Abstract

Based on its polarization dependency, second harmonic generation (PSHG) microscopy has been proven capable to structurally characterize molecular architectures in different biological samples. By exploiting this polarization dependency of the SHG signal in every pixel of the image, average quantitative structural information can be retrieved in the form of PSHG image histograms. In the present study we experimentally show how the PSHG image histograms can be affected by the organization of the SHG active molecules. Our experimental scenario grounds on two inherent properties of starch granules. Firstly, we take advantage of the radial organization of amylopectin molecules (the SHG source in starch) to attribute shifts of the image histograms to the existence of tilted off the plane molecules. Secondly, we use the property of starch to organize upon hydration to demonstrate that the degree of structural order at the molecular level affects the width of the PSHG image histograms. The shorter the width is the more organized the molecules in the sample are, resulting in a reliable method to measure order. The implication of this finding is crucial to the interpretation of PSHG images used for example in tissue diagnostics.

© 2012 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  30. P. Schön, M. Behrndt, D. Aıt-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A81(1), 013809 (2010).
    [CrossRef]
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    [CrossRef]
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2012 (2)

G. Latour, I. Gusachenko, L. Kowalczuk, I. Lamarre, and M. C. Schanne-Klein, “In vivo structural imaging of the cornea by polarization-resolved second harmonic microscopy,” Biomed. Opt. Express3(1), 1–15 (2012).
[CrossRef] [PubMed]

J. Duboisset, D. Aït-Belkacem, M. Roche, H. Rigneault, and S. Brasselet, “Generic model of the molecular orientational distribution probed by polarization-resolved second-harmonic generation,” Phys. Rev. A85(4), 043829 (2012).
[CrossRef]

2011 (1)

P. J. Su, W. L. Chen, Y. F. Chen, and C. Y. Dong, “Determination of collagen nanostructure from second-order susceptibility tensor analysis,” Biophys. J.100(8), 2053–2062 (2011).
[CrossRef] [PubMed]

2010 (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]

S. Psilodimitrakopoulos, I. Amat-Roldan, P. Loza-Alvarez, and D. Artigas, “Estimating the helical pitch angle of amylopectin in starch using polarization second harmonic generation microscopy,” J. Opt.12(8), 084007 (2010).
[CrossRef]

Z.-Y. Zhuo, C.-S. Liao, C.-H. Huang, J.-Y. Yu, Y.-Y. Tzeng, W. Lo, C.-Y. Dong, H.-C. Chui, Y.-C. Huang, H.-M. Lai, and S.-W. Chu, “Second harmonic generation imaging - a new method for unraveling molecular information of starch,” J. Struct. Biol.171(1), 88–94 (2010).
[CrossRef] [PubMed]

M. Zimmerley, R. Younger, T. Valenton, D. C. Oertel, J. L. Ward, and E. O. Potma, “Molecular orientation in dry and hydrated cellulose fibers: a coherent anti-Stokes Raman scattering microscopy study,” J. Phys. Chem. B114(31), 10200–10208 (2010).
[CrossRef] [PubMed]

I. Amat-Roldan, S. Psilodimitrakopoulos, P. Loza-Alvarez, and D. Artigas, “Fast image analysis in polarization SHG microscopy,” Opt. Express18(16), 17209–17219 (2010).
[CrossRef] [PubMed]

I. Gusachenko, G. Latour, and M.-C. Schanne-Klein, “Polarization-resolved Second Harmonic microscopy in anisotropic thick tissues,” Opt. Express18(18), 19339–19352 (2010).
[CrossRef] [PubMed]

S. Brasselet, 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. Express18(14), 14859–14870 (2010).
[CrossRef] [PubMed]

P. Schön, M. Behrndt, D. Aıt-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A81(1), 013809 (2010).
[CrossRef]

2009 (8)

Y. Chang, C. Chen, J. Chen, Y. Jin, and X. Deng, “Theoretical simulation study of linearly polarized light on microscopic second-harmonic generation in collagen type I,” J. Biomed. Opt.14(4), 044016 (2009).
[CrossRef] [PubMed]

P.-J. Su, W.-L. Chen, J.-B. Hong, T.-H. Li, R.-J. Wu, C.-K. Chou, S.-J. Chen, C. Hu, S.-J. Lin, and C.-Y. Dong, “Discrimination of collagen in normal and pathological skin dermis through second-order susceptibility microscopy,” Opt. Express17(13), 11161–11171 (2009).
[CrossRef] [PubMed]

R. Cisek, L. Spencer, N. Prent, D. Zigmantas, G. S. Espie, and V. Barzda, “Optical microscopy in photosynthesis,” Photosynth. Res.102(2-3), 111–141 (2009).
[CrossRef] [PubMed]

C. Odin, C. Heichette, D. Chretien, and Y. Le Grand, “Second harmonic microscopy of axonemes,” Opt. Express17(11), 9235–9240 (2009).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, V. Petegnief, G. Soria, I. Amat-Roldan, D. Artigas, A. M. Planas, and P. Loza-Alvarez, “Estimation of the effective orientation of the SHG source in primary cortical neurons,” Opt. Express17(16), 14418–14425 (2009).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, D. Artigas, G. Soria, I. Amat-Roldan, A. M. Planas, and P. Loza-Alvarez, “Quantitative discrimination between endogenous SHG sources in mammalian tissue, based on their polarization response,” Opt. Express17(12), 10168–10176 (2009).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, S. I. Santos, I. Amat-Roldan, A. K. Thayil, D. Artigas, and P. Loza-Alvarez, “In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy,” J. Biomed. Opt.14(1), 014001 (2009).
[CrossRef] [PubMed]

W. L. Chen, T. H. Li, P. J. Su, C. K. Chou, P. T. Fwu, S. J. Lin, D. Kim, P. T. C. So, and C. Y. Dong, “Second harmonic generation chi tensor microscopy for tissue imaging,” Appl. Phys. Lett.94, 3 (2009).

2008 (1)

2007 (3)

2006 (2)

E. Y. S. Yew and C. J. R. Sheppard, “Effects of axial field components on second harmonic generation microscopy,” Opt. Express14(3), 1167–1174 (2006).
[CrossRef] [PubMed]

S. V. Plotnikov, A. C. Millard, P. J. Campagnola, and W. A. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J.90(2), 693–703 (2006).
[CrossRef] [PubMed]

2005 (1)

G. C. Cox, N. Moreno, and J. Feijó, “Second-harmonic imaging of plant polysaccharides,” J. Biomed. Opt.10(2), 024013 (2005).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

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

2000 (1)

J. Shimada, H. Kaneko, T. Takada, S. Kitamura, and K. Kajiwara, “Conformation of amylose in aqueous solution: small-angle x-ray scattering measurements and simulations,” J. Phys. Chem. B104(9), 2136–2147 (2000).
[CrossRef]

1999 (1)

G. J. Simpson and K. L. Rowlen, “An SHG magic angle: dependence of second harmonic generation orientation measurements on the width of the orientation distribution,” J. Am. Chem. Soc.121(11), 2635–2636 (1999).
[CrossRef]

1998 (1)

K. Beck and B. Brodsky, “Supercoiled protein motifs: the collagen triple-helix and the α-helical coiled coil,” J. Struct. Biol.122(1-2), 17–29 (1998).
[CrossRef] [PubMed]

1997 (1)

T. A. Waigh, I. Hopkinson, A. M. Donald, M. F. Butler, F. Heidelbach, and C. Riekel, “Analysis of the native structure of starch granules with x-ray microfocus diffraction,” Macromolecules30(13), 3813–3820 (1997).
[CrossRef]

1963 (1)

M. Abdel-Akher and A. N. Michalinos, “Separation and purification of starch from chufa nut tubers (Cyperus esculentus),” Starch15(9), 329–334 (1963).
[CrossRef]

1947 (1)

M. A. Swanson, “Studies on the structure of polysaccharides IV. Relation of the iodine color to the structure,” J. Biol. Chem.172, 825–837 (1947).

Abdel-Akher, M.

M. Abdel-Akher and A. N. Michalinos, “Separation and purification of starch from chufa nut tubers (Cyperus esculentus),” Starch15(9), 329–334 (1963).
[CrossRef]

Ait-Belkacem, D.

P. Schön, M. Behrndt, D. Aıt-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A81(1), 013809 (2010).
[CrossRef]

Aït-Belkacem, D.

J. Duboisset, D. Aït-Belkacem, M. Roche, H. Rigneault, and S. Brasselet, “Generic model of the molecular orientational distribution probed by polarization-resolved second-harmonic generation,” Phys. Rev. A85(4), 043829 (2012).
[CrossRef]

S. Brasselet, 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. Express18(14), 14859–14870 (2010).
[CrossRef] [PubMed]

Alkilani, A.

Amat-Roldan, I.

S. Psilodimitrakopoulos, I. Amat-Roldan, P. Loza-Alvarez, and D. Artigas, “Estimating the helical pitch angle of amylopectin in starch using polarization second harmonic generation microscopy,” J. Opt.12(8), 084007 (2010).
[CrossRef]

I. Amat-Roldan, S. Psilodimitrakopoulos, P. Loza-Alvarez, and D. Artigas, “Fast image analysis in polarization SHG microscopy,” Opt. Express18(16), 17209–17219 (2010).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, V. Petegnief, G. Soria, I. Amat-Roldan, D. Artigas, A. M. Planas, and P. Loza-Alvarez, “Estimation of the effective orientation of the SHG source in primary cortical neurons,” Opt. Express17(16), 14418–14425 (2009).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, D. Artigas, G. Soria, I. Amat-Roldan, A. M. Planas, and P. Loza-Alvarez, “Quantitative discrimination between endogenous SHG sources in mammalian tissue, based on their polarization response,” Opt. Express17(12), 10168–10176 (2009).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, S. I. Santos, I. Amat-Roldan, A. K. Thayil, D. Artigas, and P. Loza-Alvarez, “In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy,” J. Biomed. Opt.14(1), 014001 (2009).
[CrossRef] [PubMed]

Artigas, D.

S. Psilodimitrakopoulos, I. Amat-Roldan, P. Loza-Alvarez, and D. Artigas, “Estimating the helical pitch angle of amylopectin in starch using polarization second harmonic generation microscopy,” J. Opt.12(8), 084007 (2010).
[CrossRef]

I. Amat-Roldan, S. Psilodimitrakopoulos, P. Loza-Alvarez, and D. Artigas, “Fast image analysis in polarization SHG microscopy,” Opt. Express18(16), 17209–17219 (2010).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, D. Artigas, G. Soria, I. Amat-Roldan, A. M. Planas, and P. Loza-Alvarez, “Quantitative discrimination between endogenous SHG sources in mammalian tissue, based on their polarization response,” Opt. Express17(12), 10168–10176 (2009).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, V. Petegnief, G. Soria, I. Amat-Roldan, D. Artigas, A. M. Planas, and P. Loza-Alvarez, “Estimation of the effective orientation of the SHG source in primary cortical neurons,” Opt. Express17(16), 14418–14425 (2009).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, S. I. Santos, I. Amat-Roldan, A. K. Thayil, D. Artigas, and P. Loza-Alvarez, “In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy,” J. Biomed. Opt.14(1), 014001 (2009).
[CrossRef] [PubMed]

Barzda, V.

R. Cisek, L. Spencer, N. Prent, D. Zigmantas, G. S. Espie, and V. Barzda, “Optical microscopy in photosynthesis,” Photosynth. Res.102(2-3), 111–141 (2009).
[CrossRef] [PubMed]

Beck, K.

K. Beck and B. Brodsky, “Supercoiled protein motifs: the collagen triple-helix and the α-helical coiled coil,” J. Struct. Biol.122(1-2), 17–29 (1998).
[CrossRef] [PubMed]

Behrndt, M.

P. Schön, M. Behrndt, D. Aıt-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A81(1), 013809 (2010).
[CrossRef]

Boryskina, O. P.

Brasselet, S.

J. Duboisset, D. Aït-Belkacem, M. Roche, H. Rigneault, and S. Brasselet, “Generic model of the molecular orientational distribution probed by polarization-resolved second-harmonic generation,” Phys. Rev. A85(4), 043829 (2012).
[CrossRef]

P. Schön, M. Behrndt, D. Aıt-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A81(1), 013809 (2010).
[CrossRef]

S. Brasselet, 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. Express18(14), 14859–14870 (2010).
[CrossRef] [PubMed]

S. Brasselet, 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. Express18(14), 14859–14870 (2010).
[CrossRef] [PubMed]

Brodsky, B.

K. Beck and B. Brodsky, “Supercoiled protein motifs: the collagen triple-helix and the α-helical coiled coil,” J. Struct. Biol.122(1-2), 17–29 (1998).
[CrossRef] [PubMed]

Brown, R. M.

Brustlein, S.

Butler, M. F.

T. A. Waigh, I. Hopkinson, A. M. Donald, M. F. Butler, F. Heidelbach, and C. Riekel, “Analysis of the native structure of starch granules with x-ray microfocus diffraction,” Macromolecules30(13), 3813–3820 (1997).
[CrossRef]

Campagnola, P. J.

Celliers, P. M.

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

Chang, Y.

Y. Chang, C. Chen, J. Chen, Y. Jin, and X. Deng, “Theoretical simulation study of linearly polarized light on microscopic second-harmonic generation in collagen type I,” J. Biomed. Opt.14(4), 044016 (2009).
[CrossRef] [PubMed]

Chen, C.

Y. Chang, C. Chen, J. Chen, Y. Jin, and X. Deng, “Theoretical simulation study of linearly polarized light on microscopic second-harmonic generation in collagen type I,” J. Biomed. Opt.14(4), 044016 (2009).
[CrossRef] [PubMed]

Chen, J.

Y. Chang, C. Chen, J. Chen, Y. Jin, and X. Deng, “Theoretical simulation study of linearly polarized light on microscopic second-harmonic generation in collagen type I,” J. Biomed. Opt.14(4), 044016 (2009).
[CrossRef] [PubMed]

Chen, S.-J.

Chen, W. L.

P. J. Su, W. L. Chen, Y. F. Chen, and C. Y. Dong, “Determination of collagen nanostructure from second-order susceptibility tensor analysis,” Biophys. J.100(8), 2053–2062 (2011).
[CrossRef] [PubMed]

W. L. Chen, T. H. Li, P. J. Su, C. K. Chou, P. T. Fwu, S. J. Lin, D. Kim, P. T. C. So, and C. Y. Dong, “Second harmonic generation chi tensor microscopy for tissue imaging,” Appl. Phys. Lett.94, 3 (2009).

Chen, W.-L.

Chen, Y. F.

P. J. Su, W. L. Chen, Y. F. Chen, and C. Y. Dong, “Determination of collagen nanostructure from second-order susceptibility tensor analysis,” Biophys. J.100(8), 2053–2062 (2011).
[CrossRef] [PubMed]

Chou, C. K.

W. L. Chen, T. H. Li, P. J. Su, C. K. Chou, P. T. Fwu, S. J. Lin, D. Kim, P. T. C. So, and C. Y. Dong, “Second harmonic generation chi tensor microscopy for tissue imaging,” Appl. Phys. Lett.94, 3 (2009).

Chou, C.-K.

Chretien, D.

Chu, S.-W.

Z.-Y. Zhuo, C.-S. Liao, C.-H. Huang, J.-Y. Yu, Y.-Y. Tzeng, W. Lo, C.-Y. Dong, H.-C. Chui, Y.-C. Huang, H.-M. Lai, and S.-W. Chu, “Second harmonic generation imaging - a new method for unraveling molecular information of starch,” J. Struct. Biol.171(1), 88–94 (2010).
[CrossRef] [PubMed]

Chui, H.-C.

Z.-Y. Zhuo, C.-S. Liao, C.-H. Huang, J.-Y. Yu, Y.-Y. Tzeng, W. Lo, C.-Y. Dong, H.-C. Chui, Y.-C. Huang, H.-M. Lai, and S.-W. Chu, “Second harmonic generation imaging - a new method for unraveling molecular information of starch,” J. Struct. Biol.171(1), 88–94 (2010).
[CrossRef] [PubMed]

Cisek, R.

R. Cisek, L. Spencer, N. Prent, D. Zigmantas, G. S. Espie, and V. Barzda, “Optical microscopy in photosynthesis,” Photosynth. Res.102(2-3), 111–141 (2009).
[CrossRef] [PubMed]

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G. C. Cox, N. Moreno, and J. Feijó, “Second-harmonic imaging of plant polysaccharides,” J. Biomed. Opt.10(2), 024013 (2005).
[CrossRef] [PubMed]

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] [PubMed]

Deng, X.

Y. Chang, C. Chen, J. Chen, Y. Jin, and X. Deng, “Theoretical simulation study of linearly polarized light on microscopic second-harmonic generation in collagen type I,” J. Biomed. Opt.14(4), 044016 (2009).
[CrossRef] [PubMed]

Donald, A. M.

T. A. Waigh, I. Hopkinson, A. M. Donald, M. F. Butler, F. Heidelbach, and C. Riekel, “Analysis of the native structure of starch granules with x-ray microfocus diffraction,” Macromolecules30(13), 3813–3820 (1997).
[CrossRef]

Dong, C. Y.

P. J. Su, W. L. Chen, Y. F. Chen, and C. Y. Dong, “Determination of collagen nanostructure from second-order susceptibility tensor analysis,” Biophys. J.100(8), 2053–2062 (2011).
[CrossRef] [PubMed]

W. L. Chen, T. H. Li, P. J. Su, C. K. Chou, P. T. Fwu, S. J. Lin, D. Kim, P. T. C. So, and C. Y. Dong, “Second harmonic generation chi tensor microscopy for tissue imaging,” Appl. Phys. Lett.94, 3 (2009).

Dong, C.-Y.

Z.-Y. Zhuo, C.-S. Liao, C.-H. Huang, J.-Y. Yu, Y.-Y. Tzeng, W. Lo, C.-Y. Dong, H.-C. Chui, Y.-C. Huang, H.-M. Lai, and S.-W. Chu, “Second harmonic generation imaging - a new method for unraveling molecular information of starch,” J. Struct. Biol.171(1), 88–94 (2010).
[CrossRef] [PubMed]

P.-J. Su, W.-L. Chen, J.-B. Hong, T.-H. Li, R.-J. Wu, C.-K. Chou, S.-J. Chen, C. Hu, S.-J. Lin, and C.-Y. Dong, “Discrimination of collagen in normal and pathological skin dermis through second-order susceptibility microscopy,” Opt. Express17(13), 11161–11171 (2009).
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J. Duboisset, D. Aït-Belkacem, M. Roche, H. Rigneault, and S. Brasselet, “Generic model of the molecular orientational distribution probed by polarization-resolved second-harmonic generation,” Phys. Rev. A85(4), 043829 (2012).
[CrossRef]

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] [PubMed]

Espie, G. S.

R. Cisek, L. Spencer, N. Prent, D. Zigmantas, G. S. Espie, and V. Barzda, “Optical microscopy in photosynthesis,” Photosynth. Res.102(2-3), 111–141 (2009).
[CrossRef] [PubMed]

Feijó, J.

G. C. Cox, N. Moreno, and J. Feijó, “Second-harmonic imaging of plant polysaccharides,” J. Biomed. Opt.10(2), 024013 (2005).
[CrossRef] [PubMed]

Fleury, V.

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]

Fwu, P. T.

W. L. Chen, T. H. Li, P. J. Su, C. K. Chou, P. T. Fwu, S. J. Lin, D. Kim, P. T. C. So, and C. Y. Dong, “Second harmonic generation chi tensor microscopy for tissue imaging,” Appl. Phys. Lett.94, 3 (2009).

Gasecka, A.

Guilbert, T.

Gusachenko, I.

Heichette, C.

Heidelbach, F.

T. A. Waigh, I. Hopkinson, A. M. Donald, M. F. Butler, F. Heidelbach, and C. Riekel, “Analysis of the native structure of starch granules with x-ray microfocus diffraction,” Macromolecules30(13), 3813–3820 (1997).
[CrossRef]

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).
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Hong, J.-B.

Hopkinson, I.

T. A. Waigh, I. Hopkinson, A. M. Donald, M. F. Butler, F. Heidelbach, and C. Riekel, “Analysis of the native structure of starch granules with x-ray microfocus diffraction,” Macromolecules30(13), 3813–3820 (1997).
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Huang, C.-H.

Z.-Y. Zhuo, C.-S. Liao, C.-H. Huang, J.-Y. Yu, Y.-Y. Tzeng, W. Lo, C.-Y. Dong, H.-C. Chui, Y.-C. Huang, H.-M. Lai, and S.-W. Chu, “Second harmonic generation imaging - a new method for unraveling molecular information of starch,” J. Struct. Biol.171(1), 88–94 (2010).
[CrossRef] [PubMed]

Huang, Y.-C.

Z.-Y. Zhuo, C.-S. Liao, C.-H. Huang, J.-Y. Yu, Y.-Y. Tzeng, W. Lo, C.-Y. Dong, H.-C. Chui, Y.-C. Huang, H.-M. Lai, and S.-W. Chu, “Second harmonic generation imaging - a new method for unraveling molecular information of starch,” J. Struct. Biol.171(1), 88–94 (2010).
[CrossRef] [PubMed]

Jin, Y.

Y. Chang, C. Chen, J. Chen, Y. Jin, and X. Deng, “Theoretical simulation study of linearly polarized light on microscopic second-harmonic generation in collagen type I,” J. Biomed. Opt.14(4), 044016 (2009).
[CrossRef] [PubMed]

Kajiwara, K.

J. Shimada, H. Kaneko, T. Takada, S. Kitamura, and K. Kajiwara, “Conformation of amylose in aqueous solution: small-angle x-ray scattering measurements and simulations,” J. Phys. Chem. B104(9), 2136–2147 (2000).
[CrossRef]

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J. Shimada, H. Kaneko, T. Takada, S. Kitamura, and K. Kajiwara, “Conformation of amylose in aqueous solution: small-angle x-ray scattering measurements and simulations,” J. Phys. Chem. B104(9), 2136–2147 (2000).
[CrossRef]

Kim, D.

W. L. Chen, T. H. Li, P. J. Su, C. K. Chou, P. T. Fwu, S. J. Lin, D. Kim, P. T. C. So, and C. Y. Dong, “Second harmonic generation chi tensor microscopy for tissue imaging,” Appl. Phys. Lett.94, 3 (2009).

Kitamura, S.

J. Shimada, H. Kaneko, T. Takada, S. Kitamura, and K. Kajiwara, “Conformation of amylose in aqueous solution: small-angle x-ray scattering measurements and simulations,” J. Phys. Chem. B104(9), 2136–2147 (2000).
[CrossRef]

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Lacomb, R. B.

Lai, H.-M.

Z.-Y. Zhuo, C.-S. Liao, C.-H. Huang, J.-Y. Yu, Y.-Y. Tzeng, W. Lo, C.-Y. Dong, H.-C. Chui, Y.-C. Huang, H.-M. Lai, and S.-W. Chu, “Second harmonic generation imaging - a new method for unraveling molecular information of starch,” J. Struct. Biol.171(1), 88–94 (2010).
[CrossRef] [PubMed]

Lamarre, I.

Latour, G.

Le Grand, Y.

Li, T. H.

W. L. Chen, T. H. Li, P. J. Su, C. K. Chou, P. T. Fwu, S. J. Lin, D. Kim, P. T. C. So, and C. Y. Dong, “Second harmonic generation chi tensor microscopy for tissue imaging,” Appl. Phys. Lett.94, 3 (2009).

Li, T.-H.

Liao, C.-S.

Z.-Y. Zhuo, C.-S. Liao, C.-H. Huang, J.-Y. Yu, Y.-Y. Tzeng, W. Lo, C.-Y. Dong, H.-C. Chui, Y.-C. Huang, H.-M. Lai, and S.-W. Chu, “Second harmonic generation imaging - a new method for unraveling molecular information of starch,” J. Struct. Biol.171(1), 88–94 (2010).
[CrossRef] [PubMed]

Lin, S. J.

W. L. Chen, T. H. Li, P. J. Su, C. K. Chou, P. T. Fwu, S. J. Lin, D. Kim, P. T. C. So, and C. Y. Dong, “Second harmonic generation chi tensor microscopy for tissue imaging,” Appl. Phys. Lett.94, 3 (2009).

Lin, S.-J.

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]

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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).
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Z.-Y. Zhuo, C.-S. Liao, C.-H. Huang, J.-Y. Yu, Y.-Y. Tzeng, W. Lo, C.-Y. Dong, H.-C. Chui, Y.-C. Huang, H.-M. Lai, and S.-W. Chu, “Second harmonic generation imaging - a new method for unraveling molecular information of starch,” J. Struct. Biol.171(1), 88–94 (2010).
[CrossRef] [PubMed]

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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).
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S. Psilodimitrakopoulos, I. Amat-Roldan, P. Loza-Alvarez, and D. Artigas, “Estimating the helical pitch angle of amylopectin in starch using polarization second harmonic generation microscopy,” J. Opt.12(8), 084007 (2010).
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I. Amat-Roldan, S. Psilodimitrakopoulos, P. Loza-Alvarez, and D. Artigas, “Fast image analysis in polarization SHG microscopy,” Opt. Express18(16), 17209–17219 (2010).
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S. Psilodimitrakopoulos, V. Petegnief, G. Soria, I. Amat-Roldan, D. Artigas, A. M. Planas, and P. Loza-Alvarez, “Estimation of the effective orientation of the SHG source in primary cortical neurons,” Opt. Express17(16), 14418–14425 (2009).
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S. Psilodimitrakopoulos, S. I. Santos, I. Amat-Roldan, A. K. Thayil, D. Artigas, and P. Loza-Alvarez, “In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy,” J. Biomed. Opt.14(1), 014001 (2009).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, D. Artigas, G. Soria, I. Amat-Roldan, A. M. Planas, and P. Loza-Alvarez, “Quantitative discrimination between endogenous SHG sources in mammalian tissue, based on their polarization response,” Opt. Express17(12), 10168–10176 (2009).
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M. Abdel-Akher and A. N. Michalinos, “Separation and purification of starch from chufa nut tubers (Cyperus esculentus),” Starch15(9), 329–334 (1963).
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S. V. Plotnikov, A. C. Millard, P. J. Campagnola, and W. A. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J.90(2), 693–703 (2006).
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R. M. Brown, A. C. Millard, and P. J. Campagnola, “Macromolecular structure of cellulose studied by second-harmonic generation imaging microscopy,” Opt. Lett.28(22), 2207–2209 (2003).
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O. Nadiarnykh, R. B. Lacomb, P. J. Campagnola, and W. A. Mohler, “Coherent and incoherent SHG in fibrillar cellulose matrices,” Opt. Express15(6), 3348–3360 (2007).
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S. V. Plotnikov, A. C. Millard, P. J. Campagnola, and W. A. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J.90(2), 693–703 (2006).
[CrossRef] [PubMed]

Moreno, N.

G. C. Cox, N. Moreno, and J. Feijó, “Second-harmonic imaging of plant polysaccharides,” J. Biomed. Opt.10(2), 024013 (2005).
[CrossRef] [PubMed]

Munhoz, F.

Nadiarnykh, O.

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).
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Odin, C.

Oertel, D. C.

M. Zimmerley, R. Younger, T. Valenton, D. C. Oertel, J. L. Ward, and E. O. Potma, “Molecular orientation in dry and hydrated cellulose fibers: a coherent anti-Stokes Raman scattering microscopy study,” J. Phys. Chem. B114(31), 10200–10208 (2010).
[CrossRef] [PubMed]

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] [PubMed]

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]

Petegnief, V.

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]

Planas, A. M.

Plotnikov, S. V.

S. V. Plotnikov, A. C. Millard, P. J. Campagnola, and W. A. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J.90(2), 693–703 (2006).
[CrossRef] [PubMed]

Potma, E. O.

M. Zimmerley, R. Younger, T. Valenton, D. C. Oertel, J. L. Ward, and E. O. Potma, “Molecular orientation in dry and hydrated cellulose fibers: a coherent anti-Stokes Raman scattering microscopy study,” J. Phys. Chem. B114(31), 10200–10208 (2010).
[CrossRef] [PubMed]

Prent, N.

R. Cisek, L. Spencer, N. Prent, D. Zigmantas, G. S. Espie, and V. Barzda, “Optical microscopy in photosynthesis,” Photosynth. Res.102(2-3), 111–141 (2009).
[CrossRef] [PubMed]

Psilodimitrakopoulos, S.

I. Amat-Roldan, S. Psilodimitrakopoulos, P. Loza-Alvarez, and D. Artigas, “Fast image analysis in polarization SHG microscopy,” Opt. Express18(16), 17209–17219 (2010).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, I. Amat-Roldan, P. Loza-Alvarez, and D. Artigas, “Estimating the helical pitch angle of amylopectin in starch using polarization second harmonic generation microscopy,” J. Opt.12(8), 084007 (2010).
[CrossRef]

S. Psilodimitrakopoulos, D. Artigas, G. Soria, I. Amat-Roldan, A. M. Planas, and P. Loza-Alvarez, “Quantitative discrimination between endogenous SHG sources in mammalian tissue, based on their polarization response,” Opt. Express17(12), 10168–10176 (2009).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, V. Petegnief, G. Soria, I. Amat-Roldan, D. Artigas, A. M. Planas, and P. Loza-Alvarez, “Estimation of the effective orientation of the SHG source in primary cortical neurons,” Opt. Express17(16), 14418–14425 (2009).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, S. I. Santos, I. Amat-Roldan, A. K. Thayil, D. Artigas, and P. Loza-Alvarez, “In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy,” J. Biomed. Opt.14(1), 014001 (2009).
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Recher, G.

Reiser, K. M.

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

Riekel, C.

T. A. Waigh, I. Hopkinson, A. M. Donald, M. F. Butler, F. Heidelbach, and C. Riekel, “Analysis of the native structure of starch granules with x-ray microfocus diffraction,” Macromolecules30(13), 3813–3820 (1997).
[CrossRef]

Rigneault, H.

J. Duboisset, D. Aït-Belkacem, M. Roche, H. Rigneault, and S. Brasselet, “Generic model of the molecular orientational distribution probed by polarization-resolved second-harmonic generation,” Phys. Rev. A85(4), 043829 (2012).
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P. Schön, M. Behrndt, D. Aıt-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A81(1), 013809 (2010).
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Roche, M.

J. Duboisset, D. Aït-Belkacem, M. Roche, H. Rigneault, and S. Brasselet, “Generic model of the molecular orientational distribution probed by polarization-resolved second-harmonic generation,” Phys. Rev. A85(4), 043829 (2012).
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Rouède, D.

Rowlen, K. L.

G. J. Simpson and K. L. Rowlen, “An SHG magic angle: dependence of second harmonic generation orientation measurements on the width of the orientation distribution,” J. Am. Chem. Soc.121(11), 2635–2636 (1999).
[CrossRef]

Rubenchik, A. M.

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

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]

Santos, S. I.

S. Psilodimitrakopoulos, S. I. Santos, I. Amat-Roldan, A. K. Thayil, D. Artigas, and P. Loza-Alvarez, “In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy,” J. Biomed. Opt.14(1), 014001 (2009).
[CrossRef] [PubMed]

Schanne-Klein, M. C.

Schanne-Klein, M.-C.

Schön, P.

P. Schön, M. Behrndt, D. Aıt-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A81(1), 013809 (2010).
[CrossRef]

Sheppard, C. J. R.

Shimada, J.

J. Shimada, H. Kaneko, T. Takada, S. Kitamura, and K. Kajiwara, “Conformation of amylose in aqueous solution: small-angle x-ray scattering measurements and simulations,” J. Phys. Chem. B104(9), 2136–2147 (2000).
[CrossRef]

Simpson, G. J.

G. J. Simpson and K. L. Rowlen, “An SHG magic angle: dependence of second harmonic generation orientation measurements on the width of the orientation distribution,” J. Am. Chem. Soc.121(11), 2635–2636 (1999).
[CrossRef]

So, P. T. C.

W. L. Chen, T. H. Li, P. J. Su, C. K. Chou, P. T. Fwu, S. J. Lin, D. Kim, P. T. C. So, and C. Y. Dong, “Second harmonic generation chi tensor microscopy for tissue imaging,” Appl. Phys. Lett.94, 3 (2009).

Soria, G.

Spencer, L.

R. Cisek, L. Spencer, N. Prent, D. Zigmantas, G. S. Espie, and V. Barzda, “Optical microscopy in photosynthesis,” Photosynth. Res.102(2-3), 111–141 (2009).
[CrossRef] [PubMed]

Stoller, P.

P. Stoller, K. M. Reiser, P. M. Celliers, and A. M. 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]

Su, P. J.

P. J. Su, W. L. Chen, Y. F. Chen, and C. Y. Dong, “Determination of collagen nanostructure from second-order susceptibility tensor analysis,” Biophys. J.100(8), 2053–2062 (2011).
[CrossRef] [PubMed]

W. L. Chen, T. H. Li, P. J. Su, C. K. Chou, P. T. Fwu, S. J. Lin, D. Kim, P. T. C. So, and C. Y. Dong, “Second harmonic generation chi tensor microscopy for tissue imaging,” Appl. Phys. Lett.94, 3 (2009).

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J. Shimada, H. Kaneko, T. Takada, S. Kitamura, and K. Kajiwara, “Conformation of amylose in aqueous solution: small-angle x-ray scattering measurements and simulations,” J. Phys. Chem. B104(9), 2136–2147 (2000).
[CrossRef]

Thayil, A. K.

S. Psilodimitrakopoulos, S. I. Santos, I. Amat-Roldan, A. K. Thayil, D. Artigas, and P. Loza-Alvarez, “In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy,” J. Biomed. Opt.14(1), 014001 (2009).
[CrossRef] [PubMed]

Tiaho, F.

Tzeng, Y.-Y.

Z.-Y. Zhuo, C.-S. Liao, C.-H. Huang, J.-Y. Yu, Y.-Y. Tzeng, W. Lo, C.-Y. Dong, H.-C. Chui, Y.-C. Huang, H.-M. Lai, and S.-W. Chu, “Second harmonic generation imaging - a new method for unraveling molecular information of starch,” J. Struct. Biol.171(1), 88–94 (2010).
[CrossRef] [PubMed]

Valenton, T.

M. Zimmerley, R. Younger, T. Valenton, D. C. Oertel, J. L. Ward, and E. O. Potma, “Molecular orientation in dry and hydrated cellulose fibers: a coherent anti-Stokes Raman scattering microscopy study,” J. Phys. Chem. B114(31), 10200–10208 (2010).
[CrossRef] [PubMed]

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]

Waigh, T. A.

T. A. Waigh, I. Hopkinson, A. M. Donald, M. F. Butler, F. Heidelbach, and C. Riekel, “Analysis of the native structure of starch granules with x-ray microfocus diffraction,” Macromolecules30(13), 3813–3820 (1997).
[CrossRef]

Ward, J. L.

M. Zimmerley, R. Younger, T. Valenton, D. C. Oertel, J. L. Ward, and E. O. Potma, “Molecular orientation in dry and hydrated cellulose fibers: a coherent anti-Stokes Raman scattering microscopy study,” J. Phys. Chem. B114(31), 10200–10208 (2010).
[CrossRef] [PubMed]

Wu, R.-J.

Yew, E. Y. S.

Younger, R.

M. Zimmerley, R. Younger, T. Valenton, D. C. Oertel, J. L. Ward, and E. O. Potma, “Molecular orientation in dry and hydrated cellulose fibers: a coherent anti-Stokes Raman scattering microscopy study,” J. Phys. Chem. B114(31), 10200–10208 (2010).
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Yu, J.-Y.

Z.-Y. Zhuo, C.-S. Liao, C.-H. Huang, J.-Y. Yu, Y.-Y. Tzeng, W. Lo, C.-Y. Dong, H.-C. Chui, Y.-C. Huang, H.-M. Lai, and S.-W. Chu, “Second harmonic generation imaging - a new method for unraveling molecular information of starch,” J. Struct. Biol.171(1), 88–94 (2010).
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R. Cisek, L. Spencer, N. Prent, D. Zigmantas, G. S. Espie, and V. Barzda, “Optical microscopy in photosynthesis,” Photosynth. Res.102(2-3), 111–141 (2009).
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M. Zimmerley, R. Younger, T. Valenton, D. C. Oertel, J. L. Ward, and E. O. Potma, “Molecular orientation in dry and hydrated cellulose fibers: a coherent anti-Stokes Raman scattering microscopy study,” J. Phys. Chem. B114(31), 10200–10208 (2010).
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Biomed. Opt. Express (1)

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Macromolecules (1)

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P.-J. Su, W.-L. Chen, J.-B. Hong, T.-H. Li, R.-J. Wu, C.-K. Chou, S.-J. Chen, C. Hu, S.-J. Lin, and C.-Y. Dong, “Discrimination of collagen in normal and pathological skin dermis through second-order susceptibility microscopy,” Opt. Express17(13), 11161–11171 (2009).
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I. Gusachenko, G. Latour, and M.-C. Schanne-Klein, “Polarization-resolved Second Harmonic microscopy in anisotropic thick tissues,” Opt. Express18(18), 19339–19352 (2010).
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F. Tiaho, G. Recher, and D. Rouède, “Estimation of helical angles of myosin and collagen by second harmonic generation imaging microscopy,” Opt. Express15(19), 12286–12295 (2007).
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Opt. Lett. (1)

Photosynth. Res. (1)

R. Cisek, L. Spencer, N. Prent, D. Zigmantas, G. S. Espie, and V. Barzda, “Optical microscopy in photosynthesis,” Photosynth. Res.102(2-3), 111–141 (2009).
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Figures (6)

Fig. 1
Fig. 1

Coordinates system of the 3D PSHG biophysical model. (a) SHG image of starch with the lab coordinate system (blue axis) and polarization orientation for the incident electric field (red). (b) Tensor (molecule) coordinate system (green axis). In purple, radius R and pitch P, helical pitch angle θe and hyperpolarizability β. The dimensions of the figure are nominal and do not correspond to reality.

Fig. 2
Fig. 2

3D-PSHG in hydrated starch (a) mean intensity of the 9 PSHG images. Scale bar corresponds to 10 μm. (b) Angle ϕ giving the orientation of the molecule in the focal plane. The radial architecture of amylopectin is shown in the evolution of the angle. (c) A = d31/d15 checks the validity of the model assumptions. (d) anisotropy parameter B defined by Eq. (11). (e) Pixel resolution representation of the helical pitch angle θe. (f) Pixel resolution representation of the tilted-off the plane angle δ.

Fig. 3
Fig. 3

Equatorial histograms of hydrated starch. (a) A = d31/d15 peak at 1.01, width of 0.50. (b) B parameter, peak at 3.54, width of 1.14. (c) Helical pitch angle θe retrieved from B considering the 2D approach. Peak at 36.1°, width of 4.9°. (d) Tilted-off the plane angle δ, peak at 48°, mean 44,8°, width of 36 °.

Fig. 4
Fig. 4

(a) Schematics of the measurement preformed in the starch granule, showing the two imaged planes for the B parameter at the equator and ~5µm up from this position. Comparison of the image histograms obtained from the two measurements for (b) A, (b) B, (c) θe, and (d) δ, showing the effect of the existence of a large number of molecules tilted-off the plane: The peak shifts between the two imaged planes for B, θe and δ, but not for A parameter.

Fig. 5
Fig. 5

The left image shows the distribution of the anisotropy parameter B in the equator of a starch granule. The three histogram for the angle δ on the right have been obtained from the three numbered regions of interest (ROI) shown in the left image.

Fig. 6
Fig. 6

Comparison between equatorial 2D and 3D-PSHG of the same dried and hydrated starch. The image histograms for the helical pitch are centered at θe(dried) = 37.5°and θe(hydrated) = 37.8° indicating that the helical pitch angle of amylopectin does not change under hydration. Under hydration starch is more organized and the width for the retrieved B parameter is ~33% narrower for the hydrated than the width of the less organized dried one. This is translated in a δ off-plane width ~17% narrower in hydrated starch.

Tables (1)

Tables Icon

Table 1 Comparative 3D-PSHG between two different imaging planes of a starch granule (n = 10)

Equations (13)

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E = E 0 ( cos α X ^ + sin α Y ^ ) exp [ k Z ω t ] .
{ X ^ = cos δ cos ϕ x ^ sin ϕ y ^ + sin δ cos ϕ z ^ Y ^ = cos δ sin ϕ x ^ + cos ϕ y ^ + sin δ sin ϕ z ^ Z ^ = sin δ x ^ + cos δ z ^
E = E 0 [ cos δ cos ( ϕ α ) x ^ + sin ( ϕ α ) y ^ + sin δ cos ( ϕ α ) z ^ ] .
{ P x 2 ω ~ E 0 2 2 d 15 { cos 2 ( ϕ α ) cos δ sin δ } P y 2 ω ~ E 0 2 d 15 { sin 2 ( ϕ α ) sin δ } P z 2 ω ~ E 0 2 { d 31 [ sin 2 ( ϕ α ) + cos 2 ( ϕ α ) cos 2 δ ] + d 33 cos 2 ( ϕ α ) sin 2 δ ] }
I 2 ω ~ d 15 2 E 0 4 sin 2 δ { sin 2 2 ( ϕ α ) + [ d 31 d 15 sin 2 ( ϕ α ) + ( d 33 d 15 sin 2 δ + ( 2 + d 31 d 15 ) cos 2 δ ) cos 2 ( ϕ α ) ] 2 } .
d 33 d 15 = 2 tan 2 θ e ,
tan θ e = 2 π R P .
I 2 ω ~ E { sin 2 2 ( α ϕ ) + [ A sin 2 ( α ϕ ) + B cos 2 ( α ϕ ) ] 2 },
E = d 15 2 E 0 4 sin 2 δ ,
A = d 31 / d 15 ,
B = d 33 d 15 sin 2 δ + ( 2 + d 31 d 15 ) cos 2 δ .
sin 2 δ = B A 2 d 33 d 15 A 2 ,
I 2 ω ~ d 15 2 E 0 4 { sin 2 2 ( α ϕ ) + [ d 31 d 15 sin 2 ( α ϕ ) + d 33 d 15 cos 2 ( α ϕ ) ] 2 } ,

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