Abstract

In this paper we describe a new Mueller matrix (MM) microscope that generalizes and makes quantitative the polarized light microscopy technique. In this instrument all the elements of the MU are simultaneously determined from the analysis in the frequency domain of the time-dependent intensity of the light beam at every pixel of the camera. The variations in intensity are created by the two compensators continuously rotating at different angular frequencies. A typical measurement is completed in a little over one minute and it can be applied to any visible wavelength. Some examples are presented to demonstrate the capabilities of the instrument.

© 2014 Optical Society of America

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References

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  1. D. B. Murphy, Fundamentals of Light Microscopy and Electronic Imaging, 1st ed. (Wiley-Liss, 2001).
  2. R. L. Long, M. P. Bange, S. G. Gordon, and G. A. Constable, “Measuring the maturity of developing cotton fibers using an automated polarized light microscopy technique,” Text. Res. J. 80, 463–471 (2010).
  3. D. B. Murphy, Handbook of Microscopy: Applications in Materials Science, Solid-State Physics and Chemistry, vol. 3 (Wiley-VCH, 1996).
  4. R. Weaver, “Rediscovering polarized light microscopy,” Am Lab 35, 55–61 (2003).
  5. S. Ross, R. Newton, Y. M. Zhou, J. Haffegee, M. W. Ho, J. P. Bolton, and D. Knight, “Quantitative image analysis of birefringent biological material,” J. Microsc. 187, 62–67 (1997).
    [CrossRef]
  6. O. Arteaga, “Mueller matrix polarimetry of anisotropic chiral media,” Ph.D. thesis, University of Barcelona (2010).
  7. O. Arteaga and A. Canillas, “Analytic inversion of the Mueller-Jones polarization matrices for homogeneous media,” Opt. Lett. 35, 559–561 (2010).
    [CrossRef]
  8. J. Schellman and H. P. Jensen, “Optical spectroscopy of oriented molecules,” Chem. Rev. 87, 1359–1399 (1987).
    [CrossRef]
  9. R. Ossikovski, “Differential matrix formalism for depolarizing anisotropic media,” Opt. Lett. 36, 2330–2332 (2011).
    [CrossRef]
  10. O. Arteaga and B. Kahr, “Characterization of homogenous depolarizing media based on Mueller matrix differential decomposition,” Opt. Lett. 38, 1134–1136 (2013).
    [CrossRef]
  11. O. Arteaga, “Number of independent parameters in the Mueller matrix representation of homogeneous depolarizing media,” Opt. Lett. 38, 1131–1133 (2013).
    [CrossRef]
  12. E. Bernabeu and J. J. Gil, “An experimental device for the dynamic determination of Mueller matrices,” J. Opt. 16, 139–141 (1985).
    [CrossRef]
  13. K. Ichimoto, K. Shinoda, T. Yamamoto, and J. Kiyohara, “Photopolarimetric measurement system of Mueller matrix with dual rotating waveplates,” Publ. Nat. Ast. Obs. J. 9, 11–19 (2006).
  14. O. Arteaga, J. Freudenthal, B. Wang, and B. Kahr, “Mueller matrix polarimetry with four photoelastic modulators: theory and calibration,” Appl. Opt. 51, 6805–6817 (2012).
    [CrossRef]
  15. A. De Martino, Y.-K. Kim, E. Garcia-Caurel, B. Laude, and B. Drévillon, “Optimized Mueller polarimeter with liquid crystals,” Opt. Lett. 28, 616–618 (2003).
    [CrossRef]
  16. R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
    [CrossRef]
  17. D. Lara and C. Dainty, “Axially resolved complete Mueller matrix confocal microscopy,” Appl. Opt. 45, 1917–1930 (2006).
    [CrossRef]
  18. S. Alali and I. A. Vitkin, “Optimization of rapid Mueller matrix imaging of turbid media using four photoelastic modulators without mechanically moving parts,” Opt. Eng. 52, 103114 (2013).
    [CrossRef]
  19. J. Freudenthal and B. Wang, Hinds Instruments, Hillsboro, Oregon 97124 (personal communication, 2013).
  20. P. S. Hauge, “Mueller matrix ellipsometry with imperfect compensators,” J. Opt. Soc. Am. 68, 1519–1528 (1978).
    [CrossRef]
  21. J. J. Gil, “Método dinámico de determinación de parámetros de Stokes y matrices de Mueller por análisis de Fourier,” Master’s thesis (Universidad de Zaragoza, 1979).
  22. R. M. A. Azzam, “Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal,” Opt. Lett. 2, 148–150 (1978).
    [CrossRef]
  23. J. H. Freudenthal, E. Hollis, and B. Kahr, “Imaging chiroptical artifacts,” Chirality 21, S20–S27 (2009).
    [CrossRef]
  24. S. Ben Hatit, M. Foldyna, A. De Martino, and B. Drévillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Stat. Sol. (a) 205, 743–747 (2008).
    [CrossRef]
  25. L. M. S. Ars, P. G. Ellingsen, and M. Kildemo, “Near infra-red Mueller matrix imaging system and application to retardance imaging of strain,” Thin Solid Films 519, 2737–2741 (2011).
    [CrossRef]
  26. D. H. Goldstein, “Mueller matrix dual-rotating retarder polarimeter,” Appl. Opt. 31, 6676–6683 (1992).
    [CrossRef]
  27. R. W. Collins and J. Koh, “Dual rotating-compensator multichannel ellipsometer: instrument design for real-time Mueller matrix spectroscopy of surfaces and films,” J. Opt. Soc. Am. A 16, 1997–2006 (1999).
    [CrossRef]
  28. Z. El-Hachemi, O. Arteaga, A. Canillas, J. Crusats, A. Sorrenti, S. Veintemillas-Verdaguer, and J. M. Ribo, “Achiral-to-chiral transition in benzil solidification: analogies with racemic conglomerates systems showing deracemization,” Chirality 25, 393–399 (2013).
    [CrossRef]

2013

S. Alali and I. A. Vitkin, “Optimization of rapid Mueller matrix imaging of turbid media using four photoelastic modulators without mechanically moving parts,” Opt. Eng. 52, 103114 (2013).
[CrossRef]

Z. El-Hachemi, O. Arteaga, A. Canillas, J. Crusats, A. Sorrenti, S. Veintemillas-Verdaguer, and J. M. Ribo, “Achiral-to-chiral transition in benzil solidification: analogies with racemic conglomerates systems showing deracemization,” Chirality 25, 393–399 (2013).
[CrossRef]

O. Arteaga, “Number of independent parameters in the Mueller matrix representation of homogeneous depolarizing media,” Opt. Lett. 38, 1131–1133 (2013).
[CrossRef]

O. Arteaga and B. Kahr, “Characterization of homogenous depolarizing media based on Mueller matrix differential decomposition,” Opt. Lett. 38, 1134–1136 (2013).
[CrossRef]

2012

2011

R. Ossikovski, “Differential matrix formalism for depolarizing anisotropic media,” Opt. Lett. 36, 2330–2332 (2011).
[CrossRef]

L. M. S. Ars, P. G. Ellingsen, and M. Kildemo, “Near infra-red Mueller matrix imaging system and application to retardance imaging of strain,” Thin Solid Films 519, 2737–2741 (2011).
[CrossRef]

2010

R. L. Long, M. P. Bange, S. G. Gordon, and G. A. Constable, “Measuring the maturity of developing cotton fibers using an automated polarized light microscopy technique,” Text. Res. J. 80, 463–471 (2010).

O. Arteaga and A. Canillas, “Analytic inversion of the Mueller-Jones polarization matrices for homogeneous media,” Opt. Lett. 35, 559–561 (2010).
[CrossRef]

2009

J. H. Freudenthal, E. Hollis, and B. Kahr, “Imaging chiroptical artifacts,” Chirality 21, S20–S27 (2009).
[CrossRef]

2008

S. Ben Hatit, M. Foldyna, A. De Martino, and B. Drévillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Stat. Sol. (a) 205, 743–747 (2008).
[CrossRef]

2006

K. Ichimoto, K. Shinoda, T. Yamamoto, and J. Kiyohara, “Photopolarimetric measurement system of Mueller matrix with dual rotating waveplates,” Publ. Nat. Ast. Obs. J. 9, 11–19 (2006).

D. Lara and C. Dainty, “Axially resolved complete Mueller matrix confocal microscopy,” Appl. Opt. 45, 1917–1930 (2006).
[CrossRef]

2003

1999

1997

S. Ross, R. Newton, Y. M. Zhou, J. Haffegee, M. W. Ho, J. P. Bolton, and D. Knight, “Quantitative image analysis of birefringent biological material,” J. Microsc. 187, 62–67 (1997).
[CrossRef]

1992

1987

J. Schellman and H. P. Jensen, “Optical spectroscopy of oriented molecules,” Chem. Rev. 87, 1359–1399 (1987).
[CrossRef]

1985

E. Bernabeu and J. J. Gil, “An experimental device for the dynamic determination of Mueller matrices,” J. Opt. 16, 139–141 (1985).
[CrossRef]

1982

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
[CrossRef]

1978

Alali, S.

S. Alali and I. A. Vitkin, “Optimization of rapid Mueller matrix imaging of turbid media using four photoelastic modulators without mechanically moving parts,” Opt. Eng. 52, 103114 (2013).
[CrossRef]

Ars, L. M. S.

L. M. S. Ars, P. G. Ellingsen, and M. Kildemo, “Near infra-red Mueller matrix imaging system and application to retardance imaging of strain,” Thin Solid Films 519, 2737–2741 (2011).
[CrossRef]

Arteaga, O.

Azzam, R. M. A.

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
[CrossRef]

R. M. A. Azzam, “Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal,” Opt. Lett. 2, 148–150 (1978).
[CrossRef]

Bange, M. P.

R. L. Long, M. P. Bange, S. G. Gordon, and G. A. Constable, “Measuring the maturity of developing cotton fibers using an automated polarized light microscopy technique,” Text. Res. J. 80, 463–471 (2010).

Ben Hatit, S.

S. Ben Hatit, M. Foldyna, A. De Martino, and B. Drévillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Stat. Sol. (a) 205, 743–747 (2008).
[CrossRef]

Bernabeu, E.

E. Bernabeu and J. J. Gil, “An experimental device for the dynamic determination of Mueller matrices,” J. Opt. 16, 139–141 (1985).
[CrossRef]

Bolton, J. P.

S. Ross, R. Newton, Y. M. Zhou, J. Haffegee, M. W. Ho, J. P. Bolton, and D. Knight, “Quantitative image analysis of birefringent biological material,” J. Microsc. 187, 62–67 (1997).
[CrossRef]

Canillas, A.

Z. El-Hachemi, O. Arteaga, A. Canillas, J. Crusats, A. Sorrenti, S. Veintemillas-Verdaguer, and J. M. Ribo, “Achiral-to-chiral transition in benzil solidification: analogies with racemic conglomerates systems showing deracemization,” Chirality 25, 393–399 (2013).
[CrossRef]

O. Arteaga and A. Canillas, “Analytic inversion of the Mueller-Jones polarization matrices for homogeneous media,” Opt. Lett. 35, 559–561 (2010).
[CrossRef]

Collins, R. W.

Constable, G. A.

R. L. Long, M. P. Bange, S. G. Gordon, and G. A. Constable, “Measuring the maturity of developing cotton fibers using an automated polarized light microscopy technique,” Text. Res. J. 80, 463–471 (2010).

Crusats, J.

Z. El-Hachemi, O. Arteaga, A. Canillas, J. Crusats, A. Sorrenti, S. Veintemillas-Verdaguer, and J. M. Ribo, “Achiral-to-chiral transition in benzil solidification: analogies with racemic conglomerates systems showing deracemization,” Chirality 25, 393–399 (2013).
[CrossRef]

Dainty, C.

De Martino, A.

S. Ben Hatit, M. Foldyna, A. De Martino, and B. Drévillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Stat. Sol. (a) 205, 743–747 (2008).
[CrossRef]

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

Drévillon, B.

S. Ben Hatit, M. Foldyna, A. De Martino, and B. Drévillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Stat. Sol. (a) 205, 743–747 (2008).
[CrossRef]

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

El-Hachemi, Z.

Z. El-Hachemi, O. Arteaga, A. Canillas, J. Crusats, A. Sorrenti, S. Veintemillas-Verdaguer, and J. M. Ribo, “Achiral-to-chiral transition in benzil solidification: analogies with racemic conglomerates systems showing deracemization,” Chirality 25, 393–399 (2013).
[CrossRef]

Ellingsen, P. G.

L. M. S. Ars, P. G. Ellingsen, and M. Kildemo, “Near infra-red Mueller matrix imaging system and application to retardance imaging of strain,” Thin Solid Films 519, 2737–2741 (2011).
[CrossRef]

Foldyna, M.

S. Ben Hatit, M. Foldyna, A. De Martino, and B. Drévillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Stat. Sol. (a) 205, 743–747 (2008).
[CrossRef]

Freudenthal, J.

Freudenthal, J. H.

J. H. Freudenthal, E. Hollis, and B. Kahr, “Imaging chiroptical artifacts,” Chirality 21, S20–S27 (2009).
[CrossRef]

Garcia-Caurel, E.

Gil, J. J.

E. Bernabeu and J. J. Gil, “An experimental device for the dynamic determination of Mueller matrices,” J. Opt. 16, 139–141 (1985).
[CrossRef]

J. J. Gil, “Método dinámico de determinación de parámetros de Stokes y matrices de Mueller por análisis de Fourier,” Master’s thesis (Universidad de Zaragoza, 1979).

Goldstein, D. H.

Gordon, S. G.

R. L. Long, M. P. Bange, S. G. Gordon, and G. A. Constable, “Measuring the maturity of developing cotton fibers using an automated polarized light microscopy technique,” Text. Res. J. 80, 463–471 (2010).

Haffegee, J.

S. Ross, R. Newton, Y. M. Zhou, J. Haffegee, M. W. Ho, J. P. Bolton, and D. Knight, “Quantitative image analysis of birefringent biological material,” J. Microsc. 187, 62–67 (1997).
[CrossRef]

Hauge, P. S.

Ho, M. W.

S. Ross, R. Newton, Y. M. Zhou, J. Haffegee, M. W. Ho, J. P. Bolton, and D. Knight, “Quantitative image analysis of birefringent biological material,” J. Microsc. 187, 62–67 (1997).
[CrossRef]

Hollis, E.

J. H. Freudenthal, E. Hollis, and B. Kahr, “Imaging chiroptical artifacts,” Chirality 21, S20–S27 (2009).
[CrossRef]

Ichimoto, K.

K. Ichimoto, K. Shinoda, T. Yamamoto, and J. Kiyohara, “Photopolarimetric measurement system of Mueller matrix with dual rotating waveplates,” Publ. Nat. Ast. Obs. J. 9, 11–19 (2006).

Jensen, H. P.

J. Schellman and H. P. Jensen, “Optical spectroscopy of oriented molecules,” Chem. Rev. 87, 1359–1399 (1987).
[CrossRef]

Kahr, B.

Kildemo, M.

L. M. S. Ars, P. G. Ellingsen, and M. Kildemo, “Near infra-red Mueller matrix imaging system and application to retardance imaging of strain,” Thin Solid Films 519, 2737–2741 (2011).
[CrossRef]

Kim, Y.-K.

Kiyohara, J.

K. Ichimoto, K. Shinoda, T. Yamamoto, and J. Kiyohara, “Photopolarimetric measurement system of Mueller matrix with dual rotating waveplates,” Publ. Nat. Ast. Obs. J. 9, 11–19 (2006).

Knight, D.

S. Ross, R. Newton, Y. M. Zhou, J. Haffegee, M. W. Ho, J. P. Bolton, and D. Knight, “Quantitative image analysis of birefringent biological material,” J. Microsc. 187, 62–67 (1997).
[CrossRef]

Koh, J.

Lara, D.

Laude, B.

Long, R. L.

R. L. Long, M. P. Bange, S. G. Gordon, and G. A. Constable, “Measuring the maturity of developing cotton fibers using an automated polarized light microscopy technique,” Text. Res. J. 80, 463–471 (2010).

Murphy, D. B.

D. B. Murphy, Handbook of Microscopy: Applications in Materials Science, Solid-State Physics and Chemistry, vol. 3 (Wiley-VCH, 1996).

D. B. Murphy, Fundamentals of Light Microscopy and Electronic Imaging, 1st ed. (Wiley-Liss, 2001).

Newton, R.

S. Ross, R. Newton, Y. M. Zhou, J. Haffegee, M. W. Ho, J. P. Bolton, and D. Knight, “Quantitative image analysis of birefringent biological material,” J. Microsc. 187, 62–67 (1997).
[CrossRef]

Ossikovski, R.

Ribo, J. M.

Z. El-Hachemi, O. Arteaga, A. Canillas, J. Crusats, A. Sorrenti, S. Veintemillas-Verdaguer, and J. M. Ribo, “Achiral-to-chiral transition in benzil solidification: analogies with racemic conglomerates systems showing deracemization,” Chirality 25, 393–399 (2013).
[CrossRef]

Ross, S.

S. Ross, R. Newton, Y. M. Zhou, J. Haffegee, M. W. Ho, J. P. Bolton, and D. Knight, “Quantitative image analysis of birefringent biological material,” J. Microsc. 187, 62–67 (1997).
[CrossRef]

Schellman, J.

J. Schellman and H. P. Jensen, “Optical spectroscopy of oriented molecules,” Chem. Rev. 87, 1359–1399 (1987).
[CrossRef]

Shinoda, K.

K. Ichimoto, K. Shinoda, T. Yamamoto, and J. Kiyohara, “Photopolarimetric measurement system of Mueller matrix with dual rotating waveplates,” Publ. Nat. Ast. Obs. J. 9, 11–19 (2006).

Sorrenti, A.

Z. El-Hachemi, O. Arteaga, A. Canillas, J. Crusats, A. Sorrenti, S. Veintemillas-Verdaguer, and J. M. Ribo, “Achiral-to-chiral transition in benzil solidification: analogies with racemic conglomerates systems showing deracemization,” Chirality 25, 393–399 (2013).
[CrossRef]

Veintemillas-Verdaguer, S.

Z. El-Hachemi, O. Arteaga, A. Canillas, J. Crusats, A. Sorrenti, S. Veintemillas-Verdaguer, and J. M. Ribo, “Achiral-to-chiral transition in benzil solidification: analogies with racemic conglomerates systems showing deracemization,” Chirality 25, 393–399 (2013).
[CrossRef]

Vitkin, I. A.

S. Alali and I. A. Vitkin, “Optimization of rapid Mueller matrix imaging of turbid media using four photoelastic modulators without mechanically moving parts,” Opt. Eng. 52, 103114 (2013).
[CrossRef]

Wang, B.

Weaver, R.

R. Weaver, “Rediscovering polarized light microscopy,” Am Lab 35, 55–61 (2003).

Yamamoto, T.

K. Ichimoto, K. Shinoda, T. Yamamoto, and J. Kiyohara, “Photopolarimetric measurement system of Mueller matrix with dual rotating waveplates,” Publ. Nat. Ast. Obs. J. 9, 11–19 (2006).

Zhou, Y. M.

S. Ross, R. Newton, Y. M. Zhou, J. Haffegee, M. W. Ho, J. P. Bolton, and D. Knight, “Quantitative image analysis of birefringent biological material,” J. Microsc. 187, 62–67 (1997).
[CrossRef]

Am Lab

R. Weaver, “Rediscovering polarized light microscopy,” Am Lab 35, 55–61 (2003).

Appl. Opt.

Chem. Rev.

J. Schellman and H. P. Jensen, “Optical spectroscopy of oriented molecules,” Chem. Rev. 87, 1359–1399 (1987).
[CrossRef]

Chirality

J. H. Freudenthal, E. Hollis, and B. Kahr, “Imaging chiroptical artifacts,” Chirality 21, S20–S27 (2009).
[CrossRef]

Z. El-Hachemi, O. Arteaga, A. Canillas, J. Crusats, A. Sorrenti, S. Veintemillas-Verdaguer, and J. M. Ribo, “Achiral-to-chiral transition in benzil solidification: analogies with racemic conglomerates systems showing deracemization,” Chirality 25, 393–399 (2013).
[CrossRef]

J. Microsc.

S. Ross, R. Newton, Y. M. Zhou, J. Haffegee, M. W. Ho, J. P. Bolton, and D. Knight, “Quantitative image analysis of birefringent biological material,” J. Microsc. 187, 62–67 (1997).
[CrossRef]

J. Opt.

E. Bernabeu and J. J. Gil, “An experimental device for the dynamic determination of Mueller matrices,” J. Opt. 16, 139–141 (1985).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Acta

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
[CrossRef]

Opt. Eng.

S. Alali and I. A. Vitkin, “Optimization of rapid Mueller matrix imaging of turbid media using four photoelastic modulators without mechanically moving parts,” Opt. Eng. 52, 103114 (2013).
[CrossRef]

Opt. Lett.

Phys. Stat. Sol. (a)

S. Ben Hatit, M. Foldyna, A. De Martino, and B. Drévillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Stat. Sol. (a) 205, 743–747 (2008).
[CrossRef]

Publ. Nat. Ast. Obs. J.

K. Ichimoto, K. Shinoda, T. Yamamoto, and J. Kiyohara, “Photopolarimetric measurement system of Mueller matrix with dual rotating waveplates,” Publ. Nat. Ast. Obs. J. 9, 11–19 (2006).

Text. Res. J.

R. L. Long, M. P. Bange, S. G. Gordon, and G. A. Constable, “Measuring the maturity of developing cotton fibers using an automated polarized light microscopy technique,” Text. Res. J. 80, 463–471 (2010).

Thin Solid Films

L. M. S. Ars, P. G. Ellingsen, and M. Kildemo, “Near infra-red Mueller matrix imaging system and application to retardance imaging of strain,” Thin Solid Films 519, 2737–2741 (2011).
[CrossRef]

Other

D. B. Murphy, Handbook of Microscopy: Applications in Materials Science, Solid-State Physics and Chemistry, vol. 3 (Wiley-VCH, 1996).

O. Arteaga, “Mueller matrix polarimetry of anisotropic chiral media,” Ph.D. thesis, University of Barcelona (2010).

J. Freudenthal and B. Wang, Hinds Instruments, Hillsboro, Oregon 97124 (personal communication, 2013).

J. J. Gil, “Método dinámico de determinación de parámetros de Stokes y matrices de Mueller por análisis de Fourier,” Master’s thesis (Universidad de Zaragoza, 1979).

D. B. Murphy, Fundamentals of Light Microscopy and Electronic Imaging, 1st ed. (Wiley-Liss, 2001).

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Figures (7)

Fig. 1.
Fig. 1.

Values of the determinant |BBT| normalized to its maximum value as a function of the ratio of the angular speeds of the two compensators, ω1/ω0. All the ratio values where the determinant drops to zero should be avoided because there BBT becomes a singular matrix. The arrow indicates the ω1/ω0=5 that we use in measurements.

Fig. 2.
Fig. 2.

Scheme and photo of the optical setup of the MM microscope.

Fig. 3.
Fig. 3.

Simulation of how errors of θ0, θ1, δ0, and δ1 in the interval between ±5° propagate among the elements of an MM.

Fig. 4.
Fig. 4.

Measurement of a polycrystalline benzil sample at 440 nm. The sample is a crystallization from the melt sandwiched between glass covers. The bottom image shows the standard deviations of the normalized MM after five measurements. The numbers appearing in some MM elements indicate the multiplying factors used to enhance the values of these elements for better visibility.

Fig. 5.
Fig. 5.

Comparison of the optical response of the different parts of an LCD panel at the subpixel level. The comparison include three different wavelengths that selectively activate certain subpixels. In the first column light transmitted through the complete LCD panel is studied. The Mueller matrices in the second and third columns correspond to measurements made after disassembling the two glass panels that sandwich the liquid crystal and removing the two film polarizers. Part A includes the color filter that defines the RGB subpixel pattern and also contains rectangular electrodes for every subpixel. Part B shows the semi-transparent transistors arranged in a square lattice.

Fig. 6.
Fig. 6.

Detail of an MM measurement of a mosquito wing at 610 nm. The numbers appearing in some MM elements indicate the multiplying factors used to enhance the values of these elements for better visibility.

Fig. 7.
Fig. 7.

Unpolarized transmittance (MM element m00) and linear dichroism image of a part of the mosquito wing. A great contrast is obtained in the fringes located in the outer part of the wing.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

MC(θ,δ)=[10000C2θ2+S2θ2CδC2θS2θ(1Cδ)S2θSδ0C2θS2θ(1Cδ)S2θ2+C2θ2CδC2θSδ0S2θSδC2θSδSδ],
SXsin(X),
CXcos(X).
θ(t)=ωt+ϕ,
Sout(t)=P1MC1(t)MSMC0(t)P0Sinput,
MS=[m00m01m02m03m10m11m12m13m20m21m22m23m30m31m32m33].
I(t)=[1C2θ02+Cδ0S2θ02C2θ0S2θ0(1Cδ0)Sδ0S2θ0(C2θ12+Cδ1S2θ12)(C2θ02+Cδ0S2θ02)(C2θ12+Cδ1S2θ12)(C2θ0S2θ0(1Cδ0))(C2θ12+Cδ1S2θ12)(Sδ0S2θ0)(C2θ12+Cδ1S2θ12)C2θ1S2θ1(1Cδ1)(C2θ02+Cδ0S2θ02)[C2θ1S2θ1(1Cδ1)][C2θ0S2θ0(1Cδ0)][C2θ1S2θ1(1Cδ1)]Sδ0S2θ0[C2θ1S2θ1(1Cδ1)]Sδ1S2θ1Sδ1S2θ1[C2θ02+Cδ0S2θ02]Sδ1S2θ1[C2θ0S2θ0(1Cδ0)]Sδ1S2θ1Sδ0S2θ0]T[m00m01m02m03m10m11m12m13m20m21m22m23m30m31m32m33].
I(t)=BT(t)A,
I=BTA,
Bj,0=1,Bj,1=cos2(2(ω0jΔt+ϕ0))+cos(δ0)sin2(2(ω0jΔt+ϕ0))),Bj,2=cos(2(ω0jΔt+ϕ0))sin(2(ω0jΔt+ϕ0))(1cosδ0),Bj,3=sin(δ0(jΔt))cos(δ0(jΔt)),[],Bj,15=sin(δ0(jΔt))cos(δ1(jΔt))cos(δ2(jΔt))sin(δ3(jΔt)),
BI=BBTA,
A=(BBT)1BI=KBI,
I(t)=1(C2θ02+Cδ0S2θ02)(C2θ12+Cδ1S2θ12)[C2θ0S2θ0(1Cδ0)][C2θ1S2θ1(1Cδ1)]+Sδ1S2θ1Sδ0S2θ0.
I(t)=I(t)+Iϕ0(t)Δϕ0+Iϕ1(t)Δϕ1+Iδ0(t)Δδ0+Iδ1(t)Δδ1+O(Δi2)+,
Mcalib=[Δδ0Δθ0Δδ1Δθ1].
Mcorrected=Mobj1Mmeasured.

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