Abstract

The principle of the polarimetric imaging method called APSCI (Adapted Polarization State Contrast Imaging) is to maximize the polarimetric contrast between an object and its background using specific polarization states of illumination and detection. We perform here a comparative study of the APSCI method with existing Classical Mueller Imaging(CMI) associated with polar decomposition in the presence of fully and partially polarized circular Gaussian speckle. The results show a noticeable increase of the Bhattacharyya distance used as our contrast parameter for the APSCI method, especially when the object and background exhibit several polarimetric properties simultaneously.

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References

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    [Crossref] [PubMed]
  2. S. Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13, 1106–1113 (1996).
    [Crossref]
  3. H. Poincaré, Théorie mathématique de la lumière (GABAY, 1892).
    [PubMed]
  4. A. Bhattacharyya, “On a measure of divergence between two statistical populations defined by probability distributions,” Bull. Calcutta Math. Soc. 35, 99–109 (1943).
  5. J. W. Goodman, Speckle Phenomena in optics (Roberts & Company Pub., Colorado, 2007) pp. 48–50.
  6. P. Drude, “Über Oberflächenschichten,” Ann. der Physik 36, 86597 (1889).
  7. I. Jung, M. Vaupel, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, J. An, and R. S. Ruoff, “Characterization of Thermally Reduced Graphene Oxide by Imaging Ellipsometry,” J. Phys. Chem. C,  112(23), 8499–8506 (2008).
    [Crossref]
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2009 (1)

2008 (1)

I. Jung, M. Vaupel, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, J. An, and R. S. Ruoff, “Characterization of Thermally Reduced Graphene Oxide by Imaging Ellipsometry,” J. Phys. Chem. C,  112(23), 8499–8506 (2008).
[Crossref]

2007 (1)

J. W. Goodman, Speckle Phenomena in optics (Roberts & Company Pub., Colorado, 2007) pp. 48–50.

1996 (2)

1995 (1)

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).

1889 (1)

P. Drude, “Über Oberflächenschichten,” Ann. der Physik 36, 86597 (1889).

An, J.

I. Jung, M. Vaupel, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, J. An, and R. S. Ruoff, “Characterization of Thermally Reduced Graphene Oxide by Imaging Ellipsometry,” J. Phys. Chem. C,  112(23), 8499–8506 (2008).
[Crossref]

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.

Dikin, D. A.

I. Jung, M. Vaupel, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, J. An, and R. S. Ruoff, “Characterization of Thermally Reduced Graphene Oxide by Imaging Ellipsometry,” J. Phys. Chem. C,  112(23), 8499–8506 (2008).
[Crossref]

Drude, P.

P. Drude, “Über Oberflächenschichten,” Ann. der Physik 36, 86597 (1889).

Engheta, N.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in optics (Roberts & Company Pub., Colorado, 2007) pp. 48–50.

Jung, I.

I. Jung, M. Vaupel, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, J. An, and R. S. Ruoff, “Characterization of Thermally Reduced Graphene Oxide by Imaging Ellipsometry,” J. Phys. Chem. C,  112(23), 8499–8506 (2008).
[Crossref]

Lu, S. Y.

Orlik, X.

Pelton, M.

I. Jung, M. Vaupel, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, J. An, and R. S. Ruoff, “Characterization of Thermally Reduced Graphene Oxide by Imaging Ellipsometry,” J. Phys. Chem. C,  112(23), 8499–8506 (2008).
[Crossref]

Piner, R.

I. Jung, M. Vaupel, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, J. An, and R. S. Ruoff, “Characterization of Thermally Reduced Graphene Oxide by Imaging Ellipsometry,” J. Phys. Chem. C,  112(23), 8499–8506 (2008).
[Crossref]

Poincaré, H.

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

Pugh, E. N.

Richert, M.

Rowe, M. P.

Ruoff, R. S.

I. Jung, M. Vaupel, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, J. An, and R. S. Ruoff, “Characterization of Thermally Reduced Graphene Oxide by Imaging Ellipsometry,” J. Phys. Chem. C,  112(23), 8499–8506 (2008).
[Crossref]

Stankovich, S.

I. Jung, M. Vaupel, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, J. An, and R. S. Ruoff, “Characterization of Thermally Reduced Graphene Oxide by Imaging Ellipsometry,” J. Phys. Chem. C,  112(23), 8499–8506 (2008).
[Crossref]

Tyo, J. S.

Vaupel, M.

I. Jung, M. Vaupel, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, J. An, and R. S. Ruoff, “Characterization of Thermally Reduced Graphene Oxide by Imaging Ellipsometry,” J. Phys. Chem. C,  112(23), 8499–8506 (2008).
[Crossref]

Ann. der Physik (1)

P. Drude, “Über Oberflächenschichten,” Ann. der Physik 36, 86597 (1889).

Appl. Opt. (1)

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 (1)

J. Phys. Chem. C (1)

I. Jung, M. Vaupel, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, J. An, and R. S. Ruoff, “Characterization of Thermally Reduced Graphene Oxide by Imaging Ellipsometry,” J. Phys. Chem. C,  112(23), 8499–8506 (2008).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Speckle Phenomena in optics (1)

J. W. Goodman, Speckle Phenomena in optics (Roberts & Company Pub., Colorado, 2007) pp. 48–50.

Other (1)

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

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Figures (2)

Fig. 1
Fig. 1

Bhattacharyya distances obtained from different SNR levels without (case a, c, e) and with (case b, d, f) speckle noise. The object and background have a difference of 10% only in scalar birefringence, scalar dichroism and linear degree of polarization respectively for the cases a & b, c & d and e & f. In case a & b, (R, λR, ɛR) represent respectively the scalar birefringence, azimuth and ellipticity of the birefringence vector R⃗. Similarly for case c & d, (D, λD, ɛD) represent respectively the scalar dichroism, azimuth and ellipticity of the dichroism vector D⃗. For the case e & f, eigen axes of depolarization of the object and background are assumed aligned and ΔDOPL and ΔDOPC represent respectively the difference between the object and background, in their ability to depolarize linear and circular polarized light.

Fig. 2
Fig. 2

Comparison of Bhattacharyya distances vs. SNR curves for the best performing parameter of CMI (in this case the scalar dichroism) vs APSCI parameter with (ws) and without speckle noise (wos). The scene is composed of an object and a background exhibiting 10% difference in scalar birefringence R, scalar dichroism D and in the linear degree of polarisation DOPL. At the same SNR level of 3.2, the embedded images (i) and (ii) are obtained respectively using the APSCI parameter and the best parameter of the CMI.

Equations (6)

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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
S out 1 = [ 1 , Δ S T / Δ S ] T , S out 2 = [ 1 , Δ S T / Δ S ] T
Δ S = [ S ˜ O 1 out S ˜ B 1 out , S ˜ O 2 out S ˜ B 2 out , S ˜ O 3 out S ˜ B 3 out ] T ,
[ S ˜ O 0 out , S ˜ O 1 out , S ˜ O 2 out , S ˜ O 3 out ] T = S ˜ O out = M ˜ O S i n , [ S ˜ B 0 out , S ˜ B 1 out , S ˜ B 2 out , S ˜ B 3 out ] T = S ˜ B out = M ˜ B S i n .
APSCI ( u , v ) = I 1 ( u , v ) I 2 ( u , v ) I 1 ( u , v ) + I 2 ( u , v ) ,
p I ( I ) = 1 P I ¯ [ exp ( 2 1 + P I I ¯ ) exp ( 2 1 P I I ¯ ) ]

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