Abstract

We consider the problem of establishing conditions on a given Mueller matrix that ensure that the scattered light is purely polarized independently of the incident light polarization. It is shown that physically realizable Mueller matrices can be decomposed into a nondepolarizing part and an input-independent additive depolarizing part. The nondepolarizing part, however, is not always derivable from a Jones matrix. Applications to polarimetric optimal transmission and reception are also discussed.

© 1992 Optical Society of America

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References

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  1. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  2. C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  3. J. Cariou, B. Le Jeune, J. Lotran, Y. Guern, “Polarization effects of sea water and underwater targets,” Appl. Opt. 29, 1689–1695 (1990).
    [CrossRef] [PubMed]
  4. W. P. Van de Merwe, D. R. Huffman, B. V. Bronk, “Reproducibility and sensitivity of polarized light scattering for identifying bacterial suspensions,” Appl. Opt. 28, 5052–5057 (1989).
    [CrossRef] [PubMed]
  5. P. M. A. Sloot, A. G. Hoekstra, H. van der Liet, C. G. Figdor, “Scattering matrix elements of biological particles measured in a flow through system: theory and practice,” Appl. Opt. 28, 1752–1762 (1989).
    [CrossRef] [PubMed]
  6. J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).
  7. S. L. Durden, J. van Zyl, H. A. Zebker, “The unpolarized component in polarimetric radar observations of forested areas,” IEEE Trans. Geosci. Remote Sensing 28, 268–271 (1990).
    [CrossRef]
  8. A. B. Kostinski, W.-M. Boerner, “Polarimetric contrast optimization,” IEEE Trans. Antennas Propag. 35, 988–990 (1987).
    [CrossRef]
  9. A. Kostinski, B. James, W.-M. Boerner, “Optimal reception of partially polarized waves,” J. Opt. Soc. Am. A 5, 58–64 (1988).
    [CrossRef]
  10. R. Barakat, “Bilinear constraints between elements of the 4 × 4 Mueller–Jones transfer matrix of polarization theory,” Opt. Commun. 38, 159–161 (1981).
    [CrossRef]
  11. K. Kim, L. Mandel, E. Wolf, “Relationship between Jones and Mueller matrices for random media,” J. Opt. Soc. Am. A 4, 433–437 (1987).
    [CrossRef]
  12. F. G. Major, “Heterodyne polarimetry technique for complete amplitude scattering matrix for radiation,” Appl. Opt. 29, 5193–5197 (1990).
    [CrossRef] [PubMed]
  13. S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–361986.
  14. R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293–297 (1982).
    [CrossRef]
  15. R. Simon, “Mueller matrices and depolarization criteria,” J. Modern Opt. 34, 569–575 (1987).
    [CrossRef]
  16. J. Gil, E. Bernabeu, “A depolarization criterion in Mueller matrices,” Opt. Acta 32, 259–261 (1985).
    [CrossRef]
  17. E. Fry, G. Kattawar, “Relationships between elements of the Stokes matrix,” Appl. Opt. 20, 2811–2814 (1981).
    [CrossRef] [PubMed]
  18. J. P. McGuire, R. A. Chipman, “Analysis of spatial pseudopolarizers in imaging systems,” Opt. Eng. 29, 1478–1484 (1990).
    [CrossRef]
  19. J. Gil, E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185–189 (1986).
    [CrossRef]

1990

J. Cariou, B. Le Jeune, J. Lotran, Y. Guern, “Polarization effects of sea water and underwater targets,” Appl. Opt. 29, 1689–1695 (1990).
[CrossRef] [PubMed]

S. L. Durden, J. van Zyl, H. A. Zebker, “The unpolarized component in polarimetric radar observations of forested areas,” IEEE Trans. Geosci. Remote Sensing 28, 268–271 (1990).
[CrossRef]

F. G. Major, “Heterodyne polarimetry technique for complete amplitude scattering matrix for radiation,” Appl. Opt. 29, 5193–5197 (1990).
[CrossRef] [PubMed]

J. P. McGuire, R. A. Chipman, “Analysis of spatial pseudopolarizers in imaging systems,” Opt. Eng. 29, 1478–1484 (1990).
[CrossRef]

1989

1988

1987

A. B. Kostinski, W.-M. Boerner, “Polarimetric contrast optimization,” IEEE Trans. Antennas Propag. 35, 988–990 (1987).
[CrossRef]

K. Kim, L. Mandel, E. Wolf, “Relationship between Jones and Mueller matrices for random media,” J. Opt. Soc. Am. A 4, 433–437 (1987).
[CrossRef]

R. Simon, “Mueller matrices and depolarization criteria,” J. Modern Opt. 34, 569–575 (1987).
[CrossRef]

1986

S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–361986.

J. Gil, E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185–189 (1986).
[CrossRef]

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).

1985

J. Gil, E. Bernabeu, “A depolarization criterion in Mueller matrices,” Opt. Acta 32, 259–261 (1985).
[CrossRef]

1982

R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293–297 (1982).
[CrossRef]

1981

E. Fry, G. Kattawar, “Relationships between elements of the Stokes matrix,” Appl. Opt. 20, 2811–2814 (1981).
[CrossRef] [PubMed]

R. Barakat, “Bilinear constraints between elements of the 4 × 4 Mueller–Jones transfer matrix of polarization theory,” Opt. Commun. 38, 159–161 (1981).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Barakat, R.

R. Barakat, “Bilinear constraints between elements of the 4 × 4 Mueller–Jones transfer matrix of polarization theory,” Opt. Commun. 38, 159–161 (1981).
[CrossRef]

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Bernabeu, E.

J. Gil, E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185–189 (1986).
[CrossRef]

J. Gil, E. Bernabeu, “A depolarization criterion in Mueller matrices,” Opt. Acta 32, 259–261 (1985).
[CrossRef]

Boerner, W.-M.

A. Kostinski, B. James, W.-M. Boerner, “Optimal reception of partially polarized waves,” J. Opt. Soc. Am. A 5, 58–64 (1988).
[CrossRef]

A. B. Kostinski, W.-M. Boerner, “Polarimetric contrast optimization,” IEEE Trans. Antennas Propag. 35, 988–990 (1987).
[CrossRef]

Bohren, C.

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Bronk, B. V.

Cariou, J.

Chipman, R. A.

J. P. McGuire, R. A. Chipman, “Analysis of spatial pseudopolarizers in imaging systems,” Opt. Eng. 29, 1478–1484 (1990).
[CrossRef]

Cloude, S. R.

S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–361986.

Durden, S. L.

S. L. Durden, J. van Zyl, H. A. Zebker, “The unpolarized component in polarimetric radar observations of forested areas,” IEEE Trans. Geosci. Remote Sensing 28, 268–271 (1990).
[CrossRef]

Figdor, C. G.

Fry, E.

Gil, J.

J. Gil, E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185–189 (1986).
[CrossRef]

J. Gil, E. Bernabeu, “A depolarization criterion in Mueller matrices,” Opt. Acta 32, 259–261 (1985).
[CrossRef]

Guern, Y.

Hoekstra, A. G.

Hovenier, J. W.

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).

Huffman, D.

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Huffman, D. R.

James, B.

Kattawar, G.

Kim, K.

Kostinski, A.

Kostinski, A. B.

A. B. Kostinski, W.-M. Boerner, “Polarimetric contrast optimization,” IEEE Trans. Antennas Propag. 35, 988–990 (1987).
[CrossRef]

Le Jeune, B.

Lotran, J.

Major, F. G.

Mandel, L.

McGuire, J. P.

J. P. McGuire, R. A. Chipman, “Analysis of spatial pseudopolarizers in imaging systems,” Opt. Eng. 29, 1478–1484 (1990).
[CrossRef]

Simon, R.

R. Simon, “Mueller matrices and depolarization criteria,” J. Modern Opt. 34, 569–575 (1987).
[CrossRef]

R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293–297 (1982).
[CrossRef]

Sloot, P. M. A.

van de Hulst, H. C.

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).

Van de Merwe, W. P.

van der Liet, H.

van der Mee, C. V. M.

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).

van Zyl, J.

S. L. Durden, J. van Zyl, H. A. Zebker, “The unpolarized component in polarimetric radar observations of forested areas,” IEEE Trans. Geosci. Remote Sensing 28, 268–271 (1990).
[CrossRef]

Wolf, E.

Zebker, H. A.

S. L. Durden, J. van Zyl, H. A. Zebker, “The unpolarized component in polarimetric radar observations of forested areas,” IEEE Trans. Geosci. Remote Sensing 28, 268–271 (1990).
[CrossRef]

Appl. Opt.

Astron. Astrophys.

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).

IEEE Trans. Antennas Propag.

A. B. Kostinski, W.-M. Boerner, “Polarimetric contrast optimization,” IEEE Trans. Antennas Propag. 35, 988–990 (1987).
[CrossRef]

IEEE Trans. Geosci. Remote Sensing

S. L. Durden, J. van Zyl, H. A. Zebker, “The unpolarized component in polarimetric radar observations of forested areas,” IEEE Trans. Geosci. Remote Sensing 28, 268–271 (1990).
[CrossRef]

J. Modern Opt.

R. Simon, “Mueller matrices and depolarization criteria,” J. Modern Opt. 34, 569–575 (1987).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Acta

J. Gil, E. Bernabeu, “A depolarization criterion in Mueller matrices,” Opt. Acta 32, 259–261 (1985).
[CrossRef]

J. Gil, E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185–189 (1986).
[CrossRef]

Opt. Commun.

R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293–297 (1982).
[CrossRef]

R. Barakat, “Bilinear constraints between elements of the 4 × 4 Mueller–Jones transfer matrix of polarization theory,” Opt. Commun. 38, 159–161 (1981).
[CrossRef]

Opt. Eng.

J. P. McGuire, R. A. Chipman, “Analysis of spatial pseudopolarizers in imaging systems,” Opt. Eng. 29, 1478–1484 (1990).
[CrossRef]

Optik

S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–361986.

Other

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

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Equations (11)

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

trace ( M T M ) = 4 m 00 2 .
trace ( M T M ) = i , j = 0 3 m i j 2 .
A = B + C ,
trace ( B T B ) = 4 b 00 2 ,
C = [ c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] .
b 00 2 = 1 / 3 [ trace ( A T A ) - a 00 2 ]
trace ( B T B ) = b 00 2 + [ trace ( B T B ) - b 00 2 ] = b 00 2 + [ trace ( A T A ) - a 00 2 ] ,
I max = ρ S 0 + 0.5 ( 1 - ρ ) S 0 ,
ρ = S 1 2 + S 2 2 + S 3 2 S 0 ,
[ 1 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 ] .
[ 1 0 0 0 0 - 1 0 0 0 0 - 1 0 0 0 0 - 1 ] , [ 1 0 0 0 0 - 1 0 0 0 0 1 0 0 0 0 1 ] .

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