Abstract

A high-speed Mueller matrix ellipsometer (MME) based on photoelastic modulator (PEM) polarization modulation and division-of-amplitude polarization demodulation has been developed, with which a temporal resolution of 11 µs has been achieved for a Mueller matrix measurement. To ensure the accuracy and stability, a novel approach combining a fast Fourier transform algorithm and Bessel function expansion is proposed for the in-situ calibration of PEM. With the proposed calibration method, the peak retardance and static retardance of the PEM can be calibrated with high accuracy and sensitivity over an ultra large retardance variation range. Both static and dynamic measurement experiments have been carried out to show the high accuracy and stability of the developed MME, which can be expected to pave the way for in-situ and real-time monitoring for rapid reaction processes.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (4)

Y. Battie, M. Stchakovsky, S. Neveu, D. Jamon, and E. Garcia-Caurel, “Synthesis and study of γ-fe2o3 and cofe2o4 based ferrofluids by means of spectroscopic mueller matrix ellipsometry,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 37(6), 062929 (2019).
[Crossref]

B. Song, H. Gu, M. Fang, Y.-T. Ho, X. Chen, H. Jiang, and S. Liu, “Complex optical conductivity of two-dimensional mos2: A striking layer dependency,” J. Phys. Chem. Lett. 10(20), 6246–6252 (2019).
[Crossref]

S. Wang, X. Han, Y. Wang, and K. Li, “Dispersion of the retardation of a photoelastic modulator,” Appl. Sci. 9(2), 341 (2019).
[Crossref]

S. Zhang, C. Chen, H. Jiang, H. Gu, X. Chen, C. Zhang, and S. Liu, “Dynamic characteristics of nematic liquid crystal variable retardere (lcvrs) investigated by a high-speed polarimetry,” J. Opt. 21(6), 065605 (2019).
[Crossref]

2018 (1)

S. Zhang, H. Gu, J. Liu, H. Jiang, X. Chen, C. Zhang, and S. Liu, “Characterization of beam splitters in the calibration of a six-channel stokes polarimeter,” J. Opt. 20(12), 125606 (2018).
[Crossref]

2017 (3)

W. Quan, Q. Wang, Y. Zhai, L. Jiang, L. Duan, and Y. Wu, “Method for simultaneously calibrating peak retardation and static retardation of a photoelastic modulator,” Appl. Opt. 56(15), 4491–4495 (2017).
[Crossref]

H. W. Chen, C.-L. Huang, Y. L. Lo, and Y. R. Chang, “Analysis of optically anisotropic properties of biological tissues under stretching based on differential mueller matrix formalism,” J. Biomed. Opt. 22(3), 035006 (2017).
[Crossref]

A. Mock, T. Carlson, J. Vanderslice, J. Mohrmann, J. A. Woollam, E. Schubert, and M. Schubert, “Multiple-layered effective medium approximation approach to modeling environmental effects on alumina passivated highly porous silicon nanostructured thin films measured by in-situ mueller matrix ellipsometry,” Appl. Surf. Sci. 421, 663–666 (2017).
[Crossref]

2016 (2)

2015 (1)

S. Liu, X. Chen, and C. Zhang, “Development of a broadband mueller matrix ellipsometer as a powerful tool for nanostructure metrology,” Thin Solid Films 584, 176–185 (2015).
[Crossref]

2014 (2)

2012 (2)

O. Arteaga, J. Freudenthal, B. Wang, and B. Kahr, “Mueller matrix polarimetry with four photoelastic modulators: Theory and calibration,” Appl. Opt. 51(28), 6805–6817 (2012).
[Crossref]

Y.-L. Lo, “Extraction of effective parameters of turbid media utilizing the mueller matrix approach: Study of glucose sensing,” J. Biomed. Opt. 17(9), 0970021 (2012).
[Crossref]

2011 (2)

2010 (2)

R. Petkovšek, J. Petelin, J. Možina, and F. Bammer, “Fast ellipsometric measurements based on a single crystal photo-elastic modulator,” Opt. Express 18(20), 21410–21418 (2010).
[Crossref]

M. Khazimullin and Y. A. Lebedev, “Fourier transform approach in modulation technique of experimental measurements,” Rev. Sci. Instrum. 81(4), 043110 (2010).
[Crossref]

2009 (1)

B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator part ii: Residual birefringence in the optical element,” Pro. SPIE 7461, 746110 (2009)
[Crossref]

2007 (2)

2004 (2)

M. Wang, F. Tsai, and Y. Chao, “In situ calibration technique for photoelastic modulator in ellipsometry,” Thin Solid Films 455-456, 78–83 (2004).
[Crossref]

M.-W. Wang, Y.-F. Chao, K.-C. Leou, F.-H. Tsai, T.-L. Lin, S.-S. Chen, and Y.-W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43(2), 827–832 (2004).
[Crossref]

2003 (1)

2000 (1)

T. C. Oakberg, J. G. Trunk, and J. C. Sutherland, “Calibration of photoelastic modulators in the vacuum uv,” Proc. SPIE 4133, 101–111 (2000).
[Crossref]

1999 (1)

B. Wang and T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level linear birefringence,” Rev. Sci. Instrum. 70(10), 3847–3854 (1999).
[Crossref]

1997 (2)

1993 (1)

R. Cline, W. Westerveld, and J. Risley, “A new method for measuring the retardation of a photoelastic modulator using single photon counting techniques,” Rev. Sci. Instrum. 64(5), 1169–1174 (1993).
[Crossref]

Alali, S.

Arteaga, O.

Arwin, H.

H. Arwin, “Application of ellipsometry techniques to biological materials,” Thin Solid Films 519(9), 2589–2592 (2011).
[Crossref]

Bammer, F.

Battie, Y.

Y. Battie, M. Stchakovsky, S. Neveu, D. Jamon, and E. Garcia-Caurel, “Synthesis and study of γ-fe2o3 and cofe2o4 based ferrofluids by means of spectroscopic mueller matrix ellipsometry,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 37(6), 062929 (2019).
[Crossref]

Bruce, N.

Cariou, J.

Carlson, T.

A. Mock, T. Carlson, J. Vanderslice, J. Mohrmann, J. A. Woollam, E. Schubert, and M. Schubert, “Multiple-layered effective medium approximation approach to modeling environmental effects on alumina passivated highly porous silicon nanostructured thin films measured by in-situ mueller matrix ellipsometry,” Appl. Surf. Sci. 421, 663–666 (2017).
[Crossref]

Chang, Y. R.

H. W. Chen, C.-L. Huang, Y. L. Lo, and Y. R. Chang, “Analysis of optically anisotropic properties of biological tissues under stretching based on differential mueller matrix formalism,” J. Biomed. Opt. 22(3), 035006 (2017).
[Crossref]

Chao, Y.

M. Wang, F. Tsai, and Y. Chao, “In situ calibration technique for photoelastic modulator in ellipsometry,” Thin Solid Films 455-456, 78–83 (2004).
[Crossref]

Chao, Y.-F.

M.-W. Wang, Y.-F. Chao, K.-C. Leou, F.-H. Tsai, T.-L. Lin, S.-S. Chen, and Y.-W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43(2), 827–832 (2004).
[Crossref]

Chen, C.

S. Zhang, C. Chen, H. Jiang, H. Gu, X. Chen, C. Zhang, and S. Liu, “Dynamic characteristics of nematic liquid crystal variable retardere (lcvrs) investigated by a high-speed polarimetry,” J. Opt. 21(6), 065605 (2019).
[Crossref]

Chen, H. W.

H. W. Chen, C.-L. Huang, Y. L. Lo, and Y. R. Chang, “Analysis of optically anisotropic properties of biological tissues under stretching based on differential mueller matrix formalism,” J. Biomed. Opt. 22(3), 035006 (2017).
[Crossref]

Chen, S.-S.

M.-W. Wang, Y.-F. Chao, K.-C. Leou, F.-H. Tsai, T.-L. Lin, S.-S. Chen, and Y.-W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43(2), 827–832 (2004).
[Crossref]

Chen, X.

S. Zhang, C. Chen, H. Jiang, H. Gu, X. Chen, C. Zhang, and S. Liu, “Dynamic characteristics of nematic liquid crystal variable retardere (lcvrs) investigated by a high-speed polarimetry,” J. Opt. 21(6), 065605 (2019).
[Crossref]

B. Song, H. Gu, M. Fang, Y.-T. Ho, X. Chen, H. Jiang, and S. Liu, “Complex optical conductivity of two-dimensional mos2: A striking layer dependency,” J. Phys. Chem. Lett. 10(20), 6246–6252 (2019).
[Crossref]

S. Zhang, H. Gu, J. Liu, H. Jiang, X. Chen, C. Zhang, and S. Liu, “Characterization of beam splitters in the calibration of a six-channel stokes polarimeter,” J. Opt. 20(12), 125606 (2018).
[Crossref]

S. Liu, X. Chen, and C. Zhang, “Development of a broadband mueller matrix ellipsometer as a powerful tool for nanostructure metrology,” Thin Solid Films 584, 176–185 (2015).
[Crossref]

X. Chen, S. Liu, C. Zhang, H. Jiang, Z. Ma, T. Sun, and Z. Xu, “Accurate characterization of nanoimprinted resist patterns using mueller matrix ellipsometry,” Opt. Express 22(12), 15165–15177 (2014).
[Crossref]

Cline, R.

R. Cline, W. Westerveld, and J. Risley, “A new method for measuring the retardation of a photoelastic modulator using single photon counting techniques,” Rev. Sci. Instrum. 64(5), 1169–1174 (1993).
[Crossref]

De Martino, A.

Dong, Z.

Drévillon, B.

Duan, L.

Dubreuil, M.

Fang, M.

B. Song, H. Gu, M. Fang, Y.-T. Ho, X. Chen, H. Jiang, and S. Liu, “Complex optical conductivity of two-dimensional mos2: A striking layer dependency,” J. Phys. Chem. Lett. 10(20), 6246–6252 (2019).
[Crossref]

Freudenthal, J.

Garcia-Caurel, E.

Y. Battie, M. Stchakovsky, S. Neveu, D. Jamon, and E. Garcia-Caurel, “Synthesis and study of γ-fe2o3 and cofe2o4 based ferrofluids by means of spectroscopic mueller matrix ellipsometry,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 37(6), 062929 (2019).
[Crossref]

A. De Martino, Y.-K. Kim, E. Garcia-Caurel, B. Laude, and B. Drévillon, “Optimized mueller polarimeter with liquid crystals,” Opt. Lett. 28(8), 616–618 (2003).
[Crossref]

Gribble, A.

Gu, H.

S. Zhang, C. Chen, H. Jiang, H. Gu, X. Chen, C. Zhang, and S. Liu, “Dynamic characteristics of nematic liquid crystal variable retardere (lcvrs) investigated by a high-speed polarimetry,” J. Opt. 21(6), 065605 (2019).
[Crossref]

B. Song, H. Gu, M. Fang, Y.-T. Ho, X. Chen, H. Jiang, and S. Liu, “Complex optical conductivity of two-dimensional mos2: A striking layer dependency,” J. Phys. Chem. Lett. 10(20), 6246–6252 (2019).
[Crossref]

S. Zhang, H. Gu, J. Liu, H. Jiang, X. Chen, C. Zhang, and S. Liu, “Characterization of beam splitters in the calibration of a six-channel stokes polarimeter,” J. Opt. 20(12), 125606 (2018).
[Crossref]

Han, X.

S. Wang, X. Han, Y. Wang, and K. Li, “Dispersion of the retardation of a photoelastic modulator,” Appl. Sci. 9(2), 341 (2019).
[Crossref]

Hinds, E.

B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator part ii: Residual birefringence in the optical element,” Pro. SPIE 7461, 746110 (2009)
[Crossref]

Ho, Y.-T.

B. Song, H. Gu, M. Fang, Y.-T. Ho, X. Chen, H. Jiang, and S. Liu, “Complex optical conductivity of two-dimensional mos2: A striking layer dependency,” J. Phys. Chem. Lett. 10(20), 6246–6252 (2019).
[Crossref]

Hu, J.

Huang, C.-L.

H. W. Chen, C.-L. Huang, Y. L. Lo, and Y. R. Chang, “Analysis of optically anisotropic properties of biological tissues under stretching based on differential mueller matrix formalism,” J. Biomed. Opt. 22(3), 035006 (2017).
[Crossref]

Huang, H.

Huang, L.

Jamon, D.

Y. Battie, M. Stchakovsky, S. Neveu, D. Jamon, and E. Garcia-Caurel, “Synthesis and study of γ-fe2o3 and cofe2o4 based ferrofluids by means of spectroscopic mueller matrix ellipsometry,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 37(6), 062929 (2019).
[Crossref]

Jellison, G. E.

Jiang, H.

B. Song, H. Gu, M. Fang, Y.-T. Ho, X. Chen, H. Jiang, and S. Liu, “Complex optical conductivity of two-dimensional mos2: A striking layer dependency,” J. Phys. Chem. Lett. 10(20), 6246–6252 (2019).
[Crossref]

S. Zhang, C. Chen, H. Jiang, H. Gu, X. Chen, C. Zhang, and S. Liu, “Dynamic characteristics of nematic liquid crystal variable retardere (lcvrs) investigated by a high-speed polarimetry,” J. Opt. 21(6), 065605 (2019).
[Crossref]

S. Zhang, H. Gu, J. Liu, H. Jiang, X. Chen, C. Zhang, and S. Liu, “Characterization of beam splitters in the calibration of a six-channel stokes polarimeter,” J. Opt. 20(12), 125606 (2018).
[Crossref]

X. Chen, S. Liu, C. Zhang, H. Jiang, Z. Ma, T. Sun, and Z. Xu, “Accurate characterization of nanoimprinted resist patterns using mueller matrix ellipsometry,” Opt. Express 22(12), 15165–15177 (2014).
[Crossref]

Jiang, L.

Kahr, B.

Khazimullin, M.

M. Khazimullin and Y. A. Lebedev, “Fourier transform approach in modulation technique of experimental measurements,” Rev. Sci. Instrum. 81(4), 043110 (2010).
[Crossref]

Kim, Y.-K.

Krivoy, E.

B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator part ii: Residual birefringence in the optical element,” Pro. SPIE 7461, 746110 (2009)
[Crossref]

Laude, B.

Le Jeune, B.

Lebedev, Y. A.

M. Khazimullin and Y. A. Lebedev, “Fourier transform approach in modulation technique of experimental measurements,” Rev. Sci. Instrum. 81(4), 043110 (2010).
[Crossref]

Leou, K.-C.

M.-W. Wang, Y.-F. Chao, K.-C. Leou, F.-H. Tsai, T.-L. Lin, S.-S. Chen, and Y.-W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43(2), 827–832 (2004).
[Crossref]

Li, F.

Li, K.

S. Wang, X. Han, Y. Wang, and K. Li, “Dispersion of the retardation of a photoelastic modulator,” Appl. Sci. 9(2), 341 (2019).
[Crossref]

Li, K.-W.

Lin, T.-L.

M.-W. Wang, Y.-F. Chao, K.-C. Leou, F.-H. Tsai, T.-L. Lin, S.-S. Chen, and Y.-W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43(2), 827–832 (2004).
[Crossref]

Liu, J.

S. Zhang, H. Gu, J. Liu, H. Jiang, X. Chen, C. Zhang, and S. Liu, “Characterization of beam splitters in the calibration of a six-channel stokes polarimeter,” J. Opt. 20(12), 125606 (2018).
[Crossref]

Liu, S.

B. Song, H. Gu, M. Fang, Y.-T. Ho, X. Chen, H. Jiang, and S. Liu, “Complex optical conductivity of two-dimensional mos2: A striking layer dependency,” J. Phys. Chem. Lett. 10(20), 6246–6252 (2019).
[Crossref]

S. Zhang, C. Chen, H. Jiang, H. Gu, X. Chen, C. Zhang, and S. Liu, “Dynamic characteristics of nematic liquid crystal variable retardere (lcvrs) investigated by a high-speed polarimetry,” J. Opt. 21(6), 065605 (2019).
[Crossref]

S. Zhang, H. Gu, J. Liu, H. Jiang, X. Chen, C. Zhang, and S. Liu, “Characterization of beam splitters in the calibration of a six-channel stokes polarimeter,” J. Opt. 20(12), 125606 (2018).
[Crossref]

S. Liu, X. Chen, and C. Zhang, “Development of a broadband mueller matrix ellipsometer as a powerful tool for nanostructure metrology,” Thin Solid Films 584, 176–185 (2015).
[Crossref]

X. Chen, S. Liu, C. Zhang, H. Jiang, Z. Ma, T. Sun, and Z. Xu, “Accurate characterization of nanoimprinted resist patterns using mueller matrix ellipsometry,” Opt. Express 22(12), 15165–15177 (2014).
[Crossref]

Liu, Y.-W.

M.-W. Wang, Y.-F. Chao, K.-C. Leou, F.-H. Tsai, T.-L. Lin, S.-S. Chen, and Y.-W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43(2), 827–832 (2004).
[Crossref]

Lo, Y. L.

H. W. Chen, C.-L. Huang, Y. L. Lo, and Y. R. Chang, “Analysis of optically anisotropic properties of biological tissues under stretching based on differential mueller matrix formalism,” J. Biomed. Opt. 22(3), 035006 (2017).
[Crossref]

Lo, Y.-L.

Y.-L. Lo, “Extraction of effective parameters of turbid media utilizing the mueller matrix approach: Study of glucose sensing,” J. Biomed. Opt. 17(9), 0970021 (2012).
[Crossref]

López-Téllez, J.

Ma, Z.

Mock, A.

A. Mock, T. Carlson, J. Vanderslice, J. Mohrmann, J. A. Woollam, E. Schubert, and M. Schubert, “Multiple-layered effective medium approximation approach to modeling environmental effects on alumina passivated highly porous silicon nanostructured thin films measured by in-situ mueller matrix ellipsometry,” Appl. Surf. Sci. 421, 663–666 (2017).
[Crossref]

Modine, F. A.

Mohrmann, J.

A. Mock, T. Carlson, J. Vanderslice, J. Mohrmann, J. A. Woollam, E. Schubert, and M. Schubert, “Multiple-layered effective medium approximation approach to modeling environmental effects on alumina passivated highly porous silicon nanostructured thin films measured by in-situ mueller matrix ellipsometry,” Appl. Surf. Sci. 421, 663–666 (2017).
[Crossref]

Možina, J.

Neveu, S.

Y. Battie, M. Stchakovsky, S. Neveu, D. Jamon, and E. Garcia-Caurel, “Synthesis and study of γ-fe2o3 and cofe2o4 based ferrofluids by means of spectroscopic mueller matrix ellipsometry,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 37(6), 062929 (2019).
[Crossref]

Oakberg, T. C.

T. C. Oakberg, J. G. Trunk, and J. C. Sutherland, “Calibration of photoelastic modulators in the vacuum uv,” Proc. SPIE 4133, 101–111 (2000).
[Crossref]

B. Wang and T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level linear birefringence,” Rev. Sci. Instrum. 70(10), 3847–3854 (1999).
[Crossref]

Petelin, J.

Petkovšek, R.

Quan, W.

Risley, J.

R. Cline, W. Westerveld, and J. Risley, “A new method for measuring the retardation of a photoelastic modulator using single photon counting techniques,” Rev. Sci. Instrum. 64(5), 1169–1174 (1993).
[Crossref]

Rivet, S.

Schubert, E.

A. Mock, T. Carlson, J. Vanderslice, J. Mohrmann, J. A. Woollam, E. Schubert, and M. Schubert, “Multiple-layered effective medium approximation approach to modeling environmental effects on alumina passivated highly porous silicon nanostructured thin films measured by in-situ mueller matrix ellipsometry,” Appl. Surf. Sci. 421, 663–666 (2017).
[Crossref]

Schubert, M.

A. Mock, T. Carlson, J. Vanderslice, J. Mohrmann, J. A. Woollam, E. Schubert, and M. Schubert, “Multiple-layered effective medium approximation approach to modeling environmental effects on alumina passivated highly porous silicon nanostructured thin films measured by in-situ mueller matrix ellipsometry,” Appl. Surf. Sci. 421, 663–666 (2017).
[Crossref]

Song, B.

B. Song, H. Gu, M. Fang, Y.-T. Ho, X. Chen, H. Jiang, and S. Liu, “Complex optical conductivity of two-dimensional mos2: A striking layer dependency,” J. Phys. Chem. Lett. 10(20), 6246–6252 (2019).
[Crossref]

Stchakovsky, M.

Y. Battie, M. Stchakovsky, S. Neveu, D. Jamon, and E. Garcia-Caurel, “Synthesis and study of γ-fe2o3 and cofe2o4 based ferrofluids by means of spectroscopic mueller matrix ellipsometry,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 37(6), 062929 (2019).
[Crossref]

Sun, T.

Sutherland, J. C.

T. C. Oakberg, J. G. Trunk, and J. C. Sutherland, “Calibration of photoelastic modulators in the vacuum uv,” Proc. SPIE 4133, 101–111 (2000).
[Crossref]

Trunk, J. G.

T. C. Oakberg, J. G. Trunk, and J. C. Sutherland, “Calibration of photoelastic modulators in the vacuum uv,” Proc. SPIE 4133, 101–111 (2000).
[Crossref]

Tsai, F.

M. Wang, F. Tsai, and Y. Chao, “In situ calibration technique for photoelastic modulator in ellipsometry,” Thin Solid Films 455-456, 78–83 (2004).
[Crossref]

Tsai, F.-H.

M.-W. Wang, Y.-F. Chao, K.-C. Leou, F.-H. Tsai, T.-L. Lin, S.-S. Chen, and Y.-W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43(2), 827–832 (2004).
[Crossref]

Vanderslice, J.

A. Mock, T. Carlson, J. Vanderslice, J. Mohrmann, J. A. Woollam, E. Schubert, and M. Schubert, “Multiple-layered effective medium approximation approach to modeling environmental effects on alumina passivated highly porous silicon nanostructured thin films measured by in-situ mueller matrix ellipsometry,” Appl. Surf. Sci. 421, 663–666 (2017).
[Crossref]

Vitkin, I. A.

Wang, B.

O. Arteaga, J. Freudenthal, B. Wang, and B. Kahr, “Mueller matrix polarimetry with four photoelastic modulators: Theory and calibration,” Appl. Opt. 51(28), 6805–6817 (2012).
[Crossref]

B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator part ii: Residual birefringence in the optical element,” Pro. SPIE 7461, 746110 (2009)
[Crossref]

B. Wang and T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level linear birefringence,” Rev. Sci. Instrum. 70(10), 3847–3854 (1999).
[Crossref]

Wang, L.-M.

Wang, M.

M. Wang, F. Tsai, and Y. Chao, “In situ calibration technique for photoelastic modulator in ellipsometry,” Thin Solid Films 455-456, 78–83 (2004).
[Crossref]

Wang, M.-W.

M.-W. Wang, Y.-F. Chao, K.-C. Leou, F.-H. Tsai, T.-L. Lin, S.-S. Chen, and Y.-W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43(2), 827–832 (2004).
[Crossref]

Wang, Q.

Wang, S.

S. Wang, X. Han, Y. Wang, and K. Li, “Dispersion of the retardation of a photoelastic modulator,” Appl. Sci. 9(2), 341 (2019).
[Crossref]

Wang, X.

Wang, Y.

S. Wang, X. Han, Y. Wang, and K. Li, “Dispersion of the retardation of a photoelastic modulator,” Appl. Sci. 9(2), 341 (2019).
[Crossref]

Wang, Z.-B.

Westerveld, W.

R. Cline, W. Westerveld, and J. Risley, “A new method for measuring the retardation of a photoelastic modulator using single photon counting techniques,” Rev. Sci. Instrum. 64(5), 1169–1174 (1993).
[Crossref]

Woollam, J. A.

A. Mock, T. Carlson, J. Vanderslice, J. Mohrmann, J. A. Woollam, E. Schubert, and M. Schubert, “Multiple-layered effective medium approximation approach to modeling environmental effects on alumina passivated highly porous silicon nanostructured thin films measured by in-situ mueller matrix ellipsometry,” Appl. Surf. Sci. 421, 663–666 (2017).
[Crossref]

Wu, Y.

Xu, Z.

Zeng, A.

Zhai, Y.

Zhang, C.

S. Zhang, C. Chen, H. Jiang, H. Gu, X. Chen, C. Zhang, and S. Liu, “Dynamic characteristics of nematic liquid crystal variable retardere (lcvrs) investigated by a high-speed polarimetry,” J. Opt. 21(6), 065605 (2019).
[Crossref]

S. Zhang, H. Gu, J. Liu, H. Jiang, X. Chen, C. Zhang, and S. Liu, “Characterization of beam splitters in the calibration of a six-channel stokes polarimeter,” J. Opt. 20(12), 125606 (2018).
[Crossref]

S. Liu, X. Chen, and C. Zhang, “Development of a broadband mueller matrix ellipsometer as a powerful tool for nanostructure metrology,” Thin Solid Films 584, 176–185 (2015).
[Crossref]

X. Chen, S. Liu, C. Zhang, H. Jiang, Z. Ma, T. Sun, and Z. Xu, “Accurate characterization of nanoimprinted resist patterns using mueller matrix ellipsometry,” Opt. Express 22(12), 15165–15177 (2014).
[Crossref]

Zhang, R.

Zhang, S.

S. Zhang, C. Chen, H. Jiang, H. Gu, X. Chen, C. Zhang, and S. Liu, “Dynamic characteristics of nematic liquid crystal variable retardere (lcvrs) investigated by a high-speed polarimetry,” J. Opt. 21(6), 065605 (2019).
[Crossref]

S. Zhang, H. Gu, J. Liu, H. Jiang, X. Chen, C. Zhang, and S. Liu, “Characterization of beam splitters in the calibration of a six-channel stokes polarimeter,” J. Opt. 20(12), 125606 (2018).
[Crossref]

Zhu, L.

Appl. Opt. (7)

Appl. Sci. (1)

S. Wang, X. Han, Y. Wang, and K. Li, “Dispersion of the retardation of a photoelastic modulator,” Appl. Sci. 9(2), 341 (2019).
[Crossref]

Appl. Surf. Sci. (1)

A. Mock, T. Carlson, J. Vanderslice, J. Mohrmann, J. A. Woollam, E. Schubert, and M. Schubert, “Multiple-layered effective medium approximation approach to modeling environmental effects on alumina passivated highly porous silicon nanostructured thin films measured by in-situ mueller matrix ellipsometry,” Appl. Surf. Sci. 421, 663–666 (2017).
[Crossref]

J. Biomed. Opt. (2)

H. W. Chen, C.-L. Huang, Y. L. Lo, and Y. R. Chang, “Analysis of optically anisotropic properties of biological tissues under stretching based on differential mueller matrix formalism,” J. Biomed. Opt. 22(3), 035006 (2017).
[Crossref]

Y.-L. Lo, “Extraction of effective parameters of turbid media utilizing the mueller matrix approach: Study of glucose sensing,” J. Biomed. Opt. 17(9), 0970021 (2012).
[Crossref]

J. Opt. (2)

S. Zhang, H. Gu, J. Liu, H. Jiang, X. Chen, C. Zhang, and S. Liu, “Characterization of beam splitters in the calibration of a six-channel stokes polarimeter,” J. Opt. 20(12), 125606 (2018).
[Crossref]

S. Zhang, C. Chen, H. Jiang, H. Gu, X. Chen, C. Zhang, and S. Liu, “Dynamic characteristics of nematic liquid crystal variable retardere (lcvrs) investigated by a high-speed polarimetry,” J. Opt. 21(6), 065605 (2019).
[Crossref]

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

J. Phys. Chem. Lett. (1)

B. Song, H. Gu, M. Fang, Y.-T. Ho, X. Chen, H. Jiang, and S. Liu, “Complex optical conductivity of two-dimensional mos2: A striking layer dependency,” J. Phys. Chem. Lett. 10(20), 6246–6252 (2019).
[Crossref]

J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. (1)

Y. Battie, M. Stchakovsky, S. Neveu, D. Jamon, and E. Garcia-Caurel, “Synthesis and study of γ-fe2o3 and cofe2o4 based ferrofluids by means of spectroscopic mueller matrix ellipsometry,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 37(6), 062929 (2019).
[Crossref]

Jpn. J. Appl. Phys. (1)

M.-W. Wang, Y.-F. Chao, K.-C. Leou, F.-H. Tsai, T.-L. Lin, S.-S. Chen, and Y.-W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43(2), 827–832 (2004).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Pro. SPIE (1)

B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator part ii: Residual birefringence in the optical element,” Pro. SPIE 7461, 746110 (2009)
[Crossref]

Proc. SPIE (1)

T. C. Oakberg, J. G. Trunk, and J. C. Sutherland, “Calibration of photoelastic modulators in the vacuum uv,” Proc. SPIE 4133, 101–111 (2000).
[Crossref]

Rev. Sci. Instrum. (3)

R. Cline, W. Westerveld, and J. Risley, “A new method for measuring the retardation of a photoelastic modulator using single photon counting techniques,” Rev. Sci. Instrum. 64(5), 1169–1174 (1993).
[Crossref]

B. Wang and T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level linear birefringence,” Rev. Sci. Instrum. 70(10), 3847–3854 (1999).
[Crossref]

M. Khazimullin and Y. A. Lebedev, “Fourier transform approach in modulation technique of experimental measurements,” Rev. Sci. Instrum. 81(4), 043110 (2010).
[Crossref]

Thin Solid Films (3)

M. Wang, F. Tsai, and Y. Chao, “In situ calibration technique for photoelastic modulator in ellipsometry,” Thin Solid Films 455-456, 78–83 (2004).
[Crossref]

S. Liu, X. Chen, and C. Zhang, “Development of a broadband mueller matrix ellipsometer as a powerful tool for nanostructure metrology,” Thin Solid Films 584, 176–185 (2015).
[Crossref]

H. Arwin, “Application of ellipsometry techniques to biological materials,” Thin Solid Films 519(9), 2589–2592 (2011).
[Crossref]

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Figures (9)

Fig. 1.
Fig. 1. A high-speed complete MME: (a) Light path diagram: P - polarizer; PEM1 and PEM2 - photoelastic modulators; C1 - half-wave plate; C2 - quart-wave plate; S –Sample; PBS - polarization beam splitter (PBS); NPBS1 - 70:30 (R:T) non-polarization beam splitter (NPBS); NPBS2 - 50:50 (R:T) NPBS; DAQ - oscilloscope; PC - personal computer; SC – signal controller; PMT - photomultiplier tubes; (b) self-developed MME prototype.
Fig. 2.
Fig. 2. The calibration results of the PEMs at a driving voltage of 4.8V: (a) the row vector S3 of the SPSG; (b) the amplitude spectrum of the calculated Bsj and measured Apeak; (c) the difference between the Bsj and Apeak.
Fig. 3.
Fig. 3. The calibration results of the PEMs within the driving voltage of 0V∼4.8 V.
Fig. 4.
Fig. 4. Stokes vector SPSG of the incident light emerging from the PSG
Fig. 5.
Fig. 5. Mean Mueller matrix of the 15 times repeated measurements under different azimuth of a quarter-wave plate.
Fig. 6.
Fig. 6. Optical parameters of the waveplate extracted from Mmean: (a) the optical rotation angle γre under different azimuth θre of the waveplate; (b) the measured azimuth θrem under different azimuth θre of the waveplate; (c) the retardance δre under different azimuth θre of the waveplate; (d) the relative transmittance Are under different azimuth θre of the waveplate.
Fig. 7.
Fig. 7. The matrix of standard deviation for each Mueller element under different azimuth of the quarter-wave plate
Fig. 8.
Fig. 8. Mueller matrix of the LCVRs under the modulation of a sawtooth driving signal with a modulation frequency of 50 Hz and an amplitude of 10 Vpp.
Fig. 9.
Fig. 9. The optical parameters measured by the MME: (a) the optical rotation angle γLC over time; (b) the azimuth θLC over time; (c) the retardance δLC over time; (d) the relative transmittance ALC over time; (e) the driving signal over time.

Equations (19)

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δ ( t ) = δ peak sin ( 2 π f t + φ ) + δ static ,
M PEM = ( 1 0 0 0 0 cos(4 θ PEM )sin( δ PEM /2 ) 2  + cos( δ PEM /2 ) 2 sin(4 θ PEM )sin( δ PEM /2 ) 2  - sin(2 θ PEM )sin( δ PEM ) 0  - sin(4 θ PEM )sin( δ PEM /2 ) 2  - cos(4 θ PEM )sin( δ PEM /2 ) 2  + cos( δ PEM /2 ) 2 cos(2 θ PEM )sin( δ PEM ) 0 sin(2 θ PEM )sin( δ PEM ) cos(2 θ PEM )sin( δ PEM ) cos( δ PEM ) ) ,
B = [ I 1 I 2 I 3 I 4 I 5 I 6 ] T = AMW ,
W = [ S PSG ( t 1 ) S PSG ( t 2 ) S PSG ( t N ) ] ,
S PSG ( t ) = R ( θ PEM ) M re ( δ PEM ( t ) ) R ( θ PEM ) R ( θ p ) M P R ( θ p ) [ 1 0 0 0 ] T = 0.5 [ 1 S 1 S 2 sin 2 ( θ p θ PEM ) sin δ PEM ] T .
S 3 = sin 2 ( θ p θ PEM ) sin δ PEM = sin 2 ( θ p θ PEM ) sin [ δ peak sin ( 2 π f t + φ ) + δ static ] = A sin [ δ peak sin ( 2 π f t + φ ) ] + B cos [ δ peak sin ( 2 π f t + φ ) ] = 2 A k = 1 J 2 k 1 ( δ peak ) sin [ ( 2 k 1 ) ( 2 π f t + φ ) ] + B J 0 ( δ peak ) + 2 B k = 1 J 2 k ( δ peak ) sin [ 2 k ( 2 π f t + φ ) ] ,
B sj = [ | B J 0 ( δ peak ) | | 2 A J 1 ( δ peak ) | | 2 B J 2 ( δ peak ) | | 2 A J 2 k 1 ( δ peak ) | | 2 B J 2 k ( δ peak ) | ] , ( k = N ) .
W m = [ w m0 w m1 w m2 w m3 ] T = A 1 B ,
w m i = x t i = h = 1 H ρ h cos ( ω h t + φ h ) , ( i = 0 , 1 , 2 , 3 ) ,
X ( k ) = t = 0 N / 2 + 1 x t e i 2 π t k / N , k = 0 , 1 ,   ,   N 1.
μ i = A peak ( i ) i = 1 A peak ( i ) .
χ 2 = i = 1 [ μ i [ A peak ( i ) B sj ( i , δ peak , δ static , Δ θ ) ] σ ( μ i A peak ( i ) ) ] 2 ,
S PEM ( t , φ PEM1 , φ PEM2 ) = R ( θ PEM2 ) M PEM ( δ PEM2 ( t ) ) R ( θ PEM2 ) R ( θ PEM1 ) × M PEM ( δ PEM1 ( t ) ) R ( θ PEM1 ) R ( θ p ) M P R ( θ p ) [ 1 0 0 1 ] T = [ S 0 ( t ) S 1 ( t ) S 2 ( t ) S 3 ( t ) ] T ,
b ( t ) = [ i 0 ( t ) i 1 ( t ) i 2 ( t ) i 3 ( t ) i 4 ( t ) i 5 ( t ) ] T = A M s S PEM ,
A  =  [ a 0 a 1 a 2 a 3 a 4 a 5 ] T .
b ( t ) = D ( t , φ FEM1 , φ FEM2 ) M s ,
B c = [ b T ( t 0 ) b T ( t 1 ) b T ( t N 1 ) ] = M s T [ D T ( t 0 , φ FEM1 , φ FEM2 ) D T ( t 1 , φ FEM1 , φ FEM2 ) D T ( t N 1 , φ FEM1 , φ FEM2 ) ] = M s T Z ( φ FEM1 , φ FEM2 ) ,
T = 1 | f 1 δ peak1 2 π f 2 δ peak2 2 π | .
M w p ( A r e , γ r e , θ r e , δ r e ) = A r e M C B ( γ r e ) M L B ( θ r e , δ r e ) ,

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