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.
Highlights
Mueller-matrix spectra of beetle cuticles have been reported by several authors
The conclusion is that M of C. aurata at larger angles of incidence is dominated by M1 and appears mainly as a mirror with a weak contribution from a circular polarizer in a narrow spectral range
The fit parameter β dominates and we conclude, from the decomposition of Muellermatrix image data taken at the wavelength of 532 nm, that reflection at near-normal incidence for C. argenteola can be represented by a circular polarizer with a minor contribution from a plane mirror
Summary
Mueller-matrix spectra of beetle cuticles have been reported by several authors. Goldstein [1] measured normal-incidence Mueller matrices on Chrysina resplendens, Chrysina gloriosa and Chrysina clypealis (In [1] the name Plusiotis is used instead of Chrysina). In some special cases with partially known forms of Mueller matrix components, a decomposition into two different components can be done without an exact knowledge of any of them [8] Another sum decomposition method has been described by Le Roy-Bréhonnet et al [9]. Foldyna et al [10] applied sum decomposition to a Mueller matrix measured in reflection mode with a beam spot covering two or three regions with different non-depolarizing Mueller matrices. Another example of the use of sum decomposition was demonstrated by Ossikovski et al [11] They analyzed reflection Mueller-matrix images from the scarab beetle Cetonia aurata which was proven to reflect light as a non-diagonal depolarizer. In this report we present Mueller-matrix images and spectra measured on two selected beetles with cuticles of different complexity. We present quantitative Cloude sum decompositions of Mueller-matrix spectra and images and introduce regression sum decomposition as an alternative
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