Abstract

In this Letter we present the equations to calculate the six independent polarization effects of an arbitrary normalized Mueller–Jones matrix corresponding to homogenous media. A comparison between this method and other inversion procedures is discussed, and the application of the analytic inversion to experimental Mueller matrices is illustrated.

© 2010 Optical Society of America

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Errata

Oriol Arteaga and Adolf Canillas, "Analytic inversion of the Mueller–Jones polarization matrices for homogeneous media: erratum," Opt. Lett. 35, 3525-3525 (2010)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-35-20-3525

References

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  1. C. R. Jones, J. Opt. Soc. Am. 38, 671 (1948).
    [CrossRef]
  2. R. M. A. Azzam, J. Opt. Soc. Am. 38, 1756 (1978).
    [CrossRef]
  3. S.-Y. Lu and R. A. Chipman, J. Opt. Soc. Am. A 13, 1106 (1996).
    [CrossRef]
  4. O. Arteaga and A. Canillas, J. Opt. Soc. Am. A 26, 783 (2009).
    [CrossRef]
  5. R. Barakat, Opt. Commun. 38, 159 (1981).
    [CrossRef]
  6. R. A. Chipman, Handbook of Optics, Vol. 2, 2nd ed. (McGraw-Hill Professional, 1994), Chap. 22.
  7. S. R. Cloude, Proc. SPIE 1166, 177 (1989).
  8. S. Savenkov, V. Grygoruk, R. Muttiah, K. Yushtin, Y. Oberemok, and V. Yakubchak, J. Quant. Spectrosc. Radiat. Transf. 110, 30, see Appendix B (2009).
    [CrossRef]
  9. O. Arteaga, A. Canillas, R. Purrello, and J. M. Ribó, Opt. Lett. 34, 2177 (2009).
    [CrossRef] [PubMed]

2009

S. Savenkov, V. Grygoruk, R. Muttiah, K. Yushtin, Y. Oberemok, and V. Yakubchak, J. Quant. Spectrosc. Radiat. Transf. 110, 30, see Appendix B (2009).
[CrossRef]

O. Arteaga and A. Canillas, J. Opt. Soc. Am. A 26, 783 (2009).
[CrossRef]

O. Arteaga, A. Canillas, R. Purrello, and J. M. Ribó, Opt. Lett. 34, 2177 (2009).
[CrossRef] [PubMed]

1996

1989

S. R. Cloude, Proc. SPIE 1166, 177 (1989).

1981

R. Barakat, Opt. Commun. 38, 159 (1981).
[CrossRef]

1978

R. M. A. Azzam, J. Opt. Soc. Am. 38, 1756 (1978).
[CrossRef]

1948

Arteaga, O.

Azzam, R. M. A.

R. M. A. Azzam, J. Opt. Soc. Am. 38, 1756 (1978).
[CrossRef]

Barakat, R.

R. Barakat, Opt. Commun. 38, 159 (1981).
[CrossRef]

Canillas, A.

Chipman, R. A.

S.-Y. Lu and R. A. Chipman, J. Opt. Soc. Am. A 13, 1106 (1996).
[CrossRef]

R. A. Chipman, Handbook of Optics, Vol. 2, 2nd ed. (McGraw-Hill Professional, 1994), Chap. 22.

Cloude, S. R.

S. R. Cloude, Proc. SPIE 1166, 177 (1989).

Grygoruk, V.

S. Savenkov, V. Grygoruk, R. Muttiah, K. Yushtin, Y. Oberemok, and V. Yakubchak, J. Quant. Spectrosc. Radiat. Transf. 110, 30, see Appendix B (2009).
[CrossRef]

Jones, C. R.

Lu, S.-Y.

Muttiah, R.

S. Savenkov, V. Grygoruk, R. Muttiah, K. Yushtin, Y. Oberemok, and V. Yakubchak, J. Quant. Spectrosc. Radiat. Transf. 110, 30, see Appendix B (2009).
[CrossRef]

Oberemok, Y.

S. Savenkov, V. Grygoruk, R. Muttiah, K. Yushtin, Y. Oberemok, and V. Yakubchak, J. Quant. Spectrosc. Radiat. Transf. 110, 30, see Appendix B (2009).
[CrossRef]

Purrello, R.

Ribó, J. M.

Savenkov, S.

S. Savenkov, V. Grygoruk, R. Muttiah, K. Yushtin, Y. Oberemok, and V. Yakubchak, J. Quant. Spectrosc. Radiat. Transf. 110, 30, see Appendix B (2009).
[CrossRef]

Yakubchak, V.

S. Savenkov, V. Grygoruk, R. Muttiah, K. Yushtin, Y. Oberemok, and V. Yakubchak, J. Quant. Spectrosc. Radiat. Transf. 110, 30, see Appendix B (2009).
[CrossRef]

Yushtin, K.

S. Savenkov, V. Grygoruk, R. Muttiah, K. Yushtin, Y. Oberemok, and V. Yakubchak, J. Quant. Spectrosc. Radiat. Transf. 110, 30, see Appendix B (2009).
[CrossRef]

J. Opt. Soc. Am.

R. M. A. Azzam, J. Opt. Soc. Am. 38, 1756 (1978).
[CrossRef]

C. R. Jones, J. Opt. Soc. Am. 38, 671 (1948).
[CrossRef]

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transf.

S. Savenkov, V. Grygoruk, R. Muttiah, K. Yushtin, Y. Oberemok, and V. Yakubchak, J. Quant. Spectrosc. Radiat. Transf. 110, 30, see Appendix B (2009).
[CrossRef]

Opt. Commun.

R. Barakat, Opt. Commun. 38, 159 (1981).
[CrossRef]

Opt. Lett.

Proc. SPIE

S. R. Cloude, Proc. SPIE 1166, 177 (1989).

Other

R. A. Chipman, Handbook of Optics, Vol. 2, 2nd ed. (McGraw-Hill Professional, 1994), Chap. 22.

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Figures (1)

Fig. 1
Fig. 1

Results of the analytic inversion (solid curve) when applied to spectroscopic series of experimentally determined Mueller matrices. Results for the pseudopolar decomposition (dashed curve) are also presented for comparison.

Tables (2)

Tables Icon

Table 1 Symbols Used and Definitions

Tables Icon

Table 2 Comparison of Methods to Analyze Homogeneous Mueller–Jones Matrices

Equations (19)

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J = ( j 00 j 01 j 10 j 11 ) = e i θ 00 ( r 00 r 01 e i ( θ 01 θ 00 ) r 10 e i ( θ 10 θ 00 ) r 11 e i ( θ 11 θ 00 ) ) .
r 00 = [ ( m 00 + m 01 + m 10 + m 11 ) 2 ] 1 2 ,
r 01 = [ ( m 00 m 01 + m 10 m 11 ) 2 ] 1 2 ,
r 10 = [ ( m 00 + m 01 m 10 m 11 ) 2 ] 1 2 ,
r 11 = [ ( m 00 m 01 m 10 + m 11 ) 2 ] 1 2 ,
e i ( θ 01 θ 00 ) = m 02 + m 12 i ( m 03 + m 13 ) [ ( m 00 + m 10 ) 2 ( m 01 + m 11 ) 2 ] 1 2 ,
e i ( θ 10 θ 00 ) = m 20 + m 21 + i ( m 30 + m 31 ) [ ( m 00 + m 01 ) 2 ( m 10 + m 11 ) 2 ] 1 2 ,
e i ( θ 11 θ 00 ) = m 22 + m 33 + i ( m 32 + m 23 ) [ ( m 00 + m 11 ) 2 ( m 10 + m 01 ) 2 ] 1 2 .
J = e i χ 2 ( cos T 2 i L T sin T 2 ( C i L ) T sin T 2 ( C + i L ) T sin T 2 cos T 2 + i L T sin T 2 ) ,
( cos T 2 i L T sin T 2 ( C i L ) T sin T 2 ( C + i L ) T sin T 2 cos T 2 + i L T sin T 2 ) = K ( r 00 r 01 e i ( θ 01 θ 00 ) r 10 e i ( θ 10 θ 00 ) r 11 e i ( θ 11 θ 00 ) ) ,
K = [ r 00 r 11 e i ( θ 11 θ 00 ) r 01 r 10 e i ( θ 01 θ 00 ) e i ( θ 10 θ 00 ) ] 1 2 .
LB = R [ i Ω ( r 00 r 11 e i ( θ 11 θ 00 ) ) ] ,
LB = R [ i Ω ( r 01 e i ( θ 01 θ 00 ) + r 10 e i ( θ 10 θ 00 ) ) ] ,
CB = R [ Ω ( r 01 e i ( θ 01 θ 00 ) r 10 e i ( θ 10 θ 00 ) ) ] ,
LD = I [ i Ω ( r 00 r 11 e i ( θ 11 θ 00 ) ) ] ,
LD = I [ i Ω ( r 01 e i ( θ 01 θ 00 ) + r 10 e i ( θ 10 θ 00 ) ) ] ,
CD = I [ Ω ( r 01 e i ( θ 01 θ 00 ) r 10 e i ( θ 10 θ 00 ) ) ] ,
β = ( i j m i j 2 ) m 00 2 3 m 00 ,
M = λ 0 M J 0 + λ 1 M J 1 + λ 2 M J 2 + λ 3 M J 3 ,

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