B. E. Williamson, Aust. J. Chem. 35, 715 (1982).
[Crossref]

1977 (1)

Z. Iqbal, V. P. Tomaselli, O. Fahrenfeld, K. D. Möller, F. A. Ruszala, and E. Kostiner, J. Phys. Chem. Solids 38, 923 (1977).
[Crossref]

1976 (1)

L. Genzel, F. Keilmann, T. P. Martin, G. Winterling, Y. Yacoby, H. Frohlich, and M. Makinen, Biopolymers 15, 219 (1976).
[Crossref]

1972 (2)

K. G. Brown, S. C. Erfurth, E. W. Small, and W. L. Peticolas, Proc. Nat. Acad. Sci. USA 69, 1467 (1972).
[Crossref]

L. A. Blatz, Appl. Spectrosc. 26, 66 (1972).
[Crossref]

1970 (1)

G. L. Carlson, W. G. Fateley, and J. Hiraishi, J. Mol. Struct. 6, 101 (1970).
[Crossref]

Acbas, G.

G. Acbas, K. A. Niessen, E. H. Snell, and A. G. Markelz, Nat. Commun. 5, 3076 (2014).
[Crossref]

Arends, J.

H. Tsuda and J. Arends, J. Dent. Res. 73, 1703 (1994).
[Crossref]

Berney, C. V.

C. V. Berney, V. Renugopalakrishnan, and R. S. Bhatnagar, Biophys. J. 52, 343 (1987).
[Crossref]

Bhatnagar, R. S.

C. V. Berney, V. Renugopalakrishnan, and R. S. Bhatnagar, Biophys. J. 52, 343 (1987).
[Crossref]

Blatz, L. A.

Brooks, B.

B. Brooks and M. Karplus, Proc. Natl. Acad. Sci. USA 82, 4995 (1985).
[Crossref]

Brown, K. G.

K. G. Brown, S. C. Erfurth, E. W. Small, and W. L. Peticolas, Proc. Nat. Acad. Sci. USA 69, 1467 (1972).
[Crossref]

Camp, C. H.

C. H. Camp, Y. J. Lee, J. M. Hddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, Nat. Photonics 8, 627 (2014).
[Crossref]

Carlson, G. L.

G. L. Carlson, W. G. Fateley, and J. Hiraishi, J. Mol. Struct. 6, 101 (1970).
[Crossref]

Chábera, P.

T. C. B. Harlang, Y. Liu, O. Gordivska, L. A. Fredin, C. S. Ponseca, P. Huang, P. Chábera, K. S. Kjaer, H. Mateos, J. Uhlig, R. Lomoth, R. Wallenberg, S. Styring, P. Persson, V. Sundström, and K. Wärnmark, Nat. Chem. 7, 883 (2015).
[Crossref]

Cheng, J.-X.

J.-X. Cheng and X. S. Xie, Science 350, aaa8870 (2015).
[Crossref]

Chou, K.-C.

K.-C. Chou, Biophys. J. 48, 289 (1985).
[Crossref]

Cicerone, M. T.

C. H. Camp, Y. J. Lee, J. M. Hddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, Nat. Photonics 8, 627 (2014).
[Crossref]

Dendramis, A. L.

A. L. Dendramis, J. W. Poser, and E. W. Schwinn, Biochim. Biophys. Acta 742, 525 (1983).
[Crossref]

Drexler, W.

Dudovich, N.

N. Dudovich, D. Oron, and Y. Silberberg, Nature 418, 512 (2002).
[Crossref]

Ellis, E. M.

D. A. Turton, H. M. Senn, T. Harwood, A. J. Lapthorn, E. M. Ellis, and K. Wynne, Nat. Commun. 5, 3999 (2014).
[Crossref]

Erfurth, S. C.

K. G. Brown, S. C. Erfurth, E. W. Small, and W. L. Peticolas, Proc. Nat. Acad. Sci. USA 69, 1467 (1972).
[Crossref]

Fahrenfeld, O.

Z. Iqbal, V. P. Tomaselli, O. Fahrenfeld, K. D. Möller, F. A. Ruszala, and E. Kostiner, J. Phys. Chem. Solids 38, 923 (1977).
[Crossref]

Fateley, W. G.

G. L. Carlson, W. G. Fateley, and J. Hiraishi, J. Mol. Struct. 6, 101 (1970).
[Crossref]

Fredin, L. A.

T. C. B. Harlang, Y. Liu, O. Gordivska, L. A. Fredin, C. S. Ponseca, P. Huang, P. Chábera, K. S. Kjaer, H. Mateos, J. Uhlig, R. Lomoth, R. Wallenberg, S. Styring, P. Persson, V. Sundström, and K. Wärnmark, Nat. Chem. 7, 883 (2015).
[Crossref]

Frohlich, H.

L. Genzel, F. Keilmann, T. P. Martin, G. Winterling, Y. Yacoby, H. Frohlich, and M. Makinen, Biopolymers 15, 219 (1976).
[Crossref]

Frostig, H.

Genzel, L.

L. Genzel, F. Keilmann, T. P. Martin, G. Winterling, Y. Yacoby, H. Frohlich, and M. Makinen, Biopolymers 15, 219 (1976).
[Crossref]

Gordivska, O.

T. C. B. Harlang, Y. Liu, O. Gordivska, L. A. Fredin, C. S. Ponseca, P. Huang, P. Chábera, K. S. Kjaer, H. Mateos, J. Uhlig, R. Lomoth, R. Wallenberg, S. Styring, P. Persson, V. Sundström, and K. Wärnmark, Nat. Chem. 7, 883 (2015).
[Crossref]

Grinvald, E.

Harlang, T. C. B.

T. C. B. Harlang, Y. Liu, O. Gordivska, L. A. Fredin, C. S. Ponseca, P. Huang, P. Chábera, K. S. Kjaer, H. Mateos, J. Uhlig, R. Lomoth, R. Wallenberg, S. Styring, P. Persson, V. Sundström, and K. Wärnmark, Nat. Chem. 7, 883 (2015).
[Crossref]

Hartshorn, C. M.

C. H. Camp, Y. J. Lee, J. M. Hddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, Nat. Photonics 8, 627 (2014).
[Crossref]

Harwood, T.

D. A. Turton, H. M. Senn, T. Harwood, A. J. Lapthorn, E. M. Ellis, and K. Wynne, Nat. Commun. 5, 3999 (2014).
[Crossref]

Hddleston, J. M.

C. H. Camp, Y. J. Lee, J. M. Hddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, Nat. Photonics 8, 627 (2014).
[Crossref]

Hermann, B.

Hiraishi, J.

G. L. Carlson, W. G. Fateley, and J. Hiraishi, J. Mol. Struct. 6, 101 (1970).
[Crossref]

Huang, P.

T. C. B. Harlang, Y. Liu, O. Gordivska, L. A. Fredin, C. S. Ponseca, P. Huang, P. Chábera, K. S. Kjaer, H. Mateos, J. Uhlig, R. Lomoth, R. Wallenberg, S. Styring, P. Persson, V. Sundström, and K. Wärnmark, Nat. Chem. 7, 883 (2015).
[Crossref]

Iqbal, Z.

Z. Iqbal, V. P. Tomaselli, O. Fahrenfeld, K. D. Möller, F. A. Ruszala, and E. Kostiner, J. Phys. Chem. Solids 38, 923 (1977).
[Crossref]

Kamali, T.

Karplus, M.

B. Brooks and M. Karplus, Proc. Natl. Acad. Sci. USA 82, 4995 (1985).
[Crossref]

Katz, O.

Keilmann, F.

L. Genzel, F. Keilmann, T. P. Martin, G. Winterling, Y. Yacoby, H. Frohlich, and M. Makinen, Biopolymers 15, 219 (1976).
[Crossref]

Kjaer, K. S.

T. C. B. Harlang, Y. Liu, O. Gordivska, L. A. Fredin, C. S. Ponseca, P. Huang, P. Chábera, K. S. Kjaer, H. Mateos, J. Uhlig, R. Lomoth, R. Wallenberg, S. Styring, P. Persson, V. Sundström, and K. Wärnmark, Nat. Chem. 7, 883 (2015).
[Crossref]

Kostiner, E.

Z. Iqbal, V. P. Tomaselli, O. Fahrenfeld, K. D. Möller, F. A. Ruszala, and E. Kostiner, J. Phys. Chem. Solids 38, 923 (1977).
[Crossref]

Kumar, S.

Lapthorn, A. J.

D. A. Turton, H. M. Senn, T. Harwood, A. J. Lapthorn, E. M. Ellis, and K. Wynne, Nat. Commun. 5, 3999 (2014).
[Crossref]

Lathia, J. D.

C. H. Camp, Y. J. Lee, J. M. Hddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, Nat. Photonics 8, 627 (2014).
[Crossref]

Lee, Y. J.

C. H. Camp, Y. J. Lee, J. M. Hddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, Nat. Photonics 8, 627 (2014).
[Crossref]

Levitt, J. M.

Levitte, J. M.

Liu, Y.

T. C. B. Harlang, Y. Liu, O. Gordivska, L. A. Fredin, C. S. Ponseca, P. Huang, P. Chábera, K. S. Kjaer, H. Mateos, J. Uhlig, R. Lomoth, R. Wallenberg, S. Styring, P. Persson, V. Sundström, and K. Wärnmark, Nat. Chem. 7, 883 (2015).
[Crossref]

Lomoth, R.

T. C. B. Harlang, Y. Liu, O. Gordivska, L. A. Fredin, C. S. Ponseca, P. Huang, P. Chábera, K. S. Kjaer, H. Mateos, J. Uhlig, R. Lomoth, R. Wallenberg, S. Styring, P. Persson, V. Sundström, and K. Wärnmark, Nat. Chem. 7, 883 (2015).
[Crossref]

Makinen, M.

L. Genzel, F. Keilmann, T. P. Martin, G. Winterling, Y. Yacoby, H. Frohlich, and M. Makinen, Biopolymers 15, 219 (1976).
[Crossref]

Markelz, A. G.

G. Acbas, K. A. Niessen, E. H. Snell, and A. G. Markelz, Nat. Commun. 5, 3076 (2014).
[Crossref]

Martin, T. P.

L. Genzel, F. Keilmann, T. P. Martin, G. Winterling, Y. Yacoby, H. Frohlich, and M. Makinen, Biopolymers 15, 219 (1976).
[Crossref]

Mateos, H.

T. C. B. Harlang, Y. Liu, O. Gordivska, L. A. Fredin, C. S. Ponseca, P. Huang, P. Chábera, K. S. Kjaer, H. Mateos, J. Uhlig, R. Lomoth, R. Wallenberg, S. Styring, P. Persson, V. Sundström, and K. Wärnmark, Nat. Chem. 7, 883 (2015).
[Crossref]

Moffatt, D. J.

A. F. Pegoraro, A. D. Slepkov, A. Ridsdale, D. J. Moffatt, and A. Stolow, J. Biophoton. 7, 49 (2014).
[Crossref]

Möller, K. D.

Z. Iqbal, V. P. Tomaselli, O. Fahrenfeld, K. D. Möller, F. A. Ruszala, and E. Kostiner, J. Phys. Chem. Solids 38, 923 (1977).
[Crossref]

Natan, A.

Nelson, D. G. A.

D. G. A. Nelson and B. E. Williamson, Aust. J. Chem. 35, 715 (1982).
[Crossref]

Niessen, K. A.

G. Acbas, K. A. Niessen, E. H. Snell, and A. G. Markelz, Nat. Commun. 5, 3076 (2014).
[Crossref]

Oron, D.

D. Raanan, L. Q. Ren, D. Oron, and Y. Silberberg, Opt. Lett. 43, 470 (2018).
[Crossref]

N. Dudovich, D. Oron, and Y. Silberberg, Nature 418, 512 (2002).
[Crossref]

Pegoraro, A. F.

A. F. Pegoraro, A. D. Slepkov, A. Ridsdale, D. J. Moffatt, and A. Stolow, J. Biophoton. 7, 49 (2014).
[Crossref]

Persson, P.

T. C. B. Harlang, Y. Liu, O. Gordivska, L. A. Fredin, C. S. Ponseca, P. Huang, P. Chábera, K. S. Kjaer, H. Mateos, J. Uhlig, R. Lomoth, R. Wallenberg, S. Styring, P. Persson, V. Sundström, and K. Wärnmark, Nat. Chem. 7, 883 (2015).
[Crossref]

Peticolas, W. L.

K. G. Brown, S. C. Erfurth, E. W. Small, and W. L. Peticolas, Proc. Nat. Acad. Sci. USA 69, 1467 (1972).
[Crossref]

Ponseca, C. S.

T. C. B. Harlang, Y. Liu, O. Gordivska, L. A. Fredin, C. S. Ponseca, P. Huang, P. Chábera, K. S. Kjaer, H. Mateos, J. Uhlig, R. Lomoth, R. Wallenberg, S. Styring, P. Persson, V. Sundström, and K. Wärnmark, Nat. Chem. 7, 883 (2015).
[Crossref]

Poser, J. W.

A. L. Dendramis, J. W. Poser, and E. W. Schwinn, Biochim. Biophys. Acta 742, 525 (1983).
[Crossref]

Považay, B.

Raanan, D.

Ren, L. Q.

Renugopalakrishnan, V.

C. V. Berney, V. Renugopalakrishnan, and R. S. Bhatnagar, Biophys. J. 52, 343 (1987).
[Crossref]

Rich, J. N.

C. H. Camp, Y. J. Lee, J. M. Hddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, Nat. Photonics 8, 627 (2014).
[Crossref]

Ridsdale, A.

A. F. Pegoraro, A. D. Slepkov, A. Ridsdale, D. J. Moffatt, and A. Stolow, J. Biophoton. 7, 49 (2014).
[Crossref]

Ruszala, F. A.

Z. Iqbal, V. P. Tomaselli, O. Fahrenfeld, K. D. Möller, F. A. Ruszala, and E. Kostiner, J. Phys. Chem. Solids 38, 923 (1977).
[Crossref]

Schwinn, E. W.

A. L. Dendramis, J. W. Poser, and E. W. Schwinn, Biochim. Biophys. Acta 742, 525 (1983).
[Crossref]

Scully, M. O.

Senn, H. M.

D. A. Turton, H. M. Senn, T. Harwood, A. J. Lapthorn, E. M. Ellis, and K. Wynne, Nat. Commun. 5, 3999 (2014).
[Crossref]

Shen, Y.

Silberberg, Y.

Slepkov, A. D.

A. F. Pegoraro, A. D. Slepkov, A. Ridsdale, D. J. Moffatt, and A. Stolow, J. Biophoton. 7, 49 (2014).
[Crossref]

Small, E. W.

K. G. Brown, S. C. Erfurth, E. W. Small, and W. L. Peticolas, Proc. Nat. Acad. Sci. USA 69, 1467 (1972).
[Crossref]

Snell, E. H.

G. Acbas, K. A. Niessen, E. H. Snell, and A. G. Markelz, Nat. Commun. 5, 3076 (2014).
[Crossref]

Sokolov, A. V.

Stolow, A.

A. F. Pegoraro, A. D. Slepkov, A. Ridsdale, D. J. Moffatt, and A. Stolow, J. Biophoton. 7, 49 (2014).
[Crossref]

Styring, S.

T. C. B. Harlang, Y. Liu, O. Gordivska, L. A. Fredin, C. S. Ponseca, P. Huang, P. Chábera, K. S. Kjaer, H. Mateos, J. Uhlig, R. Lomoth, R. Wallenberg, S. Styring, P. Persson, V. Sundström, and K. Wärnmark, Nat. Chem. 7, 883 (2015).
[Crossref]

Sundström, V.

T. C. B. Harlang, Y. Liu, O. Gordivska, L. A. Fredin, C. S. Ponseca, P. Huang, P. Chábera, K. S. Kjaer, H. Mateos, J. Uhlig, R. Lomoth, R. Wallenberg, S. Styring, P. Persson, V. Sundström, and K. Wärnmark, Nat. Chem. 7, 883 (2015).
[Crossref]

Tomaselli, V. P.

Z. Iqbal, V. P. Tomaselli, O. Fahrenfeld, K. D. Möller, F. A. Ruszala, and E. Kostiner, J. Phys. Chem. Solids 38, 923 (1977).
[Crossref]

Tsuda, H.

H. Tsuda and J. Arends, J. Dent. Res. 73, 1703 (1994).
[Crossref]

Turton, D. A.

D. A. Turton, H. M. Senn, T. Harwood, A. J. Lapthorn, E. M. Ellis, and K. Wynne, Nat. Commun. 5, 3999 (2014).
[Crossref]

Uhlig, J.

T. C. B. Harlang, Y. Liu, O. Gordivska, L. A. Fredin, C. S. Ponseca, P. Huang, P. Chábera, K. S. Kjaer, H. Mateos, J. Uhlig, R. Lomoth, R. Wallenberg, S. Styring, P. Persson, V. Sundström, and K. Wärnmark, Nat. Chem. 7, 883 (2015).
[Crossref]

Unterhuber, A.

Voronine, D. V.

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Supplementary Material (16)

NameDescription
» Data File 1       The first notch location of ENF
» Data File 2       The second notch location of ENF
» Data File 3       Measured Raw CARS spectrum I1 of tetrabromoethane with notch location at 780.1nm
» Data File 4       Measured Raw CARS spectrum I2 of tetrabromoethane with notch location at 780.4nm
» Data File 5       Non-resonant background (NRB) of CARS spectrum I1 of tetrabromoethane with notch location at 780.1nm
» Data File 6       Non-resonant background (NRB) of CARS spectrum I2 of tetrabromoethane with notch location at 780.4nm
» Data File 7       Measured raw CARS spectrum I1 of hydroxyapatite (HA) with notch location at 780.1nm
» Data File 8       Measured raw CARS spectrum I2 of hydroxyapatite (HA) with notch location at 780.4nm
» Data File 9       Non-resonant background (NRB) of CARS spectrum I1 of hydroxyapatite (HA) with notch location at 780.1nm
» Data File 10       Non-resonant background (NRB) of CARS spectrum I2 of hydroxyapatite (HA) with notch location at 780.4nm
» Data File 11       Measured raw CARS spectrum I1 of collagen with notch location at 780.1nm
» Data File 12       Measured raw CARS spectrum I2 of collagen with notch location at 780.4nm
» Data File 13       Non-resonant background (NRB) of CARS spectrum I1 of collagen (HA) with notch location at 780.1nm
» Data File 14       Non-resonant background (NRB) of CARS spectrum I2 of collagen with notch location at 780.4nm
» Supplement 1       The supplementary document includes the support information
» Visualization 1       This describes how to perform terahertz coherent anti-Stokes Raman scattering spectroscopy and microscopy

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Figures (4)

Fig. 1.
Fig. 1. THz-CARS scheme. (a) Principle of THz-CARS microscopy. ENF, excitation notch filter; ULPF, ultra-steep long-pass filter; USPF, ultra-steep short-pass filter. (b) Schematic of a THz-CARS microscope. DNF, detection notch filter; BPF, band-pass filter; DM, dichroic mirror; Obj, objective; SPF, short-pass filter. THz-CARS, SHG, FWM, and TPEF signals are collected by corresponding photomultiplier tubes, PMT-C, PMT-S, PMT-F, and PMT-T, respectively.
Fig. 2.
Fig. 2. THz-CARS spectroscopy of C2H2Br4. (a) Raw THz-CARS spectra of C2H2Br4. Inset: enlarged spectra to show a shifted feature. (b) Resolved Raman spectrum of C2H2Br4 by averaging 14 raw spectra.
Fig. 3.
Fig. 3. THz-CARS imaging of HA and collagen (C) in the bone. (a) Wide-field image (WFI) of the ROI. (b) WFI of the ROI. (c) Raw measured THz-CARS spectra of the bone at two different pixels in ROI. (d) Corresponding resolved Raman spectra of HA and C. (e) HA at 239cm1. LC, lacunae; LM, lamellae; IL, interstitial lamellae; O, osteocyte. (f) Collagen at 56cm1. (g) FWM image. (h) SHG image at 400 nm. Spatial resolution: 1 μm. Scale bars: 20 μm.
Fig. 4.
Fig. 4. THz-CARS imaging of collagen and HA in a TLT. (a) Raw measured THz-CARS spectra at two different pixels. (b) Corresponding resolved Raman spectra. (c) HA at 239cm1. A and B are the regions of the two spectra measurements. (d) Collagen at 56cm1. (e) Overlaid images of HA and collagen. (f) TPEF image at 520 nm. (g) SHG image at 400 nm. (h) Overlaid images of TPEF and SHG. Spatial resolution: 1 μm. Scale bars: 20 μm.

Equations (1)

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IRaman=(I1/I1NRBI2/I2NRB)·[(I1NRB+I2NRB)/2],