Abstract

A non-tomographic analysis method is proposed to determine the 3D angles and the order parameter of molecular orientation using polarization-dependent infrared (IR) spectroscopy. Conventional polarization-based imaging approaches provide only 2D-projected orientational information of single vibrational modes. The newly proposed method concurrently analyses polarization angle-dependent absorptance of two non-parallel transition dipole moments. The relative phase angle and the maximum-to-minimum ratios observed from the two polarization profiles are used to calculate the 3D angles of the mean molecular orientation and the order parameter of the orientational distribution. Usage of those relative observables as intermediate input parameters makes the analysis results robust against variations in concentration, thickness, absorption peak, and absorption cross-section, which can occur in typical imaging conditions. This analysis is based on a single-step, non-iterative calculation that does not require any analytical model function of an orientational distribution function. This concurrent polarization analysis method is demonstrated using two simulation data examples, followed by associated error propagation analysis and discussion on the effect of absorption strength. Application of this robust spectral analysis method to polarization IR microscopy will provide a full molecular orientation image without tilting that tomographies require.

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  24. Y. J. Lee, “Determination of 3D molecular orientation by concurrent polarization analysis of multiple Raman modes in broadband CARS spectroscopy,” Opt. Express 23, 29279 (2015).
    [Crossref] [PubMed]
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  26. H. Nakahara and K. Fukuda, “Studies on molecular orientation in multilayers of long-chain anthraquinone derivatives by polarized infrared spectra,” J. Colloid Interface Sci. 69, 24–33 (1979).
    [Crossref]
  27. F. Hide, N. A. Clark, K. Nito, A. Yasuda, and D. M. Walba, “Dynamic Polarized Infrared Spectroscopy of Electric Field-Induced Molecular Reorientation in a Chiral Smectic- A Liquid Crystal,” Phys. Rev. Lett. 75, 2344–2347 (1995).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  30. Y. Nagasaki, T. Yoshihara, and Y. Ozaki, “Polarized Infrared Spectroscopic Study on Hindered Rotation around the Molecular Axis in the Smectic-C* Phase of a Ferroelectric Liquid Crystal with a Naphthalene Ring. Application of Two-Dimensional Correlation Spectroscopy to Polarization Angle-Dependen,” The J. Phys. Chem. B 104, 2846–2852 (2000).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2017 (2)

M. Ryu, A. Balcytis, X. Wang, J. Vongsvivut, Y. Hikima, J. Li, M. J. Tobin, S. Juodkazis, and J. Morikawa, “Orientational Mapping Augmented Sub-Wavelength Hyper-Spectral Imaging of Silk,” Sci. Reports 7, 7419 (2017).
[Crossref]

W. Kossack, M. Schulz, T. Thurn-Albrecht, J. Reinmuth, V. Skokow, and F. Kremer, “Temperature-dependent IR-transition moment orientational analysis applied to thin supported films of poly-∊-caprolactone,” Soft Matter 13, 9211–9219 (2017).
[Crossref] [PubMed]

2016 (3)

T. G. Mayerhöfer, H. Mutschke, and J. Popp, “Employing Theories Far beyond Their Limits-The Case of the (Boguer-) Beer-Lambert Law,” ChemPhysChem. 17, 1948–1955 (2016).
[Crossref] [PubMed]

T. P. Wrobel, P. Mukherjee, and R. Bhargava, “Rapid visualization of macromolecular orientation by discrete frequency mid-infrared spectroscopic imaging,” Analyst. 142, 75–79 (2016).
[Crossref] [PubMed]

R. Börner, N. Ehrlich, J. Hohlbein, and C. G. Hübner, “Single Molecule 3D Orientation in Time and Space: A 6D Dynamic Study on Fluorescently Labeled Lipid Membranes,” J. Fluoresc. 26, 963–975 (2016).
[Crossref] [PubMed]

2015 (3)

C. Cleff, A. Gasecka, P. Ferrand, H. Rigneault, S. Brasselet, and J. Duboisset, “Direct imaging of molecular symmetry by coherent anti-Stokes Raman scattering,” Nat. Commun. 7, 11562 (2015).
[Crossref]

Y. J. Lee, “Determination of 3D molecular orientation by concurrent polarization analysis of multiple Raman modes in broadband CARS spectroscopy,” Opt. Express 23, 29279 (2015).
[Crossref] [PubMed]

A. M. Anton, R. Steyrleuthner, W. Kossack, D. Neher, and F. Kremer, “Infrared Transition Moment Orientational Analysis on the Structural Organization of the Distinct Molecular Subunits in Thin Layers of a High Mobility n-Type Copolymer,” J. Am. Chem. Soc. 137, 6034–6043 (2015).
[Crossref] [PubMed]

2014 (1)

A. T. Ngo, Z. J. Jakubek, Z. Lu, B. Joós, C. E. Morris, and L. J. Johnston, “Membrane order parameters for interdigitated lipid bilayers measured via polarized total-internal-reflection fluorescence microscopy,” Biochimica et Biophys. Acta - Biomembr. 1838, 2861–2869 (2014).
[Crossref]

2013 (3)

Y. Hikima, J. Morikawa, and T. Hashimoto, “Wavenumber dependence of FT-IR image of molecular orientation in banded spherulites of poly(3-hydroxybutyrate) and poly(l-lactic acid),” Macromolecules. 46, 1582–1590 (2013).
[Crossref]

M. Richard-lacroix and C. Pellerin, “Accurate New Method for Molecular Orientation Quantification Using Polarized Raman Spectroscopy,” Macromolecules. 46, 5561–5569 (2013).
[Crossref]

S. H. Parekh and K. F. Domke, “Watching orientational ordering at the nanoscale with coherent anti-stokes raman microscopy,” Chem. - A Eur. J. 19, 11822–11830 (2013).
[Crossref]

2011 (1)

Y. Hikima, J. Morikawa, and T. Hashimoto, “FT-IR image processing algorithms for in-plane orientation function and azimuth angle of uniaxially drawn polyethylene composite film,” Macromolecules. 44, 3950–3957 (2011).
[Crossref]

2008 (1)

E. A. Büyüktanir, K. Zhang, A. Gericke, and J. L. West, “Raman Imaging of Nematic and Smectic Liquid Crystals,” Mol. Cryst. Liq. Cryst. 487, 39–51 (2008).
[Crossref]

2007 (3)

A. V. Kachynski, A. N. Kuzmin, P. N. Prasad, and I. I. Smalyukh, “Coherent anti-Stokes Raman scattering polarized microscopy of three-dimensional director structures in liquid crystals,” Appl. Phys. Lett. 91, 151903 (2007).
[Crossref]

N. Sandeau, L. Le Xuan, D. Chauvat, C. Zhou, J.-F. Roch, and S. Brasselet, “Defocused imaging of second harmonic generation from a single nanocrystal,” Opt. Express 15, 16051–16060 (2007).
[Crossref] [PubMed]

P. Papadopoulos, J. Sölter, and F. Kremer, “Structure-property relationships in major ampullate spider silk as deduced from polarized FTIR spectroscopy,” Eur. Phys. J. E 24, 193–199 (2007).
[Crossref] [PubMed]

2006 (2)

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. 103, 6495–6499 (2006).
[Crossref] [PubMed]

M. Tanaka and R. J. Young, “Review Polarised Raman spectroscopy for the study of molecular orientation distributions in polymers,” J. Mater. Sci. 41, 963–991 (2006).
[Crossref]

2004 (1)

T. Elzein, M. Nasser-Eddine, C. Delaite, S. Bistac, and P. Dumas, “FTIR study of polycaprolactone chain organization at interfaces,” J. Colloid Interface Sci. 273, 381–387 (2004).
[Crossref] [PubMed]

2002 (1)

P. Stoller, K. M. Reiser, P. M. Celliers, and A. M. Rubenchik, “Polarization-Modulated Second Harmonic Generation in Collagen,” Biophys. J. 82, 3330–3342 (2002).
[Crossref] [PubMed]

2000 (3)

F. L. Labarthet, J.-L. Bruneel, T. Buffeteau, C. Sourisseau, M. R. Huber, S. J. Zilker, and T. Bieringer, “Photoinduced orientations of azobenzene chromophores in two distinct holographic diffraction gratings as studied by polarized Raman confocal microspectrometry,” Phys. Chem. Chem. Phys. 2, 5154–5167 (2000).
[Crossref]

Y. Nagasaki, T. Yoshihara, and Y. Ozaki, “Polarized Infrared Spectroscopic Study on Hindered Rotation around the Molecular Axis in the Smectic-C* Phase of a Ferroelectric Liquid Crystal with a Naphthalene Ring. Application of Two-Dimensional Correlation Spectroscopy to Polarization Angle-Dependen,” The J. Phys. Chem. B 104, 2846–2852 (2000).
[Crossref]

G. J. Simpson, S. G. Westerbuhr, and K. L. Rowlen, “Molecular Orientation and Angular Distribution Probed by Angle-Resolved Absorbance and Second Harmonic Generation,” Anal. Chem. 72, 887–898 (2000).
[Crossref] [PubMed]

1999 (2)

S. A. Empedocles, R. Neuhauser, and M. G. Bawendi, “Three-dimensional orientation measurements of symmetric single chromophores using polarization microscopy,” Nature. 399, 126–130 (1999).
[Crossref]

A. P. Bartko and R. M. Dickson, “Imaging Three-Dimensional Single Molecule Orientations,” J. Phys. Chem. B 103, 11237–11241 (1999).
[Crossref]

1995 (2)

F. Hide, N. A. Clark, K. Nito, A. Yasuda, and D. M. Walba, “Dynamic Polarized Infrared Spectroscopy of Electric Field-Induced Molecular Reorientation in a Chiral Smectic- A Liquid Crystal,” Phys. Rev. Lett. 75, 2344–2347 (1995).
[Crossref] [PubMed]

C.-P. Lafrance, A. Nabet, R. E. Prud’homme, and M. Pezolet, “On the relationship between the order parameter (P2(cos θ)) and the shape of orientation distributions,” Can. J. Chem. 73, 1497–1505 (1995).
[Crossref]

1994 (1)

1982 (1)

S. G. Boxer, A. Kuki, K. a. Wright, B. a. Katz, and N. H. Xuong, “Oriented properties of the chlorophylls: Electronic absorption spectroscopy of orthorhombic pyrochlorophyllide a-apomyoglobin single crystals,” Proc. Natl. Acad. Sci. United States Am. 79, 1121–1125 (1982).
[Crossref]

1981 (1)

D. I. Bower, “Orientation distribution functions for uniaxially oriented polymers,” J. Polym. Sci. Polym. Phys. Ed. 19, 93–107 (1981).
[Crossref]

1979 (1)

H. Nakahara and K. Fukuda, “Studies on molecular orientation in multilayers of long-chain anthraquinone derivatives by polarized infrared spectra,” J. Colloid Interface Sci. 69, 24–33 (1979).
[Crossref]

1974 (1)

A. Cunningham, G. Davies, and I. Ward, “Determination of molecular orientation by polarized infra-red radiation in an oriented polymer of high polarizability,” Polymer 15, 743–748 (1974).
[Crossref]

Anton, A. M.

A. M. Anton, R. Steyrleuthner, W. Kossack, D. Neher, and F. Kremer, “Infrared Transition Moment Orientational Analysis on the Structural Organization of the Distinct Molecular Subunits in Thin Layers of a High Mobility n-Type Copolymer,” J. Am. Chem. Soc. 137, 6034–6043 (2015).
[Crossref] [PubMed]

Balcytis, A.

M. Ryu, A. Balcytis, X. Wang, J. Vongsvivut, Y. Hikima, J. Li, M. J. Tobin, S. Juodkazis, and J. Morikawa, “Orientational Mapping Augmented Sub-Wavelength Hyper-Spectral Imaging of Silk,” Sci. Reports 7, 7419 (2017).
[Crossref]

Bartko, A. P.

A. P. Bartko and R. M. Dickson, “Imaging Three-Dimensional Single Molecule Orientations,” J. Phys. Chem. B 103, 11237–11241 (1999).
[Crossref]

Bawendi, M. G.

S. A. Empedocles, R. Neuhauser, and M. G. Bawendi, “Three-dimensional orientation measurements of symmetric single chromophores using polarization microscopy,” Nature. 399, 126–130 (1999).
[Crossref]

Bhargava, R.

T. P. Wrobel, P. Mukherjee, and R. Bhargava, “Rapid visualization of macromolecular orientation by discrete frequency mid-infrared spectroscopic imaging,” Analyst. 142, 75–79 (2016).
[Crossref] [PubMed]

Bieringer, T.

F. L. Labarthet, J.-L. Bruneel, T. Buffeteau, C. Sourisseau, M. R. Huber, S. J. Zilker, and T. Bieringer, “Photoinduced orientations of azobenzene chromophores in two distinct holographic diffraction gratings as studied by polarized Raman confocal microspectrometry,” Phys. Chem. Chem. Phys. 2, 5154–5167 (2000).
[Crossref]

Bistac, S.

T. Elzein, M. Nasser-Eddine, C. Delaite, S. Bistac, and P. Dumas, “FTIR study of polycaprolactone chain organization at interfaces,” J. Colloid Interface Sci. 273, 381–387 (2004).
[Crossref] [PubMed]

Börner, R.

R. Börner, N. Ehrlich, J. Hohlbein, and C. G. Hübner, “Single Molecule 3D Orientation in Time and Space: A 6D Dynamic Study on Fluorescently Labeled Lipid Membranes,” J. Fluoresc. 26, 963–975 (2016).
[Crossref] [PubMed]

Bower, D. I.

D. I. Bower, “Orientation distribution functions for uniaxially oriented polymers,” J. Polym. Sci. Polym. Phys. Ed. 19, 93–107 (1981).
[Crossref]

Boxer, S. G.

S. G. Boxer, A. Kuki, K. a. Wright, B. a. Katz, and N. H. Xuong, “Oriented properties of the chlorophylls: Electronic absorption spectroscopy of orthorhombic pyrochlorophyllide a-apomyoglobin single crystals,” Proc. Natl. Acad. Sci. United States Am. 79, 1121–1125 (1982).
[Crossref]

Brasselet, S.

C. Cleff, A. Gasecka, P. Ferrand, H. Rigneault, S. Brasselet, and J. Duboisset, “Direct imaging of molecular symmetry by coherent anti-Stokes Raman scattering,” Nat. Commun. 7, 11562 (2015).
[Crossref]

N. Sandeau, L. Le Xuan, D. Chauvat, C. Zhou, J.-F. Roch, and S. Brasselet, “Defocused imaging of second harmonic generation from a single nanocrystal,” Opt. Express 15, 16051–16060 (2007).
[Crossref] [PubMed]

Bruneel, J.-L.

F. L. Labarthet, J.-L. Bruneel, T. Buffeteau, C. Sourisseau, M. R. Huber, S. J. Zilker, and T. Bieringer, “Photoinduced orientations of azobenzene chromophores in two distinct holographic diffraction gratings as studied by polarized Raman confocal microspectrometry,” Phys. Chem. Chem. Phys. 2, 5154–5167 (2000).
[Crossref]

Buffeteau, T.

F. L. Labarthet, J.-L. Bruneel, T. Buffeteau, C. Sourisseau, M. R. Huber, S. J. Zilker, and T. Bieringer, “Photoinduced orientations of azobenzene chromophores in two distinct holographic diffraction gratings as studied by polarized Raman confocal microspectrometry,” Phys. Chem. Chem. Phys. 2, 5154–5167 (2000).
[Crossref]

Büyüktanir, E. A.

E. A. Büyüktanir, K. Zhang, A. Gericke, and J. L. West, “Raman Imaging of Nematic and Smectic Liquid Crystals,” Mol. Cryst. Liq. Cryst. 487, 39–51 (2008).
[Crossref]

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, 3330–3342 (2002).
[Crossref] [PubMed]

Chauvat, D.

Clark, N. A.

F. Hide, N. A. Clark, K. Nito, A. Yasuda, and D. M. Walba, “Dynamic Polarized Infrared Spectroscopy of Electric Field-Induced Molecular Reorientation in a Chiral Smectic- A Liquid Crystal,” Phys. Rev. Lett. 75, 2344–2347 (1995).
[Crossref] [PubMed]

Cleff, C.

C. Cleff, A. Gasecka, P. Ferrand, H. Rigneault, S. Brasselet, and J. Duboisset, “Direct imaging of molecular symmetry by coherent anti-Stokes Raman scattering,” Nat. Commun. 7, 11562 (2015).
[Crossref]

Cooper, S. L.

Cunningham, A.

A. Cunningham, G. Davies, and I. Ward, “Determination of molecular orientation by polarized infra-red radiation in an oriented polymer of high polarizability,” Polymer 15, 743–748 (1974).
[Crossref]

Davies, G.

A. Cunningham, G. Davies, and I. Ward, “Determination of molecular orientation by polarized infra-red radiation in an oriented polymer of high polarizability,” Polymer 15, 743–748 (1974).
[Crossref]

Delaite, C.

T. Elzein, M. Nasser-Eddine, C. Delaite, S. Bistac, and P. Dumas, “FTIR study of polycaprolactone chain organization at interfaces,” J. Colloid Interface Sci. 273, 381–387 (2004).
[Crossref] [PubMed]

Dickson, R. M.

A. P. Bartko and R. M. Dickson, “Imaging Three-Dimensional Single Molecule Orientations,” J. Phys. Chem. B 103, 11237–11241 (1999).
[Crossref]

Domke, K. F.

S. H. Parekh and K. F. Domke, “Watching orientational ordering at the nanoscale with coherent anti-stokes raman microscopy,” Chem. - A Eur. J. 19, 11822–11830 (2013).
[Crossref]

Duboisset, J.

C. Cleff, A. Gasecka, P. Ferrand, H. Rigneault, S. Brasselet, and J. Duboisset, “Direct imaging of molecular symmetry by coherent anti-Stokes Raman scattering,” Nat. Commun. 7, 11562 (2015).
[Crossref]

Dumas, P.

T. Elzein, M. Nasser-Eddine, C. Delaite, S. Bistac, and P. Dumas, “FTIR study of polycaprolactone chain organization at interfaces,” J. Colloid Interface Sci. 273, 381–387 (2004).
[Crossref] [PubMed]

Ehrlich, N.

R. Börner, N. Ehrlich, J. Hohlbein, and C. G. Hübner, “Single Molecule 3D Orientation in Time and Space: A 6D Dynamic Study on Fluorescently Labeled Lipid Membranes,” J. Fluoresc. 26, 963–975 (2016).
[Crossref] [PubMed]

Elzein, T.

T. Elzein, M. Nasser-Eddine, C. Delaite, S. Bistac, and P. Dumas, “FTIR study of polycaprolactone chain organization at interfaces,” J. Colloid Interface Sci. 273, 381–387 (2004).
[Crossref] [PubMed]

Empedocles, S. A.

S. A. Empedocles, R. Neuhauser, and M. G. Bawendi, “Three-dimensional orientation measurements of symmetric single chromophores using polarization microscopy,” Nature. 399, 126–130 (1999).
[Crossref]

Enderlein, J.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. 103, 6495–6499 (2006).
[Crossref] [PubMed]

Ferrand, P.

C. Cleff, A. Gasecka, P. Ferrand, H. Rigneault, S. Brasselet, and J. Duboisset, “Direct imaging of molecular symmetry by coherent anti-Stokes Raman scattering,” Nat. Commun. 7, 11562 (2015).
[Crossref]

Fukuda, K.

H. Nakahara and K. Fukuda, “Studies on molecular orientation in multilayers of long-chain anthraquinone derivatives by polarized infrared spectra,” J. Colloid Interface Sci. 69, 24–33 (1979).
[Crossref]

Gasecka, A.

C. Cleff, A. Gasecka, P. Ferrand, H. Rigneault, S. Brasselet, and J. Duboisset, “Direct imaging of molecular symmetry by coherent anti-Stokes Raman scattering,” Nat. Commun. 7, 11562 (2015).
[Crossref]

Gericke, A.

E. A. Büyüktanir, K. Zhang, A. Gericke, and J. L. West, “Raman Imaging of Nematic and Smectic Liquid Crystals,” Mol. Cryst. Liq. Cryst. 487, 39–51 (2008).
[Crossref]

Goldman, Y. E.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. 103, 6495–6499 (2006).
[Crossref] [PubMed]

Ha, T.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. 103, 6495–6499 (2006).
[Crossref] [PubMed]

Hashimoto, T.

Y. Hikima, J. Morikawa, and T. Hashimoto, “Wavenumber dependence of FT-IR image of molecular orientation in banded spherulites of poly(3-hydroxybutyrate) and poly(l-lactic acid),” Macromolecules. 46, 1582–1590 (2013).
[Crossref]

Y. Hikima, J. Morikawa, and T. Hashimoto, “FT-IR image processing algorithms for in-plane orientation function and azimuth angle of uniaxially drawn polyethylene composite film,” Macromolecules. 44, 3950–3957 (2011).
[Crossref]

Hide, F.

F. Hide, N. A. Clark, K. Nito, A. Yasuda, and D. M. Walba, “Dynamic Polarized Infrared Spectroscopy of Electric Field-Induced Molecular Reorientation in a Chiral Smectic- A Liquid Crystal,” Phys. Rev. Lett. 75, 2344–2347 (1995).
[Crossref] [PubMed]

Hikima, Y.

M. Ryu, A. Balcytis, X. Wang, J. Vongsvivut, Y. Hikima, J. Li, M. J. Tobin, S. Juodkazis, and J. Morikawa, “Orientational Mapping Augmented Sub-Wavelength Hyper-Spectral Imaging of Silk,” Sci. Reports 7, 7419 (2017).
[Crossref]

Y. Hikima, J. Morikawa, and T. Hashimoto, “Wavenumber dependence of FT-IR image of molecular orientation in banded spherulites of poly(3-hydroxybutyrate) and poly(l-lactic acid),” Macromolecules. 46, 1582–1590 (2013).
[Crossref]

Y. Hikima, J. Morikawa, and T. Hashimoto, “FT-IR image processing algorithms for in-plane orientation function and azimuth angle of uniaxially drawn polyethylene composite film,” Macromolecules. 44, 3950–3957 (2011).
[Crossref]

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R. Börner, N. Ehrlich, J. Hohlbein, and C. G. Hübner, “Single Molecule 3D Orientation in Time and Space: A 6D Dynamic Study on Fluorescently Labeled Lipid Membranes,” J. Fluoresc. 26, 963–975 (2016).
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Huber, M. R.

F. L. Labarthet, J.-L. Bruneel, T. Buffeteau, C. Sourisseau, M. R. Huber, S. J. Zilker, and T. Bieringer, “Photoinduced orientations of azobenzene chromophores in two distinct holographic diffraction gratings as studied by polarized Raman confocal microspectrometry,” Phys. Chem. Chem. Phys. 2, 5154–5167 (2000).
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Hübner, C. G.

R. Börner, N. Ehrlich, J. Hohlbein, and C. G. Hübner, “Single Molecule 3D Orientation in Time and Space: A 6D Dynamic Study on Fluorescently Labeled Lipid Membranes,” J. Fluoresc. 26, 963–975 (2016).
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A. T. Ngo, Z. J. Jakubek, Z. Lu, B. Joós, C. E. Morris, and L. J. Johnston, “Membrane order parameters for interdigitated lipid bilayers measured via polarized total-internal-reflection fluorescence microscopy,” Biochimica et Biophys. Acta - Biomembr. 1838, 2861–2869 (2014).
[Crossref]

Johnston, L. J.

A. T. Ngo, Z. J. Jakubek, Z. Lu, B. Joós, C. E. Morris, and L. J. Johnston, “Membrane order parameters for interdigitated lipid bilayers measured via polarized total-internal-reflection fluorescence microscopy,” Biochimica et Biophys. Acta - Biomembr. 1838, 2861–2869 (2014).
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A. T. Ngo, Z. J. Jakubek, Z. Lu, B. Joós, C. E. Morris, and L. J. Johnston, “Membrane order parameters for interdigitated lipid bilayers measured via polarized total-internal-reflection fluorescence microscopy,” Biochimica et Biophys. Acta - Biomembr. 1838, 2861–2869 (2014).
[Crossref]

Juodkazis, S.

M. Ryu, A. Balcytis, X. Wang, J. Vongsvivut, Y. Hikima, J. Li, M. J. Tobin, S. Juodkazis, and J. Morikawa, “Orientational Mapping Augmented Sub-Wavelength Hyper-Spectral Imaging of Silk,” Sci. Reports 7, 7419 (2017).
[Crossref]

Kachynski, A. V.

A. V. Kachynski, A. N. Kuzmin, P. N. Prasad, and I. I. Smalyukh, “Coherent anti-Stokes Raman scattering polarized microscopy of three-dimensional director structures in liquid crystals,” Appl. Phys. Lett. 91, 151903 (2007).
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Katz, B. a.

S. G. Boxer, A. Kuki, K. a. Wright, B. a. Katz, and N. H. Xuong, “Oriented properties of the chlorophylls: Electronic absorption spectroscopy of orthorhombic pyrochlorophyllide a-apomyoglobin single crystals,” Proc. Natl. Acad. Sci. United States Am. 79, 1121–1125 (1982).
[Crossref]

Kossack, W.

W. Kossack, M. Schulz, T. Thurn-Albrecht, J. Reinmuth, V. Skokow, and F. Kremer, “Temperature-dependent IR-transition moment orientational analysis applied to thin supported films of poly-∊-caprolactone,” Soft Matter 13, 9211–9219 (2017).
[Crossref] [PubMed]

A. M. Anton, R. Steyrleuthner, W. Kossack, D. Neher, and F. Kremer, “Infrared Transition Moment Orientational Analysis on the Structural Organization of the Distinct Molecular Subunits in Thin Layers of a High Mobility n-Type Copolymer,” J. Am. Chem. Soc. 137, 6034–6043 (2015).
[Crossref] [PubMed]

Kremer, F.

W. Kossack, M. Schulz, T. Thurn-Albrecht, J. Reinmuth, V. Skokow, and F. Kremer, “Temperature-dependent IR-transition moment orientational analysis applied to thin supported films of poly-∊-caprolactone,” Soft Matter 13, 9211–9219 (2017).
[Crossref] [PubMed]

A. M. Anton, R. Steyrleuthner, W. Kossack, D. Neher, and F. Kremer, “Infrared Transition Moment Orientational Analysis on the Structural Organization of the Distinct Molecular Subunits in Thin Layers of a High Mobility n-Type Copolymer,” J. Am. Chem. Soc. 137, 6034–6043 (2015).
[Crossref] [PubMed]

P. Papadopoulos, J. Sölter, and F. Kremer, “Structure-property relationships in major ampullate spider silk as deduced from polarized FTIR spectroscopy,” Eur. Phys. J. E 24, 193–199 (2007).
[Crossref] [PubMed]

Kuki, A.

S. G. Boxer, A. Kuki, K. a. Wright, B. a. Katz, and N. H. Xuong, “Oriented properties of the chlorophylls: Electronic absorption spectroscopy of orthorhombic pyrochlorophyllide a-apomyoglobin single crystals,” Proc. Natl. Acad. Sci. United States Am. 79, 1121–1125 (1982).
[Crossref]

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A. V. Kachynski, A. N. Kuzmin, P. N. Prasad, and I. I. Smalyukh, “Coherent anti-Stokes Raman scattering polarized microscopy of three-dimensional director structures in liquid crystals,” Appl. Phys. Lett. 91, 151903 (2007).
[Crossref]

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F. L. Labarthet, J.-L. Bruneel, T. Buffeteau, C. Sourisseau, M. R. Huber, S. J. Zilker, and T. Bieringer, “Photoinduced orientations of azobenzene chromophores in two distinct holographic diffraction gratings as studied by polarized Raman confocal microspectrometry,” Phys. Chem. Chem. Phys. 2, 5154–5167 (2000).
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C.-P. Lafrance, A. Nabet, R. E. Prud’homme, and M. Pezolet, “On the relationship between the order parameter (P2(cos θ)) and the shape of orientation distributions,” Can. J. Chem. 73, 1497–1505 (1995).
[Crossref]

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Lee, Y. J.

Li, J.

M. Ryu, A. Balcytis, X. Wang, J. Vongsvivut, Y. Hikima, J. Li, M. J. Tobin, S. Juodkazis, and J. Morikawa, “Orientational Mapping Augmented Sub-Wavelength Hyper-Spectral Imaging of Silk,” Sci. Reports 7, 7419 (2017).
[Crossref]

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A. T. Ngo, Z. J. Jakubek, Z. Lu, B. Joós, C. E. Morris, and L. J. Johnston, “Membrane order parameters for interdigitated lipid bilayers measured via polarized total-internal-reflection fluorescence microscopy,” Biochimica et Biophys. Acta - Biomembr. 1838, 2861–2869 (2014).
[Crossref]

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T. G. Mayerhöfer, H. Mutschke, and J. Popp, “Employing Theories Far beyond Their Limits-The Case of the (Boguer-) Beer-Lambert Law,” ChemPhysChem. 17, 1948–1955 (2016).
[Crossref] [PubMed]

McKinney, S. A.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. 103, 6495–6499 (2006).
[Crossref] [PubMed]

Morikawa, J.

M. Ryu, A. Balcytis, X. Wang, J. Vongsvivut, Y. Hikima, J. Li, M. J. Tobin, S. Juodkazis, and J. Morikawa, “Orientational Mapping Augmented Sub-Wavelength Hyper-Spectral Imaging of Silk,” Sci. Reports 7, 7419 (2017).
[Crossref]

Y. Hikima, J. Morikawa, and T. Hashimoto, “Wavenumber dependence of FT-IR image of molecular orientation in banded spherulites of poly(3-hydroxybutyrate) and poly(l-lactic acid),” Macromolecules. 46, 1582–1590 (2013).
[Crossref]

Y. Hikima, J. Morikawa, and T. Hashimoto, “FT-IR image processing algorithms for in-plane orientation function and azimuth angle of uniaxially drawn polyethylene composite film,” Macromolecules. 44, 3950–3957 (2011).
[Crossref]

Morris, C. E.

A. T. Ngo, Z. J. Jakubek, Z. Lu, B. Joós, C. E. Morris, and L. J. Johnston, “Membrane order parameters for interdigitated lipid bilayers measured via polarized total-internal-reflection fluorescence microscopy,” Biochimica et Biophys. Acta - Biomembr. 1838, 2861–2869 (2014).
[Crossref]

Mukherjee, P.

T. P. Wrobel, P. Mukherjee, and R. Bhargava, “Rapid visualization of macromolecular orientation by discrete frequency mid-infrared spectroscopic imaging,” Analyst. 142, 75–79 (2016).
[Crossref] [PubMed]

Mutschke, H.

T. G. Mayerhöfer, H. Mutschke, and J. Popp, “Employing Theories Far beyond Their Limits-The Case of the (Boguer-) Beer-Lambert Law,” ChemPhysChem. 17, 1948–1955 (2016).
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Nabet, A.

C.-P. Lafrance, A. Nabet, R. E. Prud’homme, and M. Pezolet, “On the relationship between the order parameter (P2(cos θ)) and the shape of orientation distributions,” Can. J. Chem. 73, 1497–1505 (1995).
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Y. Nagasaki, T. Yoshihara, and Y. Ozaki, “Polarized Infrared Spectroscopic Study on Hindered Rotation around the Molecular Axis in the Smectic-C* Phase of a Ferroelectric Liquid Crystal with a Naphthalene Ring. Application of Two-Dimensional Correlation Spectroscopy to Polarization Angle-Dependen,” The J. Phys. Chem. B 104, 2846–2852 (2000).
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Neher, D.

A. M. Anton, R. Steyrleuthner, W. Kossack, D. Neher, and F. Kremer, “Infrared Transition Moment Orientational Analysis on the Structural Organization of the Distinct Molecular Subunits in Thin Layers of a High Mobility n-Type Copolymer,” J. Am. Chem. Soc. 137, 6034–6043 (2015).
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S. A. Empedocles, R. Neuhauser, and M. G. Bawendi, “Three-dimensional orientation measurements of symmetric single chromophores using polarization microscopy,” Nature. 399, 126–130 (1999).
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Ngo, A. T.

A. T. Ngo, Z. J. Jakubek, Z. Lu, B. Joós, C. E. Morris, and L. J. Johnston, “Membrane order parameters for interdigitated lipid bilayers measured via polarized total-internal-reflection fluorescence microscopy,” Biochimica et Biophys. Acta - Biomembr. 1838, 2861–2869 (2014).
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Nito, K.

F. Hide, N. A. Clark, K. Nito, A. Yasuda, and D. M. Walba, “Dynamic Polarized Infrared Spectroscopy of Electric Field-Induced Molecular Reorientation in a Chiral Smectic- A Liquid Crystal,” Phys. Rev. Lett. 75, 2344–2347 (1995).
[Crossref] [PubMed]

Ozaki, Y.

Y. Nagasaki, T. Yoshihara, and Y. Ozaki, “Polarized Infrared Spectroscopic Study on Hindered Rotation around the Molecular Axis in the Smectic-C* Phase of a Ferroelectric Liquid Crystal with a Naphthalene Ring. Application of Two-Dimensional Correlation Spectroscopy to Polarization Angle-Dependen,” The J. Phys. Chem. B 104, 2846–2852 (2000).
[Crossref]

Papadopoulos, P.

P. Papadopoulos, J. Sölter, and F. Kremer, “Structure-property relationships in major ampullate spider silk as deduced from polarized FTIR spectroscopy,” Eur. Phys. J. E 24, 193–199 (2007).
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M. Richard-lacroix and C. Pellerin, “Accurate New Method for Molecular Orientation Quantification Using Polarized Raman Spectroscopy,” Macromolecules. 46, 5561–5569 (2013).
[Crossref]

Petschek, R. G.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. 103, 6495–6499 (2006).
[Crossref] [PubMed]

Pezolet, M.

C.-P. Lafrance, A. Nabet, R. E. Prud’homme, and M. Pezolet, “On the relationship between the order parameter (P2(cos θ)) and the shape of orientation distributions,” Can. J. Chem. 73, 1497–1505 (1995).
[Crossref]

Popp, J.

T. G. Mayerhöfer, H. Mutschke, and J. Popp, “Employing Theories Far beyond Their Limits-The Case of the (Boguer-) Beer-Lambert Law,” ChemPhysChem. 17, 1948–1955 (2016).
[Crossref] [PubMed]

Prasad, P. N.

A. V. Kachynski, A. N. Kuzmin, P. N. Prasad, and I. I. Smalyukh, “Coherent anti-Stokes Raman scattering polarized microscopy of three-dimensional director structures in liquid crystals,” Appl. Phys. Lett. 91, 151903 (2007).
[Crossref]

Prud’homme, R. E.

C.-P. Lafrance, A. Nabet, R. E. Prud’homme, and M. Pezolet, “On the relationship between the order parameter (P2(cos θ)) and the shape of orientation distributions,” Can. J. Chem. 73, 1497–1505 (1995).
[Crossref]

Reinmuth, J.

W. Kossack, M. Schulz, T. Thurn-Albrecht, J. Reinmuth, V. Skokow, and F. Kremer, “Temperature-dependent IR-transition moment orientational analysis applied to thin supported films of poly-∊-caprolactone,” Soft Matter 13, 9211–9219 (2017).
[Crossref] [PubMed]

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P. Stoller, K. M. Reiser, P. M. Celliers, and A. M. Rubenchik, “Polarization-Modulated Second Harmonic Generation in Collagen,” Biophys. J. 82, 3330–3342 (2002).
[Crossref] [PubMed]

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M. Richard-lacroix and C. Pellerin, “Accurate New Method for Molecular Orientation Quantification Using Polarized Raman Spectroscopy,” Macromolecules. 46, 5561–5569 (2013).
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G. J. Simpson, S. G. Westerbuhr, and K. L. Rowlen, “Molecular Orientation and Angular Distribution Probed by Angle-Resolved Absorbance and Second Harmonic Generation,” Anal. Chem. 72, 887–898 (2000).
[Crossref] [PubMed]

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P. Stoller, K. M. Reiser, P. M. Celliers, and A. M. Rubenchik, “Polarization-Modulated Second Harmonic Generation in Collagen,” Biophys. J. 82, 3330–3342 (2002).
[Crossref] [PubMed]

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M. Ryu, A. Balcytis, X. Wang, J. Vongsvivut, Y. Hikima, J. Li, M. J. Tobin, S. Juodkazis, and J. Morikawa, “Orientational Mapping Augmented Sub-Wavelength Hyper-Spectral Imaging of Silk,” Sci. Reports 7, 7419 (2017).
[Crossref]

Sandeau, N.

Schulz, M.

W. Kossack, M. Schulz, T. Thurn-Albrecht, J. Reinmuth, V. Skokow, and F. Kremer, “Temperature-dependent IR-transition moment orientational analysis applied to thin supported films of poly-∊-caprolactone,” Soft Matter 13, 9211–9219 (2017).
[Crossref] [PubMed]

Selvin, P. R.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. 103, 6495–6499 (2006).
[Crossref] [PubMed]

Simpson, G. J.

G. J. Simpson, S. G. Westerbuhr, and K. L. Rowlen, “Molecular Orientation and Angular Distribution Probed by Angle-Resolved Absorbance and Second Harmonic Generation,” Anal. Chem. 72, 887–898 (2000).
[Crossref] [PubMed]

Skokow, V.

W. Kossack, M. Schulz, T. Thurn-Albrecht, J. Reinmuth, V. Skokow, and F. Kremer, “Temperature-dependent IR-transition moment orientational analysis applied to thin supported films of poly-∊-caprolactone,” Soft Matter 13, 9211–9219 (2017).
[Crossref] [PubMed]

Smalyukh, I. I.

A. V. Kachynski, A. N. Kuzmin, P. N. Prasad, and I. I. Smalyukh, “Coherent anti-Stokes Raman scattering polarized microscopy of three-dimensional director structures in liquid crystals,” Appl. Phys. Lett. 91, 151903 (2007).
[Crossref]

Sölter, J.

P. Papadopoulos, J. Sölter, and F. Kremer, “Structure-property relationships in major ampullate spider silk as deduced from polarized FTIR spectroscopy,” Eur. Phys. J. E 24, 193–199 (2007).
[Crossref] [PubMed]

Sourisseau, C.

F. L. Labarthet, J.-L. Bruneel, T. Buffeteau, C. Sourisseau, M. R. Huber, S. J. Zilker, and T. Bieringer, “Photoinduced orientations of azobenzene chromophores in two distinct holographic diffraction gratings as studied by polarized Raman confocal microspectrometry,” Phys. Chem. Chem. Phys. 2, 5154–5167 (2000).
[Crossref]

Steyrleuthner, R.

A. M. Anton, R. Steyrleuthner, W. Kossack, D. Neher, and F. Kremer, “Infrared Transition Moment Orientational Analysis on the Structural Organization of the Distinct Molecular Subunits in Thin Layers of a High Mobility n-Type Copolymer,” J. Am. Chem. Soc. 137, 6034–6043 (2015).
[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, 3330–3342 (2002).
[Crossref] [PubMed]

Syed, S.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. 103, 6495–6499 (2006).
[Crossref] [PubMed]

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M. Tanaka and R. J. Young, “Review Polarised Raman spectroscopy for the study of molecular orientation distributions in polymers,” J. Mater. Sci. 41, 963–991 (2006).
[Crossref]

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W. Kossack, M. Schulz, T. Thurn-Albrecht, J. Reinmuth, V. Skokow, and F. Kremer, “Temperature-dependent IR-transition moment orientational analysis applied to thin supported films of poly-∊-caprolactone,” Soft Matter 13, 9211–9219 (2017).
[Crossref] [PubMed]

Tobin, M. J.

M. Ryu, A. Balcytis, X. Wang, J. Vongsvivut, Y. Hikima, J. Li, M. J. Tobin, S. Juodkazis, and J. Morikawa, “Orientational Mapping Augmented Sub-Wavelength Hyper-Spectral Imaging of Silk,” Sci. Reports 7, 7419 (2017).
[Crossref]

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E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. 103, 6495–6499 (2006).
[Crossref] [PubMed]

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M. Ryu, A. Balcytis, X. Wang, J. Vongsvivut, Y. Hikima, J. Li, M. J. Tobin, S. Juodkazis, and J. Morikawa, “Orientational Mapping Augmented Sub-Wavelength Hyper-Spectral Imaging of Silk,” Sci. Reports 7, 7419 (2017).
[Crossref]

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F. Hide, N. A. Clark, K. Nito, A. Yasuda, and D. M. Walba, “Dynamic Polarized Infrared Spectroscopy of Electric Field-Induced Molecular Reorientation in a Chiral Smectic- A Liquid Crystal,” Phys. Rev. Lett. 75, 2344–2347 (1995).
[Crossref] [PubMed]

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M. Ryu, A. Balcytis, X. Wang, J. Vongsvivut, Y. Hikima, J. Li, M. J. Tobin, S. Juodkazis, and J. Morikawa, “Orientational Mapping Augmented Sub-Wavelength Hyper-Spectral Imaging of Silk,” Sci. Reports 7, 7419 (2017).
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E. A. Büyüktanir, K. Zhang, A. Gericke, and J. L. West, “Raman Imaging of Nematic and Smectic Liquid Crystals,” Mol. Cryst. Liq. Cryst. 487, 39–51 (2008).
[Crossref]

Westerbuhr, S. G.

G. J. Simpson, S. G. Westerbuhr, and K. L. Rowlen, “Molecular Orientation and Angular Distribution Probed by Angle-Resolved Absorbance and Second Harmonic Generation,” Anal. Chem. 72, 887–898 (2000).
[Crossref] [PubMed]

Wright, K. a.

S. G. Boxer, A. Kuki, K. a. Wright, B. a. Katz, and N. H. Xuong, “Oriented properties of the chlorophylls: Electronic absorption spectroscopy of orthorhombic pyrochlorophyllide a-apomyoglobin single crystals,” Proc. Natl. Acad. Sci. United States Am. 79, 1121–1125 (1982).
[Crossref]

Wrobel, T. P.

T. P. Wrobel, P. Mukherjee, and R. Bhargava, “Rapid visualization of macromolecular orientation by discrete frequency mid-infrared spectroscopic imaging,” Analyst. 142, 75–79 (2016).
[Crossref] [PubMed]

Xuong, N. H.

S. G. Boxer, A. Kuki, K. a. Wright, B. a. Katz, and N. H. Xuong, “Oriented properties of the chlorophylls: Electronic absorption spectroscopy of orthorhombic pyrochlorophyllide a-apomyoglobin single crystals,” Proc. Natl. Acad. Sci. United States Am. 79, 1121–1125 (1982).
[Crossref]

Yasuda, A.

F. Hide, N. A. Clark, K. Nito, A. Yasuda, and D. M. Walba, “Dynamic Polarized Infrared Spectroscopy of Electric Field-Induced Molecular Reorientation in a Chiral Smectic- A Liquid Crystal,” Phys. Rev. Lett. 75, 2344–2347 (1995).
[Crossref] [PubMed]

Yoshihara, T.

Y. Nagasaki, T. Yoshihara, and Y. Ozaki, “Polarized Infrared Spectroscopic Study on Hindered Rotation around the Molecular Axis in the Smectic-C* Phase of a Ferroelectric Liquid Crystal with a Naphthalene Ring. Application of Two-Dimensional Correlation Spectroscopy to Polarization Angle-Dependen,” The J. Phys. Chem. B 104, 2846–2852 (2000).
[Crossref]

Young, R. J.

M. Tanaka and R. J. Young, “Review Polarised Raman spectroscopy for the study of molecular orientation distributions in polymers,” J. Mater. Sci. 41, 963–991 (2006).
[Crossref]

Zhang, K.

E. A. Büyüktanir, K. Zhang, A. Gericke, and J. L. West, “Raman Imaging of Nematic and Smectic Liquid Crystals,” Mol. Cryst. Liq. Cryst. 487, 39–51 (2008).
[Crossref]

Zhou, C.

Zilker, S. J.

F. L. Labarthet, J.-L. Bruneel, T. Buffeteau, C. Sourisseau, M. R. Huber, S. J. Zilker, and T. Bieringer, “Photoinduced orientations of azobenzene chromophores in two distinct holographic diffraction gratings as studied by polarized Raman confocal microspectrometry,” Phys. Chem. Chem. Phys. 2, 5154–5167 (2000).
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Figures (5)

Fig. 1
Fig. 1 Polarization angle dependence of transmitted light intensity through a collection of aligned transition dipole moments. The incident light, I(0), propagating along the z axis, is linearly polarized with the polarization angle rotated by η from the x axis in the xy plane. All transition dipole moments are aligned parallel in the xz plane with the tilting angle of θ from the z axis. The magnitude of the transition dipole moment, equivalent to the absorption cross section, is represented by ε. The terms d and c denote the sample thickness and the concentration, respectively. As the light passes through the sample, only Ex is reduced by absorption but Ey is unaffected.
Fig. 2
Fig. 2 Schematic presentation of broadening and rotation of molecular orientation. The orientational broadening is represented by ρ(β), where β denotes the axial angle of an individual μ from the mean orientation direction, 〈μ〉. The molecular rotation is represented by the rotation matrix R(ψ, θ, ϕ) from the molecular coordinate to the laboratory coordinate. The incident light propagates in the direction of the z axis, and the light polarization plane is on the xy plane. η is the polarization angle with respect to the x axis.
Fig. 3
Fig. 3 (a) Plots of the von Mises-Fisher function ρvMF(β) for two different κ values. (b) and (c) Plots of absorptance calculated from Eqs. (10) and (12) for the primary (red) and the secondary (blue) transition dipole moments using two different sets of orientation angles of the mean orientation directions. The 3D angles used for calculation are indicated above each figure. For comparison, absorptance profiles from unbroadened ODF (κ = ∞) are plotted as the solid lines. The dashed lines indicate absorptance profiles calculated from broadened ρvMF(β) with κ = 10 (b) and κ = 50 (c). For both (b) and (c), α 1 ° = 0.9 and α 2 ° = 0.9.
Fig. 4
Fig. 4 A flow chart of the concurrent polarization analysis method for determination of the 3D angles (ψ, θ, and ϕ) of the mean molecular orientation and the order parameter 〈P2〉 of the local orientation distribution using polarization profiles of two orthogonal IR modes. The intermediate parameters (Δη, M, and N) are calculated from the six input observables of the phase angles and the maximum and minimum absorptances of the two polarization profiles.
Fig. 5
Fig. 5 (a), (b), (c) Comparison of polarization angle-dependent absorptance calculated for ODF-broadened orientation based on the simplified and the original forms of α(η). The calculation is performed for the primary mode, and the axial angle θ = 60°. The von Mises-Fisher function with κ = 10 is used as the model ODF for the numerical calculation. (d), (e) The maximum-to-minimum ratio, represented by M in Eq. (27) is plotted as a function of α° for different θ.

Tables (1)

Tables Icon

Table 1 Demonstration of determination of the 3D angles and 〈P2〉 using observables and intermediate parameters from the simulated polarization absorptance profiles shown in Fig. 3. The input uncertainties for phase angle η and absorptance α are assumed to be 2° and 5%, respectively, for Fig. 3b, and 5° and 10% for Fig. 3c. The parentheses for θ and ϕ indicate the second solution for the 3D angles of the mirror image molecular orientation with respect to the polarization plane.

Equations (41)

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I ( d ) = I ( 0 ) { 1 [ 1 exp ( 2 ε c d sin 2 θ ) ] cos 2 ( η ψ ) }
T ( η ) I ( d ) / I ( 0 ) = 1 [ 1 exp ( 2 ε c d sin 2 θ ) ] cos 2 ( η ψ )
A ( η ) = log { 1 [ 1 exp ( 2 ε c d sin 2 θ ) ] cos 2 ( η ψ ) }
α ( η ) = [ 1 exp ( 2 ε c d sin 2 θ ) ] cos 2 ( η ψ )
α ( η ) = { 1 [ 1 ( 2 ε c d sin 2 θ ) + ( 2 ε c d sin 2 θ ) 2 / 2 ] } cos 2 ( η ψ ) = [ ( 2 ε c d sin 2 θ ) ( 2 ε c d sin 2 θ ) 2 / 2 + ] cos 2 ( η ψ ) .
α ( η ) ( 2 ε c d ) sin 2 θ cos 2 ( η ψ ) α ° sin 2 θ cos 2 ( η ψ )
α ( η ) = α ° [ e ^ E ( η ) e ^ μ ( ψ , θ ) ] 2
R ( ψ , θ , ϕ ) = ( cos ψ sin ψ 0 sin ψ cos ψ 0 0 0 1 ) ( cos θ 0 sin θ 0 1 0 sin θ 0 cos θ ) ( cos ϕ sin ϕ 0 sin ϕ cos ϕ 0 0 0 1 )
α 1 ( η ) = α 1 ° 0 2 π 0 π [ e ^ E ( η ) e ^ μ 1 ] 2 ρ ( β ) sin β d β d γ = α 1 ° 0 2 π 0 π [ e ^ E ( η ) R ( ψ , θ , ϕ ) R ( γ , β , 0 ) e ^ z ] 2 ρ ( β ) sin β d β d γ
α 1 ( η ) α 1 ° = 1 2 [ 1 sin 2 θ cos 2 ( η ψ ) ] + 1 2 [ 3 sin 2 θ cos 2 ( η ψ ) 1 ] 0 π cos 2 β ρ ( β ) sin β d β
α 2 ( η ) = α 2 ° 0 2 π 0 π [ e ^ E ( η ) R ( ψ , θ , ϕ ) R y ( π 2 ) R ( γ , β , 0 ) e ^ z ] 2 ρ ( β ) sin β d β d γ
α 2 ( η ) α 2 ° = 1 2 { [ cos θ cos ϕ cos ( η ψ ) + sin ϕ sin ( η ψ ) ] 2 1 } + 1 2 { 3 [ cos θ cos ϕ cos ( η ψ ) + sin ϕ sin ( η ψ ) ] 2 1 } × 0 π cos 2 β ρ ( β ) sin β d β
ρ ( β ) = n = 0 ( n + 1 2 ) P n P n ( cos β ) .
P 0 ( cos β ) = 1
P 2 ( cos β ) = 1 2 ( 3 cos 2 β 1 ) .
0 π cos 2 β ρ ( β ) sin β d β = 2 P 2 + 1 3 .
α 1 ( η ) α 1 ° = P 2 sin 2 θ cos 2 ( η ψ ) + 1 3 ( 1 P 2 ) .
α 2 ( η ) α 2 ° = P 2 [ cos θ cos ϕ cos ( η ψ ) + sin ϕ sin ( η ψ ) ] 2 + 1 3 ( 1 P 2 ) .
P 2 = α max α min α max + 2 α min = P 2 sin 2 θ 1 P 2 cos 2 θ
ψ = η 1 , max ( 0 ψ π )
cos ϕ cos θ sin Δ η = sin ϕ cos Δ η
Δ η = tan 1 ( tan ϕ sec θ )
α 1 , min α 1 ° = 1 3 ( 1 P 2 )
α 1 , max α 1 ° = P 2 sin 2 θ + 1 3 ( 1 P 2 )
α 2 , min α 2 ° = 1 3 ( 1 P 2 )
α 2 , max α 2 ° = P 2 ( cos 2 ϕ cos 2 θ + sin 2 ϕ ) + 1 3 ( 1 P 2 )
M ( α 1 , max α 1 , min 1 ) = 3 P 2 1 P 2 × sin 2 θ
N ( α 2 , max α 2 , min 1 ) = 3 P 2 1 P 2 ( cos 2 ϕ cos 2 θ + sin 2 ϕ )
P 3 P 2 1 P 2
sin 2 θ = M / P
cos 2 ϕ = ( P N ) / M
( N / P ) cos 2 Δ η = cos 2 ϕ cos 2 θ = cos 2 ϕ ( 1 sin 2 θ )
( P M ) ( P N ) = M N cos 2 Δ η
P = 1 2 [ ( M + N ) ± ( M + N ) 2 4 M N ( 1 cos 2 Δ η ) ] = 1 2 [ ( M + N ) ± ( M N ) 2 + 4 M N cos 2 Δ η ]
cos 2 ϕ = 1 2 M [ ( M N ) ± ( M N ) 2 + 4 M N cos 2 Δ η ] 0
cos 2 ϕ = 1 2 M [ ( M N ) + ( M N ) 2 + 4 M N cos 2 Δ η ]
P = 1 2 [ ( M + N ) + ( M N ) 2 + 4 M N cos 2 Δ η ]
P 2 = P P + 3
θ = sin 1 M / P ( 0 θ π )
ϕ = cos 1 [ ± ( P N ) / M ] ( π ϕ π )
δ f ( x 1 , , x n ) = ( f x 1 ) 2 ( δ x 1 ) 2 + + ( f x n ) 2 ( δ x n ) 2 .

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