Abstract

We propose a general method to maximize the polarimetric contrast between an object and its background using a predetermined illumination polarization state. After a first estimation of the polarimetric properties of the scene by classical Mueller imaging, we evaluate the incident polarized field that induces scattered polarization states by the object and background, as opposite as possible on the Poincaré sphere. With a detection method optimized for a 2-channel imaging system, Monte Carlo simulations of low flux coherent imaging are performed with various objects and backgrounds having different properties of retardance, dichroism and depolarization. With respect to classical Mueller imaging, possibly associated to the polar decomposition, our results show a noticeable increase in the Bhattacharyya distance used as our contrast parameter.

© 2009 Optical Society of America

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  6. R. M. A. Azzam, "Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal," Opt. Lett. 2, 148-150 (1978).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  26. R. Ossikovski, A. De Martino and S. Guyot, "Forward and reverse product decompositions of depolarizing Mueller matrices," Opt. Lett. 32, 689-691 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]

2009 (1)

2007 (2)

2005 (1)

2004 (2)

2003 (3)

2002 (1)

2000 (6)

1999 (1)

1998 (1)

1997 (1)

1996 (2)

1995 (1)

1978 (1)

1943 (1)

Q1. A. Bhattacharyya, "On a measure of divergence between two statistical populations defined by probability distributions," Bull. Calcutta Math. Soc. 35, 99-109 (1943).

Abbey, C. K.

Alfano, R. R

Alfano, R. R.

Azzam, R. M. A.

Barrett, H. H.

Bhattacharyya, A.

Q1. A. Bhattacharyya, "On a measure of divergence between two statistical populations defined by probability distributions," Bull. Calcutta Math. Soc. 35, 99-109 (1943).

Bigue, L.

Breugnot, S.

S. Breugnot and P. Clemenceau, "Modeling and performances of a polarization active imager at l =806 nm," Optical Engineering 39, 2681-2688 (2000).
[CrossRef]

Chang, P. C. Y.

Chipman, R. A.

Clarkson, E.

Clemenceau, P.

S. Breugnot and P. Clemenceau, "Modeling and performances of a polarization active imager at l =806 nm," Optical Engineering 39, 2681-2688 (2000).
[CrossRef]

De Martino, A.

Demos, S. G.

Dereniak, E. L.

Descour, M. R.

DeVlaminck, V.

Drevillon, B.

Engheta, N.

Fade, J.

Galland, F.

Garcia-Caurel, E.

Goudail, F.

Gray, D. J.

Guyot, S.

Hopcraft, K. I.

Jr, E. N.

Kattawar, G. W.

Kattawar, G.W.

Kemme, S. A.

Kim, Y-K.

Laude, B.

Lu, S. Y.

Morio, J.

Nothdurft, R.

Ossikovski, R.

Phipps, G. S.

Pugh, E. N.

Radousky, H. B.

Rakovic, M. J.

Refregier, P.

Roche, M.

Roux, N.

Rowe, M. P.

Sabatke, D. S.

Smith, M. H.

Sweatt, W. C.

Takakura, Y.

Terrier, P.

Tyo, J. S.

Walker, J. G.

Yao, G.

Appl. Opt. (8)

Bull. Calcutta Math. Soc. (1)

Q1. A. Bhattacharyya, "On a measure of divergence between two statistical populations defined by probability distributions," Bull. Calcutta Math. Soc. 35, 99-109 (1943).

J. Opt. Soc. Am. A (2)

Opt. Express (2)

Opt. Lett. (10)

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, G. S. Phipps, "Optimization of retardance for a complete Stokes polarimeter," Opt. Lett. 25, 802-804 (2000).
[CrossRef]

M. P. Rowe, E. N. Jr. Pugh, J. S. Tyo and N. Engheta "Polarization-difference imaging: a biologically inspired technique for observation through scattering media,"Opt. Lett. 20, 608-610 (1995).
[CrossRef] [PubMed]

A. De Martino, Y-K. Kim, E. Garcia-Caurel, B. Laude, B. Drevillon, "Optimized Mueller polarimeter with liquid crystals," Opt. Lett. 28, 616-618 (2003).
[CrossRef] [PubMed]

F. Goudail, "Optimization of the contrast in active Stokes images," Opt. Lett. 34, 121-123 (2009).
[CrossRef] [PubMed]

R. M. A. Azzam, "Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal," Opt. Lett. 2, 148-150 (1978).
[CrossRef] [PubMed]

J. Morio and F. Goudail, "Influence of the order of diattenuator, retarder, and polarizer in polar decomposition of Mueller matrices," Opt. Lett. 29, 2234-2236 (2004).
[CrossRef] [PubMed]

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

F. Goudail, N. Roux and P. Refregier, "Performance parameters for detection in low-flux coherent images," Opt. Lett. 28, 81-83 (2003).
[CrossRef] [PubMed]

P. Refregier, J. Fade and M. Roche, "Estimation precision of the degree of polarization from a single speckle intensity image," Opt. Lett. 32, 739-741 (2007).
[CrossRef] [PubMed]

J. S. Tyo, "Noise equalization in Stokes parameter images obtained by use of variable-retardance polarimeters," Opt. Lett. 25, 1198-1200 (2000).
[CrossRef]

Optical Engineering (1)

S. Breugnot and P. Clemenceau, "Modeling and performances of a polarization active imager at l =806 nm," Optical Engineering 39, 2681-2688 (2000).
[CrossRef]

Other (4)

M. Richert, X. Orlik, and A. De Martino, "Optimized orthogonal state contrast image," Proceedings of the 21th Congress of the International Commission for optics, 139 (2008).

H. Poincar’e, Th’eorie math’ematique de la lumi`ere (Gabay, 1892).

A. M. Baldwin, J. R. Chung, J. S. Baba, C. H. Spiegelman, M. S. Amoss and G. L. Cote, "Mueller matrix imaging for cancer detection," Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Institute of Electrical and Electronics Engineers, Mexico, 1027-1030 (2003).

R. M. A. Azzam and N. M. Bashara, "Ellipsometry and Polarized Light" (North-Holland, Amsterdam, The Netherlands, 1989).

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Figures (4)

Fig. 1.
Fig. 1.

From the Mueller matrix, we have access directly to the average linear and circular depolarization power (respectively DopL and DopC ). Performing the polar decomposition, we have access to the 3 elementary Mueller Matrices of Retardance M R , Depolarization M Δ and Diattenuation M D , from which we calculate the 16 degrees of freedom represented at the bottom of the diagram. Bhattacharyya distances will be performed on all encircled entities in order to evaluate their detection capabilities.

Fig. 2.
Fig. 2.

The scene under investigation is composed of 2 birefringent elements with a difference of 18° in the azimuth λR⃗ of their retardance vector. (a) Image of the Mueller matrices (b) a magnification of their M 11 element that exhibits the best Bhattacharyya distance (0.026) among the 16 elements and (c) the APSCI parameter that exhibits a Bhattacharyya distance of 0.249. The range of the scale bars is set by the minimum and maximum value of the pixels inside each image.

Fig. 3.
Fig. 3.

Comparison of the Bhattacharyya distances of some Mueller matrix elements and of several polarimetric parameters for 6 different situations where the object and background are: (a) 2 birefringent elements with different scalar retardances, and (b) with different retardance vector azimuths; (c) 2 dichroic elements with different scalar diattenuations and (d) with different diattenuation vector azimuths; (e) 2 depolarizing elements with different linear degrees of polarization, and (f) with different angles ϕ of axial rotations Rot[V⃗, ϕ]. On the associated Poincaré spheres (that have been drawn for the maximum value of SNR of each situation) are plotted with white dots the distribution of the optimized states Sin used by the APSCI method. In the hypothesis of a perfect evaluation of the Mueller matrices of the object and background, the colors of the sphere represent the Euclidean distance D between their scattered states in function of all the totally polarized incident states.

Fig. 4.
Fig. 4.

The black lines represent the Bhattacharyya distances of the APSCI parameter in function of the SNR and of the Euclidean distance between the object and background matrices for the 6 situations (a)-(f) depicted in Fig. 3 (filled colored parts are just a guide for eyes). We observe some noticeable differences in Euclidean distances for the various situations, and can appreciate the corresponding consequences on the value of BAPSCI .

Equations (16)

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

S=[S0S1S2S3]=[I0+I90I0I90I+45I45ILCIRC] ,
S02S12+S22+S32
Sout=M.Sin
ΔD={MΔ1MR1MD1,MΔ1MD1MR1,MR1MΔ1MD1}
DΔ={MD2MR2MΔ2,MR2MD2MΔ2,MD2MΔ2MR2}
SO˜=[SO0,SO1,SO2,SO3]T=MO˜S,
SB˜=[SB0,SB1,SB2,SB3]T=MB˜S,
D(S)=[k=13(SOkSBk)2]12
D(Sin)=maxS(D(S))
APSCI(u,v)=I1(u,v)I2(u,v)I1(u,v)+I2(u,v) ,
ΔS=[SO1SB1,SO2SB2,SO3SB3]
Sout1=[1,ΔSΔS]T,Sout2=[1,ΔSΔS]T
B(x)=ln{[PO(x)PB(x)]1/2dx}
B(M)max0i,j3(B(Mij)),
I(u,v)=AM(u,v)W
M˜(u,v)=A1I˜(u,v)W1

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