Abstract

Polarization measurements have become nearly indispensible in lidar cloud and aerosol studies. Despite polarization’s widespread use in lidar, its theoretical description has been widely varying in accuracy and completeness. Incomplete polarization lidar descriptions invariably result in poor accountability for scatterer properties and instrument effects, reducing data accuracy and disallowing the intercomparison of polarization lidar data between different systems. We introduce here the Stokes vector lidar equation, which is a full description of polarization in lidar from laser output to detector. We then interpret this theoretical description in the context of forward polar decomposition of Mueller matrices where distinct polarization attributes of diattenuation, retardance, and depolarization are elucidated. This decomposition can be applied to scattering matrices, where volumes consisting of randomly oriented particles are strictly depolarizing, while oriented ice crystals can be diattenuating, retarding, and depolarizing. For instrument effects we provide a description of how different polarization attributes will impact lidar measurements. This includes coupling effects due to retarding and depolarization attributes of the receiver, which have no description in scalar representations of polarization lidar. We also describe how the effects of polarizance in the receiver can result in nonorthogonal polarization detection channels. This violates one of the most common assumptions in polarization lidar operation.

© 2012 Optical Society of America

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    [CrossRef]
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  25. M. Anastasiadou, S. Hatit, R. Ossikovski, S. Guyot, and A. Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. Eur. Opt. Soc. Rapid Pub. 2, 07018 (2007).
    [CrossRef]
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  35. M. Hayman and J. Thayer, “Explicit description of polarization coupling in lidar applications,” Opt. Lett. 34, 611–613 (2009).
    [CrossRef]
  36. R. Simon and N. Mukunda, “Minimal three-component SU(2) gadget for polarization optics,” Phys. Lett. A 143, 165–169 (1990).
    [CrossRef]
  37. V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
    [CrossRef]
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    [CrossRef]

2011

E. J. Yorks, D. L. Hlavka, W. D. Hart, and M. J. McGill, “Statistics of cloud optical properties from airborne lidar measurements,” J. Atmos. Ocean. Technol. 28, 869–883 (2011).
[CrossRef]

J. Sanz, J. Saiz, F. González, and F. Moreno, “Polar decomposition of the Mueller matrix: a polarimetric rule of thumb for square-profile surface structure recognition,” Appl. Opt. 50, 3781–3788 (2011).
[CrossRef]

T. Tudor and V. Manea, “Ellipsoid of the polarization degree: a vectorial, pure operatorial Pauli algebraic approach,” J. Opt. Soc. Am. B 28, 596–601 (2011).
[CrossRef]

M. Hayman and J. Thayer, “Lidar polarization measurements of PMCs,” J. Atmos. Sol. Terr. Phys. 73, 2110–2117 (2011).
[CrossRef]

2009

J. Sanz, P. Albella, F. Moreno, J. Saiz, and F. González, “Application of the polar decomposition to light scattering particle systems,” J. Quant. Spectrosc. Radiat. Transfer 110, 1369–1374 (2009).
[CrossRef]

M. Hayman and J. Thayer, “Explicit description of polarization coupling in lidar applications,” Opt. Lett. 34, 611–613 (2009).
[CrossRef]

I. Mattis, M. Tesche, M. Grein, V. Freudenthaler, and D. Müller, “Systematic error of lidar profiles caused by a polarization-dependent receiver transmission: quantification and error correction scheme,” Appl. Opt. 48, 2742–2751 (2009).
[CrossRef]

N. Ghosh, M. Wood, S. Li, R. Weisel, B. Wilson, R. Li, and I. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef]

2008

2007

2006

C. Ferreira, I. S. José, J. J. Gil, and J. M. Correas, “Geometric modelling of polarimetric transformations,” Monografías del Seminario Matemático García de Galdeano 33, 115–119(2006).

Y. You, G. W. Kattawar, P. Yang, Y. X. Hu, and B. A. Baum, “Sensitivity of depolarized lidar signals to cloud and aerosol particle properties,” J. Quant. Spectrosc. Radiat. Transfer 100, 470–482 (2006).
[CrossRef]

M. Del Guasta, E. Vallar, O. Riviere, F. Castagnoli, V. Venturi, and M. Morandi, “Use of polarimetric lidar for the study of oriented ice plates in clouds,” Appl. Opt. 45, 4878–4887 (2006).
[CrossRef]

2004

2003

Y. Hu, P. Yang, B. Lin, G. Gibson, and C. Hostetler, “Discriminating between spherical and non-spherical scatterers,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 757–764 (2003).
[CrossRef]

1998

B. V. Kaul, “Lidar equation for the case of sensing optically anisotropic media,” Proc. SPIE 3495, 332–339 (1998).
[CrossRef]

A. Ben-David, “Mueller matrices and information derived from linear polarization lidar measurements: theory,” Appl. Opt. 37, 2448–2463 (1998).
[CrossRef]

1996

S. Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13, 1106–1113 (1996).
[CrossRef]

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

1995

1991

K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848–1866 (1991).
[CrossRef]

M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
[CrossRef]

1990

R. Simon, “Nondepolarizing systems and degree of polarization,” Opt. Commun. 77, 349–354 (1990).
[CrossRef]

R. Simon and N. Mukunda, “Minimal three-component SU(2) gadget for polarization optics,” Phys. Lett. A 143, 165–169 (1990).
[CrossRef]

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, and A. F. Tuck, “Airborne lidar observations in the wintertime arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

1987

J. Gil and E. Bernabéu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from its Mueller matrix,” Optik 76, 67–71 (1987).

1978

1971

R. M. Schotland, K. Sassen, and R. J. Stone, “Observations by lidar of linear depolarization ratios by hydrometeors,” J. Appl. Meteorol. 10, 1011–1017 (1971).
[CrossRef]

Albella, P.

J. Sanz, P. Albella, F. Moreno, J. Saiz, and F. González, “Application of the polar decomposition to light scattering particle systems,” J. Quant. Spectrosc. Radiat. Transfer 110, 1369–1374 (2009).
[CrossRef]

Anastasiadou, M.

M. Anastasiadou, S. Hatit, R. Ossikovski, S. Guyot, and A. Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. Eur. Opt. Soc. Rapid Pub. 2, 07018 (2007).
[CrossRef]

Bagini, V.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

Baum, B. A.

Y. You, G. W. Kattawar, P. Yang, Y. X. Hu, and B. A. Baum, “Sensitivity of depolarized lidar signals to cloud and aerosol particle properties,” J. Quant. Spectrosc. Radiat. Transfer 100, 470–482 (2006).
[CrossRef]

Ben-David, A.

Bernabéu, E.

J. Gil and E. Bernabéu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from its Mueller matrix,” Optik 76, 67–71 (1987).

Borghi, R.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

Borne, M.

M. Borne and E. Wolf, Principles of Optics, 6th ed. (Cambridge University, 1999).

Browell, E. V.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, and A. F. Tuck, “Airborne lidar observations in the wintertime arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Butler, C. F.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, and A. F. Tuck, “Airborne lidar observations in the wintertime arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Carswell, A. I.

Carter, A. F.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, and A. F. Tuck, “Airborne lidar observations in the wintertime arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Castagnoli, F.

Chen, Z.

Chipman, R.

Chipman, R. A.

Chung, J.

Correas, J. M.

C. Ferreira, I. S. José, J. J. Gil, and J. M. Correas, “Geometric modelling of polarimetric transformations,” Monografías del Seminario Matemático García de Galdeano 33, 115–119(2006).

DeBoo, B.

Del Guasta, M.

Ferreira, C.

C. Ferreira, I. S. José, J. J. Gil, and J. M. Correas, “Geometric modelling of polarimetric transformations,” Monografías del Seminario Matemático García de Galdeano 33, 115–119(2006).

Flynn, C. J.

Freudenthaler, V.

Frezza, F.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

Ghosh, N.

N. Ghosh, M. Wood, S. Li, R. Weisel, B. Wilson, R. Li, and I. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef]

Gibson, G.

Y. Hu, P. Yang, B. Lin, G. Gibson, and C. Hostetler, “Discriminating between spherical and non-spherical scatterers,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 757–764 (2003).
[CrossRef]

Gil, J.

J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. Appl. Phys. 40, 1–47 (2007).
[CrossRef]

J. Gil and E. Bernabéu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from its Mueller matrix,” Optik 76, 67–71 (1987).

Gil, J. J.

C. Ferreira, I. S. José, J. J. Gil, and J. M. Correas, “Geometric modelling of polarimetric transformations,” Monografías del Seminario Matemático García de Galdeano 33, 115–119(2006).

Gimmestad, G.

Goldstein, D. H.

D. H. Goldstein, Polarized Light, 2nd ed. (Dekker, 2003).

González, F.

J. Sanz, J. Saiz, F. González, and F. Moreno, “Polar decomposition of the Mueller matrix: a polarimetric rule of thumb for square-profile surface structure recognition,” Appl. Opt. 50, 3781–3788 (2011).
[CrossRef]

J. Sanz, P. Albella, F. Moreno, J. Saiz, and F. González, “Application of the polar decomposition to light scattering particle systems,” J. Quant. Spectrosc. Radiat. Transfer 110, 1369–1374 (2009).
[CrossRef]

Gori, F.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

Grein, M.

Guyot, S.

R. Ossikovski, A. Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing Mueller matrices,” Opt. Lett. 32, 689–691 (2007).
[CrossRef]

M. Anastasiadou, S. Hatit, R. Ossikovski, S. Guyot, and A. Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. Eur. Opt. Soc. Rapid Pub. 2, 07018 (2007).
[CrossRef]

Hammer-Wilson, M.

Hart, W. D.

E. J. Yorks, D. L. Hlavka, W. D. Hart, and M. J. McGill, “Statistics of cloud optical properties from airborne lidar measurements,” J. Atmos. Ocean. Technol. 28, 869–883 (2011).
[CrossRef]

Hatit, S.

M. Anastasiadou, S. Hatit, R. Ossikovski, S. Guyot, and A. Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. Eur. Opt. Soc. Rapid Pub. 2, 07018 (2007).
[CrossRef]

Hayman, M.

M. Hayman and J. Thayer, “Lidar polarization measurements of PMCs,” J. Atmos. Sol. Terr. Phys. 73, 2110–2117 (2011).
[CrossRef]

M. Hayman and J. Thayer, “Explicit description of polarization coupling in lidar applications,” Opt. Lett. 34, 611–613 (2009).
[CrossRef]

Higdon, N. S.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, and A. F. Tuck, “Airborne lidar observations in the wintertime arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Hlavka, D. L.

E. J. Yorks, D. L. Hlavka, W. D. Hart, and M. J. McGill, “Statistics of cloud optical properties from airborne lidar measurements,” J. Atmos. Ocean. Technol. 28, 869–883 (2011).
[CrossRef]

Hostetler, C.

Y. Hu, P. Yang, B. Lin, G. Gibson, and C. Hostetler, “Discriminating between spherical and non-spherical scatterers,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 757–764 (2003).
[CrossRef]

Houston, J. D.

Hovenier, J.

Hu, Y.

Y. Hu, P. Yang, B. Lin, G. Gibson, and C. Hostetler, “Discriminating between spherical and non-spherical scatterers,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 757–764 (2003).
[CrossRef]

Hu, Y. X.

Y. You, G. W. Kattawar, P. Yang, Y. X. Hu, and B. A. Baum, “Sensitivity of depolarized lidar signals to cloud and aerosol particle properties,” J. Quant. Spectrosc. Radiat. Transfer 100, 470–482 (2006).
[CrossRef]

Ismail, S.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, and A. F. Tuck, “Airborne lidar observations in the wintertime arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

José, I. S.

C. Ferreira, I. S. José, J. J. Gil, and J. M. Correas, “Geometric modelling of polarimetric transformations,” Monografías del Seminario Matemático García de Galdeano 33, 115–119(2006).

Jung, W.

Kattawar, G. W.

Y. You, G. W. Kattawar, P. Yang, Y. X. Hu, and B. A. Baum, “Sensitivity of depolarized lidar signals to cloud and aerosol particle properties,” J. Quant. Spectrosc. Radiat. Transfer 100, 470–482 (2006).
[CrossRef]

Kaul, B. V.

G. G. Matvienko, I. V. Samokhvalov, and B. V. Kaul, “Research of the cirrus structure with a polarization lidar: parameters of particle orientation in crystal clouds,” Proc. SPIE 5571, 393–400 (2004).
[CrossRef]

B. V. Kaul, I. V. Samokhvalov, and S. N. Volkov, “Investigating particle orientation in cirrus clouds by measuring backscattering phase matrices with lidar,” Appl. Opt. 43, 6620–6628 (2004).
[CrossRef]

B. V. Kaul, “Lidar equation for the case of sensing optically anisotropic media,” Proc. SPIE 3495, 332–339 (1998).
[CrossRef]

Li, R.

N. Ghosh, M. Wood, S. Li, R. Weisel, B. Wilson, R. Li, and I. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef]

Li, S.

N. Ghosh, M. Wood, S. Li, R. Weisel, B. Wilson, R. Li, and I. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef]

Lin, B.

Y. Hu, P. Yang, B. Lin, G. Gibson, and C. Hostetler, “Discriminating between spherical and non-spherical scatterers,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 757–764 (2003).
[CrossRef]

Lu, S. Y.

Manea, V.

Martino, A.

M. Anastasiadou, S. Hatit, R. Ossikovski, S. Guyot, and A. Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. Eur. Opt. Soc. Rapid Pub. 2, 07018 (2007).
[CrossRef]

R. Ossikovski, A. Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing Mueller matrices,” Opt. Lett. 32, 689–691 (2007).
[CrossRef]

Mathur, S.

Mattis, I.

Matvienko, G. G.

G. G. Matvienko, I. V. Samokhvalov, and B. V. Kaul, “Research of the cirrus structure with a polarization lidar: parameters of particle orientation in crystal clouds,” Proc. SPIE 5571, 393–400 (2004).
[CrossRef]

McGill, M. J.

E. J. Yorks, D. L. Hlavka, W. D. Hart, and M. J. McGill, “Statistics of cloud optical properties from airborne lidar measurements,” J. Atmos. Ocean. Technol. 28, 869–883 (2011).
[CrossRef]

Mendoza, A.

Mishchenko, M.

Mishchenko, M. I.

Morandi, M.

Moreno, F.

J. Sanz, J. Saiz, F. González, and F. Moreno, “Polar decomposition of the Mueller matrix: a polarimetric rule of thumb for square-profile surface structure recognition,” Appl. Opt. 50, 3781–3788 (2011).
[CrossRef]

J. Sanz, P. Albella, F. Moreno, J. Saiz, and F. González, “Application of the polar decomposition to light scattering particle systems,” J. Quant. Spectrosc. Radiat. Transfer 110, 1369–1374 (2009).
[CrossRef]

Mukunda, N.

R. Simon and N. Mukunda, “Minimal three-component SU(2) gadget for polarization optics,” Phys. Lett. A 143, 165–169 (1990).
[CrossRef]

Müller, D.

Ossikovski, R.

R. Ossikovski, A. Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing Mueller matrices,” Opt. Lett. 32, 689–691 (2007).
[CrossRef]

M. Anastasiadou, S. Hatit, R. Ossikovski, S. Guyot, and A. Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. Eur. Opt. Soc. Rapid Pub. 2, 07018 (2007).
[CrossRef]

Riviere, O.

Robinette, P. A.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, and A. F. Tuck, “Airborne lidar observations in the wintertime arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Saiz, J.

J. Sanz, J. Saiz, F. González, and F. Moreno, “Polar decomposition of the Mueller matrix: a polarimetric rule of thumb for square-profile surface structure recognition,” Appl. Opt. 50, 3781–3788 (2011).
[CrossRef]

J. Sanz, P. Albella, F. Moreno, J. Saiz, and F. González, “Application of the polar decomposition to light scattering particle systems,” J. Quant. Spectrosc. Radiat. Transfer 110, 1369–1374 (2009).
[CrossRef]

Samokhvalov, I. V.

G. G. Matvienko, I. V. Samokhvalov, and B. V. Kaul, “Research of the cirrus structure with a polarization lidar: parameters of particle orientation in crystal clouds,” Proc. SPIE 5571, 393–400 (2004).
[CrossRef]

B. V. Kaul, I. V. Samokhvalov, and S. N. Volkov, “Investigating particle orientation in cirrus clouds by measuring backscattering phase matrices with lidar,” Appl. Opt. 43, 6620–6628 (2004).
[CrossRef]

Santarsiero, M.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

Sanz, J.

J. Sanz, J. Saiz, F. González, and F. Moreno, “Polar decomposition of the Mueller matrix: a polarimetric rule of thumb for square-profile surface structure recognition,” Appl. Opt. 50, 3781–3788 (2011).
[CrossRef]

J. Sanz, P. Albella, F. Moreno, J. Saiz, and F. González, “Application of the polar decomposition to light scattering particle systems,” J. Quant. Spectrosc. Radiat. Transfer 110, 1369–1374 (2009).
[CrossRef]

Sasian, J.

Sassen, K.

K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848–1866 (1991).
[CrossRef]

R. M. Schotland, K. Sassen, and R. J. Stone, “Observations by lidar of linear depolarization ratios by hydrometeors,” J. Appl. Meteorol. 10, 1011–1017 (1971).
[CrossRef]

Schettini, G.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

Schoeberl, M. R.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, and A. F. Tuck, “Airborne lidar observations in the wintertime arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Schotland, R. M.

R. M. Schotland, K. Sassen, and R. J. Stone, “Observations by lidar of linear depolarization ratios by hydrometeors,” J. Appl. Meteorol. 10, 1011–1017 (1971).
[CrossRef]

Simon, R.

R. Simon, “Nondepolarizing systems and degree of polarization,” Opt. Commun. 77, 349–354 (1990).
[CrossRef]

R. Simon and N. Mukunda, “Minimal three-component SU(2) gadget for polarization optics,” Phys. Lett. A 143, 165–169 (1990).
[CrossRef]

Spagnolo, G. S.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

Stone, R. J.

R. M. Schotland, K. Sassen, and R. J. Stone, “Observations by lidar of linear depolarization ratios by hydrometeors,” J. Appl. Meteorol. 10, 1011–1017 (1971).
[CrossRef]

Strang, G.

G. Strang, Linear Algebra and Its Applications, 3rd ed.(Thomson Learning, 1988).

Tesche, M.

Thayer, J.

M. Hayman and J. Thayer, “Lidar polarization measurements of PMCs,” J. Atmos. Sol. Terr. Phys. 73, 2110–2117 (2011).
[CrossRef]

M. Hayman and J. Thayer, “Explicit description of polarization coupling in lidar applications,” Opt. Lett. 34, 611–613 (2009).
[CrossRef]

Toon, O. B.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, and A. F. Tuck, “Airborne lidar observations in the wintertime arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Tuck, A. F.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, and A. F. Tuck, “Airborne lidar observations in the wintertime arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Tudor, T.

Vallar, E.

van de Hulst, H.

H. van de Hulst, Light Scattering by Small Particles (Wiley, 1981).

Venturi, V.

Vitkin, I.

N. Ghosh, M. Wood, S. Li, R. Weisel, B. Wilson, R. Li, and I. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef]

Volkov, S. N.

Weisel, R.

N. Ghosh, M. Wood, S. Li, R. Weisel, B. Wilson, R. Li, and I. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef]

Wilder-Smith, P.

Wilson, B.

N. Ghosh, M. Wood, S. Li, R. Weisel, B. Wilson, R. Li, and I. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef]

Wolf, E.

M. Borne and E. Wolf, Principles of Optics, 6th ed. (Cambridge University, 1999).

Wood, M.

N. Ghosh, M. Wood, S. Li, R. Weisel, B. Wilson, R. Li, and I. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef]

Yang, P.

Y. You, G. W. Kattawar, P. Yang, Y. X. Hu, and B. A. Baum, “Sensitivity of depolarized lidar signals to cloud and aerosol particle properties,” J. Quant. Spectrosc. Radiat. Transfer 100, 470–482 (2006).
[CrossRef]

Y. Hu, P. Yang, B. Lin, G. Gibson, and C. Hostetler, “Discriminating between spherical and non-spherical scatterers,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 757–764 (2003).
[CrossRef]

Yorks, E. J.

E. J. Yorks, D. L. Hlavka, W. D. Hart, and M. J. McGill, “Statistics of cloud optical properties from airborne lidar measurements,” J. Atmos. Ocean. Technol. 28, 869–883 (2011).
[CrossRef]

You, Y.

Y. You, G. W. Kattawar, P. Yang, Y. X. Hu, and B. A. Baum, “Sensitivity of depolarized lidar signals to cloud and aerosol particle properties,” J. Quant. Spectrosc. Radiat. Transfer 100, 470–482 (2006).
[CrossRef]

Zheng, Y.

Appl. Opt.

G. Gimmestad, “Reexamination of depolarization in lidar measurements,” Appl. Opt. 47, 3795–3802 (2008).
[CrossRef]

J. D. Houston and A. I. Carswell, “Four-component polarization measurement of lidar atmospheric scattering,” Appl. Opt. 17, 614–620 (1978).
[CrossRef]

M. Del Guasta, E. Vallar, O. Riviere, F. Castagnoli, V. Venturi, and M. Morandi, “Use of polarimetric lidar for the study of oriented ice plates in clouds,” Appl. Opt. 45, 4878–4887 (2006).
[CrossRef]

B. V. Kaul, I. V. Samokhvalov, and S. N. Volkov, “Investigating particle orientation in cirrus clouds by measuring backscattering phase matrices with lidar,” Appl. Opt. 43, 6620–6628 (2004).
[CrossRef]

A. Ben-David, “Mueller matrices and information derived from linear polarization lidar measurements: theory,” Appl. Opt. 37, 2448–2463 (1998).
[CrossRef]

J. Sanz, J. Saiz, F. González, and F. Moreno, “Polar decomposition of the Mueller matrix: a polarimetric rule of thumb for square-profile surface structure recognition,” Appl. Opt. 50, 3781–3788 (2011).
[CrossRef]

J. Chung, W. Jung, M. Hammer-Wilson, P. Wilder-Smith, and Z. Chen, “Use of polar decomposition for the diagnosis of oral precancer,” Appl. Opt. 46, 3038–3045 (2007).
[CrossRef]

I. Mattis, M. Tesche, M. Grein, V. Freudenthaler, and D. Müller, “Systematic error of lidar profiles caused by a polarization-dependent receiver transmission: quantification and error correction scheme,” Appl. Opt. 48, 2742–2751 (2009).
[CrossRef]

Bull. Am. Meteorol. Soc.

K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848–1866 (1991).
[CrossRef]

Eur. J. Phys.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996).
[CrossRef]

Eur. Phys. J. Appl. Phys.

J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. Appl. Phys. 40, 1–47 (2007).
[CrossRef]

Geophys. Res. Lett.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, and A. F. Tuck, “Airborne lidar observations in the wintertime arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

J. Appl. Meteorol.

R. M. Schotland, K. Sassen, and R. J. Stone, “Observations by lidar of linear depolarization ratios by hydrometeors,” J. Appl. Meteorol. 10, 1011–1017 (1971).
[CrossRef]

J. Atmos. Ocean. Technol.

E. J. Yorks, D. L. Hlavka, W. D. Hart, and M. J. McGill, “Statistics of cloud optical properties from airborne lidar measurements,” J. Atmos. Ocean. Technol. 28, 869–883 (2011).
[CrossRef]

J. Atmos. Sol. Terr. Phys.

M. Hayman and J. Thayer, “Lidar polarization measurements of PMCs,” J. Atmos. Sol. Terr. Phys. 73, 2110–2117 (2011).
[CrossRef]

J. Biophotonics

N. Ghosh, M. Wood, S. Li, R. Weisel, B. Wilson, R. Li, and I. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophotonics 2, 145–156 (2009).
[CrossRef]

J. Eur. Opt. Soc. Rapid Pub.

M. Anastasiadou, S. Hatit, R. Ossikovski, S. Guyot, and A. Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. Eur. Opt. Soc. Rapid Pub. 2, 07018 (2007).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Quant. Spectrosc. Radiat. Transfer

J. Sanz, P. Albella, F. Moreno, J. Saiz, and F. González, “Application of the polar decomposition to light scattering particle systems,” J. Quant. Spectrosc. Radiat. Transfer 110, 1369–1374 (2009).
[CrossRef]

Y. Hu, P. Yang, B. Lin, G. Gibson, and C. Hostetler, “Discriminating between spherical and non-spherical scatterers,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 757–764 (2003).
[CrossRef]

Y. You, G. W. Kattawar, P. Yang, Y. X. Hu, and B. A. Baum, “Sensitivity of depolarized lidar signals to cloud and aerosol particle properties,” J. Quant. Spectrosc. Radiat. Transfer 100, 470–482 (2006).
[CrossRef]

Monografías del Seminario Matemático García de Galdeano

C. Ferreira, I. S. José, J. J. Gil, and J. M. Correas, “Geometric modelling of polarimetric transformations,” Monografías del Seminario Matemático García de Galdeano 33, 115–119(2006).

Opt. Commun.

R. Simon, “Nondepolarizing systems and degree of polarization,” Opt. Commun. 77, 349–354 (1990).
[CrossRef]

Opt. Eng.

R. A. Chipman, “Mechanics of polarization ray tracing,” Opt. Eng. 34, 1636–1645 (1995).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

J. Gil and E. Bernabéu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from its Mueller matrix,” Optik 76, 67–71 (1987).

Phys. Lett. A

R. Simon and N. Mukunda, “Minimal three-component SU(2) gadget for polarization optics,” Phys. Lett. A 143, 165–169 (1990).
[CrossRef]

Proc. SPIE

G. G. Matvienko, I. V. Samokhvalov, and B. V. Kaul, “Research of the cirrus structure with a polarization lidar: parameters of particle orientation in crystal clouds,” Proc. SPIE 5571, 393–400 (2004).
[CrossRef]

B. V. Kaul, “Lidar equation for the case of sensing optically anisotropic media,” Proc. SPIE 3495, 332–339 (1998).
[CrossRef]

Other

D. H. Goldstein, Polarized Light, 2nd ed. (Dekker, 2003).

M. Borne and E. Wolf, Principles of Optics, 6th ed. (Cambridge University, 1999).

H. van de Hulst, Light Scattering by Small Particles (Wiley, 1981).

G. Strang, Linear Algebra and Its Applications, 3rd ed.(Thomson Learning, 1988).

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Figures (6)

Fig. 1.
Fig. 1.

Poincaré sphere representation of a normalized Stokes vector. The sphere’s radius is 1, and the Stokes vector length is the DOP p. The orientation of the Stokes vector is given by the rotation and ellipticity angles ψ and χ, respectively. Linear polarizations are on the equator of the sphere and circular at the poles. Each meridian corresponds to a specific linear orientation. A Stokes vector of zero length (on the origin) is completely unpolarized.

Fig. 2.
Fig. 2.

Poincaré sphere representation of backscattered polarization states from randomly oriented scatterers with d=0.3. The incident circular, linear, and elliptical Stokes vectors (hollow blue, red, and green, respectively) are shortened after passing through the depolarizer (solid arrows of corresponding colors) while the sphere surface maintains constant radius. Totally linear or circular polarized input states have the same output polarized state, but circular components depolarize more than linear, so the elliptical polarization changes state. The π phase shifts usually associated with backscattering have been omitted for easier comparison of the incident and scattered Stokes vectors.

Fig. 3.
Fig. 3.

Graphical depiction of angular terms for scatterers oriented in the horizontal plane. The lidar tilt angle α is measured relative to zenith (z axis), and the polarization angle ψL is measured relative to the linear polarization that lies in the horizontal plane (s axis).

Fig. 4.
Fig. 4.

Poincaré sphere representation of oriented scatterers with matrix given in [10]. The incident circular, arbitrary linear, and arbitrary elliptical Stokes vectors (hollow blue, red, and green, respectively) are significantly changed after scattering (solid arrows of corresponding colors). Because of a combination of polarization effects, none of the scattered polarized states resemble the incident polarizations. The π phase shifts usually associated with backscattering have been omitted from this analysis.

Fig. 5.
Fig. 5.

Poincaré sphere representation of two orthogonal polarizations before (hollow red and blue) and after (solid red and blue) passing through a diattenuator with |P|=0.3. The polarizance vector is depicted as the solid green arrow. Though the two polarizations are orthogonal prior to the diattenuator, polarizance corrupts this relationship so they can no longer be perfectly separated using a polarizing beam splitter.

Fig. 6.
Fig. 6.

Angle between orthogonal polarization channels as a function of polarizance magnitude when polarization analyzers are preceded by a pure diattenuator at 45° to the polarization of operation. The difference in analyzer angles is reported in degrees. Even small amounts of polarizance can cause the optical system to violate the assumption that the two polarization channels are orthogonal.

Equations (37)

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

S=[S0S1S2S3],
S=S0[1pcos2ψcos2χpsin2ψcos2χpsin2χ],
p=S12+S22+S32S0.
SRX(R)=MRX[(G(R)AR2ΔR)Tatm(ks,R)×F(ki,ks,R)Tatm(ki,R)MTXSTX+SB].
N=OSRX,
N=[N1N2],
O=o[P1P2],
o=[η100000000000η2000],
N=[NN],
O=o[PP],
o=[ηD00000000000ηD000],
M=MΔMRMD,
MD=Tu[1DTPmD],
mD=1D2I+(11D2)D^D^T,
MR=[10T0mR],
MΔ=[10TPmΔ],
mΔ=T1[1d10001d20001d3]T,
F(π)=β[100001d0000d100002d1],
d=4N(N+N)(3cos4χL),
F(ki,ki)=[f11f1200f12f220000f33f3400f34f44],
δc=f11f44f11+f44.
δl=f11f22cos22ψLf33sin22ψLf11+2f12cos2ψL+f22cos22ψL+f33sin22ψL,
NRXf11+f12cos2ψL,
F(ki,ki)=[10.51000.510.8900000.5130.08000.080.40].
F(ki,ki)=f11MΔFMRFMDF,
MDF=[1f1200f12100001f12200001f122],
MRF=[1000010000cosΓFsinΓF00sinΓFcosΓF],
MΔF=[1000P11d100001(d3dxcos2θx)dx2sin2θx00dx2sin2θx1(d2+dxcos2θx)],
dx=d3d2.
P1=d1f12.
θx=ΓF2.
sin2χ=sin2θsinΓ,
PRX=|PRX|[cos2θPsin2θP0],
MD=PMD(θP,|PRX|),
MD=PMD(θP,|PRX|),
Δθpol=12arccos(D^RX·D^RX),
Δθpol=12arccos(|PRX|2(1+sin22θP)11|PRX|2cos22θP).

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