Abstract

Polar decomposition consists of representing an arbitrary Mueller matrix with a product of three simpler matrices, but, since these matrices do not commute, the result depends on the order in which they are multiplied. We show that the six possible decompositions can be classified into two families and that one of these families always leads to physical elementary matrices, whereas the other does not.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Y. Lu and R. A. Chipman, J. Opt. Soc. Am. A 13, 1106 (1996).
    [CrossRef]
  2. P. Gerligand, M. H. Smith, and R. A. Chipman, Opt. Express 4, 420 (1999), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  3. J. M. Bueno and M. C. W. Campbell, Ophthalmic Physiol. Opt. 23, 109 (2003).
    [CrossRef] [PubMed]
  4. C. Collet, J. Zallat, and Y. Takakura, Opt. Express 12, 1271 (2004), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  5. C. Brosseau, Fundamentals of Polarized Light—A Statistical Approach (Wiley, New York, 1998).
  6. W. A. Press, W. T. Vetterling, S. A. Teukolsky, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1973).

2004 (1)

2003 (1)

J. M. Bueno and M. C. W. Campbell, Ophthalmic Physiol. Opt. 23, 109 (2003).
[CrossRef] [PubMed]

1999 (1)

1996 (1)

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light—A Statistical Approach (Wiley, New York, 1998).

Bueno, J. M.

J. M. Bueno and M. C. W. Campbell, Ophthalmic Physiol. Opt. 23, 109 (2003).
[CrossRef] [PubMed]

Campbell, M. C. W.

J. M. Bueno and M. C. W. Campbell, Ophthalmic Physiol. Opt. 23, 109 (2003).
[CrossRef] [PubMed]

Chipman, R. A.

Collet, C.

Flannery, B. P.

W. A. Press, W. T. Vetterling, S. A. Teukolsky, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1973).

Gerligand, P.

Lu, S. Y.

Press, W. A.

W. A. Press, W. T. Vetterling, S. A. Teukolsky, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1973).

Smith, M. H.

Takakura, Y.

Teukolsky, S. A.

W. A. Press, W. T. Vetterling, S. A. Teukolsky, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1973).

Vetterling, W. T.

W. A. Press, W. T. Vetterling, S. A. Teukolsky, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1973).

Zallat, J.

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

Ophthalmic Physiol. Opt. (1)

J. M. Bueno and M. C. W. Campbell, Ophthalmic Physiol. Opt. 23, 109 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Other (2)

C. Brosseau, Fundamentals of Polarized Light—A Statistical Approach (Wiley, New York, 1998).

W. A. Press, W. T. Vetterling, S. A. Teukolsky, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1973).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (17)

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

M=MΔ1MR1MD1,  MΔ2MD2MR2, MR3MD3MΔ3,  MD4MR4MΔ4, MR5MΔ5MD5,  MD6MΔ6MD6,,
MR=10T0mR.
MD=Tu1DTDmD, mD=1-D21/2i+1-1-D21/2DˆDˆT,
MΔ=10TPmΔ,
M=M11M12TM21m=Tu1D1TPΔ1+mΔ1mR1D1PΔ1D1T+mΔ1mR1mD1.
M=MMD1-1=MΔ1MR11M12TM21m=10TPΔ1mΔ1mR1.
MR2=MR1,  MΔ2=MΔ1, MD2=MR1MD1MR1T,
MR5=MR1,  MD5=MD1, MΔ5=MR1TMΔ1MR1.
M=M11M12TM12Tm=Tu1+D4TmR4PΔ4D4TmR4m4D4+mD4mR4PΔ4mD4mR4mΔ4.
D4Tm=D4TmD4mR4mΔ4=D4TmR4mΔ4=M12T,
M=MMD40-1=M11M12TM21m=Tu10TmR4PΔ4mR4mΔ4.
MR3=MR4,  MΔ3=MΔ4, MD3=MR4TMD4MR4,
MR6=MR4,  MD6=MD4, MΔ6=MR4MΔ4MR4T.
Family FΔDDecompositions 1,2,5, Family FDΔDecompositions 3,4,6.
M=Tu1DTaDamD.
M=Tu1aDTDamD.
M=1D0T003*3.

Metrics