Abstract

Electromagnetic theory is used to calculate the gradual loss of polarization in light scattering from surface roughness. The receiver aperture is taken into account by means of a multiscale spatial averaging process. The polarization degrees are connected with the structural parameters of surfaces.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. W. Goodman, Statistical Optics (Wiley Classic Library, 1985).
  2. L. Mandel, and E. Wolf, eds., Optical Coherence and Quantum Optics (Cambridge University Press 1995).
  3. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, 2007).
  4. M. E. Knotts and K. A. O’Donnell, “Multiple scattering by deep perturbed gratings,” J. Opt. Soc. Am. A 11(11), 2837–2843 (1994).
    [CrossRef]
  5. E. Wolf, “Unified theory of Coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
    [CrossRef]
  6. C. Brosseau, “Polarization and Coherence Optics: Historical Perspective, Status and Future Directions,” presented at the Frontiers in Optics, 2008.
  7. E. Wolf, ed., Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, 2007).
  8. P. Réfrégier and F. Goudail, “Invariant degrees of coherence of partially polarized light,” Opt. Express 13(16), 6051–6060 (2005).
    [CrossRef] [PubMed]
  9. J. Ellis and A. Dogariu, “Complex degree of mutual polarization,” Opt. Lett. 29(6), 536–538 (2004).
    [CrossRef] [PubMed]
  10. C. Amra, M. Zerrad, L. Siozade, G. Georges, and C. Deumié, “Partial polarization of light induced by random defects at surfaces or bulks,” Opt. Express 16(14), 10372–10383 (2008).
    [CrossRef] [PubMed]
  11. J. Broky, J. Ellis, and A. Dogariu, “Identifying non-stationarities in random EM fields: are speckles really disturbing?” Opt. Express 16(19), 14469–14475 (2008).
    [CrossRef]
  12. J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics,” J. Biomed. Opt. 7(3), 307–312 (2002).
    [CrossRef] [PubMed]
  13. J. Sorrentini, M. Zerrad, and C. Amra, “Statistical signatures of random media and their correlation to polarization properties,” Opt. Lett. 34(16), 2429–2431 (2009).
    [CrossRef] [PubMed]
  14. D. Colton, and R. Kress, Integral Equations methods in Scattering Theory (New-York, 1983).
  15. S. G. Hanson and H. T. Yura, “Statistics of spatially integrated speckle intensity difference,” J. Opt. Soc. Am. A 26(2), 371–375 (2009).
    [CrossRef]
  16. L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of electromagnetic waves: numerical simulations, Wiley series in remote sensing (Wiley-Interscience, 2001).

2009

2008

2005

2004

2003

E. Wolf, “Unified theory of Coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
[CrossRef]

2002

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics,” J. Biomed. Opt. 7(3), 307–312 (2002).
[CrossRef] [PubMed]

1994

Amra, C.

Broky, J.

Deumié, C.

Dogariu, A.

Ellis, J.

Georges, G.

Goudail, F.

Hanson, S. G.

Knotts, M. E.

Li, J.

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics,” J. Biomed. Opt. 7(3), 307–312 (2002).
[CrossRef] [PubMed]

O’Donnell, K. A.

Réfrégier, P.

Siozade, L.

Sorrentini, J.

Wang, L. V.

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics,” J. Biomed. Opt. 7(3), 307–312 (2002).
[CrossRef] [PubMed]

Wolf, E.

E. Wolf, “Unified theory of Coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
[CrossRef]

Yao, G.

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics,” J. Biomed. Opt. 7(3), 307–312 (2002).
[CrossRef] [PubMed]

Yura, H. T.

Zerrad, M.

J. Biomed. Opt.

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics,” J. Biomed. Opt. 7(3), 307–312 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Phys. Lett. A

E. Wolf, “Unified theory of Coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
[CrossRef]

Other

C. Brosseau, “Polarization and Coherence Optics: Historical Perspective, Status and Future Directions,” presented at the Frontiers in Optics, 2008.

E. Wolf, ed., Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, 2007).

J. W. Goodman, Statistical Optics (Wiley Classic Library, 1985).

L. Mandel, and E. Wolf, eds., Optical Coherence and Quantum Optics (Cambridge University Press 1995).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, 2007).

D. Colton, and R. Kress, Integral Equations methods in Scattering Theory (New-York, 1983).

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of electromagnetic waves: numerical simulations, Wiley series in remote sensing (Wiley-Interscience, 2001).

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.


Figures (10)

Fig. 1
Fig. 1

Amplitude ratio β = | AP/AS| of the scattered field for two surfaces whose definition parameters are hrms = 50 nm, Lcor = 2 µm and hrms = 100 nm, Lcor = 0.1 µm (see text).

Fig. 2
Fig. 2

Polarimetric phase delay δ of the scattered field for two surfaces whose definition parameters are hrms = 50 nm, Lcor = 2 µm and hrms = 100 nm, Lcor = 0.1 µm (see text).

Fig. 3
Fig. 3

Histogram of amplitude ratio |AP/AS| of the scattered field for two surfaces whose definition parameters are hrms = 50 nm, Lcor = 2 µm (left) and hrms = 100 nm, Lcor = 0.1 µm (right).

Fig. 4
Fig. 4

Histogram of polarimetric phase delay δ of the scattered field for two surfaces whose definition parameters are hrms = 50 nm, Lcor = 2 µm (right) and hrms = 100 nm, Lcor = 0.1 µm (left).

Fig. 5
Fig. 5

Variation of the scattered polarization within 1° angular range (10°-11°), plotted on the Poincaré sphere for different surface slopes (1%-100%)-(R-C and L-C are the circular polarization states respectively right and left. L ± 45° is the linear ± 45° polarization state).

Fig. 6
Fig. 6

MDOP(1°) plotted versus increasing surface slope s for Lcor = 0.1 µm.

Fig. 7
Fig. 7

MDOP function calculated versus number of coherence areas (see text) for different surface slopes. For each surface the MDOP is calculated for three different values of the average θ0 angle (10, 10.5 and 11°)- see text.

Fig. 8
Fig. 8

Average MDOP* and its theoretical fit (f) as a function of the detector aperture for each of the 12 surfaces under study (see text). The fit is quasi perfect for each curve (MDOP* and fit are superimposed for each hrms). The average is taken in the θ0 range (0°-30°).

Fig. 9
Fig. 9

Evolution of a, c and n the 3 MDOP* fit parameters theoretical versus surface slope s.

Fig. 10
Fig. 10

MDOP(1°) levels versus roughness and correlation length.

Equations (16)

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

µ ( ρ ) = 1 α E S ( ρ , t ) E P ( ρ , t ) t
α 2 = | E S ( ρ , t ) | 2 t | E P ( ρ , t ) | 2 t     | μ | 1
µ ( ρ 1 , ρ 2 ) = 1 α 12 E S ( ρ 1 , t ) E P ( ρ 2 , t ) t
with   α 12 2 = | E S ( ρ 1 , t ) | 2 t | E P ( ρ 2 , t ) | 2 t
µ ( ρ 1 , ρ 2 , τ ) = 1 α 12 E S ( ρ 1 , t ) E P ( ρ 2 , t τ ) t
with   α 12 2 = | E S ( ρ 1 , t ) | 2 t | E P ( ρ 2 , t τ ) | 2 t
µ ( ρ 1 , ρ 2 ) = E S ( ρ 1 ) E P * ( ρ 2 ) | E S ( ρ 1 ) | 2 | E P ( ρ 2 ) | 2     | μ | = 1
µ ( ρ , Δ Ω ) = E S ( ρ ) E P * ( ρ ) Δ Ω α
with: ​   α 2 = | E S ( ρ , Δ Ω ) | 2 Δ Ω | E P ( ρ , Δ Ω ) | 2 Δ Ω
M D O P ( ρ , Δ Ω ) = 1 4 det { J ( ρ , Δ Ω ) } [ t r { J ( ρ , Δ Ω ) } ] 2
J ( ρ , Δ Ω ) = ( ( E S ) * E S Δ Ω ( E S ) * E P Δ Ω ( E P ) * E S Δ Ω ( E P ) * E P Δ Ω )
M D O P ( ρ , Δ Ω ) D O P ( ρ ) Δ Ω
M D O P ( ρ , Δ Ω = 0 ) = D O P ( ρ ) = 1
A S = I S e j δ S A P = I P e j δ P δ = δ P δ S
M D O P * ( Δ Ω ) = M D O P ( Δ Ω , θ 0 ) θ 0
M D O P * f ( Δ Ω ) = a ( b + Δ Ω ) n + c

Metrics