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Journal Articles Optics Express Year : 2015

Sum decomposition of Mueller-matrix images and spectra of beetle cuticles


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.-matrix characterization of bee-tle cuticle: polarized and unpolarized reflections from representative architectures," Appl. Opt. 49, 4558–4567 (2010).-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson," Phil. Mag. 92, 1583–1599 (2012). 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). 5. matrices: how to decompose them?," Phys. Status Solidi A 205, 720–727 (2008). 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.
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hal-01113017 , version 1 (04-02-2015)



Hans Arwin, Roger Magnusson, Enric Garcia-Caurel, Clément Fallet, Kenneth Jarrendahl,, et al.. Sum decomposition of Mueller-matrix images and spectra of beetle cuticles. Optics Express, 2015, 23, pp.1951 - 7950. ⟨10.1364/OE.23.001951⟩. ⟨hal-01113017⟩
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