Abstract

Spectral Mueller matrices measured at multiple angles of incidence as well as Mueller matrix images are recorded on the exoskeletons (cuticles) of the scarab beetles Cetonia aurata and Chrysina argenteola. Cetonia aurata is green whereas Chrysina argenteola is gold-colored. When illuminated with natural (unpolarized) light, both species reflect left-handed and near-circularly polarized light originating from helicoidal structures in their cuticles. These structures are referred to as circular Bragg reflectors. For both species the Mueller matrices are found to be nondiagonal depolarizers. The matrices are Cloude decomposed to a sum of non-depolarizing matrices and it is found that the cuticle optical response, in a first approximation can be described as a sum of Mueller matrices from an ideal mirror and an ideal circular polarizer with relative weights determined by the eigenvalues of the covariance matrices of the measured Mueller matrices. The spectral and image decompositions are consistent with each other. A regression-based decomposition of the spectral and image Mueller matrices is also presented whereby the basic optical components are assumed to be a mirror and a circular polarizer as suggested by the Cloude decomposition. The advantage with a regression decomposition compared to a Cloude decomposition is its better stability as the matrices in the decomposition are determined a priori. The origin of the depolarizing features are discussed but from present data it is not possible to conclude whether the two major components, the mirror and the circular polarizer are laterally separated in domains in the cuticle or if the depolarization originates from the intrinsic properties of the helicoidal structure.

© 2015 Optical Society of America

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References

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  1. D. H. Goldstein, “Polarization properties of Scarabaeidae,” Appl. Opt. 45, 7944–7950 (2006).
    [Crossref] [PubMed]
  2. I. Hodgkinson, S. Lowrey, L. Bourke, A. Parker, and M. W. McCall, “Mueller-matrix characterization of beetle cuticle: polarized and unpolarized reflections from representative architectures,” Appl. Opt. 49, 4558–4567 (2010).
    [Crossref] [PubMed]
  3. H. Arwin, R. Magnusson, J. Landin, and K. Järrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Phil. Mag. 92, 1583–1599 (2012).
    [Crossref]
  4. H. Arwin, T. Berlind, B. Johs, and K. Järrendahl, “Cuticle structure of the scarab beetle Cetonia aurata analyzed by regression analysis of Mueller-matrix ellipsometric data,” Opt. Express 21, 22645–22656 (2013).
    [Crossref] [PubMed]
  5. R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them,” Phys. Status Solidi A 205, 720–727 (2008).
    [Crossref]
  6. S. R. Cloude, “Group theory and polarization algebra,” Optik (Stuttgart) 75, 26–36 (1986).
  7. S. R. Cloude and E. Pottier, “A review of target decomposition theorems in radar polarimetry,” IEEE Trans. Geosci. and Remote Sensing 34, 498–518 (1996).
    [Crossref]
  8. R. Ossikovski, E. Garcia-Caurel, M. Foldyna, and J. J. Gil, “Application of the arbitrary decomposition to finite spot size Mueller matrix measurements,” Appl. Opt. 53, 6030–6036 (2014).
    [Crossref] [PubMed]
  9. F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliés, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D: Appl. Phys. 29, 34–38 (1996).
    [Crossref]
  10. M. Foldyna, E. Garcia-Caurel, R. Ossikovski, A. De Martino, and J. J. Gil, “Retrieval of a non-depolarizing component of experimentally determined depolarizing Mueller matrices,” Opt. Express 17, 12794–12806 (2009).
    [Crossref] [PubMed]
  11. R. Ossikovski, M. Foldyna, C. Fallet, and A. De Martino, “Experimental evidence for naturally occurring nondiagonal depolarizers,” Opt. Lett. 34, 2426–2428 (2009).
  12. S. Ben Hatit, M. Foldyna, A. De Martino, and B. Drevillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Status Solidi A 205, 743–747 (2008).
    [Crossref]
  13. C. Fallet, Angle resolved Mueller polarimetry, applications to periodic structures (École polytechnique, 2012).
  14. H. Arwin, L. Fernández del Río, and K. Järrendahl, “Comparison and analysis of Mueller-matrix spectra from exoskeletons of blue, green and red Cetonia aurata,” Thin Solid Films 571, 739–743 (2014).
    [Crossref]
  15. E. Collett, Polarized Light: Fundamentals and Applications, Optical Engineering21 (Marcel Dekker, Inc., 1992).
  16. R. T. Holm, “Convention confusions,” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic Press, 1991), pp. 21–55.
  17. V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325, 449–451 (2009).
    [Crossref] [PubMed]
  18. L. Fernández del Río, H. Arwin, and K. Järrendahl, “Polarizing properties and structural characteristics of the cuticle of the scarab beetle Chrysina gloriosa,” Thin Solid Films 571, 410–415 (2014).
    [Crossref]
  19. R. Ossikovski, “Canonical forms of depolarizing Mueller matrices,” J. Opt. Soc. Am. A27, 123–130 (2010).
    [Crossref]
  20. A. Lakhtakia and M. McCall, “Simple expressions for Bragg reflection from axially excited chiral sculptured thin films,” J. Modern Opt. 49, 1525–1535 (2002).
    [Crossref]
  21. E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the cuticle of the beetle Cotinis mutabilis,” Thin Solid Films 571, 660–665 (2014).
    [Crossref]
  22. A. Mendoza-Galván, E. Muñoz-Pineda, K. Järrendahl, and H. Arwin, “Evidence for a dispersion relation of optical modes in the cuticle of the scarab beetle Cotinis mutabilis,” Opt. Mater. Express 4, 2484–2496 (2014).
    [Crossref]

2014 (5)

R. Ossikovski, E. Garcia-Caurel, M. Foldyna, and J. J. Gil, “Application of the arbitrary decomposition to finite spot size Mueller matrix measurements,” Appl. Opt. 53, 6030–6036 (2014).
[Crossref] [PubMed]

H. Arwin, L. Fernández del Río, and K. Järrendahl, “Comparison and analysis of Mueller-matrix spectra from exoskeletons of blue, green and red Cetonia aurata,” Thin Solid Films 571, 739–743 (2014).
[Crossref]

L. Fernández del Río, H. Arwin, and K. Järrendahl, “Polarizing properties and structural characteristics of the cuticle of the scarab beetle Chrysina gloriosa,” Thin Solid Films 571, 410–415 (2014).
[Crossref]

E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the cuticle of the beetle Cotinis mutabilis,” Thin Solid Films 571, 660–665 (2014).
[Crossref]

A. Mendoza-Galván, E. Muñoz-Pineda, K. Järrendahl, and H. Arwin, “Evidence for a dispersion relation of optical modes in the cuticle of the scarab beetle Cotinis mutabilis,” Opt. Mater. Express 4, 2484–2496 (2014).
[Crossref]

2013 (1)

2012 (1)

H. Arwin, R. Magnusson, J. Landin, and K. Järrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Phil. Mag. 92, 1583–1599 (2012).
[Crossref]

2010 (2)

2009 (3)

2008 (2)

S. Ben Hatit, M. Foldyna, A. De Martino, and B. Drevillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Status Solidi A 205, 743–747 (2008).
[Crossref]

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them,” Phys. Status Solidi A 205, 720–727 (2008).
[Crossref]

2006 (1)

2002 (1)

A. Lakhtakia and M. McCall, “Simple expressions for Bragg reflection from axially excited chiral sculptured thin films,” J. Modern Opt. 49, 1525–1535 (2002).
[Crossref]

1996 (2)

S. R. Cloude and E. Pottier, “A review of target decomposition theorems in radar polarimetry,” IEEE Trans. Geosci. and Remote Sensing 34, 498–518 (1996).
[Crossref]

F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliés, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D: Appl. Phys. 29, 34–38 (1996).
[Crossref]

1986 (1)

S. R. Cloude, “Group theory and polarization algebra,” Optik (Stuttgart) 75, 26–36 (1986).

Anastasiadou, M.

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them,” Phys. Status Solidi A 205, 720–727 (2008).
[Crossref]

Arwin, H.

H. Arwin, L. Fernández del Río, and K. Järrendahl, “Comparison and analysis of Mueller-matrix spectra from exoskeletons of blue, green and red Cetonia aurata,” Thin Solid Films 571, 739–743 (2014).
[Crossref]

L. Fernández del Río, H. Arwin, and K. Järrendahl, “Polarizing properties and structural characteristics of the cuticle of the scarab beetle Chrysina gloriosa,” Thin Solid Films 571, 410–415 (2014).
[Crossref]

E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the cuticle of the beetle Cotinis mutabilis,” Thin Solid Films 571, 660–665 (2014).
[Crossref]

A. Mendoza-Galván, E. Muñoz-Pineda, K. Järrendahl, and H. Arwin, “Evidence for a dispersion relation of optical modes in the cuticle of the scarab beetle Cotinis mutabilis,” Opt. Mater. Express 4, 2484–2496 (2014).
[Crossref]

H. Arwin, T. Berlind, B. Johs, and K. Järrendahl, “Cuticle structure of the scarab beetle Cetonia aurata analyzed by regression analysis of Mueller-matrix ellipsometric data,” Opt. Express 21, 22645–22656 (2013).
[Crossref] [PubMed]

H. Arwin, R. Magnusson, J. Landin, and K. Järrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Phil. Mag. 92, 1583–1599 (2012).
[Crossref]

Ben Hatit, S.

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them,” Phys. Status Solidi A 205, 720–727 (2008).
[Crossref]

S. Ben Hatit, M. Foldyna, A. De Martino, and B. Drevillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Status Solidi A 205, 743–747 (2008).
[Crossref]

Berlind, T.

Bourke, L.

Cariou, J.

F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliés, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D: Appl. Phys. 29, 34–38 (1996).
[Crossref]

Cloude, S. R.

S. R. Cloude and E. Pottier, “A review of target decomposition theorems in radar polarimetry,” IEEE Trans. Geosci. and Remote Sensing 34, 498–518 (1996).
[Crossref]

S. R. Cloude, “Group theory and polarization algebra,” Optik (Stuttgart) 75, 26–36 (1986).

Collett, E.

E. Collett, Polarized Light: Fundamentals and Applications, Optical Engineering21 (Marcel Dekker, Inc., 1992).

Crne, M.

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325, 449–451 (2009).
[Crossref] [PubMed]

De Martino, A.

R. Ossikovski, M. Foldyna, C. Fallet, and A. De Martino, “Experimental evidence for naturally occurring nondiagonal depolarizers,” Opt. Lett. 34, 2426–2428 (2009).

M. Foldyna, E. Garcia-Caurel, R. Ossikovski, A. De Martino, and J. J. Gil, “Retrieval of a non-depolarizing component of experimentally determined depolarizing Mueller matrices,” Opt. Express 17, 12794–12806 (2009).
[Crossref] [PubMed]

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them,” Phys. Status Solidi A 205, 720–727 (2008).
[Crossref]

S. Ben Hatit, M. Foldyna, A. De Martino, and B. Drevillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Status Solidi A 205, 743–747 (2008).
[Crossref]

Drevillon, B.

S. Ben Hatit, M. Foldyna, A. De Martino, and B. Drevillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Status Solidi A 205, 743–747 (2008).
[Crossref]

Eliés, P.

F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliés, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D: Appl. Phys. 29, 34–38 (1996).
[Crossref]

Fallet, C.

R. Ossikovski, M. Foldyna, C. Fallet, and A. De Martino, “Experimental evidence for naturally occurring nondiagonal depolarizers,” Opt. Lett. 34, 2426–2428 (2009).

C. Fallet, Angle resolved Mueller polarimetry, applications to periodic structures (École polytechnique, 2012).

Fernández del Río, L.

H. Arwin, L. Fernández del Río, and K. Järrendahl, “Comparison and analysis of Mueller-matrix spectra from exoskeletons of blue, green and red Cetonia aurata,” Thin Solid Films 571, 739–743 (2014).
[Crossref]

L. Fernández del Río, H. Arwin, and K. Järrendahl, “Polarizing properties and structural characteristics of the cuticle of the scarab beetle Chrysina gloriosa,” Thin Solid Films 571, 410–415 (2014).
[Crossref]

Foldyna, M.

Garcia-Caurel, E.

Gil, J. J.

Goldstein, D. H.

Hodgkinson, I.

Holm, R. T.

R. T. Holm, “Convention confusions,” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic Press, 1991), pp. 21–55.

Järrendahl, K.

L. Fernández del Río, H. Arwin, and K. Järrendahl, “Polarizing properties and structural characteristics of the cuticle of the scarab beetle Chrysina gloriosa,” Thin Solid Films 571, 410–415 (2014).
[Crossref]

H. Arwin, L. Fernández del Río, and K. Järrendahl, “Comparison and analysis of Mueller-matrix spectra from exoskeletons of blue, green and red Cetonia aurata,” Thin Solid Films 571, 739–743 (2014).
[Crossref]

E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the cuticle of the beetle Cotinis mutabilis,” Thin Solid Films 571, 660–665 (2014).
[Crossref]

A. Mendoza-Galván, E. Muñoz-Pineda, K. Järrendahl, and H. Arwin, “Evidence for a dispersion relation of optical modes in the cuticle of the scarab beetle Cotinis mutabilis,” Opt. Mater. Express 4, 2484–2496 (2014).
[Crossref]

H. Arwin, T. Berlind, B. Johs, and K. Järrendahl, “Cuticle structure of the scarab beetle Cetonia aurata analyzed by regression analysis of Mueller-matrix ellipsometric data,” Opt. Express 21, 22645–22656 (2013).
[Crossref] [PubMed]

H. Arwin, R. Magnusson, J. Landin, and K. Järrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Phil. Mag. 92, 1583–1599 (2012).
[Crossref]

Johs, B.

Lakhtakia, A.

A. Lakhtakia and M. McCall, “Simple expressions for Bragg reflection from axially excited chiral sculptured thin films,” J. Modern Opt. 49, 1525–1535 (2002).
[Crossref]

Landin, J.

H. Arwin, R. Magnusson, J. Landin, and K. Järrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Phil. Mag. 92, 1583–1599 (2012).
[Crossref]

Le Jeune, B.

F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliés, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D: Appl. Phys. 29, 34–38 (1996).
[Crossref]

Le Roy-Bréhonnet, F.

F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliés, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D: Appl. Phys. 29, 34–38 (1996).
[Crossref]

Lotrian, J.

F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliés, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D: Appl. Phys. 29, 34–38 (1996).
[Crossref]

Lowrey, S.

Magnusson, R.

H. Arwin, R. Magnusson, J. Landin, and K. Järrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Phil. Mag. 92, 1583–1599 (2012).
[Crossref]

McCall, M.

A. Lakhtakia and M. McCall, “Simple expressions for Bragg reflection from axially excited chiral sculptured thin films,” J. Modern Opt. 49, 1525–1535 (2002).
[Crossref]

McCall, M. W.

Mendoza-Galván, A.

E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the cuticle of the beetle Cotinis mutabilis,” Thin Solid Films 571, 660–665 (2014).
[Crossref]

A. Mendoza-Galván, E. Muñoz-Pineda, K. Järrendahl, and H. Arwin, “Evidence for a dispersion relation of optical modes in the cuticle of the scarab beetle Cotinis mutabilis,” Opt. Mater. Express 4, 2484–2496 (2014).
[Crossref]

Muñoz-Pineda, E.

A. Mendoza-Galván, E. Muñoz-Pineda, K. Järrendahl, and H. Arwin, “Evidence for a dispersion relation of optical modes in the cuticle of the scarab beetle Cotinis mutabilis,” Opt. Mater. Express 4, 2484–2496 (2014).
[Crossref]

E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the cuticle of the beetle Cotinis mutabilis,” Thin Solid Films 571, 660–665 (2014).
[Crossref]

Ossikovski, R.

Park, J. O.

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325, 449–451 (2009).
[Crossref] [PubMed]

Parker, A.

Pottier, E.

S. R. Cloude and E. Pottier, “A review of target decomposition theorems in radar polarimetry,” IEEE Trans. Geosci. and Remote Sensing 34, 498–518 (1996).
[Crossref]

Sharma, V.

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325, 449–451 (2009).
[Crossref] [PubMed]

Srinivasarao, M.

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325, 449–451 (2009).
[Crossref] [PubMed]

Appl. Opt. (3)

IEEE Trans. Geosci. and Remote Sensing (1)

S. R. Cloude and E. Pottier, “A review of target decomposition theorems in radar polarimetry,” IEEE Trans. Geosci. and Remote Sensing 34, 498–518 (1996).
[Crossref]

J. Modern Opt. (1)

A. Lakhtakia and M. McCall, “Simple expressions for Bragg reflection from axially excited chiral sculptured thin films,” J. Modern Opt. 49, 1525–1535 (2002).
[Crossref]

J. Opt. Soc. Am. (1)

R. Ossikovski, “Canonical forms of depolarizing Mueller matrices,” J. Opt. Soc. Am. A27, 123–130 (2010).
[Crossref]

J. Phys. D: Appl. Phys. (1)

F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliés, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D: Appl. Phys. 29, 34–38 (1996).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Opt. Mater. Express (1)

Optik (Stuttgart) (1)

S. R. Cloude, “Group theory and polarization algebra,” Optik (Stuttgart) 75, 26–36 (1986).

Phil. Mag. (1)

H. Arwin, R. Magnusson, J. Landin, and K. Järrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Phil. Mag. 92, 1583–1599 (2012).
[Crossref]

Phys. Status Solidi A (2)

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them,” Phys. Status Solidi A 205, 720–727 (2008).
[Crossref]

S. Ben Hatit, M. Foldyna, A. De Martino, and B. Drevillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Status Solidi A 205, 743–747 (2008).
[Crossref]

Science (1)

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325, 449–451 (2009).
[Crossref] [PubMed]

Thin Solid Films (3)

L. Fernández del Río, H. Arwin, and K. Järrendahl, “Polarizing properties and structural characteristics of the cuticle of the scarab beetle Chrysina gloriosa,” Thin Solid Films 571, 410–415 (2014).
[Crossref]

H. Arwin, L. Fernández del Río, and K. Järrendahl, “Comparison and analysis of Mueller-matrix spectra from exoskeletons of blue, green and red Cetonia aurata,” Thin Solid Films 571, 739–743 (2014).
[Crossref]

E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the cuticle of the beetle Cotinis mutabilis,” Thin Solid Films 571, 660–665 (2014).
[Crossref]

Other (3)

E. Collett, Polarized Light: Fundamentals and Applications, Optical Engineering21 (Marcel Dekker, Inc., 1992).

R. T. Holm, “Convention confusions,” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic Press, 1991), pp. 21–55.

C. Fallet, Angle resolved Mueller polarimetry, applications to periodic structures (École polytechnique, 2012).

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Figures (10)

Fig. 1
Fig. 1 C. argenteola (left) and C. aurata (right). The measurement were done on the scutellum (spectra) and in front of the scutellum (images) on C. argenteola and on the scutellum on C. aurata as marked. The lengths are 29 and 19 mm for C. argenteola and C. aurata, respectively. (Photos J. Birch)
Fig. 2
Fig. 2 Normalized Mueller-matrix spectra measured at θ = 20° and 65° on a C. aurata beetle. The scale for all elements is the same as shown for m41.
Fig. 3
Fig. 3 Normalized Mueller-matrix spectra measured at θ = 20° and 65° on a C. argenteola beetle. The scale for all elements is the same as shown for m41.
Fig. 4
Fig. 4 Normalized Mueller-matrix images of C. aurata at wavelengths 532 nm and 633 nm.
Fig. 5
Fig. 5 Normalized Mueller-matrix images of C. argenteola at wavelengths 532 nm and 633 nm.
Fig. 6
Fig. 6 (a) The four eigenvalues obtained by a Cloude decomposition of Mueller matrices measured on C. aurata at θ = 20°. The decomposition fit parameters α and β from Eq. (7) are also shown. (b) The four eigenvalues obtained by a Cloude decomposition of Mueller matrices measured on C. aurata at θ = 55° and θ = 65°.
Fig. 7
Fig. 7 The four eigenvalues obtained by a Cloude decomposition of Mueller matrices measured on C. argenteola at (a) θ = 20° and (b) θ = 65°.
Fig. 8
Fig. 8 The top row shows the spatial variation of the four eigenvalues obtained by a Cloude decomposition of the Mueller-matrix image at 532 nm on C. aurata in Fig. 4(a). The bottom row shows the spatial variation of a mirror, a circular polarizer and a half-wave plate corresponding to α, β and γ in Eq. (6).
Fig. 9
Fig. 9 The top row shows the spatial variation of the four eigenvalues obtained by a Cloude decomposition of the Mueller-matrix image at 633 nm on C. aurata in Fig. 4(b). The bottom row shows the spatial variation of a mirror, a circular polarizer and a half-wave plate corresponding to α, β and γ.
Fig. 10
Fig. 10 The top row shows the spatial variation of the four eigenvalues obtained by a Cloude decomposition of the Mueller-matrix image at 532 nm on C. argenteola in Fig. 5(a). The bottom row shows the spatial variation of a mirror, a circular polarizer and a half-wave plate corresponding to α, β and γ. Notice that the sorting of eigenvalues after magnitude results in that λ1 is largest, whereas for the regression β as defined in Eq. (6) is largest.

Equations (9)

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

M = λ 1 M 1 + λ 2 M 2 + λ 3 M 3 + λ 4 M 4
C = i , j m i j ( σ i σ j )
σ 1 = [ 1 0 0 1 ] σ 2 = [ 1 0 0 1 ] σ 3 = [ 0 1 1 0 ] σ 4 = [ 0 i i 0 ]
C = λ 1 C 1 + λ 2 C 2 + λ 3 C 3 + λ 4 C 4
C i = e i e i i = ( 1 , 2 , 3 , 4 )
M r e g = α M 1 + β M 2 + γ M 3 + δ M 4
F = M M r e g ( α , β , γ , δ ) F
M λ 1 M 1 + λ 2 M 2 + 0 · M 3 + 0 · M 4
M λ 1 [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] + λ 2 [ 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 ]

Metrics