Abstract

We thoroughly analyze the linear propagation effects that affect polarization-resolved Second Harmonic Generation imaging of thick anisotropic tissues such as collagenous tissues. We develop a theoretical model that fully accounts for birefringence and diattenuation along the excitation propagation, and polarization scrambling upon scattering of the harmonic signal. We obtain an excellent agreement with polarization-resolved SHG images at increasing depth within a rat-tail tendon for both polarizations of the forward SHG signal. Most notably, we observe interference fringes due to birefringence in the SHG depth profile when excited at π/4 angle from the tendon axis. We also measure artifactual decrease of ρ = χxxx/χxyy with depth due to diattenuation of the excitation. We therefore derive a method that proves reliable to determine both ρ and the tendon birefringence and diattenuation.

© 2010 Optical Society of America

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  1. P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J. 82, 493–508 (2002).
    [CrossRef]
  2. W. R. Zipfel, R. Williams, R. Christie, A. Nikitin, B. Hyman, and W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100, 7075–7080 (2003).
    [CrossRef] [PubMed]
  3. A.-M. Pena, A. Fabre, D. Débarre, J. Marchal-Somme, B. Crestani, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Three-dimensional investigation and scoring of extracellular matrix remodeling during lung fibrosis using multiphoton microscopy,” Microsc. Res. Tech. 70(2), 162–170 (2007).
    [CrossRef]
  4. M. Strupler, M. Hernest, C. Fligny, J.-L. Martin, P.-L. Tharaux, and M.-C. Schanne-Klein, “Second harmonic microscopy to quantify renal interstitial fibrosis and arterial remodeling,” J. Biomed. Opt. 13, 054041 (2008).
    [CrossRef]
  5. S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90, 328–339 (2006).
    [CrossRef]
  6. F. Tiaho, G. Recher, and D. Rouède, “Estimation of helical angle of myosin and collagen by second harmonic generation imaging microscopy,” Opt. Express 15(19), 12286–12295 (2007).
    [CrossRef] [PubMed]
  7. A. Deniset-Besseau, J. Duboisset, E. Benichou, F. Hache, P.-F. Brevet, and M.-C. Schanne-Klein, “Measurement of the second order hyperpolarizability of the collagen triple helix and determination of its physical origin,” J. Phys. Chem. B 113(40), 13437–13445 (2009).
    [CrossRef] [PubMed]
  8. V. Nucciotti, C. Stringari, L. Sacconi, F. Vanzi, L. Fusi, M. Linari, G. Piazzesi, V. Lombardi, and F. S. Pavone, “Probing myosin structural conformation in vivo by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(17), 7763–7768 (2010).
    [CrossRef] [PubMed]
  9. S. Roth and I. Freund, “Second harmonic generation in collagen,” J. Chem. Phys. 70(04), 1637–1643 (1979).
    [CrossRef]
  10. P. Stoller, K. Reiser, P. Celliers, and A. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys. J. 82(6), 3330–3342 (2002).
    [CrossRef] [PubMed]
  11. P. Stoller, P. Celliers, K. Reiser, and A. Rubenchik, “Quantitative second-harmonic generation microscopy in collagen,” Appl. Opt. 42(25), 5209–5219 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  15. J. C. Mansfield, C. P. Winlove, J. Moger, and S. J. Matcher, “Collagen fiber arrangement in normal and diseased cartilage studied by polarization sensitive nonlinear microscopy,” J. Biomed. Opt. 13(4), 044020 (2008).
    [CrossRef]
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    [CrossRef] [PubMed]
  17. O. Nadiarnykh, and P. J. Campagnola, “Retention of polarization signatures in SHG microscopy of scattering tissues through optical clearing,” Opt. Express 17, 5794–5806 (2009).
    [CrossRef] [PubMed]
  18. M. Strupler, A.-M. Pena, M. Hernest, P.-L. Tharaux, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Second harmonic imaging and scoring of collagen in fibrotic tissues,” Opt. Express 15(7), 4054–4065 (2007).
    [CrossRef] [PubMed]
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  22. N. Olivier and E. Beaurepaire, “Third-harmonic generation microscopy with focus-engineered beams: a numerical study,” Opt. Express 16(19), 14703–14715 (2008).
    [CrossRef] [PubMed]
  23. P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A 81(1), 013809 (2010).
    [CrossRef]
  24. X. D. Wang and L. H. V. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
    [CrossRef]
  25. R. LaComb, O. Nadiarnykh, and S. Carey, S. and P. J. Campagnola, “Quantitative second harmonic generation imaging and modeling of the optical clearing mechanism in striated muscle and tendon,” J. Biomed. Opt. 13, 021109 (2008).
    [CrossRef]
  26. T. Boulesteix, A. Pena, N. Pagès, G. Godeau, M.-P. Sauviat, E. Beaurepaire, and M. Schanne-Klein, “Micrometer scale ex vivo multiphoton imaging of unstained arterial wall structure,” Cytometry 69A(1), 20–26 (2006).
    [CrossRef]

2010 (3)

V. Nucciotti, C. Stringari, L. Sacconi, F. Vanzi, L. Fusi, M. Linari, G. Piazzesi, V. Lombardi, and F. S. Pavone, “Probing myosin structural conformation in vivo by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(17), 7763–7768 (2010).
[CrossRef] [PubMed]

P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A 81(1), 013809 (2010).
[CrossRef]

D. Aït-Belkacem, A. Gasecka, F. Munhoz, S. Brustlein, and S. Brasselet, “Influence of birefringence on polarization resolved nonlinear microscopy and collagen SHG structural imaging,” Opt. Express 18(14), 14859–14870 (2010).
[CrossRef] [PubMed]

2009 (3)

2008 (5)

M. Strupler, M. Hernest, C. Fligny, J.-L. Martin, P.-L. Tharaux, and M.-C. Schanne-Klein, “Second harmonic microscopy to quantify renal interstitial fibrosis and arterial remodeling,” J. Biomed. Opt. 13, 054041 (2008).
[CrossRef]

R. LaComb, O. Nadiarnykh, and S. Carey, S. and P. J. Campagnola, “Quantitative second harmonic generation imaging and modeling of the optical clearing mechanism in striated muscle and tendon,” J. Biomed. Opt. 13, 021109 (2008).
[CrossRef]

J. C. Mansfield, C. P. Winlove, J. Moger, and S. J. Matcher, “Collagen fiber arrangement in normal and diseased cartilage studied by polarization sensitive nonlinear microscopy,” J. Biomed. Opt. 13(4), 044020 (2008).
[CrossRef]

X. Han, R. M. Burke, M. L. Zettel, P. Tang, and E. B. Brown, “Second harmonic properties of tumor collagen: determining the structural relationship between reactive stroma and healthy stroma,” Opt. Express 16(3), 1846–1859 (2008).
[CrossRef] [PubMed]

N. Olivier and E. Beaurepaire, “Third-harmonic generation microscopy with focus-engineered beams: a numerical study,” Opt. Express 16(19), 14703–14715 (2008).
[CrossRef] [PubMed]

2007 (4)

M. Strupler, A.-M. Pena, M. Hernest, P.-L. Tharaux, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Second harmonic imaging and scoring of collagen in fibrotic tissues,” Opt. Express 15(7), 4054–4065 (2007).
[CrossRef] [PubMed]

F. Tiaho, G. Recher, and D. Rouède, “Estimation of helical angle of myosin and collagen by second harmonic generation imaging microscopy,” Opt. Express 15(19), 12286–12295 (2007).
[CrossRef] [PubMed]

A. Erikson, J. Örtegren, T. Hompland, C. de Lange Davies, and M. Lindgren, “Quantification of the second-order nonlinear susceptibility of collagen I using a laser scanning microscope,” J. Biomed. Opt. 12(4), 044002 (2007).
[CrossRef]

A.-M. Pena, A. Fabre, D. Débarre, J. Marchal-Somme, B. Crestani, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Three-dimensional investigation and scoring of extracellular matrix remodeling during lung fibrosis using multiphoton microscopy,” Microsc. Res. Tech. 70(2), 162–170 (2007).
[CrossRef]

2006 (2)

S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90, 328–339 (2006).
[CrossRef]

T. Boulesteix, A. Pena, N. Pagès, G. Godeau, M.-P. Sauviat, E. Beaurepaire, and M. Schanne-Klein, “Micrometer scale ex vivo multiphoton imaging of unstained arterial wall structure,” Cytometry 69A(1), 20–26 (2006).
[CrossRef]

2005 (2)

2003 (2)

P. Stoller, P. Celliers, K. Reiser, and A. Rubenchik, “Quantitative second-harmonic generation microscopy in collagen,” Appl. Opt. 42(25), 5209–5219 (2003).
[CrossRef] [PubMed]

W. R. Zipfel, R. Williams, R. Christie, A. Nikitin, B. Hyman, and W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100, 7075–7080 (2003).
[CrossRef] [PubMed]

2002 (3)

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J. 82, 493–508 (2002).
[CrossRef]

X. D. Wang and L. H. V. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[CrossRef]

P. Stoller, K. Reiser, P. Celliers, and A. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys. J. 82(6), 3330–3342 (2002).
[CrossRef] [PubMed]

1979 (1)

S. Roth and I. Freund, “Second harmonic generation in collagen,” J. Chem. Phys. 70(04), 1637–1643 (1979).
[CrossRef]

Aït-Belkacem, D.

P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A 81(1), 013809 (2010).
[CrossRef]

D. Aït-Belkacem, A. Gasecka, F. Munhoz, S. Brustlein, and S. Brasselet, “Influence of birefringence on polarization resolved nonlinear microscopy and collagen SHG structural imaging,” Opt. Express 18(14), 14859–14870 (2010).
[CrossRef] [PubMed]

Beaurepaire, E.

N. Olivier and E. Beaurepaire, “Third-harmonic generation microscopy with focus-engineered beams: a numerical study,” Opt. Express 16(19), 14703–14715 (2008).
[CrossRef] [PubMed]

A.-M. Pena, A. Fabre, D. Débarre, J. Marchal-Somme, B. Crestani, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Three-dimensional investigation and scoring of extracellular matrix remodeling during lung fibrosis using multiphoton microscopy,” Microsc. Res. Tech. 70(2), 162–170 (2007).
[CrossRef]

M. Strupler, A.-M. Pena, M. Hernest, P.-L. Tharaux, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Second harmonic imaging and scoring of collagen in fibrotic tissues,” Opt. Express 15(7), 4054–4065 (2007).
[CrossRef] [PubMed]

T. Boulesteix, A. Pena, N. Pagès, G. Godeau, M.-P. Sauviat, E. Beaurepaire, and M. Schanne-Klein, “Micrometer scale ex vivo multiphoton imaging of unstained arterial wall structure,” Cytometry 69A(1), 20–26 (2006).
[CrossRef]

Behrndt, M.

P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A 81(1), 013809 (2010).
[CrossRef]

Benichou, E.

A. Deniset-Besseau, J. Duboisset, E. Benichou, F. Hache, P.-F. Brevet, and M.-C. Schanne-Klein, “Measurement of the second order hyperpolarizability of the collagen triple helix and determination of its physical origin,” J. Phys. Chem. B 113(40), 13437–13445 (2009).
[CrossRef] [PubMed]

Boulesteix, T.

T. Boulesteix, A. Pena, N. Pagès, G. Godeau, M.-P. Sauviat, E. Beaurepaire, and M. Schanne-Klein, “Micrometer scale ex vivo multiphoton imaging of unstained arterial wall structure,” Cytometry 69A(1), 20–26 (2006).
[CrossRef]

Brasselet, S.

P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A 81(1), 013809 (2010).
[CrossRef]

D. Aït-Belkacem, A. Gasecka, F. Munhoz, S. Brustlein, and S. Brasselet, “Influence of birefringence on polarization resolved nonlinear microscopy and collagen SHG structural imaging,” Opt. Express 18(14), 14859–14870 (2010).
[CrossRef] [PubMed]

Brevet, P.-F.

A. Deniset-Besseau, J. Duboisset, E. Benichou, F. Hache, P.-F. Brevet, and M.-C. Schanne-Klein, “Measurement of the second order hyperpolarizability of the collagen triple helix and determination of its physical origin,” J. Phys. Chem. B 113(40), 13437–13445 (2009).
[CrossRef] [PubMed]

Brown, E. B.

Brustlein, S.

Burke, R. M.

Campagnola, P.

S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90, 328–339 (2006).
[CrossRef]

Campagnola, P. J.

O. Nadiarnykh, and P. J. Campagnola, “Retention of polarization signatures in SHG microscopy of scattering tissues through optical clearing,” Opt. Express 17, 5794–5806 (2009).
[CrossRef] [PubMed]

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J. 82, 493–508 (2002).
[CrossRef]

Carey, S.

R. LaComb, O. Nadiarnykh, and S. Carey, S. and P. J. Campagnola, “Quantitative second harmonic generation imaging and modeling of the optical clearing mechanism in striated muscle and tendon,” J. Biomed. Opt. 13, 021109 (2008).
[CrossRef]

Celliers, P.

P. Stoller, P. Celliers, K. Reiser, and A. Rubenchik, “Quantitative second-harmonic generation microscopy in collagen,” Appl. Opt. 42(25), 5209–5219 (2003).
[CrossRef] [PubMed]

P. Stoller, K. Reiser, P. Celliers, and A. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys. J. 82(6), 3330–3342 (2002).
[CrossRef] [PubMed]

Christie, R.

W. R. Zipfel, R. Williams, R. Christie, A. Nikitin, B. Hyman, and W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100, 7075–7080 (2003).
[CrossRef] [PubMed]

Crestani, B.

A.-M. Pena, A. Fabre, D. Débarre, J. Marchal-Somme, B. Crestani, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Three-dimensional investigation and scoring of extracellular matrix remodeling during lung fibrosis using multiphoton microscopy,” Microsc. Res. Tech. 70(2), 162–170 (2007).
[CrossRef]

de Lange Davies, C.

A. Erikson, J. Örtegren, T. Hompland, C. de Lange Davies, and M. Lindgren, “Quantification of the second-order nonlinear susceptibility of collagen I using a laser scanning microscope,” J. Biomed. Opt. 12(4), 044002 (2007).
[CrossRef]

Débarre, D.

A.-M. Pena, A. Fabre, D. Débarre, J. Marchal-Somme, B. Crestani, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Three-dimensional investigation and scoring of extracellular matrix remodeling during lung fibrosis using multiphoton microscopy,” Microsc. Res. Tech. 70(2), 162–170 (2007).
[CrossRef]

Deniset-Besseau, A.

A. Deniset-Besseau, J. Duboisset, E. Benichou, F. Hache, P.-F. Brevet, and M.-C. Schanne-Klein, “Measurement of the second order hyperpolarizability of the collagen triple helix and determination of its physical origin,” J. Phys. Chem. B 113(40), 13437–13445 (2009).
[CrossRef] [PubMed]

Duboisset, J.

A. Deniset-Besseau, J. Duboisset, E. Benichou, F. Hache, P.-F. Brevet, and M.-C. Schanne-Klein, “Measurement of the second order hyperpolarizability of the collagen triple helix and determination of its physical origin,” J. Phys. Chem. B 113(40), 13437–13445 (2009).
[CrossRef] [PubMed]

Erikson, A.

A. Erikson, J. Örtegren, T. Hompland, C. de Lange Davies, and M. Lindgren, “Quantification of the second-order nonlinear susceptibility of collagen I using a laser scanning microscope,” J. Biomed. Opt. 12(4), 044002 (2007).
[CrossRef]

Fabre, A.

A.-M. Pena, A. Fabre, D. Débarre, J. Marchal-Somme, B. Crestani, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Three-dimensional investigation and scoring of extracellular matrix remodeling during lung fibrosis using multiphoton microscopy,” Microsc. Res. Tech. 70(2), 162–170 (2007).
[CrossRef]

Fligny, C.

M. Strupler, M. Hernest, C. Fligny, J.-L. Martin, P.-L. Tharaux, and M.-C. Schanne-Klein, “Second harmonic microscopy to quantify renal interstitial fibrosis and arterial remodeling,” J. Biomed. Opt. 13, 054041 (2008).
[CrossRef]

Freund, I.

S. Roth and I. Freund, “Second harmonic generation in collagen,” J. Chem. Phys. 70(04), 1637–1643 (1979).
[CrossRef]

Fusi, L.

V. Nucciotti, C. Stringari, L. Sacconi, F. Vanzi, L. Fusi, M. Linari, G. Piazzesi, V. Lombardi, and F. S. Pavone, “Probing myosin structural conformation in vivo by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(17), 7763–7768 (2010).
[CrossRef] [PubMed]

Gasecka, A.

Godeau, G.

T. Boulesteix, A. Pena, N. Pagès, G. Godeau, M.-P. Sauviat, E. Beaurepaire, and M. Schanne-Klein, “Micrometer scale ex vivo multiphoton imaging of unstained arterial wall structure,” Cytometry 69A(1), 20–26 (2006).
[CrossRef]

Hache, F.

A. Deniset-Besseau, J. Duboisset, E. Benichou, F. Hache, P.-F. Brevet, and M.-C. Schanne-Klein, “Measurement of the second order hyperpolarizability of the collagen triple helix and determination of its physical origin,” J. Phys. Chem. B 113(40), 13437–13445 (2009).
[CrossRef] [PubMed]

Han, X.

Hernest, M.

M. Strupler, M. Hernest, C. Fligny, J.-L. Martin, P.-L. Tharaux, and M.-C. Schanne-Klein, “Second harmonic microscopy to quantify renal interstitial fibrosis and arterial remodeling,” J. Biomed. Opt. 13, 054041 (2008).
[CrossRef]

M. Strupler, A.-M. Pena, M. Hernest, P.-L. Tharaux, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Second harmonic imaging and scoring of collagen in fibrotic tissues,” Opt. Express 15(7), 4054–4065 (2007).
[CrossRef] [PubMed]

Hompland, T.

A. Erikson, J. Örtegren, T. Hompland, C. de Lange Davies, and M. Lindgren, “Quantification of the second-order nonlinear susceptibility of collagen I using a laser scanning microscope,” J. Biomed. Opt. 12(4), 044002 (2007).
[CrossRef]

Hoppe, P. E.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J. 82, 493–508 (2002).
[CrossRef]

Hyman, B.

W. R. Zipfel, R. Williams, R. Christie, A. Nikitin, B. Hyman, and W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100, 7075–7080 (2003).
[CrossRef] [PubMed]

Kemp, N. J.

LaComb, R.

R. LaComb, O. Nadiarnykh, and S. Carey, S. and P. J. Campagnola, “Quantitative second harmonic generation imaging and modeling of the optical clearing mechanism in striated muscle and tendon,” J. Biomed. Opt. 13, 021109 (2008).
[CrossRef]

Linari, M.

V. Nucciotti, C. Stringari, L. Sacconi, F. Vanzi, L. Fusi, M. Linari, G. Piazzesi, V. Lombardi, and F. S. Pavone, “Probing myosin structural conformation in vivo by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(17), 7763–7768 (2010).
[CrossRef] [PubMed]

Lindgren, M.

A. Erikson, J. Örtegren, T. Hompland, C. de Lange Davies, and M. Lindgren, “Quantification of the second-order nonlinear susceptibility of collagen I using a laser scanning microscope,” J. Biomed. Opt. 12(4), 044002 (2007).
[CrossRef]

Lombardi, V.

V. Nucciotti, C. Stringari, L. Sacconi, F. Vanzi, L. Fusi, M. Linari, G. Piazzesi, V. Lombardi, and F. S. Pavone, “Probing myosin structural conformation in vivo by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(17), 7763–7768 (2010).
[CrossRef] [PubMed]

Malone, C. J.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J. 82, 493–508 (2002).
[CrossRef]

Mansfield, J. C.

J. C. Mansfield, C. P. Winlove, J. Moger, and S. J. Matcher, “Collagen fiber arrangement in normal and diseased cartilage studied by polarization sensitive nonlinear microscopy,” J. Biomed. Opt. 13(4), 044020 (2008).
[CrossRef]

Marchal-Somme, J.

A.-M. Pena, A. Fabre, D. Débarre, J. Marchal-Somme, B. Crestani, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Three-dimensional investigation and scoring of extracellular matrix remodeling during lung fibrosis using multiphoton microscopy,” Microsc. Res. Tech. 70(2), 162–170 (2007).
[CrossRef]

Martin, J.-L.

M. Strupler, M. Hernest, C. Fligny, J.-L. Martin, P.-L. Tharaux, and M.-C. Schanne-Klein, “Second harmonic microscopy to quantify renal interstitial fibrosis and arterial remodeling,” J. Biomed. Opt. 13, 054041 (2008).
[CrossRef]

A.-M. Pena, A. Fabre, D. Débarre, J. Marchal-Somme, B. Crestani, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Three-dimensional investigation and scoring of extracellular matrix remodeling during lung fibrosis using multiphoton microscopy,” Microsc. Res. Tech. 70(2), 162–170 (2007).
[CrossRef]

M. Strupler, A.-M. Pena, M. Hernest, P.-L. Tharaux, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Second harmonic imaging and scoring of collagen in fibrotic tissues,” Opt. Express 15(7), 4054–4065 (2007).
[CrossRef] [PubMed]

Matcher, S. J.

J. C. Mansfield, C. P. Winlove, J. Moger, and S. J. Matcher, “Collagen fiber arrangement in normal and diseased cartilage studied by polarization sensitive nonlinear microscopy,” J. Biomed. Opt. 13(4), 044020 (2008).
[CrossRef]

Millard, A.

S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90, 328–339 (2006).
[CrossRef]

Millard, A. C.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J. 82, 493–508 (2002).
[CrossRef]

Milner, T. E.

Moger, J.

J. C. Mansfield, C. P. Winlove, J. Moger, and S. J. Matcher, “Collagen fiber arrangement in normal and diseased cartilage studied by polarization sensitive nonlinear microscopy,” J. Biomed. Opt. 13(4), 044020 (2008).
[CrossRef]

Mohler, W.

S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90, 328–339 (2006).
[CrossRef]

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J. 82, 493–508 (2002).
[CrossRef]

Munhoz, F.

Nadiarnykh, O.

O. Nadiarnykh, and P. J. Campagnola, “Retention of polarization signatures in SHG microscopy of scattering tissues through optical clearing,” Opt. Express 17, 5794–5806 (2009).
[CrossRef] [PubMed]

R. LaComb, O. Nadiarnykh, and S. Carey, S. and P. J. Campagnola, “Quantitative second harmonic generation imaging and modeling of the optical clearing mechanism in striated muscle and tendon,” J. Biomed. Opt. 13, 021109 (2008).
[CrossRef]

Nikitin, A.

W. R. Zipfel, R. Williams, R. Christie, A. Nikitin, B. Hyman, and W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100, 7075–7080 (2003).
[CrossRef] [PubMed]

Nucciotti, V.

V. Nucciotti, C. Stringari, L. Sacconi, F. Vanzi, L. Fusi, M. Linari, G. Piazzesi, V. Lombardi, and F. S. Pavone, “Probing myosin structural conformation in vivo by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(17), 7763–7768 (2010).
[CrossRef] [PubMed]

Olivier, N.

Örtegren, J.

A. Erikson, J. Örtegren, T. Hompland, C. de Lange Davies, and M. Lindgren, “Quantification of the second-order nonlinear susceptibility of collagen I using a laser scanning microscope,” J. Biomed. Opt. 12(4), 044002 (2007).
[CrossRef]

Pagès, N.

T. Boulesteix, A. Pena, N. Pagès, G. Godeau, M.-P. Sauviat, E. Beaurepaire, and M. Schanne-Klein, “Micrometer scale ex vivo multiphoton imaging of unstained arterial wall structure,” Cytometry 69A(1), 20–26 (2006).
[CrossRef]

Park, J.

Pavone, F. S.

V. Nucciotti, C. Stringari, L. Sacconi, F. Vanzi, L. Fusi, M. Linari, G. Piazzesi, V. Lombardi, and F. S. Pavone, “Probing myosin structural conformation in vivo by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(17), 7763–7768 (2010).
[CrossRef] [PubMed]

Pena, A.

T. Boulesteix, A. Pena, N. Pagès, G. Godeau, M.-P. Sauviat, E. Beaurepaire, and M. Schanne-Klein, “Micrometer scale ex vivo multiphoton imaging of unstained arterial wall structure,” Cytometry 69A(1), 20–26 (2006).
[CrossRef]

Pena, A.-M.

A.-M. Pena, A. Fabre, D. Débarre, J. Marchal-Somme, B. Crestani, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Three-dimensional investigation and scoring of extracellular matrix remodeling during lung fibrosis using multiphoton microscopy,” Microsc. Res. Tech. 70(2), 162–170 (2007).
[CrossRef]

M. Strupler, A.-M. Pena, M. Hernest, P.-L. Tharaux, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Second harmonic imaging and scoring of collagen in fibrotic tissues,” Opt. Express 15(7), 4054–4065 (2007).
[CrossRef] [PubMed]

Piazzesi, G.

V. Nucciotti, C. Stringari, L. Sacconi, F. Vanzi, L. Fusi, M. Linari, G. Piazzesi, V. Lombardi, and F. S. Pavone, “Probing myosin structural conformation in vivo by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(17), 7763–7768 (2010).
[CrossRef] [PubMed]

Plotnikov, S. V.

S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90, 328–339 (2006).
[CrossRef]

Recher, G.

Reiser, K.

P. Stoller, P. Celliers, K. Reiser, and A. Rubenchik, “Quantitative second-harmonic generation microscopy in collagen,” Appl. Opt. 42(25), 5209–5219 (2003).
[CrossRef] [PubMed]

P. Stoller, K. Reiser, P. Celliers, and A. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys. J. 82(6), 3330–3342 (2002).
[CrossRef] [PubMed]

Rigneault, H.

P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A 81(1), 013809 (2010).
[CrossRef]

Roth, S.

S. Roth and I. Freund, “Second harmonic generation in collagen,” J. Chem. Phys. 70(04), 1637–1643 (1979).
[CrossRef]

Rouède, D.

Rubenchik, A.

P. Stoller, P. Celliers, K. Reiser, and A. Rubenchik, “Quantitative second-harmonic generation microscopy in collagen,” Appl. Opt. 42(25), 5209–5219 (2003).
[CrossRef] [PubMed]

P. Stoller, K. Reiser, P. Celliers, and A. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys. J. 82(6), 3330–3342 (2002).
[CrossRef] [PubMed]

Rylander, H. G.

Sacconi, L.

V. Nucciotti, C. Stringari, L. Sacconi, F. Vanzi, L. Fusi, M. Linari, G. Piazzesi, V. Lombardi, and F. S. Pavone, “Probing myosin structural conformation in vivo by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(17), 7763–7768 (2010).
[CrossRef] [PubMed]

Sauviat, M.-P.

T. Boulesteix, A. Pena, N. Pagès, G. Godeau, M.-P. Sauviat, E. Beaurepaire, and M. Schanne-Klein, “Micrometer scale ex vivo multiphoton imaging of unstained arterial wall structure,” Cytometry 69A(1), 20–26 (2006).
[CrossRef]

Schanne-Klein, M.

T. Boulesteix, A. Pena, N. Pagès, G. Godeau, M.-P. Sauviat, E. Beaurepaire, and M. Schanne-Klein, “Micrometer scale ex vivo multiphoton imaging of unstained arterial wall structure,” Cytometry 69A(1), 20–26 (2006).
[CrossRef]

Schanne-Klein, M.-C.

A. Deniset-Besseau, J. Duboisset, E. Benichou, F. Hache, P.-F. Brevet, and M.-C. Schanne-Klein, “Measurement of the second order hyperpolarizability of the collagen triple helix and determination of its physical origin,” J. Phys. Chem. B 113(40), 13437–13445 (2009).
[CrossRef] [PubMed]

M. Strupler, M. Hernest, C. Fligny, J.-L. Martin, P.-L. Tharaux, and M.-C. Schanne-Klein, “Second harmonic microscopy to quantify renal interstitial fibrosis and arterial remodeling,” J. Biomed. Opt. 13, 054041 (2008).
[CrossRef]

A.-M. Pena, A. Fabre, D. Débarre, J. Marchal-Somme, B. Crestani, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Three-dimensional investigation and scoring of extracellular matrix remodeling during lung fibrosis using multiphoton microscopy,” Microsc. Res. Tech. 70(2), 162–170 (2007).
[CrossRef]

M. Strupler, A.-M. Pena, M. Hernest, P.-L. Tharaux, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Second harmonic imaging and scoring of collagen in fibrotic tissues,” Opt. Express 15(7), 4054–4065 (2007).
[CrossRef] [PubMed]

Schön, P.

P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A 81(1), 013809 (2010).
[CrossRef]

Stoller, P.

P. Stoller, P. Celliers, K. Reiser, and A. Rubenchik, “Quantitative second-harmonic generation microscopy in collagen,” Appl. Opt. 42(25), 5209–5219 (2003).
[CrossRef] [PubMed]

P. Stoller, K. Reiser, P. Celliers, and A. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys. J. 82(6), 3330–3342 (2002).
[CrossRef] [PubMed]

Stringari, C.

V. Nucciotti, C. Stringari, L. Sacconi, F. Vanzi, L. Fusi, M. Linari, G. Piazzesi, V. Lombardi, and F. S. Pavone, “Probing myosin structural conformation in vivo by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(17), 7763–7768 (2010).
[CrossRef] [PubMed]

Strupler, M.

M. Strupler, M. Hernest, C. Fligny, J.-L. Martin, P.-L. Tharaux, and M.-C. Schanne-Klein, “Second harmonic microscopy to quantify renal interstitial fibrosis and arterial remodeling,” J. Biomed. Opt. 13, 054041 (2008).
[CrossRef]

M. Strupler, A.-M. Pena, M. Hernest, P.-L. Tharaux, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Second harmonic imaging and scoring of collagen in fibrotic tissues,” Opt. Express 15(7), 4054–4065 (2007).
[CrossRef] [PubMed]

Tang, P.

Terasaki, M.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J. 82, 493–508 (2002).
[CrossRef]

Tharaux, P.-L.

M. Strupler, M. Hernest, C. Fligny, J.-L. Martin, P.-L. Tharaux, and M.-C. Schanne-Klein, “Second harmonic microscopy to quantify renal interstitial fibrosis and arterial remodeling,” J. Biomed. Opt. 13, 054041 (2008).
[CrossRef]

M. Strupler, A.-M. Pena, M. Hernest, P.-L. Tharaux, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Second harmonic imaging and scoring of collagen in fibrotic tissues,” Opt. Express 15(7), 4054–4065 (2007).
[CrossRef] [PubMed]

Tiaho, F.

Vanzi, F.

V. Nucciotti, C. Stringari, L. Sacconi, F. Vanzi, L. Fusi, M. Linari, G. Piazzesi, V. Lombardi, and F. S. Pavone, “Probing myosin structural conformation in vivo by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(17), 7763–7768 (2010).
[CrossRef] [PubMed]

Wang, L. H. V.

X. D. Wang and L. H. V. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[CrossRef]

Wang, X. D.

X. D. Wang and L. H. V. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[CrossRef]

Webb, W.

R. Williams, W. R. Zipfel, and W. Webb, “Interpreting second-harmonic generation images of collagen fibrils,” Biophys. J. 88, 1377–1386 (2005).
[CrossRef]

W. R. Zipfel, R. Williams, R. Christie, A. Nikitin, B. Hyman, and W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100, 7075–7080 (2003).
[CrossRef] [PubMed]

Williams, R.

R. Williams, W. R. Zipfel, and W. Webb, “Interpreting second-harmonic generation images of collagen fibrils,” Biophys. J. 88, 1377–1386 (2005).
[CrossRef]

W. R. Zipfel, R. Williams, R. Christie, A. Nikitin, B. Hyman, and W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100, 7075–7080 (2003).
[CrossRef] [PubMed]

Winlove, C. P.

J. C. Mansfield, C. P. Winlove, J. Moger, and S. J. Matcher, “Collagen fiber arrangement in normal and diseased cartilage studied by polarization sensitive nonlinear microscopy,” J. Biomed. Opt. 13(4), 044020 (2008).
[CrossRef]

Zaatari, H. N.

Zettel, M. L.

Zipfel, W. R.

R. Williams, W. R. Zipfel, and W. Webb, “Interpreting second-harmonic generation images of collagen fibrils,” Biophys. J. 88, 1377–1386 (2005).
[CrossRef]

W. R. Zipfel, R. Williams, R. Christie, A. Nikitin, B. Hyman, and W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100, 7075–7080 (2003).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biophys. J. (4)

R. Williams, W. R. Zipfel, and W. Webb, “Interpreting second-harmonic generation images of collagen fibrils,” Biophys. J. 88, 1377–1386 (2005).
[CrossRef]

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J. 82, 493–508 (2002).
[CrossRef]

S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90, 328–339 (2006).
[CrossRef]

P. Stoller, K. Reiser, P. Celliers, and A. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys. J. 82(6), 3330–3342 (2002).
[CrossRef] [PubMed]

Cytometry (1)

T. Boulesteix, A. Pena, N. Pagès, G. Godeau, M.-P. Sauviat, E. Beaurepaire, and M. Schanne-Klein, “Micrometer scale ex vivo multiphoton imaging of unstained arterial wall structure,” Cytometry 69A(1), 20–26 (2006).
[CrossRef]

J. Biomed. Opt. (5)

X. D. Wang and L. H. V. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[CrossRef]

R. LaComb, O. Nadiarnykh, and S. Carey, S. and P. J. Campagnola, “Quantitative second harmonic generation imaging and modeling of the optical clearing mechanism in striated muscle and tendon,” J. Biomed. Opt. 13, 021109 (2008).
[CrossRef]

M. Strupler, M. Hernest, C. Fligny, J.-L. Martin, P.-L. Tharaux, and M.-C. Schanne-Klein, “Second harmonic microscopy to quantify renal interstitial fibrosis and arterial remodeling,” J. Biomed. Opt. 13, 054041 (2008).
[CrossRef]

A. Erikson, J. Örtegren, T. Hompland, C. de Lange Davies, and M. Lindgren, “Quantification of the second-order nonlinear susceptibility of collagen I using a laser scanning microscope,” J. Biomed. Opt. 12(4), 044002 (2007).
[CrossRef]

J. C. Mansfield, C. P. Winlove, J. Moger, and S. J. Matcher, “Collagen fiber arrangement in normal and diseased cartilage studied by polarization sensitive nonlinear microscopy,” J. Biomed. Opt. 13(4), 044020 (2008).
[CrossRef]

J. Chem. Phys. (1)

S. Roth and I. Freund, “Second harmonic generation in collagen,” J. Chem. Phys. 70(04), 1637–1643 (1979).
[CrossRef]

J. Phys. Chem. B (1)

A. Deniset-Besseau, J. Duboisset, E. Benichou, F. Hache, P.-F. Brevet, and M.-C. Schanne-Klein, “Measurement of the second order hyperpolarizability of the collagen triple helix and determination of its physical origin,” J. Phys. Chem. B 113(40), 13437–13445 (2009).
[CrossRef] [PubMed]

Microsc. Res. Tech. (1)

A.-M. Pena, A. Fabre, D. Débarre, J. Marchal-Somme, B. Crestani, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Three-dimensional investigation and scoring of extracellular matrix remodeling during lung fibrosis using multiphoton microscopy,” Microsc. Res. Tech. 70(2), 162–170 (2007).
[CrossRef]

Opt. Express (8)

F. Tiaho, G. Recher, and D. Rouède, “Estimation of helical angle of myosin and collagen by second harmonic generation imaging microscopy,” Opt. Express 15(19), 12286–12295 (2007).
[CrossRef] [PubMed]

D. Aït-Belkacem, A. Gasecka, F. Munhoz, S. Brustlein, and S. Brasselet, “Influence of birefringence on polarization resolved nonlinear microscopy and collagen SHG structural imaging,” Opt. Express 18(14), 14859–14870 (2010).
[CrossRef] [PubMed]

O. Nadiarnykh, and P. J. Campagnola, “Retention of polarization signatures in SHG microscopy of scattering tissues through optical clearing,” Opt. Express 17, 5794–5806 (2009).
[CrossRef] [PubMed]

M. Strupler, A.-M. Pena, M. Hernest, P.-L. Tharaux, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Second harmonic imaging and scoring of collagen in fibrotic tissues,” Opt. Express 15(7), 4054–4065 (2007).
[CrossRef] [PubMed]

X. Han, R. M. Burke, M. L. Zettel, P. Tang, and E. B. Brown, “Second harmonic properties of tumor collagen: determining the structural relationship between reactive stroma and healthy stroma,” Opt. Express 16(3), 1846–1859 (2008).
[CrossRef] [PubMed]

N. J. Kemp, H. N. Zaatari, J. Park, H. G. Rylander, and T. E. Milner, “Form-biattenuance in fibrous tissues measured with polarization-sensitive optical coherence tomography (PS-OCT),” Opt. Express 13(12), 4611–4628 (2005).
[CrossRef] [PubMed]

J. Park, N. J. Kemp, H. G. Rylander, and T. E. Milner, “Complex polarization ratio to determine polarization properties of anisotropic tissue using polarization-sensitive optical coherence tomography,” Opt. Express 17(16), 13402–13417 (2009).
[CrossRef] [PubMed]

N. Olivier and E. Beaurepaire, “Third-harmonic generation microscopy with focus-engineered beams: a numerical study,” Opt. Express 16(19), 14703–14715 (2008).
[CrossRef] [PubMed]

Phys. Rev. A (1)

P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A 81(1), 013809 (2010).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (2)

V. Nucciotti, C. Stringari, L. Sacconi, F. Vanzi, L. Fusi, M. Linari, G. Piazzesi, V. Lombardi, and F. S. Pavone, “Probing myosin structural conformation in vivo by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(17), 7763–7768 (2010).
[CrossRef] [PubMed]

W. R. Zipfel, R. Williams, R. Christie, A. Nikitin, B. Hyman, and W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100, 7075–7080 (2003).
[CrossRef] [PubMed]

Other (1)

R. Boyd, Nonlinear optics (Academic Press, 2003).

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Figures (6)

Fig. 1.
Fig. 1.

Experimental setup. (a) Laser scanning multiphoton microscope showing polarization-resolved detection of forward SHG signal and epi-detection of 2PEF signal and possibly of SHG signal. The insert displays the incident electric field relative to the tendon geometry in the focal plane. (b) x- and y-polarized forward 2PEF signal from a fluorescent slide for variable incident polarization angles. The ratio of the 2 maxima is used for calibration of polarization-resolved SHG signals. (c) Combined 2PEF (red) and SHG (green) image of a tendon labeled with fluorescent latex beads. The image is the summation of 15 images acquired 2µm apart from the tendon upper surface, with enhanced contrast. The yellow box shows a typical Region of Interest used for plotting depth-polar diagrams as in fig. 5. Scale bar: 50µm.

Fig. 2.
Fig. 2.

Simulated polar diagrams of polarization-resolved SH intensity generated by a tendon aligned along x axis. The angle represents the direction of the excitation polarization to the tendon direction (see fig. 1.a). (a) Ix 2ω and (b) Iy 2ω in a non-birefringent, non-scattering medium without diattenuation (see eq. (2)). (c) Ix 2ω and (d) Iy 2ω at 24µm depth considering birefringence (Δn = 0.0066), diattenuation (Δla = 175µm) and polarisation cross-talk due to scattering (ηxy = 0.13) (see Eq. (11)). ρ = 1.40 in all simulations.

Fig. 3.
Fig. 3.

Numerical calculation of polarization-resolved SH intensity as a function of incident polarisation angle α (see fig. 1) and depth z within tendon for different parameters. (a)–(e) Ix 2ω , (f)–(j) Iy 2ω and (k)–(o) z-profiles of Ix 2ω for α = 0 (green dotted line), α = π/4 (blue dashed line) and α = π/2 (red dash-dot line). (a), (f), (k) tendon with uniform depthattenuation: la x = la y = 190µm. (b), (g), (l) tendon with polarization cross-talk: ηxy = 0.13, ηyx = 0.2 (constant with depth). (c), (h), (m) tendon with diattenuation: le a = 91µm and lo a = 190µm. (d), (i), (n) tendon with birefringence Δn = 0.0066. (e), (j), (o) tendon with diattenuation, birefringence and polarisation cross-talk (same parameters). ρ is equal to 1.40 for all calculations.

Fig. 4.
Fig. 4.

Polarization-resolved SH images of a tendon upon excitation polarized at π/4 from the tendon axis. (a)–(c) x- and (b)–(d) y-polarized SH images and transverse profiles of a tendon aligned along x axis at (a)–(b) 39 µm depth and (c)–(d) at 57 µm depth from the tendon upper surface. x-polarisation images shows dark fringes (red arrows), whereas y-polarisation has almost uniform intensity profile in the tendon center. Scale bar: 50 µm.

Fig. 5.
Fig. 5.

Experimental polarization-resolved SH intensity from a tendon. (a) Ix 2ω and (b) Iy 2ω as a function of incident polarisation angle α (see fig. 1) and lens displacement. (c) z-profile of fluorescence signal from latex beads, peaking at the tendon surface z 0. (d) Ix 2ω (α) and (e) Iy 2ω (α) at the tendon surface (black dots), along with fits using the simplified approach (eq. 3, red line) or accounting for polarization cross-talk (eq. 9, blue line). (f) experimental z-profiles of Ix 2ω for α = 0 (green dotted line), α = π/4 (blue dashed line) and α = π/2 (red dash-dot line).

Fig. 6.
Fig. 6.

Determination of tendon characteristic parameters from experimental SH depthprofiles. (a) Ix 2ω (α = 0) (blue dots) and Ix 2ω (α = π/2) (red squares) showing diattenuation: the solid lines correspond to exponential fitting with le a = 91µm and lo a = 190µm. (b) ρ determined from polarization-resolved SHG measurements with (black) and without (green) correction for diattenuation. (c) Δ parameter evidencing birefringence (oscillations), polarization cross-talk due to scattering (non-vanishing value at the tendon surface) and diattenuation (exponential attenuation with depth). The solid line represents fitting with the following parameters: Δn = 1.40, ηxy = 0.13 near the surface and Δla = 134µm.

Equations (27)

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P i = χ ij ( 1 ) E j + χ ijk ( 2 ) E j E k
P x 2 ω ( χ xxx cos 2 α + χ xyy sin 2 α ) E 0 2
P y 2 ω ( χ xyy sin 2 α ) E 0 2
I x 2 ω = K ρ cos 2 α + sin 2 α 2
I y 2 ω = K 2 sin α cos α 2
I x 2 ω = A cos 4 α + B cos 2 α + C
I y 2 ω = K 2 ( cos 4 α + 1 )
A = K 2 ( ρ 1 2 ) 2
B = 2 K ( ρ 1 2 ) ( ρ + 1 2 )
C = K 2 ( ρ 1 2 ) 2 + K ( ρ + 1 2 ) 2
ρ 2 = A + B + C A B + C
I x 2 ω ( z ) = K ρ cos 2 α e i ϕ + sin 2 α 2 = K ( ρ cos 2 α + sin 2 α 2 + ρ 2 sin 2 2 α ( cos ϕ 1 ) )
I y 2 ω ( z ) = K sin 2 α e i 2 π ( n e + n o ) λ z 2 = K sin 2 α 2
A biref = K [ 1 2 ( ρ 1 2 ) 2 + ρ 4 ( 1 cos ϕ ) ]
B biref = 2 K ( ρ 1 2 ) ( ρ + 1 2 )
C biref = K [ 1 2 ( ρ 1 2 ) 2 + ( ρ + 1 2 ) 2 ρ 4 ( 1 cos ϕ ) ]
I x 2 ω ( z ) = K ρ cos 2 α + sin 2 α 2 + η XY K sin 2 α 2
I y 2 ω ( z ) = η YX K ρ cos 2 α + sin 2 α 2 + K sin 2 α 2
A pol = K [ 1 2 ( ρ 1 2 ) 2 η XY 2 ]
B pol = 2 K ( ρ 1 2 ) ( ρ + 1 2 )
C pol = K [ 1 2 ( ρ 1 2 ) 2 + ( ρ + 1 2 ) 2 + η XY 2 ]
I x 2 ω ( z ) = K ρ cos 2 α e z l a e + sin 2 α e z l a o 2 = Ke 2 z l a o ρ e z l a cos 2 α + sin 2 α 2
I y 2 ω ( z ) = K sin 2 α e z 2 l a o e z 2 l a e 2 = Ke 2 z l a o e z l a sin 2 α 2
I x 2 ω ( z ) = Ke 2 z l a o ( ρe z l a cos 2 α e i ϕ + sin 2 α 2 + η XY e z l a sin 2 α 2 )
ρ 2 e 2 z l a = A eff + B eff + C eff A eff B eff + C eff
( z ) = C 3 A ( A + C ) 2 B 2 2 ( A B + C )
( z ) = f a [ η XY ρ 2 ( 1 cos ϕ ) ]

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