Abstract

We have earlier proposed a 2-channel imaging technique: Adapted Polarisation State Contrast Imaging (APSCI), which noticeably enhances the polarimetric contrast between an object and its background using fully polarised incident state adapted to the scene, such that the polarimetric responses of those regions are located as far as possible on the Poincaré sphere. We address here the full analytical and graphical analysis of the ensemble of solutions of specific incident states, by introducing 3-Distance Eigen Space and explain the underlying physical structure of APSCI and the effect of noise over the measurements.

© 2011 OSA

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References

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2011 (1)

2010 (1)

2009 (3)

2008 (2)

R. Ossikovski, M. Anastasiadoua, and A. De Martino, “Product decompositions of depolarizing Mueller matrices with negative determinants,” Opt. Commun. 281(9), 2406–2410 (2008).
[CrossRef]

M. Richert, X. Orlik, and A. De Martino, “Optimized orthogonal state contrast image,” Proceedings of the 21th Congress of the Int. Comm. for Opt. (2008), Vol.  139.

2007 (1)

2006 (1)

2004 (1)

1996 (1)

1995 (1)

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry (journal paper),” Opt. Eng. 34(06), 1558–1568 (1995).
[CrossRef]

1943 (1)

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

Anastasiadoua, M.

R. Ossikovski, M. Anastasiadoua, and A. De Martino, “Product decompositions of depolarizing Mueller matrices with negative determinants,” Opt. Commun. 281(9), 2406–2410 (2008).
[CrossRef]

Béniére, A.

Bhattacharyya, A.

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

Chipman, R. A.

De Martino, A.

D. Upadhyay, M. Richert, E. Lacot, A. De Martino, and X. Orlik, “Effect of speckle on APSCI method and Mueller imaging,” Opt. Express 19(5), 4553–4559 (2010).
[CrossRef]

M. Richert, X. Orlik, and A. De Martino, “Adapted polarization state contrast image,” Opt. Express 17, 14199–14210 (2009).
[CrossRef] [PubMed]

M. Richert, X. Orlik, and A. De Martino, “Optimized orthogonal state contrast image,” Proceedings of the 21th Congress of the Int. Comm. for Opt. (2008), Vol.  139.

R. Ossikovski, M. Anastasiadoua, and A. De Martino, “Product decompositions of depolarizing Mueller matrices with negative determinants,” Opt. Commun. 281(9), 2406–2410 (2008).
[CrossRef]

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]

Delyon, G.

Goudail, F.

Guyot, S.

Kerekes, J. P.

Lacot, E.

Lu, S. Y.

Meng, L.

Orlik, X.

Ossikovski, R.

R. Ossikovski, M. Anastasiadoua, and A. De Martino, “Product decompositions of depolarizing Mueller matrices with negative determinants,” Opt. Commun. 281(9), 2406–2410 (2008).
[CrossRef]

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]

Pezzaniti, J. L.

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry (journal paper),” Opt. Eng. 34(06), 1558–1568 (1995).
[CrossRef]

Poincaré, H.

H. Poincaré, Théorie mathématique de la lumière (GABAY, 1892).
[PubMed]

Réfrégier, P.

Richert, M.

Upadhyay, D.

Wolfe, J. E.

Appl. Opt. (2)

Bull. Calcutta Math. Soc. (1)

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. Commun. (1)

R. Ossikovski, M. Anastasiadoua, and A. De Martino, “Product decompositions of depolarizing Mueller matrices with negative determinants,” Opt. Commun. 281(9), 2406–2410 (2008).
[CrossRef]

Opt. Eng. (1)

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry (journal paper),” Opt. Eng. 34(06), 1558–1568 (1995).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Proceedings of the 21th Congress of the Int. Comm. for Opt. (1)

M. Richert, X. Orlik, and A. De Martino, “Optimized orthogonal state contrast image,” Proceedings of the 21th Congress of the Int. Comm. for Opt. (2008), Vol.  139.

Other (1)

H. Poincaré, Théorie mathématique de la lumière (GABAY, 1892).
[PubMed]

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Figures (2)

Fig. 1
Fig. 1

(a) Ensemble of solutions of the incident adapted states for a scene with difference in 10% in scalar birefringence. The arrows defines the eign vectors using pure Mueller matrices(red and pink) and using Mueller matrices pertubed by a generic shot noise(light and dark green) (b) Graphical representation of the birefringence scene and at upper right corner: the ensemble of solutions over Poincaré sphere for different realisations of shot noise. (c) Ensemble of solutions for a scene with difference in 10% in azimuth of dichroic vector. The arrows show the average direction of incident adapted states from iterative simplex search method (blue) and from analytical method (green) (d) Graphical representation of the dichroic scene and at the upper right corner: the ensemble of solutions over Poincaré sphere for different realisations of shot noise. The colour mapping on the spheres at the upper right corners for (b) and (d) maps linearly the 3-Distance for all the polarimetric states on Poincaré sphere considering corresponding pure Mueller matrices respectively.

Fig. 2
Fig. 2

(a) Comparisons of contrast from different pertinent parameters by Bhattacharyya distance vs. SNR curves. (b) at SNR = 3.4, (i.) cluster of solutions from analytic (green points) and simplex search (blue points) method on Poincaré sphere, and Visual comparison of the complex scene obtained from (ii.) using best parameter of Mueller Matrix, (iii.) using APSCI by simplex search method and (iv.) using APSCI by analytical method.

Equations (19)

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

S ˜ O = [ S O 0 , S O 1 , S O 2 , S O 3 ] T = M ˜ O S , S ˜ B = [ S B 0 , S B 1 , S B 2 , S B 3 ] T = M ˜ B S
D ( S ) = k = 1 3 ( S O k S B k ) 2
D ( S m a x ) = max S 𝒫 ( D ( S ) )
Δ M = M ˜ O M ˜ B = [ Δ m 00 Δ m 01 Δ m 02 Δ m 03 Δ m 10 Δ m 11 Δ m 12 Δ m 13 Δ m 20 Δ m 21 Δ m 22 Δ m 23 Δ m 30 Δ m 31 Δ m 32 Δ m 33 ]
Δ M . S = ( M ˜ O M ˜ B ) . S = [ Δ m 00 s 0 + Δ m 01 s 1 + Δ m 02 s 2 + Δ m 03 s 3 Δ m 10 s 0 + Δ m 11 s 1 + Δ m 12 s 2 + Δ m 13 s 3 Δ m 20 s 0 + Δ m 21 s 1 + Δ m 22 s 2 + Δ m 23 s 3 Δ m 30 s 0 + Δ m 31 s 1 + Δ m 32 s 2 + Δ m 33 s 3 ]
𝒬 ( s 0 , s 1 , s 2 , s 3 ) = j = 1 3 ( i = 0 3 Δ m j i s i ) 2 = i , j = 0 3 a i j s i s j
a i j = k = 1 3 Δ m k i Δ m k j , i , j 0 , 1 , 2 , 3
A ( i , j ) = a i j = a j i , i , j 0 , 1 , 2 , 3
m a x ( 𝒬 ( s 0 , s 1 , s 2 , s 3 ) ) = m a x ( i , j = 0 3 a i j s i s j ) = m a x ( S T A S )
m a x ( 𝒬 ) = S m a x T A S m a x = λ m a x S m a x 2
T r ( A ) = i = 0 3 a i i = i = 0 3 k = 1 3 Δ m k i Δ m k i = i , k = 0 3 ( Δ m k i ) 2 j = 0 3 ( Δ m 0 j ) 2 = i = 0 3 λ i
S m a x n e w = S m a x k = 1 3 ( S m a x k ) 2
F ( S d ) = S d . S o u t O S d . S o u t B
d F ( S d ) = d S d . ( S o u t O S o u t B ) = 0
2 d S d . S d = 0
S o u t 1 = [ 1 , Δ S T / Δ S ] T , S o u t 2 = [ 1 , Δ S T / Δ S ] T
A P S C I ( u , v ) = I 1 ( u , v ) I 2 ( u , v ) I 1 ( u , v ) + I 2 ( u , v ) ,
M O = [ 0.500 0.300 0 0 0.180 0.300 0 0 0 0 0.112 0.212 0 0 0.176 0.094 ] and M B = [ 0.500 0.250 0 0 0.125 0.250 0 0 0 0 0.037 0.213 0 0 0.213 0.037 ]
M ˜ O = [ 0.501 0.296 0.001 0.002 0.182 0.297 0.002 0.003 0.001 0.001 0.112 0.209 0.002 0.001 0.171 0.091 ] and M ˜ B = [ 0.499 0.249 0.001 0.006 0.123 0.245 0.002 0.000 0.000 0.002 0.040 0.213 0.000 0.008 0.210 0.042 ]

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